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+lib64/ +parts/ +sdist/ +var/ +wheels/ +pip-wheel-metadata/ +share/python-wheels/ +*.egg-info/ +.installed.cfg +*.egg +MANIFEST + +# PyInstaller +# Usually these files are written by a python script from a template +# before PyInstaller builds the exe, so as to inject date/other infos into it. +*.manifest +*.spec + +# Installer logs +pip-log.txt +pip-delete-this-directory.txt + +# Unit test / coverage reports +htmlcov/ +.tox/ +.nox/ +.coverage +.coverage.* +.cache +nosetests.xml +coverage.xml +*.cover +*.py,cover +.hypothesis/ +.pytest_cache/ + +# Translations +*.mo +*.pot + +# Django stuff: +*.log +local_settings.py +db.sqlite3 +db.sqlite3-journal + +# Flask stuff: +instance/ +.webassets-cache + +# Scrapy stuff: +.scrapy + +# Sphinx documentation +docs/_build/ + +# PyBuilder +target/ + +# Jupyter Notebook +.ipynb_checkpoints + +# IPython +profile_default/ +ipython_config.py + +# pyenv +.python-version + +# pipenv +# According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control. +# However, in case of collaboration, if having platform-specific dependencies or dependencies +# having no cross-platform support, pipenv may install dependencies that don't work, or not +# install all needed dependencies. +#Pipfile.lock + +# PEP 582; used by e.g. github.com/David-OConnor/pyflow +__pypackages__/ + +# Celery stuff +celerybeat-schedule +celerybeat.pid + +# SageMath parsed files +*.sage.py + +# Environments +adpepsenv/ +.env +.venv +env/ +venv/ +ENV/ +env.bak/ +venv.bak/ + +# Spyder project settings +.spyderproject +.spyproject + +# Rope project settings +.ropeproject + +# mkdocs documentation +/site + +# mypy +.mypy_cache/ +.dmypy.json +dmypy.json + +# Pyre type checker +.pyre/ diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..da94fa9 --- /dev/null +++ b/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2021 b1592 + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/README.md b/README.md new file mode 100644 index 0000000..184438e --- /dev/null +++ b/README.md @@ -0,0 +1,83 @@ +# TODO + +- General code cleanup +- Observables (`adpeps/ipeps/observables.py` not used) +- Rewrite `run_ipeps_gs.py` Objective class +- Fix the numerous evaluation methods in `ipeps.py` +- Documentation + + +# AD-PEPS + +Basic implementation of iPEPS ground-state and excited-state optimization using automatic differentiation. + +The package contains three main parts: + +- The core iPEPS and CTM code, contained in `adpeps/ipeps` +- Executable scripts that run the simulations in `adpeps/simulation` +- Helper classes and functions, with custom contraction and other operations in `adpeps/tensor` and general utilities in `adpeps/utils` + +## Installation + +Download this repository + +``` +git clone https://github.com/b1592/ad-peps.git +``` + +Install the package using `pip` + +``` +cd ad-peps +pip install -e . +``` + +## Usage + +As a general starting point for simulations the package can be executed as + +``` +python -m adpeps +``` + +### Ground states + +For ground states, the package can be used with the `gs` option: + +``` +python -m adpeps gs +``` + +For each simulation, a configuration file in `yaml` format should be supplied that contains all relevant settings. +An example can be found in `examples/heis_D2.yaml`, with a description of each setting. + +### Excited states + +For excitations, the option to be used is `exci`: + +``` +python -m adpeps exci +``` + +In order to prepare for a simulation, first a ground-state simulation should be performed. +After this, a base file for the excited-state simulation can be created with the `-i` argument: + +``` +python -m adpeps exci -i +``` + +This will converge the ground-state boundary tensors, normalize the ground state tensors, shift the Hamiltonian by the ground-state energy and finally compute a basis of vectors that are orthogonal to the ground state. + +Once this is completed, the full simulation can be performed, which computes the full effective energy and norm matrices, by supplying the 'momentum index'. +This index corresponds to a certain path through momentum space, controlled by the `momentum_path` option in the configuration file. +For example, the first point in the `Bril1`, which is at `(pi,0)`, can be computed by running + +``` +python -m adpeps exci -p 1 +``` + +After the simulations are done, the results can be evaluated with the `-e` argument: + +``` +python -m adpeps exci -e +``` diff --git a/adpeps/__init__.py b/adpeps/__init__.py new file mode 100644 index 0000000..38ab50a --- /dev/null +++ b/adpeps/__init__.py @@ -0,0 +1,9 @@ +import os +from pathlib import Path + +from ._version import get_versions +__version__ = get_versions()['version'] +del get_versions + +ROOT_DIR = os.path.dirname(os.path.abspath(__file__)) +PROJECT_ROOT_DIR = Path(ROOT_DIR).parent diff --git a/adpeps/__main__.py b/adpeps/__main__.py new file mode 100644 index 0000000..74ccd63 --- /dev/null +++ b/adpeps/__main__.py @@ -0,0 +1,87 @@ +""" +Main runner +""" + +import argparse +from .simulation import run_ipeps_gs, run_ipeps_exci + +from jax.config import config +config.update("jax_enable_x64", True) + +import adpeps +from adpeps.utils import io + +""" + Main executable module for iPEPS simulations + + Select one of two modes: + > python3 -m adpeps gs + > python3 -m adpeps exci -p + + Where corresponds to a .yaml configuration file + + The following environment variables can be set for the locations + of configuration and output files: + - CONFIGDIR: base folder where the simulations look for configuration + files + - DATADIR: base folder where output data is saved + + The naming conventions for both modes are defined in utils.io as follows: + - Ground states: /__D_X.npz + - Excited states: /__D_X/__.npz +""" + +def get_parser(): + # create the top-level parser + parser = argparse.ArgumentParser() + parser.add_argument('-v', '--version', dest='version', + action='store_true', + help='Show version') + + subparsers = parser.add_subparsers(help='Simulation mode', dest='sim_mode') + + # Ground-state parser + parser_gs = subparsers.add_parser('gs', help='Ground-state simulation') + parser_gs.add_argument('config_file', type=str, + help='Configuration (.yml) file for the simulation options') + + # Excited-state parser + parser_exci = subparsers.add_parser('exci', help='Excited-state simulation') + parser_exci.add_argument('config_file', type=str, + help='config file of excited-state simulation') + parser_exci.add_argument('-p', '--p_ix', dest='momentum_ix', + default=0, type=int, + help='momentum index') + parser_exci.add_argument('-e', '--eval', dest='evaluate', + action='store_true', + help='Prepare excitation base') + parser_exci.add_argument('-i', '--init', dest='init', + action='store_true', + help='Prepare excitation base') + return parser + +if __name__ == '__main__': + parser = get_parser() + args = parser.parse_args() + print(args) + + if args.version: + print('Adpeps version:') + print(adpeps.__version__) + + elif args.sim_mode == 'gs': + print('Running ground-state sim') + args.config_file = io.localize_config_file(args.config_file) + run_ipeps_gs.run(args.config_file) + + elif args.sim_mode == 'exci': + print('Running excited-state sim') + print(args.config_file) + args.config_file = io.localize_config_file(args.config_file) + print(args.config_file) + if args.evaluate: + run_ipeps_exci.evaluate(args.config_file, args.momentum_ix-1) + elif args.init: + run_ipeps_exci.prepare(args.config_file) + else: + run_ipeps_exci.run(args.config_file, args.momentum_ix-1) diff --git a/adpeps/_version.py b/adpeps/_version.py new file mode 100644 index 0000000..ba88565 --- /dev/null +++ b/adpeps/_version.py @@ -0,0 +1,520 @@ + +# This file helps to compute a version number in source trees obtained from +# git-archive tarball (such as those provided by githubs download-from-tag +# feature). Distribution tarballs (built by setup.py sdist) and build +# directories (produced by setup.py build) will contain a much shorter file +# that just contains the computed version number. + +# This file is released into the public domain. Generated by +# versioneer-0.18 (https://github.com/warner/python-versioneer) + +"""Git implementation of _version.py.""" + +import errno +import os +import re +import subprocess +import sys + + +def get_keywords(): + """Get the keywords needed to look up the version information.""" + # these strings will be replaced by git during git-archive. + # setup.py/versioneer.py will grep for the variable names, so they must + # each be defined on a line of their own. _version.py will just call + # get_keywords(). + git_refnames = "$Format:%d$" + git_full = "$Format:%H$" + git_date = "$Format:%ci$" + keywords = {"refnames": git_refnames, "full": git_full, "date": git_date} + return keywords + + +class VersioneerConfig: + """Container for Versioneer configuration parameters.""" + + +def get_config(): + """Create, populate and return the VersioneerConfig() object.""" + # these strings are filled in when 'setup.py versioneer' creates + # _version.py + cfg = VersioneerConfig() + cfg.VCS = "git" + cfg.style = "pep440" + cfg.tag_prefix = "" + cfg.parentdir_prefix = "None" + cfg.versionfile_source = "sym_tensor/_version.py" + cfg.verbose = False + return cfg + + +class NotThisMethod(Exception): + """Exception raised if a method is not valid for the current scenario.""" + + +LONG_VERSION_PY = {} +HANDLERS = {} + + +def register_vcs_handler(vcs, method): # decorator + """Decorator to mark a method as the handler for a particular VCS.""" + def decorate(f): + """Store f in HANDLERS[vcs][method].""" + if vcs not in HANDLERS: + HANDLERS[vcs] = {} + HANDLERS[vcs][method] = f + return f + return decorate + + +def run_command(commands, args, cwd=None, verbose=False, hide_stderr=False, + env=None): + """Call the given command(s).""" + assert isinstance(commands, list) + p = None + for c in commands: + try: + dispcmd = str([c] + args) + # remember shell=False, so use git.cmd on windows, not just git + p = subprocess.Popen([c] + args, cwd=cwd, env=env, + stdout=subprocess.PIPE, + stderr=(subprocess.PIPE if hide_stderr + else None)) + break + except EnvironmentError: + e = sys.exc_info()[1] + if e.errno == errno.ENOENT: + continue + if verbose: + print("unable to run %s" % dispcmd) + print(e) + return None, None + else: + if verbose: + print("unable to find command, tried %s" % (commands,)) + return None, None + stdout = p.communicate()[0].strip() + if sys.version_info[0] >= 3: + stdout = stdout.decode() + if p.returncode != 0: + if verbose: + print("unable to run %s (error)" % dispcmd) + print("stdout was %s" % stdout) + return None, p.returncode + return stdout, p.returncode + + +def versions_from_parentdir(parentdir_prefix, root, verbose): + """Try to determine the version from the parent directory name. + + Source tarballs conventionally unpack into a directory that includes both + the project name and a version string. We will also support searching up + two directory levels for an appropriately named parent directory + """ + rootdirs = [] + + for i in range(3): + dirname = os.path.basename(root) + if dirname.startswith(parentdir_prefix): + return {"version": dirname[len(parentdir_prefix):], + "full-revisionid": None, + "dirty": False, "error": None, "date": None} + else: + rootdirs.append(root) + root = os.path.dirname(root) # up a level + + if verbose: + print("Tried directories %s but none started with prefix %s" % + (str(rootdirs), parentdir_prefix)) + raise NotThisMethod("rootdir doesn't start with parentdir_prefix") + + +@register_vcs_handler("git", "get_keywords") +def git_get_keywords(versionfile_abs): + """Extract version information from the given file.""" + # the code embedded in _version.py can just fetch the value of these + # keywords. When used from setup.py, we don't want to import _version.py, + # so we do it with a regexp instead. This function is not used from + # _version.py. + keywords = {} + try: + f = open(versionfile_abs, "r") + for line in f.readlines(): + if line.strip().startswith("git_refnames ="): + mo = re.search(r'=\s*"(.*)"', line) + if mo: + keywords["refnames"] = mo.group(1) + if line.strip().startswith("git_full ="): + mo = re.search(r'=\s*"(.*)"', line) + if mo: + keywords["full"] = mo.group(1) + if line.strip().startswith("git_date ="): + mo = re.search(r'=\s*"(.*)"', line) + if mo: + keywords["date"] = mo.group(1) + f.close() + except EnvironmentError: + pass + return keywords + + +@register_vcs_handler("git", "keywords") +def git_versions_from_keywords(keywords, tag_prefix, verbose): + """Get version information from git keywords.""" + if not keywords: + raise NotThisMethod("no keywords at all, weird") + date = keywords.get("date") + if date is not None: + # git-2.2.0 added "%cI", which expands to an ISO-8601 -compliant + # datestamp. However we prefer "%ci" (which expands to an "ISO-8601 + # -like" string, which we must then edit to make compliant), because + # it's been around since git-1.5.3, and it's too difficult to + # discover which version we're using, or to work around using an + # older one. + date = date.strip().replace(" ", "T", 1).replace(" ", "", 1) + refnames = keywords["refnames"].strip() + if refnames.startswith("$Format"): + if verbose: + print("keywords are unexpanded, not using") + raise NotThisMethod("unexpanded keywords, not a git-archive tarball") + refs = set([r.strip() for r in refnames.strip("()").split(",")]) + # starting in git-1.8.3, tags are listed as "tag: foo-1.0" instead of + # just "foo-1.0". If we see a "tag: " prefix, prefer those. + TAG = "tag: " + tags = set([r[len(TAG):] for r in refs if r.startswith(TAG)]) + if not tags: + # Either we're using git < 1.8.3, or there really are no tags. We use + # a heuristic: assume all version tags have a digit. The old git %d + # expansion behaves like git log --decorate=short and strips out the + # refs/heads/ and refs/tags/ prefixes that would let us distinguish + # between branches and tags. By ignoring refnames without digits, we + # filter out many common branch names like "release" and + # "stabilization", as well as "HEAD" and "master". + tags = set([r for r in refs if re.search(r'\d', r)]) + if verbose: + print("discarding '%s', no digits" % ",".join(refs - tags)) + if verbose: + print("likely tags: %s" % ",".join(sorted(tags))) + for ref in sorted(tags): + # sorting will prefer e.g. "2.0" over "2.0rc1" + if ref.startswith(tag_prefix): + r = ref[len(tag_prefix):] + if verbose: + print("picking %s" % r) + return {"version": r, + "full-revisionid": keywords["full"].strip(), + "dirty": False, "error": None, + "date": date} + # no suitable tags, so version is "0+unknown", but full hex is still there + if verbose: + print("no suitable tags, using unknown + full revision id") + return {"version": "0+unknown", + "full-revisionid": keywords["full"].strip(), + "dirty": False, "error": "no suitable tags", "date": None} + + +@register_vcs_handler("git", "pieces_from_vcs") +def git_pieces_from_vcs(tag_prefix, root, verbose, run_command=run_command): + """Get version from 'git describe' in the root of the source tree. + + This only gets called if the git-archive 'subst' keywords were *not* + expanded, and _version.py hasn't already been rewritten with a short + version string, meaning we're inside a checked out source tree. + """ + GITS = ["git"] + if sys.platform == "win32": + GITS = ["git.cmd", "git.exe"] + + out, rc = run_command(GITS, ["rev-parse", "--git-dir"], cwd=root, + hide_stderr=True) + if rc != 0: + if verbose: + print("Directory %s not under git control" % root) + raise NotThisMethod("'git rev-parse --git-dir' returned error") + + # if there is a tag matching tag_prefix, this yields TAG-NUM-gHEX[-dirty] + # if there isn't one, this yields HEX[-dirty] (no NUM) + describe_out, rc = run_command(GITS, ["describe", "--tags", "--dirty", + "--always", "--long", + "--match", "%s*" % tag_prefix], + cwd=root) + # --long was added in git-1.5.5 + if describe_out is None: + raise NotThisMethod("'git describe' failed") + describe_out = describe_out.strip() + full_out, rc = run_command(GITS, ["rev-parse", "HEAD"], cwd=root) + if full_out is None: + raise NotThisMethod("'git rev-parse' failed") + full_out = full_out.strip() + + pieces = {} + pieces["long"] = full_out + pieces["short"] = full_out[:7] # maybe improved later + pieces["error"] = None + + # parse describe_out. It will be like TAG-NUM-gHEX[-dirty] or HEX[-dirty] + # TAG might have hyphens. + git_describe = describe_out + + # look for -dirty suffix + dirty = git_describe.endswith("-dirty") + pieces["dirty"] = dirty + if dirty: + git_describe = git_describe[:git_describe.rindex("-dirty")] + + # now we have TAG-NUM-gHEX or HEX + + if "-" in git_describe: + # TAG-NUM-gHEX + mo = re.search(r'^(.+)-(\d+)-g([0-9a-f]+)$', git_describe) + if not mo: + # unparseable. Maybe git-describe is misbehaving? + pieces["error"] = ("unable to parse git-describe output: '%s'" + % describe_out) + return pieces + + # tag + full_tag = mo.group(1) + if not full_tag.startswith(tag_prefix): + if verbose: + fmt = "tag '%s' doesn't start with prefix '%s'" + print(fmt % (full_tag, tag_prefix)) + pieces["error"] = ("tag '%s' doesn't start with prefix '%s'" + % (full_tag, tag_prefix)) + return pieces + pieces["closest-tag"] = full_tag[len(tag_prefix):] + + # distance: number of commits since tag + pieces["distance"] = int(mo.group(2)) + + # commit: short hex revision ID + pieces["short"] = mo.group(3) + + else: + # HEX: no tags + pieces["closest-tag"] = None + count_out, rc = run_command(GITS, ["rev-list", "HEAD", "--count"], + cwd=root) + pieces["distance"] = int(count_out) # total number of commits + + # commit date: see ISO-8601 comment in git_versions_from_keywords() + date = run_command(GITS, ["show", "-s", "--format=%ci", "HEAD"], + cwd=root)[0].strip() + pieces["date"] = date.strip().replace(" ", "T", 1).replace(" ", "", 1) + + return pieces + + +def plus_or_dot(pieces): + """Return a + if we don't already have one, else return a .""" + if "+" in pieces.get("closest-tag", ""): + return "." + return "+" + + +def render_pep440(pieces): + """Build up version string, with post-release "local version identifier". + + Our goal: TAG[+DISTANCE.gHEX[.dirty]] . Note that if you + get a tagged build and then dirty it, you'll get TAG+0.gHEX.dirty + + Exceptions: + 1: no tags. git_describe was just HEX. 0+untagged.DISTANCE.gHEX[.dirty] + """ + if pieces["closest-tag"]: + rendered = pieces["closest-tag"] + if pieces["distance"] or pieces["dirty"]: + rendered += plus_or_dot(pieces) + rendered += "%d.g%s" % (pieces["distance"], pieces["short"]) + if pieces["dirty"]: + rendered += ".dirty" + else: + # exception #1 + rendered = "0+untagged.%d.g%s" % (pieces["distance"], + pieces["short"]) + if pieces["dirty"]: + rendered += ".dirty" + return rendered + + +def render_pep440_pre(pieces): + """TAG[.post.devDISTANCE] -- No -dirty. + + Exceptions: + 1: no tags. 0.post.devDISTANCE + """ + if pieces["closest-tag"]: + rendered = pieces["closest-tag"] + if pieces["distance"]: + rendered += ".post.dev%d" % pieces["distance"] + else: + # exception #1 + rendered = "0.post.dev%d" % pieces["distance"] + return rendered + + +def render_pep440_post(pieces): + """TAG[.postDISTANCE[.dev0]+gHEX] . + + The ".dev0" means dirty. Note that .dev0 sorts backwards + (a dirty tree will appear "older" than the corresponding clean one), + but you shouldn't be releasing software with -dirty anyways. + + Exceptions: + 1: no tags. 0.postDISTANCE[.dev0] + """ + if pieces["closest-tag"]: + rendered = pieces["closest-tag"] + if pieces["distance"] or pieces["dirty"]: + rendered += ".post%d" % pieces["distance"] + if pieces["dirty"]: + rendered += ".dev0" + rendered += plus_or_dot(pieces) + rendered += "g%s" % pieces["short"] + else: + # exception #1 + rendered = "0.post%d" % pieces["distance"] + if pieces["dirty"]: + rendered += ".dev0" + rendered += "+g%s" % pieces["short"] + return rendered + + +def render_pep440_old(pieces): + """TAG[.postDISTANCE[.dev0]] . + + The ".dev0" means dirty. + + Eexceptions: + 1: no tags. 0.postDISTANCE[.dev0] + """ + if pieces["closest-tag"]: + rendered = pieces["closest-tag"] + if pieces["distance"] or pieces["dirty"]: + rendered += ".post%d" % pieces["distance"] + if pieces["dirty"]: + rendered += ".dev0" + else: + # exception #1 + rendered = "0.post%d" % pieces["distance"] + if pieces["dirty"]: + rendered += ".dev0" + return rendered + + +def render_git_describe(pieces): + """TAG[-DISTANCE-gHEX][-dirty]. + + Like 'git describe --tags --dirty --always'. + + Exceptions: + 1: no tags. HEX[-dirty] (note: no 'g' prefix) + """ + if pieces["closest-tag"]: + rendered = pieces["closest-tag"] + if pieces["distance"]: + rendered += "-%d-g%s" % (pieces["distance"], pieces["short"]) + else: + # exception #1 + rendered = pieces["short"] + if pieces["dirty"]: + rendered += "-dirty" + return rendered + + +def render_git_describe_long(pieces): + """TAG-DISTANCE-gHEX[-dirty]. + + Like 'git describe --tags --dirty --always -long'. + The distance/hash is unconditional. + + Exceptions: + 1: no tags. HEX[-dirty] (note: no 'g' prefix) + """ + if pieces["closest-tag"]: + rendered = pieces["closest-tag"] + rendered += "-%d-g%s" % (pieces["distance"], pieces["short"]) + else: + # exception #1 + rendered = pieces["short"] + if pieces["dirty"]: + rendered += "-dirty" + return rendered + + +def render(pieces, style): + """Render the given version pieces into the requested style.""" + if pieces["error"]: + return {"version": "unknown", + "full-revisionid": pieces.get("long"), + "dirty": None, + "error": pieces["error"], + "date": None} + + if not style or style == "default": + style = "pep440" # the default + + if style == "pep440": + rendered = render_pep440(pieces) + elif style == "pep440-pre": + rendered = render_pep440_pre(pieces) + elif style == "pep440-post": + rendered = render_pep440_post(pieces) + elif style == "pep440-old": + rendered = render_pep440_old(pieces) + elif style == "git-describe": + rendered = render_git_describe(pieces) + elif style == "git-describe-long": + rendered = render_git_describe_long(pieces) + else: + raise ValueError("unknown style '%s'" % style) + + return {"version": rendered, "full-revisionid": pieces["long"], + "dirty": pieces["dirty"], "error": None, + "date": pieces.get("date")} + + +def get_versions(): + """Get version information or return default if unable to do so.""" + # I am in _version.py, which lives at ROOT/VERSIONFILE_SOURCE. If we have + # __file__, we can work backwards from there to the root. Some + # py2exe/bbfreeze/non-CPython implementations don't do __file__, in which + # case we can only use expanded keywords. + + cfg = get_config() + verbose = cfg.verbose + + try: + return git_versions_from_keywords(get_keywords(), cfg.tag_prefix, + verbose) + except NotThisMethod: + pass + + try: + root = os.path.realpath(__file__) + # versionfile_source is the relative path from the top of the source + # tree (where the .git directory might live) to this file. Invert + # this to find the root from __file__. + for i in cfg.versionfile_source.split('/'): + root = os.path.dirname(root) + except NameError: + return {"version": "0+unknown", "full-revisionid": None, + "dirty": None, + "error": "unable to find root of source tree", + "date": None} + + try: + pieces = git_pieces_from_vcs(cfg.tag_prefix, root, verbose) + return render(pieces, cfg.style) + except NotThisMethod: + pass + + try: + if cfg.parentdir_prefix: + return versions_from_parentdir(cfg.parentdir_prefix, root, verbose) + except NotThisMethod: + pass + + return {"version": "0+unknown", "full-revisionid": None, + "dirty": None, + "error": "unable to compute version", "date": None} diff --git a/adpeps/ipeps/__init__.py b/adpeps/ipeps/__init__.py new file mode 100644 index 0000000..8e777b6 --- /dev/null +++ b/adpeps/ipeps/__init__.py @@ -0,0 +1,2 @@ +r""" Main iPEPS package +""" diff --git a/adpeps/ipeps/config.py b/adpeps/ipeps/config.py new file mode 100644 index 0000000..e1b7454 --- /dev/null +++ b/adpeps/ipeps/config.py @@ -0,0 +1,125 @@ +""" Configuration module for iPEPS simulations + + These settings will be loaded from a configuration file :code:`.yml` file + via the :meth:`from_dict` function +""" + +from typing import Union, Iterable +import numpy as np +import math +import os + +D: int = None +""" iPEPS bond dimension """ + +chi: int = None +""" CTM boundary bond dimension """ + +model: str = None +""" Model """ + +model_params: dict = None +""" Model parameters """ + +method: str = None +""" Optimization method """ + +seed: int = 1 +""" Random seed for initial state """ + +resume: bool = False +""" Resume earlier simulation if found """ + +base_sim: Union[str, None] = None +""" Base simulation """ + +load_sim: bool = None +""" Load previous (Python) simulation """ + +max_iterations: int = 100 +""" Maximum number of optimizer iterations """ + +disp_level: int = 1 +""" Display level (`0`: no output) """ + +pattern: Union[Iterable, None] = None +""" Unit cell configuration + Defined as a 2-D array of integers that label the unique sites in the unit + cell. + + Example: + A 2x2 unit cell with a [AB, BA]-type pattern is defined by + + .. code-block:: python + + pattern = [ + [0, 1], + [1, 0] + ] +""" + +ctm_conv_tol: float = 1e-10 +""" CTM convergence criterium (singular values norm difference) """ + +ctm_min_iter: int = 5 +""" Minimal number of CTM steps """ + +ctm_max_iter: int = 20 +""" Maximal number of CTM steps """ + +flush_output: bool = False +""" Passes the :code:`flush = True` argument to the builtin :code:`print` function + when calling the :func:`adpeps.utils.printing.print` function + + Useful when deploying the code to computing clusters and capturing the output + into text files +""" + +out_prefix: str = '' +""" Optional prefix for the output file of the simulation + + Example: + :code:`.../{model}_D{D}_X{chi}.npz` + + becomes + + :code:`.../{out_prefix}_{model}_D{D}_X{chi}.npz` +""" + +# Excitation settings + +px: float = 0 * math.pi + +py: float = 0 * math.pi + +momentum_path: str = 'Bril1' +""" Momentum path through the BZ """ + +filter_null: bool = False + +def from_dict(cfg): + """ Import config from configuration (`.yml`) file """ + + cfg_vars = globals() + for name, value in cfg.items(): + if name in cfg_vars.keys(): + cfg_vars[name] = value + else: + raise ValueError(f"Option {name} = {value} not defined in iPEPS config") + try: + debug_override = os.environ.get("PY_SIM_DEBUG2") + if debug_override is not None and int(debug_override) == 1: + print("** Debug mode on (PY_SIM_DEBUG = 1) **") + cfg_vars['disp_level'] = 2 + cfg_vars['use_parallel'] = False + except: + pass + +def get_model_params(): + if model_params is not None: + try: + return '_'.join([str(p) for p in model_params.values()]) + '_' + except AttributeError: + return '_'.join([str(p) for p in model_params]) + '_' + else: + return '' diff --git a/adpeps/ipeps/contractions.yaml b/adpeps/ipeps/contractions.yaml new file mode 100644 index 0000000..d6b1674 --- /dev/null +++ b/adpeps/ipeps/contractions.yaml @@ -0,0 +1,290 @@ +# All contractions in the form of inputs for ncon +# +# Define a contraction by its name and the indices +# to be contracted over +# +# For example: +# (contractions.yaml) +# example_contraction: +# [[-1,1,2,3], [-2,1,2,3]] +# +# (example.py) +# from contractions import ncon +# new_T = ncon([T1, T2], 'example_contraction') +# +# For fermionic simulations, some contractions involve swap +# gates, which can be added by using an expanded syntax: +# +# example_contraction: +# ix: [[-1,1,2,3], [-2,1,2,3]] +# swaps: [[1,2], [-1,-2]] +# +# In contractions.py, the definitions from this file +# are parsed into a dict (so no duplicate keys) and +# a wrapper for ncon that takes a contraction key +# as input is exposed + + +# --------------------- +# CTM projectors +# --------------------- + +# get_projectors_left +proj_left_Cs1: + [[1, -2], [-1,1,-3,-4]] + +proj_left_Q1: + [[-1,1,3,6], [1,-4,2,4], [5,-2,3,2,-5], [5,-3,6,4,-6]] + +proj_left_Cs4: + [[1,-2], [-1,1,-3,-4]] + +proj_left_Q4: + [[-1,1,3,5], [-4,1,2,4], [6,-2,-5,2,3], [6,-3,-6,4,5]] + + +# get_projectors_right +proj_right_Cs2: + [[1,-2], [1,-1,-3,-4]] + +proj_right_Q2: + [[-1,1,3,6], [1,-4,2,4], [5,2,3,-2,-5], [5,4,6,-3,-6]] + +proj_right_Cs3: + [[-2,1] ,[1,-1,-3,-4]] + +proj_right_Q3: + [[-1,1,6,3], [-4,1,4,2], [5,4,-5,-2,6], [5,2,-6,-3,3]] + + +# get_projectors_top +proj_top_Cs1: + [[-2,1], [1,-1,-3,-4]] + +proj_top_Q1: + [[-1,1,3,6], [-4,1,2,4], [5,-5,2,3,-2], [5,-6,4,6,-3]] + +proj_top_Cs2: + [[-2,1], [1,-1,-3,-4]] + +proj_top_Q2: + [[-1,1,3,6], [1,-4,2,4], [5,3,2,-5,-2], [5,6,4,-6,-3]] + + +# get_projectors_bottom +proj_bottom_Cs4: + [[-2,1], [-1,1,-3,-4]] + +proj_bottom_Q4: + [[-1,1,3,6], [-4,1,2,4], [5,-5,-2,3,2], [5,-6,-3,6,4]] + +proj_bottom_Cs3: + [[1,-2], [-1,1,-3,-4]] + +proj_bottom_Q3: + [[-1,1,6,3], [1,-4,4,2], [5,6,-2,-5,4], [5,3,-3,-6,2]] + + +# get_projectors +proj_P1: + [[-1,-2,-3,1,2,3], [1,2,3,4], [4,-4]] + +proj_P2: + [[1,2,3,-1,-2,-3], [1,2,3,4], [-4,4]] + +# --------------------- +# CTM steps +# --------------------- + +# doleft +doleft_T4: + [[-1,1,3,4], [1,8,2,5], [7,-3,3,2,9], [7,-4,4,5,10], [-2,8,9,10]] + +doleft_T4_B: + [[-1,1,3,4], [1,8,2,5], [7,-3,3,2,9], [7,-4,4,5,10], [-2,8,9,10]] + +doleft_T4_Bd: + [[-1,1,3,4], [1,8,2,5], [7,-3,3,2,9], [7,-4,4,5,10], [-2,8,9,10]] + +doleft_Cs1: + [[1,-2], [-1,1,-3,-4]] + +doleft_C1: + [[-1,1,2,3], [-2,1,2,3]] + +doleft_Cs4: + [[1,-2], [-1,1,-3,-4]] + +doleft_C4: + [[-1,1,2,3], [-2,1,2,3]] + +doleft_C1_c4v: + [[1,2,3,4,5,6], [-1,1,2,3], [-2,4,5,6]] + + +# doright +doright_T2: + [[-1,1,3,6], [1,7,2,4], [5,2,3,-3,8], [5,4,6,-4,9], [-2,7,8,9]] + +doright_T2_B: + [[-1,1,3,6], [1,7,2,4], [5,2,3,-3,8], [5,4,6,-4,9], [-2,7,8,9]] + +doright_T2_Bd: + [[-1,1,3,6], [1,7,2,4], [5,2,3,-3,8], [5,4,6,-4,9], [-2,7,8,9]] + +doright_Cs2: + [[1,-2], [1,-1,-3,-4]] + +doright_C2: + [[-1,1,2,3], [-2,1,2,3]] + +doright_Cs3: + [[-2,1], [1,-1,-3,-4]] + +doright_C3: + [[-2,1,2,3], [-1,1,2,3]] + + +# dotop +dotop_T1: + [[-2,1,3,6], [7,1,2,4], [5,8,2,3,-3], [5,9,4,6,-4], [-1,7,8,9]] + +dotop_T1_B: + [[-2,1,3,6], [7,1,2,4], [5,8,2,3,-3], [5,9,4,6,-4], [-1,7,8,9]] + +dotop_T1_Bd: + [[-2,1,3,6], [7,1,2,4], [5,8,2,3,-3], [5,9,4,6,-4], [-1,7,8,9]] + +dotop_Cs1: + [[-2,1], [1,-1,-3,-4]] + +dotop_C1: + [[-2,1,2,3], [-1,1,2,3]] + +dotop_Cs2: + [[-2,1], [1,-1,-3,-4]] + +dotop_C2: + [[-2,1,2,3], [-1,1,2,3]] + + +# dobottom +dobottom_T3: + [[-2,1,3,6], [7,1,2,4], [5,8,-3,3,2], [5,9,-4,6,4], [-1,7,8,9]] + +dobottom_T3_B: + [[-2,1,3,6], [7,1,2,4], [5,8,-3,3,2], [5,9,-4,6,4], [-1,7,8,9]] + +dobottom_T3_Bd: + [[-2,1,3,6], [7,1,2,4], [5,8,-3,3,2], [5,9,-4,6,4], [-1,7,8,9]] + +dobottom_Cs3: + [[1,-2], [-1,1,-3,-4]] + +dobottom_C3: + [[-1,1,2,3], [-2,1,2,3]] + +dobottom_Cs4: + [[-2,1], [-1,1,-3,-4]] + +dobottom_C4: + [[-2,1,2,3], [-1,1,2,3]] + + +# --------------------- +# Reduced density matrices - regular +# --------------------- + +# get_dms + +# Upper half +dm_up_Cc1: + [[1,2],[-5,1,3,-4],[2,-1,4,-7],[-3,-6,3,4,-2]] + +dm_up_Cc2: + [[-2,1],[1,-7,-3,2],[-5,2,-1,-4,-6]] + +dm_up: + [[-1,-2,-3,1,2,3,4],[1,2,3,4,-4,-5,-6]] + +# Lower half +dm_low_Cc1: + [[1,2],[-4,1,4,-5],[-1,2,3,-6],[-3,-7,-2,3,4]] + +dm_low_Cc3: + [[1,-1],[-7,1,-4,2],[-5,2,-6,-3,-2]] + +dm_low: + [[-1,-2,-3,1,2,3,4],[1,2,3,4,-4,-5,-6]] + +dm_rov: + [[1,2,-1,-3,5,6], [1,2,-2,-4,5,6]] + +# Left half +dm_left_Cc2: + [[1,-1],[-4,1,-2,2],[-3,-7,2,-6,-5]] + +dm_left: + [[1,2,-3,-6,5,6,-2],[1,2,-4,-1,5,6,-5]] + +# Right half +dm_right_Cc1: + [[1,-5],[1,-1,2,-6],[-3,-7,2,-2,-8]] + +dm_right_Cc3: + [[1,2],[-1,1,-3,3],[2,-7,-4,4],[-5,3,-2,-6,4]] + +dm_right: + [[-1,-2,-3,4,5,6,7],[4,5,6,7,-4,-5,-6]] + +dm_roh: + [[1,2,-1,-3,5,6], [1,2,-2,-4,5,6]] + + +# --------------------- +# Reduced density matrices - odd-fermionic excitation variant +# --------------------- +# Variant with site tensors contracted into the row/column transfer matrices + +# Preparations: contraction of site tensors into boundaries +rov_prep_T4_A: + [[-1,-2,1,-4], [-7,-3,-5,1,-6]] + +rov_prep_T4: + [[-1,-2,1,-4], [-7,-3,-5,1,-6]] + +rov_prep_T2_A: + [[-1,-2,-3,1], [-7,1,-5,-4,-6]] + +rov_prep_T2: + [[-1,-2,-3,1], [-7,1,-5,-4,-6]] + +roh_prep_T1_A: + [[-1,-2,1,-4], [-7,-5,1,-6,-3]] + +roh_prep_T1: + [[-1,-2,1,-4], [-7,-5,1,-6,-3]] + +roh_prep_T3_A: + [[-1,-2,-3,1], [-7,-5,-4,-6,1]] + +roh_prep_T3: + [[-1,-2,-3,1], [-7,-5,-4,-6,1]] + +# Contraction of the reduced density matrices +rov_full_upper: + [[1,3], [2,8], [2,1,4,5], [8,-4,7,6,5,-3,-6], [3,-1,7,6,4,-2,-5]] + +rov_full_lower: + [[3,1], [2,8], [-4,3,6,7,-3,4,-6], [1,2,5,4], [-1,8,6,7,-2,5,-5]] + +roh_full_left: + [[3,1], [8,2], [-1,3,7,6,-2,4,-5], [-4,8,7,6,-3,5,-6], [1,2,4,5]] + +roh_full_right: + [[8,2], [1,3], [8,-1,6,7,5,-2,-5], [2,1,5,4], [3,-4,6,7,4,-3,-6]] + + +# single site dm +dm_single_site: + [[1,8],[1,2,-2,-6],[2,3],[3,7,-3,-7],[4,7],[5,4,-4,-8],[6,5],[8,6,-1,-5]] diff --git a/adpeps/ipeps/ctm.py b/adpeps/ipeps/ctm.py new file mode 100644 index 0000000..3ec7f38 --- /dev/null +++ b/adpeps/ipeps/ctm.py @@ -0,0 +1,510 @@ +""" + Main CTM code + + The individual site and boundary tensors come in a + special list-type object (TList), which has extra + indexing features, such as periodic boundary + conditions and shift contexts + + All ncon contractions are defined in contractions.yaml +""" + +import jax +import jax.numpy as np +import time +from typing import Tuple + +import adpeps.ipeps.config as sim_config +from adpeps.utils.ctmtensors import CTMTensors +from adpeps.utils.nested import Nested +from adpeps.utils.tlist import TList, cur_loc, set_pattern +from adpeps.tensor.contractions import ncon +from adpeps.tensor.ops import svd, diag_inv + +def run_ctm(tensors, chi, conv_fun=None): + ctm = CTM(tensors, chi, conv_fun) + return ctm() + +class CTM: + """ CTM class """ + + def __init__(self, tensors: CTMTensors, chi: int, conv_fun=None): + """ + Args: + tensors: input ctmtensors + chi: boundary bond dimension + """ + + self.tensors = tensors + self.chi = chi + self.conv_fun = conv_fun + self.tol = sim_config.ctm_conv_tol # Convergence tolerance (singular values) + self.min_iter = sim_config.ctm_min_iter + self.max_iter = sim_config.ctm_max_iter + + self.singular_values = None + self.last_convergence = None + self.diffs = [None] + self.n_steps = 0 + self.last_ctm_time = None + self.convergence = np.nan + self.condition_number = None + + def __call__(self): + while not self.converged: + self.show_progress() + self.update() + + return self.tensors, self.convergence + + def update(self): + """ Perform an update of all boundary tensors """ + start = time.time() + self.tensors, s = renormalize(self.tensors, self.chi) + end = time.time() + + try: + s = jax.lax.stop_gradient(s) + s_nz = s[s != 0] / np.max(s) + cond_s = np.min(s_nz) + except: + cond_s = np.nan + + self.n_steps += 1 + self.singular_values = s + self.last_ctm_time = round(end-start, 2) + self.condition_number = cond_s + + def show_progress(self): + """ Print out the current progress """ + if self.n_steps > 0 and sim_config.disp_level > 0: + if self.conv_fun is not None: + print(f" | CTM step {self.n_steps} conv: {self.diffs[-1]:.3e} time: {self.last_ctm_time} obj: {self.convergence:.6f}") + else: + print(f" | CTM step {self.n_steps} conv: {self.diffs[-1]:.3e} time: {self.last_ctm_time}") + + @property + def converged(self): + """ Check convergence with supplied convergence function """ + if self.conv_fun is not None: + s = jax.lax.stop_gradient(self.conv_fun(self.tensors)) + else: + s = self.singular_values + + self.last_convergence = self.convergence + self.convergence = s + try: + diff = np.linalg.norm(self.convergence-self.last_convergence) + self.diffs.append(diff) + except: + diff = np.nan + + if self.n_steps >= self.min_iter and self.diffs[-1] < self.tol: + return True + elif self.n_steps >= self.max_iter: + return True + else: + return False + +def renormalize(tensors: CTMTensors, chi: int) -> Tuple[CTMTensors, np.ndarray]: + """ + Performs a CTM iteration + Updates all sites in the unit cell + + Args: + tensors: input ctmtensors + chi: boundary bond dimension + + Returns: + A tuple containing + + - **tensors** (*CTMTensors*): updated tensors + - **S** (*np.ndarray*): singular values of C1 (for convergence) + """ + + with set_pattern(tensors.A.pattern): + tensors, sl = do_left(tensors, chi) + tensors = do_right(tensors, chi) + tensors = do_top(tensors, chi) + tensors = do_bottom(tensors, chi) + + # Singular values of C1[0,0] - to check for convergence + S = sl[0] + return (tensors, S) + + +""" + --------------------- + Individual left, right, top and bottom moves + --------------------- + + Each move consists of a loop through the sites of the unit cell + in which first the projectors are computed and then the boundary + tensors are updated. + + The loops are optimized for readability with a few tricks that are + implemented in the TList or CTMTensors classes: + + - cur_loc(x,y): with this context enabled, all TList objects have a + shift applied in their coordinates. + For example: + + A[0,0] = 1 + A[1,0] = 2 + with cur_loc(1,0): + print(A[0,0]) # => 2 (retrieves element A([0,0]+[1,0]) = A[1,0]) + + Using this context, the operations in the inner loops can be written + without reference to the (i,j) loop indices, as if it's just written + for one site in the unit cell. + + - CTMTensors.hold(tensor1, ...): with this context enabled, any values + stored in tensor1 (and other designated tensors) are only put in a + temporary location, so that reading the tensor still yields the + original values. After the context exits, the values will be + overwritten by the temporary values. + Example: + + # ts is a CTMTensors object containing site/boundary tensors + ts.C1[0,0] = [1] + ts.C2[0,0] = [2] + with ts.hold('C1'): + ts.C1[0,0] = [10] + ts.C2[0,0] = [20] + print(ts.C1[0,0]) # => [1] since the value [10] is not yet stored + print(ts.C2[0,0]) # => [20] + + print(ts.C1[0,0]) # => [10] since the context has exited + + With this context, there is no need to store the updated boundary + tensors in the inner loops in temporary objects (since in CTM each + update step should be performed separately). + + - TList.is_changed(x,y): tracks whether any of the tensors in the TList + have been updated since the last call to TList.reset_changed(). + This is useful for unit cells with pattern restrictions, so that + boundary tensors that correspond to equivalent sites are only + computed once. + +""" + +def do_left(ts: CTMTensors, chi: int) -> Tuple[CTMTensors, np.ndarray]: + """ + Perform left CTM move + + Args: + ts: input tensors + chi: boundary bond dimension + + Returns: + A tuple containing + + - **tensors** (*CTMTensors*): updated tensors + - **sl** (*np.ndarray*): singular values of C1 (for convergence) + + """ + A = ts.A + unit_cell = A.size + ts.C1.reset_changed() + ts.C4.reset_changed() + ts.T4.reset_changed() + Pl = TList(shape=unit_cell) # Upper projectors + Plb = TList(shape=unit_cell) # Lower projectors + sl = TList(shape=unit_cell) # Singular values (for convergence check) + # Loop over x direction of the unit cell + for i in range(A.size[0]): + # Loop over y direction + for j in range(A.size[1]): + # Change the relative shift of the lists + with cur_loc(i,j): + if not Pl.is_changed(0,1): + Pl[0,1], Plb[0,1], sl[0,1] = get_projectors_left(ts, chi) + # Only update the lists after the loop over j is completed + with ts.hold('all_C1','all_C4','all_T4'): + for j in range(A.size[1]): + with cur_loc(i,j): + if not ts.C1.is_changed(0,0): + ts.update(('C1', 'C4', 'T4'), ([0,0],[0,0],[0,0]), renorm_left(ts, Pl, Plb)) + return ts, sl + +def do_right(ts: CTMTensors, chi: int) -> CTMTensors: + """ + Perform right CTM move + + Args: + ts: input tensors + chi: boundary bond dimension + + Returns: + ts: updated tensors + + """ + A = ts.A + unit_cell = A.size + ts.C2.reset_changed() + ts.C3.reset_changed() + ts.T2.reset_changed() + Pr = TList(shape=unit_cell) + Prb = TList(shape=unit_cell) + for i in range(A.size[0]): + for j in range(A.size[1]): + with cur_loc(i,j): + if not Pr.is_changed(0,1): + Pr[0,1], Prb[0,1], _ = get_projectors_right(ts, chi) + with ts.hold('all_C2','all_C3','all_T2'): + for j in range(A.size[1]): + with cur_loc(i,j): + if not ts.C2.is_changed(1,0): + ts.update(('C2', 'C3', 'T2'), ([1,0],[1,0],[1,0]), renorm_right(ts, Pr, Prb)) + return ts + +def do_top(ts: CTMTensors, chi: int) -> CTMTensors: + """ + Perform top CTM move + + Args: + ts: input tensors + chi: boundary bond dimension + + Returns: + ts: updated tensors + + """ + A = ts.A + unit_cell = A.size + ts.C1.reset_changed() + ts.C2.reset_changed() + ts.T1.reset_changed() + Pt = TList(shape=unit_cell) + Ptb = TList(shape=unit_cell) + for j in range(A.size[1]): + for i in range(A.size[0]): + with cur_loc(i,j): + if not Pt.is_changed(0,0): + Pt[0,0], Ptb[0,0], _ = get_projectors_top(ts, chi) + with ts.hold('all_C1','all_C2','all_T1'): + for i in range(A.size[0]): + with cur_loc(i,j): + if not ts.C1.is_changed(-1,0): + ts.update(('C1', 'C2', 'T1'), ([-1,0],[2,0],[0,0]), renorm_top(ts, Pt, Ptb)) + return ts + +def do_bottom(ts: CTMTensors, chi: int) -> CTMTensors: + """ + Perform bottom CTM move + + Args: + ts: input tensors + chi: boundary bond dimension + + Returns: + ts: updated tensors + + """ + A = ts.A + unit_cell = A.size + ts.C3.reset_changed() + ts.C4.reset_changed() + ts.T3.reset_changed() + Pb = TList(shape=unit_cell) + Pbb = TList(shape=unit_cell) + for j in range(A.size[1]): + for i in range(A.size[0]): + with cur_loc(i,j): + if not Pb.is_changed(0,0): + Pb[0,0], Pbb[0,0], _ = get_projectors_bottom(ts, chi) + with ts.hold('all_C3','all_C4','all_T3'): + for i in range(A.size[0]): + with cur_loc(i,j): + if not ts.C3.is_changed(2,1): + ts.update(('C3', 'C4', 'T3'), ([2,1],[-1,1],[0,1]), renorm_bottom(ts, Pb, Pbb)) + return ts + + +""" + --------------------- + Individual left, right, top and bottom projectors + --------------------- + + The projectors are computed by contracting a corner of the + system (C-tensor + 2 T-tensors + A and Adagger tensors) + in the top (/left) half with a corner in the bottom (/right) + half and performing an svd +""" + +def get_projectors_left(ts: CTMTensors, chi: int + ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]: + """ + Returns the left projectors + """ + tensors = (ts.C1[-1,-1],ts.C4[-1,2],ts.T1[0,-1],ts.T3[0,2],ts.T4[-1,0],ts.T4[-1,1], + ts.A[0,0], ts.Ad[0,0], ts.A[0,1], ts.Ad[0,1]) + return _get_projectors_left_impl(*tensors, chi) + +def _get_projectors_left_impl(C1,C4,T1,T3,T4u,T4d,Au,Adu,Ad,Add, chi): + Cs1 = ncon([C1, T1], 'proj_left_Cs1') + Q1 = ncon([Cs1, T4u, Au, Adu], 'proj_left_Q1') + + Cs4 = ncon([C4, T3], 'proj_left_Cs4') + Q4 = ncon([Cs4, T4d, Ad, Add], 'proj_left_Q4') + + Q4 = Q4.transpose([3,4,5,0,1,2]) + return get_projectors(Q1, Q4, chi) + +def get_projectors_right(ts: CTMTensors, chi: int + ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]: + """ + Returns the right projectors + """ + tensors = (ts.C2[2,-1],ts.C3[2,2],ts.T1[1,-1],ts.T2[2,0],ts.T2[2,1],ts.T3[1,2], + ts.A[1,0], ts.Ad[1,0], ts.A[1,1], ts.Ad[1,1]) + return _get_projectors_right_impl(*tensors, chi) + +def _get_projectors_right_impl(C2,C3,T1,T2u,T2d,T3,Au,Adu,Ad,Add, chi): + Cs2 = ncon([C2, T1], 'proj_right_Cs2') + Q2 = ncon([Cs2, T2u, Au, Adu], 'proj_right_Q2') + + Cs3 = ncon([C3, T3], 'proj_right_Cs3') + Q3 = ncon([Cs3, T2d, Ad, Add], 'proj_right_Q3') + + Q3 = Q3.transpose([3,4,5,0,1,2]) + return get_projectors(Q2, Q3, chi) + +def get_projectors_top(ts: CTMTensors, chi: int + ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]: + """ + Returns the top projectors + """ + tensors = (ts.C1[-1,-1],ts.C2[2,-1],ts.T1[0,-1],ts.T1[1,-1],ts.T2[2,0],ts.T4[-1,0], + ts.A[0,0], ts.Ad[0,0], ts.A[1,0], ts.Ad[1,0]) + return _get_projectors_top_impl(*tensors, chi) + +def _get_projectors_top_impl(C1,C2,T1l,T1r,T2,T4,Al,Adl,Ar,Adr, chi): + Cs1 = ncon([C1, T4], 'proj_top_Cs1') + Q1 = ncon([Cs1, T1l, Al, Adl], 'proj_top_Q1') + + Cs2 = ncon([C2, T2], 'proj_top_Cs2') + Q2 = ncon([Cs2, T1r, Ar, Adr], 'proj_top_Q2') + + Q2 = Q2.transpose([3,4,5,0,1,2]) + return get_projectors(Q1, Q2, chi) + +def get_projectors_bottom(ts: CTMTensors, chi: int + ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]: + """ + Returns the bottom projectors + """ + tensors = (ts.C3[2,2],ts.C4[-1,2],ts.T2[2,1],ts.T3[0,2],ts.T3[1,2],ts.T4[-1,1], + ts.A[0,1], ts.Ad[0,1], ts.A[1,1], ts.Ad[1,1]) + return _get_projectors_bottom_impl(*tensors, chi) + +def _get_projectors_bottom_impl(C3,C4,T2,T3l,T3r,T4,Al,Adl,Ar,Adr, chi): + Cs4 = ncon([C4, T4], 'proj_bottom_Cs4') + Q4 = ncon([Cs4, T3l, Al, Adl], 'proj_bottom_Q4') + + Cs3 = ncon([C3, T2], 'proj_bottom_Cs3') + Q3 = ncon([Cs3, T3r, Ar, Adr], 'proj_bottom_Q3') + + Q3 = Q3.transpose([3,4,5,0,1,2]) + return get_projectors(Q4, Q3, chi) + +def get_projectors(T1: int, T2, chi): + """ Contracts the corners together and computes the + projectors by performing an svd + """ + full_chi = T1.shape[3]*T1.shape[4]*T1.shape[5] + new_chi = min(full_chi, chi) + + Rho = ncon([T1, T2], ([-1,-2,-3,1,2,3], [1,2,3,-4,-5,-6])) + Rho_shape = Rho.shape + Rho = np.reshape(Rho, [Rho_shape[0]*Rho_shape[1]*Rho_shape[2], -1]) + u,s,v = svd(Rho, new_chi, 'n') + u = np.reshape(u, [Rho_shape[0], Rho_shape[1], Rho_shape[2], -1]) + v = np.reshape(v.T, [Rho_shape[3], Rho_shape[4], Rho_shape[5], -1]) + inv_s = diag_inv(np.sqrt(s)) + + P1 = ncon([T2, v, inv_s], 'proj_P1') + P2 = ncon([T1, u, inv_s], 'proj_P2') + + P1 = P1.transpose([3,0,1,2]) + P2 = P2.transpose([3,0,1,2]) + return P1, P2, s + + +""" + --------------------- + Individual left, right, top and bottom boundary tensor updates + --------------------- + + The boundary tensors are updated for one site at a time from the + tensors of the previous iteration with the site tensors and truncated + by using the projectors + + In these functions, the boundary tensors can be wrapped as Nested tensors, + containing both ground-state and excited-state tensors. + When using these Nested tensors, all different combinations are computed + automatically. + For example: + + Nested({C1,B_C1,Bd_C1,BB_C1}) * Nested({T1,B_T1,Bd_T1,BB_T1}) -> + Nested({ + (C1 * T1), + (B_C1 * T1 + C1 * B_T1), + (Bd_C1 * T1 + C1 * Bd_T1), + (BB_C1 * T1 + B_C1 * Bd_T1 + Bd_C1 * B_T1 + C1 * BB_T1) + }) + + The phase shifts are only applied to the B and Bd parts of the Nested tensors +""" + +def renorm_left(ts: CTMTensors, Pl: np.ndarray, Plb: np.ndarray + ) -> Tuple[Nested, Nested, Nested]: + """ + + """ + new_T4 = ncon([Plb[0,0], ts.all_T4[-1,0], ts.all_A[0,0], ts.all_Ad[0,0], Pl[0,1]], 'doleft_T4', + normalize=True).shift(-sim_config.px) + + Cs1 = ncon([ts.all_C1[-1,0], ts.all_T1[0,0]], 'doleft_Cs1') + new_C1 = ncon([Cs1, Pl[0,1]], 'doleft_C1', normalize=True).shift(-sim_config.px) + + Cs4 = ncon([ts.all_C4[-1,0], ts.all_T3[0,0]], 'doleft_Cs4') + new_C4 = ncon([Cs4, Plb[0,0]], 'doleft_C4', normalize=True).shift(-sim_config.px) + + return new_C1, new_C4, new_T4 + +def renorm_right(ts, Pr, Prb): + new_T2 = ncon([Prb[0,0], ts.all_T2[2,0], ts.all_A[1,0], ts.all_Ad[1,0], Pr[0,1]], 'doright_T2', + normalize=True).shift(sim_config.px) + + Cs2 = ncon([ts.all_C2[2,0], ts.all_T1[1,0]], 'doright_Cs2') + new_C2 = ncon([Cs2, Pr[0,1]], 'doright_C2', normalize=True).shift(sim_config.px) + + Cs3 = ncon([ts.all_C3[2,0], ts.all_T3[1,0]], 'doright_Cs3') + new_C3 = ncon([Cs3, Prb[0,0]], 'doright_C3', normalize=True).shift(sim_config.px) + + return new_C2, new_C3, new_T2 + +def renorm_top(ts, Pt, Ptb): + new_T1 = ncon([Ptb[-1,0], ts.all_T1[0,-1], ts.all_A[0,0], ts.all_Ad[0,0], Pt[0,0]], 'dotop_T1', + normalize=True).shift(-sim_config.py) + + Cs1 = ncon([ts.all_C1[-1,-1], ts.all_T4[-1,0]], 'dotop_Cs1') + new_C1 = ncon([Cs1, Pt[-1,0]], 'dotop_C1', normalize=True).shift(-sim_config.py) + + Cs2 = ncon([ts.all_C2[2,-1], ts.all_T2[2,0]], 'dotop_Cs2') + new_C2 = ncon([Cs2, Ptb[1,0]], 'dotop_C2', normalize=True).shift(-sim_config.py) + + return new_C1, new_C2, new_T1 + +def renorm_bottom(ts, Pb, Pbb): + new_T3 = ncon([Pbb[-1,0], ts.all_T3[0,2], ts.all_A[0,1], ts.all_Ad[0,1], Pb[0,0]], 'dobottom_T3', + normalize=True).shift(sim_config.py) + + Cs3 = ncon([ts.all_C3[2,2], ts.all_T2[2,1]], 'dobottom_Cs3') + new_C3 = ncon([Cs3, Pbb[1,0]], 'dobottom_C3', normalize=True).shift(sim_config.py) + + Cs4 = ncon([ts.all_C4[-1,2], ts.all_T4[-1,1]], 'dobottom_Cs4') + new_C4 = ncon([Cs4, Pb[-1,0]], 'dobottom_C4', normalize=True).shift(sim_config.py) + + return new_C3, new_C4, new_T3 diff --git a/adpeps/ipeps/evaluation.py b/adpeps/ipeps/evaluation.py new file mode 100644 index 0000000..7ea4231 --- /dev/null +++ b/adpeps/ipeps/evaluation.py @@ -0,0 +1,384 @@ +from jax import random +import jax.numpy as np +import numpy as onp +import scipy.linalg as linalg +import cmath + +from adpeps.tensor.contractions import ncon +from adpeps.utils.empty_tensor import EmptyT +from adpeps.utils.nested import Nested +from adpeps.utils.printing import print +from adpeps.utils.tlist import set_pattern, cur_loc, TList +import adpeps.ipeps.config as sim_config + +""" + Evaluation module for iPEPS simulations + + This module contains the contractions of the reduced density matrices + and the computation of the expectation values for iPEPS ground- and + excited states +""" + +def get_gs_energy(H, tensors): + """ Returns ground-state energy and norm of the iPEPS """ + E, nrm, *_ = get_obs(H, tensors, measure_obs=False) + return E[0], nrm + +def get_all_energy(H, tensors): + """ Returns only energy and norm of the iPEPS """ + E, nrm, _ = get_obs(H, tensors, measure_obs=False) + return E + +def get_obs(H, tensors, measure_obs=True, only_gs=False): + """ Returns the energy and norm of the state + + The energy will be returned as a `Nested` tensor + + More observables can be added here + """ + A = tensors.A + Ad = tensors.Ad + Ehs = TList(shape=A.size, pattern=A.pattern) # Horizontal terms + Evs = TList(shape=A.size, pattern=A.pattern) # Vertical terms + Ehs_exci = TList(shape=A.size, pattern=A.pattern) # Horizontal terms + Evs_exci = TList(shape=A.size, pattern=A.pattern) # Vertical terms + nrmhs = TList(shape=A.size, pattern=A.pattern) # Horizontal terms + nrmvs = TList(shape=A.size, pattern=A.pattern) # Vertical terms + obs_evs = [TList(shape=A.size, pattern=A.pattern) for _ in tensors.observables] + + for i in A.x_major(): + with cur_loc(i): + if not Evs.is_changed(0,0): + roh, rov = get_dms(tensors) + + nrmh = np.trace(np.reshape(roh[0], (4,4))).real + nrmv = np.trace(np.reshape(rov[0], (4,4))).real + nrmhs[0,1] = nrmh + nrmvs[0,0] = nrmv + roh = roh / nrmh + rov = rov / nrmv + + Ehs[0,1] = ncon([roh, H], ([1,2,3,4],[1,2,3,4])).real + Evs[0,0] = ncon([rov, H], ([1,2,3,4],[1,2,3,4])).real + + # if measure_obs: + # ro_one = get_one_site_dm(tensors.Cs,tensors.Ts,A,Ad) + # for obs_i,obs in enumerate(tensors.observables): + # if obs.size == 1: + # try: + # obs_ev = ncon([ro_one, obs.operator], ([1,2],[1,2])) + # print(f"Obs {(obs_i,i)} {obs.__repr__()}: {obs_ev.item()}", level=2) + # obs_evs[obs_i][0,0] = obs_ev.item() + # except: + # obs_evs[obs_i][0,0] = np.nan + # elif obs.size == 2: + # try: + # obs_ev_h = ncon([roh, obs.operator], ([1,2,3,4],[1,2,3,4])) + # obs_ev_v = ncon([rov, obs.operator], ([1,2,3,4],[1,2,3,4])) + # print(f"Obs {(obs_i,i)} {obs.__repr__()}: {obs_ev_h.item()}, {obs_ev_v.item()}", level=2) + # obs_evs[obs_i][0,0] = (obs_ev_h.item(), obs_ev_v.item()) + # except: + # obs_evs[obs_i][0,0] = (np.nan, np.nan) + + # try: + # print(Ehs.mean(), Evs.mean(), level=2) + # except: + # print(Ehs.mean(), Evs.mean(), level=2) + E = (Ehs.mean() + Evs.mean()) + nrm = 0.5 * (nrmhs.mean() + nrmvs.mean()) + return E, nrm, obs_evs + +def compute_exci_norm(tensors): + """ Returns the norm of the excited state based on a one-site + environment + + Averaged over sites in the unit cell + """ + A = tensors.A + nrms = TList(shape=A.size, pattern=A.pattern) + nrms_gs = TList(shape=A.size, pattern=A.pattern) + envBs = TList(shape=A.size, pattern=A.pattern) + + for i in A.x_major(): + with cur_loc(i): + if not nrms.is_changed(0,0): + nrm, nrm_gs, envB = _compute_one_site_exci_norm(tensors) + # Exci norm + nrms[0,0] = nrm + # Ground state norm + nrms_gs[0,0] = nrm_gs + # Environment (exci norm without center Bd) + envBs[0,0] = envB + return nrms.mean(), nrms_gs.mean(), envBs, nrms_gs + +def _compute_one_site_exci_norm(ts): + """ Returns the norm of the excited state for one site in the + unit cell + """ + def get_single_site_dm(C1,T1,C2,T2,C3,T3,C4,T4): + return ncon((C2,T1,C1,T4,C4,T3,C3,T2), 'dm_single_site') + + n_tensors = [ + ts.Cs[0][-1,-1], ts.Ts[0][0,-1], ts.Cs[1][1,-1], ts.Ts[1][1,0], + ts.Cs[2][1,1], ts.Ts[2][0,1], ts.Cs[3][-1,1], ts.Ts[3][-1,0] + ] + B_tensors = [ + ts.B_Cs[0][-1,-1], ts.B_Ts[0][0,-1], ts.B_Cs[1][1,-1], ts.B_Ts[1][1,0], + ts.B_Cs[2][1,1], ts.B_Ts[2][0,1], ts.B_Cs[3][-1,1], ts.B_Ts[3][-1,0] + ] + Bd_tensors = [ + ts.Bd_Cs[0][-1,-1], ts.Bd_Ts[0][0,-1], ts.Bd_Cs[1][1,-1], ts.Bd_Ts[1][1,0], + ts.Bd_Cs[2][1,1], ts.Bd_Ts[2][0,1], ts.Bd_Cs[3][-1,1], ts.Bd_Ts[3][-1,0] + ] + + # Compute the ground state one-site reduced density matrix + n_dm = get_single_site_dm(*n_tensors) + nrm0 = ncon((ts.A[0,0], ts.Ad[0,0], n_dm), ([1,2,3,4,5],[1,6,7,8,9],[2,3,4,5,6,7,8,9])) + + B_dm = EmptyT() + for i in range(8): + # Start with all regular (ground state) boundary tensors + cur_tensors = n_tensors.copy() + cur_tensors[i] = B_tensors[i] + # Compute the one-site reduced density matrix and add it to the + # total + new_dm = get_single_site_dm(*cur_tensors) + B_dm = B_dm + new_dm + + # The full norm can be split into two parts: + # - One B and Bd on the same center site, with regular boundary tensors + # - One Bd in the center and a B in the boundaries (many terms) + nrm_exci = (ncon((ts.B[0,0], ts.Bd[0,0], n_dm), ([1,2,3,4,5],[1,6,7,8,9],[2,3,4,5,6,7,8,9])) + + ncon((ts.A[0,0], ts.Bd[0,0], B_dm), ([1,2,3,4,5],[1,6,7,8,9],[2,3,4,5,6,7,8,9]))) / nrm0 + + # The row of the norm overlap matrix (i.e. the gradient of the norm) is the + # reduced density matrix contracted with only the ket-layer of the center site + nrmB_open = (ncon((ts.B[0,0], n_dm), ([-1,2,3,4,5],[2,3,4,5,-2,-3,-4,-5])) + + ncon((ts.A[0,0], B_dm), ([-1,2,3,4,5],[2,3,4,5,-2,-3,-4,-5]))) / nrm0 + + try: + print('B norm', nrm_exci.item(), ' | Gs norm', nrm0.item(), level=1) + except: + pass + return nrm_exci.real, nrm0, nrmB_open + + +def get_orth_basis(tensors): + """ Returns a basis of vectors orthogonal to the ground state + + Each of these vectors can be used as an input for the iPEPS + excitation object + """ + def get_single_site_dm(C1,T1,C2,T2,C3,T3,C4,T4): + return ncon((C2,T1,C1,T4,C4,T3,C3,T2), 'dm_single_site') + + basis = None + A = tensors.A + Ad = tensors.Ad + nrms = TList(shape=A.size, pattern=A.pattern) + for i in A.x_major(): + with cur_loc(i): + if not nrms.is_changed(0,0): + n_tensors = [ + tensors.Cs[0][-1,-1], tensors.Ts[0][0,-1], tensors.Cs[1][1,-1], tensors.Ts[1][1,0], + tensors.Cs[2][1,1], tensors.Ts[2][0,1], tensors.Cs[3][-1,1], tensors.Ts[3][-1,0] + ] + # Compute the ground state one-site reduced density matrix + n_dm = get_single_site_dm(*n_tensors) + nrm0 = ncon((tensors.A[0,0], tensors.Ad[0,0], n_dm), ([1,2,3,4,5],[1,6,7,8,9],[2,3,4,5,6,7,8,9])) + nrms[0,0] = nrm0 + env_0 = ncon((tensors.Ad[0,0], n_dm), ([-1,6,7,8,9],[-2,-3,-4,-5,6,7,8,9])) + env_0 = np.reshape(env_0, (1,-1)) + local_basis = linalg.null_space(onp.array(env_0)) + if basis is None: + basis = local_basis + else: + basis = linalg.block_diag(basis, local_basis) + # basis = _filter_null_modes(tensors, basis) + return basis + +def filter_null_modes(tensors, basis): + def _apply_ops_h(A, B, ops): + for i in A.x_major(): + with cur_loc(i): + op_r = ops[0,0] + op_l = ops[-1,0] + phi = cmath.exp(1j * sim_config.px) + B[0,0] = phi * ncon((A[0,0], op_r), ([-1,1,-3,-4,-5],[1,-2])) + B[0,0] = B[0,0] - ncon((A[0,0], op_l), ([-1,-2,-3,1,-5],[-4,1])) + return B + + def _apply_ops_v(A, B, ops): + for i in A.x_major(): + with cur_loc(i): + op_d = ops[0,0] + op_u = ops[0,-1] + phi = cmath.exp(-1j * sim_config.py) + B[0,0] = phi * ncon((A[0,0], op_u), ([-1,-2,1,-4,-5],[-3,1])) + B[0,0] = B[0,0] - ncon((A[0,0], op_d), ([-1,-2,-3,-4,1],[1,-5])) + return B + + ops_h = TList(pattern=tensors.A.pattern) + ops_v = TList(pattern=tensors.A.pattern) + D = sim_config.D + for i in tensors.A.x_major(): + with cur_loc(i): + ops_h[0,0] = np.zeros((D, D)) + ops_v[0,0] = np.zeros((D, D)) + + key = random.PRNGKey(0) + nulls = None + for i in range(sim_config.D**2 * len(tensors.A)): + key, subkey = random.split(key) + v = random.normal(key, (ops_h.tot_numel(),)) + ops_h = ops_h.fill(v) + new_vec = _apply_ops_h(tensors.A, tensors.B, ops_h).pack_data() + new_vec = np.expand_dims(new_vec, 1) + if i == 0: + nulls = new_vec + else: + nulls = np.hstack((nulls, new_vec)) + nulls = linalg.orth(nulls) + v = random.normal(key, (ops_v.tot_numel(),)) + ops_v = ops_v.fill(v) + new_vec = _apply_ops_v(tensors.A, tensors.B, ops_v).pack_data() + new_vec = np.expand_dims(new_vec, 1) + if i == 0: + nulls = new_vec + else: + nulls = np.hstack((nulls, new_vec)) + + nulls = basis.T.conjugate() @ nulls + basis = basis @ linalg.null_space(nulls.conjugate().T) + return basis + +def get_dms(ts, only_gs=False): + """ Returns the two-site reduced density matrices + + This function relies on the Nested class, which contains + tuples of different variants of site/boundary tensors. + These variants contain either no B/Bd tensors, only a B + tensor, only a Bd tensor or both a B and a Bd tensor. + + When the Nested tensors are contracted, all possible combinations + that result again in one of these variants are computed and + summed when there are multiple results in the same variant class. + + As a result, the different terms are summed on the fly during the + contraction, which greatly reduces the computational cost. + + For example, the reduced density matrices contain 12*12=144 terms + each (all possible locations of B and Bd tensors in the various + boundaries), so that would make the energy evaluation 144 times + as expensive as the ground state energy evaluation. + Using this resummation, the total cost reduces to the maximal number + of combinations in each contraction of pairs of tensors, 9, leading + to a total computational cost of less than 9 times the ground state + energy evaluation cost (the site tensors contain only two variants, + so not every contraction contains 9 combinations). + + See the notes in nested.py for more details + + roh,rov are Nested tensors, with the following content: + ro*[0]: ground state (no B/Bd tensors) + ro*[1]: all terms with a single B tensor + ro*[2]: all terms with a single Bd tensor + ro*[3]: all terms with both a single B and Bd tensor + + The horizontal and vertical dms are located with respect + to site (0,0) as follows: + + A_up (0,0) + | + A_mid (0,1) -- A_right (1,1) + """ + + if only_gs: + A = ts.A + Ad = ts.Ad + C1 = ts.Cs(0) + C2 = ts.Cs(1) + C3 = ts.Cs(2) + C4 = ts.Cs(3) + T1 = ts.Ts(0) + T2 = ts.Ts(1) + T3 = ts.Ts(2) + T4 = ts.Ts(3) + else: + # The 'all_*' functions return Nested tensors, so for example + # ts.all_Cs(0) contains (C1, B_C1, Bd_C1, BB_C1) + A = ts.all_A + Ad = ts.all_Ad + C1 = ts.all_Cs(0) + C2 = ts.all_Cs(1) + C3 = ts.all_Cs(2) + C4 = ts.all_Cs(3) + T1 = ts.all_Ts(0) + T2 = ts.all_Ts(1) + T3 = ts.all_Ts(2) + T4 = ts.all_Ts(3) + + # Tensors that are part of the vertical reduced density matrix + v_tensors = [ + C1[-1,-1], C2[1,-1], C3[1,2], C4[-1,2], + T1[0,-1], T2[1,0], T2[1,1], T3[0,2], T4[-1,0], T4[-1,1], + A[0,0], A[0,1], Ad[0,0], Ad[0,1] + ] + + # Tensors that are part of the horizontal reduced density matrix + h_tensors = [ + C1[-1,0], C2[2,0], C3[2,2], C4[-1,2], + T1[0,0], T1[1,0], T2[2,1], T3[0,2], T3[1,2], T4[-1,1], + A[0,1], A[1,1], Ad[0,1], Ad[1,1] + ] + + # Regular variant + roh = _get_dm_h(*h_tensors) + rov = _get_dm_v(*v_tensors) + + return roh, rov + +def _get_dm_v(C1, C2, C3, C4, T1, T2u, T2d, T3, T4u, T4d, Au, Ad, Adu, Add): + """ Regular variant + + A_up (0,0) + | + A_mid (0,1) + """ + py = sim_config.py + + # Upper half + Cc1 = ncon([C1,T1,T4u,Au], 'dm_up_Cc1') + Cc2 = ncon([C2,T2u,Adu], 'dm_up_Cc2') + Cc2 = ncon([Cc1, Cc2], 'dm_up') + + # Lower half + Cc1 = ncon([C4.shift(py),T3.shift(py),T4d.shift(py),Ad.shift(py)], 'dm_low_Cc1') + Cc3 = ncon([C3.shift(py),T2d.shift(py),Add.shift(py)], 'dm_low_Cc3') + Cc3 = ncon([Cc1, Cc3], 'dm_low') + + # Contract + rov = ncon([Cc3,Cc2], 'dm_rov') + return rov + +def _get_dm_h(C1, C2, C3, C4, T1l, T1r, T2, T3l, T3r, T4, Al, Ar, Adl, Adr): + """ Regular variant + + A_mid (0,1) -- A_right (1,1) + """ + px = sim_config.px + + # Left half + Cc1 = ncon([C4, T3l, T4, Al], 'dm_low_Cc1') + Cc2 = ncon([C1, T1l, Adl], 'dm_left_Cc2') + Cc2 = ncon([Cc1, Cc2], 'dm_left') + + # Right half + Cc1 = ncon([C2.shift(px), T1r.shift(px), Ar.shift(px)], 'dm_right_Cc1') + Cc3 = ncon([C3.shift(px), T2.shift(px), T3r.shift(px), Adr.shift(px)], 'dm_right_Cc3') + Cc3 = ncon([Cc1, Cc3], 'dm_right') + + # Contract + roh = ncon([Cc2, Cc3], 'dm_roh') + return roh + diff --git a/adpeps/ipeps/ipeps.py b/adpeps/ipeps/ipeps.py new file mode 100644 index 0000000..419fe89 --- /dev/null +++ b/adpeps/ipeps/ipeps.py @@ -0,0 +1,286 @@ +""" + iPEPS module for optimization with CTM + + For an example of how to run a simulation see :mod:`adpeps.simulation.run_ipeps_gs` + + The module is initialized from one of the specific + model files, which return the initial boundary and + site tensors + + The list of parameters is set to the elements of the + individual site tensors + + Conventions for indices: + + - Site tensors:: + + A: [phys, right, top, left, bottom] + + - Boundary tensors:: + + C1: [right, bottom] + C2: [left, bottom] + C3: [top, left] + C4: [right, top] + T1: [right, left, ket, bra] + T2: [top, bottom, ket, bra] + T3: [right, left, ket, bra] + T4: [top, bottom, ket, bra] + + + Order of boundary tensors:: + + C1 - T1 - C2 + | | | + T4 - A - T2 + | | | + C4 - T3 - C3 +""" + +from functools import partial +import copy + +from jax import random +import jax +import jax.numpy as np + +from .ctm import run_ctm +from adpeps.ipeps import evaluation +from adpeps.ipeps import models +from adpeps.tensor.contractions import ncon +from adpeps.utils.ctmtensors import CTMTensors +from adpeps.utils.printing import print +from adpeps.utils.tlist import set_pattern, cur_loc, TList +import adpeps.ipeps.config as sim_config + +class iPEPS: + """ Initialize the iPEPS based on the settings in + :mod:`adpeps.ipeps.config` + """ + reinit_env = False + + def __init__(self): + # Load model Hamiltonian, observables + model = getattr(models, sim_config.model) + self.H, self.observables = model.setup() + + # Initialize tensors + self.d = self.H.shape[0] + A = init_A_tensor(self.d, sim_config.D, sim_config.pattern) + A = A.normalize() + Ad = A.conj() + Cs, Ts = init_ctm_tensors(A, A) + self.tensors = CTMTensors(A, Ad, Cs, Ts) + self.base_Cs, self.base_Ts = None, None + + # Initialize conv object + self.convergence = {} + + self.reinit_env = True + + def run(self, params: np.ndarray) -> np.ndarray: + """ + Run the simulation + + Args: + params: variational parameters + + Returns: + energy of iPEPS + """ + + if params is not None: + self.fill(params) + + if self.reinit_env: + # Construct new boundary tensors and perform ctm iterations + # until convergence + # Note: gradient tracking is disabled for this function, so + # only the ctm steps in the code after this line will be tracked + print('Performing CTM pre-steps without tracking') + self.converge_boundaries() + + # Perform the ctm routine to obtain updated boundary tensors + print('Performing CTM') + self.tensors, conv = run_ctm(self.tensors, sim_config.chi, conv_fun=self.compute_energy) + + # Evaluate energy + res = self.evaluate() + + # Stop downstream gradient tracking for iPEPS tensors, + # so they become regular arrays that can be saved + self.tensors.stop_gradient(only_boundaries=False) + + return res + + def compute_energy(self, tensors): + E, _ = evaluation.get_gs_energy(self.H, tensors) + return E + + def converge_boundaries(self): + """ Performs CTM on the boundary tensors until convergence, + without gradient tracking + """ + # Make a non-tracking version of the iPEPS tensors + orig_A = copy.deepcopy(self.tensors.A) + self.tensors.A = self.tensors.A.stop_gradient() + self.tensors.Ad = self.tensors.Ad.stop_gradient() + + # Initialize new boundary tensors + Cs, Ts = init_ctm_tensors(self.tensors.A, self.tensors.Ad) + self.tensors = CTMTensors(self.tensors.A, self.tensors.Ad, Cs, Ts) + + # Perform CTM update steps on the boundary tensors + conv_fun = self.compute_energy + self.tensors.stop_gradient() + self.tensors, conv = run_ctm(self.tensors, sim_config.chi, conv_fun=conv_fun) + self.tensors.stop_gradient() + + self.save_boundary_tensors() + + # Restore the original (tracking) site tensors + self.tensors.A = orig_A + self.tensors.Ad = orig_A.conj() + + def save_boundary_tensors(self): + self.base_Cs = copy.deepcopy(self.tensors.Cs) + self.base_Ts = copy.deepcopy(self.tensors.Ts) + + def evaluate(self): + E = self.compute_energy(self.tensors) + print('Energy:', jax.lax.stop_gradient(E).item()) + return E + + + """ Input/output methods """ + + def numel(self): + """ Number of variational parameters """ + return self.tensors.A.tot_numel() + + def parse_elements(self, elements): + """ Returns site tensors filled with the input elements """ + assert elements.size == self.numel(), f"Size of input vector ({elements.size}) does not \ + match the number of parameters of the iPEPS ({self.numel()})" + return self.tensors.A.fill(elements, self.d, sim_config.D) + + def fill(self, A): + """ Fill the site tensors with the elements + The elements can be specified either as a list of (d,D,D,D,D)-dimensional + arrays or one 1-dimensional array of all elements concatenated + """ + if isinstance(A, np.ndarray) and A.ndim == 1: + # Input is vector of elements + A = self.parse_elements(A) + self.tensors.A = A + self.tensors.Ad = A.conj() + else: + # Input is a list of arrays + assert len(A) == len(self.tensors.A), "Number of input tensors does not match \ + the number of site tensors of the iPEPS" + for i in range(len(self.tensors.A)): + self.tensors.A._data[i] = A[i] + self.tensors.Ad._data[i] = A[i].conj() + + +class iPEPS_exci(iPEPS): + """ Excited-state variant of the iPEPS class + """ + + reinit_env = False + + def __init__(self): + super().__init__() + self.substract_gs_energy() + + def normalize_gs(self): + nrm, nrm0, envBs, nrms0 = evaluation.compute_exci_norm(self.tensors) + print(f"GS norm {nrms0[0]}", level=1) + self.tensors.A._data = [a/np.sqrt(np.abs(nrms0[i])) for i, a in enumerate(self.tensors.A)] + self.tensors.Ad = self.tensors.A.conj() + nrm, nrm0, envBs, nrms0 = evaluation.compute_exci_norm(self.tensors) + print(f"GS norm {nrm0}", level=1) + + def substract_gs_energy(self): + E, _ = evaluation.get_gs_energy(self.H, self.tensors) + E = E/2 + print(f"Substracting {E} from Hamiltonian", level=1) + self.H = self.H - E * np.reshape(np.eye(self.H.shape[0]**2), self.H.shape) + # self.H = np.reshape(np.eye(self.H.shape[0]**2), self.H.shape) + + def evaluate(self): + E = evaluation.get_all_energy(self.H, self.tensors) + nrm, _, envBs, _ = evaluation.compute_exci_norm(self.tensors) + print('Energies:', jax.lax.stop_gradient(E[3]), jax.lax.stop_gradient(E[0]), level=0) + print('Norm:', jax.lax.stop_gradient(nrm), level=0) + return E[3], envBs + + def run_gc(self, *args): + res, _ = self.run(*args) + return res + + def compute_energy(self, tensors): + E = evaluation.get_all_energy(self.H, tensors) + nrm, *_ = evaluation.compute_exci_norm(tensors) + print('Energies:', jax.lax.stop_gradient(E[3]), jax.lax.stop_gradient(E[0]), level=2) + print('Norm:', jax.lax.stop_gradient(nrm), level=2) + print('Normalized E:', jax.lax.stop_gradient(E[3])/jax.lax.stop_gradient(nrm), level=2) + return E[3] / nrm + + def compute_orth_basis(self): + return evaluation.get_orth_basis(self.tensors) + + + """ Input/output methods """ + + def fill(self, B): + if isinstance(B, np.ndarray) and B.ndim == 1: + # Input is vector of elements + B = self.parse_elements(B) + self.tensors.B = B + self.tensors.Bd = B.conj() + else: + for i in range(len(self.tensors.A._data)): + self.tensors.B._data[i] = B[i] + self.tensors.Bd._data[i] = B[i].conj() + + +def init_A_tensor(d, D, pattern): + """ + The elements will be randomized based on sim_config.seed + """ + with set_pattern(pattern): + A = TList() + + key = random.PRNGKey(sim_config.seed) + for i in range(A.size[0]): + for j in range(A.size[1]): + with cur_loc(i,j): + if not A.is_changed(0,0): + key, subkey = random.split(key) + A[0,0] = random.normal(key, (d,D,D,D,D)) + return A + +def init_ctm_tensors(A, Ad): + """ + Returns initital boundary T-tensors based on the unit cell tensors and + empty trivial boundary C-tensors + """ + unit_cell = A.size + D = A[0].shape[1] + + Cs = [TList(shape=unit_cell, pattern=A.pattern) for _ in range(4)] + Ts = [TList(shape=unit_cell, pattern=A.pattern) for _ in range(4)] + + for i in range(A.size[0]): + for j in range(A.size[1]): + with cur_loc(i,j): + Cs[0][0,0] = np.expand_dims(np.array([1.]), axis=(1)) + Cs[1][0,0] = np.expand_dims(np.array([1.]), axis=(1)) + Cs[2][0,0] = np.expand_dims(np.array([1.]), axis=(1)) + Cs[3][0,0] = np.expand_dims(np.array([1.]), axis=(1)) + Ts[0][0,0] = np.expand_dims(ncon([A[0,0], Ad[0,0]], ([1,2,3,4,-1], [1,2,3,4,-2])), axis=(0,1)) + Ts[1][0,0] = np.expand_dims(ncon([A[0,0], Ad[0,0]], ([1,2,3,-1,4], [1,2,3,-2,4])), axis=(0,1)) + Ts[2][0,0] = np.expand_dims(ncon([A[0,0], Ad[0,0]], ([1,2,-1,3,4], [1,2,-2,3,4])), axis=(0,1)) + Ts[3][0,0] = np.expand_dims(ncon([A[0,0], Ad[0,0]], ([1,-1,2,3,4], [1,-2,2,3,4])), axis=(0,1)) + return Cs, Ts diff --git a/adpeps/ipeps/make_momentum_path.py b/adpeps/ipeps/make_momentum_path.py new file mode 100644 index 0000000..264eaa4 --- /dev/null +++ b/adpeps/ipeps/make_momentum_path.py @@ -0,0 +1,60 @@ +from math import pi +import numpy as np + +def make_momentum_path(name, with_plot_info=False): + n_per_piece = 5; + plot_info = {} + + if name == 'Bril1': + kxs = np.concatenate([lin_ex(pi, pi, 2*n_per_piece), lin_ex(pi, pi/2, n_per_piece), lin_ex(pi/2, 0, n_per_piece), lin_ex(0, pi, 2*n_per_piece), np.linspace(pi, pi/2, n_per_piece)]) + kys = np.concatenate([lin_ex(0, pi, 2*n_per_piece), lin_ex(pi, pi/2, n_per_piece), lin_ex(pi/2, 0, n_per_piece), lin_ex(0, 0, 2*n_per_piece), np.linspace(0, pi/2, n_per_piece)]) + if with_plot_info: + plot_info['xticks'] = { + 'ticks': [0,9,13,17,26,30], + 'labels': ['$M(\pi,0)$', '$X(\pi,\pi)$', '$S(\pi/2,\pi/2)$', '$\Gamma(0,0)$', '$M(\pi,0)$', '$S(\pi/2,\pi/2)$'] + } + return kxs, kys, plot_info + return kxs, kys + if name == 'Bril1-negy': + kxs = np.concatenate([lin_ex(pi, pi, 2*n_per_piece), lin_ex(pi, pi/2, n_per_piece), lin_ex(pi/2, 0, n_per_piece), lin_ex(0, pi, 2*n_per_piece), np.linspace(pi, pi/2, n_per_piece)]) + kys = -np.concatenate([lin_ex(0, pi, 2*n_per_piece), lin_ex(pi, pi/2, n_per_piece), lin_ex(pi/2, 0, n_per_piece), lin_ex(0, 0, 2*n_per_piece), np.linspace(0, pi/2, n_per_piece)]) + if with_plot_info: + plot_info['xticks'] = { + 'ticks': [0,9,13,17,26,30], + 'labels': ['$M(\pi,0)$', '$X(\pi,-\pi)$', '$S(\pi/2,-\pi/2)$', '$\Gamma(0,0)$', '$M(\pi,0)$', '$S(\pi/2,-\pi/2)$'] + } + return kxs, kys, plot_info + return kxs, kys + elif name == '0-2pi': + kxs = np.linspace(0, 2*pi, 33) + kys = np.linspace(0, 2*pi, 33) + return kxs, kys + elif name == '0-2pi-negy': + kxs = np.linspace(0, 2*pi, 33) + kys = -np.linspace(0, 2*pi, 33) + return kxs, kys + elif name == '0-2pi-x': + kxs = np.linspace(0, 2*pi, 33) + kys = np.linspace(0, 0, 33) + if with_plot_info: + plot_info['xticks'] = { + 'ticks': [0,16,32], + 'labels': ['$\Gamma(0,0)$', '$M(\pi,0)$', '$(2\pi,0)$'] + } + return kxs, kys, plot_info + return kxs, kys + if name == 'Bril1xy': + kys = np.concatenate([lin_ex(pi, pi, 2*n_per_piece), lin_ex(pi, pi/2, n_per_piece), lin_ex(pi/2, 0, n_per_piece), lin_ex(0, pi, 2*n_per_piece), np.linspace(pi, pi/2, n_per_piece)]) + kxs = np.concatenate([lin_ex(0, pi, 2*n_per_piece), lin_ex(pi, pi/2, n_per_piece), lin_ex(pi/2, 0, n_per_piece), lin_ex(0, 0, 2*n_per_piece), np.linspace(0, pi/2, n_per_piece)]) + if with_plot_info: + plot_info['xticks'] = { + 'ticks': [0,9,13,17,26,30], + 'labels': ['$M2(0,\pi)$', '$X(\pi,\pi)$', '$S(\pi/2,\pi/2)$', '$\Gamma(0,0)$', '$M(0,\pi)$', '$S(\pi/2,\pi/2)$'] + } + return kxs, kys, plot_info + return kxs, kys + else: + raise ValueError("Momentum path name not known") + +def lin_ex(s, e, n): + return np.linspace(s,e,n)[:-1] diff --git a/adpeps/ipeps/models/__init__.py b/adpeps/ipeps/models/__init__.py new file mode 100644 index 0000000..2905bbd --- /dev/null +++ b/adpeps/ipeps/models/__init__.py @@ -0,0 +1,7 @@ +""" Contains all models defined by Hamiltonians as part of this module +""" + +# Spin models +from . import heisenberg + +from . import common diff --git a/adpeps/ipeps/models/common.py b/adpeps/ipeps/models/common.py new file mode 100644 index 0000000..5e96d27 --- /dev/null +++ b/adpeps/ipeps/models/common.py @@ -0,0 +1,28 @@ +import jax.numpy as np + +sigmap = np.array([[0,1],[0,0]]) +sigmam = np.array([[0,0],[1,0]]) +sigmaz = np.array([[1,0],[0,-1]]) + +id2 = np.array([[1,0],[0,1]]) +id4 = np.eye(4) +nsite = np.array([[0,0],[0,1]]) + +nup = np.array([ + [0,0,0,0], + [0,1,0,0], + [0,0,0,0], + [0,0,0,1] + ]) +ndown = np.array([ + [0,0,0,0], + [0,0,0,0], + [0,0,1,0], + [0,0,0,1] + ]) +nupdown = np.array([ + [0,0,0,0], + [0,0,0,0], + [0,0,0,0], + [0,0,0,1] + ]) diff --git a/adpeps/ipeps/models/heisenberg.py b/adpeps/ipeps/models/heisenberg.py new file mode 100644 index 0000000..c99a493 --- /dev/null +++ b/adpeps/ipeps/models/heisenberg.py @@ -0,0 +1,27 @@ +""" 2D Heisenberg model """ + +import jax.numpy as np + +from .common import sigmaz, sigmap, sigmam +from adpeps.utils.tlist import set_pattern +import adpeps.ipeps.config as sim_config + +name = "Heisenberg spin-1/2 model" + +def setup(): + """ Returns the Hamiltonian """ + H = make_hamiltonian(**sim_config.model_params) + + obs = None + return H, obs + +def make_hamiltonian(J=1): + """ Heisenberg model """ + H = tprod(sigmaz, sigmaz) / 4 + \ + tprod(sigmap, sigmam) / 2 + \ + tprod(sigmam, sigmap) / 2 + H = J * H + return H + +def tprod(a,b): + return np.outer(a,b).reshape([2,2,2,2], order='F').transpose([0,2,1,3]) diff --git a/adpeps/simulation/__init__.py b/adpeps/simulation/__init__.py new file mode 100644 index 0000000..d6b8317 --- /dev/null +++ b/adpeps/simulation/__init__.py @@ -0,0 +1,7 @@ +""" Module with executable scripts for running the simulations + + Note: + The simulations are intended to be used by calling the package + directly via :code:`python -m adpeps ...`, as described in + :ref:`notes/start` +""" diff --git a/adpeps/simulation/run_ipeps_exci.py b/adpeps/simulation/run_ipeps_exci.py new file mode 100644 index 0000000..ee858b6 --- /dev/null +++ b/adpeps/simulation/run_ipeps_exci.py @@ -0,0 +1,241 @@ +""" Main excited-state executable script + + Note: + The simulations are intended to be used by calling the package + directly via :code:`python -m adpeps ...`, as described in + :ref:`notes/start` +""" + +from jax import grad, jit, vmap, value_and_grad +from jax import random +from jax.scipy.optimize import minimize +from jax.test_util import check_grads +from scipy import optimize +from scipy.linalg import eigh, eig +from yaml import safe_load, dump +import jax +import jax.numpy as np +import numpy as onp + +from adpeps.ipeps.ipeps import iPEPS, iPEPS_exci +from adpeps.ipeps.make_momentum_path import make_momentum_path +from adpeps.utils import io +from adpeps.utils.printing import print +from adpeps.ipeps.evaluation import filter_null_modes +import adpeps.ipeps.config as sim_config + +def run(config_file: str, momentum_ix: int): + """ Start the simulation + + Args: + config_file: filename of the configuration file + momentum_ix: index of the point in momentum space + """ + + print(config_file) + with open(config_file) as f: + cfg = safe_load(f) + + # Show options + print(dump(cfg)) + + sim_config.from_dict(cfg) + base_file = io.get_exci_base_file() + if not base_file.exists(): + print(f"Base file {base_file} not found. Prepare the simulation first by \ + running with option '-i'") + return + + sim = iPEPSExciSimulation(config_file, momentum_ix) + output_folder = io.get_exci_folder() + output_folder.mkdir(parents=True, exist_ok=True) + kxs, kys = make_momentum_path(sim_config.momentum_path) + sim_config.px = kxs[momentum_ix] + sim_config.py = kys[momentum_ix] + output_file = io.get_exci_file(momentum_ix) + print(f"Output: {output_file}", level=2) + basis_size = sim.basis_size + res_dtype = np.complex128 + H = onp.zeros((basis_size,basis_size), dtype=res_dtype) + N = onp.zeros((basis_size,basis_size), dtype=res_dtype) + + for m in range(basis_size): + grad_H, grad_N = sim(m) + H[:,m] = grad_H + N[:,m] = grad_N + onp.savez(output_file, H=H, N=N) + + print(H) + print(N) + onp.savez(output_file, H=H, N=N) + print('Done') + print(f"Saved to {output_file}") + +def prepare(config_file): + with open(config_file) as f: + cfg = safe_load(f) + sim_config.from_dict(cfg) + base_file = io.get_exci_base_file() + print(base_file) + peps = iPEPS() + + gs_file = io.get_gs_file() + loaded_sim = np.load(gs_file, allow_pickle=True) + peps = loaded_sim['peps'].item() + + sim_config.ctm_max_iter = 30 + sim_config.ctm_conv_tol = 1e-12 + + # Converge GS boundary tensors + peps.converge_boundaries() + + # Convert to excitations iPEPS + peps.__class__ = iPEPS_exci + + # Normalize the ground-state tensors such that the state has norm 1 + peps.normalize_gs() + + # Shift the Hamiltonian by the ground-state energy + # The excited state energy is then relative to the ground state + peps.substract_gs_energy() + + # Prepare an orthonormal basis with respect to the ground state + print('Preparing orthonormal basis') + basis = peps.compute_orth_basis() + + print(f"Saving base to {base_file}") + np.savez(base_file, peps=peps, basis=basis) + +def evaluate_single(config_file, momentum_ix): + def _compute_ev_red_basis(H, N, P, n): + P = P[:,:n] + N2 = P.T.conjugate() @ N @ P + H2 = P.T.conjugate() @ H @ P + N2 = 0.5 * (N2 + N2.T.conjugate()) + H2 = 0.5 * (H2 + H2.T.conjugate()) + ev, _ = eig(H2, N2) + return sorted(ev.real) + + + with open(config_file) as f: + cfg = safe_load(f) + + sim_config.from_dict(cfg) + kxs, kys = make_momentum_path(sim_config.momentum_path) + sim_config.px = kxs[momentum_ix] + sim_config.py = kys[momentum_ix] + base_file = io.get_exci_base_file() + base_sim = np.load(base_file, allow_pickle=True) + output_file = io.get_exci_file(momentum_ix) + print(output_file) + dat = np.load(output_file) + H, N = dat['H'], dat['N'] + basis = base_sim['basis'] + peps = base_sim['peps'].item() + + # basis = basis.T @ filter_null_modes(peps.tensors, basis) + # print(basis.shape) + # print(N.shape) + # N = basis.T @ N @ basis + # H = basis.T @ H @ basis + # H = H.conjugate() + + H = 0.5 * (H + H.T.conjugate()) + N = 0.5 * (N + N.T.conjugate()) + ev_N, P = np.linalg.eig(N) + idx = ev_N.real.argsort()[::-1] + ev_N = ev_N[idx] + selected = (ev_N/ev_N.max()) > 1e-3 + P = P[:,idx] + P = P[:,selected] + N2 = P.T.conjugate() @ N @ P + H2 = P.T.conjugate() @ H @ P + N2 = 0.5 * (N2 + N2.T.conjugate()) + H2 = 0.5 * (H2 + H2.T.conjugate()) + ev, vectors = eig(H2, N2) + ixs = np.argsort(ev) + ev = ev[ixs] + vectors = vectors[:,ixs] + + return sorted(ev.real) + +def evaluate(config_file, momentum_ix): + if momentum_ix != -2: + return evaluate_single(config_file, momentum_ix) + + with open(config_file) as f: + cfg = safe_load(f) + + # Show options + print(dump(cfg)) + + sim_config.from_dict(cfg) + kxs, kys = make_momentum_path(sim_config.momentum_path) + + import matplotlib.pyplot as plt + evs = [] + for ix in range(len(kxs)): + try: + ev = evaluate_single(config_file, ix) + except: + ev = [np.nan] + evs.append(ev[0]) + plt.plot(evs, '--+') + plt.show() + + + +class iPEPSExciSimulation: + """ Simulation class for the excited-state simulation + + Call an instance of this class directly to start the simulation + """ + def __init__(self, config_file, momentum_ix): + self.config_file = config_file + self.momentum_ix = momentum_ix + + @property + def basis_size(self): + with open(self.config_file) as f: + cfg = safe_load(f) + sim_config.from_dict(cfg) + base_file = io.get_exci_base_file() + base_sim = np.load(base_file, allow_pickle=True) + basis = base_sim['basis'] + return basis.shape[1] + + def __call__(self, ix, v=None): + print(f"Starting simulation of basis vector {ix+1}/{self.basis_size}") + with open(self.config_file) as f: + cfg = safe_load(f) + sim_config.from_dict(cfg) + + base_file = io.get_exci_base_file() + base_sim = np.load(base_file, allow_pickle=True) + basis = np.complex_(base_sim['basis']) + peps = base_sim['peps'].item() + if v is None: + v = basis[:,ix] + res, grad_H = value_and_grad(peps.run, has_aux=True)(v) + grad_H = grad_H.conj() + print('Res', res, level=2) + grad_N = res[1].pack_data() + print('Grad H', grad_H, level=2) + print('Grad N', grad_N, level=2) + print(f"========== \nFinished basis vector {ix+1}/{self.basis_size} \n") + return basis.T @ jax.lax.stop_gradient(grad_H), basis.T @ jax.lax.stop_gradient(grad_N) + + def check_grads(self, A=None): + with open(self.config_file) as f: + cfg = safe_load(f) + sim_config.from_dict(cfg) + + base_file = io.get_exci_base_file() + base_sim = np.load(base_file, allow_pickle=True) + basis = np.complex_(base_sim['basis']) + peps = base_sim['peps'].item() + print('Checking gradient') + # peps.fill(A) + check_grads(peps.run_gc, (A,), order=1, modes='rev') + print('Done check') + diff --git a/adpeps/simulation/run_ipeps_gs.py b/adpeps/simulation/run_ipeps_gs.py new file mode 100644 index 0000000..b43773a --- /dev/null +++ b/adpeps/simulation/run_ipeps_gs.py @@ -0,0 +1,183 @@ +""" Main ground-state executable script + + Note: + The simulations are intended to be used by calling the package + directly via :code:`python -m adpeps ...`, as described in + :ref:`notes/start` +""" + +from jax import grad, jit, vmap, value_and_grad +from jax import random +from jax.scipy.optimize import minimize +from jax.test_util import check_grads +from scipy import optimize +from yaml import safe_load, dump +import jax +import jax.numpy as np +import numpy as onp + +from adpeps.ipeps.ipeps import iPEPS, iPEPS_exci +from adpeps.utils import io +from adpeps.utils.printing import print +import adpeps.ipeps.config as sim_config + +def run(config_file: str): + """ Start the simulation + + Args: + config_file: filename of the configuration file + """ + + energies = [] + gradnorms = [] + def verbose(xk, step_size=None): + """ Output printing function """ + try: + energies.append(obj.cached_out) + gradnorms.append(obj.gradnrm) + except: + pass + print(' ') + print(' # ======================== #') + print(' # Step completed #') + print(' # ======================== #') + print(' ') + [print(' Step %3d E: %.12f |grad|: %2.8g' % (i,E,gradnorms[i])) for i,E in enumerate(energies)] + print('\n') + # np.savez(output_file, peps=peps, v=xk, gradnorms=gradnorms, energies=energies) + + print('Running') + print(config_file) + with open(config_file) as f: + cfg = safe_load(f) + + # Show options + print(dump(cfg)) + + # Load the configuration file into the sim_config object + sim_config.from_dict(cfg) + + # Initialize the iPEPS + peps = iPEPS() + + output_file = io.get_gs_file() + print(f"Output file {output_file}") + + if sim_config.resume and output_file.exists(): + loaded_sim = np.load(output_file, allow_pickle=True) + peps = loaded_sim['peps'].item() + v = loaded_sim['v'] + gradnorms = list(loaded_sim['gradnorms']) + energies = list(loaded_sim['energies']) + print("Resuming existing simulation") + verbose(v) + else: + print("Starting new simulation") + key = random.PRNGKey(sim_config.seed) + v = random.normal(key, (peps.numel(),)) + v = v / np.max(np.abs(v)) + + obj = Objective(peps) + + # Call SciPy's optimization function + obj.return_gn = False + xL = optimize.minimize(obj.out, v, method=sim_config.method, jac=obj.jac, + callback=verbose, options={'gtol': 1e-6, 'disp': True, + 'maxiter':sim_config.max_iterations}) + +class Objective: + """ Class containing the objective function for the optimizer + """ + + def __init__(self, peps: iPEPS): + """ + Args: + peps: iPEPS object to be optimized + """ + self.cached_v = None + self.cached_out = None + self.cached_jac = None + + self.peps = peps + """ iPEPS object """ + + self.fun = peps.run + """ Objective function - CTM iterations until convergence + followed by the evaluation of the energy + """ + self.return_gn = True + + @property + def gradnrm(self): + """ Norm of the gradient """ + return np.linalg.norm(self.cached_jac) + + def jac(self, v: np.ndarray) -> np.ndarray: + """ Computes the vector-Jacobian product (gradient) of the + iPEPS at the current point :attr:`v` in parameter space + + This function is designed to work with optimizers that make separate + calls to the objective function and the gradient, by caching both. + + Args: + v: input variational parameters for the site tensors of + the iPEPS + + Returns: + gradient of the iPEPS with respect to the input parameters :attr:`v` + """ + + # Cast the regular numpy array into a Jax numpy array for gradient tracking + v = np.array(v) + v = v / np.max(np.abs(v)) + + if (self.cached_jac is not None and self.cached_v is not None + and np.linalg.norm(v - self.cached_v) < 1e-14): + return self.cached_jac + + # Call the forward + backward pass iPEPS code + o, g = value_and_grad(self.fun)(v) + + # Convert to regular Numpy arrays so they can be passed to the optimizer + # and stored without any tracking information by Jax + o = onp.array(o) + v = onp.array(v) + g = onp.array(g) + + # Cache the results + self.cached_v = v + self.cached_out = o + self.cached_jac = g + + if self.return_gn: + return g, self.gradnrm + else: + return g + + def out(self, v): + """ Computes the objective function (energy) of the iPEPS + + Since many optimizers make separate calls to the objective function + and the gradient, but usually require both results for any given + parameter vector v, this function calls the gradient as well. + + Args: + v: input variational parameters for the site tensors of + the iPEPS + + Returns: + energy of the iPEPS at the point :attr:`v` in parameter space + """ + if self.cached_v is not None and np.linalg.norm(v - self.cached_v) < 1e-14: + return self.cached_out + else: + self.jac(v) + return self.cached_out + + def check_grads(self, A=None): + print('Checking gradient') + self.peps.fill(A) + self.peps.converge_boundaries() + check_grads(self.peps.run, (A,), order=1, modes='rev') + print('Done check') + diff --git a/adpeps/tensor/__init__.py b/adpeps/tensor/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/adpeps/tensor/config.py b/adpeps/tensor/config.py new file mode 100644 index 0000000..3162dae --- /dev/null +++ b/adpeps/tensor/config.py @@ -0,0 +1,55 @@ +# Set True to apply the apply_permute decorator, +# which applies perform_permute to all SymTensor +# outputs (necessary for gradcheck) +always_permute = True + +# Set True to check at every mult call whether +# the contracted legs have conjugate charges +check_mult_inds = False + +# In diag_inv, all elements larger than this +# value will be inverted. Normally this will +# be strictly zero, for example when inverting +# the singular values after an svd, but it needs +# to be finite for numerical gradient checking +diag_inv_zero_tol = 0 + +# Perform consistency check on each new tensor +# This has a large overhead to make sure to +# disable this in actual simulations +do_consistency_checks = False + +# Do backward svd pass based on the full tensors +# (before any truncation) +# For this it's required to save the u,s,v tensors +# so it is more expensive +do_precise_svd_backward = True + +# The inverse used in the backward svd may be unstable +# in the presence of (nearly) degenerate singular values +# Set this option to a value larger than 0 (usually 1e-12 +# should be ok) to use the 'safe inverse' instead of a +# regular inverse +safe_inv_epsilon = 0 + +# Enables an extra sign-fixing step in the svd, to ensure +# a consistent convention for the sign choices of the singular +# vectors +svd_fix_sign = False + +# Clears the stored objects in the ctx during the backward +# step - disable this when you run the backward step with +# retain_graph = True (e.g. for higher-order derivatives) +backward_clear_ctx = True + + +# Debugging feature to place breaking points in the code +break_now = False + +def from_dict(cfg): + cfg_vars = globals() + for name, value in cfg.items(): + if name in cfg_vars.keys(): + cfg_vars[name] = value + else: + raise ValueError(f"Option {name} = {value} not defined in SymTensor config") diff --git a/adpeps/tensor/contractions.py b/adpeps/tensor/contractions.py new file mode 100644 index 0000000..a1768e8 --- /dev/null +++ b/adpeps/tensor/contractions.py @@ -0,0 +1,41 @@ +from pathlib import Path + +from typing import Tuple, Callable, Optional, Iterable, Union +from yaml import safe_load +import jax.numpy as np + +from .ncon import ncon as st_ncon +from adpeps import ROOT_DIR +from adpeps.utils.empty_tensor import EmptyT +from adpeps.utils.nested import Nested + +f = open(Path(ROOT_DIR, 'ipeps', 'contractions.yaml')) +ctr = safe_load(f) + +TensorType = Union[np.ndarray, Nested, EmptyT] + +def ncon(tensors: Iterable[TensorType], indices_key: Union[str, Iterable[Iterable[int]]], + **kwargs) -> TensorType: + try: + try: + ixs = ctr[indices_key]['ix'] + order = ctr[indices_key].get('order') + except: + ixs = ctr[indices_key] + order = None + return st_ncon(tensors, ixs, empty_class=EmptyT, order=order, mult_method=mult, **kwargs) + except TypeError as e: + if isinstance(indices_key, str): + raise e + return st_ncon(tensors, indices_key, empty_class=EmptyT, mult_method=mult, **kwargs) + +def mult(x: TensorType, y: TensorType, inds: Iterable[int]) -> TensorType: + if isinstance(x, EmptyT) or isinstance(y, EmptyT): + return EmptyT() + elif hasattr(x, 'mult'): + return x.mult(y, inds) + elif hasattr(y, 'mult'): + x = Nested([x,EmptyT(),EmptyT(),EmptyT()]) + return x.mult(y, inds) + else: + return np.tensordot(x, y, inds) diff --git a/adpeps/tensor/ncon.py b/adpeps/tensor/ncon.py new file mode 100644 index 0000000..3ab9e72 --- /dev/null +++ b/adpeps/tensor/ncon.py @@ -0,0 +1,380 @@ +"""A module for the function ncon, which does contractions of several tensors. +""" +import jax.numpy as np +from collections.abc import Iterable +from typing import Union, Optional, Any, Callable + +from adpeps.utils.empty_tensor import EmptyT +from adpeps.utils.nested import Nested + +TensorType = Union[np.ndarray, Nested, EmptyT] + +# def ncon(L: Union[Iterable[TensorType], TensorType], v: Iterable[Iterable[int]], +# order: Optional[Iterable[int]]=None, forder: Optional[Iterable[int]]=None, +# check_indices: bool=True, empty_class: Any=list, normalize: bool=False, +# mult_method: Callable[[Any,Any,Iterable[int]], Any]=None +# ) -> TensorType: +def ncon(L, v, + order=None, forder=None, + check_indices=True, empty_class=list, normalize=False, + mult_method=None + ) -> TensorType: + """L = [A1, A2, ..., Ap] list of tensors. + + v = (v1, v2, ..., vp) tuple of lists of indices e.g. v1 = [3, 4, -1] labels + the three indices of tensor A1, with -1 indicating an uncontracted index + (open leg) and 3 and 4 being the contracted indices. + + order, if present, contains a list of all positive indices - if not + [1, 2, 3, 4, ...] by default. This is the order in which they are + contracted. + + forder, if present, contains the final ordering of the uncontracted indices + - if not, [-1, -2, ..i] by default. + + There is some leeway in the way the inputs are given. For example, + instead of giving a list of tensors as the first argument one can + give some different iterable of tensors, such as a tuple, or a + single tensor by itself (anything that has the attribute "shape" + will be considered a tensor). + """ + + # We want to handle the tensors as a list, regardless of what kind + # of iterable we are given. In addition, if only a single element is + # given, we make list out of it. Inputs are assumed to be non-empty. + if hasattr(L, "shape"): + L = [L] + else: + L = list(L) + if np.any(np.array([len(A) == 0 for A in L])): + if normalize: + return empty_class(), 1. + return empty_class() + v = list(v) + if not isinstance(v[0], Iterable): + # v is not a list of lists, so make it such. + v = [v] + else: + v = list(map(list, v)) + + if order is None: + order = create_order(v) + if forder is None: + forder = create_forder(v) + + if check_indices: + # Raise a RuntimeError if the indices are wrong. + do_check_indices(L, v, order, forder) + + # If the graph is dinconnected, connect it with trivial indices that + # will be contracted at the very end. + connect_graph(L, v, order) + + while len(order) > 0: + tcon = get_tcon(v, order[0]) # tcon = tensors to be contracted + # Find the indices icon that are to be contracted. + if len(tcon) == 1: + tracing = True + icon = [order[0]] + else: + tracing = False + icon = get_icon(v, tcon) + # Position in tcon[0] and tcon[1] of indices to be contracted. + # In the case of trace, pos2 = [] + pos1, pos2 = get_pos(v, tcon, icon) + if tracing: + # Trace on a tensor + new_A = trace(L[tcon[0]], axis1=pos1[0], axis2=pos1[1]) + else: + # Contraction of 2 tensors + new_A = con(L[tcon[0]], L[tcon[1]], (pos1, pos2), mult_method=mult_method) + L.append(new_A) + v.append(find_newv(v, tcon, icon)) # Add the v for the new tensor + for i in sorted(tcon, reverse=True): + # Delete the contracted tensors and indices from the lists. + # tcon is reverse sorted so that tensors are removed starting from + # the end of L, otherwise the order would get messed. + del L[i] + del v[i] + order = renew_order(order, icon) # Update order + + vlast = v[0] + A = L[0] + A = permute_final(A, vlast, forder) + if normalize: + if hasattr(A, 'normalize'): + A, factor = A.normalize() + else: + factor = np.abs(A).max() + A = A / factor + return A + + +# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # + + +def create_order(v): + """Identify all unique, positive indices and return them sorted.""" + flat_v = sum(v, []) + x = [i for i in flat_v if i > 0] + # Converting to a set and back removes duplicates + x = list(set(x)) + return sorted(x) + + +def create_forder(v): + """Identify all unique, negative indices and return them reverse sorted + (-1 first). + """ + flat_v = sum(v, []) + x = [i for i in flat_v if i < 0] + # Converting to a set and back removes duplicates + x = list(set(x)) + return sorted(x, reverse=True) + + +def connect_graph(L, v, order): + """Connect the graph of tensors to be contracted by trivial + indices, if necessary. Add these trivial indices to the end of the + contraction order. + + L, v and order are modified in place. + """ + # Build ccomponents, a list of the connected components of the graph, + # where each component is represented by a a set of indices. + unvisited = set(range(len(L))) + visited = set() + ccomponents = [] + while unvisited: + component = set() + next_visit = unvisited.pop() + to_visit = {next_visit} + while to_visit: + i = to_visit.pop() + unvisited.discard(i) + component.add(i) + visited.add(i) + # Get the indices of tensors neighbouring L[i]. + i_inds = set(v[i]) + neighs = ( + j for j, j_inds in enumerate(v) if i_inds.intersection(j_inds) + ) + for neigh in neighs: + if neigh not in visited: + to_visit.add(neigh) + ccomponents.append(component) + # If there is more than one connected component, take one of them, a + # take an arbitrary tensor (called c) out of it, and connect that + # tensor with an arbitrary tensor (called d) from all the other + # components using a trivial index. + c = ccomponents.pop().pop() + while ccomponents: + d = ccomponents.pop().pop() + A_c = L[c] + A_d = L[d] + c_axis = len(v[c]) + d_axis = len(v[d]) + try: + L[c] = A_c.expand_dims(c_axis, direction=1) + except AttributeError: + L[c] = np.expand_dims(A_c, c_axis) + try: + L[d] = A_d.expand_dims(d_axis, direction=-1) + except AttributeError: + L[d] = np.expand_dims(A_d, d_axis) + try: + dim_num = max(order) + 1 + except ValueError: + dim_num = 1 + v[c].append(dim_num) + v[d].append(dim_num) + order.append(dim_num) + return None + + +def get_tcon(v, index): + """Gets the list indices in L of the tensors that have index as their + leg. + """ + tcon = [] + for i, inds in enumerate(v): + if index in inds: + tcon.append(i) + l = len(tcon) + # If check_indices is called and it does its work properly then these + # checks should in fact be unnecessary. + if l > 2: + raise ValueError( + "In ncon.get_tcon, more than two tensors share a contraction " + "index." + ) + elif l < 1: + raise ValueError( + "In ncon.get_tcon, less than one tensor share a contraction index." + ) + elif l == 1: + # The contraction is a trace. + how_many = v[tcon[0]].count(index) + if how_many != 2: + # Only one tensor has this index but it is not a trace because it + # does not occur twice for that tensor. + raise ValueError( + "In ncon.get_tcon, a trace index is listed != 2 times for the " + "same tensor." + ) + return tcon + + +def get_icon(v, tcon): + """Returns a list of indices that are to be contracted when contractions + between the two tensors numbered in tcon are contracted. + """ + inds1 = v[tcon[0]] + inds2 = v[tcon[1]] + icon = set(inds1).intersection(inds2) + icon = list(icon) + return icon + + +def get_pos(v, tcon, icon): + """Get the positions of the indices icon in the list of legs the tensors + tcon to be contracted. + """ + pos1 = [[i for i, x in enumerate(v[tcon[0]]) if x == e] for e in icon] + pos1 = sum(pos1, []) + if len(tcon) < 2: + pos2 = [] + else: + pos2 = [[i for i, x in enumerate(v[tcon[1]]) if x == e] for e in icon] + pos2 = sum(pos2, []) + return pos1, pos2 + + +def find_newv(v, tcon, icon): + """Find the list of indices for the new tensor after contraction of + indices icon of the tensors tcon. + """ + if len(tcon) == 2: + newv = v[tcon[0]] + v[tcon[1]] + else: + newv = v[tcon[0]] + newv = [i for i in newv if i not in icon] + return newv + + +def renew_order(order, icon): + """Returns the new order with the contracted indices removed from it.""" + return [i for i in order if i not in icon] + + +def permute_final(A, v, forder): + """Returns the final tensor A with its legs permuted to the order given + in forder. + """ + perm = [v.index(i) for i in forder] + try: + permuted = A.transpose(tuple(perm)) + except (AttributeError, TypeError): + permuted = np.transpose(A, tuple(perm)) + return permuted + + +def do_check_indices(L, v, order, forder): + """Check that + 1) the number of tensors in L matches the number of index lists in v. + 2) every tensor is given the right number of indices. + 3) every contracted index is featured exactly twice and every free index + exactly once. + 4) the dimensions of the two ends of each contracted index match. + """ + + # 1) + if len(L) != len(v): + raise ValueError( + ( + "In ncon.do_check_indices, the number of tensors %i" + " does not match the number of index lists %i" + ) + % (len(L), len(v)) + ) + + # 2) + # Create a list of lists with the shapes of each A in L. + shapes = list(map(lambda A: list(A.shape), L)) + for i, inds in enumerate(v): + if len(inds) != len(shapes[i]): + raise ValueError( + ( + "In ncon.do_check_indices, len(v[%i])=%i does not match " + "the numbers of indices of L[%i] = %i" + ) + % (i, len(inds), i, len(shapes[i])) + ) + + # 3) and 4) + # v_pairs = [[(0,0), (0,1), (0,2), ...], [(1,0), (1,1), (1,2), ...], ...] + v_pairs = [[(i, j) for j in range(len(s))] for i, s in enumerate(v)] + v_pairs = sum(v_pairs, []) + v_sum = sum(v, []) + # For t, o in zip(v_pairs, v_sum) t is the tuple of the number of + # the tensor and the index and o is the contraction order of that + # index. We group these tuples by the contraction order. + order_groups = [ + [t for t, o in zip(v_pairs, v_sum) if o == e] for e in order + ] + forder_groups = [[1 for fo in v_sum if fo == e] for e in forder] + for i, o in enumerate(order_groups): + if len(o) != 2: + raise ValueError( + ( + "In ncon.do_check_indices, the contracted index %i is not " + "featured exactly twice in v." + ) + % order[i] + ) + else: + A0, ind0 = o[0] + A1, ind1 = o[1] + try: + compatible = L[A0].compatible_indices(L[A1], ind0, ind1) + except AttributeError: + compatible = L[A0].shape[ind0] == L[A1].shape[ind1] + if not compatible: + raise ValueError( + "In ncon.do_check_indices, for the contraction index %i, " + "the leg %i of tensor number %i and the leg %i of tensor " + "number %i are not compatible." + % (order[i], ind0, A0, ind1, A1) + ) + for i, fo in enumerate(forder_groups): + if len(fo) != 1: + raise ValueError( + ( + "In ncon.do_check_indices, the free index %i is not " + "featured exactly once in v." + ) + % forder[i] + ) + + # All is well if we made it here. + return True + + +#################################################################### +# The following are simple wrappers around numpy/Tensor functions, # +# but may be replaced with fancier stuff later. # +#################################################################### + + +def con(A, B, inds, mult_method=None): + if mult_method is None: + if isinstance(A, np.ndarray) and isinstance(A, np.ndarray): + return np.tensordot(A, B, inds) + else: + return A.dot(B, inds) + else: + return mult_method(A, B, inds) + + +def trace(A, axis1=0, axis2=1): + return A.trace(axis1=axis1, axis2=axis2) diff --git a/adpeps/tensor/ops.py b/adpeps/tensor/ops.py new file mode 100644 index 0000000..3b003a5 --- /dev/null +++ b/adpeps/tensor/ops.py @@ -0,0 +1,146 @@ +import jax.numpy as np +from jax import custom_vjp +import jax + +def reshape(m, left_ixs, right_ixs): + m = np.transpose(m, [*left_ixs, *right_ixs]) + left_size = np.prod(np.array([m.shape[i] for i in range(len(left_ixs))])) + return np.reshape(m, (left_size, -1)) + +def svd(m, n, mode, cutoff=1e-12, use_iter=False): + """ Performs an svd with a cutoff + + Parameters: + m (2-D array): matrix to be svd'ed + n (int): maximum number of singular values + mode (str): absorb the singular values either in + u ('l'), in v ('r') or not (otherwise) + + Returns: + torch.Tensor: u + torch.Tensor: s + torch.Tensor: v + such that u*s*v approximates m + + """ + if m.size == 0: + u = np.zeros([0,0]) + s = np.tensor([]) + v = np.zeros([0,0]) + return u,s,v + + # m = reshape(m, left_ixs, right_ixs) + + if use_iter and n < min(m.size()) and min(m.size()) > 400: + r + u, s, v = np.svd(m) + else: + # u, s, v = np.linalg.svd(m, full_matrices=False) + u, s, v = _svd_impl(m) + ix = np.argsort(s)[::-1] + s = s[ix] + u = u[:,ix] + v = v[ix,:] + + # n_above_cutoff = len(np.where(s/s.max() > cutoff)[0]) + # n = min(n, n_above_cutoff) + # if s.shape[0] > n: + # u = u[:,:n] + # s = s[:n] + # v = v[:n,:] + + u,s,v = _cutoff_matrices(u,s,v,cutoff,n) + + s = np.diag(s) + + # try: + # if config.svd_fix_sign: + # u, v = _svd_flip(u, v) + # except: + # pass + + # if mode == 'l': + # u = u @ s + # if mode == 'r': + # v = s @ v + + return u,s,v + +def _cutoff_matrices(u,s,v,cutoff,n): + # n_above_cutoff = len(np.where(s/s.max() > cutoff)[0]) + n_above_cutoff = np.count_nonzero(s/np.max(s) > cutoff) + # n_above_cutoff = 8 + n = np.min(np.array([n, n_above_cutoff])) + if n < np.inf and s.shape[0] > n: + n = int(n) + u = u[:,:n] + s = s[:n] + v = v[:n,:] + return u,s,v + +@custom_vjp +def _svd_impl(m): + u, s, v = np.linalg.svd(m, full_matrices=False) + return u, s, v + +def _svd_impl_fwd(m): + u, s, v = _svd_impl(m) + # if s.shape[0] < min(m.shape[0],m.shape[1]): + # print('SVD def') + return (u, s, v), (u,s,v) + +def _svd_impl_bwd(res, g): + U, S, V = res + dU, dS, dV = g + Vt = V + V = V.T + dV = dV.T + Ut = U.T + M = U.shape[0] + N = V.shape[0] + NS = len(S) + + # F = (S - S[:, None]) + # F = __safe_inverse(F) + # F.diagonal().fill_(0) + + F = (S - S[:, None]) + F = __safe_inverse(F) + F = jax.ops.index_update(F, np.diag_indices(F.shape[0]), 0) + + # G = (S + S[:, None]) + # G.diagonal().fill_(np.inf) + # G = 1/G + + G = (S + S[:, None]) + G = 1/G + G = jax.ops.index_update(G, np.diag_indices(G.shape[0]), 0) + + UdU = Ut @ dU + VdV = Vt @ dV + + Su = (F+G)*(UdU-UdU.T)/2 + Sv = (F-G)*(VdV-VdV.T)/2 + + dA = U @ (Su + Sv + np.diag(dS)) @ Vt + if (M>NS): + # dA = dA + (torch.eye(M, dtype=dU.dtype, device=dU.device) - U@Ut) @ (dU/S) @ Vt + dA = dA + (np.eye(M, dtype=dU.dtype) - U@Ut) @ (dU/S) @ Vt + if (N>NS): + # dA = dA + (U/S) @ dV.t() @ (torch.eye(N, dtype=dU.dtype, device=dU.device) - V@Vt) + dA = dA + (U/S) @ dV.T @ (np.eye(N, dtype=dU.dtype) - V@Vt) + return (dA,) + +_svd_impl.defvjp(_svd_impl_fwd, _svd_impl_bwd) + +def __safe_inverse(x, epsilon=1e-12): + if epsilon is None: + epsilon = config.safe_inv_epsilon + if epsilon == 0: + return 1/x + else: + return x/(x**2 + epsilon) + + +def diag_inv(m): + return np.diag(1 / np.diag(m)) diff --git a/adpeps/types.py b/adpeps/types.py new file mode 100644 index 0000000..9f9b19c --- /dev/null +++ b/adpeps/types.py @@ -0,0 +1,5 @@ +from typing import Union, Optional, Any, Callable + +import jax.numpy as np + +TensorType = Union['np.ndarray', 'Nested', 'EmptyT'] diff --git a/adpeps/utils/__init__.py b/adpeps/utils/__init__.py new file mode 100644 index 0000000..e5183f4 --- /dev/null +++ b/adpeps/utils/__init__.py @@ -0,0 +1,4 @@ +""" Utilities module with several convenience functions and classes + used during the simulations +""" + diff --git a/adpeps/utils/ctmtensors.py b/adpeps/utils/ctmtensors.py new file mode 100644 index 0000000..196ca35 --- /dev/null +++ b/adpeps/utils/ctmtensors.py @@ -0,0 +1,174 @@ +""" Contains utility class that contains all iPEPS tensors """ + +from dataclasses import dataclass, field, fields, replace, asdict +from functools import partial +from typing import List + +from .empty_tensor import EmptyT +from .nested import Nested +from .tlist import TList, hold_write + +@dataclass +class CTMTensors: + """ + This is a utility class that contains all tensors related to an iPEPS. + In effect, this forms a representation of the full state, including + the site tensors with variational parameters, the boundary tensors + generated by CTM and the projectors. + + There are several fields of this dataclass that are generated + automatically, which provide convenient wrappers for the tensors. + + For example, the :attr:`CTMTensors.A` field returns the site tensors + (contained in a :class:`adpeps.utils.tlist.TList`) + """ + A: TList + Ad: TList + Cs: List[TList] = field(default_factory=list) + Ts: List[TList] = field(default_factory=list) + + B: TList = field(default=None, metadata={'init_tlist': True}) + Bd: TList = field(default=None, metadata={'init_tlist': True}) + B_Cs: List[TList] = field(default=None, metadata={'init_tlists': True}) + B_Ts: List[TList] = field(default=None, metadata={'init_tlists': True}) + Bd_Cs: List[TList] = field(default=None, metadata={'init_tlists': True}) + Bd_Ts: List[TList] = field(default=None, metadata={'init_tlists': True}) + BB_Cs: List[TList] = field(default=None, metadata={'init_tlists': True}) + BB_Ts: List[TList] = field(default=None, metadata={'init_tlists': True}) + + Pl: TList = None + Pr: TList = None + Pt: TList = None + Pb: TList = None + Plb: TList = None + Prb: TList = None + Ptb: TList = None + Pbb: TList = None + + observables: List = field(default_factory=list) + + def _get_field_item(self, fieldname=None, ix=None): + return getattr(self, fieldname).__getitem__(ix) + + def _get_field_nested_item(self, fieldname=None, ix=None): + return getattr(self, fieldname)(ix) + + def _set_field_nested_item(self, fieldname=None, ix=None, value=None): + return getattr(self, f"{fieldname}_set")(ix, value) + + def hold(self, *fields): + def _convert_all(f): + if f.startswith('all_'): + f = f[4:] + return [f, f"B_{f}", f"Bd_{f}", f"BB_{f}"] + else: + return (f,) + fields = [field for fs in [_convert_all(f) for f in fields] for field in fs] + tensors = tuple([getattr(self, field) for field in fields]) + return hold_write(*tensors) + + def __post_init__(self): + base_tlist = self.A + for f in fields(self): + try: + if getattr(self, f.name) is None and f.metadata['init_tlist']: + setattr(self, f.name, TList.empty_like(base_tlist, empty_obj=EmptyT())) + except KeyError: + pass + try: + if getattr(self, f.name) is None and f.metadata['init_tlists']: + setattr(self, f.name, [TList.empty_like(base_tlist, empty_obj=EmptyT()) for _ in range(4)]) + except KeyError: + pass + + def all_Cs(self, ix): + base_tlist = self.A + res = TList.empty_like(base_tlist, empty_obj=EmptyT()) + for i in range(len(res._data)): + res._data[i] = Nested([self.Cs[ix][i], self.B_Cs[ix][i], + self.Bd_Cs[ix][i], self.BB_Cs[ix][i]]) + return res + + def all_Ts(self, ix): + base_tlist = self.A + res = TList.empty_like(base_tlist, empty_obj=EmptyT()) + for i in range(len(res._data)): + res._data[i] = Nested([self.Ts[ix][i], self.B_Ts[ix][i], + self.Bd_Ts[ix][i], self.BB_Ts[ix][i]]) + return res + + def update(self, fieldnames, ixs, values): + if isinstance(fieldnames, str): + fieldnames = (fieldnames,) + values = (values,) + ixs = (ixs,) + for i,f in enumerate(fieldnames): + value = values[i] + ix = ixs[i] + assert isinstance(value, Nested), "Use the all_Ci setter only with Nested tensors" + getattr(self, f)[ix] = value[0] + getattr(self, f"B_{f}")[ix] = value[1] + getattr(self, f"Bd_{f}")[ix] = value[2] + getattr(self, f"BB_{f}")[ix] = value[3] + + @property + def all_A(self): + base_tlist = self.A + res = TList.empty_like(base_tlist, empty_obj=EmptyT()) + for i in range(len(res._data)): + res._data[i] = Nested([self.A._data[i], self.B._data[i], + EmptyT(), EmptyT()]) + return res + + @property + def all_Ad(self): + base_tlist = self.A + res = TList.empty_like(base_tlist, empty_obj=EmptyT()) + for i in range(len(res._data)): + res._data[i] = Nested([self.Ad._data[i], EmptyT(), + self.Bd._data[i], EmptyT()]) + return res + + def stop_gradient(self, only_boundaries=True): + for i in range(4): + self.Cs[i] = self.Cs[i].stop_gradient() + self.Ts[i] = self.Ts[i].stop_gradient() + self.B_Cs[i] = self.B_Cs[i].stop_gradient() + self.B_Ts[i] = self.B_Ts[i].stop_gradient() + self.Bd_Cs[i] = self.Bd_Cs[i].stop_gradient() + self.Bd_Ts[i] = self.Bd_Ts[i].stop_gradient() + self.BB_Cs[i] = self.BB_Cs[i].stop_gradient() + self.BB_Ts[i] = self.BB_Ts[i].stop_gradient() + if not only_boundaries: + self.A = self.A.stop_gradient() + self.Ad = self.Ad.stop_gradient() + self.B = self.B.stop_gradient() + self.Bd = self.Bd.stop_gradient() + +def _wrap_f(self, fieldname=None, ix=None): + return self._get_field_item(fieldname, ix) + +def _wrap_nested_f(self, fieldname=None, ix=None): + return self._get_field_nested_item(fieldname, ix) + +def _wrap_nested_f_set(self, value, fieldname=None, ix=None): + return self._set_field_nested_item(fieldname, ix, value) + +attrs = ['Cs', 'Ts', 'B_Cs', 'B_Ts', 'Bd_Cs', 'Bd_Ts', 'BB_Cs', 'BB_Ts'] +for attr in attrs: + for i in range(4): + new_attr = property(partial(_wrap_f, fieldname=attr, ix=i)) + # new_attr.__doc__ = f"Boundary tensors `{attr}` computed by CTM" + new_attr.__doc__ = ":meta private:" + setattr(CTMTensors, f"{attr[:-1]}{i+1}", new_attr) +attrs = ['all_Cs', 'all_Ts'] +for attr in attrs: + for i in range(4): + new_attr = property(partial(_wrap_nested_f, fieldname=attr, ix=i), + partial(_wrap_nested_f_set, fieldname=attr, ix=i)) + new_attr.__doc__ = ":meta private:" + # new_attr.__doc__ = ":class:`adpeps.utils.tlist.TList` containing all versions \ + # (only ground-state, ground state + one `B` tensor, ground state \ + # + one `Bdagger` tensor, ground state + one `B` tensor + one `Bdagger`\ + # tensor) of the boundary tensors." + setattr(CTMTensors, f"{attr[:-1]}{i+1}", new_attr) diff --git a/adpeps/utils/empty_tensor.py b/adpeps/utils/empty_tensor.py new file mode 100644 index 0000000..6b87444 --- /dev/null +++ b/adpeps/utils/empty_tensor.py @@ -0,0 +1,88 @@ +""" Contains utility class that represents a 'zero' (empty) tensor object """ + +import jax.numpy as np + +class EmptyT: + """ Empty tensor utility class, which can be used to represent a + 'zero' tensor. + + The operations involving this type of tensor will return the expected + results, such as (Tensor * EmptyT -> EmptyT), removing the need for + checking if a tensor is empty in the part of the code where the + operation is called. + """ + tag = None + + def __repr__(self): + return "" + + def __add__(self, other): + return other + + def __radd__(self, other): + return other + + def __sub__(self, other): + return other + + def __rsub__(self, other): + return other + + def __mul__(self, other): + return self + + def __neg__(self): + return self + + def __rmul__(self, other): + if isinstance(other, int): + return [self for _ in range(other)] + else: + return self + + def __truediv__(self, other): + return self + + def copy(self): + return self + + def to_real(self): + return self + + @property + def real(self): + return self + + @property + def data(self): + return [] + + def transpose(self, *args): + return self + + def __rtruediv__(self, other): + return self + + def __len__(self): + return 0 + + def __array__(self): + return np.array([]) + + def item(self): + return self + + def __getitem__(self, ix): + return self + + def mult(self, other, *args): + return self + + def to_complex(self): + return self + + def complex(self): + return False + + def is_finite(self): + return True diff --git a/adpeps/utils/io.py b/adpeps/utils/io.py new file mode 100644 index 0000000..92f7300 --- /dev/null +++ b/adpeps/utils/io.py @@ -0,0 +1,64 @@ +""" IO module with convenience function for forming the localized filenames + and foldernames of the relevant configuration files and data files. + + Note: + The input configuration file location can be set via the + :envvar:`CONFIGDIR` variable. If it is not set, the default + input folder will be the `examples` subfolder of the package + root directory + + Note: + The output data location can be set via the :envvar:`DATADIR` + variable. If it is not set, the default output folder will be + in the `simulations` subfolder of the package root directory. +""" + +from pathlib import Path +import math +import numpy as np +import os + +import adpeps +import adpeps.ipeps.config as sim_config + + +def localize_data_file(filename): + ROOT_DIR = adpeps.PROJECT_ROOT_DIR + try: + base_out_folder = os.environ["DATADIR2"] + except KeyError: + base_out_folder = Path(ROOT_DIR, 'simulations') + return Path(base_out_folder, filename) + +def localize_config_file(filename): + ROOT_DIR = adpeps.PROJECT_ROOT_DIR + try: + base_out_folder = os.environ["CONFIGDIR"] + except KeyError: + base_out_folder = Path(ROOT_DIR, 'examples') + return Path(base_out_folder, filename).with_suffix('.yaml') + +def get_gs_file(): + if sim_config.out_prefix is not None: + filename = f"{sim_config.out_prefix}_{sim_config.model}_D{sim_config.D}_X{sim_config.chi}" + else: + filename = f"{sim_config.model}_D{sim_config.D}_X{sim_config.chi}" + filename = Path('gs', filename) + return localize_data_file(filename).with_suffix('.npz') + +def get_exci_folder(): + if sim_config.out_prefix is not None: + folder = f"{sim_config.out_prefix}_{sim_config.model}_D{sim_config.D}_X{sim_config.chi}" + else: + folder = f"{sim_config.model}_D{sim_config.D}_X{sim_config.chi}" + folder = Path('exci', folder) + return localize_data_file(folder) + +def get_exci_file(momentum_ix): + foldername = get_exci_folder() + filename = f"{momentum_ix+1}_{sim_config.px/math.pi:.5}_{sim_config.py/math.pi:.5}.npz" + return Path(foldername, filename) + +def get_exci_base_file(): + return get_exci_folder().with_suffix('.base.npz') + diff --git a/adpeps/utils/nested.py b/adpeps/utils/nested.py new file mode 100644 index 0000000..861486d --- /dev/null +++ b/adpeps/utils/nested.py @@ -0,0 +1,161 @@ +""" Contains utility class that represents a collection of tensors of + different types, with operations that can be applied to all + contained tensors at once +""" + +import cmath +import jax.numpy as np + +from adpeps.types import TensorType + + +class Nested: + """ This is a helper class for the efficient contraction of variants of tensors, + used in the energy evaluation of excited states + + A Nested tensor contains the following variants (some may be empty): + + - :attr:`tensors[0]`: regular tensor (no B or Bd) + - :attr:`tensors[1]`: (terms with) a single B tensor + - :attr:`tensors[2]`: (terms with) a single Bd tensor + - :attr:`tensors[3]`: (terms with) both a B and a Bd tensor + + When two Nested tensors x,y are contracted, all combinations are taken into account + and the result is again a Nested tensor, filled with the following variants: + + - :attr:`tensors[0]: x[0] * y[0]` + - :attr:`tensors[1]: x[1] * y[0] + x[0] * y[1]` + - :attr:`tensors[2]: x[2] * y[0] + x[0] * y[2]` + - :attr:`tensors[3]: x[3] * y[0] + x[2] * y[1] + x[1] * y[2] + x[0] * y[3]` + + By using Nested tensors in a (large) contraction, the many different terms are + resummed on the fly, leading to a potentially reduced computational cost + + Note: + Most implented functions act as wrappers for the corresponding `numpy` functions + on the individual tensors + """ + + def __init__(self, tensors): + self.tensors = tensors + + def normalize(self): + """ Normalize the contained tensors by the largest value + of the first element of :attr:`self.tensors` + """ + factor = np.abs(self[0]).max() + return self * (1 / factor), factor + + def mult(self, other: TensorType, *args) -> 'Nested': + """ + Args: + other: other tensor-like object to contract with + *args: arguments to be passed to the contraction method + (:code:`np.tensordot`) + + Returns: + res: result of the contraction + """ + def _mult_function(A, B, *args): + if hasattr(A, 'mult'): + return A.mult(B, *args) + elif len(B) == 0: + return B.mult(A, *args) + return np.tensordot(A, B, *args) + + if isinstance(other, np.ndarray): + new_data = 4 * [[]] + new_data[0] = _mult_function(self.tensors[0], other, *args) + new_data[1] = _mult_function(self.tensors[1], other, *args) + new_data[2] = _mult_function(self.tensors[2], other, *args) + new_data[3] = _mult_function(self.tensors[3], other, *args) + return Nested(new_data) + new_data = 4 * [[]] + new_data[0] = _mult_function(self.tensors[0], other.tensors[0], *args) + new_data[1] = _mult_function(self.tensors[1], other.tensors[0], *args) +\ + _mult_function(self.tensors[0], other.tensors[1], *args) + new_data[2] = _mult_function(self.tensors[2], other.tensors[0], *args) +\ + _mult_function(self.tensors[0], other.tensors[2], *args) + + new_data[3] = _mult_function(self.tensors[3], other.tensors[0], *args) +\ + _mult_function(self.tensors[2], other.tensors[1], *args) +\ + _mult_function(self.tensors[1], other.tensors[2], *args) +\ + _mult_function(self.tensors[0], other.tensors[3], *args) + res = Nested(new_data) + return res + + def transpose(self, *args) -> 'Nested': + """ Applies :code:`transpose` to each contained tensor """ + new_data = [self.tensors[i].transpose(*args) for i in range(4)] + return Nested(new_data) + + def __mul__(self, other): + new_data = [self.tensors[i] * other for i in range(4)] + return Nested(new_data) + + def __rmul__(self, other): + new_data = [other * self.tensors[i] for i in range(4)] + return Nested(new_data) + + def __truediv__(self, other): + new_data = [self.tensors[i] / other for i in range(4)] + return Nested(new_data) + + def __add__(self, other): + if isinstance(other, Nested): + new_data = [self.tensors[i] + other.tensors[i] for i in range(4)] + else: + new_data = [self.tensors[i] + other for i in range(4)] + return Nested(new_data) + + def __radd__(self, other): + return self + other + + def __getitem__(self, ix): + return self.tensors[ix] + + def __setitem__(self, ix, value): + self.tensors[ix] = value + + def __repr__(self): + return "(Nested) " + self.tensors.__repr__() + + def __neg__(self): + return Nested([-self.tensors[i] for i in range(4)]) + + def shift(self, phi): + new_data = [self.tensors[0], self.tensors[1] * exp(phi), + self.tensors[2] * exp(-phi), self.tensors[3]] + return Nested(new_data) + + def __len__(self): + try: + return len(self.tensors[0]) + except Exception: + return self.tensors[0].size + + @property + def real(self): + res = Nested([self.tensors[i].real for i in range(4)]) + return res + + @property + def shape(self): + return self.tensors[0].shape + + @property + def dims(self): + return self.tensors[0].dims + + def check_contr_inds(self, other, *args, **kwargs): + return self[0].check_contr_inds(other[0], *args, **kwargs) + + def numel(self): + return self[0].numel() + + @classmethod + def only_gs(cls, tensor, empty_obj=[]): + return cls([tensor, empty_obj, empty_obj, empty_obj]) + +def exp(phi): + return cmath.exp(1j * phi) diff --git a/adpeps/utils/printing.py b/adpeps/utils/printing.py new file mode 100644 index 0000000..9d7f00c --- /dev/null +++ b/adpeps/utils/printing.py @@ -0,0 +1,37 @@ +""" Utility module for printing output depending on the verbosity setting + :attr:`adpeps.ipeps.config.disp_level` in the configuration file. +""" + +import builtins +import time + +import adpeps.ipeps.config as sim_config + +prefix = None +show_time = False + +def print(*args, level: int=None, **kwargs): + """ Print output using builtin :code:`print` if :code:`level` + <= :attr:`adpeps.ipeps.config.disp_level` + + Args: + *args: arbitraty arguments to be passed to builtin :code:`print` + level: verbosity level, determining at which verbosity setting this + should be printed + **kwargs: arbitraty keyword arguments for builtin :code:`print` + """ + if level is None or level <= sim_config.disp_level: + if sim_config.flush_output: + kwargs['flush'] = True + if prefix is not None: + if show_time: + curtime = time.strftime("[%H:%M:%S]", time.localtime()) + builtins.print(prefix, curtime, *args, **kwargs) + else: + builtins.print(prefix, *args, **kwargs) + else: + if show_time: + curtime = time.strftime("[%H:%M:%S]", time.localtime()) + builtins.print(curtime, *args, **kwargs) + else: + builtins.print(*args, **kwargs) diff --git a/adpeps/utils/tlist.py b/adpeps/utils/tlist.py new file mode 100644 index 0000000..3ce38b8 --- /dev/null +++ b/adpeps/utils/tlist.py @@ -0,0 +1,302 @@ +""" + List object with additional features, used for storing + the iPEPS tensors + + Items in the list can be accessed by either a linear index + or a (i,j) double index, where i and j will be automatically + taken modulo the unit cell size (i.e. i = i % n_x) + + Additionally, convenience functions that work on tensors can + be defined for the whole list, e.g. conj() +""" + +import contextlib +import jax +import jax.numpy as np +import numpy as onp + +from .empty_tensor import EmptyT + + +@contextlib.contextmanager +def cur_loc(*loc: int): + """ Shift the locations of the tensors relative to a + new zero (loc) while in this context + + Args: + loc: shifts (x,y) + + Example: + >>> l = TList([[1,2], [3,4]]) + >>> l[0,0] + 1 + >>> with cur_loc(1,0): + >>> l[0,0] + 2 + >>> l[0,1] + 4 + >>> l[0,0] + 1 + + Note that this applies to ALL TList objects while + inside the context + """ + pre_patched_value = getattr(TList, '_loc') + setattr(TList, '_loc', loc) + yield TList + setattr(TList, '_loc', pre_patched_value) + +@contextlib.contextmanager +def hold_write(*lists: 'TList'): + """ Hold off on writing to the list while + inside the context + + Args: + lists: one or more TList objects that should have the writing + action delayed until the context is disabled + + Example: + >>> l = TList([[1,2], [3,4]]) + >>> with hold_write(l): + >>> l[0,0] = 100 + >>> l[0,0] + 1 + >>> l[0,0] + 100 + """ + for l in lists: + l._hold_write = True + yield + for l in lists: + l._purge_tmp() + +@contextlib.contextmanager +def set_pattern(pattern): + """ Set pattern for all new TLists that are created while + the context is active + + Args: + pattern: + """ + + pre_patched_value = getattr(TList, '_default_pattern') + setattr(TList, '_default_pattern', pattern) + yield TList + setattr(TList, '_default_pattern', pre_patched_value) + +class TList: + _loc = (0,0) + _default_pattern = None + _changed = None + + def __init__(self, data=None, shape=None, pattern=None, empty_obj=[[]]): + self._tmpdata = None + self.pattern = pattern + self._hold_write = False + self.empty_obj = empty_obj + if pattern is None and self._default_pattern is not None: + self.pattern = self._default_pattern + if self.pattern is None: + if data is not None: + try: + iter(data) # Check if iterable + data = np.array(data, dtype='object') + self._data = data.reshape([-1], order='C').tolist() + if data.ndim == 1: + self.size = (data.shape[0], 1) + else: + self.size = (data.shape[1], data.shape[0]) + except: + self._data = [data] + self.size = (1,1) + elif shape is not None: + self._data = (shape[0]*shape[1]) * empty_obj + self.size = shape + else: + self._data = None + self.size = () + else: + self.pattern = np.array(self.pattern) + self.size = (self.pattern.shape[1], self.pattern.shape[0]) + if data is not None: + try: + iter(data) # Check if iterable + data = np.array(data, dtype='object') + if data.size == np.unique(self.pattern).size: + self._data = data.reshape([-1], order='C').tolist() + else: + self._data = np.unique(self.pattern).size * empty_obj + for j in range(self.pattern.shape[1]): + for i in range(self.pattern.shape[0]): + self._data[self.pattern[i,j]] = data[i,j] + except: + self._data = [data] + self.size = (1,1) + else: + self._data = np.unique(self.pattern).size * empty_obj + assert len(self._data) == np.unique(self.pattern).size, \ + "Data must contain one element for each unique identifier in pattern" + self.reset_changed() + + def x_major(self): + return (self._conv_ix((x,y)) for y in range(self.size[1]) for x in range(self.size[0])) + + def y_major(self): + return (self._conv_ix((x,y)) for x in range(self.size[0]) for y in range(self.size[1])) + + def __len__(self): + return len(self._data) + + def mean(self): + try: + finite_elems = [x for x in self._data if isfinite(x)] + return sum(finite_elems) / len(finite_elems) + except Exception as e: + return sum(self._data) / len(self) + + def sum(self): + try: + finite_elems = [x for x in self._data if isfinite(x)] + return sum(finite_elems) + except Exception as e: + return sum(self._data) + + def normalize(self): + new_list = TList(shape=self.size, pattern=self.pattern) + new_list._data = [a / np.max(np.abs(a)) for a in self._data] + return new_list + + def conj(self): + new_list = TList(shape=self.size, pattern=self.pattern) + new_list._data = [a.conj() for a in self._data] + return new_list + def items(self): + return [a.item() for a in self._data] + + def pack_data(self): + data = [] + for a in self._data: + data.append(np.reshape(a, (-1,))) + return np.concatenate(data) + + def reset_changed(self): + if self._data is not None: + self._changed = len(self._data) * [False] + return self + + def mark_changed(self, linear_ix): + if self._changed is not None: + self._changed[linear_ix] = True + + def is_changed(self, *ix): + if self._changed is None: + return False + linear_ix = self._conv_ix(ix) + return self._changed[linear_ix] + + def fill(self, data, d=None, D=None): + new_list = TList(shape=self.size, pattern=self.pattern) + offset = 0 + new_data = [] + for i,a in enumerate(self): + siz = a.size + # new_data.append(np.reshape(data[offset:offset+siz], (d, D, D, D, D))) + new_data.append(np.reshape(data[offset:offset+siz], a.shape)) + offset = offset + siz + new_list._data = new_data + return new_list + + def tot_numel(self): + return sum([a.size for a in self._data]) + + def stop_gradient(self): + new_list = TList(shape=self.size, pattern=self.pattern) + new_list._data = [jax.lax.stop_gradient(a) if len(a)>0 else a for a in self._data] + return new_list + + def _conv_ix(self, ix): + if isinstance(ix, (tuple,list)): + if len(self._loc) == 1: + # shift_i, shift_j = onp.unravel_index(self._loc[0], self.size, order='F') + shift_j, shift_i = np.unravel_index(self._loc[0], self.size) + else: + shift_i, shift_j = self._loc + i = (ix[0] + shift_i) % self.size[0] + j = (ix[1] + shift_j) % self.size[1] + # linear_ix = np.ravel_multi_index((i,j), self.size, order='F') + linear_ix = self._linear_ix(i,j) + else: + linear_ix = ix + return linear_ix + + def _linear_ix(self, i, j): + if self.pattern is not None: + return self.pattern[j][i] + else: + return np.ravel_multi_index((i,j), self.size, order='F') + + def _purge_tmp(self): + self._tmpdata = None + self._hold_write = False + + def __eq__(self, other): + if self._data != other._data: + return False + if self.pattern is not None: + if other.pattern is None: + return False + if not (self.pattern == other.pattern).all(): + return False + return True + + def __getitem__(self, ix): + linear_ix = self._conv_ix(ix) + if self._tmpdata is not None and self._tmpdata[linear_ix] is not None: + return self._tmpdata[linear_ix] + return self._data[linear_ix] + + def __setitem__(self, ix, value): + linear_ix = self._conv_ix(ix) + if self._hold_write: + if self._tmpdata is None: + self._tmpdata = [None] * len(self) + self._tmpdata[linear_ix] = self._data[linear_ix] + self._data[linear_ix] = value + self.mark_changed(linear_ix) + + def __repr__(self): + if self._data is None: + return "TList{}[]" + repr_str = "TList{" + if self._loc is not None: + repr_str += "Loc=" + self._loc.__repr__() + if self.pattern is not None: + repr_str += ",Pat=" + self.pattern.__repr__() + repr_str += ",Size=" + self.size.__repr__() + repr_str += "}[" + for j in range(self.size[1]): + repr_str += "[" + for i in range(self.size[0]): + try: + repr_str += f"{self[i,j].shape}" + except: + repr_str += self[i,j].__repr__() + if i < self.size[0]-1: + repr_str += ", " + if j < self.size[1]-1: + repr_str += "], " + else: + repr_str += "]]" + return repr_str + + @staticmethod + def empty_like(T, empty_obj=None): + if empty_obj is None: + empty_obj = T.empty_obj + return TList(shape=T.size, pattern=T.pattern, empty_obj=empty_obj) + +def isfinite(x): + try: + return len(x) > 0 + except Exception as e: + return np.isfinite(np.array(x)) diff --git a/docs/.buildinfo b/docs/.buildinfo new file mode 100644 index 0000000..1526412 --- /dev/null +++ b/docs/.buildinfo @@ -0,0 +1,4 @@ +# Sphinx build info version 1 +# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done. +config: b36c6381b860d3fa6d2a0c9c335cb328 +tags: 645f666f9bcd5a90fca523b33c5a78b7 diff --git a/docs/.nojekyll b/docs/.nojekyll new file mode 100644 index 0000000..e69de29 diff --git a/docs/_modules/adpeps/ipeps/config.html b/docs/_modules/adpeps/ipeps/config.html new file mode 100644 index 0000000..f468630 --- /dev/null +++ b/docs/_modules/adpeps/ipeps/config.html @@ -0,0 +1,474 @@ + + + + + + + + adpeps.ipeps.config — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +

Source code for adpeps.ipeps.config

+""" Configuration module for iPEPS simulations 
+
+    These settings will be loaded from a configuration file :code:`.yml` file 
+    via the :meth:`from_dict` function
+"""
+
+from typing import Union, Iterable
+import numpy as np
+import math
+import os
+
+D: int                         = None
+""" iPEPS bond dimension """
+
+chi: int                       = None
+""" CTM boundary bond dimension """
+
+model: str                     = None
+""" Model """
+
+model_params: dict             = None
+""" Model parameters """
+
+method: str                    = None
+""" Optimization method """
+
+seed: int                      = 1
+""" Random seed for initial state """
+
+resume: bool                   = False
+""" Resume earlier simulation if found """
+
+base_sim: Union[str, None]     = None
+""" Base simulation """
+
+load_sim: bool                 = None
+""" Load previous (Python) simulation """
+
+max_iterations: int            = 100
+""" Maximum number of optimizer iterations """
+
+disp_level: int                = 1
+""" Display level (`0`: no output) """
+
+pattern: Union[Iterable, None] = None
+""" Unit cell configuration
+    Defined as a 2-D array of integers that label the unique sites in the unit 
+    cell.
+    
+    Example:
+        A 2x2 unit cell with a [AB, BA]-type pattern is defined by
+
+        .. code-block:: python
+
+            pattern            = [
+                [0, 1],
+                [1, 0]
+            ]
+"""
+
+ctm_conv_tol: float            = 1e-10
+""" CTM convergence criterium (singular values norm difference) """
+
+ctm_min_iter: int              = 5
+""" Minimal number of CTM steps """
+
+ctm_max_iter: int              = 20
+""" Maximal number of CTM steps """
+
+flush_output: bool             = False
+""" Passes the :code:`flush    = True` argument to the builtin :code:`print` function
+    when calling the :func:`adpeps.utils.printing.print` function
+
+    Useful when deploying the code to computing clusters and capturing the output 
+    into text files
+"""
+
+out_prefix: str                = ''
+""" Optional prefix for the output file of the simulation
+    
+    Example:
+        :code:`.../{model}_D{D}_X{chi}.npz`
+
+        becomes
+
+        :code:`.../{out_prefix}_{model}_D{D}_X{chi}.npz`
+"""
+
+# Excitation settings
+
+px: float                      = 0 * math.pi
+
+py: float                      = 0 * math.pi
+
+momentum_path: str             = 'Bril1'
+""" Momentum path through the BZ """
+
+filter_null: bool              = False
+
+
[docs]def from_dict(cfg):
+    """ Import config from configuration (`.yml`) file """
+
+    cfg_vars = globals()
+    for name, value in cfg.items():
+        if name in cfg_vars.keys():
+            cfg_vars[name] = value
+        else:
+            raise ValueError(f"Option {name} = {value} not defined in iPEPS config")
+    try:
+        debug_override = os.environ.get("PY_SIM_DEBUG2")
+        if debug_override is not None and int(debug_override) == 1:
+            print("** Debug mode on (PY_SIM_DEBUG = 1) **")
+            cfg_vars['disp_level'] = 2
+            cfg_vars['use_parallel'] = False
+    except:
+        pass

+
+def get_model_params():
+    if model_params is not None:
+        try:
+            return '_'.join([str(p) for p in model_params.values()]) + '_'
+        except AttributeError:
+            return '_'.join([str(p) for p in model_params]) + '_'
+    else:
+        return ''
+
+ +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/_modules/adpeps/ipeps/ctm.html b/docs/_modules/adpeps/ipeps/ctm.html new file mode 100644 index 0000000..489967a --- /dev/null +++ b/docs/_modules/adpeps/ipeps/ctm.html @@ -0,0 +1,859 @@ + + + + + + + + adpeps.ipeps.ctm — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +

Source code for adpeps.ipeps.ctm

+"""
+    Main CTM code
+
+    The individual site and boundary tensors come in a 
+    special list-type object (TList), which has extra 
+    indexing features, such as periodic boundary 
+    conditions and shift contexts
+
+    All ncon contractions are defined in contractions.yaml
+"""
+
+import jax
+import jax.numpy as np
+import time
+from typing import Tuple
+
+import adpeps.ipeps.config as sim_config
+from adpeps.utils.ctmtensors import CTMTensors
+from adpeps.utils.nested import Nested
+from adpeps.utils.tlist import TList, cur_loc, set_pattern
+from adpeps.tensor.contractions import ncon
+from adpeps.tensor.ops import svd, diag_inv
+
+def run_ctm(tensors, chi, conv_fun=None):
+    ctm = CTM(tensors, chi, conv_fun)
+    return ctm()
+
+
[docs]class CTM:
+    """ CTM class """
+
+    def __init__(self, tensors: CTMTensors, chi: int, conv_fun=None):
+        """
+        Args:
+            tensors: input ctmtensors
+            chi: boundary bond dimension
+        """
+
+        self.tensors  = tensors
+        self.chi      = chi
+        self.conv_fun = conv_fun
+        self.tol      = sim_config.ctm_conv_tol # Convergence tolerance (singular values)
+        self.min_iter = sim_config.ctm_min_iter
+        self.max_iter = sim_config.ctm_max_iter
+
+        self.singular_values  = None
+        self.last_convergence = None
+        self.diffs            = [None]
+        self.n_steps          = 0
+        self.last_ctm_time    = None
+        self.convergence      = np.nan
+        self.condition_number = None
+        
+    def __call__(self):
+        while not self.converged:
+            self.show_progress()
+            self.update()
+
+        return self.tensors, self.convergence
+
+
[docs]    def update(self):
+        """ Perform an update of all boundary tensors """
+        start = time.time()
+        self.tensors, s = renormalize(self.tensors, self.chi)
+        end = time.time()
+
+        try:
+            s = jax.lax.stop_gradient(s)
+            s_nz = s[s != 0] / np.max(s)
+            cond_s = np.min(s_nz)
+        except:
+            cond_s = np.nan
+
+        self.n_steps += 1
+        self.singular_values = s
+        self.last_ctm_time = round(end-start, 2)
+        self.condition_number = cond_s

+
+
[docs]    def show_progress(self):
+        """ Print out the current progress """
+        if self.n_steps > 0 and sim_config.disp_level > 0:
+            if self.conv_fun is not None:
+                print(f"  | CTM step {self.n_steps} conv: {self.diffs[-1]:.3e} time: {self.last_ctm_time} obj: {self.convergence:.6f}")
+            else:
+                print(f"  | CTM step {self.n_steps} conv: {self.diffs[-1]:.3e} time: {self.last_ctm_time}")

+
+    @property
+    def converged(self):
+        """ Check convergence with supplied convergence function """
+        if self.conv_fun is not None:
+            s = jax.lax.stop_gradient(self.conv_fun(self.tensors))
+        else:
+            s = self.singular_values
+
+        self.last_convergence = self.convergence
+        self.convergence = s
+        try:
+            diff = np.linalg.norm(self.convergence-self.last_convergence)
+            self.diffs.append(diff)
+        except:
+            diff = np.nan
+
+        if self.n_steps >= self.min_iter and self.diffs[-1] < self.tol:
+            return True
+        elif self.n_steps >= self.max_iter:
+            return True
+        else:
+            return False

+
+
[docs]def renormalize(tensors: CTMTensors, chi: int) -> Tuple[CTMTensors, np.ndarray]:
+    """
+    Performs a CTM iteration
+    Updates all sites in the unit cell
+
+    Args:
+        tensors: input ctmtensors
+        chi: boundary bond dimension
+
+    Returns:
+        A tuple containing
+
+        - **tensors** (*CTMTensors*): updated tensors
+        - **S** (*np.ndarray*): singular values of C1 (for convergence)
+    """
+
+    with set_pattern(tensors.A.pattern):
+        tensors, sl = do_left(tensors, chi)
+        tensors     = do_right(tensors, chi)
+        tensors     = do_top(tensors, chi)
+        tensors     = do_bottom(tensors, chi)
+
+    # Singular values of C1[0,0] - to check for convergence
+    S = sl[0]
+    return (tensors, S)

+
+
+""" 
+    ---------------------
+    Individual left, right, top and bottom moves
+    ---------------------
+
+    Each move consists of a loop through the sites of the unit cell 
+    in which first the projectors are computed and then the boundary 
+    tensors are updated.
+
+    The loops are optimized for readability with a few tricks that are 
+    implemented in the TList or CTMTensors classes:
+
+    - cur_loc(x,y): with this context enabled, all TList objects have a 
+        shift applied in their coordinates.
+        For example:
+
+        A[0,0] = 1
+        A[1,0] = 2
+        with cur_loc(1,0):
+            print(A[0,0]) # => 2 (retrieves element A([0,0]+[1,0]) = A[1,0])
+
+        Using this context, the operations in the inner loops can be written 
+        without reference to the (i,j) loop indices, as if it's just written 
+        for one site in the unit cell.
+
+    - CTMTensors.hold(tensor1, ...): with this context enabled, any values 
+        stored in tensor1 (and other designated tensors) are only put in a 
+        temporary location, so that reading the tensor still yields the 
+        original values. After the context exits, the values will be 
+        overwritten by the temporary values.
+        Example:
+
+        # ts is a CTMTensors object containing site/boundary tensors
+        ts.C1[0,0] = [1]
+        ts.C2[0,0] = [2]
+        with ts.hold('C1'):
+            ts.C1[0,0] = [10]
+            ts.C2[0,0] = [20]
+            print(ts.C1[0,0]) # => [1] since the value [10] is not yet stored
+            print(ts.C2[0,0]) # => [20]
+
+        print(ts.C1[0,0]) # => [10] since the context has exited
+
+        With this context, there is no need to store the updated boundary 
+        tensors in the inner loops in temporary objects (since in CTM each 
+        update step should be performed separately).
+
+    - TList.is_changed(x,y): tracks whether any of the tensors in the TList 
+        have been updated since the last call to TList.reset_changed().
+        This is useful for unit cells with pattern restrictions, so that 
+        boundary tensors that correspond to equivalent sites are only 
+        computed once.
+
+"""
+
+
[docs]def do_left(ts: CTMTensors, chi: int) -> Tuple[CTMTensors, np.ndarray]:
+    """ 
+    Perform left CTM move 
+
+    Args:
+        ts: input tensors
+        chi: boundary bond dimension
+
+    Returns:
+        A tuple containing
+
+        - **tensors** (*CTMTensors*): updated tensors
+        - **sl** (*np.ndarray*): singular values of C1 (for convergence)
+
+    """
+    A = ts.A
+    unit_cell = A.size
+    ts.C1.reset_changed()
+    ts.C4.reset_changed()
+    ts.T4.reset_changed()
+    Pl  = TList(shape=unit_cell) # Upper projectors
+    Plb = TList(shape=unit_cell) # Lower projectors
+    sl  = TList(shape=unit_cell) # Singular values (for convergence check)
+    # Loop over x direction of the unit cell
+    for i in range(A.size[0]): 
+        # Loop over y direction
+        for j in range(A.size[1]): 
+            # Change the relative shift of the lists
+            with cur_loc(i,j): 
+                if not Pl.is_changed(0,1):
+                    Pl[0,1], Plb[0,1], sl[0,1] = get_projectors_left(ts, chi)
+        # Only update the lists after the loop over j is completed
+        with ts.hold('all_C1','all_C4','all_T4'):
+            for j in range(A.size[1]):
+                with cur_loc(i,j):
+                    if not ts.C1.is_changed(0,0):
+                        ts.update(('C1', 'C4', 'T4'), ([0,0],[0,0],[0,0]), renorm_left(ts, Pl, Plb))
+    return ts, sl

+
+
[docs]def do_right(ts: CTMTensors, chi: int) -> CTMTensors:
+    """ 
+    Perform right CTM move 
+
+    Args:
+        ts: input tensors
+        chi: boundary bond dimension
+
+    Returns:
+        ts: updated tensors
+
+    """
+    A = ts.A
+    unit_cell = A.size
+    ts.C2.reset_changed()
+    ts.C3.reset_changed()
+    ts.T2.reset_changed()
+    Pr  = TList(shape=unit_cell)
+    Prb = TList(shape=unit_cell)
+    for i in range(A.size[0]):
+        for j in range(A.size[1]):
+            with cur_loc(i,j):
+                if not Pr.is_changed(0,1):
+                    Pr[0,1], Prb[0,1], _ = get_projectors_right(ts, chi)
+        with ts.hold('all_C2','all_C3','all_T2'):
+            for j in range(A.size[1]):
+                with cur_loc(i,j):
+                    if not ts.C2.is_changed(1,0):
+                        ts.update(('C2', 'C3', 'T2'), ([1,0],[1,0],[1,0]), renorm_right(ts, Pr, Prb))
+    return ts

+
+
[docs]def do_top(ts: CTMTensors, chi: int) -> CTMTensors:
+    """ 
+    Perform top CTM move 
+
+    Args:
+        ts: input tensors
+        chi: boundary bond dimension
+
+    Returns:
+        ts: updated tensors
+
+    """
+    A = ts.A
+    unit_cell = A.size
+    ts.C1.reset_changed()
+    ts.C2.reset_changed()
+    ts.T1.reset_changed()
+    Pt  = TList(shape=unit_cell)
+    Ptb = TList(shape=unit_cell)
+    for j in range(A.size[1]):
+        for i in range(A.size[0]):
+            with cur_loc(i,j):
+                if not Pt.is_changed(0,0):
+                    Pt[0,0], Ptb[0,0], _ = get_projectors_top(ts, chi)
+        with ts.hold('all_C1','all_C2','all_T1'):
+            for i in range(A.size[0]):
+                with cur_loc(i,j):
+                    if not ts.C1.is_changed(-1,0):
+                        ts.update(('C1', 'C2', 'T1'), ([-1,0],[2,0],[0,0]), renorm_top(ts, Pt, Ptb))
+    return ts

+
+
[docs]def do_bottom(ts: CTMTensors, chi: int) -> CTMTensors:
+    """ 
+    Perform bottom CTM move 
+
+    Args:
+        ts: input tensors
+        chi: boundary bond dimension
+
+    Returns:
+        ts: updated tensors
+
+    """
+    A = ts.A
+    unit_cell = A.size
+    ts.C3.reset_changed()
+    ts.C4.reset_changed()
+    ts.T3.reset_changed()
+    Pb  = TList(shape=unit_cell)
+    Pbb = TList(shape=unit_cell)
+    for j in range(A.size[1]):
+        for i in range(A.size[0]):
+            with cur_loc(i,j):
+                if not Pb.is_changed(0,0):
+                    Pb[0,0], Pbb[0,0], _ = get_projectors_bottom(ts, chi)
+        with ts.hold('all_C3','all_C4','all_T3'):
+            for i in range(A.size[0]):
+                with cur_loc(i,j):
+                    if not ts.C3.is_changed(2,1):
+                        ts.update(('C3', 'C4', 'T3'), ([2,1],[-1,1],[0,1]), renorm_bottom(ts, Pb, Pbb))
+    return ts

+
+
+""" 
+    ---------------------
+    Individual left, right, top and bottom projectors
+    ---------------------
+
+    The projectors are computed by contracting a corner of the 
+    system (C-tensor + 2 T-tensors + A and Adagger tensors) 
+    in the top (/left) half with a corner in the bottom (/right) 
+    half and performing an svd
+"""
+
+
[docs]def get_projectors_left(ts: CTMTensors, chi: int
+        ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
+    """ 
+    Returns the left projectors
+    """
+    tensors = (ts.C1[-1,-1],ts.C4[-1,2],ts.T1[0,-1],ts.T3[0,2],ts.T4[-1,0],ts.T4[-1,1],
+            ts.A[0,0], ts.Ad[0,0], ts.A[0,1], ts.Ad[0,1])
+    return _get_projectors_left_impl(*tensors, chi)

+
+def _get_projectors_left_impl(C1,C4,T1,T3,T4u,T4d,Au,Adu,Ad,Add, chi):
+    Cs1 = ncon([C1, T1], 'proj_left_Cs1')
+    Q1  = ncon([Cs1, T4u, Au, Adu], 'proj_left_Q1')
+
+    Cs4 = ncon([C4, T3], 'proj_left_Cs4')
+    Q4  = ncon([Cs4, T4d, Ad, Add], 'proj_left_Q4')
+
+    Q4  = Q4.transpose([3,4,5,0,1,2])
+    return get_projectors(Q1, Q4, chi)
+
+
[docs]def get_projectors_right(ts: CTMTensors, chi: int
+        ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
+    """ 
+    Returns the right projectors
+    """
+    tensors = (ts.C2[2,-1],ts.C3[2,2],ts.T1[1,-1],ts.T2[2,0],ts.T2[2,1],ts.T3[1,2],
+            ts.A[1,0], ts.Ad[1,0], ts.A[1,1], ts.Ad[1,1])
+    return _get_projectors_right_impl(*tensors, chi)

+
+def _get_projectors_right_impl(C2,C3,T1,T2u,T2d,T3,Au,Adu,Ad,Add, chi):
+    Cs2 = ncon([C2, T1], 'proj_right_Cs2')
+    Q2  = ncon([Cs2, T2u, Au, Adu], 'proj_right_Q2')
+
+    Cs3 = ncon([C3, T3], 'proj_right_Cs3')
+    Q3  = ncon([Cs3, T2d, Ad, Add], 'proj_right_Q3')
+
+    Q3  = Q3.transpose([3,4,5,0,1,2])
+    return get_projectors(Q2, Q3, chi)
+
+
[docs]def get_projectors_top(ts: CTMTensors, chi: int
+        ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
+    """ 
+    Returns the top projectors
+    """
+    tensors = (ts.C1[-1,-1],ts.C2[2,-1],ts.T1[0,-1],ts.T1[1,-1],ts.T2[2,0],ts.T4[-1,0],
+            ts.A[0,0], ts.Ad[0,0], ts.A[1,0], ts.Ad[1,0])
+    return _get_projectors_top_impl(*tensors, chi)

+
+def _get_projectors_top_impl(C1,C2,T1l,T1r,T2,T4,Al,Adl,Ar,Adr, chi):
+    Cs1 = ncon([C1, T4], 'proj_top_Cs1')
+    Q1  = ncon([Cs1, T1l, Al, Adl], 'proj_top_Q1')
+
+    Cs2 = ncon([C2, T2], 'proj_top_Cs2')
+    Q2  = ncon([Cs2, T1r, Ar, Adr], 'proj_top_Q2')
+
+    Q2  = Q2.transpose([3,4,5,0,1,2])
+    return get_projectors(Q1, Q2, chi)
+
+
[docs]def get_projectors_bottom(ts: CTMTensors, chi: int
+        ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
+    """ 
+    Returns the bottom projectors
+    """
+    tensors = (ts.C3[2,2],ts.C4[-1,2],ts.T2[2,1],ts.T3[0,2],ts.T3[1,2],ts.T4[-1,1],
+            ts.A[0,1], ts.Ad[0,1], ts.A[1,1], ts.Ad[1,1])
+    return _get_projectors_bottom_impl(*tensors, chi)

+
+def _get_projectors_bottom_impl(C3,C4,T2,T3l,T3r,T4,Al,Adl,Ar,Adr, chi):
+    Cs4 = ncon([C4, T4], 'proj_bottom_Cs4')
+    Q4  = ncon([Cs4, T3l, Al, Adl], 'proj_bottom_Q4')
+
+    Cs3 = ncon([C3, T2], 'proj_bottom_Cs3')
+    Q3  = ncon([Cs3, T3r, Ar, Adr], 'proj_bottom_Q3')
+
+    Q3  = Q3.transpose([3,4,5,0,1,2])
+    return get_projectors(Q4, Q3, chi)
+
+
[docs]def get_projectors(T1: int, T2, chi):
+    """ Contracts the corners together and computes the 
+        projectors by performing an svd
+    """
+    full_chi = T1.shape[3]*T1.shape[4]*T1.shape[5]
+    new_chi  = min(full_chi, chi)
+
+    Rho       = ncon([T1, T2], ([-1,-2,-3,1,2,3], [1,2,3,-4,-5,-6]))
+    Rho_shape = Rho.shape
+    Rho       = np.reshape(Rho, [Rho_shape[0]*Rho_shape[1]*Rho_shape[2], -1])
+    u,s,v     = svd(Rho, new_chi, 'n')
+    u         = np.reshape(u, [Rho_shape[0], Rho_shape[1], Rho_shape[2], -1])
+    v         = np.reshape(v.T, [Rho_shape[3], Rho_shape[4], Rho_shape[5], -1])
+    inv_s     = diag_inv(np.sqrt(s))
+
+    P1      = ncon([T2, v, inv_s], 'proj_P1')
+    P2      = ncon([T1, u, inv_s], 'proj_P2')
+
+    P1      = P1.transpose([3,0,1,2])
+    P2      = P2.transpose([3,0,1,2])
+    return P1, P2, s

+
+
+""" 
+    ---------------------
+    Individual left, right, top and bottom boundary tensor updates
+    ---------------------
+
+    The boundary tensors are updated for one site at a time from the 
+    tensors of the previous iteration with the site tensors and truncated 
+    by using the projectors
+
+    In these functions, the boundary tensors can be wrapped as Nested tensors, 
+    containing both ground-state and excited-state tensors.
+    When using these Nested tensors, all different combinations are computed 
+    automatically.
+    For example:
+
+        Nested({C1,B_C1,Bd_C1,BB_C1}) * Nested({T1,B_T1,Bd_T1,BB_T1}) ->
+            Nested({
+                (C1 * T1),
+                (B_C1 * T1 + C1 * B_T1),
+                (Bd_C1 * T1 + C1 * Bd_T1),
+                (BB_C1 * T1 + B_C1 * Bd_T1 + Bd_C1 * B_T1 + C1 * BB_T1)
+            })
+
+    The phase shifts are only applied to the B and Bd parts of the Nested tensors
+"""
+
+
[docs]def renorm_left(ts: CTMTensors, Pl: np.ndarray, Plb: np.ndarray
+        ) -> Tuple[Nested, Nested, Nested]:
+    """
+
+    """
+    new_T4 = ncon([Plb[0,0], ts.all_T4[-1,0], ts.all_A[0,0], ts.all_Ad[0,0], Pl[0,1]], 'doleft_T4', 
+            normalize=True).shift(-sim_config.px)
+
+    Cs1    = ncon([ts.all_C1[-1,0], ts.all_T1[0,0]], 'doleft_Cs1')
+    new_C1 = ncon([Cs1, Pl[0,1]], 'doleft_C1', normalize=True).shift(-sim_config.px)
+
+    Cs4    = ncon([ts.all_C4[-1,0], ts.all_T3[0,0]], 'doleft_Cs4')
+    new_C4 = ncon([Cs4, Plb[0,0]], 'doleft_C4', normalize=True).shift(-sim_config.px)
+
+    return new_C1, new_C4, new_T4

+
+def renorm_right(ts, Pr, Prb):
+    new_T2 = ncon([Prb[0,0], ts.all_T2[2,0], ts.all_A[1,0], ts.all_Ad[1,0], Pr[0,1]], 'doright_T2', 
+            normalize=True).shift(sim_config.px)
+
+    Cs2    = ncon([ts.all_C2[2,0], ts.all_T1[1,0]], 'doright_Cs2')
+    new_C2 = ncon([Cs2, Pr[0,1]], 'doright_C2', normalize=True).shift(sim_config.px)
+
+    Cs3    = ncon([ts.all_C3[2,0], ts.all_T3[1,0]], 'doright_Cs3')
+    new_C3 = ncon([Cs3, Prb[0,0]], 'doright_C3', normalize=True).shift(sim_config.px)
+
+    return new_C2, new_C3, new_T2
+
+def renorm_top(ts, Pt, Ptb):
+    new_T1 = ncon([Ptb[-1,0], ts.all_T1[0,-1], ts.all_A[0,0], ts.all_Ad[0,0], Pt[0,0]], 'dotop_T1', 
+            normalize=True).shift(-sim_config.py)
+
+    Cs1    = ncon([ts.all_C1[-1,-1], ts.all_T4[-1,0]], 'dotop_Cs1')
+    new_C1 = ncon([Cs1, Pt[-1,0]], 'dotop_C1', normalize=True).shift(-sim_config.py)
+
+    Cs2    = ncon([ts.all_C2[2,-1], ts.all_T2[2,0]], 'dotop_Cs2')
+    new_C2 = ncon([Cs2, Ptb[1,0]], 'dotop_C2', normalize=True).shift(-sim_config.py)
+
+    return new_C1, new_C2, new_T1
+
+def renorm_bottom(ts, Pb, Pbb):
+    new_T3 = ncon([Pbb[-1,0], ts.all_T3[0,2], ts.all_A[0,1], ts.all_Ad[0,1], Pb[0,0]], 'dobottom_T3', 
+            normalize=True).shift(sim_config.py)
+
+    Cs3    = ncon([ts.all_C3[2,2], ts.all_T2[2,1]], 'dobottom_Cs3')
+    new_C3 = ncon([Cs3, Pbb[1,0]], 'dobottom_C3', normalize=True).shift(sim_config.py)
+
+    Cs4    = ncon([ts.all_C4[-1,2], ts.all_T4[-1,1]], 'dobottom_Cs4')
+    new_C4 = ncon([Cs4, Pb[-1,0]], 'dobottom_C4', normalize=True).shift(sim_config.py)
+
+    return new_C3, new_C4, new_T3
+
+ +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/_modules/adpeps/ipeps/ipeps.html b/docs/_modules/adpeps/ipeps/ipeps.html new file mode 100644 index 0000000..f0ad27e --- /dev/null +++ b/docs/_modules/adpeps/ipeps/ipeps.html @@ -0,0 +1,635 @@ + + + + + + + + adpeps.ipeps.ipeps — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +

Source code for adpeps.ipeps.ipeps

+"""
+    iPEPS module for optimization with CTM
+
+    For an example of how to run a simulation see :mod:`adpeps.simulation.run_ipeps_gs`
+
+    The module is initialized from one of the specific 
+    model files, which return the initial boundary and 
+    site tensors
+
+    The list of parameters is set to the elements of the 
+    individual site tensors
+
+    Conventions for indices:
+
+        - Site tensors::
+
+            A: [phys, right, top, left, bottom]
+
+        - Boundary tensors::
+
+            C1: [right, bottom]
+            C2: [left,  bottom]
+            C3: [top,   left]
+            C4: [right, top]
+            T1: [right, left, ket, bra]
+            T2: [top,   bottom, ket, bra]
+            T3: [right, left, ket, bra]
+            T4: [top,   bottom, ket, bra]
+
+
+    Order of boundary tensors::
+
+        C1 - T1 - C2
+        |    |    |
+        T4 - A  - T2
+        |    |    |
+        C4 - T3 - C3
+"""
+
+from functools import partial
+import copy
+
+from jax import random
+import jax
+import jax.numpy as np
+
+from .ctm import run_ctm
+from adpeps.ipeps import evaluation
+from adpeps.ipeps import models
+from adpeps.tensor.contractions import ncon
+from adpeps.utils.ctmtensors import CTMTensors
+from adpeps.utils.printing import print
+from adpeps.utils.tlist import set_pattern, cur_loc, TList
+import adpeps.ipeps.config as sim_config
+
+
[docs]class iPEPS:
+    """ Initialize the iPEPS based on the settings in
+        :mod:`adpeps.ipeps.config`
+    """
+    reinit_env = False
+
+    def __init__(self):
+        # Load model Hamiltonian, observables
+        model = getattr(models, sim_config.model)
+        self.H, self.observables = model.setup()
+
+        # Initialize tensors
+        self.d = self.H.shape[0]
+        A = init_A_tensor(self.d, sim_config.D, sim_config.pattern)
+        A = A.normalize()
+        Ad = A.conj()
+        Cs, Ts = init_ctm_tensors(A, A)
+        self.tensors = CTMTensors(A, Ad, Cs, Ts)
+        self.base_Cs, self.base_Ts = None, None
+
+        # Initialize conv object
+        self.convergence = {}
+
+        self.reinit_env = True
+
+
[docs]    def run(self, params: np.ndarray) -> np.ndarray:
+        """ 
+        Run the simulation
+
+        Args:
+            params: variational parameters
+
+        Returns:
+            energy of iPEPS
+        """
+
+        if params is not None:
+            self.fill(params)
+
+        if self.reinit_env:
+            # Construct new boundary tensors and perform ctm iterations 
+            # until convergence
+            # Note: gradient tracking is disabled for this function, so 
+            # only the ctm steps in the code after this line will be tracked
+            print('Performing CTM pre-steps without tracking')
+            self.converge_boundaries()
+
+        # Perform the ctm routine to obtain updated boundary tensors
+        print('Performing CTM')
+        self.tensors, conv = run_ctm(self.tensors, sim_config.chi, conv_fun=self.compute_energy)
+
+        # Evaluate energy
+        res = self.evaluate()
+
+        # Stop downstream gradient tracking for iPEPS tensors, 
+        # so they become regular arrays that can be saved
+        self.tensors.stop_gradient(only_boundaries=False)
+
+        return res

+
+    def compute_energy(self, tensors):
+        E, _ = evaluation.get_gs_energy(self.H, tensors)
+        return E
+
+
[docs]    def converge_boundaries(self):
+        """ Performs CTM on the boundary tensors until convergence,
+            without gradient tracking 
+        """
+        # Make a non-tracking version of the iPEPS tensors
+        orig_A = copy.deepcopy(self.tensors.A)
+        self.tensors.A = self.tensors.A.stop_gradient()
+        self.tensors.Ad = self.tensors.Ad.stop_gradient()
+
+        # Initialize new boundary tensors
+        Cs, Ts = init_ctm_tensors(self.tensors.A, self.tensors.Ad)
+        self.tensors = CTMTensors(self.tensors.A, self.tensors.Ad, Cs, Ts)
+
+        # Perform CTM update steps on the boundary tensors
+        conv_fun = self.compute_energy
+        self.tensors.stop_gradient()
+        self.tensors, conv = run_ctm(self.tensors, sim_config.chi, conv_fun=conv_fun)
+        self.tensors.stop_gradient()
+
+        self.save_boundary_tensors()
+
+        # Restore the original (tracking) site tensors
+        self.tensors.A = orig_A
+        self.tensors.Ad = orig_A.conj()

+
+    def save_boundary_tensors(self):
+        self.base_Cs = copy.deepcopy(self.tensors.Cs)
+        self.base_Ts = copy.deepcopy(self.tensors.Ts)
+
+    def evaluate(self):
+        E = self.compute_energy(self.tensors)
+        print('Energy:', jax.lax.stop_gradient(E).item())
+        return E
+
+
+    """ Input/output methods """
+
+
[docs]    def numel(self):
+        """ Number of variational parameters """
+        return self.tensors.A.tot_numel()

+    
+
[docs]    def parse_elements(self, elements):
+        """ Returns site tensors filled with the input elements """
+        assert elements.size == self.numel(), f"Size of input vector ({elements.size}) does not \
+                match the number of parameters of the iPEPS ({self.numel()})"
+        return self.tensors.A.fill(elements, self.d, sim_config.D)

+
+
[docs]    def fill(self, A):
+        """ Fill the site tensors with the elements
+            The elements can be specified either as a list of (d,D,D,D,D)-dimensional 
+            arrays or one 1-dimensional array of all elements concatenated
+        """
+        if isinstance(A, np.ndarray) and A.ndim == 1:
+            # Input is vector of elements
+            A               = self.parse_elements(A)
+            self.tensors.A  = A
+            self.tensors.Ad = A.conj()
+        else:
+            # Input is a list of arrays
+            assert len(A) == len(self.tensors.A), "Number of input tensors does not match \
+                    the number of site tensors of the iPEPS"
+            for i in range(len(self.tensors.A)):
+                self.tensors.A._data[i] = A[i]
+                self.tensors.Ad._data[i] = A[i].conj()

+
+
+
[docs]class iPEPS_exci(iPEPS):
+    """ Excited-state variant of the iPEPS class
+    """
+
+    reinit_env = False
+
+    def __init__(self):
+        super().__init__()
+        self.substract_gs_energy()
+
+    def normalize_gs(self):
+        nrm, nrm0, envBs, nrms0 = evaluation.compute_exci_norm(self.tensors)
+        print(f"GS norm {nrms0[0]}", level=1)
+        self.tensors.A._data    = [a/np.sqrt(np.abs(nrms0[i])) for i, a in enumerate(self.tensors.A)]
+        self.tensors.Ad         = self.tensors.A.conj()
+        nrm, nrm0, envBs, nrms0 = evaluation.compute_exci_norm(self.tensors)
+        print(f"GS norm {nrm0}", level=1)
+
+    def substract_gs_energy(self):
+        E, _ = evaluation.get_gs_energy(self.H, self.tensors)
+        E = E/2
+        print(f"Substracting {E} from Hamiltonian", level=1)
+        self.H = self.H - E * np.reshape(np.eye(self.H.shape[0]**2), self.H.shape)
+        # self.H = np.reshape(np.eye(self.H.shape[0]**2), self.H.shape)
+
+    def evaluate(self):
+        E = evaluation.get_all_energy(self.H, self.tensors)
+        nrm, _, envBs, _ = evaluation.compute_exci_norm(self.tensors)
+        print('Energies:', jax.lax.stop_gradient(E[3]), jax.lax.stop_gradient(E[0]), level=0)
+        print('Norm:', jax.lax.stop_gradient(nrm), level=0)
+        return E[3], envBs
+
+    def run_gc(self, *args):
+        res, _ = self.run(*args)
+        return res
+
+    def compute_energy(self, tensors):
+        E = evaluation.get_all_energy(self.H, tensors)
+        nrm, *_ = evaluation.compute_exci_norm(tensors)
+        print('Energies:', jax.lax.stop_gradient(E[3]), jax.lax.stop_gradient(E[0]), level=2)
+        print('Norm:', jax.lax.stop_gradient(nrm), level=2)
+        print('Normalized E:', jax.lax.stop_gradient(E[3])/jax.lax.stop_gradient(nrm), level=2)
+        return E[3] / nrm
+
+    def compute_orth_basis(self):
+        return evaluation.get_orth_basis(self.tensors)
+
+
+    """ Input/output methods """
+
+
[docs]    def fill(self, B):
+        if isinstance(B, np.ndarray) and B.ndim == 1:
+            # Input is vector of elements
+            B               = self.parse_elements(B)
+            self.tensors.B  = B
+            self.tensors.Bd = B.conj()
+        else:
+            for i in range(len(self.tensors.A._data)):
+                self.tensors.B._data[i] = B[i]
+                self.tensors.Bd._data[i] = B[i].conj()

+
+
+
[docs]def init_A_tensor(d, D, pattern):
+    """
+        The elements will be randomized based on sim_config.seed
+    """
+    with set_pattern(pattern):
+        A = TList()
+
+    key = random.PRNGKey(sim_config.seed)
+    for i in range(A.size[0]):
+        for j in range(A.size[1]):
+            with cur_loc(i,j):
+                if not A.is_changed(0,0):
+                    key, subkey = random.split(key)
+                    A[0,0] = random.normal(key, (d,D,D,D,D))
+    return A

+
+
[docs]def init_ctm_tensors(A, Ad):
+    """
+    Returns initital boundary T-tensors based on the unit cell tensors and 
+    empty trivial boundary C-tensors
+    """
+    unit_cell = A.size
+    D         = A[0].shape[1]
+
+    Cs   = [TList(shape=unit_cell, pattern=A.pattern) for _ in range(4)]
+    Ts   = [TList(shape=unit_cell, pattern=A.pattern) for _ in range(4)]
+
+    for i in range(A.size[0]):
+        for j in range(A.size[1]):
+            with cur_loc(i,j):
+                Cs[0][0,0] = np.expand_dims(np.array([1.]), axis=(1))
+                Cs[1][0,0] = np.expand_dims(np.array([1.]), axis=(1))
+                Cs[2][0,0] = np.expand_dims(np.array([1.]), axis=(1))
+                Cs[3][0,0] = np.expand_dims(np.array([1.]), axis=(1))
+                Ts[0][0,0] = np.expand_dims(ncon([A[0,0], Ad[0,0]], ([1,2,3,4,-1], [1,2,3,4,-2])), axis=(0,1))
+                Ts[1][0,0] = np.expand_dims(ncon([A[0,0], Ad[0,0]], ([1,2,3,-1,4], [1,2,3,-2,4])), axis=(0,1))
+                Ts[2][0,0] = np.expand_dims(ncon([A[0,0], Ad[0,0]], ([1,2,-1,3,4], [1,2,-2,3,4])), axis=(0,1))
+                Ts[3][0,0] = np.expand_dims(ncon([A[0,0], Ad[0,0]], ([1,-1,2,3,4], [1,-2,2,3,4])), axis=(0,1))
+    return Cs, Ts

+
+ +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/_modules/adpeps/ipeps/models/heisenberg.html b/docs/_modules/adpeps/ipeps/models/heisenberg.html new file mode 100644 index 0000000..36f3dc2 --- /dev/null +++ b/docs/_modules/adpeps/ipeps/models/heisenberg.html @@ -0,0 +1,376 @@ + + + + + + + + adpeps.ipeps.models.heisenberg — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +

Source code for adpeps.ipeps.models.heisenberg

+""" 2D Heisenberg model """
+
+import jax.numpy as np
+
+from .common import sigmaz, sigmap, sigmam
+from adpeps.utils.tlist import set_pattern
+import adpeps.ipeps.config as sim_config
+
+name = "Heisenberg spin-1/2 model"
+
+
[docs]def setup():
+    """ Returns the Hamiltonian """
+    H = make_hamiltonian(**sim_config.model_params)
+
+    obs  = None
+    return H, obs

+
+
[docs]def make_hamiltonian(J=1):
+    """ Heisenberg model """
+    H = tprod(sigmaz, sigmaz) / 4 + \
+            tprod(sigmap, sigmam) / 2 + \
+            tprod(sigmam, sigmap) / 2
+    H = J * H
+    return H

+
+def tprod(a,b):
+    return np.outer(a,b).reshape([2,2,2,2], order='F').transpose([0,2,1,3])
+
+ +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/_modules/adpeps/simulation/run_ipeps_exci.html b/docs/_modules/adpeps/simulation/run_ipeps_exci.html new file mode 100644 index 0000000..30ec9c0 --- /dev/null +++ b/docs/_modules/adpeps/simulation/run_ipeps_exci.html @@ -0,0 +1,590 @@ + + + + + + + + adpeps.simulation.run_ipeps_exci — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +

Source code for adpeps.simulation.run_ipeps_exci

+""" Main excited-state executable script
+
+    Note:
+        The simulations are intended to be used by calling the package 
+        directly via :code:`python -m adpeps ...`, as described in 
+        :ref:`notes/start`
+"""
+
+from jax import grad, jit, vmap, value_and_grad
+from jax import random
+from jax.scipy.optimize import minimize
+from jax.test_util import check_grads
+from scipy import optimize
+from scipy.linalg import eigh, eig
+from yaml import safe_load, dump
+import jax
+import jax.numpy as np
+import numpy as onp
+
+from adpeps.ipeps.ipeps import iPEPS, iPEPS_exci
+from adpeps.ipeps.make_momentum_path import make_momentum_path
+from adpeps.utils import io
+from adpeps.utils.printing import print
+from adpeps.ipeps.evaluation import filter_null_modes
+import adpeps.ipeps.config as sim_config
+
+
[docs]def run(config_file: str, momentum_ix: int):
+    """ Start the simulation
+
+        Args:
+            config_file: filename of the configuration file
+            momentum_ix: index of the point in momentum space
+    """
+
+    print(config_file)
+    with open(config_file) as f:
+        cfg = safe_load(f)
+
+    # Show options
+    print(dump(cfg))
+
+    sim_config.from_dict(cfg)
+    base_file = io.get_exci_base_file()
+    if not base_file.exists():
+        print(f"Base file {base_file} not found. Prepare the simulation first by \
+                running with option '-i'")
+        return
+
+    sim = iPEPSExciSimulation(config_file, momentum_ix)
+    output_folder = io.get_exci_folder()
+    output_folder.mkdir(parents=True, exist_ok=True)
+    kxs, kys = make_momentum_path(sim_config.momentum_path)
+    sim_config.px = kxs[momentum_ix]
+    sim_config.py = kys[momentum_ix]
+    output_file = io.get_exci_file(momentum_ix)
+    print(f"Output: {output_file}", level=2)
+    basis_size = sim.basis_size
+    res_dtype = np.complex128
+    H = onp.zeros((basis_size,basis_size), dtype=res_dtype)
+    N = onp.zeros((basis_size,basis_size), dtype=res_dtype)
+
+    for m in range(basis_size):
+        grad_H, grad_N = sim(m)
+        H[:,m] = grad_H
+        N[:,m] = grad_N
+        onp.savez(output_file, H=H, N=N)
+
+    print(H)
+    print(N)
+    onp.savez(output_file, H=H, N=N)
+    print('Done')
+    print(f"Saved to {output_file}")

+
+def prepare(config_file):
+    with open(config_file) as f:
+        cfg = safe_load(f)
+    sim_config.from_dict(cfg)
+    base_file = io.get_exci_base_file()
+    print(base_file)
+    peps = iPEPS()
+
+    gs_file = io.get_gs_file()
+    loaded_sim = np.load(gs_file, allow_pickle=True)
+    peps       = loaded_sim['peps'].item()
+
+    sim_config.ctm_max_iter = 30
+    sim_config.ctm_conv_tol = 1e-12
+
+    # Converge GS boundary tensors
+    peps.converge_boundaries()
+
+    # Convert to excitations iPEPS
+    peps.__class__ = iPEPS_exci
+
+    # Normalize the ground-state tensors such that the state has norm 1
+    peps.normalize_gs()
+
+    # Shift the Hamiltonian by the ground-state energy 
+    # The excited state energy is then relative to the ground state
+    peps.substract_gs_energy()
+
+    # Prepare an orthonormal basis with respect to the ground state
+    print('Preparing orthonormal basis')
+    basis = peps.compute_orth_basis()
+
+    print(f"Saving base to {base_file}")
+    np.savez(base_file, peps=peps, basis=basis)
+
+def evaluate_single(config_file, momentum_ix):
+    def _compute_ev_red_basis(H, N, P, n):
+        P = P[:,:n]
+        N2 = P.T.conjugate() @ N @ P
+        H2 = P.T.conjugate() @ H @ P
+        N2 = 0.5 * (N2 + N2.T.conjugate())
+        H2 = 0.5 * (H2 + H2.T.conjugate())
+        ev, _ = eig(H2, N2)
+        return sorted(ev.real)
+
+
+    with open(config_file) as f:
+        cfg = safe_load(f)
+
+    sim_config.from_dict(cfg)
+    kxs, kys = make_momentum_path(sim_config.momentum_path)
+    sim_config.px = kxs[momentum_ix]
+    sim_config.py = kys[momentum_ix]
+    base_file = io.get_exci_base_file()
+    base_sim = np.load(base_file, allow_pickle=True)
+    output_file = io.get_exci_file(momentum_ix)
+    print(output_file)
+    dat = np.load(output_file)
+    H, N = dat['H'], dat['N']
+    basis = base_sim['basis']
+    peps  = base_sim['peps'].item()
+
+    # basis = basis.T @ filter_null_modes(peps.tensors, basis)
+    # print(basis.shape)
+    # print(N.shape)
+    # N = basis.T @ N @ basis
+    # H = basis.T @ H @ basis
+    # H = H.conjugate()
+
+    H = 0.5 * (H + H.T.conjugate())
+    N = 0.5 * (N + N.T.conjugate())
+    ev_N, P = np.linalg.eig(N)
+    idx = ev_N.real.argsort()[::-1]
+    ev_N = ev_N[idx]
+    selected = (ev_N/ev_N.max()) > 1e-3
+    P = P[:,idx]
+    P = P[:,selected]
+    N2 = P.T.conjugate() @ N @ P
+    H2 = P.T.conjugate() @ H @ P
+    N2 = 0.5 * (N2 + N2.T.conjugate())
+    H2 = 0.5 * (H2 + H2.T.conjugate())
+    ev, vectors = eig(H2, N2)
+    ixs = np.argsort(ev)
+    ev = ev[ixs]
+    vectors = vectors[:,ixs]
+            
+    return sorted(ev.real)
+
+def evaluate(config_file, momentum_ix):
+    if momentum_ix != -2:
+        return evaluate_single(config_file, momentum_ix)
+
+    with open(config_file) as f:
+        cfg = safe_load(f)
+
+    # Show options
+    print(dump(cfg))
+
+    sim_config.from_dict(cfg)
+    kxs, kys = make_momentum_path(sim_config.momentum_path)
+
+    import matplotlib.pyplot as plt
+    evs = []
+    for ix in range(len(kxs)):
+        try:
+            ev = evaluate_single(config_file, ix)
+        except:
+            ev = [np.nan]
+        evs.append(ev[0])
+    plt.plot(evs, '--+')
+    plt.show()
+
+
+
+
[docs]class iPEPSExciSimulation:
+    """ Simulation class for the excited-state simulation 
+
+        Call an instance of this class directly to start the simulation
+    """
+    def __init__(self, config_file, momentum_ix):
+        self.config_file = config_file
+        self.momentum_ix = momentum_ix
+
+    @property
+    def basis_size(self):
+        with open(self.config_file) as f:
+            cfg = safe_load(f)
+        sim_config.from_dict(cfg)
+        base_file = io.get_exci_base_file()
+        base_sim = np.load(base_file, allow_pickle=True)
+        basis = base_sim['basis']
+        return basis.shape[1]
+
+    def __call__(self, ix, v=None):
+        print(f"Starting simulation of basis vector {ix+1}/{self.basis_size}")
+        with open(self.config_file) as f:
+            cfg = safe_load(f)
+        sim_config.from_dict(cfg)
+
+        base_file = io.get_exci_base_file()
+        base_sim = np.load(base_file, allow_pickle=True)
+        basis = np.complex_(base_sim['basis'])
+        peps  = base_sim['peps'].item()
+        if v is None:
+            v = basis[:,ix]
+        res, grad_H = value_and_grad(peps.run, has_aux=True)(v)
+        grad_H = grad_H.conj()
+        print('Res', res, level=2)
+        grad_N = res[1].pack_data()
+        print('Grad H', grad_H, level=2)
+        print('Grad N', grad_N, level=2)
+        print(f"========== \nFinished basis vector {ix+1}/{self.basis_size} \n")
+        return basis.T @ jax.lax.stop_gradient(grad_H), basis.T @ jax.lax.stop_gradient(grad_N)
+
+    def check_grads(self, A=None):
+        with open(self.config_file) as f:
+            cfg = safe_load(f)
+        sim_config.from_dict(cfg)
+
+        base_file = io.get_exci_base_file()
+        base_sim = np.load(base_file, allow_pickle=True)
+        basis = np.complex_(base_sim['basis'])
+        peps  = base_sim['peps'].item()
+        print('Checking gradient')
+        # peps.fill(A)
+        check_grads(peps.run_gc, (A,), order=1, modes='rev')
+        print('Done check')

+
+
+ +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/_modules/adpeps/simulation/run_ipeps_gs.html b/docs/_modules/adpeps/simulation/run_ipeps_gs.html new file mode 100644 index 0000000..baa257e --- /dev/null +++ b/docs/_modules/adpeps/simulation/run_ipeps_gs.html @@ -0,0 +1,521 @@ + + + + + + + + adpeps.simulation.run_ipeps_gs — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +

Source code for adpeps.simulation.run_ipeps_gs

+""" Main ground-state executable script
+
+    Note:
+        The simulations are intended to be used by calling the package 
+        directly via :code:`python -m adpeps ...`, as described in 
+        :ref:`notes/start`
+"""
+
+from jax import grad, jit, vmap, value_and_grad
+from jax import random
+from jax.scipy.optimize import minimize
+from jax.test_util import check_grads
+from scipy import optimize
+from yaml import safe_load, dump
+import jax
+import jax.numpy as np
+import numpy as onp
+
+from adpeps.ipeps.ipeps import iPEPS, iPEPS_exci
+from adpeps.utils import io
+from adpeps.utils.printing import print
+import adpeps.ipeps.config as sim_config
+
+
[docs]def run(config_file: str):
+    """ Start the simulation
+
+        Args:
+            config_file: filename of the configuration file
+    """
+
+    energies   = []
+    gradnorms  = []
+    def verbose(xk, step_size=None):
+        """ Output printing function """
+        try:
+            energies.append(obj.cached_out)
+            gradnorms.append(obj.gradnrm)
+        except:
+            pass
+        print(' ')
+        print(' # ======================== #')
+        print(' #      Step completed      #')
+        print(' # ======================== #')
+        print(' ')
+        [print(' Step %3d  E: %.12f  |grad|: %2.8g' % (i,E,gradnorms[i])) for i,E in enumerate(energies)]
+        print('\n')
+        # np.savez(output_file, peps=peps, v=xk, gradnorms=gradnorms, energies=energies)
+
+    print('Running')
+    print(config_file)
+    with open(config_file) as f:
+        cfg = safe_load(f)
+
+    # Show options
+    print(dump(cfg))
+
+    # Load the configuration file into the sim_config object
+    sim_config.from_dict(cfg)
+
+    # Initialize the iPEPS
+    peps = iPEPS()
+
+    output_file = io.get_gs_file()
+    print(f"Output file {output_file}")
+
+    if sim_config.resume and output_file.exists():
+        loaded_sim = np.load(output_file, allow_pickle=True)
+        peps       = loaded_sim['peps'].item()
+        v          = loaded_sim['v']
+        gradnorms  = list(loaded_sim['gradnorms'])
+        energies   = list(loaded_sim['energies'])
+        print("Resuming existing simulation")
+        verbose(v)
+    else:
+        print("Starting new simulation")
+        key = random.PRNGKey(sim_config.seed)
+        v   = random.normal(key, (peps.numel(),))
+        v   = v / np.max(np.abs(v))
+
+    obj = Objective(peps)
+
+    # Call SciPy's optimization function
+    obj.return_gn = False
+    xL = optimize.minimize(obj.out, v, method=sim_config.method, jac=obj.jac,
+            callback=verbose, options={'gtol': 1e-6, 'disp': True,
+                'maxiter':sim_config.max_iterations})

+
+
[docs]class Objective:
+    """ Class containing the objective function for the optimizer
+    """
+
+    def __init__(self, peps: iPEPS):
+        """
+        Args:
+            peps: iPEPS object to be optimized
+        """
+        self.cached_v   = None
+        self.cached_out = None
+        self.cached_jac = None
+
+        self.peps       = peps
+        """ iPEPS object """
+
+        self.fun        = peps.run
+        """ Objective function - CTM iterations until convergence 
+            followed by the evaluation of the energy 
+        """
+        self.return_gn  = True
+
+    @property
+    def gradnrm(self):
+        """ Norm of the gradient """
+        return np.linalg.norm(self.cached_jac)
+
+
[docs]    def jac(self, v: np.ndarray) -> np.ndarray:
+        """ Computes the vector-Jacobian product (gradient) of the
+            iPEPS at the current point :attr:`v` in parameter space
+
+            This function is designed to work with optimizers that make separate 
+            calls to the objective function and the gradient, by caching both.
+
+            Args:
+                v: input variational parameters for the site tensors of 
+                    the iPEPS
+
+            Returns:
+                gradient of the iPEPS with respect to the input parameters :attr:`v`
+        """
+
+        # Cast the regular numpy array into a Jax numpy array for gradient tracking
+        v = np.array(v)
+        v = v / np.max(np.abs(v))
+
+        if (self.cached_jac is not None and self.cached_v is not None 
+                and np.linalg.norm(v - self.cached_v) < 1e-14):
+            return self.cached_jac
+
+        # Call the forward + backward pass iPEPS code
+        o, g = value_and_grad(self.fun)(v)
+
+        # Convert to regular Numpy arrays so they can be passed to the optimizer 
+        # and stored without any tracking information by Jax
+        o = onp.array(o)
+        v = onp.array(v)
+        g = onp.array(g)
+
+        # Cache the results
+        self.cached_v   = v
+        self.cached_out = o
+        self.cached_jac = g
+
+        if self.return_gn:
+            return g, self.gradnrm
+        else:
+            return g

+
+
[docs]    def out(self, v):
+        """ Computes the objective function (energy) of the iPEPS
+
+            Since many optimizers make separate calls to the objective function 
+            and the gradient, but usually require both results for any given 
+            parameter vector v, this function calls the gradient as well.
+
+            Args:
+                v: input variational parameters for the site tensors of 
+                    the iPEPS
+
+            Returns:
+                energy of the iPEPS at the point :attr:`v` in parameter space
+        """
+        if self.cached_v is not None and np.linalg.norm(v - self.cached_v) < 1e-14:
+            return self.cached_out
+        else:
+            self.jac(v)
+            return self.cached_out

+
+    def check_grads(self, A=None):
+        print('Checking gradient')
+        self.peps.fill(A)
+        self.peps.converge_boundaries()
+        check_grads(self.peps.run, (A,), order=1, modes='rev')
+        print('Done check')

+
+
+ +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/_modules/adpeps/utils/ctmtensors.html b/docs/_modules/adpeps/utils/ctmtensors.html new file mode 100644 index 0000000..c30f7a6 --- /dev/null +++ b/docs/_modules/adpeps/utils/ctmtensors.html @@ -0,0 +1,512 @@ + + + + + + + + adpeps.utils.ctmtensors — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +

Source code for adpeps.utils.ctmtensors

+""" Contains utility class that contains all iPEPS tensors """
+
+from dataclasses import dataclass, field, fields, replace, asdict
+from functools import partial
+from typing import List
+
+from .empty_tensor import EmptyT
+from .nested import Nested
+from .tlist import TList, hold_write
+
+
[docs]@dataclass
+class CTMTensors:
+    """ 
+    This is a utility class that contains all tensors related to an iPEPS.
+    In effect, this forms a representation of the full state, including 
+    the site tensors with variational parameters, the boundary tensors 
+    generated by CTM and the projectors.
+
+    There are several fields of this dataclass that are generated 
+    automatically, which provide convenient wrappers for the tensors.
+
+    For example, the :attr:`CTMTensors.A` field returns the site tensors 
+    (contained in a :class:`adpeps.utils.tlist.TList`)
+    """
+    A:     TList
+    Ad:    TList
+    Cs:    List[TList] = field(default_factory=list)
+    Ts:    List[TList] = field(default_factory=list)
+
+    B:     TList = field(default=None, metadata={'init_tlist': True})
+    Bd:    TList = field(default=None, metadata={'init_tlist': True})
+    B_Cs:  List[TList] = field(default=None, metadata={'init_tlists': True})
+    B_Ts:  List[TList] = field(default=None, metadata={'init_tlists': True})
+    Bd_Cs: List[TList] = field(default=None, metadata={'init_tlists': True})
+    Bd_Ts: List[TList] = field(default=None, metadata={'init_tlists': True})
+    BB_Cs: List[TList] = field(default=None, metadata={'init_tlists': True})
+    BB_Ts: List[TList] = field(default=None, metadata={'init_tlists': True})
+
+    Pl:    TList  = None
+    Pr:    TList  = None
+    Pt:    TList  = None
+    Pb:    TList  = None
+    Plb:   TList  = None
+    Prb:   TList  = None
+    Ptb:   TList  = None
+    Pbb:   TList  = None
+
+    observables: List = field(default_factory=list)
+
+    def _get_field_item(self, fieldname=None, ix=None):
+        return getattr(self, fieldname).__getitem__(ix)
+
+    def _get_field_nested_item(self, fieldname=None, ix=None):
+        return getattr(self, fieldname)(ix)
+
+    def _set_field_nested_item(self, fieldname=None, ix=None, value=None):
+        return getattr(self, f"{fieldname}_set")(ix, value)
+
+    def hold(self, *fields):
+        def _convert_all(f):
+            if f.startswith('all_'):
+                f = f[4:]
+                return [f, f"B_{f}", f"Bd_{f}", f"BB_{f}"]
+            else:
+                return (f,)
+        fields = [field for fs in [_convert_all(f) for f in fields] for field in fs]
+        tensors = tuple([getattr(self, field) for field in fields])
+        return hold_write(*tensors)
+
+    def __post_init__(self):
+        base_tlist = self.A
+        for f in fields(self):
+            try:
+                if getattr(self, f.name) is None and f.metadata['init_tlist']:
+                    setattr(self, f.name, TList.empty_like(base_tlist, empty_obj=EmptyT()))
+            except KeyError:
+                pass
+            try:
+                if getattr(self, f.name) is None and f.metadata['init_tlists']:
+                    setattr(self, f.name, [TList.empty_like(base_tlist, empty_obj=EmptyT()) for _ in range(4)])
+            except KeyError:
+                pass
+
+    def all_Cs(self, ix):
+        base_tlist = self.A
+        res = TList.empty_like(base_tlist, empty_obj=EmptyT())
+        for i in range(len(res._data)):
+            res._data[i] = Nested([self.Cs[ix][i], self.B_Cs[ix][i], 
+                self.Bd_Cs[ix][i], self.BB_Cs[ix][i]])
+        return res
+
+    def all_Ts(self, ix):
+        base_tlist = self.A
+        res = TList.empty_like(base_tlist, empty_obj=EmptyT())
+        for i in range(len(res._data)):
+            res._data[i] = Nested([self.Ts[ix][i], self.B_Ts[ix][i], 
+                self.Bd_Ts[ix][i], self.BB_Ts[ix][i]])
+        return res
+
+    def update(self, fieldnames, ixs, values):
+        if isinstance(fieldnames, str):
+            fieldnames = (fieldnames,)
+            values = (values,)
+            ixs = (ixs,)
+        for i,f in enumerate(fieldnames):
+            value = values[i]
+            ix = ixs[i]
+            assert isinstance(value, Nested), "Use the all_Ci setter only with Nested tensors"
+            getattr(self, f)[ix] = value[0]
+            getattr(self, f"B_{f}")[ix] = value[1]
+            getattr(self, f"Bd_{f}")[ix] = value[2]
+            getattr(self, f"BB_{f}")[ix] = value[3]
+
+    @property
+    def all_A(self):
+        base_tlist = self.A
+        res = TList.empty_like(base_tlist, empty_obj=EmptyT())
+        for i in range(len(res._data)):
+            res._data[i] = Nested([self.A._data[i], self.B._data[i], 
+                EmptyT(), EmptyT()])
+        return res
+
+    @property
+    def all_Ad(self):
+        base_tlist = self.A
+        res = TList.empty_like(base_tlist, empty_obj=EmptyT())
+        for i in range(len(res._data)):
+            res._data[i] = Nested([self.Ad._data[i], EmptyT(),
+                self.Bd._data[i], EmptyT()])
+        return res
+
+    def stop_gradient(self, only_boundaries=True):
+        for i in range(4):
+            self.Cs[i] = self.Cs[i].stop_gradient()
+            self.Ts[i] = self.Ts[i].stop_gradient()
+            self.B_Cs[i] = self.B_Cs[i].stop_gradient()
+            self.B_Ts[i] = self.B_Ts[i].stop_gradient()
+            self.Bd_Cs[i] = self.Bd_Cs[i].stop_gradient()
+            self.Bd_Ts[i] = self.Bd_Ts[i].stop_gradient()
+            self.BB_Cs[i] = self.BB_Cs[i].stop_gradient()
+            self.BB_Ts[i] = self.BB_Ts[i].stop_gradient()
+        if not only_boundaries:
+            self.A = self.A.stop_gradient()
+            self.Ad = self.Ad.stop_gradient()
+            self.B = self.B.stop_gradient()
+            self.Bd = self.Bd.stop_gradient()

+
+def _wrap_f(self, fieldname=None, ix=None):
+    return self._get_field_item(fieldname, ix)
+
+def _wrap_nested_f(self, fieldname=None, ix=None):
+    return self._get_field_nested_item(fieldname, ix)
+
+def _wrap_nested_f_set(self, value, fieldname=None, ix=None):
+    return self._set_field_nested_item(fieldname, ix, value)
+
+attrs = ['Cs', 'Ts', 'B_Cs', 'B_Ts', 'Bd_Cs', 'Bd_Ts', 'BB_Cs', 'BB_Ts']
+for attr in attrs:
+    for i in range(4):
+        new_attr = property(partial(_wrap_f, fieldname=attr, ix=i))
+        # new_attr.__doc__ = f"Boundary tensors `{attr}` computed by CTM"
+        new_attr.__doc__ = ":meta private:"
+        setattr(CTMTensors, f"{attr[:-1]}{i+1}", new_attr)
+attrs = ['all_Cs', 'all_Ts']
+for attr in attrs:
+    for i in range(4):
+        new_attr = property(partial(_wrap_nested_f, fieldname=attr, ix=i),
+                partial(_wrap_nested_f_set, fieldname=attr, ix=i))
+        new_attr.__doc__ = ":meta private:"
+        # new_attr.__doc__ = ":class:`adpeps.utils.tlist.TList` containing all versions \
+        #         (only ground-state, ground state + one `B` tensor, ground state \
+        #         + one `Bdagger` tensor, ground state + one `B` tensor + one `Bdagger`\
+        #         tensor) of the boundary tensors."
+        setattr(CTMTensors, f"{attr[:-1]}{i+1}", new_attr)
+
+ +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/_modules/adpeps/utils/empty_tensor.html b/docs/_modules/adpeps/utils/empty_tensor.html new file mode 100644 index 0000000..e21ae04 --- /dev/null +++ b/docs/_modules/adpeps/utils/empty_tensor.html @@ -0,0 +1,426 @@ + + + + + + + + adpeps.utils.empty_tensor — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +

Source code for adpeps.utils.empty_tensor

+""" Contains utility class that represents a 'zero' (empty) tensor object """
+
+import jax.numpy as np
+
+
[docs]class EmptyT:
+    """ Empty tensor utility class, which can be used to represent a  
+        'zero' tensor.
+
+        The operations involving this type of tensor will return the expected 
+        results, such as (Tensor * EmptyT -> EmptyT), removing the need for 
+        checking if a tensor is empty in the part of the code where the 
+        operation is called.
+    """
+    tag = None
+
+    def __repr__(self):
+        return "<empty>"
+
+    def __add__(self, other):
+        return other
+
+    def __radd__(self, other):
+        return other
+
+    def __sub__(self, other):
+        return other
+
+    def __rsub__(self, other):
+        return other
+
+    def __mul__(self, other):
+        return self
+
+    def __neg__(self):
+        return self
+
+    def __rmul__(self, other):
+        if isinstance(other, int):
+            return [self for _ in range(other)]
+        else:
+            return self
+
+    def __truediv__(self, other):
+        return self
+
+    def copy(self):
+        return self
+
+    def to_real(self):
+        return self
+
+    @property
+    def real(self):
+        return self
+
+    @property
+    def data(self):
+        return []
+
+    def transpose(self, *args):
+        return self
+
+    def __rtruediv__(self, other):
+        return self
+
+    def __len__(self):
+        return 0
+
+    def __array__(self):
+        return np.array([])
+
+    def item(self):
+        return self
+
+    def __getitem__(self, ix):
+        return self
+
+    def mult(self, other, *args):
+        return self
+
+    def to_complex(self):
+        return self
+
+    def complex(self):
+        return False
+
+    def is_finite(self):
+        return True

+
+ +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/_modules/adpeps/utils/nested.html b/docs/_modules/adpeps/utils/nested.html new file mode 100644 index 0000000..e137bcd --- /dev/null +++ b/docs/_modules/adpeps/utils/nested.html @@ -0,0 +1,499 @@ + + + + + + + + adpeps.utils.nested — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +

Source code for adpeps.utils.nested

+""" Contains utility class that represents a collection of tensors of 
+    different types, with operations that can be applied to all 
+    contained tensors at once
+"""
+
+import cmath
+import jax.numpy as np
+
+from adpeps.types import TensorType
+
+
+
[docs]class Nested:
+    """ This is a helper class for the efficient contraction of variants of tensors,
+        used in the energy evaluation of excited states
+
+        A Nested tensor contains the following variants (some may be empty):
+
+            - :attr:`tensors[0]`: regular tensor (no B or Bd)
+            - :attr:`tensors[1]`: (terms with) a single B tensor
+            - :attr:`tensors[2]`: (terms with) a single Bd tensor
+            - :attr:`tensors[3]`: (terms with) both a B and a Bd tensor
+        
+        When two Nested tensors x,y are contracted, all combinations are taken into account
+        and the result is again a Nested tensor, filled with the following variants:
+
+            - :attr:`tensors[0]: x[0] * y[0]`
+            - :attr:`tensors[1]: x[1] * y[0] + x[0] * y[1]`
+            - :attr:`tensors[2]: x[2] * y[0] + x[0] * y[2]`
+            - :attr:`tensors[3]: x[3] * y[0] + x[2] * y[1] + x[1] * y[2] + x[0] * y[3]`
+
+        By using Nested tensors in a (large) contraction, the many different terms are 
+        resummed on the fly, leading to a potentially reduced computational cost
+
+        Note:
+            Most implented functions act as wrappers for the corresponding `numpy` functions 
+            on the individual tensors
+    """
+
+    def __init__(self, tensors):
+        self.tensors = tensors
+
+
[docs]    def normalize(self):
+        """ Normalize the contained tensors by the largest value 
+            of the first element of :attr:`self.tensors`
+        """
+        factor = np.abs(self[0]).max()
+        return self * (1 / factor), factor

+
+
[docs]    def mult(self, other: TensorType, *args) -> 'Nested':
+        """
+            Args:
+                other: other tensor-like object to contract with
+                *args: arguments to be passed to the contraction method
+                    (:code:`np.tensordot`)
+
+            Returns:
+                res: result of the contraction
+        """
+        def _mult_function(A, B, *args):
+            if hasattr(A, 'mult'):
+                return A.mult(B, *args)
+            elif len(B) == 0:
+                return B.mult(A, *args)
+            return np.tensordot(A, B, *args)
+
+        if isinstance(other, np.ndarray):
+            new_data = 4 * [[]]
+            new_data[0] = _mult_function(self.tensors[0], other, *args)
+            new_data[1] = _mult_function(self.tensors[1], other, *args)
+            new_data[2] = _mult_function(self.tensors[2], other, *args)
+            new_data[3] = _mult_function(self.tensors[3], other, *args)
+            return Nested(new_data)
+        new_data = 4 * [[]]
+        new_data[0] = _mult_function(self.tensors[0], other.tensors[0], *args)
+        new_data[1] = _mult_function(self.tensors[1], other.tensors[0], *args) +\
+                      _mult_function(self.tensors[0], other.tensors[1], *args)
+        new_data[2] = _mult_function(self.tensors[2], other.tensors[0], *args) +\
+                      _mult_function(self.tensors[0], other.tensors[2], *args)
+
+        new_data[3] = _mult_function(self.tensors[3], other.tensors[0], *args) +\
+                      _mult_function(self.tensors[2], other.tensors[1], *args) +\
+                      _mult_function(self.tensors[1], other.tensors[2], *args) +\
+                      _mult_function(self.tensors[0], other.tensors[3], *args)
+        res = Nested(new_data)
+        return res

+
+
[docs]    def transpose(self, *args) -> 'Nested':
+        """ Applies :code:`transpose` to each contained tensor """
+        new_data = [self.tensors[i].transpose(*args) for i in range(4)]
+        return Nested(new_data)

+
+    def __mul__(self, other):
+        new_data = [self.tensors[i] * other for i in range(4)]
+        return Nested(new_data)
+
+    def __rmul__(self, other):
+        new_data = [other * self.tensors[i] for i in range(4)]
+        return Nested(new_data)
+
+    def __truediv__(self, other):
+        new_data = [self.tensors[i] / other for i in range(4)]
+        return Nested(new_data)
+
+    def __add__(self, other):
+        if isinstance(other, Nested):
+            new_data = [self.tensors[i] + other.tensors[i] for i in range(4)]
+        else:
+            new_data = [self.tensors[i] + other for i in range(4)]
+        return Nested(new_data)
+
+    def __radd__(self, other):
+        return self + other
+
+    def __getitem__(self, ix):
+        return self.tensors[ix]
+
+    def __setitem__(self, ix, value):
+        self.tensors[ix] = value
+
+    def __repr__(self):
+        return "(Nested) " + self.tensors.__repr__()
+
+    def __neg__(self):
+        return Nested([-self.tensors[i] for i in range(4)])
+
+    def shift(self, phi):
+        new_data = [self.tensors[0],  self.tensors[1] * exp(phi), 
+                 self.tensors[2] * exp(-phi), self.tensors[3]]
+        return Nested(new_data)
+
+    def __len__(self):
+        try:
+            return len(self.tensors[0])
+        except Exception:
+            return self.tensors[0].size
+
+    @property
+    def real(self):
+        res = Nested([self.tensors[i].real for i in range(4)])
+        return res
+
+    @property
+    def shape(self):
+        return self.tensors[0].shape
+
+    @property
+    def dims(self):
+        return self.tensors[0].dims
+
+    def check_contr_inds(self, other, *args, **kwargs):
+        return self[0].check_contr_inds(other[0], *args, **kwargs)
+
+    def numel(self):
+        return self[0].numel()
+    
+    @classmethod
+    def only_gs(cls, tensor, empty_obj=[]):
+        return cls([tensor, empty_obj, empty_obj, empty_obj])

+
+def exp(phi):
+    return cmath.exp(1j * phi)
+
+ +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/_modules/adpeps/utils/printing.html b/docs/_modules/adpeps/utils/printing.html new file mode 100644 index 0000000..9cbcc84 --- /dev/null +++ b/docs/_modules/adpeps/utils/printing.html @@ -0,0 +1,375 @@ + + + + + + + + adpeps.utils.printing — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
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+ + + + +
+ + +
+ + + +
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+ + +
+ + + + + + +
+ +
+ +

Source code for adpeps.utils.printing

+""" Utility module for printing output depending on the verbosity setting 
+    :attr:`adpeps.ipeps.config.disp_level` in the configuration file.
+"""
+
+import builtins
+import time
+
+import adpeps.ipeps.config as sim_config
+
+prefix    = None
+show_time = False
+
+
[docs]def print(*args, level: int=None, **kwargs):
+    """ Print output using builtin :code:`print` if :code:`level` 
+        <= :attr:`adpeps.ipeps.config.disp_level`
+
+        Args:
+            *args: arbitraty arguments to be passed to builtin :code:`print`
+            level: verbosity level, determining at which verbosity setting this
+                should be printed
+            **kwargs: arbitraty keyword arguments for builtin :code:`print`
+    """
+    if level is None or level <= sim_config.disp_level:
+        if sim_config.flush_output:
+            kwargs['flush'] = True
+        if prefix is not None:
+            if show_time:
+                curtime = time.strftime("[%H:%M:%S]", time.localtime())
+                builtins.print(prefix, curtime, *args, **kwargs)
+            else:
+                builtins.print(prefix, *args, **kwargs)
+        else:
+            if show_time:
+                curtime = time.strftime("[%H:%M:%S]", time.localtime())
+                builtins.print(curtime, *args, **kwargs)
+            else:
+                builtins.print(*args, **kwargs)

+
+ +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/_modules/adpeps/utils/tlist.html b/docs/_modules/adpeps/utils/tlist.html new file mode 100644 index 0000000..d9360ac --- /dev/null +++ b/docs/_modules/adpeps/utils/tlist.html @@ -0,0 +1,651 @@ + + + + + + + + adpeps.utils.tlist — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +

Source code for adpeps.utils.tlist

+"""
+    List object with additional features, used for storing 
+    the iPEPS tensors
+
+    Items in the list can be accessed by either a linear index 
+    or a (i,j) double index, where i and j will be automatically 
+    taken modulo the unit cell size (i.e. i = i % n_x)
+
+    Additionally, convenience functions that work on tensors can 
+    be defined for the whole list, e.g. conj()
+"""
+
+import contextlib
+import jax
+import jax.numpy as np
+import numpy as onp
+
+from .empty_tensor import EmptyT
+
+
+
[docs]@contextlib.contextmanager
+def cur_loc(*loc: int):
+    """ Shift the locations of the tensors relative to a 
+        new zero (loc) while in this context
+
+        Args:
+            loc: shifts (x,y)
+
+        Example:
+            >>> l = TList([[1,2], [3,4]])
+            >>> l[0,0]
+            1
+            >>> with cur_loc(1,0):
+            >>>     l[0,0]
+            2
+            >>>     l[0,1]
+            4
+            >>> l[0,0]
+            1
+
+        Note that this applies to ALL TList objects while 
+        inside the context
+    """
+    pre_patched_value = getattr(TList, '_loc')
+    setattr(TList, '_loc', loc)
+    yield TList
+    setattr(TList, '_loc', pre_patched_value)

+
+
[docs]@contextlib.contextmanager
+def hold_write(*lists: 'TList'):
+    """ Hold off on writing to the list while 
+        inside the context
+
+        Args:
+            lists: one or more TList objects that should have the writing 
+                action delayed until the context is disabled
+
+        Example:
+            >>> l = TList([[1,2], [3,4]])
+            >>> with hold_write(l):
+            >>>    l[0,0] = 100
+            >>>    l[0,0] 
+            1
+            >>> l[0,0]
+            100
+    """
+    for l in lists:
+        l._hold_write = True
+    yield
+    for l in lists:
+        l._purge_tmp()

+
+
[docs]@contextlib.contextmanager
+def set_pattern(pattern):
+    """ Set pattern for all new TLists that are created while 
+        the context is active
+
+        Args:
+            pattern:
+    """
+
+    pre_patched_value = getattr(TList, '_default_pattern')
+    setattr(TList, '_default_pattern', pattern)
+    yield TList
+    setattr(TList, '_default_pattern', pre_patched_value)

+
+class TList:
+    _loc             = (0,0)
+    _default_pattern = None
+    _changed         = None
+
+    def __init__(self, data=None, shape=None, pattern=None, empty_obj=[[]]):
+        self._tmpdata    = None
+        self.pattern     = pattern
+        self._hold_write = False
+        self.empty_obj   = empty_obj
+        if pattern is None and self._default_pattern is not None:
+            self.pattern = self._default_pattern
+        if self.pattern is None:
+            if data is not None:
+                try:
+                    iter(data) # Check if iterable
+                    data = np.array(data, dtype='object')
+                    self._data = data.reshape([-1], order='C').tolist()
+                    if data.ndim == 1:
+                        self.size = (data.shape[0], 1)
+                    else:
+                        self.size = (data.shape[1], data.shape[0])
+                except:
+                    self._data = [data]
+                    self.size = (1,1)
+            elif shape is not None:
+                self._data = (shape[0]*shape[1]) * empty_obj
+                self.size = shape
+            else:
+                self._data = None
+                self.size = ()
+        else:
+            self.pattern = np.array(self.pattern)
+            self.size = (self.pattern.shape[1], self.pattern.shape[0])
+            if data is not None:
+                try:
+                    iter(data) # Check if iterable
+                    data = np.array(data, dtype='object')
+                    if data.size == np.unique(self.pattern).size:
+                        self._data = data.reshape([-1], order='C').tolist()
+                    else:
+                        self._data = np.unique(self.pattern).size * empty_obj
+                        for j in range(self.pattern.shape[1]):
+                            for i in range(self.pattern.shape[0]):
+                                self._data[self.pattern[i,j]] = data[i,j]
+                except:
+                    self._data = [data]
+                    self.size = (1,1)
+            else:
+                self._data = np.unique(self.pattern).size * empty_obj
+                assert len(self._data) == np.unique(self.pattern).size, \
+                        "Data must contain one element for each unique identifier in pattern"
+        self.reset_changed()
+
+    def x_major(self):
+        return (self._conv_ix((x,y)) for y in range(self.size[1]) for x in range(self.size[0]))
+
+    def y_major(self):
+        return (self._conv_ix((x,y)) for x in range(self.size[0]) for y in range(self.size[1]))
+
+    def __len__(self):
+        return len(self._data)
+
+    def mean(self):
+        try:
+            finite_elems = [x for x in self._data if isfinite(x)]
+            return sum(finite_elems) / len(finite_elems)
+        except Exception as e:
+            return sum(self._data) / len(self)
+
+    def sum(self):
+        try:
+            finite_elems = [x for x in self._data if isfinite(x)]
+            return sum(finite_elems)
+        except Exception as e:
+            return sum(self._data)
+
+    def normalize(self):
+        new_list = TList(shape=self.size, pattern=self.pattern)
+        new_list._data = [a / np.max(np.abs(a)) for a in self._data]
+        return new_list
+
+    def conj(self):
+        new_list = TList(shape=self.size, pattern=self.pattern)
+        new_list._data = [a.conj() for a in self._data]
+        return new_list
+    def items(self):
+        return [a.item() for a in self._data]
+
+    def pack_data(self):
+        data = []
+        for a in self._data:
+            data.append(np.reshape(a, (-1,)))
+        return np.concatenate(data)
+
+    def reset_changed(self):
+        if self._data is not None:
+            self._changed = len(self._data) * [False]
+        return self
+
+    def mark_changed(self, linear_ix):
+        if self._changed is not None:
+            self._changed[linear_ix] = True
+
+    def is_changed(self, *ix):
+        if self._changed is None:
+            return False
+        linear_ix = self._conv_ix(ix)
+        return self._changed[linear_ix]
+
+    def fill(self, data, d=None, D=None):
+        new_list = TList(shape=self.size, pattern=self.pattern)
+        offset = 0
+        new_data = []
+        for i,a in enumerate(self):
+            siz = a.size
+            # new_data.append(np.reshape(data[offset:offset+siz], (d, D, D, D, D)))
+            new_data.append(np.reshape(data[offset:offset+siz], a.shape))
+            offset = offset + siz
+        new_list._data = new_data
+        return new_list
+
+    def tot_numel(self):
+        return sum([a.size for a in self._data])
+
+    def stop_gradient(self):
+        new_list = TList(shape=self.size, pattern=self.pattern)
+        new_list._data = [jax.lax.stop_gradient(a) if len(a)>0 else a for a in self._data]
+        return new_list
+
+    def _conv_ix(self, ix):
+        if isinstance(ix, (tuple,list)):
+            if len(self._loc) == 1:
+                # shift_i, shift_j = onp.unravel_index(self._loc[0], self.size, order='F')
+                shift_j, shift_i = np.unravel_index(self._loc[0], self.size)
+            else:
+                shift_i, shift_j = self._loc
+            i = (ix[0] + shift_i) % self.size[0]
+            j = (ix[1] + shift_j) % self.size[1]
+            # linear_ix = np.ravel_multi_index((i,j), self.size, order='F')
+            linear_ix = self._linear_ix(i,j)
+        else:
+            linear_ix = ix
+        return linear_ix
+
+    def _linear_ix(self, i, j):
+        if self.pattern is not None:
+            return self.pattern[j][i]
+        else:
+            return np.ravel_multi_index((i,j), self.size, order='F')
+
+    def _purge_tmp(self):
+        self._tmpdata    = None
+        self._hold_write = False
+
+    def __eq__(self, other):
+        if self._data != other._data:
+            return False
+        if self.pattern is not None:
+            if other.pattern is None:
+                return False
+            if not (self.pattern == other.pattern).all():
+                return False
+        return True
+
+    def __getitem__(self, ix):
+        linear_ix = self._conv_ix(ix)
+        if self._tmpdata is not None and self._tmpdata[linear_ix] is not None:
+            return self._tmpdata[linear_ix]
+        return self._data[linear_ix]
+
+    def __setitem__(self, ix, value):
+        linear_ix = self._conv_ix(ix)
+        if self._hold_write:
+            if self._tmpdata is None:
+                self._tmpdata = [None] * len(self)
+            self._tmpdata[linear_ix] = self._data[linear_ix]
+        self._data[linear_ix] = value
+        self.mark_changed(linear_ix)
+
+    def __repr__(self):
+        if self._data is None:
+            return "TList{}[]"
+        repr_str = "TList{"
+        if self._loc is not None:
+            repr_str += "Loc=" + self._loc.__repr__()
+        if self.pattern is not None:
+            repr_str += ",Pat=" + self.pattern.__repr__()
+        repr_str += ",Size=" + self.size.__repr__()
+        repr_str += "}["
+        for j in range(self.size[1]):
+            repr_str += "["
+            for i in range(self.size[0]):
+                try:
+                    repr_str += f"{self[i,j].shape}"
+                except:
+                    repr_str += self[i,j].__repr__()
+                if i < self.size[0]-1:
+                    repr_str += ", "
+            if j < self.size[1]-1:
+                repr_str += "], "
+            else:
+                repr_str += "]]"
+        return repr_str
+
+    @staticmethod
+    def empty_like(T, empty_obj=None):
+        if empty_obj is None:
+            empty_obj = T.empty_obj
+        return TList(shape=T.size, pattern=T.pattern, empty_obj=empty_obj)
+
+def isfinite(x):
+    try:
+        return len(x) > 0
+    except Exception as e:
+        return np.isfinite(np.array(x))
+
+ +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/_modules/index.html b/docs/_modules/index.html new file mode 100644 index 0000000..d11c54b --- /dev/null +++ b/docs/_modules/index.html @@ -0,0 +1,360 @@ + + + + + + + + Overview: module code — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ + + + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/_sources/extra/adpeps.ipeps.ctm.rst.txt b/docs/_sources/extra/adpeps.ipeps.ctm.rst.txt new file mode 100644 index 0000000..c011e15 --- /dev/null +++ b/docs/_sources/extra/adpeps.ipeps.ctm.rst.txt @@ -0,0 +1,10 @@ +adpeps.ipeps.ctm +================ + +.. currentmodule:: adpeps.ipeps.ctm + +.. .. toctree:: +.. :maxdepth: 2 + +.. automodule:: adpeps.ipeps.ctm + :members: diff --git a/docs/_sources/extra/adpeps.ipeps.ipeps.rst.txt b/docs/_sources/extra/adpeps.ipeps.ipeps.rst.txt new file mode 100644 index 0000000..3323f55 --- /dev/null +++ b/docs/_sources/extra/adpeps.ipeps.ipeps.rst.txt @@ -0,0 +1,35 @@ +adpeps.ipeps.ipeps +================== + +.. currentmodule:: adpeps.ipeps.ipeps + +.. .. toctree:: +.. :maxdepth: 2 + +.. automodule:: adpeps.ipeps.ipeps + :members: + + +iPEPS +----------- + +.. autoclass:: iPEPS + :members: + :member-order: bysource + +iPEPS_exci +----------- + +.. autoclass:: iPEPS_exci + :members: + :member-order: bysource + + +.. .. autosummary:: +.. :toctree: generated +.. :caption: Section 1 +.. :nosignatures: + +.. iPEPS +.. iPEPS_exci + diff --git a/docs/_sources/extra/ipeps.ipeps.rst.txt b/docs/_sources/extra/ipeps.ipeps.rst.txt new file mode 100644 index 0000000..193f163 --- /dev/null +++ b/docs/_sources/extra/ipeps.ipeps.rst.txt @@ -0,0 +1,19 @@ +iPEPSS +====== + +.. :noindex: + +.. .. currentmodule:: adpeps.ipeps.ipeps + +.. .. toctree:: +.. :maxdepth: 2 + +.. .. automodule:: adpeps.ipeps.ipeps + +.. .. autosummary:: + :toctree: generated + :nosignatures: + :caption: Classes + + iPEPS + iPEPS_exci diff --git a/docs/_sources/generated/adpeps.ipeps.config.rst.txt b/docs/_sources/generated/adpeps.ipeps.config.rst.txt new file mode 100644 index 0000000..eafaa88 --- /dev/null +++ b/docs/_sources/generated/adpeps.ipeps.config.rst.txt @@ -0,0 +1,14 @@ +adpeps.ipeps.config +=================== + +.. currentmodule:: adpeps.ipeps.config + +.. module:: adpeps.ipeps.config + + + +.. automodule:: adpeps.ipeps.config + :members: + :member-order: groupwise + + diff --git a/docs/_sources/generated/adpeps.ipeps.ctm.rst.txt b/docs/_sources/generated/adpeps.ipeps.ctm.rst.txt new file mode 100644 index 0000000..25af8d5 --- /dev/null +++ b/docs/_sources/generated/adpeps.ipeps.ctm.rst.txt @@ -0,0 +1,14 @@ +adpeps.ipeps.ctm +================ + +.. currentmodule:: adpeps.ipeps.ctm + +.. module:: adpeps.ipeps.ctm + + + +.. automodule:: adpeps.ipeps.ctm + :members: + :member-order: groupwise + + diff --git a/docs/_sources/generated/adpeps.ipeps.ipeps.evaluation.rst.txt b/docs/_sources/generated/adpeps.ipeps.ipeps.evaluation.rst.txt new file mode 100644 index 0000000..9134e28 --- /dev/null +++ b/docs/_sources/generated/adpeps.ipeps.ipeps.evaluation.rst.txt @@ -0,0 +1,14 @@ +adpeps.ipeps.ipeps.evaluation +============================= + +.. currentmodule:: adpeps.ipeps.ipeps.evaluation + +.. module:: adpeps.ipeps.ipeps.evaluation + + + +.. automodule:: adpeps.ipeps.ipeps.evaluation + :members: + :member-order: groupwise + + diff --git a/docs/_sources/generated/adpeps.ipeps.ipeps.rst.txt b/docs/_sources/generated/adpeps.ipeps.ipeps.rst.txt new file mode 100644 index 0000000..e4ac247 --- /dev/null +++ b/docs/_sources/generated/adpeps.ipeps.ipeps.rst.txt @@ -0,0 +1,14 @@ +adpeps.ipeps.ipeps +================== + +.. currentmodule:: adpeps.ipeps.ipeps + +.. module:: adpeps.ipeps.ipeps + + + +.. automodule:: adpeps.ipeps.ipeps + :members: + :member-order: groupwise + + diff --git a/docs/_sources/generated/adpeps.ipeps.models.common.rst.txt b/docs/_sources/generated/adpeps.ipeps.models.common.rst.txt new file mode 100644 index 0000000..617b7fb --- /dev/null +++ b/docs/_sources/generated/adpeps.ipeps.models.common.rst.txt @@ -0,0 +1,14 @@ +adpeps.ipeps.models.common +========================== + +.. currentmodule:: adpeps.ipeps.models.common + +.. module:: adpeps.ipeps.models.common + + + +.. automodule:: adpeps.ipeps.models.common + :members: + :member-order: groupwise + + diff --git a/docs/_sources/generated/adpeps.ipeps.models.heisenberg.rst.txt b/docs/_sources/generated/adpeps.ipeps.models.heisenberg.rst.txt new file mode 100644 index 0000000..fb407e7 --- /dev/null +++ b/docs/_sources/generated/adpeps.ipeps.models.heisenberg.rst.txt @@ -0,0 +1,14 @@ +adpeps.ipeps.models.heisenberg +============================== + +.. currentmodule:: adpeps.ipeps.models.heisenberg + +.. module:: adpeps.ipeps.models.heisenberg + + + +.. automodule:: adpeps.ipeps.models.heisenberg + :members: + :member-order: groupwise + + diff --git a/docs/_sources/generated/adpeps.ipeps.models.rst.txt b/docs/_sources/generated/adpeps.ipeps.models.rst.txt new file mode 100644 index 0000000..886d6cb --- /dev/null +++ b/docs/_sources/generated/adpeps.ipeps.models.rst.txt @@ -0,0 +1,23 @@ +adpeps.ipeps.models +=================== + +.. currentmodule:: adpeps.ipeps.models + +.. module:: adpeps.ipeps.models + + +Modules +------- + +.. automodule:: adpeps.ipeps.models + +.. autosummary:: + :toctree: + + + adpeps.ipeps.models.common + + adpeps.ipeps.models.heisenberg + + + diff --git a/docs/_sources/generated/adpeps.simulation.rst.txt b/docs/_sources/generated/adpeps.simulation.rst.txt new file mode 100644 index 0000000..d2c6305 --- /dev/null +++ b/docs/_sources/generated/adpeps.simulation.rst.txt @@ -0,0 +1,23 @@ +adpeps.simulation +================= + +.. currentmodule:: adpeps.simulation + +.. module:: adpeps.simulation + + +Modules +------- + +.. automodule:: adpeps.simulation + +.. autosummary:: + :toctree: + + + adpeps.simulation.run_ipeps_exci + + adpeps.simulation.run_ipeps_gs + + + diff --git a/docs/_sources/generated/adpeps.simulation.run_ipeps_exci.rst.txt b/docs/_sources/generated/adpeps.simulation.run_ipeps_exci.rst.txt new file mode 100644 index 0000000..70250d6 --- /dev/null +++ b/docs/_sources/generated/adpeps.simulation.run_ipeps_exci.rst.txt @@ -0,0 +1,14 @@ +adpeps.simulation.run\_ipeps\_exci +================================== + +.. currentmodule:: adpeps.simulation.run_ipeps_exci + +.. module:: adpeps.simulation.run_ipeps_exci + + + +.. automodule:: adpeps.simulation.run_ipeps_exci + :members: + :member-order: groupwise + + diff --git a/docs/_sources/generated/adpeps.simulation.run_ipeps_gs.rst.txt b/docs/_sources/generated/adpeps.simulation.run_ipeps_gs.rst.txt new file mode 100644 index 0000000..276e16a --- /dev/null +++ b/docs/_sources/generated/adpeps.simulation.run_ipeps_gs.rst.txt @@ -0,0 +1,14 @@ +adpeps.simulation.run\_ipeps\_gs +================================ + +.. currentmodule:: adpeps.simulation.run_ipeps_gs + +.. module:: adpeps.simulation.run_ipeps_gs + + + +.. automodule:: adpeps.simulation.run_ipeps_gs + :members: + :member-order: groupwise + + diff --git a/docs/_sources/generated/adpeps.utils.ctmtensors.rst.txt b/docs/_sources/generated/adpeps.utils.ctmtensors.rst.txt new file mode 100644 index 0000000..fc3a665 --- /dev/null +++ b/docs/_sources/generated/adpeps.utils.ctmtensors.rst.txt @@ -0,0 +1,14 @@ +adpeps.utils.ctmtensors +======================= + +.. currentmodule:: adpeps.utils.ctmtensors + +.. module:: adpeps.utils.ctmtensors + + + +.. automodule:: adpeps.utils.ctmtensors + :members: + :member-order: groupwise + + diff --git a/docs/_sources/generated/adpeps.utils.empty_tensor.rst.txt b/docs/_sources/generated/adpeps.utils.empty_tensor.rst.txt new file mode 100644 index 0000000..634791b --- /dev/null +++ b/docs/_sources/generated/adpeps.utils.empty_tensor.rst.txt @@ -0,0 +1,14 @@ +adpeps.utils.empty\_tensor +========================== + +.. currentmodule:: adpeps.utils.empty_tensor + +.. module:: adpeps.utils.empty_tensor + + + +.. automodule:: adpeps.utils.empty_tensor + :members: + :member-order: groupwise + + diff --git a/docs/_sources/generated/adpeps.utils.io.rst.txt b/docs/_sources/generated/adpeps.utils.io.rst.txt new file mode 100644 index 0000000..d73ab43 --- /dev/null +++ b/docs/_sources/generated/adpeps.utils.io.rst.txt @@ -0,0 +1,14 @@ +adpeps.utils.io +=============== + +.. currentmodule:: adpeps.utils.io + +.. module:: adpeps.utils.io + + + +.. automodule:: adpeps.utils.io + :members: + :member-order: groupwise + + diff --git a/docs/_sources/generated/adpeps.utils.nested.rst.txt b/docs/_sources/generated/adpeps.utils.nested.rst.txt new file mode 100644 index 0000000..4d807d9 --- /dev/null +++ b/docs/_sources/generated/adpeps.utils.nested.rst.txt @@ -0,0 +1,14 @@ +adpeps.utils.nested +=================== + +.. currentmodule:: adpeps.utils.nested + +.. module:: adpeps.utils.nested + + + +.. automodule:: adpeps.utils.nested + :members: + :member-order: groupwise + + diff --git a/docs/_sources/generated/adpeps.utils.printing.rst.txt b/docs/_sources/generated/adpeps.utils.printing.rst.txt new file mode 100644 index 0000000..a54b81a --- /dev/null +++ b/docs/_sources/generated/adpeps.utils.printing.rst.txt @@ -0,0 +1,14 @@ +adpeps.utils.printing +===================== + +.. currentmodule:: adpeps.utils.printing + +.. module:: adpeps.utils.printing + + + +.. automodule:: adpeps.utils.printing + :members: + :member-order: groupwise + + diff --git a/docs/_sources/generated/adpeps.utils.rst.txt b/docs/_sources/generated/adpeps.utils.rst.txt new file mode 100644 index 0000000..dc43a5c --- /dev/null +++ b/docs/_sources/generated/adpeps.utils.rst.txt @@ -0,0 +1,31 @@ +adpeps.utils +============ + +.. currentmodule:: adpeps.utils + +.. module:: adpeps.utils + + +Modules +------- + +.. automodule:: adpeps.utils + +.. autosummary:: + :toctree: + + + adpeps.utils.ctmtensors + + adpeps.utils.empty_tensor + + adpeps.utils.io + + adpeps.utils.nested + + adpeps.utils.printing + + adpeps.utils.tlist + + + diff --git a/docs/_sources/generated/adpeps.utils.tlist.rst.txt b/docs/_sources/generated/adpeps.utils.tlist.rst.txt new file mode 100644 index 0000000..8698206 --- /dev/null +++ b/docs/_sources/generated/adpeps.utils.tlist.rst.txt @@ -0,0 +1,14 @@ +adpeps.utils.tlist +================== + +.. currentmodule:: adpeps.utils.tlist + +.. module:: adpeps.utils.tlist + + + +.. automodule:: adpeps.utils.tlist + :members: + :member-order: groupwise + + diff --git a/docs/_sources/index.rst.txt b/docs/_sources/index.rst.txt new file mode 100644 index 0000000..78614ef --- /dev/null +++ b/docs/_sources/index.rst.txt @@ -0,0 +1,48 @@ +.. AD-PEPS documentation master file, created by + sphinx-quickstart on Mon Apr 12 16:13:24 2021. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +AD-PEPS's documentation +=================================== + +The AD-PEPS Python package is intended as a example of an implementation of iPEPS ground-state and excited-state algorithms using Automatic Differentiation, as described in +As such, the code is meant to illustrate the workings of the algorithms described the paper. +For real applications, this code would likely need to be further adapted and optimized, however the package is a complete implementation and can directly be used for simple calculations. + +.. toctree:: + + notes/install + notes/start + notes/example + notes/example2 + + +Reference +-------------- + +.. .. toctree:: +.. :maxdepth: 2 + +.. ipeps + +.. currentmodule:: adpeps + +.. autosummary:: + :toctree: generated + :recursive: + + ipeps.ipeps + ipeps.config + ipeps.ctm + ipeps.models + simulation + utils + + +Indices and tables +================== + +* :ref:`genindex` +* :ref:`modindex` +* :ref:`search` diff --git a/docs/_sources/ipeps.rst.txt b/docs/_sources/ipeps.rst.txt new file mode 100644 index 0000000..e94d9b0 --- /dev/null +++ b/docs/_sources/ipeps.rst.txt @@ -0,0 +1,17 @@ +adpeps.ipeps +============ + +.. currentmodule:: adpeps.ipeps + +.. toctree:: + :maxdepth: 2 + :caption: Contents + + adpeps.ipeps.ipeps + adpeps.ipeps.ctm + +.. autosummary:: + :toctree: generated + :nosignatures: + + adpeps.ipeps.config diff --git a/docs/_sources/notes/example.rst.txt b/docs/_sources/notes/example.rst.txt new file mode 100644 index 0000000..480ca94 --- /dev/null +++ b/docs/_sources/notes/example.rst.txt @@ -0,0 +1,81 @@ +.. _notes/example: + +Example: ground state +=========================================== + +The package includes an example configuration for a ground-state simulation of the 2D Heisenberg model, defined by the Hamiltonian + +.. math:: + + H = J \sum_i S_i \cdot S_{i+1}~. + +The configuration file `examples/heis_D2.yaml` contains the following: + +.. literalinclude:: ../../../examples/heis_D2.yaml + +This configures a simulation with bond dimension :code:`D=2` and boundary bond dimension :code:`chi=40`, using the model defined in :mod:`adpeps.ipeps.models.heisenberg`. + +Now the simulation can be started by calling the :code:`adpeps` module with the name of this configuration file: + + >>> python -m adpeps gs 'heis_D2' + WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.) + Namespace(config_file='heis_D2', sim_mode='gs', version=False) + Running ground-state sim + ... + +The simulation will continue to run and you should see output similar to this: + +.. code-block:: + + ... + Performing CTM pre-steps without tracking + | CTM step 1 conv: 4.935e-03 time: 3.17 obj: -0.658758 + | CTM step 2 conv: 7.918e-04 time: 3.74 obj: -0.659550 + | CTM step 3 conv: 1.234e-05 time: 6.42 obj: -0.659562 + Performing CTM + | CTM step 1 conv: 3.171e-07 time: 8.8 obj: -0.659563 + | CTM step 2 conv: 2.108e-08 time: 4.07 obj: -0.659563 + | CTM step 3 conv: 8.173e-09 time: 2.93 obj: -0.659563 + Energy: -0.6595625579862193 + ... + +The first cycle of iterations are not taken into account in the gradient computation, but make sure that the CTM iterations with gradient tracking start from some reasonably converged boundary tensors in order to avoid instabilities with initial CTM steps. + +.. note:: + The convergence rate of the CTM depends on the variational parameters of the iPEPS and the settings of the simulation. + Generally the convergence improves as the simulation approaches the optimum. + +Whenever a step in the optimization has completed (this could take more than one cycle of CTM iterations depending on the type of optimizer), the module will output a summary of the steps so far: + +.. code-block:: + + ... + # ======================== # + # Step completed # + # ======================== # + + Step 0 E: -0.376468389894 |grad|: 1.2103482 + Step 1 E: -0.505252956403 |grad|: 0.19064889 + Step 2 E: -0.517432085607 |grad|: 0.10910666 + Step 3 E: -0.578045570568 |grad|: 0.081472534 + Step 4 E: -0.589074339197 |grad|: 0.089438567 + Step 5 E: -0.597590746400 |grad|: 0.15282526 + Step 6 E: -0.612205652457 |grad|: 0.076385807 + Step 7 E: -0.628079118387 |grad|: 0.0684857 + Step 8 E: -0.642200026835 |grad|: 0.097849544 + Step 9 E: -0.649553574703 |grad|: 0.066648727 + Step 10 E: -0.653909263824 |grad|: 0.0264237 + Step 11 E: -0.655389076620 |grad|: 0.016836624 + Step 12 E: -0.656585389308 |grad|: 0.016954703 + Step 13 E: -0.657797020335 |grad|: 0.020011479 + Step 14 E: -0.658174755217 |grad|: 0.033691114 + Step 15 E: -0.659083649568 |grad|: 0.012202327 + Step 16 E: -0.659365377610 |grad|: 0.0064214407 + Step 17 E: -0.659562557986 |grad|: 0.007503111 + ... + +The simulation will continue until :attr:`adpeps.ipeps.config.max_iterations` has been reached. +At any point the simulation can be stopped and continued later by restarting the module. + +.. note:: + In case you would like the simulation to continue from an earlier saved simulation with the same configuration file, make sure to set :attr:`adpeps.ipeps.config.resume` :code:`= True` diff --git a/docs/_sources/notes/example2.rst.txt b/docs/_sources/notes/example2.rst.txt new file mode 100644 index 0000000..d894348 --- /dev/null +++ b/docs/_sources/notes/example2.rst.txt @@ -0,0 +1,96 @@ +.. _notes/example2: + +Example: excitations +========================================= + +.. note:: + This example continues from :ref:`the ground-state example` and requires an optimized ground state to start from. + +Here we demonstrates how to use the :mod:`adpeps` package for computing excited states of the 2D Heisenberg model. + +The configuration file `examples/heis_D2_exci.yaml` contains the following settings: + +.. literalinclude:: ../../../examples/heis_D2_exci.yaml + +Note that many of the options are the same as for the ground-state simulation, with the addition of the :attr:`adpeps.ipeps.config.momentum_path` setting, which controls which path through the Brillouin zone will be taken. + +In the configuration for excited states you do not explicitly set the momentum, but choose a preset path of points in momentum space and pass the index for each simulation. + +If we now start the simulation, we get the following response: + + >>> python -m adpeps exci 'heis_D2_exci' --p_ix=1 + ... + Running excited-state sim + ... + Base file .../exci/heisenberg_D2_X40.base.npz not found. + Prepare the simulation first by running with option '-i' + +What happened is that we first need to make some preparations for the simulation. +For excited-state simulations, we require the following: + + 1. Well-converged CTM boundary tensors + 2. A basis for the excited-state tensors, orthogonal to the ground state + +The preparations for the simulation need to be performed only once, resulting in a `base` simulation file that will be used by the simulations for every momentum. + + >>> python -m adpeps exci 'heis_D2_exci' -i + ... + Running excited-state sim + ... + | CTM step 1 conv: 1.036e-01 time: 3.64 obj: -0.665574 + | CTM step 2 conv: 3.137e-03 time: 4.23 obj: -0.662436 + | CTM step 3 conv: 7.887e-05 time: 4.0 obj: -0.662515 + | CTM step 4 conv: 1.388e-06 time: 2.2 obj: -0.662514 + | CTM step 5 conv: 2.455e-07 time: 1.35 obj: -0.662514 + | CTM step 6 conv: 3.044e-08 time: 1.35 obj: -0.662514 + | CTM step 7 conv: 4.673e-09 time: 1.37 obj: -0.662514 + | CTM step 8 conv: 4.467e-10 time: 1.36 obj: -0.662514 + | CTM step 9 conv: 5.029e-11 time: 1.35 obj: -0.662514 + | CTM step 10 conv: 5.612e-11 time: 1.38 obj: -0.662514 + | CTM step 11 conv: 2.801e-11 time: 1.36 obj: -0.662514 + | CTM step 12 conv: 1.204e-11 time: 1.65 obj: -0.662514 + | CTM step 13 conv: 4.936e-12 time: 1.42 obj: -0.662514 + | CTM step 14 conv: 1.989e-12 time: 1.39 obj: -0.662514 + GS norm 3.5890188873039093 + GS norm 1.0 + Substracting -0.33125703308289145 from Hamiltonian + +Several steps have been performed: first a full CTM contraction of the ground-state network, followed by a normalization of the ground-state tensors. +Then the Hamiltonian is shifted by the ground-state energy expectation value, in order for the excitations to have energies relative to the ground state. +Finally, the basis is prepared and we have everything to get started. + + >>> python -m adpeps exci 'heis_D2_exci' --p_ix=0 + ... + Running excited-state sim + ... + Starting simulation of basis vector 1/62 + Performing CTM + | CTM step 1 conv: 4.236e+00 time: 3.19 obj: 5.173629 + | CTM step 2 conv: 3.539e-02 time: 1.38 obj: 5.138237 + | CTM step 3 conv: 6.139e-03 time: 1.27 obj: 5.132099 + | CTM step 4 conv: 2.116e-04 time: 1.24 obj: 5.132310 + | CTM step 5 conv: 6.148e-05 time: 1.28 obj: 5.132249 + | CTM step 6 conv: 3.704e-04 time: 1.25 obj: 5.131879 + | CTM step 7 conv: 2.493e-04 time: 1.25 obj: 5.131629 + Energies: 0.04418993415167889 1.5450126399606245e-10 + Norm: 0.008611083119254162 + ========== + Finished basis vector 1/62 + - + Starting simulation of basis vector 2/62 + Performing CTM + | CTM step 1 conv: 2.004e+00 time: 0.99 obj: 3.335621 + | CTM step 2 conv: 6.150e-02 time: 1.26 obj: 3.397117 + | CTM step 3 conv: 2.017e-02 time: 1.28 obj: 3.376950 + | CTM step 4 conv: 3.838e-03 time: 1.26 obj: 3.380788 + | CTM step 5 conv: 3.650e-04 time: 1.3 obj: 3.380423 + | CTM step 6 conv: 1.246e-03 time: 1.29 obj: 3.381669 + | CTM step 7 conv: 1.288e-03 time: 1.31 obj: 3.380380 + Energies: 0.4285335373465171 1.5450126399606245e-10 + Norm: 0.12679967208649232 + ========== + Finished basis vector 2/62 + ... + +In this version of the algorithm, the full energy and norm overlap matrices will be computed. +Each of the basis vectors, as seen in the output above, is used as input in a separate CTM summation and the program will continue to run until all basis vectors have been used. diff --git a/docs/_sources/notes/install.rst.txt b/docs/_sources/notes/install.rst.txt new file mode 100644 index 0000000..b668de6 --- /dev/null +++ b/docs/_sources/notes/install.rst.txt @@ -0,0 +1,36 @@ +Installation +=================================== + +The quickest way of installing the :code:`adpeps` package is to clone the repository + +.. code-block:: bash + + git clone + + +Method 1 (recommended): `conda` +------------------------------------------ + +The repository comes with an included :code:`environment.yml` file, which automatically installs a Python environment with all required packages, which can be used as follows + +.. code-block:: bash + + cd ad-peps + conda env create -f environment.yml + conda activate adpeps + +When the installation finishes, you can check that the package is working + +.. code-block:: bash + + python -m adpeps -v + +Method 2: `pip` +------------------------------------------ + +The package can also be installed via `pip`: + +.. code-block:: bash + + cd ad-peps + pip install -e . diff --git a/docs/_sources/notes/start.rst.txt b/docs/_sources/notes/start.rst.txt new file mode 100644 index 0000000..08534e4 --- /dev/null +++ b/docs/_sources/notes/start.rst.txt @@ -0,0 +1,57 @@ +.. _notes/start: + +Getting Started +=================================== + +General +-------------- + +The main starting point for running simulations with the `adpeps` package is by loading the module directly via :code:`python -m adpeps`. + +For both ground-state and excited-state simulations the configuration can be set via configuration :code:`.yaml` files. +Each option in the configuration file corresponds to an attribute of the :mod:`adpeps.ipeps.config` module. + +The first argument for the module is the simulation mode (ground-state or excited-state): + +.. code-block:: bash + + python -m adpeps {gs,exci} ... + +.. note:: + The input configuration file location can be set via the + :envvar:`CONFIGDIR` variable. If it is not set, the default + input folder will be the `examples` subfolder of the package + root directory + +.. note:: + The output data location can be set via the :envvar:`DATADIR` + variable. If it is not set, the default output folder will be + in the `simulations` subfolder of the package root directory. + + +Ground states +-------------- + +For ground-state simulations, the only required argument is the configuration file. + +.. argparse:: + :ref: adpeps.__main__.get_parser + :prog: python -m adpeps + :path: gs + + +Excited states +-------------- + +For excited-state simulations, the first argument is again the name of a configuration file (note that the relevant options are different for excited-state simulations), and furthermore the `momentum index` :code:`-p` is required. + +The momentum index refers to a point in momentum space :math:`(k_x, k_y)` defined in a specific path through the Brillouin zone. +The corresponding momentum path can be set via the :attr:`adpeps.ipeps.config.momentum_path` option. +By default, the `'Bril1'` path is taken, which follows the cut along high symmetry points :math:`(\pi,0) - (\pi,\pi) - (\pi/2,\pi/2) - (0,0) - (\pi,0) - (\pi/2,\pi/2)` + +.. argparse:: + :ref: adpeps.__main__.get_parser + :prog: python -m adpeps + :nodefault: + :path: exci + diff --git a/docs/_static/basic.css b/docs/_static/basic.css new file mode 100644 index 0000000..5d8ae08 --- /dev/null +++ b/docs/_static/basic.css @@ -0,0 +1,861 @@ +/* + * basic.css + * ~~~~~~~~~ + * + * Sphinx stylesheet -- basic theme. + * + * :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ + +/* -- main layout ----------------------------------------------------------- */ + +div.clearer { + clear: both; +} + +div.section::after { + display: block; + content: ''; + clear: left; +} + +/* -- relbar ---------------------------------------------------------------- */ + +div.related { + width: 100%; + font-size: 90%; +} + +div.related h3 { + display: none; +} + +div.related ul { + margin: 0; + padding: 0 0 0 10px; + list-style: none; +} + +div.related li { + display: inline; +} + +div.related li.right { + float: 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(min-width:1200px){.toc-entry a{padding-right:0}}.toc-entry a:hover{color:rgba(var(--pst-color-toc-link-hover),1);text-decoration:none}.bd-sidebar{padding-top:1em}@media (min-width:720px){.bd-sidebar{border-right:1px solid rgba(0,0,0,.1)}@supports (position:-webkit-sticky) or (position:sticky){.bd-sidebar{position:-webkit-sticky;position:sticky;top:calc(var(--pst-header-height) + 20px);z-index:1000;height:calc(100vh - var(--pst-header-height) - 20px)}}}.bd-sidebar.no-sidebar{border-right:0}.bd-links{padding-top:1rem;padding-bottom:1rem;margin-right:-15px;margin-left:-15px}@media (min-width:720px){.bd-links{display:block!important}@supports (position:-webkit-sticky) or (position:sticky){.bd-links{max-height:calc(100vh - 11rem);overflow-y:auto}}}.bd-sidenav{display:none}.bd-content{padding-top:20px}.bd-content .section{max-width:100%}.bd-content .section table{display:block;overflow:auto}.bd-toc-link{display:block;padding:.25rem 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li>a:hover{color:rgba(var(--pst-color-sidebar-link-hover),1);text-decoration:none;background-color:transparent}.bd-sidebar .nav li>a.reference.external:after{font-family:Font Awesome\ 5 Free;font-weight:900;content:"\f35d";font-size:.75em;margin-left:.3em}.bd-sidebar .nav .active:hover>a,.bd-sidebar .nav .active>a{font-weight:600;color:rgba(var(--pst-color-sidebar-link-active),1)}.toc-h2{font-size:.85rem}.toc-h3{font-size:.75rem}.toc-h4{font-size:.65rem}.toc-entry>.nav-link.active{font-weight:600;color:#130654;color:rgba(var(--pst-color-toc-link-active),1);background-color:transparent;border-left:2px solid rgba(var(--pst-color-toc-link-active),1)}.nav-link:hover{border-style:none}#navbar-main-elements li.nav-item i{font-size:.7rem;padding-left:2px;vertical-align:middle}.bd-toc .nav .nav{display:none}.bd-toc .nav .nav.visible,.bd-toc .nav>.active>ul{display:block}.prev-next-bottom{margin:20px 0}.prev-next-bottom a.left-prev,.prev-next-bottom a.right-next{padding:10px;border:1px solid rgba(0,0,0,.2);max-width:45%;overflow-x:hidden;color:rgba(0,0,0,.65)}.prev-next-bottom a.left-prev{float:left}.prev-next-bottom a.left-prev:before{content:"<< "}.prev-next-bottom a.right-next{float:right}.prev-next-bottom a.right-next:after{content:" >>"}.alert{padding-bottom:0}.alert-info a{color:#e83e8c}#navbar-icon-links i.fa,#navbar-icon-links i.fab,#navbar-icon-links i.far,#navbar-icon-links i.fas{vertical-align:middle;font-style:normal;font-size:1.5rem;line-height:1.25}#navbar-icon-links i.fa-github-square:before{color:#333}#navbar-icon-links i.fa-twitter-square:before{color:#55acee}#navbar-icon-links i.fa-gitlab:before{color:#548}#navbar-icon-links i.fa-bitbucket:before{color:#0052cc}.tocsection{border-left:1px solid #eee;padding:.3rem 1.5rem}.tocsection i{padding-right:.5rem}.editthispage{padding-top:2rem}.editthispage a{color:#130754}.xr-wrap[hidden]{display:block!important}.toctree-checkbox{position:absolute;display:none}.toctree-checkbox~ul{display:none}.toctree-checkbox~label i{transform:rotate(0deg)}.toctree-checkbox:checked~ul{display:block}.toctree-checkbox:checked~label i{transform:rotate(180deg)}.bd-sidebar li{position:relative}.bd-sidebar label{position:absolute;top:0;right:0;height:30px;width:30px;cursor:pointer;display:flex;justify-content:center;align-items:center}.bd-sidebar label:hover{background:rgba(var(--pst-color-sidebar-expander-background-hover),1)}.bd-sidebar label i{display:inline-block;font-size:.75rem;text-align:center}.bd-sidebar label i:hover{color:rgba(var(--pst-color-sidebar-link-hover),1)}.bd-sidebar li.has-children>.reference{padding-right:30px}div.doctest>div.highlight span.gp,span.linenos,table.highlighttable td.linenos{user-select:none!important;-webkit-user-select:text!important;-webkit-user-select:none!important;-moz-user-select:none!important;-ms-user-select:none!important} \ No newline at end of file diff --git a/docs/_static/css/theme.css b/docs/_static/css/theme.css new file mode 100644 index 0000000..3f6e79d --- /dev/null +++ b/docs/_static/css/theme.css @@ -0,0 +1,117 @@ +:root { + /***************************************************************************** + * Theme config + **/ + --pst-header-height: 60px; + + /***************************************************************************** + * Font size + **/ + --pst-font-size-base: 15px; /* base font size - applied at body / html level */ + + /* heading font sizes */ + --pst-font-size-h1: 36px; + --pst-font-size-h2: 32px; + --pst-font-size-h3: 26px; + --pst-font-size-h4: 21px; + --pst-font-size-h5: 18px; + --pst-font-size-h6: 16px; + + /* smaller then heading font sizes*/ + --pst-font-size-milli: 12px; + + --pst-sidebar-font-size: .9em; + --pst-sidebar-caption-font-size: .9em; + + /***************************************************************************** + * Font family + **/ + /* These are adapted from https://systemfontstack.com/ */ + --pst-font-family-base-system: -apple-system, BlinkMacSystemFont, Segoe UI, "Helvetica Neue", + Arial, sans-serif, Apple Color Emoji, Segoe UI Emoji, Segoe UI Symbol; + --pst-font-family-monospace-system: "SFMono-Regular", Menlo, Consolas, Monaco, + Liberation Mono, Lucida Console, monospace; + + --pst-font-family-base: var(--pst-font-family-base-system); + --pst-font-family-heading: var(--pst-font-family-base); + --pst-font-family-monospace: var(--pst-font-family-monospace-system); + + /***************************************************************************** + * Color + * + * Colors are defined in rgb string way, "red, green, blue" + **/ + --pst-color-primary: 19, 6, 84; + --pst-color-success: 40, 167, 69; + --pst-color-info: 0, 123, 255; /*23, 162, 184;*/ + --pst-color-warning: 255, 193, 7; + --pst-color-danger: 220, 53, 69; + --pst-color-text-base: 51, 51, 51; + + --pst-color-h1: var(--pst-color-primary); + --pst-color-h2: var(--pst-color-primary); + --pst-color-h3: var(--pst-color-text-base); + --pst-color-h4: var(--pst-color-text-base); + --pst-color-h5: var(--pst-color-text-base); + --pst-color-h6: var(--pst-color-text-base); + --pst-color-paragraph: var(--pst-color-text-base); + --pst-color-link: 0, 91, 129; + --pst-color-link-hover: 227, 46, 0; + --pst-color-headerlink: 198, 15, 15; + --pst-color-headerlink-hover: 255, 255, 255; + --pst-color-preformatted-text: 34, 34, 34; + --pst-color-preformatted-background: 250, 250, 250; + --pst-color-inline-code: 232, 62, 140; + + --pst-color-active-navigation: 19, 6, 84; + --pst-color-navbar-link: 77, 77, 77; + --pst-color-navbar-link-hover: var(--pst-color-active-navigation); + --pst-color-navbar-link-active: var(--pst-color-active-navigation); + --pst-color-sidebar-link: 77, 77, 77; + --pst-color-sidebar-link-hover: var(--pst-color-active-navigation); + --pst-color-sidebar-link-active: var(--pst-color-active-navigation); + --pst-color-sidebar-expander-background-hover: 244, 244, 244; + --pst-color-sidebar-caption: 77, 77, 77; + --pst-color-toc-link: 119, 117, 122; + --pst-color-toc-link-hover: var(--pst-color-active-navigation); + --pst-color-toc-link-active: var(--pst-color-active-navigation); + + /***************************************************************************** + * Icon + **/ + + /* font awesome icons*/ + --pst-icon-check-circle: '\f058'; + --pst-icon-info-circle: '\f05a'; + --pst-icon-exclamation-triangle: '\f071'; + --pst-icon-exclamation-circle: '\f06a'; + --pst-icon-times-circle: '\f057'; + --pst-icon-lightbulb: '\f0eb'; + + /***************************************************************************** + * Admonitions + **/ + + --pst-color-admonition-default: var(--pst-color-info); + --pst-color-admonition-note: var(--pst-color-info); + --pst-color-admonition-attention: var(--pst-color-warning); + --pst-color-admonition-caution: var(--pst-color-warning); + --pst-color-admonition-warning: var(--pst-color-warning); + --pst-color-admonition-danger: var(--pst-color-danger); + --pst-color-admonition-error: var(--pst-color-danger); + --pst-color-admonition-hint: var(--pst-color-success); + --pst-color-admonition-tip: var(--pst-color-success); + --pst-color-admonition-important: var(--pst-color-success); + + --pst-icon-admonition-default: var(--pst-icon-info-circle); + --pst-icon-admonition-note: var(--pst-icon-info-circle); + --pst-icon-admonition-attention: var(--pst-icon-exclamation-circle); + --pst-icon-admonition-caution: var(--pst-icon-exclamation-triangle); + --pst-icon-admonition-warning: var(--pst-icon-exclamation-triangle); + --pst-icon-admonition-danger: var(--pst-icon-exclamation-triangle); + --pst-icon-admonition-error: var(--pst-icon-times-circle); + --pst-icon-admonition-hint: var(--pst-icon-lightbulb); + --pst-icon-admonition-tip: var(--pst-icon-lightbulb); + --pst-icon-admonition-important: var(--pst-icon-exclamation-circle); + +} diff --git a/docs/_static/doctools.js b/docs/_static/doctools.js new file mode 100644 index 0000000..61ac9d2 --- /dev/null +++ b/docs/_static/doctools.js @@ -0,0 +1,321 @@ +/* + * doctools.js + * ~~~~~~~~~~~ + * + * Sphinx JavaScript utilities for all documentation. + * + * :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ + +/** + * select a different prefix for underscore + */ +$u = _.noConflict(); + +/** + * make the code below compatible with browsers without + * an installed firebug like debugger +if (!window.console || !console.firebug) { + var names = ["log", "debug", "info", "warn", "error", "assert", "dir", + "dirxml", "group", "groupEnd", "time", "timeEnd", "count", "trace", + "profile", "profileEnd"]; + window.console = {}; + for (var i = 0; i < names.length; ++i) + window.console[names[i]] = function() {}; +} + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} + +/** + * Small JavaScript module for the documentation. + */ +var Documentation = { + + init : function() { + this.fixFirefoxAnchorBug(); + this.highlightSearchWords(); + this.initIndexTable(); + if (DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) { + this.initOnKeyListeners(); + } + }, + + /** + * i18n support + */ + TRANSLATIONS : {}, + PLURAL_EXPR : function(n) { return n === 1 ? 0 : 1; }, + LOCALE : 'unknown', + + // gettext and ngettext don't access this so that the functions + // can safely bound to a different name (_ = Documentation.gettext) + gettext : function(string) { + var translated = Documentation.TRANSLATIONS[string]; + if (typeof translated === 'undefined') + return string; + return (typeof translated === 'string') ? translated : translated[0]; + }, + + ngettext : function(singular, plural, n) { + var translated = Documentation.TRANSLATIONS[singular]; + if (typeof translated === 'undefined') + return (n == 1) ? singular : plural; + return translated[Documentation.PLURALEXPR(n)]; + }, + + addTranslations : function(catalog) { + for (var key in catalog.messages) + this.TRANSLATIONS[key] = catalog.messages[key]; + this.PLURAL_EXPR = new Function('n', 'return +(' + catalog.plural_expr + ')'); + this.LOCALE = catalog.locale; + }, + + /** + * add context elements like header anchor links + */ + addContextElements : function() { + $('div[id] > :header:first').each(function() { + $('\u00B6'). + attr('href', '#' + this.id). + attr('title', _('Permalink to this headline')). + appendTo(this); + }); + $('dt[id]').each(function() { + $('\u00B6'). + attr('href', '#' + this.id). + attr('title', _('Permalink to this definition')). + appendTo(this); + }); + }, + + /** + * workaround a firefox stupidity + * see: https://bugzilla.mozilla.org/show_bug.cgi?id=645075 + */ + fixFirefoxAnchorBug : function() { + if (document.location.hash && $.browser.mozilla) + window.setTimeout(function() { + document.location.href += ''; + }, 10); + }, + + /** + * highlight the search words provided in the url in the text + */ + highlightSearchWords : function() { + var params = $.getQueryParameters(); + var terms = (params.highlight) ? params.highlight[0].split(/\s+/) : []; + if (terms.length) { + var body = $('div.body'); + if (!body.length) { + body = $('body'); + } + window.setTimeout(function() { + $.each(terms, function() { + body.highlightText(this.toLowerCase(), 'highlighted'); + }); + }, 10); + $('

' + _('Hide Search Matches') + '

') + .appendTo($('#searchbox')); + } + }, + + /** + * init the domain index toggle buttons + */ + initIndexTable : function() { + var togglers = $('img.toggler').click(function() { + var src = $(this).attr('src'); + var idnum = $(this).attr('id').substr(7); + $('tr.cg-' + idnum).toggle(); + if (src.substr(-9) === 'minus.png') + $(this).attr('src', src.substr(0, src.length-9) + 'plus.png'); + else + $(this).attr('src', src.substr(0, src.length-8) + 'minus.png'); + }).css('display', ''); + if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) { + togglers.click(); + } + }, + + /** + * helper function to hide the search marks again + */ + hideSearchWords : function() { + $('#searchbox .highlight-link').fadeOut(300); + $('span.highlighted').removeClass('highlighted'); + }, + + /** + * make the url absolute + */ + makeURL : function(relativeURL) { + return DOCUMENTATION_OPTIONS.URL_ROOT + '/' + relativeURL; + }, + + /** + * get the current relative url + */ + getCurrentURL : function() { + var path = document.location.pathname; + var parts = path.split(/\//); + $.each(DOCUMENTATION_OPTIONS.URL_ROOT.split(/\//), function() { + if (this === '..') + parts.pop(); + }); + var url = parts.join('/'); + return path.substring(url.lastIndexOf('/') + 1, path.length - 1); + }, + + initOnKeyListeners: function() { + $(document).keydown(function(event) { + var activeElementType = document.activeElement.tagName; + // don't navigate when in search box, textarea, dropdown or button + if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT' + && activeElementType !== 'BUTTON' && !event.altKey && !event.ctrlKey && !event.metaKey + && !event.shiftKey) { + switch (event.keyCode) { + case 37: // left + var prevHref = $('link[rel="prev"]').prop('href'); + if (prevHref) { + window.location.href = prevHref; + return false; + } + case 39: // right + var nextHref = $('link[rel="next"]').prop('href'); + if (nextHref) { + window.location.href = nextHref; + return false; + } + } + } + }); + } +}; + +// quick alias for translations +_ = Documentation.gettext; + +$(document).ready(function() { + Documentation.init(); +}); diff --git a/docs/_static/documentation_options.js b/docs/_static/documentation_options.js new file mode 100644 index 0000000..75b5cf1 --- /dev/null +++ b/docs/_static/documentation_options.js @@ -0,0 +1,12 @@ +var DOCUMENTATION_OPTIONS = { + URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'), + VERSION: '', + LANGUAGE: 'None', + COLLAPSE_INDEX: false, + BUILDER: 'html', + FILE_SUFFIX: '.html', + LINK_SUFFIX: '.html', + HAS_SOURCE: true, + SOURCELINK_SUFFIX: '.txt', + NAVIGATION_WITH_KEYS: true +}; \ No newline at end of file diff --git a/docs/_static/file.png b/docs/_static/file.png new file mode 100644 index 0000000000000000000000000000000000000000..a858a410e4faa62ce324d814e4b816fff83a6fb3 GIT binary patch literal 286 zcmV+(0pb3MP)s`hMrGg#P~ix$^RISR_I47Y|r1 z_CyJOe}D1){SET-^Amu_i71Lt6eYfZjRyw@I6OQAIXXHDfiX^GbOlHe=Ae4>0m)d(f|Me07*qoM6N<$f}vM^LjV8( literal 0 HcmV?d00001 diff --git a/docs/_static/jquery-3.5.1.js b/docs/_static/jquery-3.5.1.js new file mode 100644 index 0000000..5093733 --- /dev/null +++ b/docs/_static/jquery-3.5.1.js @@ -0,0 +1,10872 @@ +/*! + * jQuery JavaScript Library v3.5.1 + * https://jquery.com/ + * + * Includes Sizzle.js + * https://sizzlejs.com/ + * + * Copyright JS Foundation and other contributors + * Released under the MIT license + * https://jquery.org/license + * + * Date: 2020-05-04T22:49Z + */ +( function( global, factory ) { + + "use strict"; + + if ( typeof module === "object" && typeof module.exports === "object" ) { + + // For CommonJS and CommonJS-like environments where a proper `window` + // is present, execute the factory and get jQuery. + // For environments that do not have a `window` with a `document` + // (such as Node.js), expose a factory as module.exports. + // This accentuates the need for the creation of a real `window`. + // e.g. var jQuery = require("jquery")(window); + // See ticket #14549 for more info. + module.exports = global.document ? + factory( global, true ) : + function( w ) { + if ( !w.document ) { + throw new Error( "jQuery requires a window with a document" ); + } + return factory( w ); + }; + } else { + factory( global ); + } + +// Pass this if window is not defined yet +} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) { + +// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1 +// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode +// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common +// enough that all such attempts are guarded in a try block. +"use strict"; + +var arr = []; + +var getProto = Object.getPrototypeOf; + +var slice = arr.slice; + +var flat = arr.flat ? function( array ) { + return arr.flat.call( array ); +} : function( array ) { + return arr.concat.apply( [], array ); +}; + + +var push = arr.push; + +var indexOf = arr.indexOf; + +var class2type = {}; + +var toString = class2type.toString; + +var hasOwn = class2type.hasOwnProperty; + +var fnToString = hasOwn.toString; + +var ObjectFunctionString = fnToString.call( Object ); + +var support = {}; + +var isFunction = function isFunction( obj ) { + + // Support: Chrome <=57, Firefox <=52 + // In some browsers, typeof returns "function" for HTML elements + // (i.e., `typeof document.createElement( "object" ) === "function"`). + // We don't want to classify *any* DOM node as a function. + return typeof obj === "function" && typeof obj.nodeType !== "number"; + }; + + +var isWindow = function isWindow( obj ) { + return obj != null && obj === obj.window; + }; + + +var document = window.document; + + + + var preservedScriptAttributes = { + type: true, + src: true, + nonce: true, + noModule: true + }; + + function DOMEval( code, node, doc ) { + doc = doc || document; + + var i, val, + script = doc.createElement( "script" ); + + script.text = code; + if ( node ) { + for ( i in preservedScriptAttributes ) { + + // Support: Firefox 64+, Edge 18+ + // Some browsers don't support the "nonce" property on scripts. + // On the other hand, just using `getAttribute` is not enough as + // the `nonce` attribute is reset to an empty string whenever it + // becomes browsing-context connected. + // See https://github.com/whatwg/html/issues/2369 + // See https://html.spec.whatwg.org/#nonce-attributes + // The `node.getAttribute` check was added for the sake of + // `jQuery.globalEval` so that it can fake a nonce-containing node + // via an object. + val = node[ i ] || node.getAttribute && node.getAttribute( i ); + if ( val ) { + script.setAttribute( i, val ); + } + } + } + doc.head.appendChild( script ).parentNode.removeChild( script ); + } + + +function toType( obj ) { + if ( obj == null ) { + return obj + ""; + } + + // Support: Android <=2.3 only (functionish RegExp) + return typeof obj === "object" || typeof obj === "function" ? + class2type[ toString.call( obj ) ] || "object" : + typeof obj; +} +/* global Symbol */ +// Defining this global in .eslintrc.json would create a danger of using the global +// unguarded in another place, it seems safer to define global only for this module + + + +var + version = "3.5.1", + + // Define a local copy of jQuery + jQuery = function( selector, context ) { + + // The jQuery object is actually just the init constructor 'enhanced' + // Need init if jQuery is called (just allow error to be thrown if not included) + return new jQuery.fn.init( selector, context ); + }; + +jQuery.fn = jQuery.prototype = { + + // The current version of jQuery being used + jquery: version, + + constructor: jQuery, + + // The default length of a jQuery object is 0 + length: 0, + + toArray: function() { + return slice.call( this ); + }, + + // Get the Nth element in the matched element set OR + // Get the whole matched element set as a clean array + get: function( num ) { + + // Return all the elements in a clean array + if ( num == null ) { + return slice.call( this ); + } + + // Return just the one element from the set + return num < 0 ? this[ num + this.length ] : this[ num ]; + }, + + // Take an array of elements and push it onto the stack + // (returning the new matched element set) + pushStack: function( elems ) { + + // Build a new jQuery matched element set + var ret = jQuery.merge( this.constructor(), elems ); + + // Add the old object onto the stack (as a reference) + ret.prevObject = this; + + // Return the newly-formed element set + return ret; + }, + + // Execute a callback for every element in the matched set. + each: function( callback ) { + return jQuery.each( this, callback ); + }, + + map: function( callback ) { + return this.pushStack( jQuery.map( this, function( elem, i ) { + return callback.call( elem, i, elem ); + } ) ); + }, + + slice: function() { + return this.pushStack( slice.apply( this, arguments ) ); + }, + + first: function() { + return this.eq( 0 ); + }, + + last: function() { + return this.eq( -1 ); + }, + + even: function() { + return this.pushStack( jQuery.grep( this, function( _elem, i ) { + return ( i + 1 ) % 2; + } ) ); + }, + + odd: function() { + return this.pushStack( jQuery.grep( this, function( _elem, i ) { + return i % 2; + } ) ); + }, + + eq: function( i ) { + var len = this.length, + j = +i + ( i < 0 ? len : 0 ); + return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] ); + }, + + end: function() { + return this.prevObject || this.constructor(); + }, + + // For internal use only. + // Behaves like an Array's method, not like a jQuery method. + push: push, + sort: arr.sort, + splice: arr.splice +}; + +jQuery.extend = jQuery.fn.extend = function() { + var options, name, src, copy, copyIsArray, clone, + target = arguments[ 0 ] || {}, + i = 1, + length = arguments.length, + deep = false; + + // Handle a deep copy situation + if ( typeof target === "boolean" ) { + deep = target; + + // Skip the boolean and the target + target = arguments[ i ] || {}; + i++; + } + + // Handle case when target is a string or something (possible in deep copy) + if ( typeof target !== "object" && !isFunction( target ) ) { + target = {}; + } + + // Extend jQuery itself if only one argument is passed + if ( i === length ) { + target = this; + i--; + } + + for ( ; i < length; i++ ) { + + // Only deal with non-null/undefined values + if ( ( options = arguments[ i ] ) != null ) { + + // Extend the base object + for ( name in options ) { + copy = options[ name ]; + + // Prevent Object.prototype pollution + // Prevent never-ending loop + if ( name === "__proto__" || target === copy ) { + continue; + } + + // Recurse if we're merging plain objects or arrays + if ( deep && copy && ( jQuery.isPlainObject( copy ) || + ( copyIsArray = Array.isArray( copy ) ) ) ) { + src = target[ name ]; + + // Ensure proper type for the source value + if ( copyIsArray && !Array.isArray( src ) ) { + clone = []; + } else if ( !copyIsArray && !jQuery.isPlainObject( src ) ) { + clone = {}; + } else { + clone = src; + } + copyIsArray = false; + + // Never move original objects, clone them + target[ name ] = jQuery.extend( deep, clone, copy ); + + // Don't bring in undefined values + } else if ( copy !== undefined ) { + target[ name ] = copy; + } + } + } + } + + // Return the modified object + return target; +}; + +jQuery.extend( { + + // Unique for each copy of jQuery on the page + expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ), + + // Assume jQuery is ready without the ready module + isReady: true, + + error: function( msg ) { + throw new Error( msg ); + }, + + noop: function() {}, + + isPlainObject: function( obj ) { + var proto, Ctor; + + // Detect obvious negatives + // Use toString instead of jQuery.type to catch host objects + if ( !obj || toString.call( obj ) !== "[object Object]" ) { + return false; + } + + proto = getProto( obj ); + + // Objects with no prototype (e.g., `Object.create( null )`) are plain + if ( !proto ) { + return true; + } + + // Objects with prototype are plain iff they were constructed by a global Object function + Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor; + return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString; + }, + + isEmptyObject: function( obj ) { + var name; + + for ( name in obj ) { + return false; + } + return true; + }, + + // Evaluates a script in a provided context; falls back to the global one + // if not specified. + globalEval: function( code, options, doc ) { + DOMEval( code, { nonce: options && options.nonce }, doc ); + }, + + each: function( obj, callback ) { + var length, i = 0; + + if ( isArrayLike( obj ) ) { + length = obj.length; + for ( ; i < length; i++ ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } else { + for ( i in obj ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } + + return obj; + }, + + // results is for internal usage only + makeArray: function( arr, results ) { + var ret = results || []; + + if ( arr != null ) { + if ( isArrayLike( Object( arr ) ) ) { + jQuery.merge( ret, + typeof arr === "string" ? + [ arr ] : arr + ); + } else { + push.call( ret, arr ); + } + } + + return ret; + }, + + inArray: function( elem, arr, i ) { + return arr == null ? -1 : indexOf.call( arr, elem, i ); + }, + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + merge: function( first, second ) { + var len = +second.length, + j = 0, + i = first.length; + + for ( ; j < len; j++ ) { + first[ i++ ] = second[ j ]; + } + + first.length = i; + + return first; + }, + + grep: function( elems, callback, invert ) { + var callbackInverse, + matches = [], + i = 0, + length = elems.length, + callbackExpect = !invert; + + // Go through the array, only saving the items + // that pass the validator function + for ( ; i < length; i++ ) { + callbackInverse = !callback( elems[ i ], i ); + if ( callbackInverse !== callbackExpect ) { + matches.push( elems[ i ] ); + } + } + + return matches; + }, + + // arg is for internal usage only + map: function( elems, callback, arg ) { + var length, value, + i = 0, + ret = []; + + // Go through the array, translating each of the items to their new values + if ( isArrayLike( elems ) ) { + length = elems.length; + for ( ; i < length; i++ ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + + // Go through every key on the object, + } else { + for ( i in elems ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + } + + // Flatten any nested arrays + return flat( ret ); + }, + + // A global GUID counter for objects + guid: 1, + + // jQuery.support is not used in Core but other projects attach their + // properties to it so it needs to exist. + support: support +} ); + +if ( typeof Symbol === "function" ) { + jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ]; +} + +// Populate the class2type map +jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ), +function( _i, name ) { + class2type[ "[object " + name + "]" ] = name.toLowerCase(); +} ); + +function isArrayLike( obj ) { + + // Support: real iOS 8.2 only (not reproducible in simulator) + // `in` check used to prevent JIT error (gh-2145) + // hasOwn isn't used here due to false negatives + // regarding Nodelist length in IE + var length = !!obj && "length" in obj && obj.length, + type = toType( obj ); + + if ( isFunction( obj ) || isWindow( obj ) ) { + return false; + } + + return type === "array" || length === 0 || + typeof length === "number" && length > 0 && ( length - 1 ) in obj; +} +var Sizzle = +/*! + * Sizzle CSS Selector Engine v2.3.5 + * https://sizzlejs.com/ + * + * Copyright JS Foundation and other contributors + * Released under the MIT license + * https://js.foundation/ + * + * Date: 2020-03-14 + */ +( function( window ) { +var i, + support, + Expr, + getText, + isXML, + tokenize, + compile, + select, + outermostContext, + sortInput, + hasDuplicate, + + // Local document vars + setDocument, + document, + docElem, + documentIsHTML, + rbuggyQSA, + rbuggyMatches, + matches, + contains, + + // Instance-specific data + expando = "sizzle" + 1 * new Date(), + preferredDoc = window.document, + dirruns = 0, + done = 0, + classCache = createCache(), + tokenCache = createCache(), + compilerCache = createCache(), + nonnativeSelectorCache = createCache(), + sortOrder = function( a, b ) { + if ( a === b ) { + hasDuplicate = true; + } + return 0; + }, + + // Instance methods + hasOwn = ( {} ).hasOwnProperty, + arr = [], + pop = arr.pop, + pushNative = arr.push, + push = arr.push, + slice = arr.slice, + + // Use a stripped-down indexOf as it's faster than native + // https://jsperf.com/thor-indexof-vs-for/5 + indexOf = function( list, elem ) { + var i = 0, + len = list.length; + for ( ; i < len; i++ ) { + if ( list[ i ] === elem ) { + return i; + } + } + return -1; + }, + + booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" + + "ismap|loop|multiple|open|readonly|required|scoped", + + // Regular expressions + + // http://www.w3.org/TR/css3-selectors/#whitespace + whitespace = "[\\x20\\t\\r\\n\\f]", + + // https://www.w3.org/TR/css-syntax-3/#ident-token-diagram + identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace + + "?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+", + + // Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors + attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace + + + // Operator (capture 2) + "*([*^$|!~]?=)" + whitespace + + + // "Attribute values must be CSS identifiers [capture 5] + // or strings [capture 3 or capture 4]" + "*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + + whitespace + "*\\]", + + pseudos = ":(" + identifier + ")(?:\\((" + + + // To reduce the number of selectors needing tokenize in the preFilter, prefer arguments: + // 1. quoted (capture 3; capture 4 or capture 5) + "('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" + + + // 2. simple (capture 6) + "((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" + + + // 3. anything else (capture 2) + ".*" + + ")\\)|)", + + // Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter + rwhitespace = new RegExp( whitespace + "+", "g" ), + rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + + whitespace + "+$", "g" ), + + rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ), + rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + + "*" ), + rdescend = new RegExp( whitespace + "|>" ), + + rpseudo = new RegExp( pseudos ), + ridentifier = new RegExp( "^" + identifier + "$" ), + + matchExpr = { + "ID": new RegExp( "^#(" + identifier + ")" ), + "CLASS": new RegExp( "^\\.(" + identifier + ")" ), + "TAG": new RegExp( "^(" + identifier + "|[*])" ), + "ATTR": new RegExp( "^" + attributes ), + "PSEUDO": new RegExp( "^" + pseudos ), + "CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + + whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + + whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ), + "bool": new RegExp( "^(?:" + booleans + ")$", "i" ), + + // For use in libraries implementing .is() + // We use this for POS matching in `select` + "needsContext": new RegExp( "^" + whitespace + + "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace + + "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" ) + }, + + rhtml = /HTML$/i, + rinputs = /^(?:input|select|textarea|button)$/i, + rheader = /^h\d$/i, + + rnative = /^[^{]+\{\s*\[native \w/, + + // Easily-parseable/retrievable ID or TAG or CLASS selectors + rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/, + + rsibling = /[+~]/, + + // CSS escapes + // http://www.w3.org/TR/CSS21/syndata.html#escaped-characters + runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ), + funescape = function( escape, nonHex ) { + var high = "0x" + escape.slice( 1 ) - 0x10000; + + return nonHex ? + + // Strip the backslash prefix from a non-hex escape sequence + nonHex : + + // Replace a hexadecimal escape sequence with the encoded Unicode code point + // Support: IE <=11+ + // For values outside the Basic Multilingual Plane (BMP), manually construct a + // surrogate pair + high < 0 ? + String.fromCharCode( high + 0x10000 ) : + String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 ); + }, + + // CSS string/identifier serialization + // https://drafts.csswg.org/cssom/#common-serializing-idioms + rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g, + fcssescape = function( ch, asCodePoint ) { + if ( asCodePoint ) { + + // U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER + if ( ch === "\0" ) { + return "\uFFFD"; + } + + // Control characters and (dependent upon position) numbers get escaped as code points + return ch.slice( 0, -1 ) + "\\" + + ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " "; + } + + // Other potentially-special ASCII characters get backslash-escaped + return "\\" + ch; + }, + + // Used for iframes + // See setDocument() + // Removing the function wrapper causes a "Permission Denied" + // error in IE + unloadHandler = function() { + setDocument(); + }, + + inDisabledFieldset = addCombinator( + function( elem ) { + return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset"; + }, + { dir: "parentNode", next: "legend" } + ); + +// Optimize for push.apply( _, NodeList ) +try { + push.apply( + ( arr = slice.call( preferredDoc.childNodes ) ), + preferredDoc.childNodes + ); + + // Support: Android<4.0 + // Detect silently failing push.apply + // eslint-disable-next-line no-unused-expressions + arr[ preferredDoc.childNodes.length ].nodeType; +} catch ( e ) { + push = { apply: arr.length ? + + // Leverage slice if possible + function( target, els ) { + pushNative.apply( target, slice.call( els ) ); + } : + + // Support: IE<9 + // Otherwise append directly + function( target, els ) { + var j = target.length, + i = 0; + + // Can't trust NodeList.length + while ( ( target[ j++ ] = els[ i++ ] ) ) {} + target.length = j - 1; + } + }; +} + +function Sizzle( selector, context, results, seed ) { + var m, i, elem, nid, match, groups, newSelector, + newContext = context && context.ownerDocument, + + // nodeType defaults to 9, since context defaults to document + nodeType = context ? context.nodeType : 9; + + results = results || []; + + // Return early from calls with invalid selector or context + if ( typeof selector !== "string" || !selector || + nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) { + + return results; + } + + // Try to shortcut find operations (as opposed to filters) in HTML documents + if ( !seed ) { + setDocument( context ); + context = context || document; + + if ( documentIsHTML ) { + + // If the selector is sufficiently simple, try using a "get*By*" DOM method + // (excepting DocumentFragment context, where the methods don't exist) + if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) { + + // ID selector + if ( ( m = match[ 1 ] ) ) { + + // Document context + if ( nodeType === 9 ) { + if ( ( elem = context.getElementById( m ) ) ) { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( elem.id === m ) { + results.push( elem ); + return results; + } + } else { + return results; + } + + // Element context + } else { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( newContext && ( elem = newContext.getElementById( m ) ) && + contains( context, elem ) && + elem.id === m ) { + + results.push( elem ); + return results; + } + } + + // Type selector + } else if ( match[ 2 ] ) { + push.apply( results, context.getElementsByTagName( selector ) ); + return results; + + // Class selector + } else if ( ( m = match[ 3 ] ) && support.getElementsByClassName && + context.getElementsByClassName ) { + + push.apply( results, context.getElementsByClassName( m ) ); + return results; + } + } + + // Take advantage of querySelectorAll + if ( support.qsa && + !nonnativeSelectorCache[ selector + " " ] && + ( !rbuggyQSA || !rbuggyQSA.test( selector ) ) && + + // Support: IE 8 only + // Exclude object elements + ( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) { + + newSelector = selector; + newContext = context; + + // qSA considers elements outside a scoping root when evaluating child or + // descendant combinators, which is not what we want. + // In such cases, we work around the behavior by prefixing every selector in the + // list with an ID selector referencing the scope context. + // The technique has to be used as well when a leading combinator is used + // as such selectors are not recognized by querySelectorAll. + // Thanks to Andrew Dupont for this technique. + if ( nodeType === 1 && + ( rdescend.test( selector ) || rcombinators.test( selector ) ) ) { + + // Expand context for sibling selectors + newContext = rsibling.test( selector ) && testContext( context.parentNode ) || + context; + + // We can use :scope instead of the ID hack if the browser + // supports it & if we're not changing the context. + if ( newContext !== context || !support.scope ) { + + // Capture the context ID, setting it first if necessary + if ( ( nid = context.getAttribute( "id" ) ) ) { + nid = nid.replace( rcssescape, fcssescape ); + } else { + context.setAttribute( "id", ( nid = expando ) ); + } + } + + // Prefix every selector in the list + groups = tokenize( selector ); + i = groups.length; + while ( i-- ) { + groups[ i ] = ( nid ? "#" + nid : ":scope" ) + " " + + toSelector( groups[ i ] ); + } + newSelector = groups.join( "," ); + } + + try { + push.apply( results, + newContext.querySelectorAll( newSelector ) + ); + return results; + } catch ( qsaError ) { + nonnativeSelectorCache( selector, true ); + } finally { + if ( nid === expando ) { + context.removeAttribute( "id" ); + } + } + } + } + } + + // All others + return select( selector.replace( rtrim, "$1" ), context, results, seed ); +} + +/** + * Create key-value caches of limited size + * @returns {function(string, object)} Returns the Object data after storing it on itself with + * property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength) + * deleting the oldest entry + */ +function createCache() { + var keys = []; + + function cache( key, value ) { + + // Use (key + " ") to avoid collision with native prototype properties (see Issue #157) + if ( keys.push( key + " " ) > Expr.cacheLength ) { + + // Only keep the most recent entries + delete cache[ keys.shift() ]; + } + return ( cache[ key + " " ] = value ); + } + return cache; +} + +/** + * Mark a function for special use by Sizzle + * @param {Function} fn The function to mark + */ +function markFunction( fn ) { + fn[ expando ] = true; + return fn; +} + +/** + * Support testing using an element + * @param {Function} fn Passed the created element and returns a boolean result + */ +function assert( fn ) { + var el = document.createElement( "fieldset" ); + + try { + return !!fn( el ); + } catch ( e ) { + return false; + } finally { + + // Remove from its parent by default + if ( el.parentNode ) { + el.parentNode.removeChild( el ); + } + + // release memory in IE + el = null; + } +} + +/** + * Adds the same handler for all of the specified attrs + * @param {String} attrs Pipe-separated list of attributes + * @param {Function} handler The method that will be applied + */ +function addHandle( attrs, handler ) { + var arr = attrs.split( "|" ), + i = arr.length; + + while ( i-- ) { + Expr.attrHandle[ arr[ i ] ] = handler; + } +} + +/** + * Checks document order of two siblings + * @param {Element} a + * @param {Element} b + * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b + */ +function siblingCheck( a, b ) { + var cur = b && a, + diff = cur && a.nodeType === 1 && b.nodeType === 1 && + a.sourceIndex - b.sourceIndex; + + // Use IE sourceIndex if available on both nodes + if ( diff ) { + return diff; + } + + // Check if b follows a + if ( cur ) { + while ( ( cur = cur.nextSibling ) ) { + if ( cur === b ) { + return -1; + } + } + } + + return a ? 1 : -1; +} + +/** + * Returns a function to use in pseudos for input types + * @param {String} type + */ +function createInputPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for buttons + * @param {String} type + */ +function createButtonPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return ( name === "input" || name === "button" ) && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for :enabled/:disabled + * @param {Boolean} disabled true for :disabled; false for :enabled + */ +function createDisabledPseudo( disabled ) { + + // Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable + return function( elem ) { + + // Only certain elements can match :enabled or :disabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled + if ( "form" in elem ) { + + // Check for inherited disabledness on relevant non-disabled elements: + // * listed form-associated elements in a disabled fieldset + // https://html.spec.whatwg.org/multipage/forms.html#category-listed + // https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled + // * option elements in a disabled optgroup + // https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled + // All such elements have a "form" property. + if ( elem.parentNode && elem.disabled === false ) { + + // Option elements defer to a parent optgroup if present + if ( "label" in elem ) { + if ( "label" in elem.parentNode ) { + return elem.parentNode.disabled === disabled; + } else { + return elem.disabled === disabled; + } + } + + // Support: IE 6 - 11 + // Use the isDisabled shortcut property to check for disabled fieldset ancestors + return elem.isDisabled === disabled || + + // Where there is no isDisabled, check manually + /* jshint -W018 */ + elem.isDisabled !== !disabled && + inDisabledFieldset( elem ) === disabled; + } + + return elem.disabled === disabled; + + // Try to winnow out elements that can't be disabled before trusting the disabled property. + // Some victims get caught in our net (label, legend, menu, track), but it shouldn't + // even exist on them, let alone have a boolean value. + } else if ( "label" in elem ) { + return elem.disabled === disabled; + } + + // Remaining elements are neither :enabled nor :disabled + return false; + }; +} + +/** + * Returns a function to use in pseudos for positionals + * @param {Function} fn + */ +function createPositionalPseudo( fn ) { + return markFunction( function( argument ) { + argument = +argument; + return markFunction( function( seed, matches ) { + var j, + matchIndexes = fn( [], seed.length, argument ), + i = matchIndexes.length; + + // Match elements found at the specified indexes + while ( i-- ) { + if ( seed[ ( j = matchIndexes[ i ] ) ] ) { + seed[ j ] = !( matches[ j ] = seed[ j ] ); + } + } + } ); + } ); +} + +/** + * Checks a node for validity as a Sizzle context + * @param {Element|Object=} context + * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value + */ +function testContext( context ) { + return context && typeof context.getElementsByTagName !== "undefined" && context; +} + +// Expose support vars for convenience +support = Sizzle.support = {}; + +/** + * Detects XML nodes + * @param {Element|Object} elem An element or a document + * @returns {Boolean} True iff elem is a non-HTML XML node + */ +isXML = Sizzle.isXML = function( elem ) { + var namespace = elem.namespaceURI, + docElem = ( elem.ownerDocument || elem ).documentElement; + + // Support: IE <=8 + // Assume HTML when documentElement doesn't yet exist, such as inside loading iframes + // https://bugs.jquery.com/ticket/4833 + return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" ); +}; + +/** + * Sets document-related variables once based on the current document + * @param {Element|Object} [doc] An element or document object to use to set the document + * @returns {Object} Returns the current document + */ +setDocument = Sizzle.setDocument = function( node ) { + var hasCompare, subWindow, + doc = node ? node.ownerDocument || node : preferredDoc; + + // Return early if doc is invalid or already selected + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( doc == document || doc.nodeType !== 9 || !doc.documentElement ) { + return document; + } + + // Update global variables + document = doc; + docElem = document.documentElement; + documentIsHTML = !isXML( document ); + + // Support: IE 9 - 11+, Edge 12 - 18+ + // Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936) + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( preferredDoc != document && + ( subWindow = document.defaultView ) && subWindow.top !== subWindow ) { + + // Support: IE 11, Edge + if ( subWindow.addEventListener ) { + subWindow.addEventListener( "unload", unloadHandler, false ); + + // Support: IE 9 - 10 only + } else if ( subWindow.attachEvent ) { + subWindow.attachEvent( "onunload", unloadHandler ); + } + } + + // Support: IE 8 - 11+, Edge 12 - 18+, Chrome <=16 - 25 only, Firefox <=3.6 - 31 only, + // Safari 4 - 5 only, Opera <=11.6 - 12.x only + // IE/Edge & older browsers don't support the :scope pseudo-class. + // Support: Safari 6.0 only + // Safari 6.0 supports :scope but it's an alias of :root there. + support.scope = assert( function( el ) { + docElem.appendChild( el ).appendChild( document.createElement( "div" ) ); + return typeof el.querySelectorAll !== "undefined" && + !el.querySelectorAll( ":scope fieldset div" ).length; + } ); + + /* Attributes + ---------------------------------------------------------------------- */ + + // Support: IE<8 + // Verify that getAttribute really returns attributes and not properties + // (excepting IE8 booleans) + support.attributes = assert( function( el ) { + el.className = "i"; + return !el.getAttribute( "className" ); + } ); + + /* getElement(s)By* + ---------------------------------------------------------------------- */ + + // Check if getElementsByTagName("*") returns only elements + support.getElementsByTagName = assert( function( el ) { + el.appendChild( document.createComment( "" ) ); + return !el.getElementsByTagName( "*" ).length; + } ); + + // Support: IE<9 + support.getElementsByClassName = rnative.test( document.getElementsByClassName ); + + // Support: IE<10 + // Check if getElementById returns elements by name + // The broken getElementById methods don't pick up programmatically-set names, + // so use a roundabout getElementsByName test + support.getById = assert( function( el ) { + docElem.appendChild( el ).id = expando; + return !document.getElementsByName || !document.getElementsByName( expando ).length; + } ); + + // ID filter and find + if ( support.getById ) { + Expr.filter[ "ID" ] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + return elem.getAttribute( "id" ) === attrId; + }; + }; + Expr.find[ "ID" ] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var elem = context.getElementById( id ); + return elem ? [ elem ] : []; + } + }; + } else { + Expr.filter[ "ID" ] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + var node = typeof elem.getAttributeNode !== "undefined" && + elem.getAttributeNode( "id" ); + return node && node.value === attrId; + }; + }; + + // Support: IE 6 - 7 only + // getElementById is not reliable as a find shortcut + Expr.find[ "ID" ] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var node, i, elems, + elem = context.getElementById( id ); + + if ( elem ) { + + // Verify the id attribute + node = elem.getAttributeNode( "id" ); + if ( node && node.value === id ) { + return [ elem ]; + } + + // Fall back on getElementsByName + elems = context.getElementsByName( id ); + i = 0; + while ( ( elem = elems[ i++ ] ) ) { + node = elem.getAttributeNode( "id" ); + if ( node && node.value === id ) { + return [ elem ]; + } + } + } + + return []; + } + }; + } + + // Tag + Expr.find[ "TAG" ] = support.getElementsByTagName ? + function( tag, context ) { + if ( typeof context.getElementsByTagName !== "undefined" ) { + return context.getElementsByTagName( tag ); + + // DocumentFragment nodes don't have gEBTN + } else if ( support.qsa ) { + return context.querySelectorAll( tag ); + } + } : + + function( tag, context ) { + var elem, + tmp = [], + i = 0, + + // By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too + results = context.getElementsByTagName( tag ); + + // Filter out possible comments + if ( tag === "*" ) { + while ( ( elem = results[ i++ ] ) ) { + if ( elem.nodeType === 1 ) { + tmp.push( elem ); + } + } + + return tmp; + } + return results; + }; + + // Class + Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) { + if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) { + return context.getElementsByClassName( className ); + } + }; + + /* QSA/matchesSelector + ---------------------------------------------------------------------- */ + + // QSA and matchesSelector support + + // matchesSelector(:active) reports false when true (IE9/Opera 11.5) + rbuggyMatches = []; + + // qSa(:focus) reports false when true (Chrome 21) + // We allow this because of a bug in IE8/9 that throws an error + // whenever `document.activeElement` is accessed on an iframe + // So, we allow :focus to pass through QSA all the time to avoid the IE error + // See https://bugs.jquery.com/ticket/13378 + rbuggyQSA = []; + + if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) { + + // Build QSA regex + // Regex strategy adopted from Diego Perini + assert( function( el ) { + + var input; + + // Select is set to empty string on purpose + // This is to test IE's treatment of not explicitly + // setting a boolean content attribute, + // since its presence should be enough + // https://bugs.jquery.com/ticket/12359 + docElem.appendChild( el ).innerHTML = "" + + ""; + + // Support: IE8, Opera 11-12.16 + // Nothing should be selected when empty strings follow ^= or $= or *= + // The test attribute must be unknown in Opera but "safe" for WinRT + // https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section + if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) { + rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" ); + } + + // Support: IE8 + // Boolean attributes and "value" are not treated correctly + if ( !el.querySelectorAll( "[selected]" ).length ) { + rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" ); + } + + // Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+ + if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) { + rbuggyQSA.push( "~=" ); + } + + // Support: IE 11+, Edge 15 - 18+ + // IE 11/Edge don't find elements on a `[name='']` query in some cases. + // Adding a temporary attribute to the document before the selection works + // around the issue. + // Interestingly, IE 10 & older don't seem to have the issue. + input = document.createElement( "input" ); + input.setAttribute( "name", "" ); + el.appendChild( input ); + if ( !el.querySelectorAll( "[name='']" ).length ) { + rbuggyQSA.push( "\\[" + whitespace + "*name" + whitespace + "*=" + + whitespace + "*(?:''|\"\")" ); + } + + // Webkit/Opera - :checked should return selected option elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + // IE8 throws error here and will not see later tests + if ( !el.querySelectorAll( ":checked" ).length ) { + rbuggyQSA.push( ":checked" ); + } + + // Support: Safari 8+, iOS 8+ + // https://bugs.webkit.org/show_bug.cgi?id=136851 + // In-page `selector#id sibling-combinator selector` fails + if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) { + rbuggyQSA.push( ".#.+[+~]" ); + } + + // Support: Firefox <=3.6 - 5 only + // Old Firefox doesn't throw on a badly-escaped identifier. + el.querySelectorAll( "\\\f" ); + rbuggyQSA.push( "[\\r\\n\\f]" ); + } ); + + assert( function( el ) { + el.innerHTML = "" + + ""; + + // Support: Windows 8 Native Apps + // The type and name attributes are restricted during .innerHTML assignment + var input = document.createElement( "input" ); + input.setAttribute( "type", "hidden" ); + el.appendChild( input ).setAttribute( "name", "D" ); + + // Support: IE8 + // Enforce case-sensitivity of name attribute + if ( el.querySelectorAll( "[name=d]" ).length ) { + rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" ); + } + + // FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled) + // IE8 throws error here and will not see later tests + if ( el.querySelectorAll( ":enabled" ).length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Support: IE9-11+ + // IE's :disabled selector does not pick up the children of disabled fieldsets + docElem.appendChild( el ).disabled = true; + if ( el.querySelectorAll( ":disabled" ).length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Support: Opera 10 - 11 only + // Opera 10-11 does not throw on post-comma invalid pseudos + el.querySelectorAll( "*,:x" ); + rbuggyQSA.push( ",.*:" ); + } ); + } + + if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches || + docElem.webkitMatchesSelector || + docElem.mozMatchesSelector || + docElem.oMatchesSelector || + docElem.msMatchesSelector ) ) ) ) { + + assert( function( el ) { + + // Check to see if it's possible to do matchesSelector + // on a disconnected node (IE 9) + support.disconnectedMatch = matches.call( el, "*" ); + + // This should fail with an exception + // Gecko does not error, returns false instead + matches.call( el, "[s!='']:x" ); + rbuggyMatches.push( "!=", pseudos ); + } ); + } + + rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) ); + rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) ); + + /* Contains + ---------------------------------------------------------------------- */ + hasCompare = rnative.test( docElem.compareDocumentPosition ); + + // Element contains another + // Purposefully self-exclusive + // As in, an element does not contain itself + contains = hasCompare || rnative.test( docElem.contains ) ? + function( a, b ) { + var adown = a.nodeType === 9 ? a.documentElement : a, + bup = b && b.parentNode; + return a === bup || !!( bup && bup.nodeType === 1 && ( + adown.contains ? + adown.contains( bup ) : + a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16 + ) ); + } : + function( a, b ) { + if ( b ) { + while ( ( b = b.parentNode ) ) { + if ( b === a ) { + return true; + } + } + } + return false; + }; + + /* Sorting + ---------------------------------------------------------------------- */ + + // Document order sorting + sortOrder = hasCompare ? + function( a, b ) { + + // Flag for duplicate removal + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + // Sort on method existence if only one input has compareDocumentPosition + var compare = !a.compareDocumentPosition - !b.compareDocumentPosition; + if ( compare ) { + return compare; + } + + // Calculate position if both inputs belong to the same document + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + compare = ( a.ownerDocument || a ) == ( b.ownerDocument || b ) ? + a.compareDocumentPosition( b ) : + + // Otherwise we know they are disconnected + 1; + + // Disconnected nodes + if ( compare & 1 || + ( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) { + + // Choose the first element that is related to our preferred document + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( a == document || a.ownerDocument == preferredDoc && + contains( preferredDoc, a ) ) { + return -1; + } + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( b == document || b.ownerDocument == preferredDoc && + contains( preferredDoc, b ) ) { + return 1; + } + + // Maintain original order + return sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + } + + return compare & 4 ? -1 : 1; + } : + function( a, b ) { + + // Exit early if the nodes are identical + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + var cur, + i = 0, + aup = a.parentNode, + bup = b.parentNode, + ap = [ a ], + bp = [ b ]; + + // Parentless nodes are either documents or disconnected + if ( !aup || !bup ) { + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + /* eslint-disable eqeqeq */ + return a == document ? -1 : + b == document ? 1 : + /* eslint-enable eqeqeq */ + aup ? -1 : + bup ? 1 : + sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + + // If the nodes are siblings, we can do a quick check + } else if ( aup === bup ) { + return siblingCheck( a, b ); + } + + // Otherwise we need full lists of their ancestors for comparison + cur = a; + while ( ( cur = cur.parentNode ) ) { + ap.unshift( cur ); + } + cur = b; + while ( ( cur = cur.parentNode ) ) { + bp.unshift( cur ); + } + + // Walk down the tree looking for a discrepancy + while ( ap[ i ] === bp[ i ] ) { + i++; + } + + return i ? + + // Do a sibling check if the nodes have a common ancestor + siblingCheck( ap[ i ], bp[ i ] ) : + + // Otherwise nodes in our document sort first + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + /* eslint-disable eqeqeq */ + ap[ i ] == preferredDoc ? -1 : + bp[ i ] == preferredDoc ? 1 : + /* eslint-enable eqeqeq */ + 0; + }; + + return document; +}; + +Sizzle.matches = function( expr, elements ) { + return Sizzle( expr, null, null, elements ); +}; + +Sizzle.matchesSelector = function( elem, expr ) { + setDocument( elem ); + + if ( support.matchesSelector && documentIsHTML && + !nonnativeSelectorCache[ expr + " " ] && + ( !rbuggyMatches || !rbuggyMatches.test( expr ) ) && + ( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) { + + try { + var ret = matches.call( elem, expr ); + + // IE 9's matchesSelector returns false on disconnected nodes + if ( ret || support.disconnectedMatch || + + // As well, disconnected nodes are said to be in a document + // fragment in IE 9 + elem.document && elem.document.nodeType !== 11 ) { + return ret; + } + } catch ( e ) { + nonnativeSelectorCache( expr, true ); + } + } + + return Sizzle( expr, document, null, [ elem ] ).length > 0; +}; + +Sizzle.contains = function( context, elem ) { + + // Set document vars if needed + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( ( context.ownerDocument || context ) != document ) { + setDocument( context ); + } + return contains( context, elem ); +}; + +Sizzle.attr = function( elem, name ) { + + // Set document vars if needed + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( ( elem.ownerDocument || elem ) != document ) { + setDocument( elem ); + } + + var fn = Expr.attrHandle[ name.toLowerCase() ], + + // Don't get fooled by Object.prototype properties (jQuery #13807) + val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ? + fn( elem, name, !documentIsHTML ) : + undefined; + + return val !== undefined ? + val : + support.attributes || !documentIsHTML ? + elem.getAttribute( name ) : + ( val = elem.getAttributeNode( name ) ) && val.specified ? + val.value : + null; +}; + +Sizzle.escape = function( sel ) { + return ( sel + "" ).replace( rcssescape, fcssescape ); +}; + +Sizzle.error = function( msg ) { + throw new Error( "Syntax error, unrecognized expression: " + msg ); +}; + +/** + * Document sorting and removing duplicates + * @param {ArrayLike} results + */ +Sizzle.uniqueSort = function( results ) { + var elem, + duplicates = [], + j = 0, + i = 0; + + // Unless we *know* we can detect duplicates, assume their presence + hasDuplicate = !support.detectDuplicates; + sortInput = !support.sortStable && results.slice( 0 ); + results.sort( sortOrder ); + + if ( hasDuplicate ) { + while ( ( elem = results[ i++ ] ) ) { + if ( elem === results[ i ] ) { + j = duplicates.push( i ); + } + } + while ( j-- ) { + results.splice( duplicates[ j ], 1 ); + } + } + + // Clear input after sorting to release objects + // See https://github.com/jquery/sizzle/pull/225 + sortInput = null; + + return results; +}; + +/** + * Utility function for retrieving the text value of an array of DOM nodes + * @param {Array|Element} elem + */ +getText = Sizzle.getText = function( elem ) { + var node, + ret = "", + i = 0, + nodeType = elem.nodeType; + + if ( !nodeType ) { + + // If no nodeType, this is expected to be an array + while ( ( node = elem[ i++ ] ) ) { + + // Do not traverse comment nodes + ret += getText( node ); + } + } else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) { + + // Use textContent for elements + // innerText usage removed for consistency of new lines (jQuery #11153) + if ( typeof elem.textContent === "string" ) { + return elem.textContent; + } else { + + // Traverse its children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + ret += getText( elem ); + } + } + } else if ( nodeType === 3 || nodeType === 4 ) { + return elem.nodeValue; + } + + // Do not include comment or processing instruction nodes + + return ret; +}; + +Expr = Sizzle.selectors = { + + // Can be adjusted by the user + cacheLength: 50, + + createPseudo: markFunction, + + match: matchExpr, + + attrHandle: {}, + + find: {}, + + relative: { + ">": { dir: "parentNode", first: true }, + " ": { dir: "parentNode" }, + "+": { dir: "previousSibling", first: true }, + "~": { dir: "previousSibling" } + }, + + preFilter: { + "ATTR": function( match ) { + match[ 1 ] = match[ 1 ].replace( runescape, funescape ); + + // Move the given value to match[3] whether quoted or unquoted + match[ 3 ] = ( match[ 3 ] || match[ 4 ] || + match[ 5 ] || "" ).replace( runescape, funescape ); + + if ( match[ 2 ] === "~=" ) { + match[ 3 ] = " " + match[ 3 ] + " "; + } + + return match.slice( 0, 4 ); + }, + + "CHILD": function( match ) { + + /* matches from matchExpr["CHILD"] + 1 type (only|nth|...) + 2 what (child|of-type) + 3 argument (even|odd|\d*|\d*n([+-]\d+)?|...) + 4 xn-component of xn+y argument ([+-]?\d*n|) + 5 sign of xn-component + 6 x of xn-component + 7 sign of y-component + 8 y of y-component + */ + match[ 1 ] = match[ 1 ].toLowerCase(); + + if ( match[ 1 ].slice( 0, 3 ) === "nth" ) { + + // nth-* requires argument + if ( !match[ 3 ] ) { + Sizzle.error( match[ 0 ] ); + } + + // numeric x and y parameters for Expr.filter.CHILD + // remember that false/true cast respectively to 0/1 + match[ 4 ] = +( match[ 4 ] ? + match[ 5 ] + ( match[ 6 ] || 1 ) : + 2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) ); + match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" ); + + // other types prohibit arguments + } else if ( match[ 3 ] ) { + Sizzle.error( match[ 0 ] ); + } + + return match; + }, + + "PSEUDO": function( match ) { + var excess, + unquoted = !match[ 6 ] && match[ 2 ]; + + if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) { + return null; + } + + // Accept quoted arguments as-is + if ( match[ 3 ] ) { + match[ 2 ] = match[ 4 ] || match[ 5 ] || ""; + + // Strip excess characters from unquoted arguments + } else if ( unquoted && rpseudo.test( unquoted ) && + + // Get excess from tokenize (recursively) + ( excess = tokenize( unquoted, true ) ) && + + // advance to the next closing parenthesis + ( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) { + + // excess is a negative index + match[ 0 ] = match[ 0 ].slice( 0, excess ); + match[ 2 ] = unquoted.slice( 0, excess ); + } + + // Return only captures needed by the pseudo filter method (type and argument) + return match.slice( 0, 3 ); + } + }, + + filter: { + + "TAG": function( nodeNameSelector ) { + var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase(); + return nodeNameSelector === "*" ? + function() { + return true; + } : + function( elem ) { + return elem.nodeName && elem.nodeName.toLowerCase() === nodeName; + }; + }, + + "CLASS": function( className ) { + var pattern = classCache[ className + " " ]; + + return pattern || + ( pattern = new RegExp( "(^|" + whitespace + + ")" + className + "(" + whitespace + "|$)" ) ) && classCache( + className, function( elem ) { + return pattern.test( + typeof elem.className === "string" && elem.className || + typeof elem.getAttribute !== "undefined" && + elem.getAttribute( "class" ) || + "" + ); + } ); + }, + + "ATTR": function( name, operator, check ) { + return function( elem ) { + var result = Sizzle.attr( elem, name ); + + if ( result == null ) { + return operator === "!="; + } + if ( !operator ) { + return true; + } + + result += ""; + + /* eslint-disable max-len */ + + return operator === "=" ? result === check : + operator === "!=" ? result !== check : + operator === "^=" ? check && result.indexOf( check ) === 0 : + operator === "*=" ? check && result.indexOf( check ) > -1 : + operator === "$=" ? check && result.slice( -check.length ) === check : + operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 : + operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" : + false; + /* eslint-enable max-len */ + + }; + }, + + "CHILD": function( type, what, _argument, first, last ) { + var simple = type.slice( 0, 3 ) !== "nth", + forward = type.slice( -4 ) !== "last", + ofType = what === "of-type"; + + return first === 1 && last === 0 ? + + // Shortcut for :nth-*(n) + function( elem ) { + return !!elem.parentNode; + } : + + function( elem, _context, xml ) { + var cache, uniqueCache, outerCache, node, nodeIndex, start, + dir = simple !== forward ? "nextSibling" : "previousSibling", + parent = elem.parentNode, + name = ofType && elem.nodeName.toLowerCase(), + useCache = !xml && !ofType, + diff = false; + + if ( parent ) { + + // :(first|last|only)-(child|of-type) + if ( simple ) { + while ( dir ) { + node = elem; + while ( ( node = node[ dir ] ) ) { + if ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) { + + return false; + } + } + + // Reverse direction for :only-* (if we haven't yet done so) + start = dir = type === "only" && !start && "nextSibling"; + } + return true; + } + + start = [ forward ? parent.firstChild : parent.lastChild ]; + + // non-xml :nth-child(...) stores cache data on `parent` + if ( forward && useCache ) { + + // Seek `elem` from a previously-cached index + + // ...in a gzip-friendly way + node = parent; + outerCache = node[ expando ] || ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex && cache[ 2 ]; + node = nodeIndex && parent.childNodes[ nodeIndex ]; + + while ( ( node = ++nodeIndex && node && node[ dir ] || + + // Fallback to seeking `elem` from the start + ( diff = nodeIndex = 0 ) || start.pop() ) ) { + + // When found, cache indexes on `parent` and break + if ( node.nodeType === 1 && ++diff && node === elem ) { + uniqueCache[ type ] = [ dirruns, nodeIndex, diff ]; + break; + } + } + + } else { + + // Use previously-cached element index if available + if ( useCache ) { + + // ...in a gzip-friendly way + node = elem; + outerCache = node[ expando ] || ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex; + } + + // xml :nth-child(...) + // or :nth-last-child(...) or :nth(-last)?-of-type(...) + if ( diff === false ) { + + // Use the same loop as above to seek `elem` from the start + while ( ( node = ++nodeIndex && node && node[ dir ] || + ( diff = nodeIndex = 0 ) || start.pop() ) ) { + + if ( ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) && + ++diff ) { + + // Cache the index of each encountered element + if ( useCache ) { + outerCache = node[ expando ] || + ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + uniqueCache[ type ] = [ dirruns, diff ]; + } + + if ( node === elem ) { + break; + } + } + } + } + } + + // Incorporate the offset, then check against cycle size + diff -= last; + return diff === first || ( diff % first === 0 && diff / first >= 0 ); + } + }; + }, + + "PSEUDO": function( pseudo, argument ) { + + // pseudo-class names are case-insensitive + // http://www.w3.org/TR/selectors/#pseudo-classes + // Prioritize by case sensitivity in case custom pseudos are added with uppercase letters + // Remember that setFilters inherits from pseudos + var args, + fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] || + Sizzle.error( "unsupported pseudo: " + pseudo ); + + // The user may use createPseudo to indicate that + // arguments are needed to create the filter function + // just as Sizzle does + if ( fn[ expando ] ) { + return fn( argument ); + } + + // But maintain support for old signatures + if ( fn.length > 1 ) { + args = [ pseudo, pseudo, "", argument ]; + return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ? + markFunction( function( seed, matches ) { + var idx, + matched = fn( seed, argument ), + i = matched.length; + while ( i-- ) { + idx = indexOf( seed, matched[ i ] ); + seed[ idx ] = !( matches[ idx ] = matched[ i ] ); + } + } ) : + function( elem ) { + return fn( elem, 0, args ); + }; + } + + return fn; + } + }, + + pseudos: { + + // Potentially complex pseudos + "not": markFunction( function( selector ) { + + // Trim the selector passed to compile + // to avoid treating leading and trailing + // spaces as combinators + var input = [], + results = [], + matcher = compile( selector.replace( rtrim, "$1" ) ); + + return matcher[ expando ] ? + markFunction( function( seed, matches, _context, xml ) { + var elem, + unmatched = matcher( seed, null, xml, [] ), + i = seed.length; + + // Match elements unmatched by `matcher` + while ( i-- ) { + if ( ( elem = unmatched[ i ] ) ) { + seed[ i ] = !( matches[ i ] = elem ); + } + } + } ) : + function( elem, _context, xml ) { + input[ 0 ] = elem; + matcher( input, null, xml, results ); + + // Don't keep the element (issue #299) + input[ 0 ] = null; + return !results.pop(); + }; + } ), + + "has": markFunction( function( selector ) { + return function( elem ) { + return Sizzle( selector, elem ).length > 0; + }; + } ), + + "contains": markFunction( function( text ) { + text = text.replace( runescape, funescape ); + return function( elem ) { + return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1; + }; + } ), + + // "Whether an element is represented by a :lang() selector + // is based solely on the element's language value + // being equal to the identifier C, + // or beginning with the identifier C immediately followed by "-". + // The matching of C against the element's language value is performed case-insensitively. + // The identifier C does not have to be a valid language name." + // http://www.w3.org/TR/selectors/#lang-pseudo + "lang": markFunction( function( lang ) { + + // lang value must be a valid identifier + if ( !ridentifier.test( lang || "" ) ) { + Sizzle.error( "unsupported lang: " + lang ); + } + lang = lang.replace( runescape, funescape ).toLowerCase(); + return function( elem ) { + var elemLang; + do { + if ( ( elemLang = documentIsHTML ? + elem.lang : + elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) { + + elemLang = elemLang.toLowerCase(); + return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0; + } + } while ( ( elem = elem.parentNode ) && elem.nodeType === 1 ); + return false; + }; + } ), + + // Miscellaneous + "target": function( elem ) { + var hash = window.location && window.location.hash; + return hash && hash.slice( 1 ) === elem.id; + }, + + "root": function( elem ) { + return elem === docElem; + }, + + "focus": function( elem ) { + return elem === document.activeElement && + ( !document.hasFocus || document.hasFocus() ) && + !!( elem.type || elem.href || ~elem.tabIndex ); + }, + + // Boolean properties + "enabled": createDisabledPseudo( false ), + "disabled": createDisabledPseudo( true ), + + "checked": function( elem ) { + + // In CSS3, :checked should return both checked and selected elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + var nodeName = elem.nodeName.toLowerCase(); + return ( nodeName === "input" && !!elem.checked ) || + ( nodeName === "option" && !!elem.selected ); + }, + + "selected": function( elem ) { + + // Accessing this property makes selected-by-default + // options in Safari work properly + if ( elem.parentNode ) { + // eslint-disable-next-line no-unused-expressions + elem.parentNode.selectedIndex; + } + + return elem.selected === true; + }, + + // Contents + "empty": function( elem ) { + + // http://www.w3.org/TR/selectors/#empty-pseudo + // :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5), + // but not by others (comment: 8; processing instruction: 7; etc.) + // nodeType < 6 works because attributes (2) do not appear as children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + if ( elem.nodeType < 6 ) { + return false; + } + } + return true; + }, + + "parent": function( elem ) { + return !Expr.pseudos[ "empty" ]( elem ); + }, + + // Element/input types + "header": function( elem ) { + return rheader.test( elem.nodeName ); + }, + + "input": function( elem ) { + return rinputs.test( elem.nodeName ); + }, + + "button": function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === "button" || name === "button"; + }, + + "text": function( elem ) { + var attr; + return elem.nodeName.toLowerCase() === "input" && + elem.type === "text" && + + // Support: IE<8 + // New HTML5 attribute values (e.g., "search") appear with elem.type === "text" + ( ( attr = elem.getAttribute( "type" ) ) == null || + attr.toLowerCase() === "text" ); + }, + + // Position-in-collection + "first": createPositionalPseudo( function() { + return [ 0 ]; + } ), + + "last": createPositionalPseudo( function( _matchIndexes, length ) { + return [ length - 1 ]; + } ), + + "eq": createPositionalPseudo( function( _matchIndexes, length, argument ) { + return [ argument < 0 ? argument + length : argument ]; + } ), + + "even": createPositionalPseudo( function( matchIndexes, length ) { + var i = 0; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "odd": createPositionalPseudo( function( matchIndexes, length ) { + var i = 1; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "lt": createPositionalPseudo( function( matchIndexes, length, argument ) { + var i = argument < 0 ? + argument + length : + argument > length ? + length : + argument; + for ( ; --i >= 0; ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "gt": createPositionalPseudo( function( matchIndexes, length, argument ) { + var i = argument < 0 ? argument + length : argument; + for ( ; ++i < length; ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ) + } +}; + +Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ]; + +// Add button/input type pseudos +for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) { + Expr.pseudos[ i ] = createInputPseudo( i ); +} +for ( i in { submit: true, reset: true } ) { + Expr.pseudos[ i ] = createButtonPseudo( i ); +} + +// Easy API for creating new setFilters +function setFilters() {} +setFilters.prototype = Expr.filters = Expr.pseudos; +Expr.setFilters = new setFilters(); + +tokenize = Sizzle.tokenize = function( selector, parseOnly ) { + var matched, match, tokens, type, + soFar, groups, preFilters, + cached = tokenCache[ selector + " " ]; + + if ( cached ) { + return parseOnly ? 0 : cached.slice( 0 ); + } + + soFar = selector; + groups = []; + preFilters = Expr.preFilter; + + while ( soFar ) { + + // Comma and first run + if ( !matched || ( match = rcomma.exec( soFar ) ) ) { + if ( match ) { + + // Don't consume trailing commas as valid + soFar = soFar.slice( match[ 0 ].length ) || soFar; + } + groups.push( ( tokens = [] ) ); + } + + matched = false; + + // Combinators + if ( ( match = rcombinators.exec( soFar ) ) ) { + matched = match.shift(); + tokens.push( { + value: matched, + + // Cast descendant combinators to space + type: match[ 0 ].replace( rtrim, " " ) + } ); + soFar = soFar.slice( matched.length ); + } + + // Filters + for ( type in Expr.filter ) { + if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] || + ( match = preFilters[ type ]( match ) ) ) ) { + matched = match.shift(); + tokens.push( { + value: matched, + type: type, + matches: match + } ); + soFar = soFar.slice( matched.length ); + } + } + + if ( !matched ) { + break; + } + } + + // Return the length of the invalid excess + // if we're just parsing + // Otherwise, throw an error or return tokens + return parseOnly ? + soFar.length : + soFar ? + Sizzle.error( selector ) : + + // Cache the tokens + tokenCache( selector, groups ).slice( 0 ); +}; + +function toSelector( tokens ) { + var i = 0, + len = tokens.length, + selector = ""; + for ( ; i < len; i++ ) { + selector += tokens[ i ].value; + } + return selector; +} + +function addCombinator( matcher, combinator, base ) { + var dir = combinator.dir, + skip = combinator.next, + key = skip || dir, + checkNonElements = base && key === "parentNode", + doneName = done++; + + return combinator.first ? + + // Check against closest ancestor/preceding element + function( elem, context, xml ) { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + return matcher( elem, context, xml ); + } + } + return false; + } : + + // Check against all ancestor/preceding elements + function( elem, context, xml ) { + var oldCache, uniqueCache, outerCache, + newCache = [ dirruns, doneName ]; + + // We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching + if ( xml ) { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + if ( matcher( elem, context, xml ) ) { + return true; + } + } + } + } else { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + outerCache = elem[ expando ] || ( elem[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ elem.uniqueID ] || + ( outerCache[ elem.uniqueID ] = {} ); + + if ( skip && skip === elem.nodeName.toLowerCase() ) { + elem = elem[ dir ] || elem; + } else if ( ( oldCache = uniqueCache[ key ] ) && + oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) { + + // Assign to newCache so results back-propagate to previous elements + return ( newCache[ 2 ] = oldCache[ 2 ] ); + } else { + + // Reuse newcache so results back-propagate to previous elements + uniqueCache[ key ] = newCache; + + // A match means we're done; a fail means we have to keep checking + if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) { + return true; + } + } + } + } + } + return false; + }; +} + +function elementMatcher( matchers ) { + return matchers.length > 1 ? + function( elem, context, xml ) { + var i = matchers.length; + while ( i-- ) { + if ( !matchers[ i ]( elem, context, xml ) ) { + return false; + } + } + return true; + } : + matchers[ 0 ]; +} + +function multipleContexts( selector, contexts, results ) { + var i = 0, + len = contexts.length; + for ( ; i < len; i++ ) { + Sizzle( selector, contexts[ i ], results ); + } + return results; +} + +function condense( unmatched, map, filter, context, xml ) { + var elem, + newUnmatched = [], + i = 0, + len = unmatched.length, + mapped = map != null; + + for ( ; i < len; i++ ) { + if ( ( elem = unmatched[ i ] ) ) { + if ( !filter || filter( elem, context, xml ) ) { + newUnmatched.push( elem ); + if ( mapped ) { + map.push( i ); + } + } + } + } + + return newUnmatched; +} + +function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) { + if ( postFilter && !postFilter[ expando ] ) { + postFilter = setMatcher( postFilter ); + } + if ( postFinder && !postFinder[ expando ] ) { + postFinder = setMatcher( postFinder, postSelector ); + } + return markFunction( function( seed, results, context, xml ) { + var temp, i, elem, + preMap = [], + postMap = [], + preexisting = results.length, + + // Get initial elements from seed or context + elems = seed || multipleContexts( + selector || "*", + context.nodeType ? [ context ] : context, + [] + ), + + // Prefilter to get matcher input, preserving a map for seed-results synchronization + matcherIn = preFilter && ( seed || !selector ) ? + condense( elems, preMap, preFilter, context, xml ) : + elems, + + matcherOut = matcher ? + + // If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results, + postFinder || ( seed ? preFilter : preexisting || postFilter ) ? + + // ...intermediate processing is necessary + [] : + + // ...otherwise use results directly + results : + matcherIn; + + // Find primary matches + if ( matcher ) { + matcher( matcherIn, matcherOut, context, xml ); + } + + // Apply postFilter + if ( postFilter ) { + temp = condense( matcherOut, postMap ); + postFilter( temp, [], context, xml ); + + // Un-match failing elements by moving them back to matcherIn + i = temp.length; + while ( i-- ) { + if ( ( elem = temp[ i ] ) ) { + matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem ); + } + } + } + + if ( seed ) { + if ( postFinder || preFilter ) { + if ( postFinder ) { + + // Get the final matcherOut by condensing this intermediate into postFinder contexts + temp = []; + i = matcherOut.length; + while ( i-- ) { + if ( ( elem = matcherOut[ i ] ) ) { + + // Restore matcherIn since elem is not yet a final match + temp.push( ( matcherIn[ i ] = elem ) ); + } + } + postFinder( null, ( matcherOut = [] ), temp, xml ); + } + + // Move matched elements from seed to results to keep them synchronized + i = matcherOut.length; + while ( i-- ) { + if ( ( elem = matcherOut[ i ] ) && + ( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) { + + seed[ temp ] = !( results[ temp ] = elem ); + } + } + } + + // Add elements to results, through postFinder if defined + } else { + matcherOut = condense( + matcherOut === results ? + matcherOut.splice( preexisting, matcherOut.length ) : + matcherOut + ); + if ( postFinder ) { + postFinder( null, results, matcherOut, xml ); + } else { + push.apply( results, matcherOut ); + } + } + } ); +} + +function matcherFromTokens( tokens ) { + var checkContext, matcher, j, + len = tokens.length, + leadingRelative = Expr.relative[ tokens[ 0 ].type ], + implicitRelative = leadingRelative || Expr.relative[ " " ], + i = leadingRelative ? 1 : 0, + + // The foundational matcher ensures that elements are reachable from top-level context(s) + matchContext = addCombinator( function( elem ) { + return elem === checkContext; + }, implicitRelative, true ), + matchAnyContext = addCombinator( function( elem ) { + return indexOf( checkContext, elem ) > -1; + }, implicitRelative, true ), + matchers = [ function( elem, context, xml ) { + var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || ( + ( checkContext = context ).nodeType ? + matchContext( elem, context, xml ) : + matchAnyContext( elem, context, xml ) ); + + // Avoid hanging onto element (issue #299) + checkContext = null; + return ret; + } ]; + + for ( ; i < len; i++ ) { + if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) { + matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ]; + } else { + matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches ); + + // Return special upon seeing a positional matcher + if ( matcher[ expando ] ) { + + // Find the next relative operator (if any) for proper handling + j = ++i; + for ( ; j < len; j++ ) { + if ( Expr.relative[ tokens[ j ].type ] ) { + break; + } + } + return setMatcher( + i > 1 && elementMatcher( matchers ), + i > 1 && toSelector( + + // If the preceding token was a descendant combinator, insert an implicit any-element `*` + tokens + .slice( 0, i - 1 ) + .concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } ) + ).replace( rtrim, "$1" ), + matcher, + i < j && matcherFromTokens( tokens.slice( i, j ) ), + j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ), + j < len && toSelector( tokens ) + ); + } + matchers.push( matcher ); + } + } + + return elementMatcher( matchers ); +} + +function matcherFromGroupMatchers( elementMatchers, setMatchers ) { + var bySet = setMatchers.length > 0, + byElement = elementMatchers.length > 0, + superMatcher = function( seed, context, xml, results, outermost ) { + var elem, j, matcher, + matchedCount = 0, + i = "0", + unmatched = seed && [], + setMatched = [], + contextBackup = outermostContext, + + // We must always have either seed elements or outermost context + elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ), + + // Use integer dirruns iff this is the outermost matcher + dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ), + len = elems.length; + + if ( outermost ) { + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + outermostContext = context == document || context || outermost; + } + + // Add elements passing elementMatchers directly to results + // Support: IE<9, Safari + // Tolerate NodeList properties (IE: "length"; Safari: ) matching elements by id + for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) { + if ( byElement && elem ) { + j = 0; + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( !context && elem.ownerDocument != document ) { + setDocument( elem ); + xml = !documentIsHTML; + } + while ( ( matcher = elementMatchers[ j++ ] ) ) { + if ( matcher( elem, context || document, xml ) ) { + results.push( elem ); + break; + } + } + if ( outermost ) { + dirruns = dirrunsUnique; + } + } + + // Track unmatched elements for set filters + if ( bySet ) { + + // They will have gone through all possible matchers + if ( ( elem = !matcher && elem ) ) { + matchedCount--; + } + + // Lengthen the array for every element, matched or not + if ( seed ) { + unmatched.push( elem ); + } + } + } + + // `i` is now the count of elements visited above, and adding it to `matchedCount` + // makes the latter nonnegative. + matchedCount += i; + + // Apply set filters to unmatched elements + // NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount` + // equals `i`), unless we didn't visit _any_ elements in the above loop because we have + // no element matchers and no seed. + // Incrementing an initially-string "0" `i` allows `i` to remain a string only in that + // case, which will result in a "00" `matchedCount` that differs from `i` but is also + // numerically zero. + if ( bySet && i !== matchedCount ) { + j = 0; + while ( ( matcher = setMatchers[ j++ ] ) ) { + matcher( unmatched, setMatched, context, xml ); + } + + if ( seed ) { + + // Reintegrate element matches to eliminate the need for sorting + if ( matchedCount > 0 ) { + while ( i-- ) { + if ( !( unmatched[ i ] || setMatched[ i ] ) ) { + setMatched[ i ] = pop.call( results ); + } + } + } + + // Discard index placeholder values to get only actual matches + setMatched = condense( setMatched ); + } + + // Add matches to results + push.apply( results, setMatched ); + + // Seedless set matches succeeding multiple successful matchers stipulate sorting + if ( outermost && !seed && setMatched.length > 0 && + ( matchedCount + setMatchers.length ) > 1 ) { + + Sizzle.uniqueSort( results ); + } + } + + // Override manipulation of globals by nested matchers + if ( outermost ) { + dirruns = dirrunsUnique; + outermostContext = contextBackup; + } + + return unmatched; + }; + + return bySet ? + markFunction( superMatcher ) : + superMatcher; +} + +compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) { + var i, + setMatchers = [], + elementMatchers = [], + cached = compilerCache[ selector + " " ]; + + if ( !cached ) { + + // Generate a function of recursive functions that can be used to check each element + if ( !match ) { + match = tokenize( selector ); + } + i = match.length; + while ( i-- ) { + cached = matcherFromTokens( match[ i ] ); + if ( cached[ expando ] ) { + setMatchers.push( cached ); + } else { + elementMatchers.push( cached ); + } + } + + // Cache the compiled function + cached = compilerCache( + selector, + matcherFromGroupMatchers( elementMatchers, setMatchers ) + ); + + // Save selector and tokenization + cached.selector = selector; + } + return cached; +}; + +/** + * A low-level selection function that works with Sizzle's compiled + * selector functions + * @param {String|Function} selector A selector or a pre-compiled + * selector function built with Sizzle.compile + * @param {Element} context + * @param {Array} [results] + * @param {Array} [seed] A set of elements to match against + */ +select = Sizzle.select = function( selector, context, results, seed ) { + var i, tokens, token, type, find, + compiled = typeof selector === "function" && selector, + match = !seed && tokenize( ( selector = compiled.selector || selector ) ); + + results = results || []; + + // Try to minimize operations if there is only one selector in the list and no seed + // (the latter of which guarantees us context) + if ( match.length === 1 ) { + + // Reduce context if the leading compound selector is an ID + tokens = match[ 0 ] = match[ 0 ].slice( 0 ); + if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" && + context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) { + + context = ( Expr.find[ "ID" ]( token.matches[ 0 ] + .replace( runescape, funescape ), context ) || [] )[ 0 ]; + if ( !context ) { + return results; + + // Precompiled matchers will still verify ancestry, so step up a level + } else if ( compiled ) { + context = context.parentNode; + } + + selector = selector.slice( tokens.shift().value.length ); + } + + // Fetch a seed set for right-to-left matching + i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length; + while ( i-- ) { + token = tokens[ i ]; + + // Abort if we hit a combinator + if ( Expr.relative[ ( type = token.type ) ] ) { + break; + } + if ( ( find = Expr.find[ type ] ) ) { + + // Search, expanding context for leading sibling combinators + if ( ( seed = find( + token.matches[ 0 ].replace( runescape, funescape ), + rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) || + context + ) ) ) { + + // If seed is empty or no tokens remain, we can return early + tokens.splice( i, 1 ); + selector = seed.length && toSelector( tokens ); + if ( !selector ) { + push.apply( results, seed ); + return results; + } + + break; + } + } + } + } + + // Compile and execute a filtering function if one is not provided + // Provide `match` to avoid retokenization if we modified the selector above + ( compiled || compile( selector, match ) )( + seed, + context, + !documentIsHTML, + results, + !context || rsibling.test( selector ) && testContext( context.parentNode ) || context + ); + return results; +}; + +// One-time assignments + +// Sort stability +support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando; + +// Support: Chrome 14-35+ +// Always assume duplicates if they aren't passed to the comparison function +support.detectDuplicates = !!hasDuplicate; + +// Initialize against the default document +setDocument(); + +// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27) +// Detached nodes confoundingly follow *each other* +support.sortDetached = assert( function( el ) { + + // Should return 1, but returns 4 (following) + return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1; +} ); + +// Support: IE<8 +// Prevent attribute/property "interpolation" +// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx +if ( !assert( function( el ) { + el.innerHTML = ""; + return el.firstChild.getAttribute( "href" ) === "#"; +} ) ) { + addHandle( "type|href|height|width", function( elem, name, isXML ) { + if ( !isXML ) { + return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 ); + } + } ); +} + +// Support: IE<9 +// Use defaultValue in place of getAttribute("value") +if ( !support.attributes || !assert( function( el ) { + el.innerHTML = ""; + el.firstChild.setAttribute( "value", "" ); + return el.firstChild.getAttribute( "value" ) === ""; +} ) ) { + addHandle( "value", function( elem, _name, isXML ) { + if ( !isXML && elem.nodeName.toLowerCase() === "input" ) { + return elem.defaultValue; + } + } ); +} + +// Support: IE<9 +// Use getAttributeNode to fetch booleans when getAttribute lies +if ( !assert( function( el ) { + return el.getAttribute( "disabled" ) == null; +} ) ) { + addHandle( booleans, function( elem, name, isXML ) { + var val; + if ( !isXML ) { + return elem[ name ] === true ? name.toLowerCase() : + ( val = elem.getAttributeNode( name ) ) && val.specified ? + val.value : + null; + } + } ); +} + +return Sizzle; + +} )( window ); + + + +jQuery.find = Sizzle; +jQuery.expr = Sizzle.selectors; + +// Deprecated +jQuery.expr[ ":" ] = jQuery.expr.pseudos; +jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort; +jQuery.text = Sizzle.getText; +jQuery.isXMLDoc = Sizzle.isXML; +jQuery.contains = Sizzle.contains; +jQuery.escapeSelector = Sizzle.escape; + + + + +var dir = function( elem, dir, until ) { + var matched = [], + truncate = until !== undefined; + + while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) { + if ( elem.nodeType === 1 ) { + if ( truncate && jQuery( elem ).is( until ) ) { + break; + } + matched.push( elem ); + } + } + return matched; +}; + + +var siblings = function( n, elem ) { + var matched = []; + + for ( ; n; n = n.nextSibling ) { + if ( n.nodeType === 1 && n !== elem ) { + matched.push( n ); + } + } + + return matched; +}; + + +var rneedsContext = jQuery.expr.match.needsContext; + + + +function nodeName( elem, name ) { + + return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase(); + +}; +var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i ); + + + +// Implement the identical functionality for filter and not +function winnow( elements, qualifier, not ) { + if ( isFunction( qualifier ) ) { + return jQuery.grep( elements, function( elem, i ) { + return !!qualifier.call( elem, i, elem ) !== not; + } ); + } + + // Single element + if ( qualifier.nodeType ) { + return jQuery.grep( elements, function( elem ) { + return ( elem === qualifier ) !== not; + } ); + } + + // Arraylike of elements (jQuery, arguments, Array) + if ( typeof qualifier !== "string" ) { + return jQuery.grep( elements, function( elem ) { + return ( indexOf.call( qualifier, elem ) > -1 ) !== not; + } ); + } + + // Filtered directly for both simple and complex selectors + return jQuery.filter( qualifier, elements, not ); +} + +jQuery.filter = function( expr, elems, not ) { + var elem = elems[ 0 ]; + + if ( not ) { + expr = ":not(" + expr + ")"; + } + + if ( elems.length === 1 && elem.nodeType === 1 ) { + return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : []; + } + + return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) { + return elem.nodeType === 1; + } ) ); +}; + +jQuery.fn.extend( { + find: function( selector ) { + var i, ret, + len = this.length, + self = this; + + if ( typeof selector !== "string" ) { + return this.pushStack( jQuery( selector ).filter( function() { + for ( i = 0; i < len; i++ ) { + if ( jQuery.contains( self[ i ], this ) ) { + return true; + } + } + } ) ); + } + + ret = this.pushStack( [] ); + + for ( i = 0; i < len; i++ ) { + jQuery.find( selector, self[ i ], ret ); + } + + return len > 1 ? jQuery.uniqueSort( ret ) : ret; + }, + filter: function( selector ) { + return this.pushStack( winnow( this, selector || [], false ) ); + }, + not: function( selector ) { + return this.pushStack( winnow( this, selector || [], true ) ); + }, + is: function( selector ) { + return !!winnow( + this, + + // If this is a positional/relative selector, check membership in the returned set + // so $("p:first").is("p:last") won't return true for a doc with two "p". + typeof selector === "string" && rneedsContext.test( selector ) ? + jQuery( selector ) : + selector || [], + false + ).length; + } +} ); + + +// Initialize a jQuery object + + +// A central reference to the root jQuery(document) +var rootjQuery, + + // A simple way to check for HTML strings + // Prioritize #id over to avoid XSS via location.hash (#9521) + // Strict HTML recognition (#11290: must start with <) + // Shortcut simple #id case for speed + rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/, + + init = jQuery.fn.init = function( selector, context, root ) { + var match, elem; + + // HANDLE: $(""), $(null), $(undefined), $(false) + if ( !selector ) { + return this; + } + + // Method init() accepts an alternate rootjQuery + // so migrate can support jQuery.sub (gh-2101) + root = root || rootjQuery; + + // Handle HTML strings + if ( typeof selector === "string" ) { + if ( selector[ 0 ] === "<" && + selector[ selector.length - 1 ] === ">" && + selector.length >= 3 ) { + + // Assume that strings that start and end with <> are HTML and skip the regex check + match = [ null, selector, null ]; + + } else { + match = rquickExpr.exec( selector ); + } + + // Match html or make sure no context is specified for #id + if ( match && ( match[ 1 ] || !context ) ) { + + // HANDLE: $(html) -> $(array) + if ( match[ 1 ] ) { + context = context instanceof jQuery ? context[ 0 ] : context; + + // Option to run scripts is true for back-compat + // Intentionally let the error be thrown if parseHTML is not present + jQuery.merge( this, jQuery.parseHTML( + match[ 1 ], + context && context.nodeType ? context.ownerDocument || context : document, + true + ) ); + + // HANDLE: $(html, props) + if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) { + for ( match in context ) { + + // Properties of context are called as methods if possible + if ( isFunction( this[ match ] ) ) { + this[ match ]( context[ match ] ); + + // ...and otherwise set as attributes + } else { + this.attr( match, context[ match ] ); + } + } + } + + return this; + + // HANDLE: $(#id) + } else { + elem = document.getElementById( match[ 2 ] ); + + if ( elem ) { + + // Inject the element directly into the jQuery object + this[ 0 ] = elem; + this.length = 1; + } + return this; + } + + // HANDLE: $(expr, $(...)) + } else if ( !context || context.jquery ) { + return ( context || root ).find( selector ); + + // HANDLE: $(expr, context) + // (which is just equivalent to: $(context).find(expr) + } else { + return this.constructor( context ).find( selector ); + } + + // HANDLE: $(DOMElement) + } else if ( selector.nodeType ) { + this[ 0 ] = selector; + this.length = 1; + return this; + + // HANDLE: $(function) + // Shortcut for document ready + } else if ( isFunction( selector ) ) { + return root.ready !== undefined ? + root.ready( selector ) : + + // Execute immediately if ready is not present + selector( jQuery ); + } + + return jQuery.makeArray( selector, this ); + }; + +// Give the init function the jQuery prototype for later instantiation +init.prototype = jQuery.fn; + +// Initialize central reference +rootjQuery = jQuery( document ); + + +var rparentsprev = /^(?:parents|prev(?:Until|All))/, + + // Methods guaranteed to produce a unique set when starting from a unique set + guaranteedUnique = { + children: true, + contents: true, + next: true, + prev: true + }; + +jQuery.fn.extend( { + has: function( target ) { + var targets = jQuery( target, this ), + l = targets.length; + + return this.filter( function() { + var i = 0; + for ( ; i < l; i++ ) { + if ( jQuery.contains( this, targets[ i ] ) ) { + return true; + } + } + } ); + }, + + closest: function( selectors, context ) { + var cur, + i = 0, + l = this.length, + matched = [], + targets = typeof selectors !== "string" && jQuery( selectors ); + + // Positional selectors never match, since there's no _selection_ context + if ( !rneedsContext.test( selectors ) ) { + for ( ; i < l; i++ ) { + for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) { + + // Always skip document fragments + if ( cur.nodeType < 11 && ( targets ? + targets.index( cur ) > -1 : + + // Don't pass non-elements to Sizzle + cur.nodeType === 1 && + jQuery.find.matchesSelector( cur, selectors ) ) ) { + + matched.push( cur ); + break; + } + } + } + } + + return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched ); + }, + + // Determine the position of an element within the set + index: function( elem ) { + + // No argument, return index in parent + if ( !elem ) { + return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1; + } + + // Index in selector + if ( typeof elem === "string" ) { + return indexOf.call( jQuery( elem ), this[ 0 ] ); + } + + // Locate the position of the desired element + return indexOf.call( this, + + // If it receives a jQuery object, the first element is used + elem.jquery ? elem[ 0 ] : elem + ); + }, + + add: function( selector, context ) { + return this.pushStack( + jQuery.uniqueSort( + jQuery.merge( this.get(), jQuery( selector, context ) ) + ) + ); + }, + + addBack: function( selector ) { + return this.add( selector == null ? + this.prevObject : this.prevObject.filter( selector ) + ); + } +} ); + +function sibling( cur, dir ) { + while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {} + return cur; +} + +jQuery.each( { + parent: function( elem ) { + var parent = elem.parentNode; + return parent && parent.nodeType !== 11 ? parent : null; + }, + parents: function( elem ) { + return dir( elem, "parentNode" ); + }, + parentsUntil: function( elem, _i, until ) { + return dir( elem, "parentNode", until ); + }, + next: function( elem ) { + return sibling( elem, "nextSibling" ); + }, + prev: function( elem ) { + return sibling( elem, "previousSibling" ); + }, + nextAll: function( elem ) { + return dir( elem, "nextSibling" ); + }, + prevAll: function( elem ) { + return dir( elem, "previousSibling" ); + }, + nextUntil: function( elem, _i, until ) { + return dir( elem, "nextSibling", until ); + }, + prevUntil: function( elem, _i, until ) { + return dir( elem, "previousSibling", until ); + }, + siblings: function( elem ) { + return siblings( ( elem.parentNode || {} ).firstChild, elem ); + }, + children: function( elem ) { + return siblings( elem.firstChild ); + }, + contents: function( elem ) { + if ( elem.contentDocument != null && + + // Support: IE 11+ + // elements with no `data` attribute has an object + // `contentDocument` with a `null` prototype. + getProto( elem.contentDocument ) ) { + + return elem.contentDocument; + } + + // Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only + // Treat the template element as a regular one in browsers that + // don't support it. + if ( nodeName( elem, "template" ) ) { + elem = elem.content || elem; + } + + return jQuery.merge( [], elem.childNodes ); + } +}, function( name, fn ) { + jQuery.fn[ name ] = function( until, selector ) { + var matched = jQuery.map( this, fn, until ); + + if ( name.slice( -5 ) !== "Until" ) { + selector = until; + } + + if ( selector && typeof selector === "string" ) { + matched = jQuery.filter( selector, matched ); + } + + if ( this.length > 1 ) { + + // Remove duplicates + if ( !guaranteedUnique[ name ] ) { + jQuery.uniqueSort( matched ); + } + + // Reverse order for parents* and prev-derivatives + if ( rparentsprev.test( name ) ) { + matched.reverse(); + } + } + + return this.pushStack( matched ); + }; +} ); +var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g ); + + + +// Convert String-formatted options into Object-formatted ones +function createOptions( options ) { + var object = {}; + jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) { + object[ flag ] = true; + } ); + return object; +} + +/* + * Create a callback list using the following parameters: + * + * options: an optional list of space-separated options that will change how + * the callback list behaves or a more traditional option object + * + * By default a callback list will act like an event callback list and can be + * "fired" multiple times. + * + * Possible options: + * + * once: will ensure the callback list can only be fired once (like a Deferred) + * + * memory: will keep track of previous values and will call any callback added + * after the list has been fired right away with the latest "memorized" + * values (like a Deferred) + * + * unique: will ensure a callback can only be added once (no duplicate in the list) + * + * stopOnFalse: interrupt callings when a callback returns false + * + */ +jQuery.Callbacks = function( options ) { + + // Convert options from String-formatted to Object-formatted if needed + // (we check in cache first) + options = typeof options === "string" ? + createOptions( options ) : + jQuery.extend( {}, options ); + + var // Flag to know if list is currently firing + firing, + + // Last fire value for non-forgettable lists + memory, + + // Flag to know if list was already fired + fired, + + // Flag to prevent firing + locked, + + // Actual callback list + list = [], + + // Queue of execution data for repeatable lists + queue = [], + + // Index of currently firing callback (modified by add/remove as needed) + firingIndex = -1, + + // Fire callbacks + fire = function() { + + // Enforce single-firing + locked = locked || options.once; + + // Execute callbacks for all pending executions, + // respecting firingIndex overrides and runtime changes + fired = firing = true; + for ( ; queue.length; firingIndex = -1 ) { + memory = queue.shift(); + while ( ++firingIndex < list.length ) { + + // Run callback and check for early termination + if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false && + options.stopOnFalse ) { + + // Jump to end and forget the data so .add doesn't re-fire + firingIndex = list.length; + memory = false; + } + } + } + + // Forget the data if we're done with it + if ( !options.memory ) { + memory = false; + } + + firing = false; + + // Clean up if we're done firing for good + if ( locked ) { + + // Keep an empty list if we have data for future add calls + if ( memory ) { + list = []; + + // Otherwise, this object is spent + } else { + list = ""; + } + } + }, + + // Actual Callbacks object + self = { + + // Add a callback or a collection of callbacks to the list + add: function() { + if ( list ) { + + // If we have memory from a past run, we should fire after adding + if ( memory && !firing ) { + firingIndex = list.length - 1; + queue.push( memory ); + } + + ( function add( args ) { + jQuery.each( args, function( _, arg ) { + if ( isFunction( arg ) ) { + if ( !options.unique || !self.has( arg ) ) { + list.push( arg ); + } + } else if ( arg && arg.length && toType( arg ) !== "string" ) { + + // Inspect recursively + add( arg ); + } + } ); + } )( arguments ); + + if ( memory && !firing ) { + fire(); + } + } + return this; + }, + + // Remove a callback from the list + remove: function() { + jQuery.each( arguments, function( _, arg ) { + var index; + while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) { + list.splice( index, 1 ); + + // Handle firing indexes + if ( index <= firingIndex ) { + firingIndex--; + } + } + } ); + return this; + }, + + // Check if a given callback is in the list. + // If no argument is given, return whether or not list has callbacks attached. + has: function( fn ) { + return fn ? + jQuery.inArray( fn, list ) > -1 : + list.length > 0; + }, + + // Remove all callbacks from the list + empty: function() { + if ( list ) { + list = []; + } + return this; + }, + + // Disable .fire and .add + // Abort any current/pending executions + // Clear all callbacks and values + disable: function() { + locked = queue = []; + list = memory = ""; + return this; + }, + disabled: function() { + return !list; + }, + + // Disable .fire + // Also disable .add unless we have memory (since it would have no effect) + // Abort any pending executions + lock: function() { + locked = queue = []; + if ( !memory && !firing ) { + list = memory = ""; + } + return this; + }, + locked: function() { + return !!locked; + }, + + // Call all callbacks with the given context and arguments + fireWith: function( context, args ) { + if ( !locked ) { + args = args || []; + args = [ context, args.slice ? args.slice() : args ]; + queue.push( args ); + if ( !firing ) { + fire(); + } + } + return this; + }, + + // Call all the callbacks with the given arguments + fire: function() { + self.fireWith( this, arguments ); + return this; + }, + + // To know if the callbacks have already been called at least once + fired: function() { + return !!fired; + } + }; + + return self; +}; + + +function Identity( v ) { + return v; +} +function Thrower( ex ) { + throw ex; +} + +function adoptValue( value, resolve, reject, noValue ) { + var method; + + try { + + // Check for promise aspect first to privilege synchronous behavior + if ( value && isFunction( ( method = value.promise ) ) ) { + method.call( value ).done( resolve ).fail( reject ); + + // Other thenables + } else if ( value && isFunction( ( method = value.then ) ) ) { + method.call( value, resolve, reject ); + + // Other non-thenables + } else { + + // Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer: + // * false: [ value ].slice( 0 ) => resolve( value ) + // * true: [ value ].slice( 1 ) => resolve() + resolve.apply( undefined, [ value ].slice( noValue ) ); + } + + // For Promises/A+, convert exceptions into rejections + // Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in + // Deferred#then to conditionally suppress rejection. + } catch ( value ) { + + // Support: Android 4.0 only + // Strict mode functions invoked without .call/.apply get global-object context + reject.apply( undefined, [ value ] ); + } +} + +jQuery.extend( { + + Deferred: function( func ) { + var tuples = [ + + // action, add listener, callbacks, + // ... .then handlers, argument index, [final state] + [ "notify", "progress", jQuery.Callbacks( "memory" ), + jQuery.Callbacks( "memory" ), 2 ], + [ "resolve", "done", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 0, "resolved" ], + [ "reject", "fail", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 1, "rejected" ] + ], + state = "pending", + promise = { + state: function() { + return state; + }, + always: function() { + deferred.done( arguments ).fail( arguments ); + return this; + }, + "catch": function( fn ) { + return promise.then( null, fn ); + }, + + // Keep pipe for back-compat + pipe: function( /* fnDone, fnFail, fnProgress */ ) { + var fns = arguments; + + return jQuery.Deferred( function( newDefer ) { + jQuery.each( tuples, function( _i, tuple ) { + + // Map tuples (progress, done, fail) to arguments (done, fail, progress) + var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ]; + + // deferred.progress(function() { bind to newDefer or newDefer.notify }) + // deferred.done(function() { bind to newDefer or newDefer.resolve }) + // deferred.fail(function() { bind to newDefer or newDefer.reject }) + deferred[ tuple[ 1 ] ]( function() { + var returned = fn && fn.apply( this, arguments ); + if ( returned && isFunction( returned.promise ) ) { + returned.promise() + .progress( newDefer.notify ) + .done( newDefer.resolve ) + .fail( newDefer.reject ); + } else { + newDefer[ tuple[ 0 ] + "With" ]( + this, + fn ? [ returned ] : arguments + ); + } + } ); + } ); + fns = null; + } ).promise(); + }, + then: function( onFulfilled, onRejected, onProgress ) { + var maxDepth = 0; + function resolve( depth, deferred, handler, special ) { + return function() { + var that = this, + args = arguments, + mightThrow = function() { + var returned, then; + + // Support: Promises/A+ section 2.3.3.3.3 + // https://promisesaplus.com/#point-59 + // Ignore double-resolution attempts + if ( depth < maxDepth ) { + return; + } + + returned = handler.apply( that, args ); + + // Support: Promises/A+ section 2.3.1 + // https://promisesaplus.com/#point-48 + if ( returned === deferred.promise() ) { + throw new TypeError( "Thenable self-resolution" ); + } + + // Support: Promises/A+ sections 2.3.3.1, 3.5 + // https://promisesaplus.com/#point-54 + // https://promisesaplus.com/#point-75 + // Retrieve `then` only once + then = returned && + + // Support: Promises/A+ section 2.3.4 + // https://promisesaplus.com/#point-64 + // Only check objects and functions for thenability + ( typeof returned === "object" || + typeof returned === "function" ) && + returned.then; + + // Handle a returned thenable + if ( isFunction( then ) ) { + + // Special processors (notify) just wait for resolution + if ( special ) { + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ) + ); + + // Normal processors (resolve) also hook into progress + } else { + + // ...and disregard older resolution values + maxDepth++; + + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ), + resolve( maxDepth, deferred, Identity, + deferred.notifyWith ) + ); + } + + // Handle all other returned values + } else { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Identity ) { + that = undefined; + args = [ returned ]; + } + + // Process the value(s) + // Default process is resolve + ( special || deferred.resolveWith )( that, args ); + } + }, + + // Only normal processors (resolve) catch and reject exceptions + process = special ? + mightThrow : + function() { + try { + mightThrow(); + } catch ( e ) { + + if ( jQuery.Deferred.exceptionHook ) { + jQuery.Deferred.exceptionHook( e, + process.stackTrace ); + } + + // Support: Promises/A+ section 2.3.3.3.4.1 + // https://promisesaplus.com/#point-61 + // Ignore post-resolution exceptions + if ( depth + 1 >= maxDepth ) { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Thrower ) { + that = undefined; + args = [ e ]; + } + + deferred.rejectWith( that, args ); + } + } + }; + + // Support: Promises/A+ section 2.3.3.3.1 + // https://promisesaplus.com/#point-57 + // Re-resolve promises immediately to dodge false rejection from + // subsequent errors + if ( depth ) { + process(); + } else { + + // Call an optional hook to record the stack, in case of exception + // since it's otherwise lost when execution goes async + if ( jQuery.Deferred.getStackHook ) { + process.stackTrace = jQuery.Deferred.getStackHook(); + } + window.setTimeout( process ); + } + }; + } + + return jQuery.Deferred( function( newDefer ) { + + // progress_handlers.add( ... ) + tuples[ 0 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onProgress ) ? + onProgress : + Identity, + newDefer.notifyWith + ) + ); + + // fulfilled_handlers.add( ... ) + tuples[ 1 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onFulfilled ) ? + onFulfilled : + Identity + ) + ); + + // rejected_handlers.add( ... ) + tuples[ 2 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onRejected ) ? + onRejected : + Thrower + ) + ); + } ).promise(); + }, + + // Get a promise for this deferred + // If obj is provided, the promise aspect is added to the object + promise: function( obj ) { + return obj != null ? jQuery.extend( obj, promise ) : promise; + } + }, + deferred = {}; + + // Add list-specific methods + jQuery.each( tuples, function( i, tuple ) { + var list = tuple[ 2 ], + stateString = tuple[ 5 ]; + + // promise.progress = list.add + // promise.done = list.add + // promise.fail = list.add + promise[ tuple[ 1 ] ] = list.add; + + // Handle state + if ( stateString ) { + list.add( + function() { + + // state = "resolved" (i.e., fulfilled) + // state = "rejected" + state = stateString; + }, + + // rejected_callbacks.disable + // fulfilled_callbacks.disable + tuples[ 3 - i ][ 2 ].disable, + + // rejected_handlers.disable + // fulfilled_handlers.disable + tuples[ 3 - i ][ 3 ].disable, + + // progress_callbacks.lock + tuples[ 0 ][ 2 ].lock, + + // progress_handlers.lock + tuples[ 0 ][ 3 ].lock + ); + } + + // progress_handlers.fire + // fulfilled_handlers.fire + // rejected_handlers.fire + list.add( tuple[ 3 ].fire ); + + // deferred.notify = function() { deferred.notifyWith(...) } + // deferred.resolve = function() { deferred.resolveWith(...) } + // deferred.reject = function() { deferred.rejectWith(...) } + deferred[ tuple[ 0 ] ] = function() { + deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments ); + return this; + }; + + // deferred.notifyWith = list.fireWith + // deferred.resolveWith = list.fireWith + // deferred.rejectWith = list.fireWith + deferred[ tuple[ 0 ] + "With" ] = list.fireWith; + } ); + + // Make the deferred a promise + promise.promise( deferred ); + + // Call given func if any + if ( func ) { + func.call( deferred, deferred ); + } + + // All done! + return deferred; + }, + + // Deferred helper + when: function( singleValue ) { + var + + // count of uncompleted subordinates + remaining = arguments.length, + + // count of unprocessed arguments + i = remaining, + + // subordinate fulfillment data + resolveContexts = Array( i ), + resolveValues = slice.call( arguments ), + + // the master Deferred + master = jQuery.Deferred(), + + // subordinate callback factory + updateFunc = function( i ) { + return function( value ) { + resolveContexts[ i ] = this; + resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value; + if ( !( --remaining ) ) { + master.resolveWith( resolveContexts, resolveValues ); + } + }; + }; + + // Single- and empty arguments are adopted like Promise.resolve + if ( remaining <= 1 ) { + adoptValue( singleValue, master.done( updateFunc( i ) ).resolve, master.reject, + !remaining ); + + // Use .then() to unwrap secondary thenables (cf. gh-3000) + if ( master.state() === "pending" || + isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) { + + return master.then(); + } + } + + // Multiple arguments are aggregated like Promise.all array elements + while ( i-- ) { + adoptValue( resolveValues[ i ], updateFunc( i ), master.reject ); + } + + return master.promise(); + } +} ); + + +// These usually indicate a programmer mistake during development, +// warn about them ASAP rather than swallowing them by default. +var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/; + +jQuery.Deferred.exceptionHook = function( error, stack ) { + + // Support: IE 8 - 9 only + // Console exists when dev tools are open, which can happen at any time + if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) { + window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack ); + } +}; + + + + +jQuery.readyException = function( error ) { + window.setTimeout( function() { + throw error; + } ); +}; + + + + +// The deferred used on DOM ready +var readyList = jQuery.Deferred(); + +jQuery.fn.ready = function( fn ) { + + readyList + .then( fn ) + + // Wrap jQuery.readyException in a function so that the lookup + // happens at the time of error handling instead of callback + // registration. + .catch( function( error ) { + jQuery.readyException( error ); + } ); + + return this; +}; + +jQuery.extend( { + + // Is the DOM ready to be used? Set to true once it occurs. + isReady: false, + + // A counter to track how many items to wait for before + // the ready event fires. See #6781 + readyWait: 1, + + // Handle when the DOM is ready + ready: function( wait ) { + + // Abort if there are pending holds or we're already ready + if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) { + return; + } + + // Remember that the DOM is ready + jQuery.isReady = true; + + // If a normal DOM Ready event fired, decrement, and wait if need be + if ( wait !== true && --jQuery.readyWait > 0 ) { + return; + } + + // If there are functions bound, to execute + readyList.resolveWith( document, [ jQuery ] ); + } +} ); + +jQuery.ready.then = readyList.then; + +// The ready event handler and self cleanup method +function completed() { + document.removeEventListener( "DOMContentLoaded", completed ); + window.removeEventListener( "load", completed ); + jQuery.ready(); +} + +// Catch cases where $(document).ready() is called +// after the browser event has already occurred. +// Support: IE <=9 - 10 only +// Older IE sometimes signals "interactive" too soon +if ( document.readyState === "complete" || + ( document.readyState !== "loading" && !document.documentElement.doScroll ) ) { + + // Handle it asynchronously to allow scripts the opportunity to delay ready + window.setTimeout( jQuery.ready ); + +} else { + + // Use the handy event callback + document.addEventListener( "DOMContentLoaded", completed ); + + // A fallback to window.onload, that will always work + window.addEventListener( "load", completed ); +} + + + + +// Multifunctional method to get and set values of a collection +// The value/s can optionally be executed if it's a function +var access = function( elems, fn, key, value, chainable, emptyGet, raw ) { + var i = 0, + len = elems.length, + bulk = key == null; + + // Sets many values + if ( toType( key ) === "object" ) { + chainable = true; + for ( i in key ) { + access( elems, fn, i, key[ i ], true, emptyGet, raw ); + } + + // Sets one value + } else if ( value !== undefined ) { + chainable = true; + + if ( !isFunction( value ) ) { + raw = true; + } + + if ( bulk ) { + + // Bulk operations run against the entire set + if ( raw ) { + fn.call( elems, value ); + fn = null; + + // ...except when executing function values + } else { + bulk = fn; + fn = function( elem, _key, value ) { + return bulk.call( jQuery( elem ), value ); + }; + } + } + + if ( fn ) { + for ( ; i < len; i++ ) { + fn( + elems[ i ], key, raw ? + value : + value.call( elems[ i ], i, fn( elems[ i ], key ) ) + ); + } + } + } + + if ( chainable ) { + return elems; + } + + // Gets + if ( bulk ) { + return fn.call( elems ); + } + + return len ? fn( elems[ 0 ], key ) : emptyGet; +}; + + +// Matches dashed string for camelizing +var rmsPrefix = /^-ms-/, + rdashAlpha = /-([a-z])/g; + +// Used by camelCase as callback to replace() +function fcamelCase( _all, letter ) { + return letter.toUpperCase(); +} + +// Convert dashed to camelCase; used by the css and data modules +// Support: IE <=9 - 11, Edge 12 - 15 +// Microsoft forgot to hump their vendor prefix (#9572) +function camelCase( string ) { + return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase ); +} +var acceptData = function( owner ) { + + // Accepts only: + // - Node + // - Node.ELEMENT_NODE + // - Node.DOCUMENT_NODE + // - Object + // - Any + return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType ); +}; + + + + +function Data() { + this.expando = jQuery.expando + Data.uid++; +} + +Data.uid = 1; + +Data.prototype = { + + cache: function( owner ) { + + // Check if the owner object already has a cache + var value = owner[ this.expando ]; + + // If not, create one + if ( !value ) { + value = {}; + + // We can accept data for non-element nodes in modern browsers, + // but we should not, see #8335. + // Always return an empty object. + if ( acceptData( owner ) ) { + + // If it is a node unlikely to be stringify-ed or looped over + // use plain assignment + if ( owner.nodeType ) { + owner[ this.expando ] = value; + + // Otherwise secure it in a non-enumerable property + // configurable must be true to allow the property to be + // deleted when data is removed + } else { + Object.defineProperty( owner, this.expando, { + value: value, + configurable: true + } ); + } + } + } + + return value; + }, + set: function( owner, data, value ) { + var prop, + cache = this.cache( owner ); + + // Handle: [ owner, key, value ] args + // Always use camelCase key (gh-2257) + if ( typeof data === "string" ) { + cache[ camelCase( data ) ] = value; + + // Handle: [ owner, { properties } ] args + } else { + + // Copy the properties one-by-one to the cache object + for ( prop in data ) { + cache[ camelCase( prop ) ] = data[ prop ]; + } + } + return cache; + }, + get: function( owner, key ) { + return key === undefined ? + this.cache( owner ) : + + // Always use camelCase key (gh-2257) + owner[ this.expando ] && owner[ this.expando ][ camelCase( key ) ]; + }, + access: function( owner, key, value ) { + + // In cases where either: + // + // 1. No key was specified + // 2. A string key was specified, but no value provided + // + // Take the "read" path and allow the get method to determine + // which value to return, respectively either: + // + // 1. The entire cache object + // 2. The data stored at the key + // + if ( key === undefined || + ( ( key && typeof key === "string" ) && value === undefined ) ) { + + return this.get( owner, key ); + } + + // When the key is not a string, or both a key and value + // are specified, set or extend (existing objects) with either: + // + // 1. An object of properties + // 2. A key and value + // + this.set( owner, key, value ); + + // Since the "set" path can have two possible entry points + // return the expected data based on which path was taken[*] + return value !== undefined ? value : key; + }, + remove: function( owner, key ) { + var i, + cache = owner[ this.expando ]; + + if ( cache === undefined ) { + return; + } + + if ( key !== undefined ) { + + // Support array or space separated string of keys + if ( Array.isArray( key ) ) { + + // If key is an array of keys... + // We always set camelCase keys, so remove that. + key = key.map( camelCase ); + } else { + key = camelCase( key ); + + // If a key with the spaces exists, use it. + // Otherwise, create an array by matching non-whitespace + key = key in cache ? + [ key ] : + ( key.match( rnothtmlwhite ) || [] ); + } + + i = key.length; + + while ( i-- ) { + delete cache[ key[ i ] ]; + } + } + + // Remove the expando if there's no more data + if ( key === undefined || jQuery.isEmptyObject( cache ) ) { + + // Support: Chrome <=35 - 45 + // Webkit & Blink performance suffers when deleting properties + // from DOM nodes, so set to undefined instead + // https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted) + if ( owner.nodeType ) { + owner[ this.expando ] = undefined; + } else { + delete owner[ this.expando ]; + } + } + }, + hasData: function( owner ) { + var cache = owner[ this.expando ]; + return cache !== undefined && !jQuery.isEmptyObject( cache ); + } +}; +var dataPriv = new Data(); + +var dataUser = new Data(); + + + +// Implementation Summary +// +// 1. Enforce API surface and semantic compatibility with 1.9.x branch +// 2. Improve the module's maintainability by reducing the storage +// paths to a single mechanism. +// 3. Use the same single mechanism to support "private" and "user" data. +// 4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData) +// 5. Avoid exposing implementation details on user objects (eg. expando properties) +// 6. Provide a clear path for implementation upgrade to WeakMap in 2014 + +var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/, + rmultiDash = /[A-Z]/g; + +function getData( data ) { + if ( data === "true" ) { + return true; + } + + if ( data === "false" ) { + return false; + } + + if ( data === "null" ) { + return null; + } + + // Only convert to a number if it doesn't change the string + if ( data === +data + "" ) { + return +data; + } + + if ( rbrace.test( data ) ) { + return JSON.parse( data ); + } + + return data; +} + +function dataAttr( elem, key, data ) { + var name; + + // If nothing was found internally, try to fetch any + // data from the HTML5 data-* attribute + if ( data === undefined && elem.nodeType === 1 ) { + name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase(); + data = elem.getAttribute( name ); + + if ( typeof data === "string" ) { + try { + data = getData( data ); + } catch ( e ) {} + + // Make sure we set the data so it isn't changed later + dataUser.set( elem, key, data ); + } else { + data = undefined; + } + } + return data; +} + +jQuery.extend( { + hasData: function( elem ) { + return dataUser.hasData( elem ) || dataPriv.hasData( elem ); + }, + + data: function( elem, name, data ) { + return dataUser.access( elem, name, data ); + }, + + removeData: function( elem, name ) { + dataUser.remove( elem, name ); + }, + + // TODO: Now that all calls to _data and _removeData have been replaced + // with direct calls to dataPriv methods, these can be deprecated. + _data: function( elem, name, data ) { + return dataPriv.access( elem, name, data ); + }, + + _removeData: function( elem, name ) { + dataPriv.remove( elem, name ); + } +} ); + +jQuery.fn.extend( { + data: function( key, value ) { + var i, name, data, + elem = this[ 0 ], + attrs = elem && elem.attributes; + + // Gets all values + if ( key === undefined ) { + if ( this.length ) { + data = dataUser.get( elem ); + + if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) { + i = attrs.length; + while ( i-- ) { + + // Support: IE 11 only + // The attrs elements can be null (#14894) + if ( attrs[ i ] ) { + name = attrs[ i ].name; + if ( name.indexOf( "data-" ) === 0 ) { + name = camelCase( name.slice( 5 ) ); + dataAttr( elem, name, data[ name ] ); + } + } + } + dataPriv.set( elem, "hasDataAttrs", true ); + } + } + + return data; + } + + // Sets multiple values + if ( typeof key === "object" ) { + return this.each( function() { + dataUser.set( this, key ); + } ); + } + + return access( this, function( value ) { + var data; + + // The calling jQuery object (element matches) is not empty + // (and therefore has an element appears at this[ 0 ]) and the + // `value` parameter was not undefined. An empty jQuery object + // will result in `undefined` for elem = this[ 0 ] which will + // throw an exception if an attempt to read a data cache is made. + if ( elem && value === undefined ) { + + // Attempt to get data from the cache + // The key will always be camelCased in Data + data = dataUser.get( elem, key ); + if ( data !== undefined ) { + return data; + } + + // Attempt to "discover" the data in + // HTML5 custom data-* attrs + data = dataAttr( elem, key ); + if ( data !== undefined ) { + return data; + } + + // We tried really hard, but the data doesn't exist. + return; + } + + // Set the data... + this.each( function() { + + // We always store the camelCased key + dataUser.set( this, key, value ); + } ); + }, null, value, arguments.length > 1, null, true ); + }, + + removeData: function( key ) { + return this.each( function() { + dataUser.remove( this, key ); + } ); + } +} ); + + +jQuery.extend( { + queue: function( elem, type, data ) { + var queue; + + if ( elem ) { + type = ( type || "fx" ) + "queue"; + queue = dataPriv.get( elem, type ); + + // Speed up dequeue by getting out quickly if this is just a lookup + if ( data ) { + if ( !queue || Array.isArray( data ) ) { + queue = dataPriv.access( elem, type, jQuery.makeArray( data ) ); + } else { + queue.push( data ); + } + } + return queue || []; + } + }, + + dequeue: function( elem, type ) { + type = type || "fx"; + + var queue = jQuery.queue( elem, type ), + startLength = queue.length, + fn = queue.shift(), + hooks = jQuery._queueHooks( elem, type ), + next = function() { + jQuery.dequeue( elem, type ); + }; + + // If the fx queue is dequeued, always remove the progress sentinel + if ( fn === "inprogress" ) { + fn = queue.shift(); + startLength--; + } + + if ( fn ) { + + // Add a progress sentinel to prevent the fx queue from being + // automatically dequeued + if ( type === "fx" ) { + queue.unshift( "inprogress" ); + } + + // Clear up the last queue stop function + delete hooks.stop; + fn.call( elem, next, hooks ); + } + + if ( !startLength && hooks ) { + hooks.empty.fire(); + } + }, + + // Not public - generate a queueHooks object, or return the current one + _queueHooks: function( elem, type ) { + var key = type + "queueHooks"; + return dataPriv.get( elem, key ) || dataPriv.access( elem, key, { + empty: jQuery.Callbacks( "once memory" ).add( function() { + dataPriv.remove( elem, [ type + "queue", key ] ); + } ) + } ); + } +} ); + +jQuery.fn.extend( { + queue: function( type, data ) { + var setter = 2; + + if ( typeof type !== "string" ) { + data = type; + type = "fx"; + setter--; + } + + if ( arguments.length < setter ) { + return jQuery.queue( this[ 0 ], type ); + } + + return data === undefined ? + this : + this.each( function() { + var queue = jQuery.queue( this, type, data ); + + // Ensure a hooks for this queue + jQuery._queueHooks( this, type ); + + if ( type === "fx" && queue[ 0 ] !== "inprogress" ) { + jQuery.dequeue( this, type ); + } + } ); + }, + dequeue: function( type ) { + return this.each( function() { + jQuery.dequeue( this, type ); + } ); + }, + clearQueue: function( type ) { + return this.queue( type || "fx", [] ); + }, + + // Get a promise resolved when queues of a certain type + // are emptied (fx is the type by default) + promise: function( type, obj ) { + var tmp, + count = 1, + defer = jQuery.Deferred(), + elements = this, + i = this.length, + resolve = function() { + if ( !( --count ) ) { + defer.resolveWith( elements, [ elements ] ); + } + }; + + if ( typeof type !== "string" ) { + obj = type; + type = undefined; + } + type = type || "fx"; + + while ( i-- ) { + tmp = dataPriv.get( elements[ i ], type + "queueHooks" ); + if ( tmp && tmp.empty ) { + count++; + tmp.empty.add( resolve ); + } + } + resolve(); + return defer.promise( obj ); + } +} ); +var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source; + +var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" ); + + +var cssExpand = [ "Top", "Right", "Bottom", "Left" ]; + +var documentElement = document.documentElement; + + + + var isAttached = function( elem ) { + return jQuery.contains( elem.ownerDocument, elem ); + }, + composed = { composed: true }; + + // Support: IE 9 - 11+, Edge 12 - 18+, iOS 10.0 - 10.2 only + // Check attachment across shadow DOM boundaries when possible (gh-3504) + // Support: iOS 10.0-10.2 only + // Early iOS 10 versions support `attachShadow` but not `getRootNode`, + // leading to errors. We need to check for `getRootNode`. + if ( documentElement.getRootNode ) { + isAttached = function( elem ) { + return jQuery.contains( elem.ownerDocument, elem ) || + elem.getRootNode( composed ) === elem.ownerDocument; + }; + } +var isHiddenWithinTree = function( elem, el ) { + + // isHiddenWithinTree might be called from jQuery#filter function; + // in that case, element will be second argument + elem = el || elem; + + // Inline style trumps all + return elem.style.display === "none" || + elem.style.display === "" && + + // Otherwise, check computed style + // Support: Firefox <=43 - 45 + // Disconnected elements can have computed display: none, so first confirm that elem is + // in the document. + isAttached( elem ) && + + jQuery.css( elem, "display" ) === "none"; + }; + + + +function adjustCSS( elem, prop, valueParts, tween ) { + var adjusted, scale, + maxIterations = 20, + currentValue = tween ? + function() { + return tween.cur(); + } : + function() { + return jQuery.css( elem, prop, "" ); + }, + initial = currentValue(), + unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ), + + // Starting value computation is required for potential unit mismatches + initialInUnit = elem.nodeType && + ( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) && + rcssNum.exec( jQuery.css( elem, prop ) ); + + if ( initialInUnit && initialInUnit[ 3 ] !== unit ) { + + // Support: Firefox <=54 + // Halve the iteration target value to prevent interference from CSS upper bounds (gh-2144) + initial = initial / 2; + + // Trust units reported by jQuery.css + unit = unit || initialInUnit[ 3 ]; + + // Iteratively approximate from a nonzero starting point + initialInUnit = +initial || 1; + + while ( maxIterations-- ) { + + // Evaluate and update our best guess (doubling guesses that zero out). + // Finish if the scale equals or crosses 1 (making the old*new product non-positive). + jQuery.style( elem, prop, initialInUnit + unit ); + if ( ( 1 - scale ) * ( 1 - ( scale = currentValue() / initial || 0.5 ) ) <= 0 ) { + maxIterations = 0; + } + initialInUnit = initialInUnit / scale; + + } + + initialInUnit = initialInUnit * 2; + jQuery.style( elem, prop, initialInUnit + unit ); + + // Make sure we update the tween properties later on + valueParts = valueParts || []; + } + + if ( valueParts ) { + initialInUnit = +initialInUnit || +initial || 0; + + // Apply relative offset (+=/-=) if specified + adjusted = valueParts[ 1 ] ? + initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] : + +valueParts[ 2 ]; + if ( tween ) { + tween.unit = unit; + tween.start = initialInUnit; + tween.end = adjusted; + } + } + return adjusted; +} + + +var defaultDisplayMap = {}; + +function getDefaultDisplay( elem ) { + var temp, + doc = elem.ownerDocument, + nodeName = elem.nodeName, + display = defaultDisplayMap[ nodeName ]; + + if ( display ) { + return display; + } + + temp = doc.body.appendChild( doc.createElement( nodeName ) ); + display = jQuery.css( temp, "display" ); + + temp.parentNode.removeChild( temp ); + + if ( display === "none" ) { + display = "block"; + } + defaultDisplayMap[ nodeName ] = display; + + return display; +} + +function showHide( elements, show ) { + var display, elem, + values = [], + index = 0, + length = elements.length; + + // Determine new display value for elements that need to change + for ( ; index < length; index++ ) { + elem = elements[ index ]; + if ( !elem.style ) { + continue; + } + + display = elem.style.display; + if ( show ) { + + // Since we force visibility upon cascade-hidden elements, an immediate (and slow) + // check is required in this first loop unless we have a nonempty display value (either + // inline or about-to-be-restored) + if ( display === "none" ) { + values[ index ] = dataPriv.get( elem, "display" ) || null; + if ( !values[ index ] ) { + elem.style.display = ""; + } + } + if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) { + values[ index ] = getDefaultDisplay( elem ); + } + } else { + if ( display !== "none" ) { + values[ index ] = "none"; + + // Remember what we're overwriting + dataPriv.set( elem, "display", display ); + } + } + } + + // Set the display of the elements in a second loop to avoid constant reflow + for ( index = 0; index < length; index++ ) { + if ( values[ index ] != null ) { + elements[ index ].style.display = values[ index ]; + } + } + + return elements; +} + +jQuery.fn.extend( { + show: function() { + return showHide( this, true ); + }, + hide: function() { + return showHide( this ); + }, + toggle: function( state ) { + if ( typeof state === "boolean" ) { + return state ? this.show() : this.hide(); + } + + return this.each( function() { + if ( isHiddenWithinTree( this ) ) { + jQuery( this ).show(); + } else { + jQuery( this ).hide(); + } + } ); + } +} ); +var rcheckableType = ( /^(?:checkbox|radio)$/i ); + +var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]*)/i ); + +var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i ); + + + +( function() { + var fragment = document.createDocumentFragment(), + div = fragment.appendChild( document.createElement( "div" ) ), + input = document.createElement( "input" ); + + // Support: Android 4.0 - 4.3 only + // Check state lost if the name is set (#11217) + // Support: Windows Web Apps (WWA) + // `name` and `type` must use .setAttribute for WWA (#14901) + input.setAttribute( "type", "radio" ); + input.setAttribute( "checked", "checked" ); + input.setAttribute( "name", "t" ); + + div.appendChild( input ); + + // Support: Android <=4.1 only + // Older WebKit doesn't clone checked state correctly in fragments + support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked; + + // Support: IE <=11 only + // Make sure textarea (and checkbox) defaultValue is properly cloned + div.innerHTML = ""; + support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue; + + // Support: IE <=9 only + // IE <=9 replaces "; + support.option = !!div.lastChild; +} )(); + + +// We have to close these tags to support XHTML (#13200) +var wrapMap = { + + // XHTML parsers do not magically insert elements in the + // same way that tag soup parsers do. So we cannot shorten + // this by omitting or other required elements. + thead: [ 1, "", "
" ], + col: [ 2, "", "
" ], + tr: [ 2, "", "
" ], + td: [ 3, "", "
" ], + + _default: [ 0, "", "" ] +}; + +wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead; +wrapMap.th = wrapMap.td; + +// Support: IE <=9 only +if ( !support.option ) { + wrapMap.optgroup = wrapMap.option = [ 1, "" ]; +} + + +function getAll( context, tag ) { + + // Support: IE <=9 - 11 only + // Use typeof to avoid zero-argument method invocation on host objects (#15151) + var ret; + + if ( typeof context.getElementsByTagName !== "undefined" ) { + ret = context.getElementsByTagName( tag || "*" ); + + } else if ( typeof context.querySelectorAll !== "undefined" ) { + ret = context.querySelectorAll( tag || "*" ); + + } else { + ret = []; + } + + if ( tag === undefined || tag && nodeName( context, tag ) ) { + return jQuery.merge( [ context ], ret ); + } + + return ret; +} + + +// Mark scripts as having already been evaluated +function setGlobalEval( elems, refElements ) { + var i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + dataPriv.set( + elems[ i ], + "globalEval", + !refElements || dataPriv.get( refElements[ i ], "globalEval" ) + ); + } +} + + +var rhtml = /<|&#?\w+;/; + +function buildFragment( elems, context, scripts, selection, ignored ) { + var elem, tmp, tag, wrap, attached, j, + fragment = context.createDocumentFragment(), + nodes = [], + i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + elem = elems[ i ]; + + if ( elem || elem === 0 ) { + + // Add nodes directly + if ( toType( elem ) === "object" ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem ); + + // Convert non-html into a text node + } else if ( !rhtml.test( elem ) ) { + nodes.push( context.createTextNode( elem ) ); + + // Convert html into DOM nodes + } else { + tmp = tmp || fragment.appendChild( context.createElement( "div" ) ); + + // Deserialize a standard representation + tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase(); + wrap = wrapMap[ tag ] || wrapMap._default; + tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ]; + + // Descend through wrappers to the right content + j = wrap[ 0 ]; + while ( j-- ) { + tmp = tmp.lastChild; + } + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, tmp.childNodes ); + + // Remember the top-level container + tmp = fragment.firstChild; + + // Ensure the created nodes are orphaned (#12392) + tmp.textContent = ""; + } + } + } + + // Remove wrapper from fragment + fragment.textContent = ""; + + i = 0; + while ( ( elem = nodes[ i++ ] ) ) { + + // Skip elements already in the context collection (trac-4087) + if ( selection && jQuery.inArray( elem, selection ) > -1 ) { + if ( ignored ) { + ignored.push( elem ); + } + continue; + } + + attached = isAttached( elem ); + + // Append to fragment + tmp = getAll( fragment.appendChild( elem ), "script" ); + + // Preserve script evaluation history + if ( attached ) { + setGlobalEval( tmp ); + } + + // Capture executables + if ( scripts ) { + j = 0; + while ( ( elem = tmp[ j++ ] ) ) { + if ( rscriptType.test( elem.type || "" ) ) { + scripts.push( elem ); + } + } + } + } + + return fragment; +} + + +var + rkeyEvent = /^key/, + rmouseEvent = /^(?:mouse|pointer|contextmenu|drag|drop)|click/, + rtypenamespace = /^([^.]*)(?:\.(.+)|)/; + +function returnTrue() { + return true; +} + +function returnFalse() { + return false; +} + +// Support: IE <=9 - 11+ +// focus() and blur() are asynchronous, except when they are no-op. +// So expect focus to be synchronous when the element is already active, +// and blur to be synchronous when the element is not already active. +// (focus and blur are always synchronous in other supported browsers, +// this just defines when we can count on it). +function expectSync( elem, type ) { + return ( elem === safeActiveElement() ) === ( type === "focus" ); +} + +// Support: IE <=9 only +// Accessing document.activeElement can throw unexpectedly +// https://bugs.jquery.com/ticket/13393 +function safeActiveElement() { + try { + return document.activeElement; + } catch ( err ) { } +} + +function on( elem, types, selector, data, fn, one ) { + var origFn, type; + + // Types can be a map of types/handlers + if ( typeof types === "object" ) { + + // ( types-Object, selector, data ) + if ( typeof selector !== "string" ) { + + // ( types-Object, data ) + data = data || selector; + selector = undefined; + } + for ( type in types ) { + on( elem, type, selector, data, types[ type ], one ); + } + return elem; + } + + if ( data == null && fn == null ) { + + // ( types, fn ) + fn = selector; + data = selector = undefined; + } else if ( fn == null ) { + if ( typeof selector === "string" ) { + + // ( types, selector, fn ) + fn = data; + data = undefined; + } else { + + // ( types, data, fn ) + fn = data; + data = selector; + selector = undefined; + } + } + if ( fn === false ) { + fn = returnFalse; + } else if ( !fn ) { + return elem; + } + + if ( one === 1 ) { + origFn = fn; + fn = function( event ) { + + // Can use an empty set, since event contains the info + jQuery().off( event ); + return origFn.apply( this, arguments ); + }; + + // Use same guid so caller can remove using origFn + fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ ); + } + return elem.each( function() { + jQuery.event.add( this, types, fn, data, selector ); + } ); +} + +/* + * Helper functions for managing events -- not part of the public interface. + * Props to Dean Edwards' addEvent library for many of the ideas. + */ +jQuery.event = { + + global: {}, + + add: function( elem, types, handler, data, selector ) { + + var handleObjIn, eventHandle, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.get( elem ); + + // Only attach events to objects that accept data + if ( !acceptData( elem ) ) { + return; + } + + // Caller can pass in an object of custom data in lieu of the handler + if ( handler.handler ) { + handleObjIn = handler; + handler = handleObjIn.handler; + selector = handleObjIn.selector; + } + + // Ensure that invalid selectors throw exceptions at attach time + // Evaluate against documentElement in case elem is a non-element node (e.g., document) + if ( selector ) { + jQuery.find.matchesSelector( documentElement, selector ); + } + + // Make sure that the handler has a unique ID, used to find/remove it later + if ( !handler.guid ) { + handler.guid = jQuery.guid++; + } + + // Init the element's event structure and main handler, if this is the first + if ( !( events = elemData.events ) ) { + events = elemData.events = Object.create( null ); + } + if ( !( eventHandle = elemData.handle ) ) { + eventHandle = elemData.handle = function( e ) { + + // Discard the second event of a jQuery.event.trigger() and + // when an event is called after a page has unloaded + return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ? + jQuery.event.dispatch.apply( elem, arguments ) : undefined; + }; + } + + // Handle multiple events separated by a space + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // There *must* be a type, no attaching namespace-only handlers + if ( !type ) { + continue; + } + + // If event changes its type, use the special event handlers for the changed type + special = jQuery.event.special[ type ] || {}; + + // If selector defined, determine special event api type, otherwise given type + type = ( selector ? special.delegateType : special.bindType ) || type; + + // Update special based on newly reset type + special = jQuery.event.special[ type ] || {}; + + // handleObj is passed to all event handlers + handleObj = jQuery.extend( { + type: type, + origType: origType, + data: data, + handler: handler, + guid: handler.guid, + selector: selector, + needsContext: selector && jQuery.expr.match.needsContext.test( selector ), + namespace: namespaces.join( "." ) + }, handleObjIn ); + + // Init the event handler queue if we're the first + if ( !( handlers = events[ type ] ) ) { + handlers = events[ type ] = []; + handlers.delegateCount = 0; + + // Only use addEventListener if the special events handler returns false + if ( !special.setup || + special.setup.call( elem, data, namespaces, eventHandle ) === false ) { + + if ( elem.addEventListener ) { + elem.addEventListener( type, eventHandle ); + } + } + } + + if ( special.add ) { + special.add.call( elem, handleObj ); + + if ( !handleObj.handler.guid ) { + handleObj.handler.guid = handler.guid; + } + } + + // Add to the element's handler list, delegates in front + if ( selector ) { + handlers.splice( handlers.delegateCount++, 0, handleObj ); + } else { + handlers.push( handleObj ); + } + + // Keep track of which events have ever been used, for event optimization + jQuery.event.global[ type ] = true; + } + + }, + + // Detach an event or set of events from an element + remove: function( elem, types, handler, selector, mappedTypes ) { + + var j, origCount, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.hasData( elem ) && dataPriv.get( elem ); + + if ( !elemData || !( events = elemData.events ) ) { + return; + } + + // Once for each type.namespace in types; type may be omitted + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // Unbind all events (on this namespace, if provided) for the element + if ( !type ) { + for ( type in events ) { + jQuery.event.remove( elem, type + types[ t ], handler, selector, true ); + } + continue; + } + + special = jQuery.event.special[ type ] || {}; + type = ( selector ? special.delegateType : special.bindType ) || type; + handlers = events[ type ] || []; + tmp = tmp[ 2 ] && + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ); + + // Remove matching events + origCount = j = handlers.length; + while ( j-- ) { + handleObj = handlers[ j ]; + + if ( ( mappedTypes || origType === handleObj.origType ) && + ( !handler || handler.guid === handleObj.guid ) && + ( !tmp || tmp.test( handleObj.namespace ) ) && + ( !selector || selector === handleObj.selector || + selector === "**" && handleObj.selector ) ) { + handlers.splice( j, 1 ); + + if ( handleObj.selector ) { + handlers.delegateCount--; + } + if ( special.remove ) { + special.remove.call( elem, handleObj ); + } + } + } + + // Remove generic event handler if we removed something and no more handlers exist + // (avoids potential for endless recursion during removal of special event handlers) + if ( origCount && !handlers.length ) { + if ( !special.teardown || + special.teardown.call( elem, namespaces, elemData.handle ) === false ) { + + jQuery.removeEvent( elem, type, elemData.handle ); + } + + delete events[ type ]; + } + } + + // Remove data and the expando if it's no longer used + if ( jQuery.isEmptyObject( events ) ) { + dataPriv.remove( elem, "handle events" ); + } + }, + + dispatch: function( nativeEvent ) { + + var i, j, ret, matched, handleObj, handlerQueue, + args = new Array( arguments.length ), + + // Make a writable jQuery.Event from the native event object + event = jQuery.event.fix( nativeEvent ), + + handlers = ( + dataPriv.get( this, "events" ) || Object.create( null ) + )[ event.type ] || [], + special = jQuery.event.special[ event.type ] || {}; + + // Use the fix-ed jQuery.Event rather than the (read-only) native event + args[ 0 ] = event; + + for ( i = 1; i < arguments.length; i++ ) { + args[ i ] = arguments[ i ]; + } + + event.delegateTarget = this; + + // Call the preDispatch hook for the mapped type, and let it bail if desired + if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) { + return; + } + + // Determine handlers + handlerQueue = jQuery.event.handlers.call( this, event, handlers ); + + // Run delegates first; they may want to stop propagation beneath us + i = 0; + while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) { + event.currentTarget = matched.elem; + + j = 0; + while ( ( handleObj = matched.handlers[ j++ ] ) && + !event.isImmediatePropagationStopped() ) { + + // If the event is namespaced, then each handler is only invoked if it is + // specially universal or its namespaces are a superset of the event's. + if ( !event.rnamespace || handleObj.namespace === false || + event.rnamespace.test( handleObj.namespace ) ) { + + event.handleObj = handleObj; + event.data = handleObj.data; + + ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle || + handleObj.handler ).apply( matched.elem, args ); + + if ( ret !== undefined ) { + if ( ( event.result = ret ) === false ) { + event.preventDefault(); + event.stopPropagation(); + } + } + } + } + } + + // Call the postDispatch hook for the mapped type + if ( special.postDispatch ) { + special.postDispatch.call( this, event ); + } + + return event.result; + }, + + handlers: function( event, handlers ) { + var i, handleObj, sel, matchedHandlers, matchedSelectors, + handlerQueue = [], + delegateCount = handlers.delegateCount, + cur = event.target; + + // Find delegate handlers + if ( delegateCount && + + // Support: IE <=9 + // Black-hole SVG instance trees (trac-13180) + cur.nodeType && + + // Support: Firefox <=42 + // Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861) + // https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click + // Support: IE 11 only + // ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343) + !( event.type === "click" && event.button >= 1 ) ) { + + for ( ; cur !== this; cur = cur.parentNode || this ) { + + // Don't check non-elements (#13208) + // Don't process clicks on disabled elements (#6911, #8165, #11382, #11764) + if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) { + matchedHandlers = []; + matchedSelectors = {}; + for ( i = 0; i < delegateCount; i++ ) { + handleObj = handlers[ i ]; + + // Don't conflict with Object.prototype properties (#13203) + sel = handleObj.selector + " "; + + if ( matchedSelectors[ sel ] === undefined ) { + matchedSelectors[ sel ] = handleObj.needsContext ? + jQuery( sel, this ).index( cur ) > -1 : + jQuery.find( sel, this, null, [ cur ] ).length; + } + if ( matchedSelectors[ sel ] ) { + matchedHandlers.push( handleObj ); + } + } + if ( matchedHandlers.length ) { + handlerQueue.push( { elem: cur, handlers: matchedHandlers } ); + } + } + } + } + + // Add the remaining (directly-bound) handlers + cur = this; + if ( delegateCount < handlers.length ) { + handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } ); + } + + return handlerQueue; + }, + + addProp: function( name, hook ) { + Object.defineProperty( jQuery.Event.prototype, name, { + enumerable: true, + configurable: true, + + get: isFunction( hook ) ? + function() { + if ( this.originalEvent ) { + return hook( this.originalEvent ); + } + } : + function() { + if ( this.originalEvent ) { + return this.originalEvent[ name ]; + } + }, + + set: function( value ) { + Object.defineProperty( this, name, { + enumerable: true, + configurable: true, + writable: true, + value: value + } ); + } + } ); + }, + + fix: function( originalEvent ) { + return originalEvent[ jQuery.expando ] ? + originalEvent : + new jQuery.Event( originalEvent ); + }, + + special: { + load: { + + // Prevent triggered image.load events from bubbling to window.load + noBubble: true + }, + click: { + + // Utilize native event to ensure correct state for checkable inputs + setup: function( data ) { + + // For mutual compressibility with _default, replace `this` access with a local var. + // `|| data` is dead code meant only to preserve the variable through minification. + var el = this || data; + + // Claim the first handler + if ( rcheckableType.test( el.type ) && + el.click && nodeName( el, "input" ) ) { + + // dataPriv.set( el, "click", ... ) + leverageNative( el, "click", returnTrue ); + } + + // Return false to allow normal processing in the caller + return false; + }, + trigger: function( data ) { + + // For mutual compressibility with _default, replace `this` access with a local var. + // `|| data` is dead code meant only to preserve the variable through minification. + var el = this || data; + + // Force setup before triggering a click + if ( rcheckableType.test( el.type ) && + el.click && nodeName( el, "input" ) ) { + + leverageNative( el, "click" ); + } + + // Return non-false to allow normal event-path propagation + return true; + }, + + // For cross-browser consistency, suppress native .click() on links + // Also prevent it if we're currently inside a leveraged native-event stack + _default: function( event ) { + var target = event.target; + return rcheckableType.test( target.type ) && + target.click && nodeName( target, "input" ) && + dataPriv.get( target, "click" ) || + nodeName( target, "a" ); + } + }, + + beforeunload: { + postDispatch: function( event ) { + + // Support: Firefox 20+ + // Firefox doesn't alert if the returnValue field is not set. + if ( event.result !== undefined && event.originalEvent ) { + event.originalEvent.returnValue = event.result; + } + } + } + } +}; + +// Ensure the presence of an event listener that handles manually-triggered +// synthetic events by interrupting progress until reinvoked in response to +// *native* events that it fires directly, ensuring that state changes have +// already occurred before other listeners are invoked. +function leverageNative( el, type, expectSync ) { + + // Missing expectSync indicates a trigger call, which must force setup through jQuery.event.add + if ( !expectSync ) { + if ( dataPriv.get( el, type ) === undefined ) { + jQuery.event.add( el, type, returnTrue ); + } + return; + } + + // Register the controller as a special universal handler for all event namespaces + dataPriv.set( el, type, false ); + jQuery.event.add( el, type, { + namespace: false, + handler: function( event ) { + var notAsync, result, + saved = dataPriv.get( this, type ); + + if ( ( event.isTrigger & 1 ) && this[ type ] ) { + + // Interrupt processing of the outer synthetic .trigger()ed event + // Saved data should be false in such cases, but might be a leftover capture object + // from an async native handler (gh-4350) + if ( !saved.length ) { + + // Store arguments for use when handling the inner native event + // There will always be at least one argument (an event object), so this array + // will not be confused with a leftover capture object. + saved = slice.call( arguments ); + dataPriv.set( this, type, saved ); + + // Trigger the native event and capture its result + // Support: IE <=9 - 11+ + // focus() and blur() are asynchronous + notAsync = expectSync( this, type ); + this[ type ](); + result = dataPriv.get( this, type ); + if ( saved !== result || notAsync ) { + dataPriv.set( this, type, false ); + } else { + result = {}; + } + if ( saved !== result ) { + + // Cancel the outer synthetic event + event.stopImmediatePropagation(); + event.preventDefault(); + return result.value; + } + + // If this is an inner synthetic event for an event with a bubbling surrogate + // (focus or blur), assume that the surrogate already propagated from triggering the + // native event and prevent that from happening again here. + // This technically gets the ordering wrong w.r.t. to `.trigger()` (in which the + // bubbling surrogate propagates *after* the non-bubbling base), but that seems + // less bad than duplication. + } else if ( ( jQuery.event.special[ type ] || {} ).delegateType ) { + event.stopPropagation(); + } + + // If this is a native event triggered above, everything is now in order + // Fire an inner synthetic event with the original arguments + } else if ( saved.length ) { + + // ...and capture the result + dataPriv.set( this, type, { + value: jQuery.event.trigger( + + // Support: IE <=9 - 11+ + // Extend with the prototype to reset the above stopImmediatePropagation() + jQuery.extend( saved[ 0 ], jQuery.Event.prototype ), + saved.slice( 1 ), + this + ) + } ); + + // Abort handling of the native event + event.stopImmediatePropagation(); + } + } + } ); +} + +jQuery.removeEvent = function( elem, type, handle ) { + + // This "if" is needed for plain objects + if ( elem.removeEventListener ) { + elem.removeEventListener( type, handle ); + } +}; + +jQuery.Event = function( src, props ) { + + // Allow instantiation without the 'new' keyword + if ( !( this instanceof jQuery.Event ) ) { + return new jQuery.Event( src, props ); + } + + // Event object + if ( src && src.type ) { + this.originalEvent = src; + this.type = src.type; + + // Events bubbling up the document may have been marked as prevented + // by a handler lower down the tree; reflect the correct value. + this.isDefaultPrevented = src.defaultPrevented || + src.defaultPrevented === undefined && + + // Support: Android <=2.3 only + src.returnValue === false ? + returnTrue : + returnFalse; + + // Create target properties + // Support: Safari <=6 - 7 only + // Target should not be a text node (#504, #13143) + this.target = ( src.target && src.target.nodeType === 3 ) ? + src.target.parentNode : + src.target; + + this.currentTarget = src.currentTarget; + this.relatedTarget = src.relatedTarget; + + // Event type + } else { + this.type = src; + } + + // Put explicitly provided properties onto the event object + if ( props ) { + jQuery.extend( this, props ); + } + + // Create a timestamp if incoming event doesn't have one + this.timeStamp = src && src.timeStamp || Date.now(); + + // Mark it as fixed + this[ jQuery.expando ] = true; +}; + +// jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding +// https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html +jQuery.Event.prototype = { + constructor: jQuery.Event, + isDefaultPrevented: returnFalse, + isPropagationStopped: returnFalse, + isImmediatePropagationStopped: returnFalse, + isSimulated: false, + + preventDefault: function() { + var e = this.originalEvent; + + this.isDefaultPrevented = returnTrue; + + if ( e && !this.isSimulated ) { + e.preventDefault(); + } + }, + stopPropagation: function() { + var e = this.originalEvent; + + this.isPropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopPropagation(); + } + }, + stopImmediatePropagation: function() { + var e = this.originalEvent; + + this.isImmediatePropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopImmediatePropagation(); + } + + this.stopPropagation(); + } +}; + +// Includes all common event props including KeyEvent and MouseEvent specific props +jQuery.each( { + altKey: true, + bubbles: true, + cancelable: true, + changedTouches: true, + ctrlKey: true, + detail: true, + eventPhase: true, + metaKey: true, + pageX: true, + pageY: true, + shiftKey: true, + view: true, + "char": true, + code: true, + charCode: true, + key: true, + keyCode: true, + button: true, + buttons: true, + clientX: true, + clientY: true, + offsetX: true, + offsetY: true, + pointerId: true, + pointerType: true, + screenX: true, + screenY: true, + targetTouches: true, + toElement: true, + touches: true, + + which: function( event ) { + var button = event.button; + + // Add which for key events + if ( event.which == null && rkeyEvent.test( event.type ) ) { + return event.charCode != null ? event.charCode : event.keyCode; + } + + // Add which for click: 1 === left; 2 === middle; 3 === right + if ( !event.which && button !== undefined && rmouseEvent.test( event.type ) ) { + if ( button & 1 ) { + return 1; + } + + if ( button & 2 ) { + return 3; + } + + if ( button & 4 ) { + return 2; + } + + return 0; + } + + return event.which; + } +}, jQuery.event.addProp ); + +jQuery.each( { focus: "focusin", blur: "focusout" }, function( type, delegateType ) { + jQuery.event.special[ type ] = { + + // Utilize native event if possible so blur/focus sequence is correct + setup: function() { + + // Claim the first handler + // dataPriv.set( this, "focus", ... ) + // dataPriv.set( this, "blur", ... ) + leverageNative( this, type, expectSync ); + + // Return false to allow normal processing in the caller + return false; + }, + trigger: function() { + + // Force setup before trigger + leverageNative( this, type ); + + // Return non-false to allow normal event-path propagation + return true; + }, + + delegateType: delegateType + }; +} ); + +// Create mouseenter/leave events using mouseover/out and event-time checks +// so that event delegation works in jQuery. +// Do the same for pointerenter/pointerleave and pointerover/pointerout +// +// Support: Safari 7 only +// Safari sends mouseenter too often; see: +// https://bugs.chromium.org/p/chromium/issues/detail?id=470258 +// for the description of the bug (it existed in older Chrome versions as well). +jQuery.each( { + mouseenter: "mouseover", + mouseleave: "mouseout", + pointerenter: "pointerover", + pointerleave: "pointerout" +}, function( orig, fix ) { + jQuery.event.special[ orig ] = { + delegateType: fix, + bindType: fix, + + handle: function( event ) { + var ret, + target = this, + related = event.relatedTarget, + handleObj = event.handleObj; + + // For mouseenter/leave call the handler if related is outside the target. + // NB: No relatedTarget if the mouse left/entered the browser window + if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) { + event.type = handleObj.origType; + ret = handleObj.handler.apply( this, arguments ); + event.type = fix; + } + return ret; + } + }; +} ); + +jQuery.fn.extend( { + + on: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn ); + }, + one: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn, 1 ); + }, + off: function( types, selector, fn ) { + var handleObj, type; + if ( types && types.preventDefault && types.handleObj ) { + + // ( event ) dispatched jQuery.Event + handleObj = types.handleObj; + jQuery( types.delegateTarget ).off( + handleObj.namespace ? + handleObj.origType + "." + handleObj.namespace : + handleObj.origType, + handleObj.selector, + handleObj.handler + ); + return this; + } + if ( typeof types === "object" ) { + + // ( types-object [, selector] ) + for ( type in types ) { + this.off( type, selector, types[ type ] ); + } + return this; + } + if ( selector === false || typeof selector === "function" ) { + + // ( types [, fn] ) + fn = selector; + selector = undefined; + } + if ( fn === false ) { + fn = returnFalse; + } + return this.each( function() { + jQuery.event.remove( this, types, fn, selector ); + } ); + } +} ); + + +var + + // Support: IE <=10 - 11, Edge 12 - 13 only + // In IE/Edge using regex groups here causes severe slowdowns. + // See https://connect.microsoft.com/IE/feedback/details/1736512/ + rnoInnerhtml = /\s*$/g; + +// Prefer a tbody over its parent table for containing new rows +function manipulationTarget( elem, content ) { + if ( nodeName( elem, "table" ) && + nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) { + + return jQuery( elem ).children( "tbody" )[ 0 ] || elem; + } + + return elem; +} + +// Replace/restore the type attribute of script elements for safe DOM manipulation +function disableScript( elem ) { + elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type; + return elem; +} +function restoreScript( elem ) { + if ( ( elem.type || "" ).slice( 0, 5 ) === "true/" ) { + elem.type = elem.type.slice( 5 ); + } else { + elem.removeAttribute( "type" ); + } + + return elem; +} + +function cloneCopyEvent( src, dest ) { + var i, l, type, pdataOld, udataOld, udataCur, events; + + if ( dest.nodeType !== 1 ) { + return; + } + + // 1. Copy private data: events, handlers, etc. + if ( dataPriv.hasData( src ) ) { + pdataOld = dataPriv.get( src ); + events = pdataOld.events; + + if ( events ) { + dataPriv.remove( dest, "handle events" ); + + for ( type in events ) { + for ( i = 0, l = events[ type ].length; i < l; i++ ) { + jQuery.event.add( dest, type, events[ type ][ i ] ); + } + } + } + } + + // 2. Copy user data + if ( dataUser.hasData( src ) ) { + udataOld = dataUser.access( src ); + udataCur = jQuery.extend( {}, udataOld ); + + dataUser.set( dest, udataCur ); + } +} + +// Fix IE bugs, see support tests +function fixInput( src, dest ) { + var nodeName = dest.nodeName.toLowerCase(); + + // Fails to persist the checked state of a cloned checkbox or radio button. + if ( nodeName === "input" && rcheckableType.test( src.type ) ) { + dest.checked = src.checked; + + // Fails to return the selected option to the default selected state when cloning options + } else if ( nodeName === "input" || nodeName === "textarea" ) { + dest.defaultValue = src.defaultValue; + } +} + +function domManip( collection, args, callback, ignored ) { + + // Flatten any nested arrays + args = flat( args ); + + var fragment, first, scripts, hasScripts, node, doc, + i = 0, + l = collection.length, + iNoClone = l - 1, + value = args[ 0 ], + valueIsFunction = isFunction( value ); + + // We can't cloneNode fragments that contain checked, in WebKit + if ( valueIsFunction || + ( l > 1 && typeof value === "string" && + !support.checkClone && rchecked.test( value ) ) ) { + return collection.each( function( index ) { + var self = collection.eq( index ); + if ( valueIsFunction ) { + args[ 0 ] = value.call( this, index, self.html() ); + } + domManip( self, args, callback, ignored ); + } ); + } + + if ( l ) { + fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored ); + first = fragment.firstChild; + + if ( fragment.childNodes.length === 1 ) { + fragment = first; + } + + // Require either new content or an interest in ignored elements to invoke the callback + if ( first || ignored ) { + scripts = jQuery.map( getAll( fragment, "script" ), disableScript ); + hasScripts = scripts.length; + + // Use the original fragment for the last item + // instead of the first because it can end up + // being emptied incorrectly in certain situations (#8070). + for ( ; i < l; i++ ) { + node = fragment; + + if ( i !== iNoClone ) { + node = jQuery.clone( node, true, true ); + + // Keep references to cloned scripts for later restoration + if ( hasScripts ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( scripts, getAll( node, "script" ) ); + } + } + + callback.call( collection[ i ], node, i ); + } + + if ( hasScripts ) { + doc = scripts[ scripts.length - 1 ].ownerDocument; + + // Reenable scripts + jQuery.map( scripts, restoreScript ); + + // Evaluate executable scripts on first document insertion + for ( i = 0; i < hasScripts; i++ ) { + node = scripts[ i ]; + if ( rscriptType.test( node.type || "" ) && + !dataPriv.access( node, "globalEval" ) && + jQuery.contains( doc, node ) ) { + + if ( node.src && ( node.type || "" ).toLowerCase() !== "module" ) { + + // Optional AJAX dependency, but won't run scripts if not present + if ( jQuery._evalUrl && !node.noModule ) { + jQuery._evalUrl( node.src, { + nonce: node.nonce || node.getAttribute( "nonce" ) + }, doc ); + } + } else { + DOMEval( node.textContent.replace( rcleanScript, "" ), node, doc ); + } + } + } + } + } + } + + return collection; +} + +function remove( elem, selector, keepData ) { + var node, + nodes = selector ? jQuery.filter( selector, elem ) : elem, + i = 0; + + for ( ; ( node = nodes[ i ] ) != null; i++ ) { + if ( !keepData && node.nodeType === 1 ) { + jQuery.cleanData( getAll( node ) ); + } + + if ( node.parentNode ) { + if ( keepData && isAttached( node ) ) { + setGlobalEval( getAll( node, "script" ) ); + } + node.parentNode.removeChild( node ); + } + } + + return elem; +} + +jQuery.extend( { + htmlPrefilter: function( html ) { + return html; + }, + + clone: function( elem, dataAndEvents, deepDataAndEvents ) { + var i, l, srcElements, destElements, + clone = elem.cloneNode( true ), + inPage = isAttached( elem ); + + // Fix IE cloning issues + if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) && + !jQuery.isXMLDoc( elem ) ) { + + // We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2 + destElements = getAll( clone ); + srcElements = getAll( elem ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + fixInput( srcElements[ i ], destElements[ i ] ); + } + } + + // Copy the events from the original to the clone + if ( dataAndEvents ) { + if ( deepDataAndEvents ) { + srcElements = srcElements || getAll( elem ); + destElements = destElements || getAll( clone ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + cloneCopyEvent( srcElements[ i ], destElements[ i ] ); + } + } else { + cloneCopyEvent( elem, clone ); + } + } + + // Preserve script evaluation history + destElements = getAll( clone, "script" ); + if ( destElements.length > 0 ) { + setGlobalEval( destElements, !inPage && getAll( elem, "script" ) ); + } + + // Return the cloned set + return clone; + }, + + cleanData: function( elems ) { + var data, elem, type, + special = jQuery.event.special, + i = 0; + + for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) { + if ( acceptData( elem ) ) { + if ( ( data = elem[ dataPriv.expando ] ) ) { + if ( data.events ) { + for ( type in data.events ) { + if ( special[ type ] ) { + jQuery.event.remove( elem, type ); + + // This is a shortcut to avoid jQuery.event.remove's overhead + } else { + jQuery.removeEvent( elem, type, data.handle ); + } + } + } + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataPriv.expando ] = undefined; + } + if ( elem[ dataUser.expando ] ) { + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataUser.expando ] = undefined; + } + } + } + } +} ); + +jQuery.fn.extend( { + detach: function( selector ) { + return remove( this, selector, true ); + }, + + remove: function( selector ) { + return remove( this, selector ); + }, + + text: function( value ) { + return access( this, function( value ) { + return value === undefined ? + jQuery.text( this ) : + this.empty().each( function() { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + this.textContent = value; + } + } ); + }, null, value, arguments.length ); + }, + + append: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.appendChild( elem ); + } + } ); + }, + + prepend: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.insertBefore( elem, target.firstChild ); + } + } ); + }, + + before: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this ); + } + } ); + }, + + after: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this.nextSibling ); + } + } ); + }, + + empty: function() { + var elem, + i = 0; + + for ( ; ( elem = this[ i ] ) != null; i++ ) { + if ( elem.nodeType === 1 ) { + + // Prevent memory leaks + jQuery.cleanData( getAll( elem, false ) ); + + // Remove any remaining nodes + elem.textContent = ""; + } + } + + return this; + }, + + clone: function( dataAndEvents, deepDataAndEvents ) { + dataAndEvents = dataAndEvents == null ? false : dataAndEvents; + deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents; + + return this.map( function() { + return jQuery.clone( this, dataAndEvents, deepDataAndEvents ); + } ); + }, + + html: function( value ) { + return access( this, function( value ) { + var elem = this[ 0 ] || {}, + i = 0, + l = this.length; + + if ( value === undefined && elem.nodeType === 1 ) { + return elem.innerHTML; + } + + // See if we can take a shortcut and just use innerHTML + if ( typeof value === "string" && !rnoInnerhtml.test( value ) && + !wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) { + + value = jQuery.htmlPrefilter( value ); + + try { + for ( ; i < l; i++ ) { + elem = this[ i ] || {}; + + // Remove element nodes and prevent memory leaks + if ( elem.nodeType === 1 ) { + jQuery.cleanData( getAll( elem, false ) ); + elem.innerHTML = value; + } + } + + elem = 0; + + // If using innerHTML throws an exception, use the fallback method + } catch ( e ) {} + } + + if ( elem ) { + this.empty().append( value ); + } + }, null, value, arguments.length ); + }, + + replaceWith: function() { + var ignored = []; + + // Make the changes, replacing each non-ignored context element with the new content + return domManip( this, arguments, function( elem ) { + var parent = this.parentNode; + + if ( jQuery.inArray( this, ignored ) < 0 ) { + jQuery.cleanData( getAll( this ) ); + if ( parent ) { + parent.replaceChild( elem, this ); + } + } + + // Force callback invocation + }, ignored ); + } +} ); + +jQuery.each( { + appendTo: "append", + prependTo: "prepend", + insertBefore: "before", + insertAfter: "after", + replaceAll: "replaceWith" +}, function( name, original ) { + jQuery.fn[ name ] = function( selector ) { + var elems, + ret = [], + insert = jQuery( selector ), + last = insert.length - 1, + i = 0; + + for ( ; i <= last; i++ ) { + elems = i === last ? this : this.clone( true ); + jQuery( insert[ i ] )[ original ]( elems ); + + // Support: Android <=4.0 only, PhantomJS 1 only + // .get() because push.apply(_, arraylike) throws on ancient WebKit + push.apply( ret, elems.get() ); + } + + return this.pushStack( ret ); + }; +} ); +var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" ); + +var getStyles = function( elem ) { + + // Support: IE <=11 only, Firefox <=30 (#15098, #14150) + // IE throws on elements created in popups + // FF meanwhile throws on frame elements through "defaultView.getComputedStyle" + var view = elem.ownerDocument.defaultView; + + if ( !view || !view.opener ) { + view = window; + } + + return view.getComputedStyle( elem ); + }; + +var swap = function( elem, options, callback ) { + var ret, name, + old = {}; + + // Remember the old values, and insert the new ones + for ( name in options ) { + old[ name ] = elem.style[ name ]; + elem.style[ name ] = options[ name ]; + } + + ret = callback.call( elem ); + + // Revert the old values + for ( name in options ) { + elem.style[ name ] = old[ name ]; + } + + return ret; +}; + + +var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" ); + + + +( function() { + + // Executing both pixelPosition & boxSizingReliable tests require only one layout + // so they're executed at the same time to save the second computation. + function computeStyleTests() { + + // This is a singleton, we need to execute it only once + if ( !div ) { + return; + } + + container.style.cssText = "position:absolute;left:-11111px;width:60px;" + + "margin-top:1px;padding:0;border:0"; + div.style.cssText = + "position:relative;display:block;box-sizing:border-box;overflow:scroll;" + + "margin:auto;border:1px;padding:1px;" + + "width:60%;top:1%"; + documentElement.appendChild( container ).appendChild( div ); + + var divStyle = window.getComputedStyle( div ); + pixelPositionVal = divStyle.top !== "1%"; + + // Support: Android 4.0 - 4.3 only, Firefox <=3 - 44 + reliableMarginLeftVal = roundPixelMeasures( divStyle.marginLeft ) === 12; + + // Support: Android 4.0 - 4.3 only, Safari <=9.1 - 10.1, iOS <=7.0 - 9.3 + // Some styles come back with percentage values, even though they shouldn't + div.style.right = "60%"; + pixelBoxStylesVal = roundPixelMeasures( divStyle.right ) === 36; + + // Support: IE 9 - 11 only + // Detect misreporting of content dimensions for box-sizing:border-box elements + boxSizingReliableVal = roundPixelMeasures( divStyle.width ) === 36; + + // Support: IE 9 only + // Detect overflow:scroll screwiness (gh-3699) + // Support: Chrome <=64 + // Don't get tricked when zoom affects offsetWidth (gh-4029) + div.style.position = "absolute"; + scrollboxSizeVal = roundPixelMeasures( div.offsetWidth / 3 ) === 12; + + documentElement.removeChild( container ); + + // Nullify the div so it wouldn't be stored in the memory and + // it will also be a sign that checks already performed + div = null; + } + + function roundPixelMeasures( measure ) { + return Math.round( parseFloat( measure ) ); + } + + var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal, + reliableTrDimensionsVal, reliableMarginLeftVal, + container = document.createElement( "div" ), + div = document.createElement( "div" ); + + // Finish early in limited (non-browser) environments + if ( !div.style ) { + return; + } + + // Support: IE <=9 - 11 only + // Style of cloned element affects source element cloned (#8908) + div.style.backgroundClip = "content-box"; + div.cloneNode( true ).style.backgroundClip = ""; + support.clearCloneStyle = div.style.backgroundClip === "content-box"; + + jQuery.extend( support, { + boxSizingReliable: function() { + computeStyleTests(); + return boxSizingReliableVal; + }, + pixelBoxStyles: function() { + computeStyleTests(); + return pixelBoxStylesVal; + }, + pixelPosition: function() { + computeStyleTests(); + return pixelPositionVal; + }, + reliableMarginLeft: function() { + computeStyleTests(); + return reliableMarginLeftVal; + }, + scrollboxSize: function() { + computeStyleTests(); + return scrollboxSizeVal; + }, + + // Support: IE 9 - 11+, Edge 15 - 18+ + // IE/Edge misreport `getComputedStyle` of table rows with width/height + // set in CSS while `offset*` properties report correct values. + // Behavior in IE 9 is more subtle than in newer versions & it passes + // some versions of this test; make sure not to make it pass there! + reliableTrDimensions: function() { + var table, tr, trChild, trStyle; + if ( reliableTrDimensionsVal == null ) { + table = document.createElement( "table" ); + tr = document.createElement( "tr" ); + trChild = document.createElement( "div" ); + + table.style.cssText = "position:absolute;left:-11111px"; + tr.style.height = "1px"; + trChild.style.height = "9px"; + + documentElement + .appendChild( table ) + .appendChild( tr ) + .appendChild( trChild ); + + trStyle = window.getComputedStyle( tr ); + reliableTrDimensionsVal = parseInt( trStyle.height ) > 3; + + documentElement.removeChild( table ); + } + return reliableTrDimensionsVal; + } + } ); +} )(); + + +function curCSS( elem, name, computed ) { + var width, minWidth, maxWidth, ret, + + // Support: Firefox 51+ + // Retrieving style before computed somehow + // fixes an issue with getting wrong values + // on detached elements + style = elem.style; + + computed = computed || getStyles( elem ); + + // getPropertyValue is needed for: + // .css('filter') (IE 9 only, #12537) + // .css('--customProperty) (#3144) + if ( computed ) { + ret = computed.getPropertyValue( name ) || computed[ name ]; + + if ( ret === "" && !isAttached( elem ) ) { + ret = jQuery.style( elem, name ); + } + + // A tribute to the "awesome hack by Dean Edwards" + // Android Browser returns percentage for some values, + // but width seems to be reliably pixels. + // This is against the CSSOM draft spec: + // https://drafts.csswg.org/cssom/#resolved-values + if ( !support.pixelBoxStyles() && rnumnonpx.test( ret ) && rboxStyle.test( name ) ) { + + // Remember the original values + width = style.width; + minWidth = style.minWidth; + maxWidth = style.maxWidth; + + // Put in the new values to get a computed value out + style.minWidth = style.maxWidth = style.width = ret; + ret = computed.width; + + // Revert the changed values + style.width = width; + style.minWidth = minWidth; + style.maxWidth = maxWidth; + } + } + + return ret !== undefined ? + + // Support: IE <=9 - 11 only + // IE returns zIndex value as an integer. + ret + "" : + ret; +} + + +function addGetHookIf( conditionFn, hookFn ) { + + // Define the hook, we'll check on the first run if it's really needed. + return { + get: function() { + if ( conditionFn() ) { + + // Hook not needed (or it's not possible to use it due + // to missing dependency), remove it. + delete this.get; + return; + } + + // Hook needed; redefine it so that the support test is not executed again. + return ( this.get = hookFn ).apply( this, arguments ); + } + }; +} + + +var cssPrefixes = [ "Webkit", "Moz", "ms" ], + emptyStyle = document.createElement( "div" ).style, + vendorProps = {}; + +// Return a vendor-prefixed property or undefined +function vendorPropName( name ) { + + // Check for vendor prefixed names + var capName = name[ 0 ].toUpperCase() + name.slice( 1 ), + i = cssPrefixes.length; + + while ( i-- ) { + name = cssPrefixes[ i ] + capName; + if ( name in emptyStyle ) { + return name; + } + } +} + +// Return a potentially-mapped jQuery.cssProps or vendor prefixed property +function finalPropName( name ) { + var final = jQuery.cssProps[ name ] || vendorProps[ name ]; + + if ( final ) { + return final; + } + if ( name in emptyStyle ) { + return name; + } + return vendorProps[ name ] = vendorPropName( name ) || name; +} + + +var + + // Swappable if display is none or starts with table + // except "table", "table-cell", or "table-caption" + // See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display + rdisplayswap = /^(none|table(?!-c[ea]).+)/, + rcustomProp = /^--/, + cssShow = { position: "absolute", visibility: "hidden", display: "block" }, + cssNormalTransform = { + letterSpacing: "0", + fontWeight: "400" + }; + +function setPositiveNumber( _elem, value, subtract ) { + + // Any relative (+/-) values have already been + // normalized at this point + var matches = rcssNum.exec( value ); + return matches ? + + // Guard against undefined "subtract", e.g., when used as in cssHooks + Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) : + value; +} + +function boxModelAdjustment( elem, dimension, box, isBorderBox, styles, computedVal ) { + var i = dimension === "width" ? 1 : 0, + extra = 0, + delta = 0; + + // Adjustment may not be necessary + if ( box === ( isBorderBox ? "border" : "content" ) ) { + return 0; + } + + for ( ; i < 4; i += 2 ) { + + // Both box models exclude margin + if ( box === "margin" ) { + delta += jQuery.css( elem, box + cssExpand[ i ], true, styles ); + } + + // If we get here with a content-box, we're seeking "padding" or "border" or "margin" + if ( !isBorderBox ) { + + // Add padding + delta += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + + // For "border" or "margin", add border + if ( box !== "padding" ) { + delta += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + + // But still keep track of it otherwise + } else { + extra += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + + // If we get here with a border-box (content + padding + border), we're seeking "content" or + // "padding" or "margin" + } else { + + // For "content", subtract padding + if ( box === "content" ) { + delta -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + } + + // For "content" or "padding", subtract border + if ( box !== "margin" ) { + delta -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + } + } + + // Account for positive content-box scroll gutter when requested by providing computedVal + if ( !isBorderBox && computedVal >= 0 ) { + + // offsetWidth/offsetHeight is a rounded sum of content, padding, scroll gutter, and border + // Assuming integer scroll gutter, subtract the rest and round down + delta += Math.max( 0, Math.ceil( + elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - + computedVal - + delta - + extra - + 0.5 + + // If offsetWidth/offsetHeight is unknown, then we can't determine content-box scroll gutter + // Use an explicit zero to avoid NaN (gh-3964) + ) ) || 0; + } + + return delta; +} + +function getWidthOrHeight( elem, dimension, extra ) { + + // Start with computed style + var styles = getStyles( elem ), + + // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-4322). + // Fake content-box until we know it's needed to know the true value. + boxSizingNeeded = !support.boxSizingReliable() || extra, + isBorderBox = boxSizingNeeded && + jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + valueIsBorderBox = isBorderBox, + + val = curCSS( elem, dimension, styles ), + offsetProp = "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ); + + // Support: Firefox <=54 + // Return a confounding non-pixel value or feign ignorance, as appropriate. + if ( rnumnonpx.test( val ) ) { + if ( !extra ) { + return val; + } + val = "auto"; + } + + + // Support: IE 9 - 11 only + // Use offsetWidth/offsetHeight for when box sizing is unreliable. + // In those cases, the computed value can be trusted to be border-box. + if ( ( !support.boxSizingReliable() && isBorderBox || + + // Support: IE 10 - 11+, Edge 15 - 18+ + // IE/Edge misreport `getComputedStyle` of table rows with width/height + // set in CSS while `offset*` properties report correct values. + // Interestingly, in some cases IE 9 doesn't suffer from this issue. + !support.reliableTrDimensions() && nodeName( elem, "tr" ) || + + // Fall back to offsetWidth/offsetHeight when value is "auto" + // This happens for inline elements with no explicit setting (gh-3571) + val === "auto" || + + // Support: Android <=4.1 - 4.3 only + // Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602) + !parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) && + + // Make sure the element is visible & connected + elem.getClientRects().length ) { + + isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box"; + + // Where available, offsetWidth/offsetHeight approximate border box dimensions. + // Where not available (e.g., SVG), assume unreliable box-sizing and interpret the + // retrieved value as a content box dimension. + valueIsBorderBox = offsetProp in elem; + if ( valueIsBorderBox ) { + val = elem[ offsetProp ]; + } + } + + // Normalize "" and auto + val = parseFloat( val ) || 0; + + // Adjust for the element's box model + return ( val + + boxModelAdjustment( + elem, + dimension, + extra || ( isBorderBox ? "border" : "content" ), + valueIsBorderBox, + styles, + + // Provide the current computed size to request scroll gutter calculation (gh-3589) + val + ) + ) + "px"; +} + +jQuery.extend( { + + // Add in style property hooks for overriding the default + // behavior of getting and setting a style property + cssHooks: { + opacity: { + get: function( elem, computed ) { + if ( computed ) { + + // We should always get a number back from opacity + var ret = curCSS( elem, "opacity" ); + return ret === "" ? "1" : ret; + } + } + } + }, + + // Don't automatically add "px" to these possibly-unitless properties + cssNumber: { + "animationIterationCount": true, + "columnCount": true, + "fillOpacity": true, + "flexGrow": true, + "flexShrink": true, + "fontWeight": true, + "gridArea": true, + "gridColumn": true, + "gridColumnEnd": true, + "gridColumnStart": true, + "gridRow": true, + "gridRowEnd": true, + "gridRowStart": true, + "lineHeight": true, + "opacity": true, + "order": true, + "orphans": true, + "widows": true, + "zIndex": true, + "zoom": true + }, + + // Add in properties whose names you wish to fix before + // setting or getting the value + cssProps: {}, + + // Get and set the style property on a DOM Node + style: function( elem, name, value, extra ) { + + // Don't set styles on text and comment nodes + if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) { + return; + } + + // Make sure that we're working with the right name + var ret, type, hooks, + origName = camelCase( name ), + isCustomProp = rcustomProp.test( name ), + style = elem.style; + + // Make sure that we're working with the right name. We don't + // want to query the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Gets hook for the prefixed version, then unprefixed version + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // Check if we're setting a value + if ( value !== undefined ) { + type = typeof value; + + // Convert "+=" or "-=" to relative numbers (#7345) + if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) { + value = adjustCSS( elem, name, ret ); + + // Fixes bug #9237 + type = "number"; + } + + // Make sure that null and NaN values aren't set (#7116) + if ( value == null || value !== value ) { + return; + } + + // If a number was passed in, add the unit (except for certain CSS properties) + // The isCustomProp check can be removed in jQuery 4.0 when we only auto-append + // "px" to a few hardcoded values. + if ( type === "number" && !isCustomProp ) { + value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" ); + } + + // background-* props affect original clone's values + if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) { + style[ name ] = "inherit"; + } + + // If a hook was provided, use that value, otherwise just set the specified value + if ( !hooks || !( "set" in hooks ) || + ( value = hooks.set( elem, value, extra ) ) !== undefined ) { + + if ( isCustomProp ) { + style.setProperty( name, value ); + } else { + style[ name ] = value; + } + } + + } else { + + // If a hook was provided get the non-computed value from there + if ( hooks && "get" in hooks && + ( ret = hooks.get( elem, false, extra ) ) !== undefined ) { + + return ret; + } + + // Otherwise just get the value from the style object + return style[ name ]; + } + }, + + css: function( elem, name, extra, styles ) { + var val, num, hooks, + origName = camelCase( name ), + isCustomProp = rcustomProp.test( name ); + + // Make sure that we're working with the right name. We don't + // want to modify the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Try prefixed name followed by the unprefixed name + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // If a hook was provided get the computed value from there + if ( hooks && "get" in hooks ) { + val = hooks.get( elem, true, extra ); + } + + // Otherwise, if a way to get the computed value exists, use that + if ( val === undefined ) { + val = curCSS( elem, name, styles ); + } + + // Convert "normal" to computed value + if ( val === "normal" && name in cssNormalTransform ) { + val = cssNormalTransform[ name ]; + } + + // Make numeric if forced or a qualifier was provided and val looks numeric + if ( extra === "" || extra ) { + num = parseFloat( val ); + return extra === true || isFinite( num ) ? num || 0 : val; + } + + return val; + } +} ); + +jQuery.each( [ "height", "width" ], function( _i, dimension ) { + jQuery.cssHooks[ dimension ] = { + get: function( elem, computed, extra ) { + if ( computed ) { + + // Certain elements can have dimension info if we invisibly show them + // but it must have a current display style that would benefit + return rdisplayswap.test( jQuery.css( elem, "display" ) ) && + + // Support: Safari 8+ + // Table columns in Safari have non-zero offsetWidth & zero + // getBoundingClientRect().width unless display is changed. + // Support: IE <=11 only + // Running getBoundingClientRect on a disconnected node + // in IE throws an error. + ( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ? + swap( elem, cssShow, function() { + return getWidthOrHeight( elem, dimension, extra ); + } ) : + getWidthOrHeight( elem, dimension, extra ); + } + }, + + set: function( elem, value, extra ) { + var matches, + styles = getStyles( elem ), + + // Only read styles.position if the test has a chance to fail + // to avoid forcing a reflow. + scrollboxSizeBuggy = !support.scrollboxSize() && + styles.position === "absolute", + + // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-3991) + boxSizingNeeded = scrollboxSizeBuggy || extra, + isBorderBox = boxSizingNeeded && + jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + subtract = extra ? + boxModelAdjustment( + elem, + dimension, + extra, + isBorderBox, + styles + ) : + 0; + + // Account for unreliable border-box dimensions by comparing offset* to computed and + // faking a content-box to get border and padding (gh-3699) + if ( isBorderBox && scrollboxSizeBuggy ) { + subtract -= Math.ceil( + elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - + parseFloat( styles[ dimension ] ) - + boxModelAdjustment( elem, dimension, "border", false, styles ) - + 0.5 + ); + } + + // Convert to pixels if value adjustment is needed + if ( subtract && ( matches = rcssNum.exec( value ) ) && + ( matches[ 3 ] || "px" ) !== "px" ) { + + elem.style[ dimension ] = value; + value = jQuery.css( elem, dimension ); + } + + return setPositiveNumber( elem, value, subtract ); + } + }; +} ); + +jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft, + function( elem, computed ) { + if ( computed ) { + return ( parseFloat( curCSS( elem, "marginLeft" ) ) || + elem.getBoundingClientRect().left - + swap( elem, { marginLeft: 0 }, function() { + return elem.getBoundingClientRect().left; + } ) + ) + "px"; + } + } +); + +// These hooks are used by animate to expand properties +jQuery.each( { + margin: "", + padding: "", + border: "Width" +}, function( prefix, suffix ) { + jQuery.cssHooks[ prefix + suffix ] = { + expand: function( value ) { + var i = 0, + expanded = {}, + + // Assumes a single number if not a string + parts = typeof value === "string" ? value.split( " " ) : [ value ]; + + for ( ; i < 4; i++ ) { + expanded[ prefix + cssExpand[ i ] + suffix ] = + parts[ i ] || parts[ i - 2 ] || parts[ 0 ]; + } + + return expanded; + } + }; + + if ( prefix !== "margin" ) { + jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber; + } +} ); + +jQuery.fn.extend( { + css: function( name, value ) { + return access( this, function( elem, name, value ) { + var styles, len, + map = {}, + i = 0; + + if ( Array.isArray( name ) ) { + styles = getStyles( elem ); + len = name.length; + + for ( ; i < len; i++ ) { + map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles ); + } + + return map; + } + + return value !== undefined ? + jQuery.style( elem, name, value ) : + jQuery.css( elem, name ); + }, name, value, arguments.length > 1 ); + } +} ); + + +function Tween( elem, options, prop, end, easing ) { + return new Tween.prototype.init( elem, options, prop, end, easing ); +} +jQuery.Tween = Tween; + +Tween.prototype = { + constructor: Tween, + init: function( elem, options, prop, end, easing, unit ) { + this.elem = elem; + this.prop = prop; + this.easing = easing || jQuery.easing._default; + this.options = options; + this.start = this.now = this.cur(); + this.end = end; + this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" ); + }, + cur: function() { + var hooks = Tween.propHooks[ this.prop ]; + + return hooks && hooks.get ? + hooks.get( this ) : + Tween.propHooks._default.get( this ); + }, + run: function( percent ) { + var eased, + hooks = Tween.propHooks[ this.prop ]; + + if ( this.options.duration ) { + this.pos = eased = jQuery.easing[ this.easing ]( + percent, this.options.duration * percent, 0, 1, this.options.duration + ); + } else { + this.pos = eased = percent; + } + this.now = ( this.end - this.start ) * eased + this.start; + + if ( this.options.step ) { + this.options.step.call( this.elem, this.now, this ); + } + + if ( hooks && hooks.set ) { + hooks.set( this ); + } else { + Tween.propHooks._default.set( this ); + } + return this; + } +}; + +Tween.prototype.init.prototype = Tween.prototype; + +Tween.propHooks = { + _default: { + get: function( tween ) { + var result; + + // Use a property on the element directly when it is not a DOM element, + // or when there is no matching style property that exists. + if ( tween.elem.nodeType !== 1 || + tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) { + return tween.elem[ tween.prop ]; + } + + // Passing an empty string as a 3rd parameter to .css will automatically + // attempt a parseFloat and fallback to a string if the parse fails. + // Simple values such as "10px" are parsed to Float; + // complex values such as "rotate(1rad)" are returned as-is. + result = jQuery.css( tween.elem, tween.prop, "" ); + + // Empty strings, null, undefined and "auto" are converted to 0. + return !result || result === "auto" ? 0 : result; + }, + set: function( tween ) { + + // Use step hook for back compat. + // Use cssHook if its there. + // Use .style if available and use plain properties where available. + if ( jQuery.fx.step[ tween.prop ] ) { + jQuery.fx.step[ tween.prop ]( tween ); + } else if ( tween.elem.nodeType === 1 && ( + jQuery.cssHooks[ tween.prop ] || + tween.elem.style[ finalPropName( tween.prop ) ] != null ) ) { + jQuery.style( tween.elem, tween.prop, tween.now + tween.unit ); + } else { + tween.elem[ tween.prop ] = tween.now; + } + } + } +}; + +// Support: IE <=9 only +// Panic based approach to setting things on disconnected nodes +Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = { + set: function( tween ) { + if ( tween.elem.nodeType && tween.elem.parentNode ) { + tween.elem[ tween.prop ] = tween.now; + } + } +}; + +jQuery.easing = { + linear: function( p ) { + return p; + }, + swing: function( p ) { + return 0.5 - Math.cos( p * Math.PI ) / 2; + }, + _default: "swing" +}; + +jQuery.fx = Tween.prototype.init; + +// Back compat <1.8 extension point +jQuery.fx.step = {}; + + + + +var + fxNow, inProgress, + rfxtypes = /^(?:toggle|show|hide)$/, + rrun = /queueHooks$/; + +function schedule() { + if ( inProgress ) { + if ( document.hidden === false && window.requestAnimationFrame ) { + window.requestAnimationFrame( schedule ); + } else { + window.setTimeout( schedule, jQuery.fx.interval ); + } + + jQuery.fx.tick(); + } +} + +// Animations created synchronously will run synchronously +function createFxNow() { + window.setTimeout( function() { + fxNow = undefined; + } ); + return ( fxNow = Date.now() ); +} + +// Generate parameters to create a standard animation +function genFx( type, includeWidth ) { + var which, + i = 0, + attrs = { height: type }; + + // If we include width, step value is 1 to do all cssExpand values, + // otherwise step value is 2 to skip over Left and Right + includeWidth = includeWidth ? 1 : 0; + for ( ; i < 4; i += 2 - includeWidth ) { + which = cssExpand[ i ]; + attrs[ "margin" + which ] = attrs[ "padding" + which ] = type; + } + + if ( includeWidth ) { + attrs.opacity = attrs.width = type; + } + + return attrs; +} + +function createTween( value, prop, animation ) { + var tween, + collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ), + index = 0, + length = collection.length; + for ( ; index < length; index++ ) { + if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) { + + // We're done with this property + return tween; + } + } +} + +function defaultPrefilter( elem, props, opts ) { + var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display, + isBox = "width" in props || "height" in props, + anim = this, + orig = {}, + style = elem.style, + hidden = elem.nodeType && isHiddenWithinTree( elem ), + dataShow = dataPriv.get( elem, "fxshow" ); + + // Queue-skipping animations hijack the fx hooks + if ( !opts.queue ) { + hooks = jQuery._queueHooks( elem, "fx" ); + if ( hooks.unqueued == null ) { + hooks.unqueued = 0; + oldfire = hooks.empty.fire; + hooks.empty.fire = function() { + if ( !hooks.unqueued ) { + oldfire(); + } + }; + } + hooks.unqueued++; + + anim.always( function() { + + // Ensure the complete handler is called before this completes + anim.always( function() { + hooks.unqueued--; + if ( !jQuery.queue( elem, "fx" ).length ) { + hooks.empty.fire(); + } + } ); + } ); + } + + // Detect show/hide animations + for ( prop in props ) { + value = props[ prop ]; + if ( rfxtypes.test( value ) ) { + delete props[ prop ]; + toggle = toggle || value === "toggle"; + if ( value === ( hidden ? "hide" : "show" ) ) { + + // Pretend to be hidden if this is a "show" and + // there is still data from a stopped show/hide + if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) { + hidden = true; + + // Ignore all other no-op show/hide data + } else { + continue; + } + } + orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop ); + } + } + + // Bail out if this is a no-op like .hide().hide() + propTween = !jQuery.isEmptyObject( props ); + if ( !propTween && jQuery.isEmptyObject( orig ) ) { + return; + } + + // Restrict "overflow" and "display" styles during box animations + if ( isBox && elem.nodeType === 1 ) { + + // Support: IE <=9 - 11, Edge 12 - 15 + // Record all 3 overflow attributes because IE does not infer the shorthand + // from identically-valued overflowX and overflowY and Edge just mirrors + // the overflowX value there. + opts.overflow = [ style.overflow, style.overflowX, style.overflowY ]; + + // Identify a display type, preferring old show/hide data over the CSS cascade + restoreDisplay = dataShow && dataShow.display; + if ( restoreDisplay == null ) { + restoreDisplay = dataPriv.get( elem, "display" ); + } + display = jQuery.css( elem, "display" ); + if ( display === "none" ) { + if ( restoreDisplay ) { + display = restoreDisplay; + } else { + + // Get nonempty value(s) by temporarily forcing visibility + showHide( [ elem ], true ); + restoreDisplay = elem.style.display || restoreDisplay; + display = jQuery.css( elem, "display" ); + showHide( [ elem ] ); + } + } + + // Animate inline elements as inline-block + if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) { + if ( jQuery.css( elem, "float" ) === "none" ) { + + // Restore the original display value at the end of pure show/hide animations + if ( !propTween ) { + anim.done( function() { + style.display = restoreDisplay; + } ); + if ( restoreDisplay == null ) { + display = style.display; + restoreDisplay = display === "none" ? "" : display; + } + } + style.display = "inline-block"; + } + } + } + + if ( opts.overflow ) { + style.overflow = "hidden"; + anim.always( function() { + style.overflow = opts.overflow[ 0 ]; + style.overflowX = opts.overflow[ 1 ]; + style.overflowY = opts.overflow[ 2 ]; + } ); + } + + // Implement show/hide animations + propTween = false; + for ( prop in orig ) { + + // General show/hide setup for this element animation + if ( !propTween ) { + if ( dataShow ) { + if ( "hidden" in dataShow ) { + hidden = dataShow.hidden; + } + } else { + dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } ); + } + + // Store hidden/visible for toggle so `.stop().toggle()` "reverses" + if ( toggle ) { + dataShow.hidden = !hidden; + } + + // Show elements before animating them + if ( hidden ) { + showHide( [ elem ], true ); + } + + /* eslint-disable no-loop-func */ + + anim.done( function() { + + /* eslint-enable no-loop-func */ + + // The final step of a "hide" animation is actually hiding the element + if ( !hidden ) { + showHide( [ elem ] ); + } + dataPriv.remove( elem, "fxshow" ); + for ( prop in orig ) { + jQuery.style( elem, prop, orig[ prop ] ); + } + } ); + } + + // Per-property setup + propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim ); + if ( !( prop in dataShow ) ) { + dataShow[ prop ] = propTween.start; + if ( hidden ) { + propTween.end = propTween.start; + propTween.start = 0; + } + } + } +} + +function propFilter( props, specialEasing ) { + var index, name, easing, value, hooks; + + // camelCase, specialEasing and expand cssHook pass + for ( index in props ) { + name = camelCase( index ); + easing = specialEasing[ name ]; + value = props[ index ]; + if ( Array.isArray( value ) ) { + easing = value[ 1 ]; + value = props[ index ] = value[ 0 ]; + } + + if ( index !== name ) { + props[ name ] = value; + delete props[ index ]; + } + + hooks = jQuery.cssHooks[ name ]; + if ( hooks && "expand" in hooks ) { + value = hooks.expand( value ); + delete props[ name ]; + + // Not quite $.extend, this won't overwrite existing keys. + // Reusing 'index' because we have the correct "name" + for ( index in value ) { + if ( !( index in props ) ) { + props[ index ] = value[ index ]; + specialEasing[ index ] = easing; + } + } + } else { + specialEasing[ name ] = easing; + } + } +} + +function Animation( elem, properties, options ) { + var result, + stopped, + index = 0, + length = Animation.prefilters.length, + deferred = jQuery.Deferred().always( function() { + + // Don't match elem in the :animated selector + delete tick.elem; + } ), + tick = function() { + if ( stopped ) { + return false; + } + var currentTime = fxNow || createFxNow(), + remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ), + + // Support: Android 2.3 only + // Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497) + temp = remaining / animation.duration || 0, + percent = 1 - temp, + index = 0, + length = animation.tweens.length; + + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( percent ); + } + + deferred.notifyWith( elem, [ animation, percent, remaining ] ); + + // If there's more to do, yield + if ( percent < 1 && length ) { + return remaining; + } + + // If this was an empty animation, synthesize a final progress notification + if ( !length ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + } + + // Resolve the animation and report its conclusion + deferred.resolveWith( elem, [ animation ] ); + return false; + }, + animation = deferred.promise( { + elem: elem, + props: jQuery.extend( {}, properties ), + opts: jQuery.extend( true, { + specialEasing: {}, + easing: jQuery.easing._default + }, options ), + originalProperties: properties, + originalOptions: options, + startTime: fxNow || createFxNow(), + duration: options.duration, + tweens: [], + createTween: function( prop, end ) { + var tween = jQuery.Tween( elem, animation.opts, prop, end, + animation.opts.specialEasing[ prop ] || animation.opts.easing ); + animation.tweens.push( tween ); + return tween; + }, + stop: function( gotoEnd ) { + var index = 0, + + // If we are going to the end, we want to run all the tweens + // otherwise we skip this part + length = gotoEnd ? animation.tweens.length : 0; + if ( stopped ) { + return this; + } + stopped = true; + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( 1 ); + } + + // Resolve when we played the last frame; otherwise, reject + if ( gotoEnd ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + deferred.resolveWith( elem, [ animation, gotoEnd ] ); + } else { + deferred.rejectWith( elem, [ animation, gotoEnd ] ); + } + return this; + } + } ), + props = animation.props; + + propFilter( props, animation.opts.specialEasing ); + + for ( ; index < length; index++ ) { + result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts ); + if ( result ) { + if ( isFunction( result.stop ) ) { + jQuery._queueHooks( animation.elem, animation.opts.queue ).stop = + result.stop.bind( result ); + } + return result; + } + } + + jQuery.map( props, createTween, animation ); + + if ( isFunction( animation.opts.start ) ) { + animation.opts.start.call( elem, animation ); + } + + // Attach callbacks from options + animation + .progress( animation.opts.progress ) + .done( animation.opts.done, animation.opts.complete ) + .fail( animation.opts.fail ) + .always( animation.opts.always ); + + jQuery.fx.timer( + jQuery.extend( tick, { + elem: elem, + anim: animation, + queue: animation.opts.queue + } ) + ); + + return animation; +} + +jQuery.Animation = jQuery.extend( Animation, { + + tweeners: { + "*": [ function( prop, value ) { + var tween = this.createTween( prop, value ); + adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween ); + return tween; + } ] + }, + + tweener: function( props, callback ) { + if ( isFunction( props ) ) { + callback = props; + props = [ "*" ]; + } else { + props = props.match( rnothtmlwhite ); + } + + var prop, + index = 0, + length = props.length; + + for ( ; index < length; index++ ) { + prop = props[ index ]; + Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || []; + Animation.tweeners[ prop ].unshift( callback ); + } + }, + + prefilters: [ defaultPrefilter ], + + prefilter: function( callback, prepend ) { + if ( prepend ) { + Animation.prefilters.unshift( callback ); + } else { + Animation.prefilters.push( callback ); + } + } +} ); + +jQuery.speed = function( speed, easing, fn ) { + var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : { + complete: fn || !fn && easing || + isFunction( speed ) && speed, + duration: speed, + easing: fn && easing || easing && !isFunction( easing ) && easing + }; + + // Go to the end state if fx are off + if ( jQuery.fx.off ) { + opt.duration = 0; + + } else { + if ( typeof opt.duration !== "number" ) { + if ( opt.duration in jQuery.fx.speeds ) { + opt.duration = jQuery.fx.speeds[ opt.duration ]; + + } else { + opt.duration = jQuery.fx.speeds._default; + } + } + } + + // Normalize opt.queue - true/undefined/null -> "fx" + if ( opt.queue == null || opt.queue === true ) { + opt.queue = "fx"; + } + + // Queueing + opt.old = opt.complete; + + opt.complete = function() { + if ( isFunction( opt.old ) ) { + opt.old.call( this ); + } + + if ( opt.queue ) { + jQuery.dequeue( this, opt.queue ); + } + }; + + return opt; +}; + +jQuery.fn.extend( { + fadeTo: function( speed, to, easing, callback ) { + + // Show any hidden elements after setting opacity to 0 + return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show() + + // Animate to the value specified + .end().animate( { opacity: to }, speed, easing, callback ); + }, + animate: function( prop, speed, easing, callback ) { + var empty = jQuery.isEmptyObject( prop ), + optall = jQuery.speed( speed, easing, callback ), + doAnimation = function() { + + // Operate on a copy of prop so per-property easing won't be lost + var anim = Animation( this, jQuery.extend( {}, prop ), optall ); + + // Empty animations, or finishing resolves immediately + if ( empty || dataPriv.get( this, "finish" ) ) { + anim.stop( true ); + } + }; + doAnimation.finish = doAnimation; + + return empty || optall.queue === false ? + this.each( doAnimation ) : + this.queue( optall.queue, doAnimation ); + }, + stop: function( type, clearQueue, gotoEnd ) { + var stopQueue = function( hooks ) { + var stop = hooks.stop; + delete hooks.stop; + stop( gotoEnd ); + }; + + if ( typeof type !== "string" ) { + gotoEnd = clearQueue; + clearQueue = type; + type = undefined; + } + if ( clearQueue ) { + this.queue( type || "fx", [] ); + } + + return this.each( function() { + var dequeue = true, + index = type != null && type + "queueHooks", + timers = jQuery.timers, + data = dataPriv.get( this ); + + if ( index ) { + if ( data[ index ] && data[ index ].stop ) { + stopQueue( data[ index ] ); + } + } else { + for ( index in data ) { + if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) { + stopQueue( data[ index ] ); + } + } + } + + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && + ( type == null || timers[ index ].queue === type ) ) { + + timers[ index ].anim.stop( gotoEnd ); + dequeue = false; + timers.splice( index, 1 ); + } + } + + // Start the next in the queue if the last step wasn't forced. + // Timers currently will call their complete callbacks, which + // will dequeue but only if they were gotoEnd. + if ( dequeue || !gotoEnd ) { + jQuery.dequeue( this, type ); + } + } ); + }, + finish: function( type ) { + if ( type !== false ) { + type = type || "fx"; + } + return this.each( function() { + var index, + data = dataPriv.get( this ), + queue = data[ type + "queue" ], + hooks = data[ type + "queueHooks" ], + timers = jQuery.timers, + length = queue ? queue.length : 0; + + // Enable finishing flag on private data + data.finish = true; + + // Empty the queue first + jQuery.queue( this, type, [] ); + + if ( hooks && hooks.stop ) { + hooks.stop.call( this, true ); + } + + // Look for any active animations, and finish them + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && timers[ index ].queue === type ) { + timers[ index ].anim.stop( true ); + timers.splice( index, 1 ); + } + } + + // Look for any animations in the old queue and finish them + for ( index = 0; index < length; index++ ) { + if ( queue[ index ] && queue[ index ].finish ) { + queue[ index ].finish.call( this ); + } + } + + // Turn off finishing flag + delete data.finish; + } ); + } +} ); + +jQuery.each( [ "toggle", "show", "hide" ], function( _i, name ) { + var cssFn = jQuery.fn[ name ]; + jQuery.fn[ name ] = function( speed, easing, callback ) { + return speed == null || typeof speed === "boolean" ? + cssFn.apply( this, arguments ) : + this.animate( genFx( name, true ), speed, easing, callback ); + }; +} ); + +// Generate shortcuts for custom animations +jQuery.each( { + slideDown: genFx( "show" ), + slideUp: genFx( "hide" ), + slideToggle: genFx( "toggle" ), + fadeIn: { opacity: "show" }, + fadeOut: { opacity: "hide" }, + fadeToggle: { opacity: "toggle" } +}, function( name, props ) { + jQuery.fn[ name ] = function( speed, easing, callback ) { + return this.animate( props, speed, easing, callback ); + }; +} ); + +jQuery.timers = []; +jQuery.fx.tick = function() { + var timer, + i = 0, + timers = jQuery.timers; + + fxNow = Date.now(); + + for ( ; i < timers.length; i++ ) { + timer = timers[ i ]; + + // Run the timer and safely remove it when done (allowing for external removal) + if ( !timer() && timers[ i ] === timer ) { + timers.splice( i--, 1 ); + } + } + + if ( !timers.length ) { + jQuery.fx.stop(); + } + fxNow = undefined; +}; + +jQuery.fx.timer = function( timer ) { + jQuery.timers.push( timer ); + jQuery.fx.start(); +}; + +jQuery.fx.interval = 13; +jQuery.fx.start = function() { + if ( inProgress ) { + return; + } + + inProgress = true; + schedule(); +}; + +jQuery.fx.stop = function() { + inProgress = null; +}; + +jQuery.fx.speeds = { + slow: 600, + fast: 200, + + // Default speed + _default: 400 +}; + + +// Based off of the plugin by Clint Helfers, with permission. +// https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/ +jQuery.fn.delay = function( time, type ) { + time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time; + type = type || "fx"; + + return this.queue( type, function( next, hooks ) { + var timeout = window.setTimeout( next, time ); + hooks.stop = function() { + window.clearTimeout( timeout ); + }; + } ); +}; + + +( function() { + var input = document.createElement( "input" ), + select = document.createElement( "select" ), + opt = select.appendChild( document.createElement( "option" ) ); + + input.type = "checkbox"; + + // Support: Android <=4.3 only + // Default value for a checkbox should be "on" + support.checkOn = input.value !== ""; + + // Support: IE <=11 only + // Must access selectedIndex to make default options select + support.optSelected = opt.selected; + + // Support: IE <=11 only + // An input loses its value after becoming a radio + input = document.createElement( "input" ); + input.value = "t"; + input.type = "radio"; + support.radioValue = input.value === "t"; +} )(); + + +var boolHook, + attrHandle = jQuery.expr.attrHandle; + +jQuery.fn.extend( { + attr: function( name, value ) { + return access( this, jQuery.attr, name, value, arguments.length > 1 ); + }, + + removeAttr: function( name ) { + return this.each( function() { + jQuery.removeAttr( this, name ); + } ); + } +} ); + +jQuery.extend( { + attr: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set attributes on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + // Fallback to prop when attributes are not supported + if ( typeof elem.getAttribute === "undefined" ) { + return jQuery.prop( elem, name, value ); + } + + // Attribute hooks are determined by the lowercase version + // Grab necessary hook if one is defined + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + hooks = jQuery.attrHooks[ name.toLowerCase() ] || + ( jQuery.expr.match.bool.test( name ) ? boolHook : undefined ); + } + + if ( value !== undefined ) { + if ( value === null ) { + jQuery.removeAttr( elem, name ); + return; + } + + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + elem.setAttribute( name, value + "" ); + return value; + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + ret = jQuery.find.attr( elem, name ); + + // Non-existent attributes return null, we normalize to undefined + return ret == null ? undefined : ret; + }, + + attrHooks: { + type: { + set: function( elem, value ) { + if ( !support.radioValue && value === "radio" && + nodeName( elem, "input" ) ) { + var val = elem.value; + elem.setAttribute( "type", value ); + if ( val ) { + elem.value = val; + } + return value; + } + } + } + }, + + removeAttr: function( elem, value ) { + var name, + i = 0, + + // Attribute names can contain non-HTML whitespace characters + // https://html.spec.whatwg.org/multipage/syntax.html#attributes-2 + attrNames = value && value.match( rnothtmlwhite ); + + if ( attrNames && elem.nodeType === 1 ) { + while ( ( name = attrNames[ i++ ] ) ) { + elem.removeAttribute( name ); + } + } + } +} ); + +// Hooks for boolean attributes +boolHook = { + set: function( elem, value, name ) { + if ( value === false ) { + + // Remove boolean attributes when set to false + jQuery.removeAttr( elem, name ); + } else { + elem.setAttribute( name, name ); + } + return name; + } +}; + +jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( _i, name ) { + var getter = attrHandle[ name ] || jQuery.find.attr; + + attrHandle[ name ] = function( elem, name, isXML ) { + var ret, handle, + lowercaseName = name.toLowerCase(); + + if ( !isXML ) { + + // Avoid an infinite loop by temporarily removing this function from the getter + handle = attrHandle[ lowercaseName ]; + attrHandle[ lowercaseName ] = ret; + ret = getter( elem, name, isXML ) != null ? + lowercaseName : + null; + attrHandle[ lowercaseName ] = handle; + } + return ret; + }; +} ); + + + + +var rfocusable = /^(?:input|select|textarea|button)$/i, + rclickable = /^(?:a|area)$/i; + +jQuery.fn.extend( { + prop: function( name, value ) { + return access( this, jQuery.prop, name, value, arguments.length > 1 ); + }, + + removeProp: function( name ) { + return this.each( function() { + delete this[ jQuery.propFix[ name ] || name ]; + } ); + } +} ); + +jQuery.extend( { + prop: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set properties on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + + // Fix name and attach hooks + name = jQuery.propFix[ name ] || name; + hooks = jQuery.propHooks[ name ]; + } + + if ( value !== undefined ) { + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + return ( elem[ name ] = value ); + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + return elem[ name ]; + }, + + propHooks: { + tabIndex: { + get: function( elem ) { + + // Support: IE <=9 - 11 only + // elem.tabIndex doesn't always return the + // correct value when it hasn't been explicitly set + // https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/ + // Use proper attribute retrieval(#12072) + var tabindex = jQuery.find.attr( elem, "tabindex" ); + + if ( tabindex ) { + return parseInt( tabindex, 10 ); + } + + if ( + rfocusable.test( elem.nodeName ) || + rclickable.test( elem.nodeName ) && + elem.href + ) { + return 0; + } + + return -1; + } + } + }, + + propFix: { + "for": "htmlFor", + "class": "className" + } +} ); + +// Support: IE <=11 only +// Accessing the selectedIndex property +// forces the browser to respect setting selected +// on the option +// The getter ensures a default option is selected +// when in an optgroup +// eslint rule "no-unused-expressions" is disabled for this code +// since it considers such accessions noop +if ( !support.optSelected ) { + jQuery.propHooks.selected = { + get: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent && parent.parentNode ) { + parent.parentNode.selectedIndex; + } + return null; + }, + set: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent ) { + parent.selectedIndex; + + if ( parent.parentNode ) { + parent.parentNode.selectedIndex; + } + } + } + }; +} + +jQuery.each( [ + "tabIndex", + "readOnly", + "maxLength", + "cellSpacing", + "cellPadding", + "rowSpan", + "colSpan", + "useMap", + "frameBorder", + "contentEditable" +], function() { + jQuery.propFix[ this.toLowerCase() ] = this; +} ); + + + + + // Strip and collapse whitespace according to HTML spec + // https://infra.spec.whatwg.org/#strip-and-collapse-ascii-whitespace + function stripAndCollapse( value ) { + var tokens = value.match( rnothtmlwhite ) || []; + return tokens.join( " " ); + } + + +function getClass( elem ) { + return elem.getAttribute && elem.getAttribute( "class" ) || ""; +} + +function classesToArray( value ) { + if ( Array.isArray( value ) ) { + return value; + } + if ( typeof value === "string" ) { + return value.match( rnothtmlwhite ) || []; + } + return []; +} + +jQuery.fn.extend( { + addClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).addClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + classes = classesToArray( value ); + + if ( classes.length ) { + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + if ( cur.indexOf( " " + clazz + " " ) < 0 ) { + cur += clazz + " "; + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + removeClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + if ( !arguments.length ) { + return this.attr( "class", "" ); + } + + classes = classesToArray( value ); + + if ( classes.length ) { + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + + // This expression is here for better compressibility (see addClass) + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + + // Remove *all* instances + while ( cur.indexOf( " " + clazz + " " ) > -1 ) { + cur = cur.replace( " " + clazz + " ", " " ); + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + toggleClass: function( value, stateVal ) { + var type = typeof value, + isValidValue = type === "string" || Array.isArray( value ); + + if ( typeof stateVal === "boolean" && isValidValue ) { + return stateVal ? this.addClass( value ) : this.removeClass( value ); + } + + if ( isFunction( value ) ) { + return this.each( function( i ) { + jQuery( this ).toggleClass( + value.call( this, i, getClass( this ), stateVal ), + stateVal + ); + } ); + } + + return this.each( function() { + var className, i, self, classNames; + + if ( isValidValue ) { + + // Toggle individual class names + i = 0; + self = jQuery( this ); + classNames = classesToArray( value ); + + while ( ( className = classNames[ i++ ] ) ) { + + // Check each className given, space separated list + if ( self.hasClass( className ) ) { + self.removeClass( className ); + } else { + self.addClass( className ); + } + } + + // Toggle whole class name + } else if ( value === undefined || type === "boolean" ) { + className = getClass( this ); + if ( className ) { + + // Store className if set + dataPriv.set( this, "__className__", className ); + } + + // If the element has a class name or if we're passed `false`, + // then remove the whole classname (if there was one, the above saved it). + // Otherwise bring back whatever was previously saved (if anything), + // falling back to the empty string if nothing was stored. + if ( this.setAttribute ) { + this.setAttribute( "class", + className || value === false ? + "" : + dataPriv.get( this, "__className__" ) || "" + ); + } + } + } ); + }, + + hasClass: function( selector ) { + var className, elem, + i = 0; + + className = " " + selector + " "; + while ( ( elem = this[ i++ ] ) ) { + if ( elem.nodeType === 1 && + ( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) { + return true; + } + } + + return false; + } +} ); + + + + +var rreturn = /\r/g; + +jQuery.fn.extend( { + val: function( value ) { + var hooks, ret, valueIsFunction, + elem = this[ 0 ]; + + if ( !arguments.length ) { + if ( elem ) { + hooks = jQuery.valHooks[ elem.type ] || + jQuery.valHooks[ elem.nodeName.toLowerCase() ]; + + if ( hooks && + "get" in hooks && + ( ret = hooks.get( elem, "value" ) ) !== undefined + ) { + return ret; + } + + ret = elem.value; + + // Handle most common string cases + if ( typeof ret === "string" ) { + return ret.replace( rreturn, "" ); + } + + // Handle cases where value is null/undef or number + return ret == null ? "" : ret; + } + + return; + } + + valueIsFunction = isFunction( value ); + + return this.each( function( i ) { + var val; + + if ( this.nodeType !== 1 ) { + return; + } + + if ( valueIsFunction ) { + val = value.call( this, i, jQuery( this ).val() ); + } else { + val = value; + } + + // Treat null/undefined as ""; convert numbers to string + if ( val == null ) { + val = ""; + + } else if ( typeof val === "number" ) { + val += ""; + + } else if ( Array.isArray( val ) ) { + val = jQuery.map( val, function( value ) { + return value == null ? "" : value + ""; + } ); + } + + hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ]; + + // If set returns undefined, fall back to normal setting + if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) { + this.value = val; + } + } ); + } +} ); + +jQuery.extend( { + valHooks: { + option: { + get: function( elem ) { + + var val = jQuery.find.attr( elem, "value" ); + return val != null ? + val : + + // Support: IE <=10 - 11 only + // option.text throws exceptions (#14686, #14858) + // Strip and collapse whitespace + // https://html.spec.whatwg.org/#strip-and-collapse-whitespace + stripAndCollapse( jQuery.text( elem ) ); + } + }, + select: { + get: function( elem ) { + var value, option, i, + options = elem.options, + index = elem.selectedIndex, + one = elem.type === "select-one", + values = one ? null : [], + max = one ? index + 1 : options.length; + + if ( index < 0 ) { + i = max; + + } else { + i = one ? index : 0; + } + + // Loop through all the selected options + for ( ; i < max; i++ ) { + option = options[ i ]; + + // Support: IE <=9 only + // IE8-9 doesn't update selected after form reset (#2551) + if ( ( option.selected || i === index ) && + + // Don't return options that are disabled or in a disabled optgroup + !option.disabled && + ( !option.parentNode.disabled || + !nodeName( option.parentNode, "optgroup" ) ) ) { + + // Get the specific value for the option + value = jQuery( option ).val(); + + // We don't need an array for one selects + if ( one ) { + return value; + } + + // Multi-Selects return an array + values.push( value ); + } + } + + return values; + }, + + set: function( elem, value ) { + var optionSet, option, + options = elem.options, + values = jQuery.makeArray( value ), + i = options.length; + + while ( i-- ) { + option = options[ i ]; + + /* eslint-disable no-cond-assign */ + + if ( option.selected = + jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1 + ) { + optionSet = true; + } + + /* eslint-enable no-cond-assign */ + } + + // Force browsers to behave consistently when non-matching value is set + if ( !optionSet ) { + elem.selectedIndex = -1; + } + return values; + } + } + } +} ); + +// Radios and checkboxes getter/setter +jQuery.each( [ "radio", "checkbox" ], function() { + jQuery.valHooks[ this ] = { + set: function( elem, value ) { + if ( Array.isArray( value ) ) { + return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 ); + } + } + }; + if ( !support.checkOn ) { + jQuery.valHooks[ this ].get = function( elem ) { + return elem.getAttribute( "value" ) === null ? "on" : elem.value; + }; + } +} ); + + + + +// Return jQuery for attributes-only inclusion + + +support.focusin = "onfocusin" in window; + + +var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/, + stopPropagationCallback = function( e ) { + e.stopPropagation(); + }; + +jQuery.extend( jQuery.event, { + + trigger: function( event, data, elem, onlyHandlers ) { + + var i, cur, tmp, bubbleType, ontype, handle, special, lastElement, + eventPath = [ elem || document ], + type = hasOwn.call( event, "type" ) ? event.type : event, + namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : []; + + cur = lastElement = tmp = elem = elem || document; + + // Don't do events on text and comment nodes + if ( elem.nodeType === 3 || elem.nodeType === 8 ) { + return; + } + + // focus/blur morphs to focusin/out; ensure we're not firing them right now + if ( rfocusMorph.test( type + jQuery.event.triggered ) ) { + return; + } + + if ( type.indexOf( "." ) > -1 ) { + + // Namespaced trigger; create a regexp to match event type in handle() + namespaces = type.split( "." ); + type = namespaces.shift(); + namespaces.sort(); + } + ontype = type.indexOf( ":" ) < 0 && "on" + type; + + // Caller can pass in a jQuery.Event object, Object, or just an event type string + event = event[ jQuery.expando ] ? + event : + new jQuery.Event( type, typeof event === "object" && event ); + + // Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true) + event.isTrigger = onlyHandlers ? 2 : 3; + event.namespace = namespaces.join( "." ); + event.rnamespace = event.namespace ? + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) : + null; + + // Clean up the event in case it is being reused + event.result = undefined; + if ( !event.target ) { + event.target = elem; + } + + // Clone any incoming data and prepend the event, creating the handler arg list + data = data == null ? + [ event ] : + jQuery.makeArray( data, [ event ] ); + + // Allow special events to draw outside the lines + special = jQuery.event.special[ type ] || {}; + if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) { + return; + } + + // Determine event propagation path in advance, per W3C events spec (#9951) + // Bubble up to document, then to window; watch for a global ownerDocument var (#9724) + if ( !onlyHandlers && !special.noBubble && !isWindow( elem ) ) { + + bubbleType = special.delegateType || type; + if ( !rfocusMorph.test( bubbleType + type ) ) { + cur = cur.parentNode; + } + for ( ; cur; cur = cur.parentNode ) { + eventPath.push( cur ); + tmp = cur; + } + + // Only add window if we got to document (e.g., not plain obj or detached DOM) + if ( tmp === ( elem.ownerDocument || document ) ) { + eventPath.push( tmp.defaultView || tmp.parentWindow || window ); + } + } + + // Fire handlers on the event path + i = 0; + while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) { + lastElement = cur; + event.type = i > 1 ? + bubbleType : + special.bindType || type; + + // jQuery handler + handle = ( + dataPriv.get( cur, "events" ) || Object.create( null ) + )[ event.type ] && + dataPriv.get( cur, "handle" ); + if ( handle ) { + handle.apply( cur, data ); + } + + // Native handler + handle = ontype && cur[ ontype ]; + if ( handle && handle.apply && acceptData( cur ) ) { + event.result = handle.apply( cur, data ); + if ( event.result === false ) { + event.preventDefault(); + } + } + } + event.type = type; + + // If nobody prevented the default action, do it now + if ( !onlyHandlers && !event.isDefaultPrevented() ) { + + if ( ( !special._default || + special._default.apply( eventPath.pop(), data ) === false ) && + acceptData( elem ) ) { + + // Call a native DOM method on the target with the same name as the event. + // Don't do default actions on window, that's where global variables be (#6170) + if ( ontype && isFunction( elem[ type ] ) && !isWindow( elem ) ) { + + // Don't re-trigger an onFOO event when we call its FOO() method + tmp = elem[ ontype ]; + + if ( tmp ) { + elem[ ontype ] = null; + } + + // Prevent re-triggering of the same event, since we already bubbled it above + jQuery.event.triggered = type; + + if ( event.isPropagationStopped() ) { + lastElement.addEventListener( type, stopPropagationCallback ); + } + + elem[ type ](); + + if ( event.isPropagationStopped() ) { + lastElement.removeEventListener( type, stopPropagationCallback ); + } + + jQuery.event.triggered = undefined; + + if ( tmp ) { + elem[ ontype ] = tmp; + } + } + } + } + + return event.result; + }, + + // Piggyback on a donor event to simulate a different one + // Used only for `focus(in | out)` events + simulate: function( type, elem, event ) { + var e = jQuery.extend( + new jQuery.Event(), + event, + { + type: type, + isSimulated: true + } + ); + + jQuery.event.trigger( e, null, elem ); + } + +} ); + +jQuery.fn.extend( { + + trigger: function( type, data ) { + return this.each( function() { + jQuery.event.trigger( type, data, this ); + } ); + }, + triggerHandler: function( type, data ) { + var elem = this[ 0 ]; + if ( elem ) { + return jQuery.event.trigger( type, data, elem, true ); + } + } +} ); + + +// Support: Firefox <=44 +// Firefox doesn't have focus(in | out) events +// Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787 +// +// Support: Chrome <=48 - 49, Safari <=9.0 - 9.1 +// focus(in | out) events fire after focus & blur events, +// which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order +// Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857 +if ( !support.focusin ) { + jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) { + + // Attach a single capturing handler on the document while someone wants focusin/focusout + var handler = function( event ) { + jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) ); + }; + + jQuery.event.special[ fix ] = { + setup: function() { + + // Handle: regular nodes (via `this.ownerDocument`), window + // (via `this.document`) & document (via `this`). + var doc = this.ownerDocument || this.document || this, + attaches = dataPriv.access( doc, fix ); + + if ( !attaches ) { + doc.addEventListener( orig, handler, true ); + } + dataPriv.access( doc, fix, ( attaches || 0 ) + 1 ); + }, + teardown: function() { + var doc = this.ownerDocument || this.document || this, + attaches = dataPriv.access( doc, fix ) - 1; + + if ( !attaches ) { + doc.removeEventListener( orig, handler, true ); + dataPriv.remove( doc, fix ); + + } else { + dataPriv.access( doc, fix, attaches ); + } + } + }; + } ); +} +var location = window.location; + +var nonce = { guid: Date.now() }; + +var rquery = ( /\?/ ); + + + +// Cross-browser xml parsing +jQuery.parseXML = function( data ) { + var xml; + if ( !data || typeof data !== "string" ) { + return null; + } + + // Support: IE 9 - 11 only + // IE throws on parseFromString with invalid input. + try { + xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" ); + } catch ( e ) { + xml = undefined; + } + + if ( !xml || xml.getElementsByTagName( "parsererror" ).length ) { + jQuery.error( "Invalid XML: " + data ); + } + return xml; +}; + + +var + rbracket = /\[\]$/, + rCRLF = /\r?\n/g, + rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i, + rsubmittable = /^(?:input|select|textarea|keygen)/i; + +function buildParams( prefix, obj, traditional, add ) { + var name; + + if ( Array.isArray( obj ) ) { + + // Serialize array item. + jQuery.each( obj, function( i, v ) { + if ( traditional || rbracket.test( prefix ) ) { + + // Treat each array item as a scalar. + add( prefix, v ); + + } else { + + // Item is non-scalar (array or object), encode its numeric index. + buildParams( + prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]", + v, + traditional, + add + ); + } + } ); + + } else if ( !traditional && toType( obj ) === "object" ) { + + // Serialize object item. + for ( name in obj ) { + buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add ); + } + + } else { + + // Serialize scalar item. + add( prefix, obj ); + } +} + +// Serialize an array of form elements or a set of +// key/values into a query string +jQuery.param = function( a, traditional ) { + var prefix, + s = [], + add = function( key, valueOrFunction ) { + + // If value is a function, invoke it and use its return value + var value = isFunction( valueOrFunction ) ? + valueOrFunction() : + valueOrFunction; + + s[ s.length ] = encodeURIComponent( key ) + "=" + + encodeURIComponent( value == null ? "" : value ); + }; + + if ( a == null ) { + return ""; + } + + // If an array was passed in, assume that it is an array of form elements. + if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) { + + // Serialize the form elements + jQuery.each( a, function() { + add( this.name, this.value ); + } ); + + } else { + + // If traditional, encode the "old" way (the way 1.3.2 or older + // did it), otherwise encode params recursively. + for ( prefix in a ) { + buildParams( prefix, a[ prefix ], traditional, add ); + } + } + + // Return the resulting serialization + return s.join( "&" ); +}; + +jQuery.fn.extend( { + serialize: function() { + return jQuery.param( this.serializeArray() ); + }, + serializeArray: function() { + return this.map( function() { + + // Can add propHook for "elements" to filter or add form elements + var elements = jQuery.prop( this, "elements" ); + return elements ? jQuery.makeArray( elements ) : this; + } ) + .filter( function() { + var type = this.type; + + // Use .is( ":disabled" ) so that fieldset[disabled] works + return this.name && !jQuery( this ).is( ":disabled" ) && + rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) && + ( this.checked || !rcheckableType.test( type ) ); + } ) + .map( function( _i, elem ) { + var val = jQuery( this ).val(); + + if ( val == null ) { + return null; + } + + if ( Array.isArray( val ) ) { + return jQuery.map( val, function( val ) { + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ); + } + + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ).get(); + } +} ); + + +var + r20 = /%20/g, + rhash = /#.*$/, + rantiCache = /([?&])_=[^&]*/, + rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg, + + // #7653, #8125, #8152: local protocol detection + rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/, + rnoContent = /^(?:GET|HEAD)$/, + rprotocol = /^\/\//, + + /* Prefilters + * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example) + * 2) These are called: + * - BEFORE asking for a transport + * - AFTER param serialization (s.data is a string if s.processData is true) + * 3) key is the dataType + * 4) the catchall symbol "*" can be used + * 5) execution will start with transport dataType and THEN continue down to "*" if needed + */ + prefilters = {}, + + /* Transports bindings + * 1) key is the dataType + * 2) the catchall symbol "*" can be used + * 3) selection will start with transport dataType and THEN go to "*" if needed + */ + transports = {}, + + // Avoid comment-prolog char sequence (#10098); must appease lint and evade compression + allTypes = "*/".concat( "*" ), + + // Anchor tag for parsing the document origin + originAnchor = document.createElement( "a" ); + originAnchor.href = location.href; + +// Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport +function addToPrefiltersOrTransports( structure ) { + + // dataTypeExpression is optional and defaults to "*" + return function( dataTypeExpression, func ) { + + if ( typeof dataTypeExpression !== "string" ) { + func = dataTypeExpression; + dataTypeExpression = "*"; + } + + var dataType, + i = 0, + dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || []; + + if ( isFunction( func ) ) { + + // For each dataType in the dataTypeExpression + while ( ( dataType = dataTypes[ i++ ] ) ) { + + // Prepend if requested + if ( dataType[ 0 ] === "+" ) { + dataType = dataType.slice( 1 ) || "*"; + ( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func ); + + // Otherwise append + } else { + ( structure[ dataType ] = structure[ dataType ] || [] ).push( func ); + } + } + } + }; +} + +// Base inspection function for prefilters and transports +function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) { + + var inspected = {}, + seekingTransport = ( structure === transports ); + + function inspect( dataType ) { + var selected; + inspected[ dataType ] = true; + jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) { + var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR ); + if ( typeof dataTypeOrTransport === "string" && + !seekingTransport && !inspected[ dataTypeOrTransport ] ) { + + options.dataTypes.unshift( dataTypeOrTransport ); + inspect( dataTypeOrTransport ); + return false; + } else if ( seekingTransport ) { + return !( selected = dataTypeOrTransport ); + } + } ); + return selected; + } + + return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" ); +} + +// A special extend for ajax options +// that takes "flat" options (not to be deep extended) +// Fixes #9887 +function ajaxExtend( target, src ) { + var key, deep, + flatOptions = jQuery.ajaxSettings.flatOptions || {}; + + for ( key in src ) { + if ( src[ key ] !== undefined ) { + ( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ]; + } + } + if ( deep ) { + jQuery.extend( true, target, deep ); + } + + return target; +} + +/* Handles responses to an ajax request: + * - finds the right dataType (mediates between content-type and expected dataType) + * - returns the corresponding response + */ +function ajaxHandleResponses( s, jqXHR, responses ) { + + var ct, type, finalDataType, firstDataType, + contents = s.contents, + dataTypes = s.dataTypes; + + // Remove auto dataType and get content-type in the process + while ( dataTypes[ 0 ] === "*" ) { + dataTypes.shift(); + if ( ct === undefined ) { + ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" ); + } + } + + // Check if we're dealing with a known content-type + if ( ct ) { + for ( type in contents ) { + if ( contents[ type ] && contents[ type ].test( ct ) ) { + dataTypes.unshift( type ); + break; + } + } + } + + // Check to see if we have a response for the expected dataType + if ( dataTypes[ 0 ] in responses ) { + finalDataType = dataTypes[ 0 ]; + } else { + + // Try convertible dataTypes + for ( type in responses ) { + if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) { + finalDataType = type; + break; + } + if ( !firstDataType ) { + firstDataType = type; + } + } + + // Or just use first one + finalDataType = finalDataType || firstDataType; + } + + // If we found a dataType + // We add the dataType to the list if needed + // and return the corresponding response + if ( finalDataType ) { + if ( finalDataType !== dataTypes[ 0 ] ) { + dataTypes.unshift( finalDataType ); + } + return responses[ finalDataType ]; + } +} + +/* Chain conversions given the request and the original response + * Also sets the responseXXX fields on the jqXHR instance + */ +function ajaxConvert( s, response, jqXHR, isSuccess ) { + var conv2, current, conv, tmp, prev, + converters = {}, + + // Work with a copy of dataTypes in case we need to modify it for conversion + dataTypes = s.dataTypes.slice(); + + // Create converters map with lowercased keys + if ( dataTypes[ 1 ] ) { + for ( conv in s.converters ) { + converters[ conv.toLowerCase() ] = s.converters[ conv ]; + } + } + + current = dataTypes.shift(); + + // Convert to each sequential dataType + while ( current ) { + + if ( s.responseFields[ current ] ) { + jqXHR[ s.responseFields[ current ] ] = response; + } + + // Apply the dataFilter if provided + if ( !prev && isSuccess && s.dataFilter ) { + response = s.dataFilter( response, s.dataType ); + } + + prev = current; + current = dataTypes.shift(); + + if ( current ) { + + // There's only work to do if current dataType is non-auto + if ( current === "*" ) { + + current = prev; + + // Convert response if prev dataType is non-auto and differs from current + } else if ( prev !== "*" && prev !== current ) { + + // Seek a direct converter + conv = converters[ prev + " " + current ] || converters[ "* " + current ]; + + // If none found, seek a pair + if ( !conv ) { + for ( conv2 in converters ) { + + // If conv2 outputs current + tmp = conv2.split( " " ); + if ( tmp[ 1 ] === current ) { + + // If prev can be converted to accepted input + conv = converters[ prev + " " + tmp[ 0 ] ] || + converters[ "* " + tmp[ 0 ] ]; + if ( conv ) { + + // Condense equivalence converters + if ( conv === true ) { + conv = converters[ conv2 ]; + + // Otherwise, insert the intermediate dataType + } else if ( converters[ conv2 ] !== true ) { + current = tmp[ 0 ]; + dataTypes.unshift( tmp[ 1 ] ); + } + break; + } + } + } + } + + // Apply converter (if not an equivalence) + if ( conv !== true ) { + + // Unless errors are allowed to bubble, catch and return them + if ( conv && s.throws ) { + response = conv( response ); + } else { + try { + response = conv( response ); + } catch ( e ) { + return { + state: "parsererror", + error: conv ? e : "No conversion from " + prev + " to " + current + }; + } + } + } + } + } + } + + return { state: "success", data: response }; +} + +jQuery.extend( { + + // Counter for holding the number of active queries + active: 0, + + // Last-Modified header cache for next request + lastModified: {}, + etag: {}, + + ajaxSettings: { + url: location.href, + type: "GET", + isLocal: rlocalProtocol.test( location.protocol ), + global: true, + processData: true, + async: true, + contentType: "application/x-www-form-urlencoded; charset=UTF-8", + + /* + timeout: 0, + data: null, + dataType: null, + username: null, + password: null, + cache: null, + throws: false, + traditional: false, + headers: {}, + */ + + accepts: { + "*": allTypes, + text: "text/plain", + html: "text/html", + xml: "application/xml, text/xml", + json: "application/json, text/javascript" + }, + + contents: { + xml: /\bxml\b/, + html: /\bhtml/, + json: /\bjson\b/ + }, + + responseFields: { + xml: "responseXML", + text: "responseText", + json: "responseJSON" + }, + + // Data converters + // Keys separate source (or catchall "*") and destination types with a single space + converters: { + + // Convert anything to text + "* text": String, + + // Text to html (true = no transformation) + "text html": true, + + // Evaluate text as a json expression + "text json": JSON.parse, + + // Parse text as xml + "text xml": jQuery.parseXML + }, + + // For options that shouldn't be deep extended: + // you can add your own custom options here if + // and when you create one that shouldn't be + // deep extended (see ajaxExtend) + flatOptions: { + url: true, + context: true + } + }, + + // Creates a full fledged settings object into target + // with both ajaxSettings and settings fields. + // If target is omitted, writes into ajaxSettings. + ajaxSetup: function( target, settings ) { + return settings ? + + // Building a settings object + ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) : + + // Extending ajaxSettings + ajaxExtend( jQuery.ajaxSettings, target ); + }, + + ajaxPrefilter: addToPrefiltersOrTransports( prefilters ), + ajaxTransport: addToPrefiltersOrTransports( transports ), + + // Main method + ajax: function( url, options ) { + + // If url is an object, simulate pre-1.5 signature + if ( typeof url === "object" ) { + options = url; + url = undefined; + } + + // Force options to be an object + options = options || {}; + + var transport, + + // URL without anti-cache param + cacheURL, + + // Response headers + responseHeadersString, + responseHeaders, + + // timeout handle + timeoutTimer, + + // Url cleanup var + urlAnchor, + + // Request state (becomes false upon send and true upon completion) + completed, + + // To know if global events are to be dispatched + fireGlobals, + + // Loop variable + i, + + // uncached part of the url + uncached, + + // Create the final options object + s = jQuery.ajaxSetup( {}, options ), + + // Callbacks context + callbackContext = s.context || s, + + // Context for global events is callbackContext if it is a DOM node or jQuery collection + globalEventContext = s.context && + ( callbackContext.nodeType || callbackContext.jquery ) ? + jQuery( callbackContext ) : + jQuery.event, + + // Deferreds + deferred = jQuery.Deferred(), + completeDeferred = jQuery.Callbacks( "once memory" ), + + // Status-dependent callbacks + statusCode = s.statusCode || {}, + + // Headers (they are sent all at once) + requestHeaders = {}, + requestHeadersNames = {}, + + // Default abort message + strAbort = "canceled", + + // Fake xhr + jqXHR = { + readyState: 0, + + // Builds headers hashtable if needed + getResponseHeader: function( key ) { + var match; + if ( completed ) { + if ( !responseHeaders ) { + responseHeaders = {}; + while ( ( match = rheaders.exec( responseHeadersString ) ) ) { + responseHeaders[ match[ 1 ].toLowerCase() + " " ] = + ( responseHeaders[ match[ 1 ].toLowerCase() + " " ] || [] ) + .concat( match[ 2 ] ); + } + } + match = responseHeaders[ key.toLowerCase() + " " ]; + } + return match == null ? null : match.join( ", " ); + }, + + // Raw string + getAllResponseHeaders: function() { + return completed ? responseHeadersString : null; + }, + + // Caches the header + setRequestHeader: function( name, value ) { + if ( completed == null ) { + name = requestHeadersNames[ name.toLowerCase() ] = + requestHeadersNames[ name.toLowerCase() ] || name; + requestHeaders[ name ] = value; + } + return this; + }, + + // Overrides response content-type header + overrideMimeType: function( type ) { + if ( completed == null ) { + s.mimeType = type; + } + return this; + }, + + // Status-dependent callbacks + statusCode: function( map ) { + var code; + if ( map ) { + if ( completed ) { + + // Execute the appropriate callbacks + jqXHR.always( map[ jqXHR.status ] ); + } else { + + // Lazy-add the new callbacks in a way that preserves old ones + for ( code in map ) { + statusCode[ code ] = [ statusCode[ code ], map[ code ] ]; + } + } + } + return this; + }, + + // Cancel the request + abort: function( statusText ) { + var finalText = statusText || strAbort; + if ( transport ) { + transport.abort( finalText ); + } + done( 0, finalText ); + return this; + } + }; + + // Attach deferreds + deferred.promise( jqXHR ); + + // Add protocol if not provided (prefilters might expect it) + // Handle falsy url in the settings object (#10093: consistency with old signature) + // We also use the url parameter if available + s.url = ( ( url || s.url || location.href ) + "" ) + .replace( rprotocol, location.protocol + "//" ); + + // Alias method option to type as per ticket #12004 + s.type = options.method || options.type || s.method || s.type; + + // Extract dataTypes list + s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ]; + + // A cross-domain request is in order when the origin doesn't match the current origin. + if ( s.crossDomain == null ) { + urlAnchor = document.createElement( "a" ); + + // Support: IE <=8 - 11, Edge 12 - 15 + // IE throws exception on accessing the href property if url is malformed, + // e.g. http://example.com:80x/ + try { + urlAnchor.href = s.url; + + // Support: IE <=8 - 11 only + // Anchor's host property isn't correctly set when s.url is relative + urlAnchor.href = urlAnchor.href; + s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !== + urlAnchor.protocol + "//" + urlAnchor.host; + } catch ( e ) { + + // If there is an error parsing the URL, assume it is crossDomain, + // it can be rejected by the transport if it is invalid + s.crossDomain = true; + } + } + + // Convert data if not already a string + if ( s.data && s.processData && typeof s.data !== "string" ) { + s.data = jQuery.param( s.data, s.traditional ); + } + + // Apply prefilters + inspectPrefiltersOrTransports( prefilters, s, options, jqXHR ); + + // If request was aborted inside a prefilter, stop there + if ( completed ) { + return jqXHR; + } + + // We can fire global events as of now if asked to + // Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118) + fireGlobals = jQuery.event && s.global; + + // Watch for a new set of requests + if ( fireGlobals && jQuery.active++ === 0 ) { + jQuery.event.trigger( "ajaxStart" ); + } + + // Uppercase the type + s.type = s.type.toUpperCase(); + + // Determine if request has content + s.hasContent = !rnoContent.test( s.type ); + + // Save the URL in case we're toying with the If-Modified-Since + // and/or If-None-Match header later on + // Remove hash to simplify url manipulation + cacheURL = s.url.replace( rhash, "" ); + + // More options handling for requests with no content + if ( !s.hasContent ) { + + // Remember the hash so we can put it back + uncached = s.url.slice( cacheURL.length ); + + // If data is available and should be processed, append data to url + if ( s.data && ( s.processData || typeof s.data === "string" ) ) { + cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data; + + // #9682: remove data so that it's not used in an eventual retry + delete s.data; + } + + // Add or update anti-cache param if needed + if ( s.cache === false ) { + cacheURL = cacheURL.replace( rantiCache, "$1" ); + uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce.guid++ ) + + uncached; + } + + // Put hash and anti-cache on the URL that will be requested (gh-1732) + s.url = cacheURL + uncached; + + // Change '%20' to '+' if this is encoded form body content (gh-2658) + } else if ( s.data && s.processData && + ( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) { + s.data = s.data.replace( r20, "+" ); + } + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + if ( jQuery.lastModified[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] ); + } + if ( jQuery.etag[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] ); + } + } + + // Set the correct header, if data is being sent + if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) { + jqXHR.setRequestHeader( "Content-Type", s.contentType ); + } + + // Set the Accepts header for the server, depending on the dataType + jqXHR.setRequestHeader( + "Accept", + s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ? + s.accepts[ s.dataTypes[ 0 ] ] + + ( s.dataTypes[ 0 ] !== "*" ? ", " + allTypes + "; q=0.01" : "" ) : + s.accepts[ "*" ] + ); + + // Check for headers option + for ( i in s.headers ) { + jqXHR.setRequestHeader( i, s.headers[ i ] ); + } + + // Allow custom headers/mimetypes and early abort + if ( s.beforeSend && + ( s.beforeSend.call( callbackContext, jqXHR, s ) === false || completed ) ) { + + // Abort if not done already and return + return jqXHR.abort(); + } + + // Aborting is no longer a cancellation + strAbort = "abort"; + + // Install callbacks on deferreds + completeDeferred.add( s.complete ); + jqXHR.done( s.success ); + jqXHR.fail( s.error ); + + // Get transport + transport = inspectPrefiltersOrTransports( transports, s, options, jqXHR ); + + // If no transport, we auto-abort + if ( !transport ) { + done( -1, "No Transport" ); + } else { + jqXHR.readyState = 1; + + // Send global event + if ( fireGlobals ) { + globalEventContext.trigger( "ajaxSend", [ jqXHR, s ] ); + } + + // If request was aborted inside ajaxSend, stop there + if ( completed ) { + return jqXHR; + } + + // Timeout + if ( s.async && s.timeout > 0 ) { + timeoutTimer = window.setTimeout( function() { + jqXHR.abort( "timeout" ); + }, s.timeout ); + } + + try { + completed = false; + transport.send( requestHeaders, done ); + } catch ( e ) { + + // Rethrow post-completion exceptions + if ( completed ) { + throw e; + } + + // Propagate others as results + done( -1, e ); + } + } + + // Callback for when everything is done + function done( status, nativeStatusText, responses, headers ) { + var isSuccess, success, error, response, modified, + statusText = nativeStatusText; + + // Ignore repeat invocations + if ( completed ) { + return; + } + + completed = true; + + // Clear timeout if it exists + if ( timeoutTimer ) { + window.clearTimeout( timeoutTimer ); + } + + // Dereference transport for early garbage collection + // (no matter how long the jqXHR object will be used) + transport = undefined; + + // Cache response headers + responseHeadersString = headers || ""; + + // Set readyState + jqXHR.readyState = status > 0 ? 4 : 0; + + // Determine if successful + isSuccess = status >= 200 && status < 300 || status === 304; + + // Get response data + if ( responses ) { + response = ajaxHandleResponses( s, jqXHR, responses ); + } + + // Use a noop converter for missing script + if ( !isSuccess && jQuery.inArray( "script", s.dataTypes ) > -1 ) { + s.converters[ "text script" ] = function() {}; + } + + // Convert no matter what (that way responseXXX fields are always set) + response = ajaxConvert( s, response, jqXHR, isSuccess ); + + // If successful, handle type chaining + if ( isSuccess ) { + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + modified = jqXHR.getResponseHeader( "Last-Modified" ); + if ( modified ) { + jQuery.lastModified[ cacheURL ] = modified; + } + modified = jqXHR.getResponseHeader( "etag" ); + if ( modified ) { + jQuery.etag[ cacheURL ] = modified; + } + } + + // if no content + if ( status === 204 || s.type === "HEAD" ) { + statusText = "nocontent"; + + // if not modified + } else if ( status === 304 ) { + statusText = "notmodified"; + + // If we have data, let's convert it + } else { + statusText = response.state; + success = response.data; + error = response.error; + isSuccess = !error; + } + } else { + + // Extract error from statusText and normalize for non-aborts + error = statusText; + if ( status || !statusText ) { + statusText = "error"; + if ( status < 0 ) { + status = 0; + } + } + } + + // Set data for the fake xhr object + jqXHR.status = status; + jqXHR.statusText = ( nativeStatusText || statusText ) + ""; + + // Success/Error + if ( isSuccess ) { + deferred.resolveWith( callbackContext, [ success, statusText, jqXHR ] ); + } else { + deferred.rejectWith( callbackContext, [ jqXHR, statusText, error ] ); + } + + // Status-dependent callbacks + jqXHR.statusCode( statusCode ); + statusCode = undefined; + + if ( fireGlobals ) { + globalEventContext.trigger( isSuccess ? "ajaxSuccess" : "ajaxError", + [ jqXHR, s, isSuccess ? success : error ] ); + } + + // Complete + completeDeferred.fireWith( callbackContext, [ jqXHR, statusText ] ); + + if ( fireGlobals ) { + globalEventContext.trigger( "ajaxComplete", [ jqXHR, s ] ); + + // Handle the global AJAX counter + if ( !( --jQuery.active ) ) { + jQuery.event.trigger( "ajaxStop" ); + } + } + } + + return jqXHR; + }, + + getJSON: function( url, data, callback ) { + return jQuery.get( url, data, callback, "json" ); + }, + + getScript: function( url, callback ) { + return jQuery.get( url, undefined, callback, "script" ); + } +} ); + +jQuery.each( [ "get", "post" ], function( _i, method ) { + jQuery[ method ] = function( url, data, callback, type ) { + + // Shift arguments if data argument was omitted + if ( isFunction( data ) ) { + type = type || callback; + callback = data; + data = undefined; + } + + // The url can be an options object (which then must have .url) + return jQuery.ajax( jQuery.extend( { + url: url, + type: method, + dataType: type, + data: data, + success: callback + }, jQuery.isPlainObject( url ) && url ) ); + }; +} ); + +jQuery.ajaxPrefilter( function( s ) { + var i; + for ( i in s.headers ) { + if ( i.toLowerCase() === "content-type" ) { + s.contentType = s.headers[ i ] || ""; + } + } +} ); + + +jQuery._evalUrl = function( url, options, doc ) { + return jQuery.ajax( { + url: url, + + // Make this explicit, since user can override this through ajaxSetup (#11264) + type: "GET", + dataType: "script", + cache: true, + async: false, + global: false, + + // Only evaluate the response if it is successful (gh-4126) + // dataFilter is not invoked for failure responses, so using it instead + // of the default converter is kludgy but it works. + converters: { + "text script": function() {} + }, + dataFilter: function( response ) { + jQuery.globalEval( response, options, doc ); + } + } ); +}; + + +jQuery.fn.extend( { + wrapAll: function( html ) { + var wrap; + + if ( this[ 0 ] ) { + if ( isFunction( html ) ) { + html = html.call( this[ 0 ] ); + } + + // The elements to wrap the target around + wrap = jQuery( html, this[ 0 ].ownerDocument ).eq( 0 ).clone( true ); + + if ( this[ 0 ].parentNode ) { + wrap.insertBefore( this[ 0 ] ); + } + + wrap.map( function() { + var elem = this; + + while ( elem.firstElementChild ) { + elem = elem.firstElementChild; + } + + return elem; + } ).append( this ); + } + + return this; + }, + + wrapInner: function( html ) { + if ( isFunction( html ) ) { + return this.each( function( i ) { + jQuery( this ).wrapInner( html.call( this, i ) ); + } ); + } + + return this.each( function() { + var self = jQuery( this ), + contents = self.contents(); + + if ( contents.length ) { + contents.wrapAll( html ); + + } else { + self.append( html ); + } + } ); + }, + + wrap: function( html ) { + var htmlIsFunction = isFunction( html ); + + return this.each( function( i ) { + jQuery( this ).wrapAll( htmlIsFunction ? html.call( this, i ) : html ); + } ); + }, + + unwrap: function( selector ) { + this.parent( selector ).not( "body" ).each( function() { + jQuery( this ).replaceWith( this.childNodes ); + } ); + return this; + } +} ); + + +jQuery.expr.pseudos.hidden = function( elem ) { + return !jQuery.expr.pseudos.visible( elem ); +}; +jQuery.expr.pseudos.visible = function( elem ) { + return !!( elem.offsetWidth || elem.offsetHeight || elem.getClientRects().length ); +}; + + + + +jQuery.ajaxSettings.xhr = function() { + try { + return new window.XMLHttpRequest(); + } catch ( e ) {} +}; + +var xhrSuccessStatus = { + + // File protocol always yields status code 0, assume 200 + 0: 200, + + // Support: IE <=9 only + // #1450: sometimes IE returns 1223 when it should be 204 + 1223: 204 + }, + xhrSupported = jQuery.ajaxSettings.xhr(); + +support.cors = !!xhrSupported && ( "withCredentials" in xhrSupported ); +support.ajax = xhrSupported = !!xhrSupported; + +jQuery.ajaxTransport( function( options ) { + var callback, errorCallback; + + // Cross domain only allowed if supported through XMLHttpRequest + if ( support.cors || xhrSupported && !options.crossDomain ) { + return { + send: function( headers, complete ) { + var i, + xhr = options.xhr(); + + xhr.open( + options.type, + options.url, + options.async, + options.username, + options.password + ); + + // Apply custom fields if provided + if ( options.xhrFields ) { + for ( i in options.xhrFields ) { + xhr[ i ] = options.xhrFields[ i ]; + } + } + + // Override mime type if needed + if ( options.mimeType && xhr.overrideMimeType ) { + xhr.overrideMimeType( options.mimeType ); + } + + // X-Requested-With header + // For cross-domain requests, seeing as conditions for a preflight are + // akin to a jigsaw puzzle, we simply never set it to be sure. + // (it can always be set on a per-request basis or even using ajaxSetup) + // For same-domain requests, won't change header if already provided. + if ( !options.crossDomain && !headers[ "X-Requested-With" ] ) { + headers[ "X-Requested-With" ] = "XMLHttpRequest"; + } + + // Set headers + for ( i in headers ) { + xhr.setRequestHeader( i, headers[ i ] ); + } + + // Callback + callback = function( type ) { + return function() { + if ( callback ) { + callback = errorCallback = xhr.onload = + xhr.onerror = xhr.onabort = xhr.ontimeout = + xhr.onreadystatechange = null; + + if ( type === "abort" ) { + xhr.abort(); + } else if ( type === "error" ) { + + // Support: IE <=9 only + // On a manual native abort, IE9 throws + // errors on any property access that is not readyState + if ( typeof xhr.status !== "number" ) { + complete( 0, "error" ); + } else { + complete( + + // File: protocol always yields status 0; see #8605, #14207 + xhr.status, + xhr.statusText + ); + } + } else { + complete( + xhrSuccessStatus[ xhr.status ] || xhr.status, + xhr.statusText, + + // Support: IE <=9 only + // IE9 has no XHR2 but throws on binary (trac-11426) + // For XHR2 non-text, let the caller handle it (gh-2498) + ( xhr.responseType || "text" ) !== "text" || + typeof xhr.responseText !== "string" ? + { binary: xhr.response } : + { text: xhr.responseText }, + xhr.getAllResponseHeaders() + ); + } + } + }; + }; + + // Listen to events + xhr.onload = callback(); + errorCallback = xhr.onerror = xhr.ontimeout = callback( "error" ); + + // Support: IE 9 only + // Use onreadystatechange to replace onabort + // to handle uncaught aborts + if ( xhr.onabort !== undefined ) { + xhr.onabort = errorCallback; + } else { + xhr.onreadystatechange = function() { + + // Check readyState before timeout as it changes + if ( xhr.readyState === 4 ) { + + // Allow onerror to be called first, + // but that will not handle a native abort + // Also, save errorCallback to a variable + // as xhr.onerror cannot be accessed + window.setTimeout( function() { + if ( callback ) { + errorCallback(); + } + } ); + } + }; + } + + // Create the abort callback + callback = callback( "abort" ); + + try { + + // Do send the request (this may raise an exception) + xhr.send( options.hasContent && options.data || null ); + } catch ( e ) { + + // #14683: Only rethrow if this hasn't been notified as an error yet + if ( callback ) { + throw e; + } + } + }, + + abort: function() { + if ( callback ) { + callback(); + } + } + }; + } +} ); + + + + +// Prevent auto-execution of scripts when no explicit dataType was provided (See gh-2432) +jQuery.ajaxPrefilter( function( s ) { + if ( s.crossDomain ) { + s.contents.script = false; + } +} ); + +// Install script dataType +jQuery.ajaxSetup( { + accepts: { + script: "text/javascript, application/javascript, " + + "application/ecmascript, application/x-ecmascript" + }, + contents: { + script: /\b(?:java|ecma)script\b/ + }, + converters: { + "text script": function( text ) { + jQuery.globalEval( text ); + return text; + } + } +} ); + +// Handle cache's special case and crossDomain +jQuery.ajaxPrefilter( "script", function( s ) { + if ( s.cache === undefined ) { + s.cache = false; + } + if ( s.crossDomain ) { + s.type = "GET"; + } +} ); + +// Bind script tag hack transport +jQuery.ajaxTransport( "script", function( s ) { + + // This transport only deals with cross domain or forced-by-attrs requests + if ( s.crossDomain || s.scriptAttrs ) { + var script, callback; + return { + send: function( _, complete ) { + script = jQuery( " +{% endmacro %} \ No newline at end of file diff --git a/docs/extra/adpeps.ipeps.ctm.html b/docs/extra/adpeps.ipeps.ctm.html new file mode 100644 index 0000000..2d91dd3 --- /dev/null +++ b/docs/extra/adpeps.ipeps.ctm.html @@ -0,0 +1,606 @@ + + + + + + + + adpeps.ipeps.ctm — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.ipeps.ctm

+

Main CTM code

+

The individual site and boundary tensors come in a +special list-type object (TList), which has extra +indexing features, such as periodic boundary +conditions and shift contexts

+

All ncon contractions are defined in contractions.yaml

+
+
+class CTM(tensors, chi, conv_fun=None)[source]
+

CTM class

+
+
Parameters
+
+
+
+
+
+property converged
+

Check convergence with supplied convergence function

+
+ +
+
+show_progress()[source]
+

Print out the current progress

+
+ +
+
+update()[source]
+

Perform an update of all boundary tensors

+
+ +
+ +
+
+do_bottom(ts, chi)[source]
+

Perform bottom CTM move

+
+
Parameters
+
+
+
Returns
+

updated tensors

+
+
Return type
+

ts

+
+
Return type
+

CTMTensors

+
+
+
+ +
+
+do_left(ts, chi)[source]
+

Perform left CTM move

+
+
Parameters
+
+
+
Returns
+

A tuple containing

+
    +

  • tensors (CTMTensors): updated tensors

    • +

  • sl (np.ndarray): singular values of C1 (for convergence)

    • +
+

+
+
Return type
+

Tuple[CTMTensors, ndarray]

+
+
+
+ +
+
+do_right(ts, chi)[source]
+

Perform right CTM move

+
+
Parameters
+
+
+
Returns
+

updated tensors

+
+
Return type
+

ts

+
+
Return type
+

CTMTensors

+
+
+
+ +
+
+do_top(ts, chi)[source]
+

Perform top CTM move

+
+
Parameters
+
+
+
Returns
+

updated tensors

+
+
Return type
+

ts

+
+
Return type
+

CTMTensors

+
+
+
+ +
+
+get_projectors(T1, T2, chi)[source]
+

Contracts the corners together and computes the +projectors by performing an svd

+
+
Parameters
+

T1 (int) –

+
+
+
+ +
+
+get_projectors_bottom(ts, chi)[source]
+

Returns the bottom projectors

+
+
Return type
+

Tuple[ndarray, ndarray, ndarray]

+
+
Parameters
+
+
+
+
+ +
+
+get_projectors_left(ts, chi)[source]
+

Returns the left projectors

+
+
Return type
+

Tuple[ndarray, ndarray, ndarray]

+
+
Parameters
+
+
+
+
+ +
+
+get_projectors_right(ts, chi)[source]
+

Returns the right projectors

+
+
Return type
+

Tuple[ndarray, ndarray, ndarray]

+
+
Parameters
+
+
+
+
+ +
+
+get_projectors_top(ts, chi)[source]
+

Returns the top projectors

+
+
Return type
+

Tuple[ndarray, ndarray, ndarray]

+
+
Parameters
+
+
+
+
+ +
+
+renorm_left(ts, Pl, Plb)[source]
+
+
Return type
+

Tuple[Nested, Nested, Nested]

+
+
Parameters
+
+
+
+
+ +
+
+renormalize(tensors, chi)[source]
+

Performs a CTM iteration +Updates all sites in the unit cell

+
+
Parameters
+
+
+
Returns
+

A tuple containing

+
    +

  • tensors (CTMTensors): updated tensors

    • +

  • S (np.ndarray): singular values of C1 (for convergence)

    • +
+

+
+
Return type
+

Tuple[CTMTensors, ndarray]

+
+
+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/extra/adpeps.ipeps.ipeps.html b/docs/extra/adpeps.ipeps.ipeps.html new file mode 100644 index 0000000..ba660c5 --- /dev/null +++ b/docs/extra/adpeps.ipeps.ipeps.html @@ -0,0 +1,552 @@ + + + + + + + + adpeps.ipeps.ipeps — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ +
+ On this page +
+ + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.ipeps.ipeps

+

iPEPS module for optimization with CTM

+

For an example of how to run a simulation see adpeps.simulation.run_ipeps_gs

+

The module is initialized from one of the specific +model files, which return the initial boundary and +site tensors

+

The list of parameters is set to the elements of the +individual site tensors

+

Conventions for indices:

+
+
    +

  • Site tensors:

    +
    A: [phys, right, top, left, bottom]
+
    +
    +
    • +

  • Boundary tensors:

    +
    C1: [right, bottom]
+C2: [left,  bottom]
+C3: [top,   left]
+C4: [right, top]
+T1: [right, left, ket, bra]
+T2: [top,   bottom, ket, bra]
+T3: [right, left, ket, bra]
+T4: [top,   bottom, ket, bra]
+
    +
    +
    • +
+
+

Order of boundary tensors:

+
C1 - T1 - C2
+|    |    |
+T4 - A  - T2
+|    |    |
+C4 - T3 - C3
+
+
+
+
+class iPEPS[source]
+

Initialize the iPEPS based on the settings in +adpeps.ipeps.config

+
+
+converge_boundaries()[source]
+

Performs CTM on the boundary tensors until convergence, +without gradient tracking

+
+ +
+
+fill(A)[source]
+

Fill the site tensors with the elements +The elements can be specified either as a list of (d,D,D,D,D)-dimensional +arrays or one 1-dimensional array of all elements concatenated

+
+ +
+
+numel()[source]
+

Number of variational parameters

+
+ +
+
+parse_elements(elements)[source]
+

Returns site tensors filled with the input elements

+
+ +
+
+run(params)[source]
+

Run the simulation

+
+
Parameters
+

params (jax._src.numpy.lax_numpy.ndarray) – variational parameters

+
+
Returns
+

energy of iPEPS

+
+
Return type
+

ndarray

+
+
+
+ +
+ +
+
+class iPEPS_exci[source]
+

Excited-state variant of the iPEPS class

+
+
+fill(B)[source]
+

Fill the site tensors with the elements +The elements can be specified either as a list of (d,D,D,D,D)-dimensional +arrays or one 1-dimensional array of all elements concatenated

+
+ +
+ +
+
+init_A_tensor(d, D, pattern)[source]
+

The elements will be randomized based on sim_config.seed

+
+ +
+
+init_ctm_tensors(A, Ad)[source]
+

Returns initital boundary T-tensors based on the unit cell tensors and +empty trivial boundary C-tensors

+
+ +
+

iPEPS

+
+
+class iPEPS[source]
+

Initialize the iPEPS based on the settings in +adpeps.ipeps.config

+
+
+run(params)[source]
+

Run the simulation

+
+
Parameters
+

params (jax._src.numpy.lax_numpy.ndarray) – variational parameters

+
+
Returns
+

energy of iPEPS

+
+
Return type
+

ndarray

+
+
+
+ +
+
+converge_boundaries()[source]
+

Performs CTM on the boundary tensors until convergence, +without gradient tracking

+
+ +
+
+numel()[source]
+

Number of variational parameters

+
+ +
+
+parse_elements(elements)[source]
+

Returns site tensors filled with the input elements

+
+ +
+
+fill(A)[source]
+

Fill the site tensors with the elements +The elements can be specified either as a list of (d,D,D,D,D)-dimensional +arrays or one 1-dimensional array of all elements concatenated

+
+ +
+ +
+
+

iPEPS_exci

+
+
+class iPEPS_exci[source]
+

Excited-state variant of the iPEPS class

+
+
+fill(B)[source]
+

Fill the site tensors with the elements +The elements can be specified either as a list of (d,D,D,D,D)-dimensional +arrays or one 1-dimensional array of all elements concatenated

+
+ +
+ +
+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/extra/ipeps.ipeps.html b/docs/extra/ipeps.ipeps.html new file mode 100644 index 0000000..be03447 --- /dev/null +++ b/docs/extra/ipeps.ipeps.html @@ -0,0 +1,340 @@ + + + + + + + + iPEPSS — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

iPEPSS

+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/generated/adpeps.ipeps.config.html b/docs/generated/adpeps.ipeps.config.html new file mode 100644 index 0000000..5532291 --- /dev/null +++ b/docs/generated/adpeps.ipeps.config.html @@ -0,0 +1,492 @@ + + + + + + + + adpeps.ipeps.config — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.ipeps.config

+

Configuration module for iPEPS simulations

+

These settings will be loaded from a configuration file .yml file +via the from_dict() function

+
+
+from_dict(cfg)[source]
+

Import config from configuration (.yml) file

+
+ +
+
+D: int = None
+

iPEPS bond dimension

+
+ +
+
+base_sim: Optional[str] = None
+

Base simulation

+
+ +
+
+chi: int = None
+

CTM boundary bond dimension

+
+ +
+
+ctm_conv_tol: float = 1e-10
+

CTM convergence criterium (singular values norm difference)

+
+ +
+
+ctm_max_iter: int = 20
+

Maximal number of CTM steps

+
+ +
+
+ctm_min_iter: int = 5
+

Minimal number of CTM steps

+
+ +
+
+disp_level: int = 1
+

no output)

+
+
Type
+

Display level (0

+
+
+
+ +
+
+flush_output: bool = False
+

Passes the flush    = True argument to the builtin print function +when calling the adpeps.utils.printing.print() function

+

Useful when deploying the code to computing clusters and capturing the output +into text files

+
+ +
+
+load_sim: bool = None
+

Load previous (Python) simulation

+
+ +
+
+max_iterations: int = 100
+

Maximum number of optimizer iterations

+
+ +
+
+method: str = None
+

Optimization method

+
+ +
+
+model: str = None
+

Model

+
+ +
+
+model_params: dict = None
+

Model parameters

+
+ +
+
+momentum_path: str = 'Bril1'
+

Momentum path through the BZ

+
+ +
+
+out_prefix: str = ''
+

Optional prefix for the output file of the simulation

+

Example

+

.../{model}_D{D}_X{chi}.npz

+

becomes

+

.../{out_prefix}_{model}_D{D}_X{chi}.npz

+
+ +
+
+pattern: Optional[Iterable] = None
+

Unit cell configuration +Defined as a 2-D array of integers that label the unique sites in the unit +cell.

+

Example

+

A 2x2 unit cell with a [AB, BA]-type pattern is defined by

+
pattern            = [
+    [0, 1],
+    [1, 0]
+]
+
+
+
+ +
+
+resume: bool = False
+

Resume earlier simulation if found

+
+ +
+
+seed: int = 1
+

Random seed for initial state

+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/generated/adpeps.ipeps.ctm.html b/docs/generated/adpeps.ipeps.ctm.html new file mode 100644 index 0000000..5673031 --- /dev/null +++ b/docs/generated/adpeps.ipeps.ctm.html @@ -0,0 +1,608 @@ + + + + + + + + adpeps.ipeps.ctm — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.ipeps.ctm

+

Main CTM code

+

The individual site and boundary tensors come in a +special list-type object (TList), which has extra +indexing features, such as periodic boundary +conditions and shift contexts

+

All ncon contractions are defined in contractions.yaml

+
+
+class CTM(tensors, chi, conv_fun=None)[source]
+

CTM class

+
+
Parameters
+
+
+
+
+
+show_progress()[source]
+

Print out the current progress

+
+ +
+
+update()[source]
+

Perform an update of all boundary tensors

+
+ +
+
+property converged
+

Check convergence with supplied convergence function

+
+ +
+ +
+
+do_bottom(ts, chi)[source]
+

Perform bottom CTM move

+
+
Parameters
+
+
+
Returns
+

updated tensors

+
+
Return type
+

ts

+
+
Return type
+

CTMTensors

+
+
+
+ +
+
+do_left(ts, chi)[source]
+

Perform left CTM move

+
+
Parameters
+
+
+
Returns
+

A tuple containing

+
    +

  • tensors (CTMTensors): updated tensors

    • +

  • sl (np.ndarray): singular values of C1 (for convergence)

    • +
+

+
+
Return type
+

Tuple[CTMTensors, ndarray]

+
+
+
+ +
+
+do_right(ts, chi)[source]
+

Perform right CTM move

+
+
Parameters
+
+
+
Returns
+

updated tensors

+
+
Return type
+

ts

+
+
Return type
+

CTMTensors

+
+
+
+ +
+
+do_top(ts, chi)[source]
+

Perform top CTM move

+
+
Parameters
+
+
+
Returns
+

updated tensors

+
+
Return type
+

ts

+
+
Return type
+

CTMTensors

+
+
+
+ +
+
+get_projectors(T1, T2, chi)[source]
+

Contracts the corners together and computes the +projectors by performing an svd

+
+
Parameters
+

T1 (int) –

+
+
+
+ +
+
+get_projectors_bottom(ts, chi)[source]
+

Returns the bottom projectors

+
+
Return type
+

Tuple[ndarray, ndarray, ndarray]

+
+
Parameters
+
+
+
+
+ +
+
+get_projectors_left(ts, chi)[source]
+

Returns the left projectors

+
+
Return type
+

Tuple[ndarray, ndarray, ndarray]

+
+
Parameters
+
+
+
+
+ +
+
+get_projectors_right(ts, chi)[source]
+

Returns the right projectors

+
+
Return type
+

Tuple[ndarray, ndarray, ndarray]

+
+
Parameters
+
+
+
+
+ +
+
+get_projectors_top(ts, chi)[source]
+

Returns the top projectors

+
+
Return type
+

Tuple[ndarray, ndarray, ndarray]

+
+
Parameters
+
+
+
+
+ +
+
+renorm_left(ts, Pl, Plb)[source]
+
+
Return type
+

Tuple[Nested, Nested, Nested]

+
+
Parameters
+
+
+
+
+ +
+
+renormalize(tensors, chi)[source]
+

Performs a CTM iteration +Updates all sites in the unit cell

+
+
Parameters
+
+
+
Returns
+

A tuple containing

+
    +

  • tensors (CTMTensors): updated tensors

    • +

  • S (np.ndarray): singular values of C1 (for convergence)

    • +
+

+
+
Return type
+

Tuple[CTMTensors, ndarray]

+
+
+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/generated/adpeps.ipeps.ipeps.evaluation.html b/docs/generated/adpeps.ipeps.ipeps.evaluation.html new file mode 100644 index 0000000..aa14e80 --- /dev/null +++ b/docs/generated/adpeps.ipeps.ipeps.evaluation.html @@ -0,0 +1,364 @@ + + + + + + + + adpeps.ipeps.ipeps.evaluation — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.ipeps.ipeps.evaluation

+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/generated/adpeps.ipeps.ipeps.html b/docs/generated/adpeps.ipeps.ipeps.html new file mode 100644 index 0000000..3c40ce7 --- /dev/null +++ b/docs/generated/adpeps.ipeps.ipeps.html @@ -0,0 +1,468 @@ + + + + + + + + adpeps.ipeps.ipeps — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.ipeps.ipeps

+

iPEPS module for optimization with CTM

+

For an example of how to run a simulation see adpeps.simulation.run_ipeps_gs

+

The module is initialized from one of the specific +model files, which return the initial boundary and +site tensors

+

The list of parameters is set to the elements of the +individual site tensors

+

Conventions for indices:

+
+
    +

  • Site tensors:

    +
    A: [phys, right, top, left, bottom]
+
    +
    +
    • +

  • Boundary tensors:

    +
    C1: [right, bottom]
+C2: [left,  bottom]
+C3: [top,   left]
+C4: [right, top]
+T1: [right, left, ket, bra]
+T2: [top,   bottom, ket, bra]
+T3: [right, left, ket, bra]
+T4: [top,   bottom, ket, bra]
+
    +
    +
    • +
+
+

Order of boundary tensors:

+
C1 - T1 - C2
+|    |    |
+T4 - A  - T2
+|    |    |
+C4 - T3 - C3
+
+
+
+
+class iPEPS[source]
+

Initialize the iPEPS based on the settings in +adpeps.ipeps.config

+
+
+converge_boundaries()[source]
+

Performs CTM on the boundary tensors until convergence, +without gradient tracking

+
+ +
+
+fill(A)[source]
+

Fill the site tensors with the elements +The elements can be specified either as a list of (d,D,D,D,D)-dimensional +arrays or one 1-dimensional array of all elements concatenated

+
+ +
+
+numel()[source]
+

Number of variational parameters

+
+ +
+
+parse_elements(elements)[source]
+

Returns site tensors filled with the input elements

+
+ +
+
+run(params)[source]
+

Run the simulation

+
+
Parameters
+

params (jax._src.numpy.lax_numpy.ndarray) – variational parameters

+
+
Returns
+

energy of iPEPS

+
+
Return type
+

ndarray

+
+
+
+ +
+ +
+
+class iPEPS_exci[source]
+

Excited-state variant of the iPEPS class

+
+
+fill(B)[source]
+

Fill the site tensors with the elements +The elements can be specified either as a list of (d,D,D,D,D)-dimensional +arrays or one 1-dimensional array of all elements concatenated

+
+ +
+ +
+
+init_A_tensor(d, D, pattern)[source]
+

The elements will be randomized based on sim_config.seed

+
+ +
+
+init_ctm_tensors(A, Ad)[source]
+

Returns initital boundary T-tensors based on the unit cell tensors and +empty trivial boundary C-tensors

+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/generated/adpeps.ipeps.models.common.html b/docs/generated/adpeps.ipeps.models.common.html new file mode 100644 index 0000000..52a83e8 --- /dev/null +++ b/docs/generated/adpeps.ipeps.models.common.html @@ -0,0 +1,342 @@ + + + + + + + + adpeps.ipeps.models.common — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.ipeps.models.common

+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/generated/adpeps.ipeps.models.heisenberg.html b/docs/generated/adpeps.ipeps.models.heisenberg.html new file mode 100644 index 0000000..e542042 --- /dev/null +++ b/docs/generated/adpeps.ipeps.models.heisenberg.html @@ -0,0 +1,366 @@ + + + + + + + + adpeps.ipeps.models.heisenberg — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.ipeps.models.heisenberg

+

2D Heisenberg model

+
+
+make_hamiltonian(J=1)[source]
+

Heisenberg model

+
+ +
+
+setup()[source]
+

Returns the Hamiltonian

+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/generated/adpeps.ipeps.models.html b/docs/generated/adpeps.ipeps.models.html new file mode 100644 index 0000000..9e9cec9 --- /dev/null +++ b/docs/generated/adpeps.ipeps.models.html @@ -0,0 +1,381 @@ + + + + + + + + adpeps.ipeps.models — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ +
+ On this page +
+ + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.ipeps.models

+
+

Modules

+

Contains all models defined by Hamiltonians as part of this module

+ ++++ + + + + + + + + +

adpeps.ipeps.models.common

adpeps.ipeps.models.heisenberg

2D Heisenberg model

+
+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/generated/adpeps.simulation.html b/docs/generated/adpeps.simulation.html new file mode 100644 index 0000000..3723b3c --- /dev/null +++ b/docs/generated/adpeps.simulation.html @@ -0,0 +1,387 @@ + + + + + + + + adpeps.simulation — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ +
+ On this page +
+ + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.simulation

+
+

Modules

+

Module with executable scripts for running the simulations

+
+

Note

+

The simulations are intended to be used by calling the package +directly via python -m adpeps ..., as described in +Getting Started

+
+ ++++ + + + + + + + + +

adpeps.simulation.run_ipeps_exci

Main excited-state executable script

adpeps.simulation.run_ipeps_gs

Main ground-state executable script

+
+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/generated/adpeps.simulation.run_ipeps_exci.html b/docs/generated/adpeps.simulation.run_ipeps_exci.html new file mode 100644 index 0000000..00a2a35 --- /dev/null +++ b/docs/generated/adpeps.simulation.run_ipeps_exci.html @@ -0,0 +1,381 @@ + + + + + + + + adpeps.simulation.run_ipeps_exci — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.simulation.run_ipeps_exci

+

Main excited-state executable script

+
+

Note

+

The simulations are intended to be used by calling the package +directly via python -m adpeps ..., as described in +Getting Started

+
+
+
+class iPEPSExciSimulation(config_file, momentum_ix)[source]
+

Simulation class for the excited-state simulation

+

Call an instance of this class directly to start the simulation

+
+ +
+
+run(config_file, momentum_ix)[source]
+

Start the simulation

+
+
Parameters
+
    +

  • config_file (str) – filename of the configuration file

    • +

  • momentum_ix (int) – index of the point in momentum space

    • +
+
+
+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/generated/adpeps.simulation.run_ipeps_gs.html b/docs/generated/adpeps.simulation.run_ipeps_gs.html new file mode 100644 index 0000000..ead30ae --- /dev/null +++ b/docs/generated/adpeps.simulation.run_ipeps_gs.html @@ -0,0 +1,440 @@ + + + + + + + + adpeps.simulation.run_ipeps_gs — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.simulation.run_ipeps_gs

+

Main ground-state executable script

+
+

Note

+

The simulations are intended to be used by calling the package +directly via python -m adpeps ..., as described in +Getting Started

+
+
+
+class Objective(peps)[source]
+

Class containing the objective function for the optimizer

+
+
Parameters
+

peps (adpeps.ipeps.ipeps.iPEPS) – iPEPS object to be optimized

+
+
+
+
+jac(v)[source]
+

Computes the vector-Jacobian product (gradient) of the +iPEPS at the current point v in parameter space

+

This function is designed to work with optimizers that make separate +calls to the objective function and the gradient, by caching both.

+
+
Parameters
+

v (jax._src.numpy.lax_numpy.ndarray) – input variational parameters for the site tensors of +the iPEPS

+
+
Returns
+

gradient of the iPEPS with respect to the input parameters v

+
+
Return type
+

ndarray

+
+
+
+ +
+
+out(v)[source]
+

Computes the objective function (energy) of the iPEPS

+

Since many optimizers make separate calls to the objective function +and the gradient, but usually require both results for any given +parameter vector v, this function calls the gradient as well.

+
+
Parameters
+

v – input variational parameters for the site tensors of +the iPEPS

+
+
Returns
+

energy of the iPEPS at the point v in parameter space

+
+
+
+ +
+
+fun
+

Objective function - CTM iterations until convergence +followed by the evaluation of the energy

+
+ +
+
+property gradnrm
+

Norm of the gradient

+
+ +
+
+peps
+

iPEPS object

+
+ +
+ +
+
+run(config_file)[source]
+

Start the simulation

+
+
Parameters
+

config_file (str) – filename of the configuration file

+
+
+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/generated/adpeps.utils.ctmtensors.html b/docs/generated/adpeps.utils.ctmtensors.html new file mode 100644 index 0000000..14279de --- /dev/null +++ b/docs/generated/adpeps.utils.ctmtensors.html @@ -0,0 +1,397 @@ + + + + + + + + adpeps.utils.ctmtensors — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.utils.ctmtensors

+

Contains utility class that contains all iPEPS tensors

+
+
+class CTMTensors(A, Ad, Cs=<factory>, Ts=<factory>, B=None, Bd=None, B_Cs=None, B_Ts=None, Bd_Cs=None, Bd_Ts=None, BB_Cs=None, BB_Ts=None, Pl=None, Pr=None, Pt=None, Pb=None, Plb=None, Prb=None, Ptb=None, Pbb=None, observables=<factory>)[source]
+

This is a utility class that contains all tensors related to an iPEPS. +In effect, this forms a representation of the full state, including +the site tensors with variational parameters, the boundary tensors +generated by CTM and the projectors.

+

There are several fields of this dataclass that are generated +automatically, which provide convenient wrappers for the tensors.

+

For example, the CTMTensors.A field returns the site tensors +(contained in a adpeps.utils.tlist.TList)

+
+
Parameters
+
    +

  • A (adpeps.utils.tlist.TList) –

    • +

  • Ad (adpeps.utils.tlist.TList) –

    • +

  • Cs (List[adpeps.utils.tlist.TList]) –

    • +

  • Ts (List[adpeps.utils.tlist.TList]) –

    • +

  • B (adpeps.utils.tlist.TList) –

    • +

  • Bd (adpeps.utils.tlist.TList) –

    • +

  • B_Cs (List[adpeps.utils.tlist.TList]) –

    • +

  • B_Ts (List[adpeps.utils.tlist.TList]) –

    • +

  • Bd_Cs (List[adpeps.utils.tlist.TList]) –

    • +

  • Bd_Ts (List[adpeps.utils.tlist.TList]) –

    • +

  • BB_Cs (List[adpeps.utils.tlist.TList]) –

    • +

  • BB_Ts (List[adpeps.utils.tlist.TList]) –

    • +

  • Pl (adpeps.utils.tlist.TList) –

    • +

  • Pr (adpeps.utils.tlist.TList) –

    • +

  • Pt (adpeps.utils.tlist.TList) –

    • +

  • Pb (adpeps.utils.tlist.TList) –

    • +

  • Plb (adpeps.utils.tlist.TList) –

    • +

  • Prb (adpeps.utils.tlist.TList) –

    • +

  • Ptb (adpeps.utils.tlist.TList) –

    • +

  • Pbb (adpeps.utils.tlist.TList) –

    • +

  • observables (List) –

    • +
+
+
Return type
+

None

+
+
+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/generated/adpeps.utils.empty_tensor.html b/docs/generated/adpeps.utils.empty_tensor.html new file mode 100644 index 0000000..6efd574 --- /dev/null +++ b/docs/generated/adpeps.utils.empty_tensor.html @@ -0,0 +1,354 @@ + + + + + + + + adpeps.utils.empty_tensor — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.utils.empty_tensor

+

Contains utility class that represents a ‘zero’ (empty) tensor object

+
+
+class EmptyT[source]
+

Empty tensor utility class, which can be used to represent a +‘zero’ tensor.

+

The operations involving this type of tensor will return the expected +results, such as (Tensor * EmptyT -> EmptyT), removing the need for +checking if a tensor is empty in the part of the code where the +operation is called.

+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/generated/adpeps.utils.html b/docs/generated/adpeps.utils.html new file mode 100644 index 0000000..461583c --- /dev/null +++ b/docs/generated/adpeps.utils.html @@ -0,0 +1,394 @@ + + + + + + + + adpeps.utils — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ +
+ On this page +
+ + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.utils

+
+

Modules

+

Utilities module with several convenience functions and classes +used during the simulations

+ ++++ + + + + + + + + + + + + + + + + + + + + +

adpeps.utils.ctmtensors

Contains utility class that contains all iPEPS tensors

adpeps.utils.empty_tensor

Contains utility class that represents a ‘zero’ (empty) tensor object

adpeps.utils.io

IO module with convenience function for forming the localized filenames and foldernames of the relevant configuration files and data files.

adpeps.utils.nested

Contains utility class that represents a collection of tensors of different types, with operations that can be applied to all contained tensors at once

adpeps.utils.printing

Utility module for printing output depending on the verbosity setting adpeps.ipeps.config.disp_level in the configuration file.

adpeps.utils.tlist

List object with additional features, used for storing the iPEPS tensors

+
+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/generated/adpeps.utils.io.html b/docs/generated/adpeps.utils.io.html new file mode 100644 index 0000000..77201ad --- /dev/null +++ b/docs/generated/adpeps.utils.io.html @@ -0,0 +1,357 @@ + + + + + + + + adpeps.utils.io — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.utils.io

+

IO module with convenience function for forming the localized filenames +and foldernames of the relevant configuration files and data files.

+
+

Note

+

The input configuration file location can be set via the +CONFIGDIR variable. If it is not set, the default +input folder will be the examples subfolder of the package +root directory

+
+
+

Note

+

The output data location can be set via the DATADIR +variable. If it is not set, the default output folder will be +in the simulations subfolder of the package root directory.

+
+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/generated/adpeps.utils.nested.html b/docs/generated/adpeps.utils.nested.html new file mode 100644 index 0000000..892d7d2 --- /dev/null +++ b/docs/generated/adpeps.utils.nested.html @@ -0,0 +1,419 @@ + + + + + + + + adpeps.utils.nested — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.utils.nested

+

Contains utility class that represents a collection of tensors of +different types, with operations that can be applied to all +contained tensors at once

+
+
+class Nested(tensors)[source]
+

This is a helper class for the efficient contraction of variants of tensors, +used in the energy evaluation of excited states

+

A Nested tensor contains the following variants (some may be empty):

+
+
    +

  • tensors[0]: regular tensor (no B or Bd)

    • +

  • tensors[1]: (terms with) a single B tensor

    • +

  • tensors[2]: (terms with) a single Bd tensor

    • +

  • tensors[3]: (terms with) both a B and a Bd tensor

    • +
+
+

When two Nested tensors x,y are contracted, all combinations are taken into account +and the result is again a Nested tensor, filled with the following variants:

+
+
    +

  • tensors[0]: x[0] * y[0]

    • +

  • tensors[1]: x[1] * y[0] + x[0] * y[1]

    • +

  • tensors[2]: x[2] * y[0] + x[0] * y[2]

    • +

  • tensors[3]: x[3] * y[0] + x[2] * y[1] + x[1] * y[2] + x[0] * y[3]

    • +
+
+

By using Nested tensors in a (large) contraction, the many different terms are +resummed on the fly, leading to a potentially reduced computational cost

+
+

Note

+

Most implented functions act as wrappers for the corresponding numpy functions +on the individual tensors

+
+
+
+mult(other, *args)[source]
+
+
Parameters
+
    +

  • other (Union[np.ndarray, Nested, EmptyT]) – other tensor-like object to contract with

    • +

  • *args – arguments to be passed to the contraction method +(np.tensordot)

    • +
+
+
Returns
+

result of the contraction

+
+
Return type
+

res

+
+
Return type
+

Nested

+
+
+
+ +
+
+normalize()[source]
+

Normalize the contained tensors by the largest value +of the first element of self.tensors

+
+ +
+
+transpose(*args)[source]
+

Applies transpose to each contained tensor

+
+
Return type
+

Nested

+
+
+
+ +
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/generated/adpeps.utils.printing.html b/docs/generated/adpeps.utils.printing.html new file mode 100644 index 0000000..9d2114f --- /dev/null +++ b/docs/generated/adpeps.utils.printing.html @@ -0,0 +1,361 @@ + + + + + + + + adpeps.utils.printing — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.utils.printing

+

Utility module for printing output depending on the verbosity setting +adpeps.ipeps.config.disp_level in the configuration file.

+
+
+print(*args, level=None, **kwargs)[source]
+

Print output using builtin print if level +<= adpeps.ipeps.config.disp_level

+
+
Parameters
+
    +

  • *args – arbitraty arguments to be passed to builtin print

    • +

  • level (Optional[int]) – verbosity level, determining at which verbosity setting this +should be printed

    • +

  • **kwargs – arbitraty keyword arguments for builtin print

    • +
+
+
+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/generated/adpeps.utils.tlist.html b/docs/generated/adpeps.utils.tlist.html new file mode 100644 index 0000000..1b7d9a5 --- /dev/null +++ b/docs/generated/adpeps.utils.tlist.html @@ -0,0 +1,421 @@ + + + + + + + + adpeps.utils.tlist — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.utils.tlist

+

List object with additional features, used for storing +the iPEPS tensors

+

Items in the list can be accessed by either a linear index +or a (i,j) double index, where i and j will be automatically +taken modulo the unit cell size (i.e. i = i % n_x)

+

Additionally, convenience functions that work on tensors can +be defined for the whole list, e.g. conj()

+
+
+cur_loc(*loc)[source]
+

Shift the locations of the tensors relative to a +new zero (loc) while in this context

+
+
Parameters
+

loc (int) – shifts (x,y)

+
+
+

Example

+
>>> l = TList([[1,2], [3,4]])
+>>> l[0,0]
+1
+>>> with cur_loc(1,0):
+>>>     l[0,0]
+2
+>>>     l[0,1]
+4
+>>> l[0,0]
+1
+
+
+

Note that this applies to ALL TList objects while +inside the context

+
+ +
+
+hold_write(*lists)[source]
+

Hold off on writing to the list while +inside the context

+
+
Parameters
+

lists (adpeps.utils.tlist.TList) – one or more TList objects that should have the writing +action delayed until the context is disabled

+
+
+

Example

+
>>> l = TList([[1,2], [3,4]])
+>>> with hold_write(l):
+>>>    l[0,0] = 100
+>>>    l[0,0]
+1
+>>> l[0,0]
+100
+
+
+
+ +
+
+set_pattern(pattern)[source]
+

Set pattern for all new TLists that are created while +the context is active

+
+
Parameters
+

pattern –

+
+
+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/genindex.html b/docs/genindex.html new file mode 100644 index 0000000..9b475ca --- /dev/null +++ b/docs/genindex.html @@ -0,0 +1,816 @@ + + + + + + + + Index — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ + +

Index

+ +
+ A + | B + | C + | D + | E + | F + | G + | H + | I + | J + | L + | M + | N + | O + | P + | R + | S + | T + | U + +
+

A

+ + + +
    +
  • + adpeps.ipeps.config + +
    • +
  • + adpeps.ipeps.ctm + +
    • +
  • + adpeps.ipeps.ipeps + +
    • +
  • + adpeps.ipeps.ipeps.evaluation + +
    • +
  • + adpeps.ipeps.models + +
    • +
  • + adpeps.ipeps.models.common + +
    • +
  • + adpeps.ipeps.models.heisenberg + +
    • +
  • + adpeps.simulation + +
    • +
  • + adpeps.simulation.run_ipeps_exci + +
    • +
    +
  • + adpeps.simulation.run_ipeps_gs + +
    • +
  • + adpeps.utils + +
    • +
  • + adpeps.utils.ctmtensors + +
    • +
  • + adpeps.utils.empty_tensor + +
    • +
  • + adpeps.utils.io + +
    • +
  • + adpeps.utils.nested + +
    • +
  • + adpeps.utils.printing + +
    • +
  • + adpeps.utils.tlist + +
    • +
+ +

B

+ + +
+ +

C

+ + + +
+ +

D

+ + + +
+ +

E

+ + +
+ +

F

+ + + +
+ +

G

+ + + +
+ +

H

+ + +
+ +

I

+ + + +
+ +

J

+ + +
+ +

L

+ + +
+ +

M

+ + + +
+ +

N

+ + + +
+ +

O

+ + + +
+ +

P

+ + + +
+ +

R

+ + + +
+ +

S

+ + + +
+ +

T

+ + +
+ +

U

+ + +
+ + + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/index.html b/docs/index.html new file mode 100644 index 0000000..1cac0da --- /dev/null +++ b/docs/index.html @@ -0,0 +1,438 @@ + + + + + + + + AD-PEPS’s documentation — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ +
+ On this page +
+ + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

AD-PEPS’s documentation

+

The AD-PEPS Python package is intended as a example of an implementation of iPEPS ground-state and excited-state algorithms using Automatic Differentiation, as described in <paper> +As such, the code is meant to illustrate the workings of the algorithms described the paper. +For real applications, this code would likely need to be further adapted and optimized, however the package is a complete implementation and can directly be used for simple calculations.

+
+ +
+
+

Reference

+ ++++ + + + + + + + + + + + + + + + + + + + + +

ipeps.ipeps

iPEPS module for optimization with CTM

ipeps.config

Configuration module for iPEPS simulations

ipeps.ctm

Main CTM code

ipeps.models

Contains all models defined by Hamiltonians as part of this module

simulation

Module with executable scripts for running the simulations

utils

Utilities module with several convenience functions and classes used during the simulations

+
+
+
+

Indices and tables

+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/ipeps.html b/docs/ipeps.html new file mode 100644 index 0000000..d2bb43e --- /dev/null +++ b/docs/ipeps.html @@ -0,0 +1,364 @@ + + + + + + + + adpeps.ipeps — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.ipeps

+
+
+ ++++ + + + + + +

adpeps.ipeps.config

Configuration module for iPEPS simulations

+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/notes/example.html b/docs/notes/example.html new file mode 100644 index 0000000..ed9e92a --- /dev/null +++ b/docs/notes/example.html @@ -0,0 +1,469 @@ + + + + + + + + Example: ground state — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

Example: ground state

+

The package includes an example configuration for a ground-state simulation of the 2D Heisenberg model, defined by the Hamiltonian

+
+\[H = J \sum_i S_i \cdot S_{i+1}~.\]
+

The configuration file examples/heis_D2.yaml contains the following:

+
# Base configuration file for iPEPS simulation
+# See the individual config modules for more information
+
+# Simulation options
+# -> ipeps/config.py
+D:             2
+chi:           41
+model:         'heisenberg'
+
+# (Ground state) Optimizer
+method:        'L-BFGS-B'
+
+# If an existing state is loaded in the model initialization, 
+# the seed controls the random (small) noise that is added to 
+# the site tensors
+seed:          1
+
+# Prefix for output file
+out_prefix:
+
+# Resume earlier simulation if found
+resume:        True
+
+model_params:
+  J:           1
+
+# Set to 0 to suppress all output besides printing each step
+disp_level:    2
+
+# CTM convergence criterium (singular values norm difference)
+ctm_conv_tol:  1.e-6
+
+# Minimal number of CTM steps
+ctm_min_iter:  4
+
+# Maximal number of CTM steps
+ctm_max_iter:  8
+
+# Flush output (prints with print(*args, flush=True))
+flush_output:  True
+
+# Unit cell pattern (Neel order)
+pattern:
+  [
+    [0,1],
+    [1,0],
+  ]
+
+
+

This configures a simulation with bond dimension D=2 and boundary bond dimension chi=40, using the model defined in adpeps.ipeps.models.heisenberg.

+

Now the simulation can be started by calling the adpeps module with the name of this configuration file:

+
>>> python -m adpeps gs 'heis_D2'
+WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)
+Namespace(config_file='heis_D2', sim_mode='gs', version=False)
+Running ground-state sim
+...
+
+
+

The simulation will continue to run and you should see output similar to this:

+
...
+Performing CTM pre-steps without tracking
+  | CTM step 1 conv: 4.935e-03 time: 3.17 obj: -0.658758
+  | CTM step 2 conv: 7.918e-04 time: 3.74 obj: -0.659550
+  | CTM step 3 conv: 1.234e-05 time: 6.42 obj: -0.659562
+Performing CTM
+  | CTM step 1 conv: 3.171e-07 time: 8.8 obj: -0.659563
+  | CTM step 2 conv: 2.108e-08 time: 4.07 obj: -0.659563
+  | CTM step 3 conv: 8.173e-09 time: 2.93 obj: -0.659563
+Energy: -0.6595625579862193
+...
+
+
+

The first cycle of iterations are not taken into account in the gradient computation, but make sure that the CTM iterations with gradient tracking start from some reasonably converged boundary tensors in order to avoid instabilities with initial CTM steps.

+
+

Note

+

The convergence rate of the CTM depends on the variational parameters of the iPEPS and the settings of the simulation. +Generally the convergence improves as the simulation approaches the optimum.

+
+

Whenever a step in the optimization has completed (this could take more than one cycle of CTM iterations depending on the type of optimizer), the module will output a summary of the steps so far:

+
...
+# ======================== #
+#      Step completed      #
+# ======================== #
+
+Step   0  E: -0.376468389894  |grad|: 1.2103482
+Step   1  E: -0.505252956403  |grad|: 0.19064889
+Step   2  E: -0.517432085607  |grad|: 0.10910666
+Step   3  E: -0.578045570568  |grad|: 0.081472534
+Step   4  E: -0.589074339197  |grad|: 0.089438567
+Step   5  E: -0.597590746400  |grad|: 0.15282526
+Step   6  E: -0.612205652457  |grad|: 0.076385807
+Step   7  E: -0.628079118387  |grad|: 0.0684857
+Step   8  E: -0.642200026835  |grad|: 0.097849544
+Step   9  E: -0.649553574703  |grad|: 0.066648727
+Step  10  E: -0.653909263824  |grad|: 0.0264237
+Step  11  E: -0.655389076620  |grad|: 0.016836624
+Step  12  E: -0.656585389308  |grad|: 0.016954703
+Step  13  E: -0.657797020335  |grad|: 0.020011479
+Step  14  E: -0.658174755217  |grad|: 0.033691114
+Step  15  E: -0.659083649568  |grad|: 0.012202327
+Step  16  E: -0.659365377610  |grad|: 0.0064214407
+Step  17  E: -0.659562557986  |grad|: 0.007503111
+...
+
+
+

The simulation will continue until adpeps.ipeps.config.max_iterations has been reached. +At any point the simulation can be stopped and continued later by restarting the module.

+
+

Note

+

In case you would like the simulation to continue from an earlier saved simulation with the same configuration file, make sure to set adpeps.ipeps.config.resume = True

+
+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/notes/example2.html b/docs/notes/example2.html new file mode 100644 index 0000000..92c1eec --- /dev/null +++ b/docs/notes/example2.html @@ -0,0 +1,485 @@ + + + + + + + + Example: excitations — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

Example: excitations

+
+

Note

+

This example continues from the ground-state example and requires an optimized ground state to start from.

+
+

Here we demonstrates how to use the adpeps package for computing excited states of the 2D Heisenberg model.

+

The configuration file examples/heis_D2_exci.yaml contains the following settings:

+
# Base configuration file for iPEPS simulation
+# See the individual config modules for more information
+
+# Simulation options
+# -> ipeps/config.py
+D:             2
+chi:           40
+model:         'heisenberg'
+
+# Prefix for output file
+out_prefix:
+
+# Resume earlier simulation if found
+resume:        True
+
+model_params:
+  J:           1
+
+# Set to 0 to suppress all output besides printing each step
+disp_level:    1
+
+# CTM convergence criterium (singular values norm difference)
+ctm_conv_tol:  1.e-6
+
+# Minimal number of CTM steps
+ctm_min_iter:  4
+
+# Maximal number of CTM steps
+ctm_max_iter:  20
+
+# Flush output (prints with print(*args, flush=True))
+flush_output:  True
+
+# Unit cell pattern (Neel order)
+pattern:
+  [
+    [0,1],
+    [1,0],
+  ]
+
+# Excitations
+momentum_path: 'Bril1'
+
+
+

Note that many of the options are the same as for the ground-state simulation, with the addition of the adpeps.ipeps.config.momentum_path setting, which controls which path through the Brillouin zone will be taken.

+

In the configuration for excited states you do not explicitly set the momentum, but choose a preset path of points in momentum space and pass the index for each simulation.

+

If we now start the simulation, we get the following response:

+
>>> python -m adpeps exci 'heis_D2_exci' --p_ix=1
+...
+Running excited-state sim
+...
+Base file .../exci/heisenberg_D2_X40.base.npz not found.
+Prepare the simulation first by running with option '-i'
+
+
+

What happened is that we first need to make some preparations for the simulation. +For excited-state simulations, we require the following:

+
+
    +

  1. Well-converged CTM boundary tensors

    2. +

  2. A basis for the excited-state tensors, orthogonal to the ground state

    3. +
+
+

The preparations for the simulation need to be performed only once, resulting in a base simulation file that will be used by the simulations for every momentum.

+
>>> python -m adpeps exci 'heis_D2_exci' -i
+...
+Running excited-state sim
+...
+  | CTM step 1 conv: 1.036e-01 time: 3.64 obj: -0.665574
+  | CTM step 2 conv: 3.137e-03 time: 4.23 obj: -0.662436
+  | CTM step 3 conv: 7.887e-05 time: 4.0 obj: -0.662515
+  | CTM step 4 conv: 1.388e-06 time: 2.2 obj: -0.662514
+  | CTM step 5 conv: 2.455e-07 time: 1.35 obj: -0.662514
+  | CTM step 6 conv: 3.044e-08 time: 1.35 obj: -0.662514
+  | CTM step 7 conv: 4.673e-09 time: 1.37 obj: -0.662514
+  | CTM step 8 conv: 4.467e-10 time: 1.36 obj: -0.662514
+  | CTM step 9 conv: 5.029e-11 time: 1.35 obj: -0.662514
+  | CTM step 10 conv: 5.612e-11 time: 1.38 obj: -0.662514
+  | CTM step 11 conv: 2.801e-11 time: 1.36 obj: -0.662514
+  | CTM step 12 conv: 1.204e-11 time: 1.65 obj: -0.662514
+  | CTM step 13 conv: 4.936e-12 time: 1.42 obj: -0.662514
+  | CTM step 14 conv: 1.989e-12 time: 1.39 obj: -0.662514
+GS norm 3.5890188873039093
+GS norm 1.0
+Substracting -0.33125703308289145 from Hamiltonian
+
+
+

Several steps have been performed: first a full CTM contraction of the ground-state network, followed by a normalization of the ground-state tensors. +Then the Hamiltonian is shifted by the ground-state energy expectation value, in order for the excitations to have energies relative to the ground state. +Finally, the basis is prepared and we have everything to get started.

+
>>> python -m adpeps exci 'heis_D2_exci' --p_ix=0
+...
+Running excited-state sim
+...
+Starting simulation of basis vector 1/62
+Performing CTM
+  | CTM step 1 conv: 4.236e+00 time: 3.19 obj: 5.173629
+  | CTM step 2 conv: 3.539e-02 time: 1.38 obj: 5.138237
+  | CTM step 3 conv: 6.139e-03 time: 1.27 obj: 5.132099
+  | CTM step 4 conv: 2.116e-04 time: 1.24 obj: 5.132310
+  | CTM step 5 conv: 6.148e-05 time: 1.28 obj: 5.132249
+  | CTM step 6 conv: 3.704e-04 time: 1.25 obj: 5.131879
+  | CTM step 7 conv: 2.493e-04 time: 1.25 obj: 5.131629
+Energies: 0.04418993415167889 1.5450126399606245e-10
+Norm: 0.008611083119254162
+==========
+Finished basis vector 1/62
+-
+Starting simulation of basis vector 2/62
+Performing CTM
+  | CTM step 1 conv: 2.004e+00 time: 0.99 obj: 3.335621
+  | CTM step 2 conv: 6.150e-02 time: 1.26 obj: 3.397117
+  | CTM step 3 conv: 2.017e-02 time: 1.28 obj: 3.376950
+  | CTM step 4 conv: 3.838e-03 time: 1.26 obj: 3.380788
+  | CTM step 5 conv: 3.650e-04 time: 1.3 obj: 3.380423
+  | CTM step 6 conv: 1.246e-03 time: 1.29 obj: 3.381669
+  | CTM step 7 conv: 1.288e-03 time: 1.31 obj: 3.380380
+Energies: 0.4285335373465171 1.5450126399606245e-10
+Norm: 0.12679967208649232
+==========
+Finished basis vector 2/62
+...
+
+
+

In this version of the algorithm, the full energy and norm overlap matrices will be computed. +Each of the basis vectors, as seen in the output above, is used as input in a separate CTM summation and the program will continue to run until all basis vectors have been used.

+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/notes/install.html b/docs/notes/install.html new file mode 100644 index 0000000..3282054 --- /dev/null +++ b/docs/notes/install.html @@ -0,0 +1,388 @@ + + + + + + + + Installation — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
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+
+ + + + +
+ + +
+ +
+ On this page +
+ + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

Installation

+

The quickest way of installing the adpeps package is to clone the repository

+
git clone <repo>
+
+
+ +
+

Method 2: pip

+

The package can also be installed via pip:

+
cd ad-peps
+pip install -e .
+
+
+
+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/notes/start.html b/docs/notes/start.html new file mode 100644 index 0000000..6eeb332 --- /dev/null +++ b/docs/notes/start.html @@ -0,0 +1,453 @@ + + + + + + + + Getting Started — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ +
+ On this page +
+ + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

Getting Started

+
+

General

+

The main starting point for running simulations with the adpeps package is by loading the module directly via python -m adpeps.

+

For both ground-state and excited-state simulations the configuration can be set via configuration .yaml files. +Each option in the configuration file corresponds to an attribute of the adpeps.ipeps.config module.

+

The first argument for the module is the simulation mode (ground-state or excited-state):

+
python -m adpeps {gs,exci} ...
+
+
+
+

Note

+

The input configuration file location can be set via the +CONFIGDIR variable. If it is not set, the default +input folder will be the examples subfolder of the package +root directory

+
+
+

Note

+

The output data location can be set via the DATADIR +variable. If it is not set, the default output folder will be +in the simulations subfolder of the package root directory.

+
+
+
+

Ground states

+

For ground-state simulations, the only required argument is the configuration file.

+
usage: python -m adpeps gs [-h] config_file
+
+
+
+

Positional Arguments

+
+
config_file
+

Configuration (.yml) file for the simulation options

+
+
+
+
+
+

Excited states

+

For excited-state simulations, the first argument is again the name of a configuration file (note that the relevant options are different for excited-state simulations), and furthermore the momentum index -p is required.

+

The momentum index refers to a point in momentum space \((k_x, k_y)\) defined in a specific path through the Brillouin zone. +The corresponding momentum path can be set via the adpeps.ipeps.config.momentum_path option. +By default, the ‘Bril1’ path is taken, which follows the cut along high symmetry points \((\pi,0) - (\pi,\pi) - (\pi/2,\pi/2) - (0,0) - (\pi,0) - (\pi/2,\pi/2)\)

+
usage: python -m adpeps exci [-h] [-p MOMENTUM_IX] [-e] [-i]
+                             config_file
+
+
+
+

Positional Arguments

+
+
config_file
+

config file of excited-state simulation

+
+
+
+
+

Named Arguments

+
+
-p, --p_ix
+

momentum index

+
+
-e, --eval
+

Prepare excitation base

+
+
-i, --init
+

Prepare excitation base

+
+
+
+
+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
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+
+ + \ No newline at end of file diff --git a/docs/objects.inv b/docs/objects.inv new file mode 100644 index 0000000000000000000000000000000000000000..36defe275d4427b585270567c7b705d79d40f8f6 GIT binary patch literal 1350 zcmV-M1-beoAX9K?X>NERX>N99Zgg*Qc_4OWa&u{KZXhxWBOp+6Z)#;@bUGkGL@iK7 zP*VycAXa5^b7^mGIv@%oAXI2&AaZ4GVQFq;WpW^IW*~HEX>%ZEX>4U6X>%ZBZ*6dL zWpi_7WFU2OX>MmAdTeQ8E(&Jf>Fh zctk-@DYKv>5}Axh%$ccD4o8SI=L4@znX1}WwT(p7N~Aft$&QE5dr6|p9&1V~#82eoA!q}zOHrQyI%ad^%$=Uo{Groq$# z;;;E^zPtUP3b*to z4zjM?lEeM1T%~(utrEziZ4JiZU?ZV4E6P|btEw2J0-Cs1-ypL}oA|_tz8HaH`DKKS z=A#ielD{-arA4&KdmQELZ@3rN{$kEO{~J8{{4X3SuiFFwkL|}`G_dEV=NH8JIxu+? zAYD#bx9e+}Q_TQ%IAZY!#(7Mhbhl?P5_}q@C?ir6WP$O|SvKsU zi&Xouc4o|xCq`P%jKx^k3Wm+|B3Z3dt}>i;1M0kKyHfEy{jQmXSVYr2U-XZ(HzVQX z_Q>SzfEb%U=5F5Gk7Qn=C6ICJ9L_&Dgn@neLZff{sddT-7vrF zl8=OCl0c3X)Hx~($)q{KmqS=ZGes0xlS;5jcglJlumUB}tq?H}(z-|rfk6mV0KxBvhE literal 0 HcmV?d00001 diff --git a/docs/py-modindex.html b/docs/py-modindex.html new file mode 100644 index 0000000..2adebfa --- /dev/null +++ b/docs/py-modindex.html @@ -0,0 +1,454 @@ + + + + + + + + Python Module Index — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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Python Module Index

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+ a
+ adpeps +
    + adpeps.ipeps.config +
    + adpeps.ipeps.ctm +
    + adpeps.ipeps.ipeps +
    + adpeps.ipeps.ipeps.evaluation +
    + adpeps.ipeps.models +
    + adpeps.ipeps.models.common +
    + adpeps.ipeps.models.heisenberg +
    + adpeps.simulation +
    + adpeps.simulation.run_ipeps_exci +
    + adpeps.simulation.run_ipeps_gs +
    + adpeps.utils +
    + adpeps.utils.ctmtensors +
    + adpeps.utils.empty_tensor +
    + adpeps.utils.io +
    + adpeps.utils.nested +
    + adpeps.utils.printing +
    + adpeps.utils.tlist +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
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+Created using Sphinx 3.5.4.
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+# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done. +config: b36c6381b860d3fa6d2a0c9c335cb328 +tags: 645f666f9bcd5a90fca523b33c5a78b7 diff --git a/docs/source/_build/html/_modules/adpeps/ipeps/config.html b/docs/source/_build/html/_modules/adpeps/ipeps/config.html new file mode 100644 index 0000000..f468630 --- /dev/null +++ b/docs/source/_build/html/_modules/adpeps/ipeps/config.html @@ -0,0 +1,474 @@ + + + + + + + + adpeps.ipeps.config — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +

Source code for adpeps.ipeps.config

+""" Configuration module for iPEPS simulations 
+
+    These settings will be loaded from a configuration file :code:`.yml` file 
+    via the :meth:`from_dict` function
+"""
+
+from typing import Union, Iterable
+import numpy as np
+import math
+import os
+
+D: int                         = None
+""" iPEPS bond dimension """
+
+chi: int                       = None
+""" CTM boundary bond dimension """
+
+model: str                     = None
+""" Model """
+
+model_params: dict             = None
+""" Model parameters """
+
+method: str                    = None
+""" Optimization method """
+
+seed: int                      = 1
+""" Random seed for initial state """
+
+resume: bool                   = False
+""" Resume earlier simulation if found """
+
+base_sim: Union[str, None]     = None
+""" Base simulation """
+
+load_sim: bool                 = None
+""" Load previous (Python) simulation """
+
+max_iterations: int            = 100
+""" Maximum number of optimizer iterations """
+
+disp_level: int                = 1
+""" Display level (`0`: no output) """
+
+pattern: Union[Iterable, None] = None
+""" Unit cell configuration
+    Defined as a 2-D array of integers that label the unique sites in the unit 
+    cell.
+    
+    Example:
+        A 2x2 unit cell with a [AB, BA]-type pattern is defined by
+
+        .. code-block:: python
+
+            pattern            = [
+                [0, 1],
+                [1, 0]
+            ]
+"""
+
+ctm_conv_tol: float            = 1e-10
+""" CTM convergence criterium (singular values norm difference) """
+
+ctm_min_iter: int              = 5
+""" Minimal number of CTM steps """
+
+ctm_max_iter: int              = 20
+""" Maximal number of CTM steps """
+
+flush_output: bool             = False
+""" Passes the :code:`flush    = True` argument to the builtin :code:`print` function
+    when calling the :func:`adpeps.utils.printing.print` function
+
+    Useful when deploying the code to computing clusters and capturing the output 
+    into text files
+"""
+
+out_prefix: str                = ''
+""" Optional prefix for the output file of the simulation
+    
+    Example:
+        :code:`.../{model}_D{D}_X{chi}.npz`
+
+        becomes
+
+        :code:`.../{out_prefix}_{model}_D{D}_X{chi}.npz`
+"""
+
+# Excitation settings
+
+px: float                      = 0 * math.pi
+
+py: float                      = 0 * math.pi
+
+momentum_path: str             = 'Bril1'
+""" Momentum path through the BZ """
+
+filter_null: bool              = False
+
+
[docs]def from_dict(cfg):
+    """ Import config from configuration (`.yml`) file """
+
+    cfg_vars = globals()
+    for name, value in cfg.items():
+        if name in cfg_vars.keys():
+            cfg_vars[name] = value
+        else:
+            raise ValueError(f"Option {name} = {value} not defined in iPEPS config")
+    try:
+        debug_override = os.environ.get("PY_SIM_DEBUG2")
+        if debug_override is not None and int(debug_override) == 1:
+            print("** Debug mode on (PY_SIM_DEBUG = 1) **")
+            cfg_vars['disp_level'] = 2
+            cfg_vars['use_parallel'] = False
+    except:
+        pass

+
+def get_model_params():
+    if model_params is not None:
+        try:
+            return '_'.join([str(p) for p in model_params.values()]) + '_'
+        except AttributeError:
+            return '_'.join([str(p) for p in model_params]) + '_'
+    else:
+        return ''
+
+ +
+ + +
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+ + + + +
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+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/_modules/adpeps/ipeps/ctm.html b/docs/source/_build/html/_modules/adpeps/ipeps/ctm.html new file mode 100644 index 0000000..489967a --- /dev/null +++ b/docs/source/_build/html/_modules/adpeps/ipeps/ctm.html @@ -0,0 +1,859 @@ + + + + + + + + adpeps.ipeps.ctm — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+ +

Source code for adpeps.ipeps.ctm

+"""
+    Main CTM code
+
+    The individual site and boundary tensors come in a 
+    special list-type object (TList), which has extra 
+    indexing features, such as periodic boundary 
+    conditions and shift contexts
+
+    All ncon contractions are defined in contractions.yaml
+"""
+
+import jax
+import jax.numpy as np
+import time
+from typing import Tuple
+
+import adpeps.ipeps.config as sim_config
+from adpeps.utils.ctmtensors import CTMTensors
+from adpeps.utils.nested import Nested
+from adpeps.utils.tlist import TList, cur_loc, set_pattern
+from adpeps.tensor.contractions import ncon
+from adpeps.tensor.ops import svd, diag_inv
+
+def run_ctm(tensors, chi, conv_fun=None):
+    ctm = CTM(tensors, chi, conv_fun)
+    return ctm()
+
+
[docs]class CTM:
+    """ CTM class """
+
+    def __init__(self, tensors: CTMTensors, chi: int, conv_fun=None):
+        """
+        Args:
+            tensors: input ctmtensors
+            chi: boundary bond dimension
+        """
+
+        self.tensors  = tensors
+        self.chi      = chi
+        self.conv_fun = conv_fun
+        self.tol      = sim_config.ctm_conv_tol # Convergence tolerance (singular values)
+        self.min_iter = sim_config.ctm_min_iter
+        self.max_iter = sim_config.ctm_max_iter
+
+        self.singular_values  = None
+        self.last_convergence = None
+        self.diffs            = [None]
+        self.n_steps          = 0
+        self.last_ctm_time    = None
+        self.convergence      = np.nan
+        self.condition_number = None
+        
+    def __call__(self):
+        while not self.converged:
+            self.show_progress()
+            self.update()
+
+        return self.tensors, self.convergence
+
+
[docs]    def update(self):
+        """ Perform an update of all boundary tensors """
+        start = time.time()
+        self.tensors, s = renormalize(self.tensors, self.chi)
+        end = time.time()
+
+        try:
+            s = jax.lax.stop_gradient(s)
+            s_nz = s[s != 0] / np.max(s)
+            cond_s = np.min(s_nz)
+        except:
+            cond_s = np.nan
+
+        self.n_steps += 1
+        self.singular_values = s
+        self.last_ctm_time = round(end-start, 2)
+        self.condition_number = cond_s

+
+
[docs]    def show_progress(self):
+        """ Print out the current progress """
+        if self.n_steps > 0 and sim_config.disp_level > 0:
+            if self.conv_fun is not None:
+                print(f"  | CTM step {self.n_steps} conv: {self.diffs[-1]:.3e} time: {self.last_ctm_time} obj: {self.convergence:.6f}")
+            else:
+                print(f"  | CTM step {self.n_steps} conv: {self.diffs[-1]:.3e} time: {self.last_ctm_time}")

+
+    @property
+    def converged(self):
+        """ Check convergence with supplied convergence function """
+        if self.conv_fun is not None:
+            s = jax.lax.stop_gradient(self.conv_fun(self.tensors))
+        else:
+            s = self.singular_values
+
+        self.last_convergence = self.convergence
+        self.convergence = s
+        try:
+            diff = np.linalg.norm(self.convergence-self.last_convergence)
+            self.diffs.append(diff)
+        except:
+            diff = np.nan
+
+        if self.n_steps >= self.min_iter and self.diffs[-1] < self.tol:
+            return True
+        elif self.n_steps >= self.max_iter:
+            return True
+        else:
+            return False

+
+
[docs]def renormalize(tensors: CTMTensors, chi: int) -> Tuple[CTMTensors, np.ndarray]:
+    """
+    Performs a CTM iteration
+    Updates all sites in the unit cell
+
+    Args:
+        tensors: input ctmtensors
+        chi: boundary bond dimension
+
+    Returns:
+        A tuple containing
+
+        - **tensors** (*CTMTensors*): updated tensors
+        - **S** (*np.ndarray*): singular values of C1 (for convergence)
+    """
+
+    with set_pattern(tensors.A.pattern):
+        tensors, sl = do_left(tensors, chi)
+        tensors     = do_right(tensors, chi)
+        tensors     = do_top(tensors, chi)
+        tensors     = do_bottom(tensors, chi)
+
+    # Singular values of C1[0,0] - to check for convergence
+    S = sl[0]
+    return (tensors, S)

+
+
+""" 
+    ---------------------
+    Individual left, right, top and bottom moves
+    ---------------------
+
+    Each move consists of a loop through the sites of the unit cell 
+    in which first the projectors are computed and then the boundary 
+    tensors are updated.
+
+    The loops are optimized for readability with a few tricks that are 
+    implemented in the TList or CTMTensors classes:
+
+    - cur_loc(x,y): with this context enabled, all TList objects have a 
+        shift applied in their coordinates.
+        For example:
+
+        A[0,0] = 1
+        A[1,0] = 2
+        with cur_loc(1,0):
+            print(A[0,0]) # => 2 (retrieves element A([0,0]+[1,0]) = A[1,0])
+
+        Using this context, the operations in the inner loops can be written 
+        without reference to the (i,j) loop indices, as if it's just written 
+        for one site in the unit cell.
+
+    - CTMTensors.hold(tensor1, ...): with this context enabled, any values 
+        stored in tensor1 (and other designated tensors) are only put in a 
+        temporary location, so that reading the tensor still yields the 
+        original values. After the context exits, the values will be 
+        overwritten by the temporary values.
+        Example:
+
+        # ts is a CTMTensors object containing site/boundary tensors
+        ts.C1[0,0] = [1]
+        ts.C2[0,0] = [2]
+        with ts.hold('C1'):
+            ts.C1[0,0] = [10]
+            ts.C2[0,0] = [20]
+            print(ts.C1[0,0]) # => [1] since the value [10] is not yet stored
+            print(ts.C2[0,0]) # => [20]
+
+        print(ts.C1[0,0]) # => [10] since the context has exited
+
+        With this context, there is no need to store the updated boundary 
+        tensors in the inner loops in temporary objects (since in CTM each 
+        update step should be performed separately).
+
+    - TList.is_changed(x,y): tracks whether any of the tensors in the TList 
+        have been updated since the last call to TList.reset_changed().
+        This is useful for unit cells with pattern restrictions, so that 
+        boundary tensors that correspond to equivalent sites are only 
+        computed once.
+
+"""
+
+
[docs]def do_left(ts: CTMTensors, chi: int) -> Tuple[CTMTensors, np.ndarray]:
+    """ 
+    Perform left CTM move 
+
+    Args:
+        ts: input tensors
+        chi: boundary bond dimension
+
+    Returns:
+        A tuple containing
+
+        - **tensors** (*CTMTensors*): updated tensors
+        - **sl** (*np.ndarray*): singular values of C1 (for convergence)
+
+    """
+    A = ts.A
+    unit_cell = A.size
+    ts.C1.reset_changed()
+    ts.C4.reset_changed()
+    ts.T4.reset_changed()
+    Pl  = TList(shape=unit_cell) # Upper projectors
+    Plb = TList(shape=unit_cell) # Lower projectors
+    sl  = TList(shape=unit_cell) # Singular values (for convergence check)
+    # Loop over x direction of the unit cell
+    for i in range(A.size[0]): 
+        # Loop over y direction
+        for j in range(A.size[1]): 
+            # Change the relative shift of the lists
+            with cur_loc(i,j): 
+                if not Pl.is_changed(0,1):
+                    Pl[0,1], Plb[0,1], sl[0,1] = get_projectors_left(ts, chi)
+        # Only update the lists after the loop over j is completed
+        with ts.hold('all_C1','all_C4','all_T4'):
+            for j in range(A.size[1]):
+                with cur_loc(i,j):
+                    if not ts.C1.is_changed(0,0):
+                        ts.update(('C1', 'C4', 'T4'), ([0,0],[0,0],[0,0]), renorm_left(ts, Pl, Plb))
+    return ts, sl

+
+
[docs]def do_right(ts: CTMTensors, chi: int) -> CTMTensors:
+    """ 
+    Perform right CTM move 
+
+    Args:
+        ts: input tensors
+        chi: boundary bond dimension
+
+    Returns:
+        ts: updated tensors
+
+    """
+    A = ts.A
+    unit_cell = A.size
+    ts.C2.reset_changed()
+    ts.C3.reset_changed()
+    ts.T2.reset_changed()
+    Pr  = TList(shape=unit_cell)
+    Prb = TList(shape=unit_cell)
+    for i in range(A.size[0]):
+        for j in range(A.size[1]):
+            with cur_loc(i,j):
+                if not Pr.is_changed(0,1):
+                    Pr[0,1], Prb[0,1], _ = get_projectors_right(ts, chi)
+        with ts.hold('all_C2','all_C3','all_T2'):
+            for j in range(A.size[1]):
+                with cur_loc(i,j):
+                    if not ts.C2.is_changed(1,0):
+                        ts.update(('C2', 'C3', 'T2'), ([1,0],[1,0],[1,0]), renorm_right(ts, Pr, Prb))
+    return ts

+
+
[docs]def do_top(ts: CTMTensors, chi: int) -> CTMTensors:
+    """ 
+    Perform top CTM move 
+
+    Args:
+        ts: input tensors
+        chi: boundary bond dimension
+
+    Returns:
+        ts: updated tensors
+
+    """
+    A = ts.A
+    unit_cell = A.size
+    ts.C1.reset_changed()
+    ts.C2.reset_changed()
+    ts.T1.reset_changed()
+    Pt  = TList(shape=unit_cell)
+    Ptb = TList(shape=unit_cell)
+    for j in range(A.size[1]):
+        for i in range(A.size[0]):
+            with cur_loc(i,j):
+                if not Pt.is_changed(0,0):
+                    Pt[0,0], Ptb[0,0], _ = get_projectors_top(ts, chi)
+        with ts.hold('all_C1','all_C2','all_T1'):
+            for i in range(A.size[0]):
+                with cur_loc(i,j):
+                    if not ts.C1.is_changed(-1,0):
+                        ts.update(('C1', 'C2', 'T1'), ([-1,0],[2,0],[0,0]), renorm_top(ts, Pt, Ptb))
+    return ts

+
+
[docs]def do_bottom(ts: CTMTensors, chi: int) -> CTMTensors:
+    """ 
+    Perform bottom CTM move 
+
+    Args:
+        ts: input tensors
+        chi: boundary bond dimension
+
+    Returns:
+        ts: updated tensors
+
+    """
+    A = ts.A
+    unit_cell = A.size
+    ts.C3.reset_changed()
+    ts.C4.reset_changed()
+    ts.T3.reset_changed()
+    Pb  = TList(shape=unit_cell)
+    Pbb = TList(shape=unit_cell)
+    for j in range(A.size[1]):
+        for i in range(A.size[0]):
+            with cur_loc(i,j):
+                if not Pb.is_changed(0,0):
+                    Pb[0,0], Pbb[0,0], _ = get_projectors_bottom(ts, chi)
+        with ts.hold('all_C3','all_C4','all_T3'):
+            for i in range(A.size[0]):
+                with cur_loc(i,j):
+                    if not ts.C3.is_changed(2,1):
+                        ts.update(('C3', 'C4', 'T3'), ([2,1],[-1,1],[0,1]), renorm_bottom(ts, Pb, Pbb))
+    return ts

+
+
+""" 
+    ---------------------
+    Individual left, right, top and bottom projectors
+    ---------------------
+
+    The projectors are computed by contracting a corner of the 
+    system (C-tensor + 2 T-tensors + A and Adagger tensors) 
+    in the top (/left) half with a corner in the bottom (/right) 
+    half and performing an svd
+"""
+
+
[docs]def get_projectors_left(ts: CTMTensors, chi: int
+        ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
+    """ 
+    Returns the left projectors
+    """
+    tensors = (ts.C1[-1,-1],ts.C4[-1,2],ts.T1[0,-1],ts.T3[0,2],ts.T4[-1,0],ts.T4[-1,1],
+            ts.A[0,0], ts.Ad[0,0], ts.A[0,1], ts.Ad[0,1])
+    return _get_projectors_left_impl(*tensors, chi)

+
+def _get_projectors_left_impl(C1,C4,T1,T3,T4u,T4d,Au,Adu,Ad,Add, chi):
+    Cs1 = ncon([C1, T1], 'proj_left_Cs1')
+    Q1  = ncon([Cs1, T4u, Au, Adu], 'proj_left_Q1')
+
+    Cs4 = ncon([C4, T3], 'proj_left_Cs4')
+    Q4  = ncon([Cs4, T4d, Ad, Add], 'proj_left_Q4')
+
+    Q4  = Q4.transpose([3,4,5,0,1,2])
+    return get_projectors(Q1, Q4, chi)
+
+
[docs]def get_projectors_right(ts: CTMTensors, chi: int
+        ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
+    """ 
+    Returns the right projectors
+    """
+    tensors = (ts.C2[2,-1],ts.C3[2,2],ts.T1[1,-1],ts.T2[2,0],ts.T2[2,1],ts.T3[1,2],
+            ts.A[1,0], ts.Ad[1,0], ts.A[1,1], ts.Ad[1,1])
+    return _get_projectors_right_impl(*tensors, chi)

+
+def _get_projectors_right_impl(C2,C3,T1,T2u,T2d,T3,Au,Adu,Ad,Add, chi):
+    Cs2 = ncon([C2, T1], 'proj_right_Cs2')
+    Q2  = ncon([Cs2, T2u, Au, Adu], 'proj_right_Q2')
+
+    Cs3 = ncon([C3, T3], 'proj_right_Cs3')
+    Q3  = ncon([Cs3, T2d, Ad, Add], 'proj_right_Q3')
+
+    Q3  = Q3.transpose([3,4,5,0,1,2])
+    return get_projectors(Q2, Q3, chi)
+
+
[docs]def get_projectors_top(ts: CTMTensors, chi: int
+        ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
+    """ 
+    Returns the top projectors
+    """
+    tensors = (ts.C1[-1,-1],ts.C2[2,-1],ts.T1[0,-1],ts.T1[1,-1],ts.T2[2,0],ts.T4[-1,0],
+            ts.A[0,0], ts.Ad[0,0], ts.A[1,0], ts.Ad[1,0])
+    return _get_projectors_top_impl(*tensors, chi)

+
+def _get_projectors_top_impl(C1,C2,T1l,T1r,T2,T4,Al,Adl,Ar,Adr, chi):
+    Cs1 = ncon([C1, T4], 'proj_top_Cs1')
+    Q1  = ncon([Cs1, T1l, Al, Adl], 'proj_top_Q1')
+
+    Cs2 = ncon([C2, T2], 'proj_top_Cs2')
+    Q2  = ncon([Cs2, T1r, Ar, Adr], 'proj_top_Q2')
+
+    Q2  = Q2.transpose([3,4,5,0,1,2])
+    return get_projectors(Q1, Q2, chi)
+
+
[docs]def get_projectors_bottom(ts: CTMTensors, chi: int
+        ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
+    """ 
+    Returns the bottom projectors
+    """
+    tensors = (ts.C3[2,2],ts.C4[-1,2],ts.T2[2,1],ts.T3[0,2],ts.T3[1,2],ts.T4[-1,1],
+            ts.A[0,1], ts.Ad[0,1], ts.A[1,1], ts.Ad[1,1])
+    return _get_projectors_bottom_impl(*tensors, chi)

+
+def _get_projectors_bottom_impl(C3,C4,T2,T3l,T3r,T4,Al,Adl,Ar,Adr, chi):
+    Cs4 = ncon([C4, T4], 'proj_bottom_Cs4')
+    Q4  = ncon([Cs4, T3l, Al, Adl], 'proj_bottom_Q4')
+
+    Cs3 = ncon([C3, T2], 'proj_bottom_Cs3')
+    Q3  = ncon([Cs3, T3r, Ar, Adr], 'proj_bottom_Q3')
+
+    Q3  = Q3.transpose([3,4,5,0,1,2])
+    return get_projectors(Q4, Q3, chi)
+
+
[docs]def get_projectors(T1: int, T2, chi):
+    """ Contracts the corners together and computes the 
+        projectors by performing an svd
+    """
+    full_chi = T1.shape[3]*T1.shape[4]*T1.shape[5]
+    new_chi  = min(full_chi, chi)
+
+    Rho       = ncon([T1, T2], ([-1,-2,-3,1,2,3], [1,2,3,-4,-5,-6]))
+    Rho_shape = Rho.shape
+    Rho       = np.reshape(Rho, [Rho_shape[0]*Rho_shape[1]*Rho_shape[2], -1])
+    u,s,v     = svd(Rho, new_chi, 'n')
+    u         = np.reshape(u, [Rho_shape[0], Rho_shape[1], Rho_shape[2], -1])
+    v         = np.reshape(v.T, [Rho_shape[3], Rho_shape[4], Rho_shape[5], -1])
+    inv_s     = diag_inv(np.sqrt(s))
+
+    P1      = ncon([T2, v, inv_s], 'proj_P1')
+    P2      = ncon([T1, u, inv_s], 'proj_P2')
+
+    P1      = P1.transpose([3,0,1,2])
+    P2      = P2.transpose([3,0,1,2])
+    return P1, P2, s

+
+
+""" 
+    ---------------------
+    Individual left, right, top and bottom boundary tensor updates
+    ---------------------
+
+    The boundary tensors are updated for one site at a time from the 
+    tensors of the previous iteration with the site tensors and truncated 
+    by using the projectors
+
+    In these functions, the boundary tensors can be wrapped as Nested tensors, 
+    containing both ground-state and excited-state tensors.
+    When using these Nested tensors, all different combinations are computed 
+    automatically.
+    For example:
+
+        Nested({C1,B_C1,Bd_C1,BB_C1}) * Nested({T1,B_T1,Bd_T1,BB_T1}) ->
+            Nested({
+                (C1 * T1),
+                (B_C1 * T1 + C1 * B_T1),
+                (Bd_C1 * T1 + C1 * Bd_T1),
+                (BB_C1 * T1 + B_C1 * Bd_T1 + Bd_C1 * B_T1 + C1 * BB_T1)
+            })
+
+    The phase shifts are only applied to the B and Bd parts of the Nested tensors
+"""
+
+
[docs]def renorm_left(ts: CTMTensors, Pl: np.ndarray, Plb: np.ndarray
+        ) -> Tuple[Nested, Nested, Nested]:
+    """
+
+    """
+    new_T4 = ncon([Plb[0,0], ts.all_T4[-1,0], ts.all_A[0,0], ts.all_Ad[0,0], Pl[0,1]], 'doleft_T4', 
+            normalize=True).shift(-sim_config.px)
+
+    Cs1    = ncon([ts.all_C1[-1,0], ts.all_T1[0,0]], 'doleft_Cs1')
+    new_C1 = ncon([Cs1, Pl[0,1]], 'doleft_C1', normalize=True).shift(-sim_config.px)
+
+    Cs4    = ncon([ts.all_C4[-1,0], ts.all_T3[0,0]], 'doleft_Cs4')
+    new_C4 = ncon([Cs4, Plb[0,0]], 'doleft_C4', normalize=True).shift(-sim_config.px)
+
+    return new_C1, new_C4, new_T4

+
+def renorm_right(ts, Pr, Prb):
+    new_T2 = ncon([Prb[0,0], ts.all_T2[2,0], ts.all_A[1,0], ts.all_Ad[1,0], Pr[0,1]], 'doright_T2', 
+            normalize=True).shift(sim_config.px)
+
+    Cs2    = ncon([ts.all_C2[2,0], ts.all_T1[1,0]], 'doright_Cs2')
+    new_C2 = ncon([Cs2, Pr[0,1]], 'doright_C2', normalize=True).shift(sim_config.px)
+
+    Cs3    = ncon([ts.all_C3[2,0], ts.all_T3[1,0]], 'doright_Cs3')
+    new_C3 = ncon([Cs3, Prb[0,0]], 'doright_C3', normalize=True).shift(sim_config.px)
+
+    return new_C2, new_C3, new_T2
+
+def renorm_top(ts, Pt, Ptb):
+    new_T1 = ncon([Ptb[-1,0], ts.all_T1[0,-1], ts.all_A[0,0], ts.all_Ad[0,0], Pt[0,0]], 'dotop_T1', 
+            normalize=True).shift(-sim_config.py)
+
+    Cs1    = ncon([ts.all_C1[-1,-1], ts.all_T4[-1,0]], 'dotop_Cs1')
+    new_C1 = ncon([Cs1, Pt[-1,0]], 'dotop_C1', normalize=True).shift(-sim_config.py)
+
+    Cs2    = ncon([ts.all_C2[2,-1], ts.all_T2[2,0]], 'dotop_Cs2')
+    new_C2 = ncon([Cs2, Ptb[1,0]], 'dotop_C2', normalize=True).shift(-sim_config.py)
+
+    return new_C1, new_C2, new_T1
+
+def renorm_bottom(ts, Pb, Pbb):
+    new_T3 = ncon([Pbb[-1,0], ts.all_T3[0,2], ts.all_A[0,1], ts.all_Ad[0,1], Pb[0,0]], 'dobottom_T3', 
+            normalize=True).shift(sim_config.py)
+
+    Cs3    = ncon([ts.all_C3[2,2], ts.all_T2[2,1]], 'dobottom_Cs3')
+    new_C3 = ncon([Cs3, Pbb[1,0]], 'dobottom_C3', normalize=True).shift(sim_config.py)
+
+    Cs4    = ncon([ts.all_C4[-1,2], ts.all_T4[-1,1]], 'dobottom_Cs4')
+    new_C4 = ncon([Cs4, Pb[-1,0]], 'dobottom_C4', normalize=True).shift(sim_config.py)
+
+    return new_C3, new_C4, new_T3
+
+ +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/_modules/adpeps/ipeps/ipeps.html b/docs/source/_build/html/_modules/adpeps/ipeps/ipeps.html new file mode 100644 index 0000000..f0ad27e --- /dev/null +++ b/docs/source/_build/html/_modules/adpeps/ipeps/ipeps.html @@ -0,0 +1,635 @@ + + + + + + + + adpeps.ipeps.ipeps — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+ + + + + + +
+ +
+ +

Source code for adpeps.ipeps.ipeps

+"""
+    iPEPS module for optimization with CTM
+
+    For an example of how to run a simulation see :mod:`adpeps.simulation.run_ipeps_gs`
+
+    The module is initialized from one of the specific 
+    model files, which return the initial boundary and 
+    site tensors
+
+    The list of parameters is set to the elements of the 
+    individual site tensors
+
+    Conventions for indices:
+
+        - Site tensors::
+
+            A: [phys, right, top, left, bottom]
+
+        - Boundary tensors::
+
+            C1: [right, bottom]
+            C2: [left,  bottom]
+            C3: [top,   left]
+            C4: [right, top]
+            T1: [right, left, ket, bra]
+            T2: [top,   bottom, ket, bra]
+            T3: [right, left, ket, bra]
+            T4: [top,   bottom, ket, bra]
+
+
+    Order of boundary tensors::
+
+        C1 - T1 - C2
+        |    |    |
+        T4 - A  - T2
+        |    |    |
+        C4 - T3 - C3
+"""
+
+from functools import partial
+import copy
+
+from jax import random
+import jax
+import jax.numpy as np
+
+from .ctm import run_ctm
+from adpeps.ipeps import evaluation
+from adpeps.ipeps import models
+from adpeps.tensor.contractions import ncon
+from adpeps.utils.ctmtensors import CTMTensors
+from adpeps.utils.printing import print
+from adpeps.utils.tlist import set_pattern, cur_loc, TList
+import adpeps.ipeps.config as sim_config
+
+
[docs]class iPEPS:
+    """ Initialize the iPEPS based on the settings in
+        :mod:`adpeps.ipeps.config`
+    """
+    reinit_env = False
+
+    def __init__(self):
+        # Load model Hamiltonian, observables
+        model = getattr(models, sim_config.model)
+        self.H, self.observables = model.setup()
+
+        # Initialize tensors
+        self.d = self.H.shape[0]
+        A = init_A_tensor(self.d, sim_config.D, sim_config.pattern)
+        A = A.normalize()
+        Ad = A.conj()
+        Cs, Ts = init_ctm_tensors(A, A)
+        self.tensors = CTMTensors(A, Ad, Cs, Ts)
+        self.base_Cs, self.base_Ts = None, None
+
+        # Initialize conv object
+        self.convergence = {}
+
+        self.reinit_env = True
+
+
[docs]    def run(self, params: np.ndarray) -> np.ndarray:
+        """ 
+        Run the simulation
+
+        Args:
+            params: variational parameters
+
+        Returns:
+            energy of iPEPS
+        """
+
+        if params is not None:
+            self.fill(params)
+
+        if self.reinit_env:
+            # Construct new boundary tensors and perform ctm iterations 
+            # until convergence
+            # Note: gradient tracking is disabled for this function, so 
+            # only the ctm steps in the code after this line will be tracked
+            print('Performing CTM pre-steps without tracking')
+            self.converge_boundaries()
+
+        # Perform the ctm routine to obtain updated boundary tensors
+        print('Performing CTM')
+        self.tensors, conv = run_ctm(self.tensors, sim_config.chi, conv_fun=self.compute_energy)
+
+        # Evaluate energy
+        res = self.evaluate()
+
+        # Stop downstream gradient tracking for iPEPS tensors, 
+        # so they become regular arrays that can be saved
+        self.tensors.stop_gradient(only_boundaries=False)
+
+        return res

+
+    def compute_energy(self, tensors):
+        E, _ = evaluation.get_gs_energy(self.H, tensors)
+        return E
+
+
[docs]    def converge_boundaries(self):
+        """ Performs CTM on the boundary tensors until convergence,
+            without gradient tracking 
+        """
+        # Make a non-tracking version of the iPEPS tensors
+        orig_A = copy.deepcopy(self.tensors.A)
+        self.tensors.A = self.tensors.A.stop_gradient()
+        self.tensors.Ad = self.tensors.Ad.stop_gradient()
+
+        # Initialize new boundary tensors
+        Cs, Ts = init_ctm_tensors(self.tensors.A, self.tensors.Ad)
+        self.tensors = CTMTensors(self.tensors.A, self.tensors.Ad, Cs, Ts)
+
+        # Perform CTM update steps on the boundary tensors
+        conv_fun = self.compute_energy
+        self.tensors.stop_gradient()
+        self.tensors, conv = run_ctm(self.tensors, sim_config.chi, conv_fun=conv_fun)
+        self.tensors.stop_gradient()
+
+        self.save_boundary_tensors()
+
+        # Restore the original (tracking) site tensors
+        self.tensors.A = orig_A
+        self.tensors.Ad = orig_A.conj()

+
+    def save_boundary_tensors(self):
+        self.base_Cs = copy.deepcopy(self.tensors.Cs)
+        self.base_Ts = copy.deepcopy(self.tensors.Ts)
+
+    def evaluate(self):
+        E = self.compute_energy(self.tensors)
+        print('Energy:', jax.lax.stop_gradient(E).item())
+        return E
+
+
+    """ Input/output methods """
+
+
[docs]    def numel(self):
+        """ Number of variational parameters """
+        return self.tensors.A.tot_numel()

+    
+
[docs]    def parse_elements(self, elements):
+        """ Returns site tensors filled with the input elements """
+        assert elements.size == self.numel(), f"Size of input vector ({elements.size}) does not \
+                match the number of parameters of the iPEPS ({self.numel()})"
+        return self.tensors.A.fill(elements, self.d, sim_config.D)

+
+
[docs]    def fill(self, A):
+        """ Fill the site tensors with the elements
+            The elements can be specified either as a list of (d,D,D,D,D)-dimensional 
+            arrays or one 1-dimensional array of all elements concatenated
+        """
+        if isinstance(A, np.ndarray) and A.ndim == 1:
+            # Input is vector of elements
+            A               = self.parse_elements(A)
+            self.tensors.A  = A
+            self.tensors.Ad = A.conj()
+        else:
+            # Input is a list of arrays
+            assert len(A) == len(self.tensors.A), "Number of input tensors does not match \
+                    the number of site tensors of the iPEPS"
+            for i in range(len(self.tensors.A)):
+                self.tensors.A._data[i] = A[i]
+                self.tensors.Ad._data[i] = A[i].conj()

+
+
+
[docs]class iPEPS_exci(iPEPS):
+    """ Excited-state variant of the iPEPS class
+    """
+
+    reinit_env = False
+
+    def __init__(self):
+        super().__init__()
+        self.substract_gs_energy()
+
+    def normalize_gs(self):
+        nrm, nrm0, envBs, nrms0 = evaluation.compute_exci_norm(self.tensors)
+        print(f"GS norm {nrms0[0]}", level=1)
+        self.tensors.A._data    = [a/np.sqrt(np.abs(nrms0[i])) for i, a in enumerate(self.tensors.A)]
+        self.tensors.Ad         = self.tensors.A.conj()
+        nrm, nrm0, envBs, nrms0 = evaluation.compute_exci_norm(self.tensors)
+        print(f"GS norm {nrm0}", level=1)
+
+    def substract_gs_energy(self):
+        E, _ = evaluation.get_gs_energy(self.H, self.tensors)
+        E = E/2
+        print(f"Substracting {E} from Hamiltonian", level=1)
+        self.H = self.H - E * np.reshape(np.eye(self.H.shape[0]**2), self.H.shape)
+        # self.H = np.reshape(np.eye(self.H.shape[0]**2), self.H.shape)
+
+    def evaluate(self):
+        E = evaluation.get_all_energy(self.H, self.tensors)
+        nrm, _, envBs, _ = evaluation.compute_exci_norm(self.tensors)
+        print('Energies:', jax.lax.stop_gradient(E[3]), jax.lax.stop_gradient(E[0]), level=0)
+        print('Norm:', jax.lax.stop_gradient(nrm), level=0)
+        return E[3], envBs
+
+    def run_gc(self, *args):
+        res, _ = self.run(*args)
+        return res
+
+    def compute_energy(self, tensors):
+        E = evaluation.get_all_energy(self.H, tensors)
+        nrm, *_ = evaluation.compute_exci_norm(tensors)
+        print('Energies:', jax.lax.stop_gradient(E[3]), jax.lax.stop_gradient(E[0]), level=2)
+        print('Norm:', jax.lax.stop_gradient(nrm), level=2)
+        print('Normalized E:', jax.lax.stop_gradient(E[3])/jax.lax.stop_gradient(nrm), level=2)
+        return E[3] / nrm
+
+    def compute_orth_basis(self):
+        return evaluation.get_orth_basis(self.tensors)
+
+
+    """ Input/output methods """
+
+
[docs]    def fill(self, B):
+        if isinstance(B, np.ndarray) and B.ndim == 1:
+            # Input is vector of elements
+            B               = self.parse_elements(B)
+            self.tensors.B  = B
+            self.tensors.Bd = B.conj()
+        else:
+            for i in range(len(self.tensors.A._data)):
+                self.tensors.B._data[i] = B[i]
+                self.tensors.Bd._data[i] = B[i].conj()

+
+
+
[docs]def init_A_tensor(d, D, pattern):
+    """
+        The elements will be randomized based on sim_config.seed
+    """
+    with set_pattern(pattern):
+        A = TList()
+
+    key = random.PRNGKey(sim_config.seed)
+    for i in range(A.size[0]):
+        for j in range(A.size[1]):
+            with cur_loc(i,j):
+                if not A.is_changed(0,0):
+                    key, subkey = random.split(key)
+                    A[0,0] = random.normal(key, (d,D,D,D,D))
+    return A

+
+
[docs]def init_ctm_tensors(A, Ad):
+    """
+    Returns initital boundary T-tensors based on the unit cell tensors and 
+    empty trivial boundary C-tensors
+    """
+    unit_cell = A.size
+    D         = A[0].shape[1]
+
+    Cs   = [TList(shape=unit_cell, pattern=A.pattern) for _ in range(4)]
+    Ts   = [TList(shape=unit_cell, pattern=A.pattern) for _ in range(4)]
+
+    for i in range(A.size[0]):
+        for j in range(A.size[1]):
+            with cur_loc(i,j):
+                Cs[0][0,0] = np.expand_dims(np.array([1.]), axis=(1))
+                Cs[1][0,0] = np.expand_dims(np.array([1.]), axis=(1))
+                Cs[2][0,0] = np.expand_dims(np.array([1.]), axis=(1))
+                Cs[3][0,0] = np.expand_dims(np.array([1.]), axis=(1))
+                Ts[0][0,0] = np.expand_dims(ncon([A[0,0], Ad[0,0]], ([1,2,3,4,-1], [1,2,3,4,-2])), axis=(0,1))
+                Ts[1][0,0] = np.expand_dims(ncon([A[0,0], Ad[0,0]], ([1,2,3,-1,4], [1,2,3,-2,4])), axis=(0,1))
+                Ts[2][0,0] = np.expand_dims(ncon([A[0,0], Ad[0,0]], ([1,2,-1,3,4], [1,2,-2,3,4])), axis=(0,1))
+                Ts[3][0,0] = np.expand_dims(ncon([A[0,0], Ad[0,0]], ([1,-1,2,3,4], [1,-2,2,3,4])), axis=(0,1))
+    return Cs, Ts

+
+ +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/_modules/adpeps/ipeps/models/heisenberg.html b/docs/source/_build/html/_modules/adpeps/ipeps/models/heisenberg.html new file mode 100644 index 0000000..36f3dc2 --- /dev/null +++ b/docs/source/_build/html/_modules/adpeps/ipeps/models/heisenberg.html @@ -0,0 +1,376 @@ + + + + + + + + adpeps.ipeps.models.heisenberg — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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Source code for adpeps.ipeps.models.heisenberg

+""" 2D Heisenberg model """
+
+import jax.numpy as np
+
+from .common import sigmaz, sigmap, sigmam
+from adpeps.utils.tlist import set_pattern
+import adpeps.ipeps.config as sim_config
+
+name = "Heisenberg spin-1/2 model"
+
+
[docs]def setup():
+    """ Returns the Hamiltonian """
+    H = make_hamiltonian(**sim_config.model_params)
+
+    obs  = None
+    return H, obs

+
+
[docs]def make_hamiltonian(J=1):
+    """ Heisenberg model """
+    H = tprod(sigmaz, sigmaz) / 4 + \
+            tprod(sigmap, sigmam) / 2 + \
+            tprod(sigmam, sigmap) / 2
+    H = J * H
+    return H

+
+def tprod(a,b):
+    return np.outer(a,b).reshape([2,2,2,2], order='F').transpose([0,2,1,3])
+
+ +
+ + +
+ + +
+
+ + + + +
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+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/_modules/adpeps/simulation/run_ipeps_exci.html b/docs/source/_build/html/_modules/adpeps/simulation/run_ipeps_exci.html new file mode 100644 index 0000000..30ec9c0 --- /dev/null +++ b/docs/source/_build/html/_modules/adpeps/simulation/run_ipeps_exci.html @@ -0,0 +1,590 @@ + + + + + + + + adpeps.simulation.run_ipeps_exci — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
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+ + +
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+ +
+ +
+ + +
+ + + + + + +
+ +
+ +

Source code for adpeps.simulation.run_ipeps_exci

+""" Main excited-state executable script
+
+    Note:
+        The simulations are intended to be used by calling the package 
+        directly via :code:`python -m adpeps ...`, as described in 
+        :ref:`notes/start`
+"""
+
+from jax import grad, jit, vmap, value_and_grad
+from jax import random
+from jax.scipy.optimize import minimize
+from jax.test_util import check_grads
+from scipy import optimize
+from scipy.linalg import eigh, eig
+from yaml import safe_load, dump
+import jax
+import jax.numpy as np
+import numpy as onp
+
+from adpeps.ipeps.ipeps import iPEPS, iPEPS_exci
+from adpeps.ipeps.make_momentum_path import make_momentum_path
+from adpeps.utils import io
+from adpeps.utils.printing import print
+from adpeps.ipeps.evaluation import filter_null_modes
+import adpeps.ipeps.config as sim_config
+
+
[docs]def run(config_file: str, momentum_ix: int):
+    """ Start the simulation
+
+        Args:
+            config_file: filename of the configuration file
+            momentum_ix: index of the point in momentum space
+    """
+
+    print(config_file)
+    with open(config_file) as f:
+        cfg = safe_load(f)
+
+    # Show options
+    print(dump(cfg))
+
+    sim_config.from_dict(cfg)
+    base_file = io.get_exci_base_file()
+    if not base_file.exists():
+        print(f"Base file {base_file} not found. Prepare the simulation first by \
+                running with option '-i'")
+        return
+
+    sim = iPEPSExciSimulation(config_file, momentum_ix)
+    output_folder = io.get_exci_folder()
+    output_folder.mkdir(parents=True, exist_ok=True)
+    kxs, kys = make_momentum_path(sim_config.momentum_path)
+    sim_config.px = kxs[momentum_ix]
+    sim_config.py = kys[momentum_ix]
+    output_file = io.get_exci_file(momentum_ix)
+    print(f"Output: {output_file}", level=2)
+    basis_size = sim.basis_size
+    res_dtype = np.complex128
+    H = onp.zeros((basis_size,basis_size), dtype=res_dtype)
+    N = onp.zeros((basis_size,basis_size), dtype=res_dtype)
+
+    for m in range(basis_size):
+        grad_H, grad_N = sim(m)
+        H[:,m] = grad_H
+        N[:,m] = grad_N
+        onp.savez(output_file, H=H, N=N)
+
+    print(H)
+    print(N)
+    onp.savez(output_file, H=H, N=N)
+    print('Done')
+    print(f"Saved to {output_file}")

+
+def prepare(config_file):
+    with open(config_file) as f:
+        cfg = safe_load(f)
+    sim_config.from_dict(cfg)
+    base_file = io.get_exci_base_file()
+    print(base_file)
+    peps = iPEPS()
+
+    gs_file = io.get_gs_file()
+    loaded_sim = np.load(gs_file, allow_pickle=True)
+    peps       = loaded_sim['peps'].item()
+
+    sim_config.ctm_max_iter = 30
+    sim_config.ctm_conv_tol = 1e-12
+
+    # Converge GS boundary tensors
+    peps.converge_boundaries()
+
+    # Convert to excitations iPEPS
+    peps.__class__ = iPEPS_exci
+
+    # Normalize the ground-state tensors such that the state has norm 1
+    peps.normalize_gs()
+
+    # Shift the Hamiltonian by the ground-state energy 
+    # The excited state energy is then relative to the ground state
+    peps.substract_gs_energy()
+
+    # Prepare an orthonormal basis with respect to the ground state
+    print('Preparing orthonormal basis')
+    basis = peps.compute_orth_basis()
+
+    print(f"Saving base to {base_file}")
+    np.savez(base_file, peps=peps, basis=basis)
+
+def evaluate_single(config_file, momentum_ix):
+    def _compute_ev_red_basis(H, N, P, n):
+        P = P[:,:n]
+        N2 = P.T.conjugate() @ N @ P
+        H2 = P.T.conjugate() @ H @ P
+        N2 = 0.5 * (N2 + N2.T.conjugate())
+        H2 = 0.5 * (H2 + H2.T.conjugate())
+        ev, _ = eig(H2, N2)
+        return sorted(ev.real)
+
+
+    with open(config_file) as f:
+        cfg = safe_load(f)
+
+    sim_config.from_dict(cfg)
+    kxs, kys = make_momentum_path(sim_config.momentum_path)
+    sim_config.px = kxs[momentum_ix]
+    sim_config.py = kys[momentum_ix]
+    base_file = io.get_exci_base_file()
+    base_sim = np.load(base_file, allow_pickle=True)
+    output_file = io.get_exci_file(momentum_ix)
+    print(output_file)
+    dat = np.load(output_file)
+    H, N = dat['H'], dat['N']
+    basis = base_sim['basis']
+    peps  = base_sim['peps'].item()
+
+    # basis = basis.T @ filter_null_modes(peps.tensors, basis)
+    # print(basis.shape)
+    # print(N.shape)
+    # N = basis.T @ N @ basis
+    # H = basis.T @ H @ basis
+    # H = H.conjugate()
+
+    H = 0.5 * (H + H.T.conjugate())
+    N = 0.5 * (N + N.T.conjugate())
+    ev_N, P = np.linalg.eig(N)
+    idx = ev_N.real.argsort()[::-1]
+    ev_N = ev_N[idx]
+    selected = (ev_N/ev_N.max()) > 1e-3
+    P = P[:,idx]
+    P = P[:,selected]
+    N2 = P.T.conjugate() @ N @ P
+    H2 = P.T.conjugate() @ H @ P
+    N2 = 0.5 * (N2 + N2.T.conjugate())
+    H2 = 0.5 * (H2 + H2.T.conjugate())
+    ev, vectors = eig(H2, N2)
+    ixs = np.argsort(ev)
+    ev = ev[ixs]
+    vectors = vectors[:,ixs]
+            
+    return sorted(ev.real)
+
+def evaluate(config_file, momentum_ix):
+    if momentum_ix != -2:
+        return evaluate_single(config_file, momentum_ix)
+
+    with open(config_file) as f:
+        cfg = safe_load(f)
+
+    # Show options
+    print(dump(cfg))
+
+    sim_config.from_dict(cfg)
+    kxs, kys = make_momentum_path(sim_config.momentum_path)
+
+    import matplotlib.pyplot as plt
+    evs = []
+    for ix in range(len(kxs)):
+        try:
+            ev = evaluate_single(config_file, ix)
+        except:
+            ev = [np.nan]
+        evs.append(ev[0])
+    plt.plot(evs, '--+')
+    plt.show()
+
+
+
+
[docs]class iPEPSExciSimulation:
+    """ Simulation class for the excited-state simulation 
+
+        Call an instance of this class directly to start the simulation
+    """
+    def __init__(self, config_file, momentum_ix):
+        self.config_file = config_file
+        self.momentum_ix = momentum_ix
+
+    @property
+    def basis_size(self):
+        with open(self.config_file) as f:
+            cfg = safe_load(f)
+        sim_config.from_dict(cfg)
+        base_file = io.get_exci_base_file()
+        base_sim = np.load(base_file, allow_pickle=True)
+        basis = base_sim['basis']
+        return basis.shape[1]
+
+    def __call__(self, ix, v=None):
+        print(f"Starting simulation of basis vector {ix+1}/{self.basis_size}")
+        with open(self.config_file) as f:
+            cfg = safe_load(f)
+        sim_config.from_dict(cfg)
+
+        base_file = io.get_exci_base_file()
+        base_sim = np.load(base_file, allow_pickle=True)
+        basis = np.complex_(base_sim['basis'])
+        peps  = base_sim['peps'].item()
+        if v is None:
+            v = basis[:,ix]
+        res, grad_H = value_and_grad(peps.run, has_aux=True)(v)
+        grad_H = grad_H.conj()
+        print('Res', res, level=2)
+        grad_N = res[1].pack_data()
+        print('Grad H', grad_H, level=2)
+        print('Grad N', grad_N, level=2)
+        print(f"========== \nFinished basis vector {ix+1}/{self.basis_size} \n")
+        return basis.T @ jax.lax.stop_gradient(grad_H), basis.T @ jax.lax.stop_gradient(grad_N)
+
+    def check_grads(self, A=None):
+        with open(self.config_file) as f:
+            cfg = safe_load(f)
+        sim_config.from_dict(cfg)
+
+        base_file = io.get_exci_base_file()
+        base_sim = np.load(base_file, allow_pickle=True)
+        basis = np.complex_(base_sim['basis'])
+        peps  = base_sim['peps'].item()
+        print('Checking gradient')
+        # peps.fill(A)
+        check_grads(peps.run_gc, (A,), order=1, modes='rev')
+        print('Done check')

+
+
+ +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/_modules/adpeps/simulation/run_ipeps_gs.html b/docs/source/_build/html/_modules/adpeps/simulation/run_ipeps_gs.html new file mode 100644 index 0000000..baa257e --- /dev/null +++ b/docs/source/_build/html/_modules/adpeps/simulation/run_ipeps_gs.html @@ -0,0 +1,521 @@ + + + + + + + + adpeps.simulation.run_ipeps_gs — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +

Source code for adpeps.simulation.run_ipeps_gs

+""" Main ground-state executable script
+
+    Note:
+        The simulations are intended to be used by calling the package 
+        directly via :code:`python -m adpeps ...`, as described in 
+        :ref:`notes/start`
+"""
+
+from jax import grad, jit, vmap, value_and_grad
+from jax import random
+from jax.scipy.optimize import minimize
+from jax.test_util import check_grads
+from scipy import optimize
+from yaml import safe_load, dump
+import jax
+import jax.numpy as np
+import numpy as onp
+
+from adpeps.ipeps.ipeps import iPEPS, iPEPS_exci
+from adpeps.utils import io
+from adpeps.utils.printing import print
+import adpeps.ipeps.config as sim_config
+
+
[docs]def run(config_file: str):
+    """ Start the simulation
+
+        Args:
+            config_file: filename of the configuration file
+    """
+
+    energies   = []
+    gradnorms  = []
+    def verbose(xk, step_size=None):
+        """ Output printing function """
+        try:
+            energies.append(obj.cached_out)
+            gradnorms.append(obj.gradnrm)
+        except:
+            pass
+        print(' ')
+        print(' # ======================== #')
+        print(' #      Step completed      #')
+        print(' # ======================== #')
+        print(' ')
+        [print(' Step %3d  E: %.12f  |grad|: %2.8g' % (i,E,gradnorms[i])) for i,E in enumerate(energies)]
+        print('\n')
+        # np.savez(output_file, peps=peps, v=xk, gradnorms=gradnorms, energies=energies)
+
+    print('Running')
+    print(config_file)
+    with open(config_file) as f:
+        cfg = safe_load(f)
+
+    # Show options
+    print(dump(cfg))
+
+    # Load the configuration file into the sim_config object
+    sim_config.from_dict(cfg)
+
+    # Initialize the iPEPS
+    peps = iPEPS()
+
+    output_file = io.get_gs_file()
+    print(f"Output file {output_file}")
+
+    if sim_config.resume and output_file.exists():
+        loaded_sim = np.load(output_file, allow_pickle=True)
+        peps       = loaded_sim['peps'].item()
+        v          = loaded_sim['v']
+        gradnorms  = list(loaded_sim['gradnorms'])
+        energies   = list(loaded_sim['energies'])
+        print("Resuming existing simulation")
+        verbose(v)
+    else:
+        print("Starting new simulation")
+        key = random.PRNGKey(sim_config.seed)
+        v   = random.normal(key, (peps.numel(),))
+        v   = v / np.max(np.abs(v))
+
+    obj = Objective(peps)
+
+    # Call SciPy's optimization function
+    obj.return_gn = False
+    xL = optimize.minimize(obj.out, v, method=sim_config.method, jac=obj.jac,
+            callback=verbose, options={'gtol': 1e-6, 'disp': True,
+                'maxiter':sim_config.max_iterations})

+
+
[docs]class Objective:
+    """ Class containing the objective function for the optimizer
+    """
+
+    def __init__(self, peps: iPEPS):
+        """
+        Args:
+            peps: iPEPS object to be optimized
+        """
+        self.cached_v   = None
+        self.cached_out = None
+        self.cached_jac = None
+
+        self.peps       = peps
+        """ iPEPS object """
+
+        self.fun        = peps.run
+        """ Objective function - CTM iterations until convergence 
+            followed by the evaluation of the energy 
+        """
+        self.return_gn  = True
+
+    @property
+    def gradnrm(self):
+        """ Norm of the gradient """
+        return np.linalg.norm(self.cached_jac)
+
+
[docs]    def jac(self, v: np.ndarray) -> np.ndarray:
+        """ Computes the vector-Jacobian product (gradient) of the
+            iPEPS at the current point :attr:`v` in parameter space
+
+            This function is designed to work with optimizers that make separate 
+            calls to the objective function and the gradient, by caching both.
+
+            Args:
+                v: input variational parameters for the site tensors of 
+                    the iPEPS
+
+            Returns:
+                gradient of the iPEPS with respect to the input parameters :attr:`v`
+        """
+
+        # Cast the regular numpy array into a Jax numpy array for gradient tracking
+        v = np.array(v)
+        v = v / np.max(np.abs(v))
+
+        if (self.cached_jac is not None and self.cached_v is not None 
+                and np.linalg.norm(v - self.cached_v) < 1e-14):
+            return self.cached_jac
+
+        # Call the forward + backward pass iPEPS code
+        o, g = value_and_grad(self.fun)(v)
+
+        # Convert to regular Numpy arrays so they can be passed to the optimizer 
+        # and stored without any tracking information by Jax
+        o = onp.array(o)
+        v = onp.array(v)
+        g = onp.array(g)
+
+        # Cache the results
+        self.cached_v   = v
+        self.cached_out = o
+        self.cached_jac = g
+
+        if self.return_gn:
+            return g, self.gradnrm
+        else:
+            return g

+
+
[docs]    def out(self, v):
+        """ Computes the objective function (energy) of the iPEPS
+
+            Since many optimizers make separate calls to the objective function 
+            and the gradient, but usually require both results for any given 
+            parameter vector v, this function calls the gradient as well.
+
+            Args:
+                v: input variational parameters for the site tensors of 
+                    the iPEPS
+
+            Returns:
+                energy of the iPEPS at the point :attr:`v` in parameter space
+        """
+        if self.cached_v is not None and np.linalg.norm(v - self.cached_v) < 1e-14:
+            return self.cached_out
+        else:
+            self.jac(v)
+            return self.cached_out

+
+    def check_grads(self, A=None):
+        print('Checking gradient')
+        self.peps.fill(A)
+        self.peps.converge_boundaries()
+        check_grads(self.peps.run, (A,), order=1, modes='rev')
+        print('Done check')

+
+
+ +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/_modules/adpeps/utils/ctmtensors.html b/docs/source/_build/html/_modules/adpeps/utils/ctmtensors.html new file mode 100644 index 0000000..c30f7a6 --- /dev/null +++ b/docs/source/_build/html/_modules/adpeps/utils/ctmtensors.html @@ -0,0 +1,512 @@ + + + + + + + + adpeps.utils.ctmtensors — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +

Source code for adpeps.utils.ctmtensors

+""" Contains utility class that contains all iPEPS tensors """
+
+from dataclasses import dataclass, field, fields, replace, asdict
+from functools import partial
+from typing import List
+
+from .empty_tensor import EmptyT
+from .nested import Nested
+from .tlist import TList, hold_write
+
+
[docs]@dataclass
+class CTMTensors:
+    """ 
+    This is a utility class that contains all tensors related to an iPEPS.
+    In effect, this forms a representation of the full state, including 
+    the site tensors with variational parameters, the boundary tensors 
+    generated by CTM and the projectors.
+
+    There are several fields of this dataclass that are generated 
+    automatically, which provide convenient wrappers for the tensors.
+
+    For example, the :attr:`CTMTensors.A` field returns the site tensors 
+    (contained in a :class:`adpeps.utils.tlist.TList`)
+    """
+    A:     TList
+    Ad:    TList
+    Cs:    List[TList] = field(default_factory=list)
+    Ts:    List[TList] = field(default_factory=list)
+
+    B:     TList = field(default=None, metadata={'init_tlist': True})
+    Bd:    TList = field(default=None, metadata={'init_tlist': True})
+    B_Cs:  List[TList] = field(default=None, metadata={'init_tlists': True})
+    B_Ts:  List[TList] = field(default=None, metadata={'init_tlists': True})
+    Bd_Cs: List[TList] = field(default=None, metadata={'init_tlists': True})
+    Bd_Ts: List[TList] = field(default=None, metadata={'init_tlists': True})
+    BB_Cs: List[TList] = field(default=None, metadata={'init_tlists': True})
+    BB_Ts: List[TList] = field(default=None, metadata={'init_tlists': True})
+
+    Pl:    TList  = None
+    Pr:    TList  = None
+    Pt:    TList  = None
+    Pb:    TList  = None
+    Plb:   TList  = None
+    Prb:   TList  = None
+    Ptb:   TList  = None
+    Pbb:   TList  = None
+
+    observables: List = field(default_factory=list)
+
+    def _get_field_item(self, fieldname=None, ix=None):
+        return getattr(self, fieldname).__getitem__(ix)
+
+    def _get_field_nested_item(self, fieldname=None, ix=None):
+        return getattr(self, fieldname)(ix)
+
+    def _set_field_nested_item(self, fieldname=None, ix=None, value=None):
+        return getattr(self, f"{fieldname}_set")(ix, value)
+
+    def hold(self, *fields):
+        def _convert_all(f):
+            if f.startswith('all_'):
+                f = f[4:]
+                return [f, f"B_{f}", f"Bd_{f}", f"BB_{f}"]
+            else:
+                return (f,)
+        fields = [field for fs in [_convert_all(f) for f in fields] for field in fs]
+        tensors = tuple([getattr(self, field) for field in fields])
+        return hold_write(*tensors)
+
+    def __post_init__(self):
+        base_tlist = self.A
+        for f in fields(self):
+            try:
+                if getattr(self, f.name) is None and f.metadata['init_tlist']:
+                    setattr(self, f.name, TList.empty_like(base_tlist, empty_obj=EmptyT()))
+            except KeyError:
+                pass
+            try:
+                if getattr(self, f.name) is None and f.metadata['init_tlists']:
+                    setattr(self, f.name, [TList.empty_like(base_tlist, empty_obj=EmptyT()) for _ in range(4)])
+            except KeyError:
+                pass
+
+    def all_Cs(self, ix):
+        base_tlist = self.A
+        res = TList.empty_like(base_tlist, empty_obj=EmptyT())
+        for i in range(len(res._data)):
+            res._data[i] = Nested([self.Cs[ix][i], self.B_Cs[ix][i], 
+                self.Bd_Cs[ix][i], self.BB_Cs[ix][i]])
+        return res
+
+    def all_Ts(self, ix):
+        base_tlist = self.A
+        res = TList.empty_like(base_tlist, empty_obj=EmptyT())
+        for i in range(len(res._data)):
+            res._data[i] = Nested([self.Ts[ix][i], self.B_Ts[ix][i], 
+                self.Bd_Ts[ix][i], self.BB_Ts[ix][i]])
+        return res
+
+    def update(self, fieldnames, ixs, values):
+        if isinstance(fieldnames, str):
+            fieldnames = (fieldnames,)
+            values = (values,)
+            ixs = (ixs,)
+        for i,f in enumerate(fieldnames):
+            value = values[i]
+            ix = ixs[i]
+            assert isinstance(value, Nested), "Use the all_Ci setter only with Nested tensors"
+            getattr(self, f)[ix] = value[0]
+            getattr(self, f"B_{f}")[ix] = value[1]
+            getattr(self, f"Bd_{f}")[ix] = value[2]
+            getattr(self, f"BB_{f}")[ix] = value[3]
+
+    @property
+    def all_A(self):
+        base_tlist = self.A
+        res = TList.empty_like(base_tlist, empty_obj=EmptyT())
+        for i in range(len(res._data)):
+            res._data[i] = Nested([self.A._data[i], self.B._data[i], 
+                EmptyT(), EmptyT()])
+        return res
+
+    @property
+    def all_Ad(self):
+        base_tlist = self.A
+        res = TList.empty_like(base_tlist, empty_obj=EmptyT())
+        for i in range(len(res._data)):
+            res._data[i] = Nested([self.Ad._data[i], EmptyT(),
+                self.Bd._data[i], EmptyT()])
+        return res
+
+    def stop_gradient(self, only_boundaries=True):
+        for i in range(4):
+            self.Cs[i] = self.Cs[i].stop_gradient()
+            self.Ts[i] = self.Ts[i].stop_gradient()
+            self.B_Cs[i] = self.B_Cs[i].stop_gradient()
+            self.B_Ts[i] = self.B_Ts[i].stop_gradient()
+            self.Bd_Cs[i] = self.Bd_Cs[i].stop_gradient()
+            self.Bd_Ts[i] = self.Bd_Ts[i].stop_gradient()
+            self.BB_Cs[i] = self.BB_Cs[i].stop_gradient()
+            self.BB_Ts[i] = self.BB_Ts[i].stop_gradient()
+        if not only_boundaries:
+            self.A = self.A.stop_gradient()
+            self.Ad = self.Ad.stop_gradient()
+            self.B = self.B.stop_gradient()
+            self.Bd = self.Bd.stop_gradient()

+
+def _wrap_f(self, fieldname=None, ix=None):
+    return self._get_field_item(fieldname, ix)
+
+def _wrap_nested_f(self, fieldname=None, ix=None):
+    return self._get_field_nested_item(fieldname, ix)
+
+def _wrap_nested_f_set(self, value, fieldname=None, ix=None):
+    return self._set_field_nested_item(fieldname, ix, value)
+
+attrs = ['Cs', 'Ts', 'B_Cs', 'B_Ts', 'Bd_Cs', 'Bd_Ts', 'BB_Cs', 'BB_Ts']
+for attr in attrs:
+    for i in range(4):
+        new_attr = property(partial(_wrap_f, fieldname=attr, ix=i))
+        # new_attr.__doc__ = f"Boundary tensors `{attr}` computed by CTM"
+        new_attr.__doc__ = ":meta private:"
+        setattr(CTMTensors, f"{attr[:-1]}{i+1}", new_attr)
+attrs = ['all_Cs', 'all_Ts']
+for attr in attrs:
+    for i in range(4):
+        new_attr = property(partial(_wrap_nested_f, fieldname=attr, ix=i),
+                partial(_wrap_nested_f_set, fieldname=attr, ix=i))
+        new_attr.__doc__ = ":meta private:"
+        # new_attr.__doc__ = ":class:`adpeps.utils.tlist.TList` containing all versions \
+        #         (only ground-state, ground state + one `B` tensor, ground state \
+        #         + one `Bdagger` tensor, ground state + one `B` tensor + one `Bdagger`\
+        #         tensor) of the boundary tensors."
+        setattr(CTMTensors, f"{attr[:-1]}{i+1}", new_attr)
+
+ +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/_modules/adpeps/utils/empty_tensor.html b/docs/source/_build/html/_modules/adpeps/utils/empty_tensor.html new file mode 100644 index 0000000..e21ae04 --- /dev/null +++ b/docs/source/_build/html/_modules/adpeps/utils/empty_tensor.html @@ -0,0 +1,426 @@ + + + + + + + + adpeps.utils.empty_tensor — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +

Source code for adpeps.utils.empty_tensor

+""" Contains utility class that represents a 'zero' (empty) tensor object """
+
+import jax.numpy as np
+
+
[docs]class EmptyT:
+    """ Empty tensor utility class, which can be used to represent a  
+        'zero' tensor.
+
+        The operations involving this type of tensor will return the expected 
+        results, such as (Tensor * EmptyT -> EmptyT), removing the need for 
+        checking if a tensor is empty in the part of the code where the 
+        operation is called.
+    """
+    tag = None
+
+    def __repr__(self):
+        return "<empty>"
+
+    def __add__(self, other):
+        return other
+
+    def __radd__(self, other):
+        return other
+
+    def __sub__(self, other):
+        return other
+
+    def __rsub__(self, other):
+        return other
+
+    def __mul__(self, other):
+        return self
+
+    def __neg__(self):
+        return self
+
+    def __rmul__(self, other):
+        if isinstance(other, int):
+            return [self for _ in range(other)]
+        else:
+            return self
+
+    def __truediv__(self, other):
+        return self
+
+    def copy(self):
+        return self
+
+    def to_real(self):
+        return self
+
+    @property
+    def real(self):
+        return self
+
+    @property
+    def data(self):
+        return []
+
+    def transpose(self, *args):
+        return self
+
+    def __rtruediv__(self, other):
+        return self
+
+    def __len__(self):
+        return 0
+
+    def __array__(self):
+        return np.array([])
+
+    def item(self):
+        return self
+
+    def __getitem__(self, ix):
+        return self
+
+    def mult(self, other, *args):
+        return self
+
+    def to_complex(self):
+        return self
+
+    def complex(self):
+        return False
+
+    def is_finite(self):
+        return True

+
+ +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/_modules/adpeps/utils/nested.html b/docs/source/_build/html/_modules/adpeps/utils/nested.html new file mode 100644 index 0000000..e137bcd --- /dev/null +++ b/docs/source/_build/html/_modules/adpeps/utils/nested.html @@ -0,0 +1,499 @@ + + + + + + + + adpeps.utils.nested — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +

Source code for adpeps.utils.nested

+""" Contains utility class that represents a collection of tensors of 
+    different types, with operations that can be applied to all 
+    contained tensors at once
+"""
+
+import cmath
+import jax.numpy as np
+
+from adpeps.types import TensorType
+
+
+
[docs]class Nested:
+    """ This is a helper class for the efficient contraction of variants of tensors,
+        used in the energy evaluation of excited states
+
+        A Nested tensor contains the following variants (some may be empty):
+
+            - :attr:`tensors[0]`: regular tensor (no B or Bd)
+            - :attr:`tensors[1]`: (terms with) a single B tensor
+            - :attr:`tensors[2]`: (terms with) a single Bd tensor
+            - :attr:`tensors[3]`: (terms with) both a B and a Bd tensor
+        
+        When two Nested tensors x,y are contracted, all combinations are taken into account
+        and the result is again a Nested tensor, filled with the following variants:
+
+            - :attr:`tensors[0]: x[0] * y[0]`
+            - :attr:`tensors[1]: x[1] * y[0] + x[0] * y[1]`
+            - :attr:`tensors[2]: x[2] * y[0] + x[0] * y[2]`
+            - :attr:`tensors[3]: x[3] * y[0] + x[2] * y[1] + x[1] * y[2] + x[0] * y[3]`
+
+        By using Nested tensors in a (large) contraction, the many different terms are 
+        resummed on the fly, leading to a potentially reduced computational cost
+
+        Note:
+            Most implented functions act as wrappers for the corresponding `numpy` functions 
+            on the individual tensors
+    """
+
+    def __init__(self, tensors):
+        self.tensors = tensors
+
+
[docs]    def normalize(self):
+        """ Normalize the contained tensors by the largest value 
+            of the first element of :attr:`self.tensors`
+        """
+        factor = np.abs(self[0]).max()
+        return self * (1 / factor), factor

+
+
[docs]    def mult(self, other: TensorType, *args) -> 'Nested':
+        """
+            Args:
+                other: other tensor-like object to contract with
+                *args: arguments to be passed to the contraction method
+                    (:code:`np.tensordot`)
+
+            Returns:
+                res: result of the contraction
+        """
+        def _mult_function(A, B, *args):
+            if hasattr(A, 'mult'):
+                return A.mult(B, *args)
+            elif len(B) == 0:
+                return B.mult(A, *args)
+            return np.tensordot(A, B, *args)
+
+        if isinstance(other, np.ndarray):
+            new_data = 4 * [[]]
+            new_data[0] = _mult_function(self.tensors[0], other, *args)
+            new_data[1] = _mult_function(self.tensors[1], other, *args)
+            new_data[2] = _mult_function(self.tensors[2], other, *args)
+            new_data[3] = _mult_function(self.tensors[3], other, *args)
+            return Nested(new_data)
+        new_data = 4 * [[]]
+        new_data[0] = _mult_function(self.tensors[0], other.tensors[0], *args)
+        new_data[1] = _mult_function(self.tensors[1], other.tensors[0], *args) +\
+                      _mult_function(self.tensors[0], other.tensors[1], *args)
+        new_data[2] = _mult_function(self.tensors[2], other.tensors[0], *args) +\
+                      _mult_function(self.tensors[0], other.tensors[2], *args)
+
+        new_data[3] = _mult_function(self.tensors[3], other.tensors[0], *args) +\
+                      _mult_function(self.tensors[2], other.tensors[1], *args) +\
+                      _mult_function(self.tensors[1], other.tensors[2], *args) +\
+                      _mult_function(self.tensors[0], other.tensors[3], *args)
+        res = Nested(new_data)
+        return res

+
+
[docs]    def transpose(self, *args) -> 'Nested':
+        """ Applies :code:`transpose` to each contained tensor """
+        new_data = [self.tensors[i].transpose(*args) for i in range(4)]
+        return Nested(new_data)

+
+    def __mul__(self, other):
+        new_data = [self.tensors[i] * other for i in range(4)]
+        return Nested(new_data)
+
+    def __rmul__(self, other):
+        new_data = [other * self.tensors[i] for i in range(4)]
+        return Nested(new_data)
+
+    def __truediv__(self, other):
+        new_data = [self.tensors[i] / other for i in range(4)]
+        return Nested(new_data)
+
+    def __add__(self, other):
+        if isinstance(other, Nested):
+            new_data = [self.tensors[i] + other.tensors[i] for i in range(4)]
+        else:
+            new_data = [self.tensors[i] + other for i in range(4)]
+        return Nested(new_data)
+
+    def __radd__(self, other):
+        return self + other
+
+    def __getitem__(self, ix):
+        return self.tensors[ix]
+
+    def __setitem__(self, ix, value):
+        self.tensors[ix] = value
+
+    def __repr__(self):
+        return "(Nested) " + self.tensors.__repr__()
+
+    def __neg__(self):
+        return Nested([-self.tensors[i] for i in range(4)])
+
+    def shift(self, phi):
+        new_data = [self.tensors[0],  self.tensors[1] * exp(phi), 
+                 self.tensors[2] * exp(-phi), self.tensors[3]]
+        return Nested(new_data)
+
+    def __len__(self):
+        try:
+            return len(self.tensors[0])
+        except Exception:
+            return self.tensors[0].size
+
+    @property
+    def real(self):
+        res = Nested([self.tensors[i].real for i in range(4)])
+        return res
+
+    @property
+    def shape(self):
+        return self.tensors[0].shape
+
+    @property
+    def dims(self):
+        return self.tensors[0].dims
+
+    def check_contr_inds(self, other, *args, **kwargs):
+        return self[0].check_contr_inds(other[0], *args, **kwargs)
+
+    def numel(self):
+        return self[0].numel()
+    
+    @classmethod
+    def only_gs(cls, tensor, empty_obj=[]):
+        return cls([tensor, empty_obj, empty_obj, empty_obj])

+
+def exp(phi):
+    return cmath.exp(1j * phi)
+
+ +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/_modules/adpeps/utils/printing.html b/docs/source/_build/html/_modules/adpeps/utils/printing.html new file mode 100644 index 0000000..9cbcc84 --- /dev/null +++ b/docs/source/_build/html/_modules/adpeps/utils/printing.html @@ -0,0 +1,375 @@ + + + + + + + + adpeps.utils.printing — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +

Source code for adpeps.utils.printing

+""" Utility module for printing output depending on the verbosity setting 
+    :attr:`adpeps.ipeps.config.disp_level` in the configuration file.
+"""
+
+import builtins
+import time
+
+import adpeps.ipeps.config as sim_config
+
+prefix    = None
+show_time = False
+
+
[docs]def print(*args, level: int=None, **kwargs):
+    """ Print output using builtin :code:`print` if :code:`level` 
+        <= :attr:`adpeps.ipeps.config.disp_level`
+
+        Args:
+            *args: arbitraty arguments to be passed to builtin :code:`print`
+            level: verbosity level, determining at which verbosity setting this
+                should be printed
+            **kwargs: arbitraty keyword arguments for builtin :code:`print`
+    """
+    if level is None or level <= sim_config.disp_level:
+        if sim_config.flush_output:
+            kwargs['flush'] = True
+        if prefix is not None:
+            if show_time:
+                curtime = time.strftime("[%H:%M:%S]", time.localtime())
+                builtins.print(prefix, curtime, *args, **kwargs)
+            else:
+                builtins.print(prefix, *args, **kwargs)
+        else:
+            if show_time:
+                curtime = time.strftime("[%H:%M:%S]", time.localtime())
+                builtins.print(curtime, *args, **kwargs)
+            else:
+                builtins.print(*args, **kwargs)

+
+ +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/_modules/adpeps/utils/tlist.html b/docs/source/_build/html/_modules/adpeps/utils/tlist.html new file mode 100644 index 0000000..d9360ac --- /dev/null +++ b/docs/source/_build/html/_modules/adpeps/utils/tlist.html @@ -0,0 +1,651 @@ + + + + + + + + adpeps.utils.tlist — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +

Source code for adpeps.utils.tlist

+"""
+    List object with additional features, used for storing 
+    the iPEPS tensors
+
+    Items in the list can be accessed by either a linear index 
+    or a (i,j) double index, where i and j will be automatically 
+    taken modulo the unit cell size (i.e. i = i % n_x)
+
+    Additionally, convenience functions that work on tensors can 
+    be defined for the whole list, e.g. conj()
+"""
+
+import contextlib
+import jax
+import jax.numpy as np
+import numpy as onp
+
+from .empty_tensor import EmptyT
+
+
+
[docs]@contextlib.contextmanager
+def cur_loc(*loc: int):
+    """ Shift the locations of the tensors relative to a 
+        new zero (loc) while in this context
+
+        Args:
+            loc: shifts (x,y)
+
+        Example:
+            >>> l = TList([[1,2], [3,4]])
+            >>> l[0,0]
+            1
+            >>> with cur_loc(1,0):
+            >>>     l[0,0]
+            2
+            >>>     l[0,1]
+            4
+            >>> l[0,0]
+            1
+
+        Note that this applies to ALL TList objects while 
+        inside the context
+    """
+    pre_patched_value = getattr(TList, '_loc')
+    setattr(TList, '_loc', loc)
+    yield TList
+    setattr(TList, '_loc', pre_patched_value)

+
+
[docs]@contextlib.contextmanager
+def hold_write(*lists: 'TList'):
+    """ Hold off on writing to the list while 
+        inside the context
+
+        Args:
+            lists: one or more TList objects that should have the writing 
+                action delayed until the context is disabled
+
+        Example:
+            >>> l = TList([[1,2], [3,4]])
+            >>> with hold_write(l):
+            >>>    l[0,0] = 100
+            >>>    l[0,0] 
+            1
+            >>> l[0,0]
+            100
+    """
+    for l in lists:
+        l._hold_write = True
+    yield
+    for l in lists:
+        l._purge_tmp()

+
+
[docs]@contextlib.contextmanager
+def set_pattern(pattern):
+    """ Set pattern for all new TLists that are created while 
+        the context is active
+
+        Args:
+            pattern:
+    """
+
+    pre_patched_value = getattr(TList, '_default_pattern')
+    setattr(TList, '_default_pattern', pattern)
+    yield TList
+    setattr(TList, '_default_pattern', pre_patched_value)

+
+class TList:
+    _loc             = (0,0)
+    _default_pattern = None
+    _changed         = None
+
+    def __init__(self, data=None, shape=None, pattern=None, empty_obj=[[]]):
+        self._tmpdata    = None
+        self.pattern     = pattern
+        self._hold_write = False
+        self.empty_obj   = empty_obj
+        if pattern is None and self._default_pattern is not None:
+            self.pattern = self._default_pattern
+        if self.pattern is None:
+            if data is not None:
+                try:
+                    iter(data) # Check if iterable
+                    data = np.array(data, dtype='object')
+                    self._data = data.reshape([-1], order='C').tolist()
+                    if data.ndim == 1:
+                        self.size = (data.shape[0], 1)
+                    else:
+                        self.size = (data.shape[1], data.shape[0])
+                except:
+                    self._data = [data]
+                    self.size = (1,1)
+            elif shape is not None:
+                self._data = (shape[0]*shape[1]) * empty_obj
+                self.size = shape
+            else:
+                self._data = None
+                self.size = ()
+        else:
+            self.pattern = np.array(self.pattern)
+            self.size = (self.pattern.shape[1], self.pattern.shape[0])
+            if data is not None:
+                try:
+                    iter(data) # Check if iterable
+                    data = np.array(data, dtype='object')
+                    if data.size == np.unique(self.pattern).size:
+                        self._data = data.reshape([-1], order='C').tolist()
+                    else:
+                        self._data = np.unique(self.pattern).size * empty_obj
+                        for j in range(self.pattern.shape[1]):
+                            for i in range(self.pattern.shape[0]):
+                                self._data[self.pattern[i,j]] = data[i,j]
+                except:
+                    self._data = [data]
+                    self.size = (1,1)
+            else:
+                self._data = np.unique(self.pattern).size * empty_obj
+                assert len(self._data) == np.unique(self.pattern).size, \
+                        "Data must contain one element for each unique identifier in pattern"
+        self.reset_changed()
+
+    def x_major(self):
+        return (self._conv_ix((x,y)) for y in range(self.size[1]) for x in range(self.size[0]))
+
+    def y_major(self):
+        return (self._conv_ix((x,y)) for x in range(self.size[0]) for y in range(self.size[1]))
+
+    def __len__(self):
+        return len(self._data)
+
+    def mean(self):
+        try:
+            finite_elems = [x for x in self._data if isfinite(x)]
+            return sum(finite_elems) / len(finite_elems)
+        except Exception as e:
+            return sum(self._data) / len(self)
+
+    def sum(self):
+        try:
+            finite_elems = [x for x in self._data if isfinite(x)]
+            return sum(finite_elems)
+        except Exception as e:
+            return sum(self._data)
+
+    def normalize(self):
+        new_list = TList(shape=self.size, pattern=self.pattern)
+        new_list._data = [a / np.max(np.abs(a)) for a in self._data]
+        return new_list
+
+    def conj(self):
+        new_list = TList(shape=self.size, pattern=self.pattern)
+        new_list._data = [a.conj() for a in self._data]
+        return new_list
+    def items(self):
+        return [a.item() for a in self._data]
+
+    def pack_data(self):
+        data = []
+        for a in self._data:
+            data.append(np.reshape(a, (-1,)))
+        return np.concatenate(data)
+
+    def reset_changed(self):
+        if self._data is not None:
+            self._changed = len(self._data) * [False]
+        return self
+
+    def mark_changed(self, linear_ix):
+        if self._changed is not None:
+            self._changed[linear_ix] = True
+
+    def is_changed(self, *ix):
+        if self._changed is None:
+            return False
+        linear_ix = self._conv_ix(ix)
+        return self._changed[linear_ix]
+
+    def fill(self, data, d=None, D=None):
+        new_list = TList(shape=self.size, pattern=self.pattern)
+        offset = 0
+        new_data = []
+        for i,a in enumerate(self):
+            siz = a.size
+            # new_data.append(np.reshape(data[offset:offset+siz], (d, D, D, D, D)))
+            new_data.append(np.reshape(data[offset:offset+siz], a.shape))
+            offset = offset + siz
+        new_list._data = new_data
+        return new_list
+
+    def tot_numel(self):
+        return sum([a.size for a in self._data])
+
+    def stop_gradient(self):
+        new_list = TList(shape=self.size, pattern=self.pattern)
+        new_list._data = [jax.lax.stop_gradient(a) if len(a)>0 else a for a in self._data]
+        return new_list
+
+    def _conv_ix(self, ix):
+        if isinstance(ix, (tuple,list)):
+            if len(self._loc) == 1:
+                # shift_i, shift_j = onp.unravel_index(self._loc[0], self.size, order='F')
+                shift_j, shift_i = np.unravel_index(self._loc[0], self.size)
+            else:
+                shift_i, shift_j = self._loc
+            i = (ix[0] + shift_i) % self.size[0]
+            j = (ix[1] + shift_j) % self.size[1]
+            # linear_ix = np.ravel_multi_index((i,j), self.size, order='F')
+            linear_ix = self._linear_ix(i,j)
+        else:
+            linear_ix = ix
+        return linear_ix
+
+    def _linear_ix(self, i, j):
+        if self.pattern is not None:
+            return self.pattern[j][i]
+        else:
+            return np.ravel_multi_index((i,j), self.size, order='F')
+
+    def _purge_tmp(self):
+        self._tmpdata    = None
+        self._hold_write = False
+
+    def __eq__(self, other):
+        if self._data != other._data:
+            return False
+        if self.pattern is not None:
+            if other.pattern is None:
+                return False
+            if not (self.pattern == other.pattern).all():
+                return False
+        return True
+
+    def __getitem__(self, ix):
+        linear_ix = self._conv_ix(ix)
+        if self._tmpdata is not None and self._tmpdata[linear_ix] is not None:
+            return self._tmpdata[linear_ix]
+        return self._data[linear_ix]
+
+    def __setitem__(self, ix, value):
+        linear_ix = self._conv_ix(ix)
+        if self._hold_write:
+            if self._tmpdata is None:
+                self._tmpdata = [None] * len(self)
+            self._tmpdata[linear_ix] = self._data[linear_ix]
+        self._data[linear_ix] = value
+        self.mark_changed(linear_ix)
+
+    def __repr__(self):
+        if self._data is None:
+            return "TList{}[]"
+        repr_str = "TList{"
+        if self._loc is not None:
+            repr_str += "Loc=" + self._loc.__repr__()
+        if self.pattern is not None:
+            repr_str += ",Pat=" + self.pattern.__repr__()
+        repr_str += ",Size=" + self.size.__repr__()
+        repr_str += "}["
+        for j in range(self.size[1]):
+            repr_str += "["
+            for i in range(self.size[0]):
+                try:
+                    repr_str += f"{self[i,j].shape}"
+                except:
+                    repr_str += self[i,j].__repr__()
+                if i < self.size[0]-1:
+                    repr_str += ", "
+            if j < self.size[1]-1:
+                repr_str += "], "
+            else:
+                repr_str += "]]"
+        return repr_str
+
+    @staticmethod
+    def empty_like(T, empty_obj=None):
+        if empty_obj is None:
+            empty_obj = T.empty_obj
+        return TList(shape=T.size, pattern=T.pattern, empty_obj=empty_obj)
+
+def isfinite(x):
+    try:
+        return len(x) > 0
+    except Exception as e:
+        return np.isfinite(np.array(x))
+
+ +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/_modules/index.html b/docs/source/_build/html/_modules/index.html new file mode 100644 index 0000000..d11c54b --- /dev/null +++ b/docs/source/_build/html/_modules/index.html @@ -0,0 +1,360 @@ + + + + + + + + Overview: module code — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ + + + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/_sources/extra/adpeps.ipeps.ctm.rst.txt b/docs/source/_build/html/_sources/extra/adpeps.ipeps.ctm.rst.txt new file mode 100644 index 0000000..c011e15 --- /dev/null +++ b/docs/source/_build/html/_sources/extra/adpeps.ipeps.ctm.rst.txt @@ -0,0 +1,10 @@ +adpeps.ipeps.ctm +================ + +.. currentmodule:: adpeps.ipeps.ctm + +.. .. toctree:: +.. :maxdepth: 2 + +.. automodule:: adpeps.ipeps.ctm + :members: diff --git a/docs/source/_build/html/_sources/extra/adpeps.ipeps.ipeps.rst.txt b/docs/source/_build/html/_sources/extra/adpeps.ipeps.ipeps.rst.txt new file mode 100644 index 0000000..3323f55 --- /dev/null +++ b/docs/source/_build/html/_sources/extra/adpeps.ipeps.ipeps.rst.txt @@ -0,0 +1,35 @@ +adpeps.ipeps.ipeps +================== + +.. currentmodule:: adpeps.ipeps.ipeps + +.. .. toctree:: +.. :maxdepth: 2 + +.. automodule:: adpeps.ipeps.ipeps + :members: + + +iPEPS +----------- + +.. autoclass:: iPEPS + :members: + :member-order: bysource + +iPEPS_exci +----------- + +.. autoclass:: iPEPS_exci + :members: + :member-order: bysource + + +.. .. autosummary:: +.. :toctree: generated +.. :caption: Section 1 +.. :nosignatures: + +.. iPEPS +.. iPEPS_exci + diff --git a/docs/source/_build/html/_sources/extra/ipeps.ipeps.rst.txt b/docs/source/_build/html/_sources/extra/ipeps.ipeps.rst.txt new file mode 100644 index 0000000..193f163 --- /dev/null +++ b/docs/source/_build/html/_sources/extra/ipeps.ipeps.rst.txt @@ -0,0 +1,19 @@ +iPEPSS +====== + +.. :noindex: + +.. .. currentmodule:: adpeps.ipeps.ipeps + +.. .. toctree:: +.. :maxdepth: 2 + +.. .. automodule:: adpeps.ipeps.ipeps + +.. .. autosummary:: + :toctree: generated + :nosignatures: + :caption: Classes + + iPEPS + iPEPS_exci diff --git a/docs/source/_build/html/_sources/generated/adpeps.ipeps.config.rst.txt b/docs/source/_build/html/_sources/generated/adpeps.ipeps.config.rst.txt new file mode 100644 index 0000000..eafaa88 --- /dev/null +++ b/docs/source/_build/html/_sources/generated/adpeps.ipeps.config.rst.txt @@ -0,0 +1,14 @@ +adpeps.ipeps.config +=================== + +.. currentmodule:: adpeps.ipeps.config + +.. module:: adpeps.ipeps.config + + + +.. automodule:: adpeps.ipeps.config + :members: + :member-order: groupwise + + diff --git a/docs/source/_build/html/_sources/generated/adpeps.ipeps.ctm.rst.txt b/docs/source/_build/html/_sources/generated/adpeps.ipeps.ctm.rst.txt new file mode 100644 index 0000000..25af8d5 --- /dev/null +++ b/docs/source/_build/html/_sources/generated/adpeps.ipeps.ctm.rst.txt @@ -0,0 +1,14 @@ +adpeps.ipeps.ctm +================ + +.. currentmodule:: adpeps.ipeps.ctm + +.. module:: adpeps.ipeps.ctm + + + +.. automodule:: adpeps.ipeps.ctm + :members: + :member-order: groupwise + + diff --git a/docs/source/_build/html/_sources/generated/adpeps.ipeps.ipeps.evaluation.rst.txt b/docs/source/_build/html/_sources/generated/adpeps.ipeps.ipeps.evaluation.rst.txt new file mode 100644 index 0000000..9134e28 --- /dev/null +++ b/docs/source/_build/html/_sources/generated/adpeps.ipeps.ipeps.evaluation.rst.txt @@ -0,0 +1,14 @@ +adpeps.ipeps.ipeps.evaluation +============================= + +.. currentmodule:: adpeps.ipeps.ipeps.evaluation + +.. module:: adpeps.ipeps.ipeps.evaluation + + + +.. automodule:: adpeps.ipeps.ipeps.evaluation + :members: + :member-order: groupwise + + diff --git a/docs/source/_build/html/_sources/generated/adpeps.ipeps.ipeps.rst.txt b/docs/source/_build/html/_sources/generated/adpeps.ipeps.ipeps.rst.txt new file mode 100644 index 0000000..e4ac247 --- /dev/null +++ b/docs/source/_build/html/_sources/generated/adpeps.ipeps.ipeps.rst.txt @@ -0,0 +1,14 @@ +adpeps.ipeps.ipeps +================== + +.. currentmodule:: adpeps.ipeps.ipeps + +.. module:: adpeps.ipeps.ipeps + + + +.. automodule:: adpeps.ipeps.ipeps + :members: + :member-order: groupwise + + diff --git a/docs/source/_build/html/_sources/generated/adpeps.ipeps.models.common.rst.txt b/docs/source/_build/html/_sources/generated/adpeps.ipeps.models.common.rst.txt new file mode 100644 index 0000000..617b7fb --- /dev/null +++ b/docs/source/_build/html/_sources/generated/adpeps.ipeps.models.common.rst.txt @@ -0,0 +1,14 @@ +adpeps.ipeps.models.common +========================== + +.. currentmodule:: adpeps.ipeps.models.common + +.. module:: adpeps.ipeps.models.common + + + +.. automodule:: adpeps.ipeps.models.common + :members: + :member-order: groupwise + + diff --git a/docs/source/_build/html/_sources/generated/adpeps.ipeps.models.heisenberg.rst.txt b/docs/source/_build/html/_sources/generated/adpeps.ipeps.models.heisenberg.rst.txt new file mode 100644 index 0000000..fb407e7 --- /dev/null +++ b/docs/source/_build/html/_sources/generated/adpeps.ipeps.models.heisenberg.rst.txt @@ -0,0 +1,14 @@ +adpeps.ipeps.models.heisenberg +============================== + +.. currentmodule:: adpeps.ipeps.models.heisenberg + +.. module:: adpeps.ipeps.models.heisenberg + + + +.. automodule:: adpeps.ipeps.models.heisenberg + :members: + :member-order: groupwise + + diff --git a/docs/source/_build/html/_sources/generated/adpeps.ipeps.models.rst.txt b/docs/source/_build/html/_sources/generated/adpeps.ipeps.models.rst.txt new file mode 100644 index 0000000..886d6cb --- /dev/null +++ b/docs/source/_build/html/_sources/generated/adpeps.ipeps.models.rst.txt @@ -0,0 +1,23 @@ +adpeps.ipeps.models +=================== + +.. currentmodule:: adpeps.ipeps.models + +.. module:: adpeps.ipeps.models + + +Modules +------- + +.. automodule:: adpeps.ipeps.models + +.. autosummary:: + :toctree: + + + adpeps.ipeps.models.common + + adpeps.ipeps.models.heisenberg + + + diff --git a/docs/source/_build/html/_sources/generated/adpeps.simulation.rst.txt b/docs/source/_build/html/_sources/generated/adpeps.simulation.rst.txt new file mode 100644 index 0000000..d2c6305 --- /dev/null +++ b/docs/source/_build/html/_sources/generated/adpeps.simulation.rst.txt @@ -0,0 +1,23 @@ +adpeps.simulation +================= + +.. currentmodule:: adpeps.simulation + +.. module:: adpeps.simulation + + +Modules +------- + +.. automodule:: adpeps.simulation + +.. autosummary:: + :toctree: + + + adpeps.simulation.run_ipeps_exci + + adpeps.simulation.run_ipeps_gs + + + diff --git a/docs/source/_build/html/_sources/generated/adpeps.simulation.run_ipeps_exci.rst.txt b/docs/source/_build/html/_sources/generated/adpeps.simulation.run_ipeps_exci.rst.txt new file mode 100644 index 0000000..70250d6 --- /dev/null +++ b/docs/source/_build/html/_sources/generated/adpeps.simulation.run_ipeps_exci.rst.txt @@ -0,0 +1,14 @@ +adpeps.simulation.run\_ipeps\_exci +================================== + +.. currentmodule:: adpeps.simulation.run_ipeps_exci + +.. module:: adpeps.simulation.run_ipeps_exci + + + +.. automodule:: adpeps.simulation.run_ipeps_exci + :members: + :member-order: groupwise + + diff --git a/docs/source/_build/html/_sources/generated/adpeps.simulation.run_ipeps_gs.rst.txt b/docs/source/_build/html/_sources/generated/adpeps.simulation.run_ipeps_gs.rst.txt new file mode 100644 index 0000000..276e16a --- /dev/null +++ b/docs/source/_build/html/_sources/generated/adpeps.simulation.run_ipeps_gs.rst.txt @@ -0,0 +1,14 @@ +adpeps.simulation.run\_ipeps\_gs +================================ + +.. currentmodule:: adpeps.simulation.run_ipeps_gs + +.. module:: adpeps.simulation.run_ipeps_gs + + + +.. automodule:: adpeps.simulation.run_ipeps_gs + :members: + :member-order: groupwise + + diff --git a/docs/source/_build/html/_sources/generated/adpeps.utils.ctmtensors.rst.txt b/docs/source/_build/html/_sources/generated/adpeps.utils.ctmtensors.rst.txt new file mode 100644 index 0000000..fc3a665 --- /dev/null +++ b/docs/source/_build/html/_sources/generated/adpeps.utils.ctmtensors.rst.txt @@ -0,0 +1,14 @@ +adpeps.utils.ctmtensors +======================= + +.. currentmodule:: adpeps.utils.ctmtensors + +.. module:: adpeps.utils.ctmtensors + + + +.. automodule:: adpeps.utils.ctmtensors + :members: + :member-order: groupwise + + diff --git a/docs/source/_build/html/_sources/generated/adpeps.utils.empty_tensor.rst.txt b/docs/source/_build/html/_sources/generated/adpeps.utils.empty_tensor.rst.txt new file mode 100644 index 0000000..634791b --- /dev/null +++ b/docs/source/_build/html/_sources/generated/adpeps.utils.empty_tensor.rst.txt @@ -0,0 +1,14 @@ +adpeps.utils.empty\_tensor +========================== + +.. currentmodule:: adpeps.utils.empty_tensor + +.. module:: adpeps.utils.empty_tensor + + + +.. automodule:: adpeps.utils.empty_tensor + :members: + :member-order: groupwise + + diff --git a/docs/source/_build/html/_sources/generated/adpeps.utils.io.rst.txt b/docs/source/_build/html/_sources/generated/adpeps.utils.io.rst.txt new file mode 100644 index 0000000..d73ab43 --- /dev/null +++ b/docs/source/_build/html/_sources/generated/adpeps.utils.io.rst.txt @@ -0,0 +1,14 @@ +adpeps.utils.io +=============== + +.. currentmodule:: adpeps.utils.io + +.. module:: adpeps.utils.io + + + +.. automodule:: adpeps.utils.io + :members: + :member-order: groupwise + + diff --git a/docs/source/_build/html/_sources/generated/adpeps.utils.nested.rst.txt b/docs/source/_build/html/_sources/generated/adpeps.utils.nested.rst.txt new file mode 100644 index 0000000..4d807d9 --- /dev/null +++ b/docs/source/_build/html/_sources/generated/adpeps.utils.nested.rst.txt @@ -0,0 +1,14 @@ +adpeps.utils.nested +=================== + +.. currentmodule:: adpeps.utils.nested + +.. module:: adpeps.utils.nested + + + +.. automodule:: adpeps.utils.nested + :members: + :member-order: groupwise + + diff --git a/docs/source/_build/html/_sources/generated/adpeps.utils.printing.rst.txt b/docs/source/_build/html/_sources/generated/adpeps.utils.printing.rst.txt new file mode 100644 index 0000000..a54b81a --- /dev/null +++ b/docs/source/_build/html/_sources/generated/adpeps.utils.printing.rst.txt @@ -0,0 +1,14 @@ +adpeps.utils.printing +===================== + +.. currentmodule:: adpeps.utils.printing + +.. module:: adpeps.utils.printing + + + +.. automodule:: adpeps.utils.printing + :members: + :member-order: groupwise + + diff --git a/docs/source/_build/html/_sources/generated/adpeps.utils.rst.txt b/docs/source/_build/html/_sources/generated/adpeps.utils.rst.txt new file mode 100644 index 0000000..dc43a5c --- /dev/null +++ b/docs/source/_build/html/_sources/generated/adpeps.utils.rst.txt @@ -0,0 +1,31 @@ +adpeps.utils +============ + +.. currentmodule:: adpeps.utils + +.. module:: adpeps.utils + + +Modules +------- + +.. automodule:: adpeps.utils + +.. autosummary:: + :toctree: + + + adpeps.utils.ctmtensors + + adpeps.utils.empty_tensor + + adpeps.utils.io + + adpeps.utils.nested + + adpeps.utils.printing + + adpeps.utils.tlist + + + diff --git a/docs/source/_build/html/_sources/generated/adpeps.utils.tlist.rst.txt b/docs/source/_build/html/_sources/generated/adpeps.utils.tlist.rst.txt new file mode 100644 index 0000000..8698206 --- /dev/null +++ b/docs/source/_build/html/_sources/generated/adpeps.utils.tlist.rst.txt @@ -0,0 +1,14 @@ +adpeps.utils.tlist +================== + +.. currentmodule:: adpeps.utils.tlist + +.. module:: adpeps.utils.tlist + + + +.. automodule:: adpeps.utils.tlist + :members: + :member-order: groupwise + + diff --git a/docs/source/_build/html/_sources/index.rst.txt b/docs/source/_build/html/_sources/index.rst.txt new file mode 100644 index 0000000..78614ef --- /dev/null +++ b/docs/source/_build/html/_sources/index.rst.txt @@ -0,0 +1,48 @@ +.. AD-PEPS documentation master file, created by + sphinx-quickstart on Mon Apr 12 16:13:24 2021. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +AD-PEPS's documentation +=================================== + +The AD-PEPS Python package is intended as a example of an implementation of iPEPS ground-state and excited-state algorithms using Automatic Differentiation, as described in +As such, the code is meant to illustrate the workings of the algorithms described the paper. +For real applications, this code would likely need to be further adapted and optimized, however the package is a complete implementation and can directly be used for simple calculations. + +.. toctree:: + + notes/install + notes/start + notes/example + notes/example2 + + +Reference +-------------- + +.. .. toctree:: +.. :maxdepth: 2 + +.. ipeps + +.. currentmodule:: adpeps + +.. autosummary:: + :toctree: generated + :recursive: + + ipeps.ipeps + ipeps.config + ipeps.ctm + ipeps.models + simulation + utils + + +Indices and tables +================== + +* :ref:`genindex` +* :ref:`modindex` +* :ref:`search` diff --git a/docs/source/_build/html/_sources/ipeps.rst.txt b/docs/source/_build/html/_sources/ipeps.rst.txt new file mode 100644 index 0000000..e94d9b0 --- /dev/null +++ b/docs/source/_build/html/_sources/ipeps.rst.txt @@ -0,0 +1,17 @@ +adpeps.ipeps +============ + +.. currentmodule:: adpeps.ipeps + +.. toctree:: + :maxdepth: 2 + :caption: Contents + + adpeps.ipeps.ipeps + adpeps.ipeps.ctm + +.. autosummary:: + :toctree: generated + :nosignatures: + + adpeps.ipeps.config diff --git a/docs/source/_build/html/_sources/notes/example.rst.txt b/docs/source/_build/html/_sources/notes/example.rst.txt new file mode 100644 index 0000000..480ca94 --- /dev/null +++ b/docs/source/_build/html/_sources/notes/example.rst.txt @@ -0,0 +1,81 @@ +.. _notes/example: + +Example: ground state +=========================================== + +The package includes an example configuration for a ground-state simulation of the 2D Heisenberg model, defined by the Hamiltonian + +.. math:: + + H = J \sum_i S_i \cdot S_{i+1}~. + +The configuration file `examples/heis_D2.yaml` contains the following: + +.. literalinclude:: ../../../examples/heis_D2.yaml + +This configures a simulation with bond dimension :code:`D=2` and boundary bond dimension :code:`chi=40`, using the model defined in :mod:`adpeps.ipeps.models.heisenberg`. + +Now the simulation can be started by calling the :code:`adpeps` module with the name of this configuration file: + + >>> python -m adpeps gs 'heis_D2' + WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.) + Namespace(config_file='heis_D2', sim_mode='gs', version=False) + Running ground-state sim + ... + +The simulation will continue to run and you should see output similar to this: + +.. code-block:: + + ... + Performing CTM pre-steps without tracking + | CTM step 1 conv: 4.935e-03 time: 3.17 obj: -0.658758 + | CTM step 2 conv: 7.918e-04 time: 3.74 obj: -0.659550 + | CTM step 3 conv: 1.234e-05 time: 6.42 obj: -0.659562 + Performing CTM + | CTM step 1 conv: 3.171e-07 time: 8.8 obj: -0.659563 + | CTM step 2 conv: 2.108e-08 time: 4.07 obj: -0.659563 + | CTM step 3 conv: 8.173e-09 time: 2.93 obj: -0.659563 + Energy: -0.6595625579862193 + ... + +The first cycle of iterations are not taken into account in the gradient computation, but make sure that the CTM iterations with gradient tracking start from some reasonably converged boundary tensors in order to avoid instabilities with initial CTM steps. + +.. note:: + The convergence rate of the CTM depends on the variational parameters of the iPEPS and the settings of the simulation. + Generally the convergence improves as the simulation approaches the optimum. + +Whenever a step in the optimization has completed (this could take more than one cycle of CTM iterations depending on the type of optimizer), the module will output a summary of the steps so far: + +.. code-block:: + + ... + # ======================== # + # Step completed # + # ======================== # + + Step 0 E: -0.376468389894 |grad|: 1.2103482 + Step 1 E: -0.505252956403 |grad|: 0.19064889 + Step 2 E: -0.517432085607 |grad|: 0.10910666 + Step 3 E: -0.578045570568 |grad|: 0.081472534 + Step 4 E: -0.589074339197 |grad|: 0.089438567 + Step 5 E: -0.597590746400 |grad|: 0.15282526 + Step 6 E: -0.612205652457 |grad|: 0.076385807 + Step 7 E: -0.628079118387 |grad|: 0.0684857 + Step 8 E: -0.642200026835 |grad|: 0.097849544 + Step 9 E: -0.649553574703 |grad|: 0.066648727 + Step 10 E: -0.653909263824 |grad|: 0.0264237 + Step 11 E: -0.655389076620 |grad|: 0.016836624 + Step 12 E: -0.656585389308 |grad|: 0.016954703 + Step 13 E: -0.657797020335 |grad|: 0.020011479 + Step 14 E: -0.658174755217 |grad|: 0.033691114 + Step 15 E: -0.659083649568 |grad|: 0.012202327 + Step 16 E: -0.659365377610 |grad|: 0.0064214407 + Step 17 E: -0.659562557986 |grad|: 0.007503111 + ... + +The simulation will continue until :attr:`adpeps.ipeps.config.max_iterations` has been reached. +At any point the simulation can be stopped and continued later by restarting the module. + +.. note:: + In case you would like the simulation to continue from an earlier saved simulation with the same configuration file, make sure to set :attr:`adpeps.ipeps.config.resume` :code:`= True` diff --git a/docs/source/_build/html/_sources/notes/example2.rst.txt b/docs/source/_build/html/_sources/notes/example2.rst.txt new file mode 100644 index 0000000..d894348 --- /dev/null +++ b/docs/source/_build/html/_sources/notes/example2.rst.txt @@ -0,0 +1,96 @@ +.. _notes/example2: + +Example: excitations +========================================= + +.. note:: + This example continues from :ref:`the ground-state example` and requires an optimized ground state to start from. + +Here we demonstrates how to use the :mod:`adpeps` package for computing excited states of the 2D Heisenberg model. + +The configuration file `examples/heis_D2_exci.yaml` contains the following settings: + +.. literalinclude:: ../../../examples/heis_D2_exci.yaml + +Note that many of the options are the same as for the ground-state simulation, with the addition of the :attr:`adpeps.ipeps.config.momentum_path` setting, which controls which path through the Brillouin zone will be taken. + +In the configuration for excited states you do not explicitly set the momentum, but choose a preset path of points in momentum space and pass the index for each simulation. + +If we now start the simulation, we get the following response: + + >>> python -m adpeps exci 'heis_D2_exci' --p_ix=1 + ... + Running excited-state sim + ... + Base file .../exci/heisenberg_D2_X40.base.npz not found. + Prepare the simulation first by running with option '-i' + +What happened is that we first need to make some preparations for the simulation. +For excited-state simulations, we require the following: + + 1. Well-converged CTM boundary tensors + 2. A basis for the excited-state tensors, orthogonal to the ground state + +The preparations for the simulation need to be performed only once, resulting in a `base` simulation file that will be used by the simulations for every momentum. + + >>> python -m adpeps exci 'heis_D2_exci' -i + ... + Running excited-state sim + ... + | CTM step 1 conv: 1.036e-01 time: 3.64 obj: -0.665574 + | CTM step 2 conv: 3.137e-03 time: 4.23 obj: -0.662436 + | CTM step 3 conv: 7.887e-05 time: 4.0 obj: -0.662515 + | CTM step 4 conv: 1.388e-06 time: 2.2 obj: -0.662514 + | CTM step 5 conv: 2.455e-07 time: 1.35 obj: -0.662514 + | CTM step 6 conv: 3.044e-08 time: 1.35 obj: -0.662514 + | CTM step 7 conv: 4.673e-09 time: 1.37 obj: -0.662514 + | CTM step 8 conv: 4.467e-10 time: 1.36 obj: -0.662514 + | CTM step 9 conv: 5.029e-11 time: 1.35 obj: -0.662514 + | CTM step 10 conv: 5.612e-11 time: 1.38 obj: -0.662514 + | CTM step 11 conv: 2.801e-11 time: 1.36 obj: -0.662514 + | CTM step 12 conv: 1.204e-11 time: 1.65 obj: -0.662514 + | CTM step 13 conv: 4.936e-12 time: 1.42 obj: -0.662514 + | CTM step 14 conv: 1.989e-12 time: 1.39 obj: -0.662514 + GS norm 3.5890188873039093 + GS norm 1.0 + Substracting -0.33125703308289145 from Hamiltonian + +Several steps have been performed: first a full CTM contraction of the ground-state network, followed by a normalization of the ground-state tensors. +Then the Hamiltonian is shifted by the ground-state energy expectation value, in order for the excitations to have energies relative to the ground state. +Finally, the basis is prepared and we have everything to get started. + + >>> python -m adpeps exci 'heis_D2_exci' --p_ix=0 + ... + Running excited-state sim + ... + Starting simulation of basis vector 1/62 + Performing CTM + | CTM step 1 conv: 4.236e+00 time: 3.19 obj: 5.173629 + | CTM step 2 conv: 3.539e-02 time: 1.38 obj: 5.138237 + | CTM step 3 conv: 6.139e-03 time: 1.27 obj: 5.132099 + | CTM step 4 conv: 2.116e-04 time: 1.24 obj: 5.132310 + | CTM step 5 conv: 6.148e-05 time: 1.28 obj: 5.132249 + | CTM step 6 conv: 3.704e-04 time: 1.25 obj: 5.131879 + | CTM step 7 conv: 2.493e-04 time: 1.25 obj: 5.131629 + Energies: 0.04418993415167889 1.5450126399606245e-10 + Norm: 0.008611083119254162 + ========== + Finished basis vector 1/62 + - + Starting simulation of basis vector 2/62 + Performing CTM + | CTM step 1 conv: 2.004e+00 time: 0.99 obj: 3.335621 + | CTM step 2 conv: 6.150e-02 time: 1.26 obj: 3.397117 + | CTM step 3 conv: 2.017e-02 time: 1.28 obj: 3.376950 + | CTM step 4 conv: 3.838e-03 time: 1.26 obj: 3.380788 + | CTM step 5 conv: 3.650e-04 time: 1.3 obj: 3.380423 + | CTM step 6 conv: 1.246e-03 time: 1.29 obj: 3.381669 + | CTM step 7 conv: 1.288e-03 time: 1.31 obj: 3.380380 + Energies: 0.4285335373465171 1.5450126399606245e-10 + Norm: 0.12679967208649232 + ========== + Finished basis vector 2/62 + ... + +In this version of the algorithm, the full energy and norm overlap matrices will be computed. +Each of the basis vectors, as seen in the output above, is used as input in a separate CTM summation and the program will continue to run until all basis vectors have been used. diff --git a/docs/source/_build/html/_sources/notes/install.rst.txt b/docs/source/_build/html/_sources/notes/install.rst.txt new file mode 100644 index 0000000..b668de6 --- /dev/null +++ b/docs/source/_build/html/_sources/notes/install.rst.txt @@ -0,0 +1,36 @@ +Installation +=================================== + +The quickest way of installing the :code:`adpeps` package is to clone the repository + +.. code-block:: bash + + git clone + + +Method 1 (recommended): `conda` +------------------------------------------ + +The repository comes with an included :code:`environment.yml` file, which automatically installs a Python environment with all required packages, which can be used as follows + +.. code-block:: bash + + cd ad-peps + conda env create -f environment.yml + conda activate adpeps + +When the installation finishes, you can check that the package is working + +.. code-block:: bash + + python -m adpeps -v + +Method 2: `pip` +------------------------------------------ + +The package can also be installed via `pip`: + +.. code-block:: bash + + cd ad-peps + pip install -e . diff --git a/docs/source/_build/html/_sources/notes/start.rst.txt b/docs/source/_build/html/_sources/notes/start.rst.txt new file mode 100644 index 0000000..08534e4 --- /dev/null +++ b/docs/source/_build/html/_sources/notes/start.rst.txt @@ -0,0 +1,57 @@ +.. _notes/start: + +Getting Started +=================================== + +General +-------------- + +The main starting point for running simulations with the `adpeps` package is by loading the module directly via :code:`python -m adpeps`. + +For both ground-state and excited-state simulations the configuration can be set via configuration :code:`.yaml` files. +Each option in the configuration file corresponds to an attribute of the :mod:`adpeps.ipeps.config` module. + +The first argument for the module is the simulation mode (ground-state or excited-state): + +.. code-block:: bash + + python -m adpeps {gs,exci} ... + +.. note:: + The input configuration file location can be set via the + :envvar:`CONFIGDIR` variable. If it is not set, the default + input folder will be the `examples` subfolder of the package + root directory + +.. note:: + The output data location can be set via the :envvar:`DATADIR` + variable. If it is not set, the default output folder will be + in the `simulations` subfolder of the package root directory. + + +Ground states +-------------- + +For ground-state simulations, the only required argument is the configuration file. + +.. argparse:: + :ref: adpeps.__main__.get_parser + :prog: python -m adpeps + :path: gs + + +Excited states +-------------- + +For excited-state simulations, the first argument is again the name of a configuration file (note that the relevant options are different for excited-state simulations), and furthermore the `momentum index` :code:`-p` is required. + +The momentum index refers to a point in momentum space :math:`(k_x, k_y)` defined in a specific path through the Brillouin zone. +The corresponding momentum path can be set via the :attr:`adpeps.ipeps.config.momentum_path` option. +By default, the `'Bril1'` path is taken, which follows the cut along high symmetry points :math:`(\pi,0) - (\pi,\pi) - (\pi/2,\pi/2) - (0,0) - (\pi,0) - (\pi/2,\pi/2)` + +.. argparse:: + :ref: adpeps.__main__.get_parser + :prog: python -m adpeps + :nodefault: + :path: exci + diff --git a/docs/source/_build/html/_static/basic.css b/docs/source/_build/html/_static/basic.css new file mode 100644 index 0000000..5d8ae08 --- /dev/null +++ b/docs/source/_build/html/_static/basic.css @@ -0,0 +1,861 @@ +/* + * basic.css + * ~~~~~~~~~ + * + * Sphinx stylesheet -- basic theme. + * + * :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ + +/* -- main layout ----------------------------------------------------------- */ + +div.clearer { + clear: both; +} + +div.section::after { + display: block; + content: ''; + clear: left; +} + +/* -- relbar ---------------------------------------------------------------- */ + +div.related { + width: 100%; + font-size: 90%; +} + +div.related h3 { + display: none; +} + +div.related ul { + margin: 0; + padding: 0 0 0 10px; + list-style: none; +} + +div.related li { 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solid;border-left-color:rgba(var(--pst-color-admonition-default),1);border-bottom-color:rgba(var(--pst-color-admonition-default),1);border-right-color:rgba(var(--pst-color-admonition-default),1);border-top-color:rgba(var(--pst-color-admonition-default),1);border-radius:.1rem;box-shadow:0 .2rem .5rem rgba(0,0,0,.05),0 0 .05rem rgba(0,0,0,.1);transition:color .25s,background-color .25s,border-color .25s}.admonition :last-child{margin-bottom:0}.admonition p.admonition-title~*{padding:0 1.4rem}.admonition>ol,.admonition>ul{margin-left:1em}.admonition .admonition-title{position:relative;margin:0 -.6rem!important;padding:.4rem .6rem .4rem 2rem;font-weight:700;background-color:rgba(var(--pst-color-admonition-default),.1)}.admonition .admonition-title:before{position:absolute;left:.6rem;width:1rem;height:1rem;color:rgba(var(--pst-color-admonition-default),1);font-family:Font Awesome\ 5 Free;font-weight:900;content:var(--pst-icon-admonition-default)}.admonition .admonition-title+*{margin-top:.4em}.admonition.attention{border-color:rgba(var(--pst-color-admonition-attention),1)}.admonition.attention .admonition-title{background-color:rgba(var(--pst-color-admonition-attention),.1)}.admonition.attention .admonition-title:before{color:rgba(var(--pst-color-admonition-attention),1);content:var(--pst-icon-admonition-attention)}.admonition.caution{border-color:rgba(var(--pst-color-admonition-caution),1)}.admonition.caution .admonition-title{background-color:rgba(var(--pst-color-admonition-caution),.1)}.admonition.caution .admonition-title:before{color:rgba(var(--pst-color-admonition-caution),1);content:var(--pst-icon-admonition-caution)}.admonition.warning{border-color:rgba(var(--pst-color-admonition-warning),1)}.admonition.warning .admonition-title{background-color:rgba(var(--pst-color-admonition-warning),.1)}.admonition.warning .admonition-title:before{color:rgba(var(--pst-color-admonition-warning),1);content:var(--pst-icon-admonition-warning)}.admonition.danger{border-color:rgba(var(--pst-color-admonition-danger),1)}.admonition.danger .admonition-title{background-color:rgba(var(--pst-color-admonition-danger),.1)}.admonition.danger .admonition-title:before{color:rgba(var(--pst-color-admonition-danger),1);content:var(--pst-icon-admonition-danger)}.admonition.error{border-color:rgba(var(--pst-color-admonition-error),1)}.admonition.error .admonition-title{background-color:rgba(var(--pst-color-admonition-error),.1)}.admonition.error .admonition-title:before{color:rgba(var(--pst-color-admonition-error),1);content:var(--pst-icon-admonition-error)}.admonition.hint{border-color:rgba(var(--pst-color-admonition-hint),1)}.admonition.hint .admonition-title{background-color:rgba(var(--pst-color-admonition-hint),.1)}.admonition.hint .admonition-title:before{color:rgba(var(--pst-color-admonition-hint),1);content:var(--pst-icon-admonition-hint)}.admonition.tip{border-color:rgba(var(--pst-color-admonition-tip),1)}.admonition.tip .admonition-title{background-color:rgba(var(--pst-color-admonition-tip),.1)}.admonition.tip .admonition-title:before{color:rgba(var(--pst-color-admonition-tip),1);content:var(--pst-icon-admonition-tip)}.admonition.important{border-color:rgba(var(--pst-color-admonition-important),1)}.admonition.important .admonition-title{background-color:rgba(var(--pst-color-admonition-important),.1)}.admonition.important .admonition-title:before{color:rgba(var(--pst-color-admonition-important),1);content:var(--pst-icon-admonition-important)}.admonition.note{border-color:rgba(var(--pst-color-admonition-note),1)}.admonition.note .admonition-title{background-color:rgba(var(--pst-color-admonition-note),.1)}.admonition.note .admonition-title:before{color:rgba(var(--pst-color-admonition-note),1);content:var(--pst-icon-admonition-note)}div.deprecated{margin-bottom:10px;margin-top:10px;padding:7px;background-color:#f3e5e5;border:1px solid #eed3d7;border-radius:.5rem}div.deprecated p{color:#b94a48;display:inline}.topic{background-color:#eee}.seealso dd{margin-top:0;margin-bottom:0}.viewcode-back{font-family:var(--pst-font-family-base)}.viewcode-block:target{background-color:#f4debf;border-top:1px solid #ac9;border-bottom:1px solid #ac9}span.guilabel{border:1px solid #7fbbe3;background:#e7f2fa;font-size:80%;font-weight:700;border-radius:4px;padding:2.4px 6px;margin:auto 2px}table.field-list{border-collapse:separate;border-spacing:10px;margin-left:1px}table.field-list th.field-name{padding:1px 8px 1px 5px;white-space:nowrap;background-color:#eee}table.field-list td.field-body p{font-style:italic}table.field-list td.field-body p>strong{font-style:normal}table.field-list td.field-body 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(min-width:1200px){.toc-entry a{padding-right:0}}.toc-entry a:hover{color:rgba(var(--pst-color-toc-link-hover),1);text-decoration:none}.bd-sidebar{padding-top:1em}@media (min-width:720px){.bd-sidebar{border-right:1px solid rgba(0,0,0,.1)}@supports (position:-webkit-sticky) or (position:sticky){.bd-sidebar{position:-webkit-sticky;position:sticky;top:calc(var(--pst-header-height) + 20px);z-index:1000;height:calc(100vh - var(--pst-header-height) - 20px)}}}.bd-sidebar.no-sidebar{border-right:0}.bd-links{padding-top:1rem;padding-bottom:1rem;margin-right:-15px;margin-left:-15px}@media (min-width:720px){.bd-links{display:block!important}@supports (position:-webkit-sticky) or (position:sticky){.bd-links{max-height:calc(100vh - 11rem);overflow-y:auto}}}.bd-sidenav{display:none}.bd-content{padding-top:20px}.bd-content .section{max-width:100%}.bd-content .section table{display:block;overflow:auto}.bd-toc-link{display:block;padding:.25rem 1.5rem;font-weight:600;color:rgba(0,0,0,.65)}.bd-toc-link:hover{color:rgba(0,0,0,.85);text-decoration:none}.bd-toc-item.active{margin-bottom:1rem}.bd-toc-item.active:not(:first-child){margin-top:1rem}.bd-toc-item.active>.bd-toc-link{color:rgba(0,0,0,.85)}.bd-toc-item.active>.bd-toc-link:hover{background-color:transparent}.bd-toc-item.active>.bd-sidenav{display:block}nav.bd-links p.caption{font-size:var(--pst-sidebar-caption-font-size);text-transform:uppercase;font-weight:700;position:relative;margin-top:1.25em;margin-bottom:.5em;padding:0 1.5rem;color:rgba(var(--pst-color-sidebar-caption),1)}nav.bd-links p.caption:first-child{margin-top:0}.bd-sidebar .nav{font-size:var(--pst-sidebar-font-size)}.bd-sidebar .nav ul{list-style:none;padding:0 0 0 1.5rem}.bd-sidebar .nav li>a{display:block;padding:.25rem 1.5rem;color:rgba(var(--pst-color-sidebar-link),1)}.bd-sidebar .nav li>a:hover{color:rgba(var(--pst-color-sidebar-link-hover),1);text-decoration:none;background-color:transparent}.bd-sidebar .nav li>a.reference.external:after{font-family:Font Awesome\ 5 Free;font-weight:900;content:"\f35d";font-size:.75em;margin-left:.3em}.bd-sidebar .nav .active:hover>a,.bd-sidebar .nav .active>a{font-weight:600;color:rgba(var(--pst-color-sidebar-link-active),1)}.toc-h2{font-size:.85rem}.toc-h3{font-size:.75rem}.toc-h4{font-size:.65rem}.toc-entry>.nav-link.active{font-weight:600;color:#130654;color:rgba(var(--pst-color-toc-link-active),1);background-color:transparent;border-left:2px solid rgba(var(--pst-color-toc-link-active),1)}.nav-link:hover{border-style:none}#navbar-main-elements li.nav-item i{font-size:.7rem;padding-left:2px;vertical-align:middle}.bd-toc .nav .nav{display:none}.bd-toc .nav .nav.visible,.bd-toc .nav>.active>ul{display:block}.prev-next-bottom{margin:20px 0}.prev-next-bottom a.left-prev,.prev-next-bottom a.right-next{padding:10px;border:1px solid rgba(0,0,0,.2);max-width:45%;overflow-x:hidden;color:rgba(0,0,0,.65)}.prev-next-bottom a.left-prev{float:left}.prev-next-bottom a.left-prev:before{content:"<< "}.prev-next-bottom a.right-next{float:right}.prev-next-bottom a.right-next:after{content:" >>"}.alert{padding-bottom:0}.alert-info a{color:#e83e8c}#navbar-icon-links i.fa,#navbar-icon-links i.fab,#navbar-icon-links i.far,#navbar-icon-links i.fas{vertical-align:middle;font-style:normal;font-size:1.5rem;line-height:1.25}#navbar-icon-links i.fa-github-square:before{color:#333}#navbar-icon-links i.fa-twitter-square:before{color:#55acee}#navbar-icon-links i.fa-gitlab:before{color:#548}#navbar-icon-links i.fa-bitbucket:before{color:#0052cc}.tocsection{border-left:1px solid #eee;padding:.3rem 1.5rem}.tocsection i{padding-right:.5rem}.editthispage{padding-top:2rem}.editthispage a{color:#130754}.xr-wrap[hidden]{display:block!important}.toctree-checkbox{position:absolute;display:none}.toctree-checkbox~ul{display:none}.toctree-checkbox~label i{transform:rotate(0deg)}.toctree-checkbox:checked~ul{display:block}.toctree-checkbox:checked~label i{transform:rotate(180deg)}.bd-sidebar li{position:relative}.bd-sidebar label{position:absolute;top:0;right:0;height:30px;width:30px;cursor:pointer;display:flex;justify-content:center;align-items:center}.bd-sidebar label:hover{background:rgba(var(--pst-color-sidebar-expander-background-hover),1)}.bd-sidebar label i{display:inline-block;font-size:.75rem;text-align:center}.bd-sidebar label i:hover{color:rgba(var(--pst-color-sidebar-link-hover),1)}.bd-sidebar li.has-children>.reference{padding-right:30px}div.doctest>div.highlight span.gp,span.linenos,table.highlighttable td.linenos{user-select:none!important;-webkit-user-select:text!important;-webkit-user-select:none!important;-moz-user-select:none!important;-ms-user-select:none!important} \ No newline at end of file diff --git a/docs/source/_build/html/_static/css/theme.css b/docs/source/_build/html/_static/css/theme.css new file mode 100644 index 0000000..3f6e79d --- /dev/null +++ b/docs/source/_build/html/_static/css/theme.css @@ -0,0 +1,117 @@ +:root { + /***************************************************************************** + * Theme config + **/ + --pst-header-height: 60px; + + /***************************************************************************** + * Font size + **/ + --pst-font-size-base: 15px; /* base font size - applied at body / html level */ + + /* heading font sizes */ + --pst-font-size-h1: 36px; + --pst-font-size-h2: 32px; + --pst-font-size-h3: 26px; + --pst-font-size-h4: 21px; + --pst-font-size-h5: 18px; + --pst-font-size-h6: 16px; + + /* smaller then heading font sizes*/ + --pst-font-size-milli: 12px; + + --pst-sidebar-font-size: .9em; + --pst-sidebar-caption-font-size: .9em; + + /***************************************************************************** + * Font family + **/ + /* These are adapted from https://systemfontstack.com/ */ + --pst-font-family-base-system: -apple-system, BlinkMacSystemFont, Segoe UI, "Helvetica Neue", + Arial, sans-serif, Apple Color Emoji, Segoe UI Emoji, Segoe UI Symbol; + --pst-font-family-monospace-system: "SFMono-Regular", Menlo, Consolas, Monaco, + Liberation Mono, Lucida Console, monospace; + + --pst-font-family-base: var(--pst-font-family-base-system); + --pst-font-family-heading: var(--pst-font-family-base); + --pst-font-family-monospace: var(--pst-font-family-monospace-system); + + /***************************************************************************** + * Color + * + * Colors are defined in rgb string way, "red, green, blue" + **/ + --pst-color-primary: 19, 6, 84; + --pst-color-success: 40, 167, 69; + --pst-color-info: 0, 123, 255; /*23, 162, 184;*/ + --pst-color-warning: 255, 193, 7; + --pst-color-danger: 220, 53, 69; + --pst-color-text-base: 51, 51, 51; + + --pst-color-h1: var(--pst-color-primary); + --pst-color-h2: var(--pst-color-primary); + --pst-color-h3: var(--pst-color-text-base); + --pst-color-h4: var(--pst-color-text-base); + --pst-color-h5: var(--pst-color-text-base); + --pst-color-h6: var(--pst-color-text-base); + --pst-color-paragraph: var(--pst-color-text-base); + --pst-color-link: 0, 91, 129; + --pst-color-link-hover: 227, 46, 0; + --pst-color-headerlink: 198, 15, 15; + --pst-color-headerlink-hover: 255, 255, 255; + --pst-color-preformatted-text: 34, 34, 34; + --pst-color-preformatted-background: 250, 250, 250; + --pst-color-inline-code: 232, 62, 140; + + --pst-color-active-navigation: 19, 6, 84; + --pst-color-navbar-link: 77, 77, 77; + --pst-color-navbar-link-hover: var(--pst-color-active-navigation); + --pst-color-navbar-link-active: var(--pst-color-active-navigation); + --pst-color-sidebar-link: 77, 77, 77; + --pst-color-sidebar-link-hover: var(--pst-color-active-navigation); + --pst-color-sidebar-link-active: var(--pst-color-active-navigation); + --pst-color-sidebar-expander-background-hover: 244, 244, 244; + --pst-color-sidebar-caption: 77, 77, 77; + --pst-color-toc-link: 119, 117, 122; + --pst-color-toc-link-hover: var(--pst-color-active-navigation); + --pst-color-toc-link-active: var(--pst-color-active-navigation); + + /***************************************************************************** + * Icon + **/ + + /* font awesome icons*/ + --pst-icon-check-circle: '\f058'; + --pst-icon-info-circle: '\f05a'; + --pst-icon-exclamation-triangle: '\f071'; + --pst-icon-exclamation-circle: '\f06a'; + --pst-icon-times-circle: '\f057'; + --pst-icon-lightbulb: '\f0eb'; + + /***************************************************************************** + * Admonitions + **/ + + --pst-color-admonition-default: var(--pst-color-info); + --pst-color-admonition-note: var(--pst-color-info); + --pst-color-admonition-attention: var(--pst-color-warning); + --pst-color-admonition-caution: var(--pst-color-warning); + --pst-color-admonition-warning: var(--pst-color-warning); + --pst-color-admonition-danger: var(--pst-color-danger); + --pst-color-admonition-error: var(--pst-color-danger); + --pst-color-admonition-hint: var(--pst-color-success); + --pst-color-admonition-tip: var(--pst-color-success); + --pst-color-admonition-important: var(--pst-color-success); + + --pst-icon-admonition-default: var(--pst-icon-info-circle); + --pst-icon-admonition-note: var(--pst-icon-info-circle); + --pst-icon-admonition-attention: var(--pst-icon-exclamation-circle); + --pst-icon-admonition-caution: var(--pst-icon-exclamation-triangle); + --pst-icon-admonition-warning: var(--pst-icon-exclamation-triangle); + --pst-icon-admonition-danger: var(--pst-icon-exclamation-triangle); + --pst-icon-admonition-error: var(--pst-icon-times-circle); + --pst-icon-admonition-hint: var(--pst-icon-lightbulb); + --pst-icon-admonition-tip: var(--pst-icon-lightbulb); + --pst-icon-admonition-important: var(--pst-icon-exclamation-circle); + +} diff --git a/docs/source/_build/html/_static/doctools.js b/docs/source/_build/html/_static/doctools.js new file mode 100644 index 0000000..61ac9d2 --- /dev/null +++ b/docs/source/_build/html/_static/doctools.js @@ -0,0 +1,321 @@ +/* + * doctools.js + * ~~~~~~~~~~~ + * + * Sphinx JavaScript utilities for all documentation. + * + * :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ + +/** + * select a different prefix for underscore + */ +$u = _.noConflict(); + +/** + * make the code below compatible with browsers without + * an installed firebug like debugger +if (!window.console || !console.firebug) { + var names = ["log", "debug", "info", "warn", "error", "assert", "dir", + "dirxml", "group", "groupEnd", "time", "timeEnd", "count", "trace", + "profile", "profileEnd"]; + window.console = {}; + for (var i = 0; i < names.length; ++i) + window.console[names[i]] = function() {}; +} + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} + +/** + * Small JavaScript module for the documentation. + */ +var Documentation = { + + init : function() { + this.fixFirefoxAnchorBug(); + this.highlightSearchWords(); + this.initIndexTable(); + if (DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) { + this.initOnKeyListeners(); + } + }, + + /** + * i18n support + */ + TRANSLATIONS : {}, + PLURAL_EXPR : function(n) { return n === 1 ? 0 : 1; }, + LOCALE : 'unknown', + + // gettext and ngettext don't access this so that the functions + // can safely bound to a different name (_ = Documentation.gettext) + gettext : function(string) { + var translated = Documentation.TRANSLATIONS[string]; + if (typeof translated === 'undefined') + return string; + return (typeof translated === 'string') ? translated : translated[0]; + }, + + ngettext : function(singular, plural, n) { + var translated = Documentation.TRANSLATIONS[singular]; + if (typeof translated === 'undefined') + return (n == 1) ? singular : plural; + return translated[Documentation.PLURALEXPR(n)]; + }, + + addTranslations : function(catalog) { + for (var key in catalog.messages) + this.TRANSLATIONS[key] = catalog.messages[key]; + this.PLURAL_EXPR = new Function('n', 'return +(' + catalog.plural_expr + ')'); + this.LOCALE = catalog.locale; + }, + + /** + * add context elements like header anchor links + */ + addContextElements : function() { + $('div[id] > :header:first').each(function() { + $('\u00B6'). + attr('href', '#' + this.id). + attr('title', _('Permalink to this headline')). + appendTo(this); + }); + $('dt[id]').each(function() { + $('\u00B6'). + attr('href', '#' + this.id). + attr('title', _('Permalink to this definition')). + appendTo(this); + }); + }, + + /** + * workaround a firefox stupidity + * see: https://bugzilla.mozilla.org/show_bug.cgi?id=645075 + */ + fixFirefoxAnchorBug : function() { + if (document.location.hash && $.browser.mozilla) + window.setTimeout(function() { + document.location.href += ''; + }, 10); + }, + + /** + * highlight the search words provided in the url in the text + */ + highlightSearchWords : function() { + var params = $.getQueryParameters(); + var terms = (params.highlight) ? params.highlight[0].split(/\s+/) : []; + if (terms.length) { + var body = $('div.body'); + if (!body.length) { + body = $('body'); + } + window.setTimeout(function() { + $.each(terms, function() { + body.highlightText(this.toLowerCase(), 'highlighted'); + }); + }, 10); + $('

' + _('Hide Search Matches') + '

') + .appendTo($('#searchbox')); + } + }, + + /** + * init the domain index toggle buttons + */ + initIndexTable : function() { + var togglers = $('img.toggler').click(function() { + var src = $(this).attr('src'); + var idnum = $(this).attr('id').substr(7); + $('tr.cg-' + idnum).toggle(); + if (src.substr(-9) === 'minus.png') + $(this).attr('src', src.substr(0, src.length-9) + 'plus.png'); + else + $(this).attr('src', src.substr(0, src.length-8) + 'minus.png'); + }).css('display', ''); + if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) { + togglers.click(); + } + }, + + /** + * helper function to hide the search marks again + */ + hideSearchWords : function() { + $('#searchbox .highlight-link').fadeOut(300); + $('span.highlighted').removeClass('highlighted'); + }, + + /** + * make the url absolute + */ + makeURL : function(relativeURL) { + return DOCUMENTATION_OPTIONS.URL_ROOT + '/' + relativeURL; + }, + + /** + * get the current relative url + */ + getCurrentURL : function() { + var path = document.location.pathname; + var parts = path.split(/\//); + $.each(DOCUMENTATION_OPTIONS.URL_ROOT.split(/\//), function() { + if (this === '..') + parts.pop(); + }); + var url = parts.join('/'); + return path.substring(url.lastIndexOf('/') + 1, path.length - 1); + }, + + initOnKeyListeners: function() { + $(document).keydown(function(event) { + var activeElementType = document.activeElement.tagName; + // don't navigate when in search box, textarea, dropdown or button + if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT' + && activeElementType !== 'BUTTON' && !event.altKey && !event.ctrlKey && !event.metaKey + && !event.shiftKey) { + switch (event.keyCode) { + case 37: // left + var prevHref = $('link[rel="prev"]').prop('href'); + if (prevHref) { + window.location.href = prevHref; + return false; + } + case 39: // right + var nextHref = $('link[rel="next"]').prop('href'); + if (nextHref) { + window.location.href = nextHref; + return false; + } + } + } + }); + } +}; + +// quick alias for translations +_ = Documentation.gettext; + +$(document).ready(function() { + Documentation.init(); +}); diff --git a/docs/source/_build/html/_static/documentation_options.js b/docs/source/_build/html/_static/documentation_options.js new file mode 100644 index 0000000..75b5cf1 --- /dev/null +++ b/docs/source/_build/html/_static/documentation_options.js @@ -0,0 +1,12 @@ +var DOCUMENTATION_OPTIONS = { + URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'), + VERSION: '', + LANGUAGE: 'None', + COLLAPSE_INDEX: false, + BUILDER: 'html', + FILE_SUFFIX: '.html', + LINK_SUFFIX: '.html', + HAS_SOURCE: true, + SOURCELINK_SUFFIX: '.txt', + NAVIGATION_WITH_KEYS: true +}; \ No newline at end of file diff --git a/docs/source/_build/html/_static/file.png b/docs/source/_build/html/_static/file.png new file mode 100644 index 0000000000000000000000000000000000000000..a858a410e4faa62ce324d814e4b816fff83a6fb3 GIT binary patch literal 286 zcmV+(0pb3MP)s`hMrGg#P~ix$^RISR_I47Y|r1 z_CyJOe}D1){SET-^Amu_i71Lt6eYfZjRyw@I6OQAIXXHDfiX^GbOlHe=Ae4>0m)d(f|Me07*qoM6N<$f}vM^LjV8( literal 0 HcmV?d00001 diff --git a/docs/source/_build/html/_static/jquery-3.5.1.js b/docs/source/_build/html/_static/jquery-3.5.1.js new file mode 100644 index 0000000..5093733 --- /dev/null +++ b/docs/source/_build/html/_static/jquery-3.5.1.js @@ -0,0 +1,10872 @@ +/*! + * jQuery JavaScript Library v3.5.1 + * https://jquery.com/ + * + * Includes Sizzle.js + * https://sizzlejs.com/ + * + * Copyright JS Foundation and other contributors + * Released under the MIT license + * https://jquery.org/license + * + * Date: 2020-05-04T22:49Z + */ +( function( global, factory ) { + + "use strict"; + + if ( typeof module === "object" && typeof module.exports === "object" ) { + + // For CommonJS and CommonJS-like environments where a proper `window` + // is present, execute the factory and get jQuery. + // For environments that do not have a `window` with a `document` + // (such as Node.js), expose a factory as module.exports. + // This accentuates the need for the creation of a real `window`. + // e.g. var jQuery = require("jquery")(window); + // See ticket #14549 for more info. + module.exports = global.document ? + factory( global, true ) : + function( w ) { + if ( !w.document ) { + throw new Error( "jQuery requires a window with a document" ); + } + return factory( w ); + }; + } else { + factory( global ); + } + +// Pass this if window is not defined yet +} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) { + +// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1 +// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode +// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common +// enough that all such attempts are guarded in a try block. +"use strict"; + +var arr = []; + +var getProto = Object.getPrototypeOf; + +var slice = arr.slice; + +var flat = arr.flat ? function( array ) { + return arr.flat.call( array ); +} : function( array ) { + return arr.concat.apply( [], array ); +}; + + +var push = arr.push; + +var indexOf = arr.indexOf; + +var class2type = {}; + +var toString = class2type.toString; + +var hasOwn = class2type.hasOwnProperty; + +var fnToString = hasOwn.toString; + +var ObjectFunctionString = fnToString.call( Object ); + +var support = {}; + +var isFunction = function isFunction( obj ) { + + // Support: Chrome <=57, Firefox <=52 + // In some browsers, typeof returns "function" for HTML elements + // (i.e., `typeof document.createElement( "object" ) === "function"`). + // We don't want to classify *any* DOM node as a function. + return typeof obj === "function" && typeof obj.nodeType !== "number"; + }; + + +var isWindow = function isWindow( obj ) { + return obj != null && obj === obj.window; + }; + + +var document = window.document; + + + + var preservedScriptAttributes = { + type: true, + src: true, + nonce: true, + noModule: true + }; + + function DOMEval( code, node, doc ) { + doc = doc || document; + + var i, val, + script = doc.createElement( "script" ); + + script.text = code; + if ( node ) { + for ( i in preservedScriptAttributes ) { + + // Support: Firefox 64+, Edge 18+ + // Some browsers don't support the "nonce" property on scripts. + // On the other hand, just using `getAttribute` is not enough as + // the `nonce` attribute is reset to an empty string whenever it + // becomes browsing-context connected. + // See https://github.com/whatwg/html/issues/2369 + // See https://html.spec.whatwg.org/#nonce-attributes + // The `node.getAttribute` check was added for the sake of + // `jQuery.globalEval` so that it can fake a nonce-containing node + // via an object. + val = node[ i ] || node.getAttribute && node.getAttribute( i ); + if ( val ) { + script.setAttribute( i, val ); + } + } + } + doc.head.appendChild( script ).parentNode.removeChild( script ); + } + + +function toType( obj ) { + if ( obj == null ) { + return obj + ""; + } + + // Support: Android <=2.3 only (functionish RegExp) + return typeof obj === "object" || typeof obj === "function" ? + class2type[ toString.call( obj ) ] || "object" : + typeof obj; +} +/* global Symbol */ +// Defining this global in .eslintrc.json would create a danger of using the global +// unguarded in another place, it seems safer to define global only for this module + + + +var + version = "3.5.1", + + // Define a local copy of jQuery + jQuery = function( selector, context ) { + + // The jQuery object is actually just the init constructor 'enhanced' + // Need init if jQuery is called (just allow error to be thrown if not included) + return new jQuery.fn.init( selector, context ); + }; + +jQuery.fn = jQuery.prototype = { + + // The current version of jQuery being used + jquery: version, + + constructor: jQuery, + + // The default length of a jQuery object is 0 + length: 0, + + toArray: function() { + return slice.call( this ); + }, + + // Get the Nth element in the matched element set OR + // Get the whole matched element set as a clean array + get: function( num ) { + + // Return all the elements in a clean array + if ( num == null ) { + return slice.call( this ); + } + + // Return just the one element from the set + return num < 0 ? this[ num + this.length ] : this[ num ]; + }, + + // Take an array of elements and push it onto the stack + // (returning the new matched element set) + pushStack: function( elems ) { + + // Build a new jQuery matched element set + var ret = jQuery.merge( this.constructor(), elems ); + + // Add the old object onto the stack (as a reference) + ret.prevObject = this; + + // Return the newly-formed element set + return ret; + }, + + // Execute a callback for every element in the matched set. + each: function( callback ) { + return jQuery.each( this, callback ); + }, + + map: function( callback ) { + return this.pushStack( jQuery.map( this, function( elem, i ) { + return callback.call( elem, i, elem ); + } ) ); + }, + + slice: function() { + return this.pushStack( slice.apply( this, arguments ) ); + }, + + first: function() { + return this.eq( 0 ); + }, + + last: function() { + return this.eq( -1 ); + }, + + even: function() { + return this.pushStack( jQuery.grep( this, function( _elem, i ) { + return ( i + 1 ) % 2; + } ) ); + }, + + odd: function() { + return this.pushStack( jQuery.grep( this, function( _elem, i ) { + return i % 2; + } ) ); + }, + + eq: function( i ) { + var len = this.length, + j = +i + ( i < 0 ? len : 0 ); + return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] ); + }, + + end: function() { + return this.prevObject || this.constructor(); + }, + + // For internal use only. + // Behaves like an Array's method, not like a jQuery method. + push: push, + sort: arr.sort, + splice: arr.splice +}; + +jQuery.extend = jQuery.fn.extend = function() { + var options, name, src, copy, copyIsArray, clone, + target = arguments[ 0 ] || {}, + i = 1, + length = arguments.length, + deep = false; + + // Handle a deep copy situation + if ( typeof target === "boolean" ) { + deep = target; + + // Skip the boolean and the target + target = arguments[ i ] || {}; + i++; + } + + // Handle case when target is a string or something (possible in deep copy) + if ( typeof target !== "object" && !isFunction( target ) ) { + target = {}; + } + + // Extend jQuery itself if only one argument is passed + if ( i === length ) { + target = this; + i--; + } + + for ( ; i < length; i++ ) { + + // Only deal with non-null/undefined values + if ( ( options = arguments[ i ] ) != null ) { + + // Extend the base object + for ( name in options ) { + copy = options[ name ]; + + // Prevent Object.prototype pollution + // Prevent never-ending loop + if ( name === "__proto__" || target === copy ) { + continue; + } + + // Recurse if we're merging plain objects or arrays + if ( deep && copy && ( jQuery.isPlainObject( copy ) || + ( copyIsArray = Array.isArray( copy ) ) ) ) { + src = target[ name ]; + + // Ensure proper type for the source value + if ( copyIsArray && !Array.isArray( src ) ) { + clone = []; + } else if ( !copyIsArray && !jQuery.isPlainObject( src ) ) { + clone = {}; + } else { + clone = src; + } + copyIsArray = false; + + // Never move original objects, clone them + target[ name ] = jQuery.extend( deep, clone, copy ); + + // Don't bring in undefined values + } else if ( copy !== undefined ) { + target[ name ] = copy; + } + } + } + } + + // Return the modified object + return target; +}; + +jQuery.extend( { + + // Unique for each copy of jQuery on the page + expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ), + + // Assume jQuery is ready without the ready module + isReady: true, + + error: function( msg ) { + throw new Error( msg ); + }, + + noop: function() {}, + + isPlainObject: function( obj ) { + var proto, Ctor; + + // Detect obvious negatives + // Use toString instead of jQuery.type to catch host objects + if ( !obj || toString.call( obj ) !== "[object Object]" ) { + return false; + } + + proto = getProto( obj ); + + // Objects with no prototype (e.g., `Object.create( null )`) are plain + if ( !proto ) { + return true; + } + + // Objects with prototype are plain iff they were constructed by a global Object function + Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor; + return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString; + }, + + isEmptyObject: function( obj ) { + var name; + + for ( name in obj ) { + return false; + } + return true; + }, + + // Evaluates a script in a provided context; falls back to the global one + // if not specified. + globalEval: function( code, options, doc ) { + DOMEval( code, { nonce: options && options.nonce }, doc ); + }, + + each: function( obj, callback ) { + var length, i = 0; + + if ( isArrayLike( obj ) ) { + length = obj.length; + for ( ; i < length; i++ ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } else { + for ( i in obj ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } + + return obj; + }, + + // results is for internal usage only + makeArray: function( arr, results ) { + var ret = results || []; + + if ( arr != null ) { + if ( isArrayLike( Object( arr ) ) ) { + jQuery.merge( ret, + typeof arr === "string" ? + [ arr ] : arr + ); + } else { + push.call( ret, arr ); + } + } + + return ret; + }, + + inArray: function( elem, arr, i ) { + return arr == null ? -1 : indexOf.call( arr, elem, i ); + }, + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + merge: function( first, second ) { + var len = +second.length, + j = 0, + i = first.length; + + for ( ; j < len; j++ ) { + first[ i++ ] = second[ j ]; + } + + first.length = i; + + return first; + }, + + grep: function( elems, callback, invert ) { + var callbackInverse, + matches = [], + i = 0, + length = elems.length, + callbackExpect = !invert; + + // Go through the array, only saving the items + // that pass the validator function + for ( ; i < length; i++ ) { + callbackInverse = !callback( elems[ i ], i ); + if ( callbackInverse !== callbackExpect ) { + matches.push( elems[ i ] ); + } + } + + return matches; + }, + + // arg is for internal usage only + map: function( elems, callback, arg ) { + var length, value, + i = 0, + ret = []; + + // Go through the array, translating each of the items to their new values + if ( isArrayLike( elems ) ) { + length = elems.length; + for ( ; i < length; i++ ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + + // Go through every key on the object, + } else { + for ( i in elems ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + } + + // Flatten any nested arrays + return flat( ret ); + }, + + // A global GUID counter for objects + guid: 1, + + // jQuery.support is not used in Core but other projects attach their + // properties to it so it needs to exist. + support: support +} ); + +if ( typeof Symbol === "function" ) { + jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ]; +} + +// Populate the class2type map +jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ), +function( _i, name ) { + class2type[ "[object " + name + "]" ] = name.toLowerCase(); +} ); + +function isArrayLike( obj ) { + + // Support: real iOS 8.2 only (not reproducible in simulator) + // `in` check used to prevent JIT error (gh-2145) + // hasOwn isn't used here due to false negatives + // regarding Nodelist length in IE + var length = !!obj && "length" in obj && obj.length, + type = toType( obj ); + + if ( isFunction( obj ) || isWindow( obj ) ) { + return false; + } + + return type === "array" || length === 0 || + typeof length === "number" && length > 0 && ( length - 1 ) in obj; +} +var Sizzle = +/*! + * Sizzle CSS Selector Engine v2.3.5 + * https://sizzlejs.com/ + * + * Copyright JS Foundation and other contributors + * Released under the MIT license + * https://js.foundation/ + * + * Date: 2020-03-14 + */ +( function( window ) { +var i, + support, + Expr, + getText, + isXML, + tokenize, + compile, + select, + outermostContext, + sortInput, + hasDuplicate, + + // Local document vars + setDocument, + document, + docElem, + documentIsHTML, + rbuggyQSA, + rbuggyMatches, + matches, + contains, + + // Instance-specific data + expando = "sizzle" + 1 * new Date(), + preferredDoc = window.document, + dirruns = 0, + done = 0, + classCache = createCache(), + tokenCache = createCache(), + compilerCache = createCache(), + nonnativeSelectorCache = createCache(), + sortOrder = function( a, b ) { + if ( a === b ) { + hasDuplicate = true; + } + return 0; + }, + + // Instance methods + hasOwn = ( {} ).hasOwnProperty, + arr = [], + pop = arr.pop, + pushNative = arr.push, + push = arr.push, + slice = arr.slice, + + // Use a stripped-down indexOf as it's faster than native + // https://jsperf.com/thor-indexof-vs-for/5 + indexOf = function( list, elem ) { + var i = 0, + len = list.length; + for ( ; i < len; i++ ) { + if ( list[ i ] === elem ) { + return i; + } + } + return -1; + }, + + booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" + + "ismap|loop|multiple|open|readonly|required|scoped", + + // Regular expressions + + // http://www.w3.org/TR/css3-selectors/#whitespace + whitespace = "[\\x20\\t\\r\\n\\f]", + + // https://www.w3.org/TR/css-syntax-3/#ident-token-diagram + identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace + + "?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+", + + // Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors + attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace + + + // Operator (capture 2) + "*([*^$|!~]?=)" + whitespace + + + // "Attribute values must be CSS identifiers [capture 5] + // or strings [capture 3 or capture 4]" + "*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + + whitespace + "*\\]", + + pseudos = ":(" + identifier + ")(?:\\((" + + + // To reduce the number of selectors needing tokenize in the preFilter, prefer arguments: + // 1. quoted (capture 3; capture 4 or capture 5) + "('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" + + + // 2. simple (capture 6) + "((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" + + + // 3. anything else (capture 2) + ".*" + + ")\\)|)", + + // Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter + rwhitespace = new RegExp( whitespace + "+", "g" ), + rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + + whitespace + "+$", "g" ), + + rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ), + rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + + "*" ), + rdescend = new RegExp( whitespace + "|>" ), + + rpseudo = new RegExp( pseudos ), + ridentifier = new RegExp( "^" + identifier + "$" ), + + matchExpr = { + "ID": new RegExp( "^#(" + identifier + ")" ), + "CLASS": new RegExp( "^\\.(" + identifier + ")" ), + "TAG": new RegExp( "^(" + identifier + "|[*])" ), + "ATTR": new RegExp( "^" + attributes ), + "PSEUDO": new RegExp( "^" + pseudos ), + "CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + + whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + + whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ), + "bool": new RegExp( "^(?:" + booleans + ")$", "i" ), + + // For use in libraries implementing .is() + // We use this for POS matching in `select` + "needsContext": new RegExp( "^" + whitespace + + "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace + + "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" ) + }, + + rhtml = /HTML$/i, + rinputs = /^(?:input|select|textarea|button)$/i, + rheader = /^h\d$/i, + + rnative = /^[^{]+\{\s*\[native \w/, + + // Easily-parseable/retrievable ID or TAG or CLASS selectors + rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/, + + rsibling = /[+~]/, + + // CSS escapes + // http://www.w3.org/TR/CSS21/syndata.html#escaped-characters + runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ), + funescape = function( escape, nonHex ) { + var high = "0x" + escape.slice( 1 ) - 0x10000; + + return nonHex ? + + // Strip the backslash prefix from a non-hex escape sequence + nonHex : + + // Replace a hexadecimal escape sequence with the encoded Unicode code point + // Support: IE <=11+ + // For values outside the Basic Multilingual Plane (BMP), manually construct a + // surrogate pair + high < 0 ? + String.fromCharCode( high + 0x10000 ) : + String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 ); + }, + + // CSS string/identifier serialization + // https://drafts.csswg.org/cssom/#common-serializing-idioms + rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g, + fcssescape = function( ch, asCodePoint ) { + if ( asCodePoint ) { + + // U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER + if ( ch === "\0" ) { + return "\uFFFD"; + } + + // Control characters and (dependent upon position) numbers get escaped as code points + return ch.slice( 0, -1 ) + "\\" + + ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " "; + } + + // Other potentially-special ASCII characters get backslash-escaped + return "\\" + ch; + }, + + // Used for iframes + // See setDocument() + // Removing the function wrapper causes a "Permission Denied" + // error in IE + unloadHandler = function() { + setDocument(); + }, + + inDisabledFieldset = addCombinator( + function( elem ) { + return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset"; + }, + { dir: "parentNode", next: "legend" } + ); + +// Optimize for push.apply( _, NodeList ) +try { + push.apply( + ( arr = slice.call( preferredDoc.childNodes ) ), + preferredDoc.childNodes + ); + + // Support: Android<4.0 + // Detect silently failing push.apply + // eslint-disable-next-line no-unused-expressions + arr[ preferredDoc.childNodes.length ].nodeType; +} catch ( e ) { + push = { apply: arr.length ? + + // Leverage slice if possible + function( target, els ) { + pushNative.apply( target, slice.call( els ) ); + } : + + // Support: IE<9 + // Otherwise append directly + function( target, els ) { + var j = target.length, + i = 0; + + // Can't trust NodeList.length + while ( ( target[ j++ ] = els[ i++ ] ) ) {} + target.length = j - 1; + } + }; +} + +function Sizzle( selector, context, results, seed ) { + var m, i, elem, nid, match, groups, newSelector, + newContext = context && context.ownerDocument, + + // nodeType defaults to 9, since context defaults to document + nodeType = context ? context.nodeType : 9; + + results = results || []; + + // Return early from calls with invalid selector or context + if ( typeof selector !== "string" || !selector || + nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) { + + return results; + } + + // Try to shortcut find operations (as opposed to filters) in HTML documents + if ( !seed ) { + setDocument( context ); + context = context || document; + + if ( documentIsHTML ) { + + // If the selector is sufficiently simple, try using a "get*By*" DOM method + // (excepting DocumentFragment context, where the methods don't exist) + if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) { + + // ID selector + if ( ( m = match[ 1 ] ) ) { + + // Document context + if ( nodeType === 9 ) { + if ( ( elem = context.getElementById( m ) ) ) { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( elem.id === m ) { + results.push( elem ); + return results; + } + } else { + return results; + } + + // Element context + } else { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( newContext && ( elem = newContext.getElementById( m ) ) && + contains( context, elem ) && + elem.id === m ) { + + results.push( elem ); + return results; + } + } + + // Type selector + } else if ( match[ 2 ] ) { + push.apply( results, context.getElementsByTagName( selector ) ); + return results; + + // Class selector + } else if ( ( m = match[ 3 ] ) && support.getElementsByClassName && + context.getElementsByClassName ) { + + push.apply( results, context.getElementsByClassName( m ) ); + return results; + } + } + + // Take advantage of querySelectorAll + if ( support.qsa && + !nonnativeSelectorCache[ selector + " " ] && + ( !rbuggyQSA || !rbuggyQSA.test( selector ) ) && + + // Support: IE 8 only + // Exclude object elements + ( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) { + + newSelector = selector; + newContext = context; + + // qSA considers elements outside a scoping root when evaluating child or + // descendant combinators, which is not what we want. + // In such cases, we work around the behavior by prefixing every selector in the + // list with an ID selector referencing the scope context. + // The technique has to be used as well when a leading combinator is used + // as such selectors are not recognized by querySelectorAll. + // Thanks to Andrew Dupont for this technique. + if ( nodeType === 1 && + ( rdescend.test( selector ) || rcombinators.test( selector ) ) ) { + + // Expand context for sibling selectors + newContext = rsibling.test( selector ) && testContext( context.parentNode ) || + context; + + // We can use :scope instead of the ID hack if the browser + // supports it & if we're not changing the context. + if ( newContext !== context || !support.scope ) { + + // Capture the context ID, setting it first if necessary + if ( ( nid = context.getAttribute( "id" ) ) ) { + nid = nid.replace( rcssescape, fcssescape ); + } else { + context.setAttribute( "id", ( nid = expando ) ); + } + } + + // Prefix every selector in the list + groups = tokenize( selector ); + i = groups.length; + while ( i-- ) { + groups[ i ] = ( nid ? "#" + nid : ":scope" ) + " " + + toSelector( groups[ i ] ); + } + newSelector = groups.join( "," ); + } + + try { + push.apply( results, + newContext.querySelectorAll( newSelector ) + ); + return results; + } catch ( qsaError ) { + nonnativeSelectorCache( selector, true ); + } finally { + if ( nid === expando ) { + context.removeAttribute( "id" ); + } + } + } + } + } + + // All others + return select( selector.replace( rtrim, "$1" ), context, results, seed ); +} + +/** + * Create key-value caches of limited size + * @returns {function(string, object)} Returns the Object data after storing it on itself with + * property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength) + * deleting the oldest entry + */ +function createCache() { + var keys = []; + + function cache( key, value ) { + + // Use (key + " ") to avoid collision with native prototype properties (see Issue #157) + if ( keys.push( key + " " ) > Expr.cacheLength ) { + + // Only keep the most recent entries + delete cache[ keys.shift() ]; + } + return ( cache[ key + " " ] = value ); + } + return cache; +} + +/** + * Mark a function for special use by Sizzle + * @param {Function} fn The function to mark + */ +function markFunction( fn ) { + fn[ expando ] = true; + return fn; +} + +/** + * Support testing using an element + * @param {Function} fn Passed the created element and returns a boolean result + */ +function assert( fn ) { + var el = document.createElement( "fieldset" ); + + try { + return !!fn( el ); + } catch ( e ) { + return false; + } finally { + + // Remove from its parent by default + if ( el.parentNode ) { + el.parentNode.removeChild( el ); + } + + // release memory in IE + el = null; + } +} + +/** + * Adds the same handler for all of the specified attrs + * @param {String} attrs Pipe-separated list of attributes + * @param {Function} handler The method that will be applied + */ +function addHandle( attrs, handler ) { + var arr = attrs.split( "|" ), + i = arr.length; + + while ( i-- ) { + Expr.attrHandle[ arr[ i ] ] = handler; + } +} + +/** + * Checks document order of two siblings + * @param {Element} a + * @param {Element} b + * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b + */ +function siblingCheck( a, b ) { + var cur = b && a, + diff = cur && a.nodeType === 1 && b.nodeType === 1 && + a.sourceIndex - b.sourceIndex; + + // Use IE sourceIndex if available on both nodes + if ( diff ) { + return diff; + } + + // Check if b follows a + if ( cur ) { + while ( ( cur = cur.nextSibling ) ) { + if ( cur === b ) { + return -1; + } + } + } + + return a ? 1 : -1; +} + +/** + * Returns a function to use in pseudos for input types + * @param {String} type + */ +function createInputPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for buttons + * @param {String} type + */ +function createButtonPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return ( name === "input" || name === "button" ) && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for :enabled/:disabled + * @param {Boolean} disabled true for :disabled; false for :enabled + */ +function createDisabledPseudo( disabled ) { + + // Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable + return function( elem ) { + + // Only certain elements can match :enabled or :disabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled + if ( "form" in elem ) { + + // Check for inherited disabledness on relevant non-disabled elements: + // * listed form-associated elements in a disabled fieldset + // https://html.spec.whatwg.org/multipage/forms.html#category-listed + // https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled + // * option elements in a disabled optgroup + // https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled + // All such elements have a "form" property. + if ( elem.parentNode && elem.disabled === false ) { + + // Option elements defer to a parent optgroup if present + if ( "label" in elem ) { + if ( "label" in elem.parentNode ) { + return elem.parentNode.disabled === disabled; + } else { + return elem.disabled === disabled; + } + } + + // Support: IE 6 - 11 + // Use the isDisabled shortcut property to check for disabled fieldset ancestors + return elem.isDisabled === disabled || + + // Where there is no isDisabled, check manually + /* jshint -W018 */ + elem.isDisabled !== !disabled && + inDisabledFieldset( elem ) === disabled; + } + + return elem.disabled === disabled; + + // Try to winnow out elements that can't be disabled before trusting the disabled property. + // Some victims get caught in our net (label, legend, menu, track), but it shouldn't + // even exist on them, let alone have a boolean value. + } else if ( "label" in elem ) { + return elem.disabled === disabled; + } + + // Remaining elements are neither :enabled nor :disabled + return false; + }; +} + +/** + * Returns a function to use in pseudos for positionals + * @param {Function} fn + */ +function createPositionalPseudo( fn ) { + return markFunction( function( argument ) { + argument = +argument; + return markFunction( function( seed, matches ) { + var j, + matchIndexes = fn( [], seed.length, argument ), + i = matchIndexes.length; + + // Match elements found at the specified indexes + while ( i-- ) { + if ( seed[ ( j = matchIndexes[ i ] ) ] ) { + seed[ j ] = !( matches[ j ] = seed[ j ] ); + } + } + } ); + } ); +} + +/** + * Checks a node for validity as a Sizzle context + * @param {Element|Object=} context + * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value + */ +function testContext( context ) { + return context && typeof context.getElementsByTagName !== "undefined" && context; +} + +// Expose support vars for convenience +support = Sizzle.support = {}; + +/** + * Detects XML nodes + * @param {Element|Object} elem An element or a document + * @returns {Boolean} True iff elem is a non-HTML XML node + */ +isXML = Sizzle.isXML = function( elem ) { + var namespace = elem.namespaceURI, + docElem = ( elem.ownerDocument || elem ).documentElement; + + // Support: IE <=8 + // Assume HTML when documentElement doesn't yet exist, such as inside loading iframes + // https://bugs.jquery.com/ticket/4833 + return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" ); +}; + +/** + * Sets document-related variables once based on the current document + * @param {Element|Object} [doc] An element or document object to use to set the document + * @returns {Object} Returns the current document + */ +setDocument = Sizzle.setDocument = function( node ) { + var hasCompare, subWindow, + doc = node ? node.ownerDocument || node : preferredDoc; + + // Return early if doc is invalid or already selected + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( doc == document || doc.nodeType !== 9 || !doc.documentElement ) { + return document; + } + + // Update global variables + document = doc; + docElem = document.documentElement; + documentIsHTML = !isXML( document ); + + // Support: IE 9 - 11+, Edge 12 - 18+ + // Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936) + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( preferredDoc != document && + ( subWindow = document.defaultView ) && subWindow.top !== subWindow ) { + + // Support: IE 11, Edge + if ( subWindow.addEventListener ) { + subWindow.addEventListener( "unload", unloadHandler, false ); + + // Support: IE 9 - 10 only + } else if ( subWindow.attachEvent ) { + subWindow.attachEvent( "onunload", unloadHandler ); + } + } + + // Support: IE 8 - 11+, Edge 12 - 18+, Chrome <=16 - 25 only, Firefox <=3.6 - 31 only, + // Safari 4 - 5 only, Opera <=11.6 - 12.x only + // IE/Edge & older browsers don't support the :scope pseudo-class. + // Support: Safari 6.0 only + // Safari 6.0 supports :scope but it's an alias of :root there. + support.scope = assert( function( el ) { + docElem.appendChild( el ).appendChild( document.createElement( "div" ) ); + return typeof el.querySelectorAll !== "undefined" && + !el.querySelectorAll( ":scope fieldset div" ).length; + } ); + + /* Attributes + ---------------------------------------------------------------------- */ + + // Support: IE<8 + // Verify that getAttribute really returns attributes and not properties + // (excepting IE8 booleans) + support.attributes = assert( function( el ) { + el.className = "i"; + return !el.getAttribute( "className" ); + } ); + + /* getElement(s)By* + ---------------------------------------------------------------------- */ + + // Check if getElementsByTagName("*") returns only elements + support.getElementsByTagName = assert( function( el ) { + el.appendChild( document.createComment( "" ) ); + return !el.getElementsByTagName( "*" ).length; + } ); + + // Support: IE<9 + support.getElementsByClassName = rnative.test( document.getElementsByClassName ); + + // Support: IE<10 + // Check if getElementById returns elements by name + // The broken getElementById methods don't pick up programmatically-set names, + // so use a roundabout getElementsByName test + support.getById = assert( function( el ) { + docElem.appendChild( el ).id = expando; + return !document.getElementsByName || !document.getElementsByName( expando ).length; + } ); + + // ID filter and find + if ( support.getById ) { + Expr.filter[ "ID" ] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + return elem.getAttribute( "id" ) === attrId; + }; + }; + Expr.find[ "ID" ] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var elem = context.getElementById( id ); + return elem ? [ elem ] : []; + } + }; + } else { + Expr.filter[ "ID" ] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + var node = typeof elem.getAttributeNode !== "undefined" && + elem.getAttributeNode( "id" ); + return node && node.value === attrId; + }; + }; + + // Support: IE 6 - 7 only + // getElementById is not reliable as a find shortcut + Expr.find[ "ID" ] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var node, i, elems, + elem = context.getElementById( id ); + + if ( elem ) { + + // Verify the id attribute + node = elem.getAttributeNode( "id" ); + if ( node && node.value === id ) { + return [ elem ]; + } + + // Fall back on getElementsByName + elems = context.getElementsByName( id ); + i = 0; + while ( ( elem = elems[ i++ ] ) ) { + node = elem.getAttributeNode( "id" ); + if ( node && node.value === id ) { + return [ elem ]; + } + } + } + + return []; + } + }; + } + + // Tag + Expr.find[ "TAG" ] = support.getElementsByTagName ? + function( tag, context ) { + if ( typeof context.getElementsByTagName !== "undefined" ) { + return context.getElementsByTagName( tag ); + + // DocumentFragment nodes don't have gEBTN + } else if ( support.qsa ) { + return context.querySelectorAll( tag ); + } + } : + + function( tag, context ) { + var elem, + tmp = [], + i = 0, + + // By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too + results = context.getElementsByTagName( tag ); + + // Filter out possible comments + if ( tag === "*" ) { + while ( ( elem = results[ i++ ] ) ) { + if ( elem.nodeType === 1 ) { + tmp.push( elem ); + } + } + + return tmp; + } + return results; + }; + + // Class + Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) { + if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) { + return context.getElementsByClassName( className ); + } + }; + + /* QSA/matchesSelector + ---------------------------------------------------------------------- */ + + // QSA and matchesSelector support + + // matchesSelector(:active) reports false when true (IE9/Opera 11.5) + rbuggyMatches = []; + + // qSa(:focus) reports false when true (Chrome 21) + // We allow this because of a bug in IE8/9 that throws an error + // whenever `document.activeElement` is accessed on an iframe + // So, we allow :focus to pass through QSA all the time to avoid the IE error + // See https://bugs.jquery.com/ticket/13378 + rbuggyQSA = []; + + if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) { + + // Build QSA regex + // Regex strategy adopted from Diego Perini + assert( function( el ) { + + var input; + + // Select is set to empty string on purpose + // This is to test IE's treatment of not explicitly + // setting a boolean content attribute, + // since its presence should be enough + // https://bugs.jquery.com/ticket/12359 + docElem.appendChild( el ).innerHTML = "" + + ""; + + // Support: IE8, Opera 11-12.16 + // Nothing should be selected when empty strings follow ^= or $= or *= + // The test attribute must be unknown in Opera but "safe" for WinRT + // https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section + if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) { + rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" ); + } + + // Support: IE8 + // Boolean attributes and "value" are not treated correctly + if ( !el.querySelectorAll( "[selected]" ).length ) { + rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" ); + } + + // Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+ + if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) { + rbuggyQSA.push( "~=" ); + } + + // Support: IE 11+, Edge 15 - 18+ + // IE 11/Edge don't find elements on a `[name='']` query in some cases. + // Adding a temporary attribute to the document before the selection works + // around the issue. + // Interestingly, IE 10 & older don't seem to have the issue. + input = document.createElement( "input" ); + input.setAttribute( "name", "" ); + el.appendChild( input ); + if ( !el.querySelectorAll( "[name='']" ).length ) { + rbuggyQSA.push( "\\[" + whitespace + "*name" + whitespace + "*=" + + whitespace + "*(?:''|\"\")" ); + } + + // Webkit/Opera - :checked should return selected option elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + // IE8 throws error here and will not see later tests + if ( !el.querySelectorAll( ":checked" ).length ) { + rbuggyQSA.push( ":checked" ); + } + + // Support: Safari 8+, iOS 8+ + // https://bugs.webkit.org/show_bug.cgi?id=136851 + // In-page `selector#id sibling-combinator selector` fails + if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) { + rbuggyQSA.push( ".#.+[+~]" ); + } + + // Support: Firefox <=3.6 - 5 only + // Old Firefox doesn't throw on a badly-escaped identifier. + el.querySelectorAll( "\\\f" ); + rbuggyQSA.push( "[\\r\\n\\f]" ); + } ); + + assert( function( el ) { + el.innerHTML = "" + + ""; + + // Support: Windows 8 Native Apps + // The type and name attributes are restricted during .innerHTML assignment + var input = document.createElement( "input" ); + input.setAttribute( "type", "hidden" ); + el.appendChild( input ).setAttribute( "name", "D" ); + + // Support: IE8 + // Enforce case-sensitivity of name attribute + if ( el.querySelectorAll( "[name=d]" ).length ) { + rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" ); + } + + // FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled) + // IE8 throws error here and will not see later tests + if ( el.querySelectorAll( ":enabled" ).length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Support: IE9-11+ + // IE's :disabled selector does not pick up the children of disabled fieldsets + docElem.appendChild( el ).disabled = true; + if ( el.querySelectorAll( ":disabled" ).length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Support: Opera 10 - 11 only + // Opera 10-11 does not throw on post-comma invalid pseudos + el.querySelectorAll( "*,:x" ); + rbuggyQSA.push( ",.*:" ); + } ); + } + + if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches || + docElem.webkitMatchesSelector || + docElem.mozMatchesSelector || + docElem.oMatchesSelector || + docElem.msMatchesSelector ) ) ) ) { + + assert( function( el ) { + + // Check to see if it's possible to do matchesSelector + // on a disconnected node (IE 9) + support.disconnectedMatch = matches.call( el, "*" ); + + // This should fail with an exception + // Gecko does not error, returns false instead + matches.call( el, "[s!='']:x" ); + rbuggyMatches.push( "!=", pseudos ); + } ); + } + + rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) ); + rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) ); + + /* Contains + ---------------------------------------------------------------------- */ + hasCompare = rnative.test( docElem.compareDocumentPosition ); + + // Element contains another + // Purposefully self-exclusive + // As in, an element does not contain itself + contains = hasCompare || rnative.test( docElem.contains ) ? + function( a, b ) { + var adown = a.nodeType === 9 ? a.documentElement : a, + bup = b && b.parentNode; + return a === bup || !!( bup && bup.nodeType === 1 && ( + adown.contains ? + adown.contains( bup ) : + a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16 + ) ); + } : + function( a, b ) { + if ( b ) { + while ( ( b = b.parentNode ) ) { + if ( b === a ) { + return true; + } + } + } + return false; + }; + + /* Sorting + ---------------------------------------------------------------------- */ + + // Document order sorting + sortOrder = hasCompare ? + function( a, b ) { + + // Flag for duplicate removal + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + // Sort on method existence if only one input has compareDocumentPosition + var compare = !a.compareDocumentPosition - !b.compareDocumentPosition; + if ( compare ) { + return compare; + } + + // Calculate position if both inputs belong to the same document + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + compare = ( a.ownerDocument || a ) == ( b.ownerDocument || b ) ? + a.compareDocumentPosition( b ) : + + // Otherwise we know they are disconnected + 1; + + // Disconnected nodes + if ( compare & 1 || + ( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) { + + // Choose the first element that is related to our preferred document + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( a == document || a.ownerDocument == preferredDoc && + contains( preferredDoc, a ) ) { + return -1; + } + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( b == document || b.ownerDocument == preferredDoc && + contains( preferredDoc, b ) ) { + return 1; + } + + // Maintain original order + return sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + } + + return compare & 4 ? -1 : 1; + } : + function( a, b ) { + + // Exit early if the nodes are identical + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + var cur, + i = 0, + aup = a.parentNode, + bup = b.parentNode, + ap = [ a ], + bp = [ b ]; + + // Parentless nodes are either documents or disconnected + if ( !aup || !bup ) { + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + /* eslint-disable eqeqeq */ + return a == document ? -1 : + b == document ? 1 : + /* eslint-enable eqeqeq */ + aup ? -1 : + bup ? 1 : + sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + + // If the nodes are siblings, we can do a quick check + } else if ( aup === bup ) { + return siblingCheck( a, b ); + } + + // Otherwise we need full lists of their ancestors for comparison + cur = a; + while ( ( cur = cur.parentNode ) ) { + ap.unshift( cur ); + } + cur = b; + while ( ( cur = cur.parentNode ) ) { + bp.unshift( cur ); + } + + // Walk down the tree looking for a discrepancy + while ( ap[ i ] === bp[ i ] ) { + i++; + } + + return i ? + + // Do a sibling check if the nodes have a common ancestor + siblingCheck( ap[ i ], bp[ i ] ) : + + // Otherwise nodes in our document sort first + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + /* eslint-disable eqeqeq */ + ap[ i ] == preferredDoc ? -1 : + bp[ i ] == preferredDoc ? 1 : + /* eslint-enable eqeqeq */ + 0; + }; + + return document; +}; + +Sizzle.matches = function( expr, elements ) { + return Sizzle( expr, null, null, elements ); +}; + +Sizzle.matchesSelector = function( elem, expr ) { + setDocument( elem ); + + if ( support.matchesSelector && documentIsHTML && + !nonnativeSelectorCache[ expr + " " ] && + ( !rbuggyMatches || !rbuggyMatches.test( expr ) ) && + ( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) { + + try { + var ret = matches.call( elem, expr ); + + // IE 9's matchesSelector returns false on disconnected nodes + if ( ret || support.disconnectedMatch || + + // As well, disconnected nodes are said to be in a document + // fragment in IE 9 + elem.document && elem.document.nodeType !== 11 ) { + return ret; + } + } catch ( e ) { + nonnativeSelectorCache( expr, true ); + } + } + + return Sizzle( expr, document, null, [ elem ] ).length > 0; +}; + +Sizzle.contains = function( context, elem ) { + + // Set document vars if needed + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( ( context.ownerDocument || context ) != document ) { + setDocument( context ); + } + return contains( context, elem ); +}; + +Sizzle.attr = function( elem, name ) { + + // Set document vars if needed + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( ( elem.ownerDocument || elem ) != document ) { + setDocument( elem ); + } + + var fn = Expr.attrHandle[ name.toLowerCase() ], + + // Don't get fooled by Object.prototype properties (jQuery #13807) + val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ? + fn( elem, name, !documentIsHTML ) : + undefined; + + return val !== undefined ? + val : + support.attributes || !documentIsHTML ? + elem.getAttribute( name ) : + ( val = elem.getAttributeNode( name ) ) && val.specified ? + val.value : + null; +}; + +Sizzle.escape = function( sel ) { + return ( sel + "" ).replace( rcssescape, fcssescape ); +}; + +Sizzle.error = function( msg ) { + throw new Error( "Syntax error, unrecognized expression: " + msg ); +}; + +/** + * Document sorting and removing duplicates + * @param {ArrayLike} results + */ +Sizzle.uniqueSort = function( results ) { + var elem, + duplicates = [], + j = 0, + i = 0; + + // Unless we *know* we can detect duplicates, assume their presence + hasDuplicate = !support.detectDuplicates; + sortInput = !support.sortStable && results.slice( 0 ); + results.sort( sortOrder ); + + if ( hasDuplicate ) { + while ( ( elem = results[ i++ ] ) ) { + if ( elem === results[ i ] ) { + j = duplicates.push( i ); + } + } + while ( j-- ) { + results.splice( duplicates[ j ], 1 ); + } + } + + // Clear input after sorting to release objects + // See https://github.com/jquery/sizzle/pull/225 + sortInput = null; + + return results; +}; + +/** + * Utility function for retrieving the text value of an array of DOM nodes + * @param {Array|Element} elem + */ +getText = Sizzle.getText = function( elem ) { + var node, + ret = "", + i = 0, + nodeType = elem.nodeType; + + if ( !nodeType ) { + + // If no nodeType, this is expected to be an array + while ( ( node = elem[ i++ ] ) ) { + + // Do not traverse comment nodes + ret += getText( node ); + } + } else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) { + + // Use textContent for elements + // innerText usage removed for consistency of new lines (jQuery #11153) + if ( typeof elem.textContent === "string" ) { + return elem.textContent; + } else { + + // Traverse its children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + ret += getText( elem ); + } + } + } else if ( nodeType === 3 || nodeType === 4 ) { + return elem.nodeValue; + } + + // Do not include comment or processing instruction nodes + + return ret; +}; + +Expr = Sizzle.selectors = { + + // Can be adjusted by the user + cacheLength: 50, + + createPseudo: markFunction, + + match: matchExpr, + + attrHandle: {}, + + find: {}, + + relative: { + ">": { dir: "parentNode", first: true }, + " ": { dir: "parentNode" }, + "+": { dir: "previousSibling", first: true }, + "~": { dir: "previousSibling" } + }, + + preFilter: { + "ATTR": function( match ) { + match[ 1 ] = match[ 1 ].replace( runescape, funescape ); + + // Move the given value to match[3] whether quoted or unquoted + match[ 3 ] = ( match[ 3 ] || match[ 4 ] || + match[ 5 ] || "" ).replace( runescape, funescape ); + + if ( match[ 2 ] === "~=" ) { + match[ 3 ] = " " + match[ 3 ] + " "; + } + + return match.slice( 0, 4 ); + }, + + "CHILD": function( match ) { + + /* matches from matchExpr["CHILD"] + 1 type (only|nth|...) + 2 what (child|of-type) + 3 argument (even|odd|\d*|\d*n([+-]\d+)?|...) + 4 xn-component of xn+y argument ([+-]?\d*n|) + 5 sign of xn-component + 6 x of xn-component + 7 sign of y-component + 8 y of y-component + */ + match[ 1 ] = match[ 1 ].toLowerCase(); + + if ( match[ 1 ].slice( 0, 3 ) === "nth" ) { + + // nth-* requires argument + if ( !match[ 3 ] ) { + Sizzle.error( match[ 0 ] ); + } + + // numeric x and y parameters for Expr.filter.CHILD + // remember that false/true cast respectively to 0/1 + match[ 4 ] = +( match[ 4 ] ? + match[ 5 ] + ( match[ 6 ] || 1 ) : + 2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) ); + match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" ); + + // other types prohibit arguments + } else if ( match[ 3 ] ) { + Sizzle.error( match[ 0 ] ); + } + + return match; + }, + + "PSEUDO": function( match ) { + var excess, + unquoted = !match[ 6 ] && match[ 2 ]; + + if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) { + return null; + } + + // Accept quoted arguments as-is + if ( match[ 3 ] ) { + match[ 2 ] = match[ 4 ] || match[ 5 ] || ""; + + // Strip excess characters from unquoted arguments + } else if ( unquoted && rpseudo.test( unquoted ) && + + // Get excess from tokenize (recursively) + ( excess = tokenize( unquoted, true ) ) && + + // advance to the next closing parenthesis + ( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) { + + // excess is a negative index + match[ 0 ] = match[ 0 ].slice( 0, excess ); + match[ 2 ] = unquoted.slice( 0, excess ); + } + + // Return only captures needed by the pseudo filter method (type and argument) + return match.slice( 0, 3 ); + } + }, + + filter: { + + "TAG": function( nodeNameSelector ) { + var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase(); + return nodeNameSelector === "*" ? + function() { + return true; + } : + function( elem ) { + return elem.nodeName && elem.nodeName.toLowerCase() === nodeName; + }; + }, + + "CLASS": function( className ) { + var pattern = classCache[ className + " " ]; + + return pattern || + ( pattern = new RegExp( "(^|" + whitespace + + ")" + className + "(" + whitespace + "|$)" ) ) && classCache( + className, function( elem ) { + return pattern.test( + typeof elem.className === "string" && elem.className || + typeof elem.getAttribute !== "undefined" && + elem.getAttribute( "class" ) || + "" + ); + } ); + }, + + "ATTR": function( name, operator, check ) { + return function( elem ) { + var result = Sizzle.attr( elem, name ); + + if ( result == null ) { + return operator === "!="; + } + if ( !operator ) { + return true; + } + + result += ""; + + /* eslint-disable max-len */ + + return operator === "=" ? result === check : + operator === "!=" ? result !== check : + operator === "^=" ? check && result.indexOf( check ) === 0 : + operator === "*=" ? check && result.indexOf( check ) > -1 : + operator === "$=" ? check && result.slice( -check.length ) === check : + operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 : + operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" : + false; + /* eslint-enable max-len */ + + }; + }, + + "CHILD": function( type, what, _argument, first, last ) { + var simple = type.slice( 0, 3 ) !== "nth", + forward = type.slice( -4 ) !== "last", + ofType = what === "of-type"; + + return first === 1 && last === 0 ? + + // Shortcut for :nth-*(n) + function( elem ) { + return !!elem.parentNode; + } : + + function( elem, _context, xml ) { + var cache, uniqueCache, outerCache, node, nodeIndex, start, + dir = simple !== forward ? "nextSibling" : "previousSibling", + parent = elem.parentNode, + name = ofType && elem.nodeName.toLowerCase(), + useCache = !xml && !ofType, + diff = false; + + if ( parent ) { + + // :(first|last|only)-(child|of-type) + if ( simple ) { + while ( dir ) { + node = elem; + while ( ( node = node[ dir ] ) ) { + if ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) { + + return false; + } + } + + // Reverse direction for :only-* (if we haven't yet done so) + start = dir = type === "only" && !start && "nextSibling"; + } + return true; + } + + start = [ forward ? parent.firstChild : parent.lastChild ]; + + // non-xml :nth-child(...) stores cache data on `parent` + if ( forward && useCache ) { + + // Seek `elem` from a previously-cached index + + // ...in a gzip-friendly way + node = parent; + outerCache = node[ expando ] || ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex && cache[ 2 ]; + node = nodeIndex && parent.childNodes[ nodeIndex ]; + + while ( ( node = ++nodeIndex && node && node[ dir ] || + + // Fallback to seeking `elem` from the start + ( diff = nodeIndex = 0 ) || start.pop() ) ) { + + // When found, cache indexes on `parent` and break + if ( node.nodeType === 1 && ++diff && node === elem ) { + uniqueCache[ type ] = [ dirruns, nodeIndex, diff ]; + break; + } + } + + } else { + + // Use previously-cached element index if available + if ( useCache ) { + + // ...in a gzip-friendly way + node = elem; + outerCache = node[ expando ] || ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex; + } + + // xml :nth-child(...) + // or :nth-last-child(...) or :nth(-last)?-of-type(...) + if ( diff === false ) { + + // Use the same loop as above to seek `elem` from the start + while ( ( node = ++nodeIndex && node && node[ dir ] || + ( diff = nodeIndex = 0 ) || start.pop() ) ) { + + if ( ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) && + ++diff ) { + + // Cache the index of each encountered element + if ( useCache ) { + outerCache = node[ expando ] || + ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + uniqueCache[ type ] = [ dirruns, diff ]; + } + + if ( node === elem ) { + break; + } + } + } + } + } + + // Incorporate the offset, then check against cycle size + diff -= last; + return diff === first || ( diff % first === 0 && diff / first >= 0 ); + } + }; + }, + + "PSEUDO": function( pseudo, argument ) { + + // pseudo-class names are case-insensitive + // http://www.w3.org/TR/selectors/#pseudo-classes + // Prioritize by case sensitivity in case custom pseudos are added with uppercase letters + // Remember that setFilters inherits from pseudos + var args, + fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] || + Sizzle.error( "unsupported pseudo: " + pseudo ); + + // The user may use createPseudo to indicate that + // arguments are needed to create the filter function + // just as Sizzle does + if ( fn[ expando ] ) { + return fn( argument ); + } + + // But maintain support for old signatures + if ( fn.length > 1 ) { + args = [ pseudo, pseudo, "", argument ]; + return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ? + markFunction( function( seed, matches ) { + var idx, + matched = fn( seed, argument ), + i = matched.length; + while ( i-- ) { + idx = indexOf( seed, matched[ i ] ); + seed[ idx ] = !( matches[ idx ] = matched[ i ] ); + } + } ) : + function( elem ) { + return fn( elem, 0, args ); + }; + } + + return fn; + } + }, + + pseudos: { + + // Potentially complex pseudos + "not": markFunction( function( selector ) { + + // Trim the selector passed to compile + // to avoid treating leading and trailing + // spaces as combinators + var input = [], + results = [], + matcher = compile( selector.replace( rtrim, "$1" ) ); + + return matcher[ expando ] ? + markFunction( function( seed, matches, _context, xml ) { + var elem, + unmatched = matcher( seed, null, xml, [] ), + i = seed.length; + + // Match elements unmatched by `matcher` + while ( i-- ) { + if ( ( elem = unmatched[ i ] ) ) { + seed[ i ] = !( matches[ i ] = elem ); + } + } + } ) : + function( elem, _context, xml ) { + input[ 0 ] = elem; + matcher( input, null, xml, results ); + + // Don't keep the element (issue #299) + input[ 0 ] = null; + return !results.pop(); + }; + } ), + + "has": markFunction( function( selector ) { + return function( elem ) { + return Sizzle( selector, elem ).length > 0; + }; + } ), + + "contains": markFunction( function( text ) { + text = text.replace( runescape, funescape ); + return function( elem ) { + return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1; + }; + } ), + + // "Whether an element is represented by a :lang() selector + // is based solely on the element's language value + // being equal to the identifier C, + // or beginning with the identifier C immediately followed by "-". + // The matching of C against the element's language value is performed case-insensitively. + // The identifier C does not have to be a valid language name." + // http://www.w3.org/TR/selectors/#lang-pseudo + "lang": markFunction( function( lang ) { + + // lang value must be a valid identifier + if ( !ridentifier.test( lang || "" ) ) { + Sizzle.error( "unsupported lang: " + lang ); + } + lang = lang.replace( runescape, funescape ).toLowerCase(); + return function( elem ) { + var elemLang; + do { + if ( ( elemLang = documentIsHTML ? + elem.lang : + elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) { + + elemLang = elemLang.toLowerCase(); + return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0; + } + } while ( ( elem = elem.parentNode ) && elem.nodeType === 1 ); + return false; + }; + } ), + + // Miscellaneous + "target": function( elem ) { + var hash = window.location && window.location.hash; + return hash && hash.slice( 1 ) === elem.id; + }, + + "root": function( elem ) { + return elem === docElem; + }, + + "focus": function( elem ) { + return elem === document.activeElement && + ( !document.hasFocus || document.hasFocus() ) && + !!( elem.type || elem.href || ~elem.tabIndex ); + }, + + // Boolean properties + "enabled": createDisabledPseudo( false ), + "disabled": createDisabledPseudo( true ), + + "checked": function( elem ) { + + // In CSS3, :checked should return both checked and selected elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + var nodeName = elem.nodeName.toLowerCase(); + return ( nodeName === "input" && !!elem.checked ) || + ( nodeName === "option" && !!elem.selected ); + }, + + "selected": function( elem ) { + + // Accessing this property makes selected-by-default + // options in Safari work properly + if ( elem.parentNode ) { + // eslint-disable-next-line no-unused-expressions + elem.parentNode.selectedIndex; + } + + return elem.selected === true; + }, + + // Contents + "empty": function( elem ) { + + // http://www.w3.org/TR/selectors/#empty-pseudo + // :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5), + // but not by others (comment: 8; processing instruction: 7; etc.) + // nodeType < 6 works because attributes (2) do not appear as children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + if ( elem.nodeType < 6 ) { + return false; + } + } + return true; + }, + + "parent": function( elem ) { + return !Expr.pseudos[ "empty" ]( elem ); + }, + + // Element/input types + "header": function( elem ) { + return rheader.test( elem.nodeName ); + }, + + "input": function( elem ) { + return rinputs.test( elem.nodeName ); + }, + + "button": function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === "button" || name === "button"; + }, + + "text": function( elem ) { + var attr; + return elem.nodeName.toLowerCase() === "input" && + elem.type === "text" && + + // Support: IE<8 + // New HTML5 attribute values (e.g., "search") appear with elem.type === "text" + ( ( attr = elem.getAttribute( "type" ) ) == null || + attr.toLowerCase() === "text" ); + }, + + // Position-in-collection + "first": createPositionalPseudo( function() { + return [ 0 ]; + } ), + + "last": createPositionalPseudo( function( _matchIndexes, length ) { + return [ length - 1 ]; + } ), + + "eq": createPositionalPseudo( function( _matchIndexes, length, argument ) { + return [ argument < 0 ? argument + length : argument ]; + } ), + + "even": createPositionalPseudo( function( matchIndexes, length ) { + var i = 0; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "odd": createPositionalPseudo( function( matchIndexes, length ) { + var i = 1; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "lt": createPositionalPseudo( function( matchIndexes, length, argument ) { + var i = argument < 0 ? + argument + length : + argument > length ? + length : + argument; + for ( ; --i >= 0; ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "gt": createPositionalPseudo( function( matchIndexes, length, argument ) { + var i = argument < 0 ? argument + length : argument; + for ( ; ++i < length; ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ) + } +}; + +Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ]; + +// Add button/input type pseudos +for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) { + Expr.pseudos[ i ] = createInputPseudo( i ); +} +for ( i in { submit: true, reset: true } ) { + Expr.pseudos[ i ] = createButtonPseudo( i ); +} + +// Easy API for creating new setFilters +function setFilters() {} +setFilters.prototype = Expr.filters = Expr.pseudos; +Expr.setFilters = new setFilters(); + +tokenize = Sizzle.tokenize = function( selector, parseOnly ) { + var matched, match, tokens, type, + soFar, groups, preFilters, + cached = tokenCache[ selector + " " ]; + + if ( cached ) { + return parseOnly ? 0 : cached.slice( 0 ); + } + + soFar = selector; + groups = []; + preFilters = Expr.preFilter; + + while ( soFar ) { + + // Comma and first run + if ( !matched || ( match = rcomma.exec( soFar ) ) ) { + if ( match ) { + + // Don't consume trailing commas as valid + soFar = soFar.slice( match[ 0 ].length ) || soFar; + } + groups.push( ( tokens = [] ) ); + } + + matched = false; + + // Combinators + if ( ( match = rcombinators.exec( soFar ) ) ) { + matched = match.shift(); + tokens.push( { + value: matched, + + // Cast descendant combinators to space + type: match[ 0 ].replace( rtrim, " " ) + } ); + soFar = soFar.slice( matched.length ); + } + + // Filters + for ( type in Expr.filter ) { + if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] || + ( match = preFilters[ type ]( match ) ) ) ) { + matched = match.shift(); + tokens.push( { + value: matched, + type: type, + matches: match + } ); + soFar = soFar.slice( matched.length ); + } + } + + if ( !matched ) { + break; + } + } + + // Return the length of the invalid excess + // if we're just parsing + // Otherwise, throw an error or return tokens + return parseOnly ? + soFar.length : + soFar ? + Sizzle.error( selector ) : + + // Cache the tokens + tokenCache( selector, groups ).slice( 0 ); +}; + +function toSelector( tokens ) { + var i = 0, + len = tokens.length, + selector = ""; + for ( ; i < len; i++ ) { + selector += tokens[ i ].value; + } + return selector; +} + +function addCombinator( matcher, combinator, base ) { + var dir = combinator.dir, + skip = combinator.next, + key = skip || dir, + checkNonElements = base && key === "parentNode", + doneName = done++; + + return combinator.first ? + + // Check against closest ancestor/preceding element + function( elem, context, xml ) { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + return matcher( elem, context, xml ); + } + } + return false; + } : + + // Check against all ancestor/preceding elements + function( elem, context, xml ) { + var oldCache, uniqueCache, outerCache, + newCache = [ dirruns, doneName ]; + + // We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching + if ( xml ) { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + if ( matcher( elem, context, xml ) ) { + return true; + } + } + } + } else { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + outerCache = elem[ expando ] || ( elem[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ elem.uniqueID ] || + ( outerCache[ elem.uniqueID ] = {} ); + + if ( skip && skip === elem.nodeName.toLowerCase() ) { + elem = elem[ dir ] || elem; + } else if ( ( oldCache = uniqueCache[ key ] ) && + oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) { + + // Assign to newCache so results back-propagate to previous elements + return ( newCache[ 2 ] = oldCache[ 2 ] ); + } else { + + // Reuse newcache so results back-propagate to previous elements + uniqueCache[ key ] = newCache; + + // A match means we're done; a fail means we have to keep checking + if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) { + return true; + } + } + } + } + } + return false; + }; +} + +function elementMatcher( matchers ) { + return matchers.length > 1 ? + function( elem, context, xml ) { + var i = matchers.length; + while ( i-- ) { + if ( !matchers[ i ]( elem, context, xml ) ) { + return false; + } + } + return true; + } : + matchers[ 0 ]; +} + +function multipleContexts( selector, contexts, results ) { + var i = 0, + len = contexts.length; + for ( ; i < len; i++ ) { + Sizzle( selector, contexts[ i ], results ); + } + return results; +} + +function condense( unmatched, map, filter, context, xml ) { + var elem, + newUnmatched = [], + i = 0, + len = unmatched.length, + mapped = map != null; + + for ( ; i < len; i++ ) { + if ( ( elem = unmatched[ i ] ) ) { + if ( !filter || filter( elem, context, xml ) ) { + newUnmatched.push( elem ); + if ( mapped ) { + map.push( i ); + } + } + } + } + + return newUnmatched; +} + +function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) { + if ( postFilter && !postFilter[ expando ] ) { + postFilter = setMatcher( postFilter ); + } + if ( postFinder && !postFinder[ expando ] ) { + postFinder = setMatcher( postFinder, postSelector ); + } + return markFunction( function( seed, results, context, xml ) { + var temp, i, elem, + preMap = [], + postMap = [], + preexisting = results.length, + + // Get initial elements from seed or context + elems = seed || multipleContexts( + selector || "*", + context.nodeType ? [ context ] : context, + [] + ), + + // Prefilter to get matcher input, preserving a map for seed-results synchronization + matcherIn = preFilter && ( seed || !selector ) ? + condense( elems, preMap, preFilter, context, xml ) : + elems, + + matcherOut = matcher ? + + // If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results, + postFinder || ( seed ? preFilter : preexisting || postFilter ) ? + + // ...intermediate processing is necessary + [] : + + // ...otherwise use results directly + results : + matcherIn; + + // Find primary matches + if ( matcher ) { + matcher( matcherIn, matcherOut, context, xml ); + } + + // Apply postFilter + if ( postFilter ) { + temp = condense( matcherOut, postMap ); + postFilter( temp, [], context, xml ); + + // Un-match failing elements by moving them back to matcherIn + i = temp.length; + while ( i-- ) { + if ( ( elem = temp[ i ] ) ) { + matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem ); + } + } + } + + if ( seed ) { + if ( postFinder || preFilter ) { + if ( postFinder ) { + + // Get the final matcherOut by condensing this intermediate into postFinder contexts + temp = []; + i = matcherOut.length; + while ( i-- ) { + if ( ( elem = matcherOut[ i ] ) ) { + + // Restore matcherIn since elem is not yet a final match + temp.push( ( matcherIn[ i ] = elem ) ); + } + } + postFinder( null, ( matcherOut = [] ), temp, xml ); + } + + // Move matched elements from seed to results to keep them synchronized + i = matcherOut.length; + while ( i-- ) { + if ( ( elem = matcherOut[ i ] ) && + ( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) { + + seed[ temp ] = !( results[ temp ] = elem ); + } + } + } + + // Add elements to results, through postFinder if defined + } else { + matcherOut = condense( + matcherOut === results ? + matcherOut.splice( preexisting, matcherOut.length ) : + matcherOut + ); + if ( postFinder ) { + postFinder( null, results, matcherOut, xml ); + } else { + push.apply( results, matcherOut ); + } + } + } ); +} + +function matcherFromTokens( tokens ) { + var checkContext, matcher, j, + len = tokens.length, + leadingRelative = Expr.relative[ tokens[ 0 ].type ], + implicitRelative = leadingRelative || Expr.relative[ " " ], + i = leadingRelative ? 1 : 0, + + // The foundational matcher ensures that elements are reachable from top-level context(s) + matchContext = addCombinator( function( elem ) { + return elem === checkContext; + }, implicitRelative, true ), + matchAnyContext = addCombinator( function( elem ) { + return indexOf( checkContext, elem ) > -1; + }, implicitRelative, true ), + matchers = [ function( elem, context, xml ) { + var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || ( + ( checkContext = context ).nodeType ? + matchContext( elem, context, xml ) : + matchAnyContext( elem, context, xml ) ); + + // Avoid hanging onto element (issue #299) + checkContext = null; + return ret; + } ]; + + for ( ; i < len; i++ ) { + if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) { + matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ]; + } else { + matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches ); + + // Return special upon seeing a positional matcher + if ( matcher[ expando ] ) { + + // Find the next relative operator (if any) for proper handling + j = ++i; + for ( ; j < len; j++ ) { + if ( Expr.relative[ tokens[ j ].type ] ) { + break; + } + } + return setMatcher( + i > 1 && elementMatcher( matchers ), + i > 1 && toSelector( + + // If the preceding token was a descendant combinator, insert an implicit any-element `*` + tokens + .slice( 0, i - 1 ) + .concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } ) + ).replace( rtrim, "$1" ), + matcher, + i < j && matcherFromTokens( tokens.slice( i, j ) ), + j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ), + j < len && toSelector( tokens ) + ); + } + matchers.push( matcher ); + } + } + + return elementMatcher( matchers ); +} + +function matcherFromGroupMatchers( elementMatchers, setMatchers ) { + var bySet = setMatchers.length > 0, + byElement = elementMatchers.length > 0, + superMatcher = function( seed, context, xml, results, outermost ) { + var elem, j, matcher, + matchedCount = 0, + i = "0", + unmatched = seed && [], + setMatched = [], + contextBackup = outermostContext, + + // We must always have either seed elements or outermost context + elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ), + + // Use integer dirruns iff this is the outermost matcher + dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ), + len = elems.length; + + if ( outermost ) { + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + outermostContext = context == document || context || outermost; + } + + // Add elements passing elementMatchers directly to results + // Support: IE<9, Safari + // Tolerate NodeList properties (IE: "length"; Safari: ) matching elements by id + for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) { + if ( byElement && elem ) { + j = 0; + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( !context && elem.ownerDocument != document ) { + setDocument( elem ); + xml = !documentIsHTML; + } + while ( ( matcher = elementMatchers[ j++ ] ) ) { + if ( matcher( elem, context || document, xml ) ) { + results.push( elem ); + break; + } + } + if ( outermost ) { + dirruns = dirrunsUnique; + } + } + + // Track unmatched elements for set filters + if ( bySet ) { + + // They will have gone through all possible matchers + if ( ( elem = !matcher && elem ) ) { + matchedCount--; + } + + // Lengthen the array for every element, matched or not + if ( seed ) { + unmatched.push( elem ); + } + } + } + + // `i` is now the count of elements visited above, and adding it to `matchedCount` + // makes the latter nonnegative. + matchedCount += i; + + // Apply set filters to unmatched elements + // NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount` + // equals `i`), unless we didn't visit _any_ elements in the above loop because we have + // no element matchers and no seed. + // Incrementing an initially-string "0" `i` allows `i` to remain a string only in that + // case, which will result in a "00" `matchedCount` that differs from `i` but is also + // numerically zero. + if ( bySet && i !== matchedCount ) { + j = 0; + while ( ( matcher = setMatchers[ j++ ] ) ) { + matcher( unmatched, setMatched, context, xml ); + } + + if ( seed ) { + + // Reintegrate element matches to eliminate the need for sorting + if ( matchedCount > 0 ) { + while ( i-- ) { + if ( !( unmatched[ i ] || setMatched[ i ] ) ) { + setMatched[ i ] = pop.call( results ); + } + } + } + + // Discard index placeholder values to get only actual matches + setMatched = condense( setMatched ); + } + + // Add matches to results + push.apply( results, setMatched ); + + // Seedless set matches succeeding multiple successful matchers stipulate sorting + if ( outermost && !seed && setMatched.length > 0 && + ( matchedCount + setMatchers.length ) > 1 ) { + + Sizzle.uniqueSort( results ); + } + } + + // Override manipulation of globals by nested matchers + if ( outermost ) { + dirruns = dirrunsUnique; + outermostContext = contextBackup; + } + + return unmatched; + }; + + return bySet ? + markFunction( superMatcher ) : + superMatcher; +} + +compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) { + var i, + setMatchers = [], + elementMatchers = [], + cached = compilerCache[ selector + " " ]; + + if ( !cached ) { + + // Generate a function of recursive functions that can be used to check each element + if ( !match ) { + match = tokenize( selector ); + } + i = match.length; + while ( i-- ) { + cached = matcherFromTokens( match[ i ] ); + if ( cached[ expando ] ) { + setMatchers.push( cached ); + } else { + elementMatchers.push( cached ); + } + } + + // Cache the compiled function + cached = compilerCache( + selector, + matcherFromGroupMatchers( elementMatchers, setMatchers ) + ); + + // Save selector and tokenization + cached.selector = selector; + } + return cached; +}; + +/** + * A low-level selection function that works with Sizzle's compiled + * selector functions + * @param {String|Function} selector A selector or a pre-compiled + * selector function built with Sizzle.compile + * @param {Element} context + * @param {Array} [results] + * @param {Array} [seed] A set of elements to match against + */ +select = Sizzle.select = function( selector, context, results, seed ) { + var i, tokens, token, type, find, + compiled = typeof selector === "function" && selector, + match = !seed && tokenize( ( selector = compiled.selector || selector ) ); + + results = results || []; + + // Try to minimize operations if there is only one selector in the list and no seed + // (the latter of which guarantees us context) + if ( match.length === 1 ) { + + // Reduce context if the leading compound selector is an ID + tokens = match[ 0 ] = match[ 0 ].slice( 0 ); + if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" && + context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) { + + context = ( Expr.find[ "ID" ]( token.matches[ 0 ] + .replace( runescape, funescape ), context ) || [] )[ 0 ]; + if ( !context ) { + return results; + + // Precompiled matchers will still verify ancestry, so step up a level + } else if ( compiled ) { + context = context.parentNode; + } + + selector = selector.slice( tokens.shift().value.length ); + } + + // Fetch a seed set for right-to-left matching + i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length; + while ( i-- ) { + token = tokens[ i ]; + + // Abort if we hit a combinator + if ( Expr.relative[ ( type = token.type ) ] ) { + break; + } + if ( ( find = Expr.find[ type ] ) ) { + + // Search, expanding context for leading sibling combinators + if ( ( seed = find( + token.matches[ 0 ].replace( runescape, funescape ), + rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) || + context + ) ) ) { + + // If seed is empty or no tokens remain, we can return early + tokens.splice( i, 1 ); + selector = seed.length && toSelector( tokens ); + if ( !selector ) { + push.apply( results, seed ); + return results; + } + + break; + } + } + } + } + + // Compile and execute a filtering function if one is not provided + // Provide `match` to avoid retokenization if we modified the selector above + ( compiled || compile( selector, match ) )( + seed, + context, + !documentIsHTML, + results, + !context || rsibling.test( selector ) && testContext( context.parentNode ) || context + ); + return results; +}; + +// One-time assignments + +// Sort stability +support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando; + +// Support: Chrome 14-35+ +// Always assume duplicates if they aren't passed to the comparison function +support.detectDuplicates = !!hasDuplicate; + +// Initialize against the default document +setDocument(); + +// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27) +// Detached nodes confoundingly follow *each other* +support.sortDetached = assert( function( el ) { + + // Should return 1, but returns 4 (following) + return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1; +} ); + +// Support: IE<8 +// Prevent attribute/property "interpolation" +// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx +if ( !assert( function( el ) { + el.innerHTML = ""; + return el.firstChild.getAttribute( "href" ) === "#"; +} ) ) { + addHandle( "type|href|height|width", function( elem, name, isXML ) { + if ( !isXML ) { + return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 ); + } + } ); +} + +// Support: IE<9 +// Use defaultValue in place of getAttribute("value") +if ( !support.attributes || !assert( function( el ) { + el.innerHTML = ""; + el.firstChild.setAttribute( "value", "" ); + return el.firstChild.getAttribute( "value" ) === ""; +} ) ) { + addHandle( "value", function( elem, _name, isXML ) { + if ( !isXML && elem.nodeName.toLowerCase() === "input" ) { + return elem.defaultValue; + } + } ); +} + +// Support: IE<9 +// Use getAttributeNode to fetch booleans when getAttribute lies +if ( !assert( function( el ) { + return el.getAttribute( "disabled" ) == null; +} ) ) { + addHandle( booleans, function( elem, name, isXML ) { + var val; + if ( !isXML ) { + return elem[ name ] === true ? name.toLowerCase() : + ( val = elem.getAttributeNode( name ) ) && val.specified ? + val.value : + null; + } + } ); +} + +return Sizzle; + +} )( window ); + + + +jQuery.find = Sizzle; +jQuery.expr = Sizzle.selectors; + +// Deprecated +jQuery.expr[ ":" ] = jQuery.expr.pseudos; +jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort; +jQuery.text = Sizzle.getText; +jQuery.isXMLDoc = Sizzle.isXML; +jQuery.contains = Sizzle.contains; +jQuery.escapeSelector = Sizzle.escape; + + + + +var dir = function( elem, dir, until ) { + var matched = [], + truncate = until !== undefined; + + while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) { + if ( elem.nodeType === 1 ) { + if ( truncate && jQuery( elem ).is( until ) ) { + break; + } + matched.push( elem ); + } + } + return matched; +}; + + +var siblings = function( n, elem ) { + var matched = []; + + for ( ; n; n = n.nextSibling ) { + if ( n.nodeType === 1 && n !== elem ) { + matched.push( n ); + } + } + + return matched; +}; + + +var rneedsContext = jQuery.expr.match.needsContext; + + + +function nodeName( elem, name ) { + + return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase(); + +}; +var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i ); + + + +// Implement the identical functionality for filter and not +function winnow( elements, qualifier, not ) { + if ( isFunction( qualifier ) ) { + return jQuery.grep( elements, function( elem, i ) { + return !!qualifier.call( elem, i, elem ) !== not; + } ); + } + + // Single element + if ( qualifier.nodeType ) { + return jQuery.grep( elements, function( elem ) { + return ( elem === qualifier ) !== not; + } ); + } + + // Arraylike of elements (jQuery, arguments, Array) + if ( typeof qualifier !== "string" ) { + return jQuery.grep( elements, function( elem ) { + return ( indexOf.call( qualifier, elem ) > -1 ) !== not; + } ); + } + + // Filtered directly for both simple and complex selectors + return jQuery.filter( qualifier, elements, not ); +} + +jQuery.filter = function( expr, elems, not ) { + var elem = elems[ 0 ]; + + if ( not ) { + expr = ":not(" + expr + ")"; + } + + if ( elems.length === 1 && elem.nodeType === 1 ) { + return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : []; + } + + return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) { + return elem.nodeType === 1; + } ) ); +}; + +jQuery.fn.extend( { + find: function( selector ) { + var i, ret, + len = this.length, + self = this; + + if ( typeof selector !== "string" ) { + return this.pushStack( jQuery( selector ).filter( function() { + for ( i = 0; i < len; i++ ) { + if ( jQuery.contains( self[ i ], this ) ) { + return true; + } + } + } ) ); + } + + ret = this.pushStack( [] ); + + for ( i = 0; i < len; i++ ) { + jQuery.find( selector, self[ i ], ret ); + } + + return len > 1 ? jQuery.uniqueSort( ret ) : ret; + }, + filter: function( selector ) { + return this.pushStack( winnow( this, selector || [], false ) ); + }, + not: function( selector ) { + return this.pushStack( winnow( this, selector || [], true ) ); + }, + is: function( selector ) { + return !!winnow( + this, + + // If this is a positional/relative selector, check membership in the returned set + // so $("p:first").is("p:last") won't return true for a doc with two "p". + typeof selector === "string" && rneedsContext.test( selector ) ? + jQuery( selector ) : + selector || [], + false + ).length; + } +} ); + + +// Initialize a jQuery object + + +// A central reference to the root jQuery(document) +var rootjQuery, + + // A simple way to check for HTML strings + // Prioritize #id over to avoid XSS via location.hash (#9521) + // Strict HTML recognition (#11290: must start with <) + // Shortcut simple #id case for speed + rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/, + + init = jQuery.fn.init = function( selector, context, root ) { + var match, elem; + + // HANDLE: $(""), $(null), $(undefined), $(false) + if ( !selector ) { + return this; + } + + // Method init() accepts an alternate rootjQuery + // so migrate can support jQuery.sub (gh-2101) + root = root || rootjQuery; + + // Handle HTML strings + if ( typeof selector === "string" ) { + if ( selector[ 0 ] === "<" && + selector[ selector.length - 1 ] === ">" && + selector.length >= 3 ) { + + // Assume that strings that start and end with <> are HTML and skip the regex check + match = [ null, selector, null ]; + + } else { + match = rquickExpr.exec( selector ); + } + + // Match html or make sure no context is specified for #id + if ( match && ( match[ 1 ] || !context ) ) { + + // HANDLE: $(html) -> $(array) + if ( match[ 1 ] ) { + context = context instanceof jQuery ? context[ 0 ] : context; + + // Option to run scripts is true for back-compat + // Intentionally let the error be thrown if parseHTML is not present + jQuery.merge( this, jQuery.parseHTML( + match[ 1 ], + context && context.nodeType ? context.ownerDocument || context : document, + true + ) ); + + // HANDLE: $(html, props) + if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) { + for ( match in context ) { + + // Properties of context are called as methods if possible + if ( isFunction( this[ match ] ) ) { + this[ match ]( context[ match ] ); + + // ...and otherwise set as attributes + } else { + this.attr( match, context[ match ] ); + } + } + } + + return this; + + // HANDLE: $(#id) + } else { + elem = document.getElementById( match[ 2 ] ); + + if ( elem ) { + + // Inject the element directly into the jQuery object + this[ 0 ] = elem; + this.length = 1; + } + return this; + } + + // HANDLE: $(expr, $(...)) + } else if ( !context || context.jquery ) { + return ( context || root ).find( selector ); + + // HANDLE: $(expr, context) + // (which is just equivalent to: $(context).find(expr) + } else { + return this.constructor( context ).find( selector ); + } + + // HANDLE: $(DOMElement) + } else if ( selector.nodeType ) { + this[ 0 ] = selector; + this.length = 1; + return this; + + // HANDLE: $(function) + // Shortcut for document ready + } else if ( isFunction( selector ) ) { + return root.ready !== undefined ? + root.ready( selector ) : + + // Execute immediately if ready is not present + selector( jQuery ); + } + + return jQuery.makeArray( selector, this ); + }; + +// Give the init function the jQuery prototype for later instantiation +init.prototype = jQuery.fn; + +// Initialize central reference +rootjQuery = jQuery( document ); + + +var rparentsprev = /^(?:parents|prev(?:Until|All))/, + + // Methods guaranteed to produce a unique set when starting from a unique set + guaranteedUnique = { + children: true, + contents: true, + next: true, + prev: true + }; + +jQuery.fn.extend( { + has: function( target ) { + var targets = jQuery( target, this ), + l = targets.length; + + return this.filter( function() { + var i = 0; + for ( ; i < l; i++ ) { + if ( jQuery.contains( this, targets[ i ] ) ) { + return true; + } + } + } ); + }, + + closest: function( selectors, context ) { + var cur, + i = 0, + l = this.length, + matched = [], + targets = typeof selectors !== "string" && jQuery( selectors ); + + // Positional selectors never match, since there's no _selection_ context + if ( !rneedsContext.test( selectors ) ) { + for ( ; i < l; i++ ) { + for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) { + + // Always skip document fragments + if ( cur.nodeType < 11 && ( targets ? + targets.index( cur ) > -1 : + + // Don't pass non-elements to Sizzle + cur.nodeType === 1 && + jQuery.find.matchesSelector( cur, selectors ) ) ) { + + matched.push( cur ); + break; + } + } + } + } + + return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched ); + }, + + // Determine the position of an element within the set + index: function( elem ) { + + // No argument, return index in parent + if ( !elem ) { + return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1; + } + + // Index in selector + if ( typeof elem === "string" ) { + return indexOf.call( jQuery( elem ), this[ 0 ] ); + } + + // Locate the position of the desired element + return indexOf.call( this, + + // If it receives a jQuery object, the first element is used + elem.jquery ? elem[ 0 ] : elem + ); + }, + + add: function( selector, context ) { + return this.pushStack( + jQuery.uniqueSort( + jQuery.merge( this.get(), jQuery( selector, context ) ) + ) + ); + }, + + addBack: function( selector ) { + return this.add( selector == null ? + this.prevObject : this.prevObject.filter( selector ) + ); + } +} ); + +function sibling( cur, dir ) { + while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {} + return cur; +} + +jQuery.each( { + parent: function( elem ) { + var parent = elem.parentNode; + return parent && parent.nodeType !== 11 ? parent : null; + }, + parents: function( elem ) { + return dir( elem, "parentNode" ); + }, + parentsUntil: function( elem, _i, until ) { + return dir( elem, "parentNode", until ); + }, + next: function( elem ) { + return sibling( elem, "nextSibling" ); + }, + prev: function( elem ) { + return sibling( elem, "previousSibling" ); + }, + nextAll: function( elem ) { + return dir( elem, "nextSibling" ); + }, + prevAll: function( elem ) { + return dir( elem, "previousSibling" ); + }, + nextUntil: function( elem, _i, until ) { + return dir( elem, "nextSibling", until ); + }, + prevUntil: function( elem, _i, until ) { + return dir( elem, "previousSibling", until ); + }, + siblings: function( elem ) { + return siblings( ( elem.parentNode || {} ).firstChild, elem ); + }, + children: function( elem ) { + return siblings( elem.firstChild ); + }, + contents: function( elem ) { + if ( elem.contentDocument != null && + + // Support: IE 11+ + // elements with no `data` attribute has an object + // `contentDocument` with a `null` prototype. + getProto( elem.contentDocument ) ) { + + return elem.contentDocument; + } + + // Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only + // Treat the template element as a regular one in browsers that + // don't support it. + if ( nodeName( elem, "template" ) ) { + elem = elem.content || elem; + } + + return jQuery.merge( [], elem.childNodes ); + } +}, function( name, fn ) { + jQuery.fn[ name ] = function( until, selector ) { + var matched = jQuery.map( this, fn, until ); + + if ( name.slice( -5 ) !== "Until" ) { + selector = until; + } + + if ( selector && typeof selector === "string" ) { + matched = jQuery.filter( selector, matched ); + } + + if ( this.length > 1 ) { + + // Remove duplicates + if ( !guaranteedUnique[ name ] ) { + jQuery.uniqueSort( matched ); + } + + // Reverse order for parents* and prev-derivatives + if ( rparentsprev.test( name ) ) { + matched.reverse(); + } + } + + return this.pushStack( matched ); + }; +} ); +var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g ); + + + +// Convert String-formatted options into Object-formatted ones +function createOptions( options ) { + var object = {}; + jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) { + object[ flag ] = true; + } ); + return object; +} + +/* + * Create a callback list using the following parameters: + * + * options: an optional list of space-separated options that will change how + * the callback list behaves or a more traditional option object + * + * By default a callback list will act like an event callback list and can be + * "fired" multiple times. + * + * Possible options: + * + * once: will ensure the callback list can only be fired once (like a Deferred) + * + * memory: will keep track of previous values and will call any callback added + * after the list has been fired right away with the latest "memorized" + * values (like a Deferred) + * + * unique: will ensure a callback can only be added once (no duplicate in the list) + * + * stopOnFalse: interrupt callings when a callback returns false + * + */ +jQuery.Callbacks = function( options ) { + + // Convert options from String-formatted to Object-formatted if needed + // (we check in cache first) + options = typeof options === "string" ? + createOptions( options ) : + jQuery.extend( {}, options ); + + var // Flag to know if list is currently firing + firing, + + // Last fire value for non-forgettable lists + memory, + + // Flag to know if list was already fired + fired, + + // Flag to prevent firing + locked, + + // Actual callback list + list = [], + + // Queue of execution data for repeatable lists + queue = [], + + // Index of currently firing callback (modified by add/remove as needed) + firingIndex = -1, + + // Fire callbacks + fire = function() { + + // Enforce single-firing + locked = locked || options.once; + + // Execute callbacks for all pending executions, + // respecting firingIndex overrides and runtime changes + fired = firing = true; + for ( ; queue.length; firingIndex = -1 ) { + memory = queue.shift(); + while ( ++firingIndex < list.length ) { + + // Run callback and check for early termination + if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false && + options.stopOnFalse ) { + + // Jump to end and forget the data so .add doesn't re-fire + firingIndex = list.length; + memory = false; + } + } + } + + // Forget the data if we're done with it + if ( !options.memory ) { + memory = false; + } + + firing = false; + + // Clean up if we're done firing for good + if ( locked ) { + + // Keep an empty list if we have data for future add calls + if ( memory ) { + list = []; + + // Otherwise, this object is spent + } else { + list = ""; + } + } + }, + + // Actual Callbacks object + self = { + + // Add a callback or a collection of callbacks to the list + add: function() { + if ( list ) { + + // If we have memory from a past run, we should fire after adding + if ( memory && !firing ) { + firingIndex = list.length - 1; + queue.push( memory ); + } + + ( function add( args ) { + jQuery.each( args, function( _, arg ) { + if ( isFunction( arg ) ) { + if ( !options.unique || !self.has( arg ) ) { + list.push( arg ); + } + } else if ( arg && arg.length && toType( arg ) !== "string" ) { + + // Inspect recursively + add( arg ); + } + } ); + } )( arguments ); + + if ( memory && !firing ) { + fire(); + } + } + return this; + }, + + // Remove a callback from the list + remove: function() { + jQuery.each( arguments, function( _, arg ) { + var index; + while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) { + list.splice( index, 1 ); + + // Handle firing indexes + if ( index <= firingIndex ) { + firingIndex--; + } + } + } ); + return this; + }, + + // Check if a given callback is in the list. + // If no argument is given, return whether or not list has callbacks attached. + has: function( fn ) { + return fn ? + jQuery.inArray( fn, list ) > -1 : + list.length > 0; + }, + + // Remove all callbacks from the list + empty: function() { + if ( list ) { + list = []; + } + return this; + }, + + // Disable .fire and .add + // Abort any current/pending executions + // Clear all callbacks and values + disable: function() { + locked = queue = []; + list = memory = ""; + return this; + }, + disabled: function() { + return !list; + }, + + // Disable .fire + // Also disable .add unless we have memory (since it would have no effect) + // Abort any pending executions + lock: function() { + locked = queue = []; + if ( !memory && !firing ) { + list = memory = ""; + } + return this; + }, + locked: function() { + return !!locked; + }, + + // Call all callbacks with the given context and arguments + fireWith: function( context, args ) { + if ( !locked ) { + args = args || []; + args = [ context, args.slice ? args.slice() : args ]; + queue.push( args ); + if ( !firing ) { + fire(); + } + } + return this; + }, + + // Call all the callbacks with the given arguments + fire: function() { + self.fireWith( this, arguments ); + return this; + }, + + // To know if the callbacks have already been called at least once + fired: function() { + return !!fired; + } + }; + + return self; +}; + + +function Identity( v ) { + return v; +} +function Thrower( ex ) { + throw ex; +} + +function adoptValue( value, resolve, reject, noValue ) { + var method; + + try { + + // Check for promise aspect first to privilege synchronous behavior + if ( value && isFunction( ( method = value.promise ) ) ) { + method.call( value ).done( resolve ).fail( reject ); + + // Other thenables + } else if ( value && isFunction( ( method = value.then ) ) ) { + method.call( value, resolve, reject ); + + // Other non-thenables + } else { + + // Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer: + // * false: [ value ].slice( 0 ) => resolve( value ) + // * true: [ value ].slice( 1 ) => resolve() + resolve.apply( undefined, [ value ].slice( noValue ) ); + } + + // For Promises/A+, convert exceptions into rejections + // Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in + // Deferred#then to conditionally suppress rejection. + } catch ( value ) { + + // Support: Android 4.0 only + // Strict mode functions invoked without .call/.apply get global-object context + reject.apply( undefined, [ value ] ); + } +} + +jQuery.extend( { + + Deferred: function( func ) { + var tuples = [ + + // action, add listener, callbacks, + // ... .then handlers, argument index, [final state] + [ "notify", "progress", jQuery.Callbacks( "memory" ), + jQuery.Callbacks( "memory" ), 2 ], + [ "resolve", "done", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 0, "resolved" ], + [ "reject", "fail", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 1, "rejected" ] + ], + state = "pending", + promise = { + state: function() { + return state; + }, + always: function() { + deferred.done( arguments ).fail( arguments ); + return this; + }, + "catch": function( fn ) { + return promise.then( null, fn ); + }, + + // Keep pipe for back-compat + pipe: function( /* fnDone, fnFail, fnProgress */ ) { + var fns = arguments; + + return jQuery.Deferred( function( newDefer ) { + jQuery.each( tuples, function( _i, tuple ) { + + // Map tuples (progress, done, fail) to arguments (done, fail, progress) + var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ]; + + // deferred.progress(function() { bind to newDefer or newDefer.notify }) + // deferred.done(function() { bind to newDefer or newDefer.resolve }) + // deferred.fail(function() { bind to newDefer or newDefer.reject }) + deferred[ tuple[ 1 ] ]( function() { + var returned = fn && fn.apply( this, arguments ); + if ( returned && isFunction( returned.promise ) ) { + returned.promise() + .progress( newDefer.notify ) + .done( newDefer.resolve ) + .fail( newDefer.reject ); + } else { + newDefer[ tuple[ 0 ] + "With" ]( + this, + fn ? [ returned ] : arguments + ); + } + } ); + } ); + fns = null; + } ).promise(); + }, + then: function( onFulfilled, onRejected, onProgress ) { + var maxDepth = 0; + function resolve( depth, deferred, handler, special ) { + return function() { + var that = this, + args = arguments, + mightThrow = function() { + var returned, then; + + // Support: Promises/A+ section 2.3.3.3.3 + // https://promisesaplus.com/#point-59 + // Ignore double-resolution attempts + if ( depth < maxDepth ) { + return; + } + + returned = handler.apply( that, args ); + + // Support: Promises/A+ section 2.3.1 + // https://promisesaplus.com/#point-48 + if ( returned === deferred.promise() ) { + throw new TypeError( "Thenable self-resolution" ); + } + + // Support: Promises/A+ sections 2.3.3.1, 3.5 + // https://promisesaplus.com/#point-54 + // https://promisesaplus.com/#point-75 + // Retrieve `then` only once + then = returned && + + // Support: Promises/A+ section 2.3.4 + // https://promisesaplus.com/#point-64 + // Only check objects and functions for thenability + ( typeof returned === "object" || + typeof returned === "function" ) && + returned.then; + + // Handle a returned thenable + if ( isFunction( then ) ) { + + // Special processors (notify) just wait for resolution + if ( special ) { + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ) + ); + + // Normal processors (resolve) also hook into progress + } else { + + // ...and disregard older resolution values + maxDepth++; + + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ), + resolve( maxDepth, deferred, Identity, + deferred.notifyWith ) + ); + } + + // Handle all other returned values + } else { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Identity ) { + that = undefined; + args = [ returned ]; + } + + // Process the value(s) + // Default process is resolve + ( special || deferred.resolveWith )( that, args ); + } + }, + + // Only normal processors (resolve) catch and reject exceptions + process = special ? + mightThrow : + function() { + try { + mightThrow(); + } catch ( e ) { + + if ( jQuery.Deferred.exceptionHook ) { + jQuery.Deferred.exceptionHook( e, + process.stackTrace ); + } + + // Support: Promises/A+ section 2.3.3.3.4.1 + // https://promisesaplus.com/#point-61 + // Ignore post-resolution exceptions + if ( depth + 1 >= maxDepth ) { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Thrower ) { + that = undefined; + args = [ e ]; + } + + deferred.rejectWith( that, args ); + } + } + }; + + // Support: Promises/A+ section 2.3.3.3.1 + // https://promisesaplus.com/#point-57 + // Re-resolve promises immediately to dodge false rejection from + // subsequent errors + if ( depth ) { + process(); + } else { + + // Call an optional hook to record the stack, in case of exception + // since it's otherwise lost when execution goes async + if ( jQuery.Deferred.getStackHook ) { + process.stackTrace = jQuery.Deferred.getStackHook(); + } + window.setTimeout( process ); + } + }; + } + + return jQuery.Deferred( function( newDefer ) { + + // progress_handlers.add( ... ) + tuples[ 0 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onProgress ) ? + onProgress : + Identity, + newDefer.notifyWith + ) + ); + + // fulfilled_handlers.add( ... ) + tuples[ 1 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onFulfilled ) ? + onFulfilled : + Identity + ) + ); + + // rejected_handlers.add( ... ) + tuples[ 2 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onRejected ) ? + onRejected : + Thrower + ) + ); + } ).promise(); + }, + + // Get a promise for this deferred + // If obj is provided, the promise aspect is added to the object + promise: function( obj ) { + return obj != null ? jQuery.extend( obj, promise ) : promise; + } + }, + deferred = {}; + + // Add list-specific methods + jQuery.each( tuples, function( i, tuple ) { + var list = tuple[ 2 ], + stateString = tuple[ 5 ]; + + // promise.progress = list.add + // promise.done = list.add + // promise.fail = list.add + promise[ tuple[ 1 ] ] = list.add; + + // Handle state + if ( stateString ) { + list.add( + function() { + + // state = "resolved" (i.e., fulfilled) + // state = "rejected" + state = stateString; + }, + + // rejected_callbacks.disable + // fulfilled_callbacks.disable + tuples[ 3 - i ][ 2 ].disable, + + // rejected_handlers.disable + // fulfilled_handlers.disable + tuples[ 3 - i ][ 3 ].disable, + + // progress_callbacks.lock + tuples[ 0 ][ 2 ].lock, + + // progress_handlers.lock + tuples[ 0 ][ 3 ].lock + ); + } + + // progress_handlers.fire + // fulfilled_handlers.fire + // rejected_handlers.fire + list.add( tuple[ 3 ].fire ); + + // deferred.notify = function() { deferred.notifyWith(...) } + // deferred.resolve = function() { deferred.resolveWith(...) } + // deferred.reject = function() { deferred.rejectWith(...) } + deferred[ tuple[ 0 ] ] = function() { + deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments ); + return this; + }; + + // deferred.notifyWith = list.fireWith + // deferred.resolveWith = list.fireWith + // deferred.rejectWith = list.fireWith + deferred[ tuple[ 0 ] + "With" ] = list.fireWith; + } ); + + // Make the deferred a promise + promise.promise( deferred ); + + // Call given func if any + if ( func ) { + func.call( deferred, deferred ); + } + + // All done! + return deferred; + }, + + // Deferred helper + when: function( singleValue ) { + var + + // count of uncompleted subordinates + remaining = arguments.length, + + // count of unprocessed arguments + i = remaining, + + // subordinate fulfillment data + resolveContexts = Array( i ), + resolveValues = slice.call( arguments ), + + // the master Deferred + master = jQuery.Deferred(), + + // subordinate callback factory + updateFunc = function( i ) { + return function( value ) { + resolveContexts[ i ] = this; + resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value; + if ( !( --remaining ) ) { + master.resolveWith( resolveContexts, resolveValues ); + } + }; + }; + + // Single- and empty arguments are adopted like Promise.resolve + if ( remaining <= 1 ) { + adoptValue( singleValue, master.done( updateFunc( i ) ).resolve, master.reject, + !remaining ); + + // Use .then() to unwrap secondary thenables (cf. gh-3000) + if ( master.state() === "pending" || + isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) { + + return master.then(); + } + } + + // Multiple arguments are aggregated like Promise.all array elements + while ( i-- ) { + adoptValue( resolveValues[ i ], updateFunc( i ), master.reject ); + } + + return master.promise(); + } +} ); + + +// These usually indicate a programmer mistake during development, +// warn about them ASAP rather than swallowing them by default. +var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/; + +jQuery.Deferred.exceptionHook = function( error, stack ) { + + // Support: IE 8 - 9 only + // Console exists when dev tools are open, which can happen at any time + if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) { + window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack ); + } +}; + + + + +jQuery.readyException = function( error ) { + window.setTimeout( function() { + throw error; + } ); +}; + + + + +// The deferred used on DOM ready +var readyList = jQuery.Deferred(); + +jQuery.fn.ready = function( fn ) { + + readyList + .then( fn ) + + // Wrap jQuery.readyException in a function so that the lookup + // happens at the time of error handling instead of callback + // registration. + .catch( function( error ) { + jQuery.readyException( error ); + } ); + + return this; +}; + +jQuery.extend( { + + // Is the DOM ready to be used? Set to true once it occurs. + isReady: false, + + // A counter to track how many items to wait for before + // the ready event fires. See #6781 + readyWait: 1, + + // Handle when the DOM is ready + ready: function( wait ) { + + // Abort if there are pending holds or we're already ready + if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) { + return; + } + + // Remember that the DOM is ready + jQuery.isReady = true; + + // If a normal DOM Ready event fired, decrement, and wait if need be + if ( wait !== true && --jQuery.readyWait > 0 ) { + return; + } + + // If there are functions bound, to execute + readyList.resolveWith( document, [ jQuery ] ); + } +} ); + +jQuery.ready.then = readyList.then; + +// The ready event handler and self cleanup method +function completed() { + document.removeEventListener( "DOMContentLoaded", completed ); + window.removeEventListener( "load", completed ); + jQuery.ready(); +} + +// Catch cases where $(document).ready() is called +// after the browser event has already occurred. +// Support: IE <=9 - 10 only +// Older IE sometimes signals "interactive" too soon +if ( document.readyState === "complete" || + ( document.readyState !== "loading" && !document.documentElement.doScroll ) ) { + + // Handle it asynchronously to allow scripts the opportunity to delay ready + window.setTimeout( jQuery.ready ); + +} else { + + // Use the handy event callback + document.addEventListener( "DOMContentLoaded", completed ); + + // A fallback to window.onload, that will always work + window.addEventListener( "load", completed ); +} + + + + +// Multifunctional method to get and set values of a collection +// The value/s can optionally be executed if it's a function +var access = function( elems, fn, key, value, chainable, emptyGet, raw ) { + var i = 0, + len = elems.length, + bulk = key == null; + + // Sets many values + if ( toType( key ) === "object" ) { + chainable = true; + for ( i in key ) { + access( elems, fn, i, key[ i ], true, emptyGet, raw ); + } + + // Sets one value + } else if ( value !== undefined ) { + chainable = true; + + if ( !isFunction( value ) ) { + raw = true; + } + + if ( bulk ) { + + // Bulk operations run against the entire set + if ( raw ) { + fn.call( elems, value ); + fn = null; + + // ...except when executing function values + } else { + bulk = fn; + fn = function( elem, _key, value ) { + return bulk.call( jQuery( elem ), value ); + }; + } + } + + if ( fn ) { + for ( ; i < len; i++ ) { + fn( + elems[ i ], key, raw ? + value : + value.call( elems[ i ], i, fn( elems[ i ], key ) ) + ); + } + } + } + + if ( chainable ) { + return elems; + } + + // Gets + if ( bulk ) { + return fn.call( elems ); + } + + return len ? fn( elems[ 0 ], key ) : emptyGet; +}; + + +// Matches dashed string for camelizing +var rmsPrefix = /^-ms-/, + rdashAlpha = /-([a-z])/g; + +// Used by camelCase as callback to replace() +function fcamelCase( _all, letter ) { + return letter.toUpperCase(); +} + +// Convert dashed to camelCase; used by the css and data modules +// Support: IE <=9 - 11, Edge 12 - 15 +// Microsoft forgot to hump their vendor prefix (#9572) +function camelCase( string ) { + return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase ); +} +var acceptData = function( owner ) { + + // Accepts only: + // - Node + // - Node.ELEMENT_NODE + // - Node.DOCUMENT_NODE + // - Object + // - Any + return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType ); +}; + + + + +function Data() { + this.expando = jQuery.expando + Data.uid++; +} + +Data.uid = 1; + +Data.prototype = { + + cache: function( owner ) { + + // Check if the owner object already has a cache + var value = owner[ this.expando ]; + + // If not, create one + if ( !value ) { + value = {}; + + // We can accept data for non-element nodes in modern browsers, + // but we should not, see #8335. + // Always return an empty object. + if ( acceptData( owner ) ) { + + // If it is a node unlikely to be stringify-ed or looped over + // use plain assignment + if ( owner.nodeType ) { + owner[ this.expando ] = value; + + // Otherwise secure it in a non-enumerable property + // configurable must be true to allow the property to be + // deleted when data is removed + } else { + Object.defineProperty( owner, this.expando, { + value: value, + configurable: true + } ); + } + } + } + + return value; + }, + set: function( owner, data, value ) { + var prop, + cache = this.cache( owner ); + + // Handle: [ owner, key, value ] args + // Always use camelCase key (gh-2257) + if ( typeof data === "string" ) { + cache[ camelCase( data ) ] = value; + + // Handle: [ owner, { properties } ] args + } else { + + // Copy the properties one-by-one to the cache object + for ( prop in data ) { + cache[ camelCase( prop ) ] = data[ prop ]; + } + } + return cache; + }, + get: function( owner, key ) { + return key === undefined ? + this.cache( owner ) : + + // Always use camelCase key (gh-2257) + owner[ this.expando ] && owner[ this.expando ][ camelCase( key ) ]; + }, + access: function( owner, key, value ) { + + // In cases where either: + // + // 1. No key was specified + // 2. A string key was specified, but no value provided + // + // Take the "read" path and allow the get method to determine + // which value to return, respectively either: + // + // 1. The entire cache object + // 2. The data stored at the key + // + if ( key === undefined || + ( ( key && typeof key === "string" ) && value === undefined ) ) { + + return this.get( owner, key ); + } + + // When the key is not a string, or both a key and value + // are specified, set or extend (existing objects) with either: + // + // 1. An object of properties + // 2. A key and value + // + this.set( owner, key, value ); + + // Since the "set" path can have two possible entry points + // return the expected data based on which path was taken[*] + return value !== undefined ? value : key; + }, + remove: function( owner, key ) { + var i, + cache = owner[ this.expando ]; + + if ( cache === undefined ) { + return; + } + + if ( key !== undefined ) { + + // Support array or space separated string of keys + if ( Array.isArray( key ) ) { + + // If key is an array of keys... + // We always set camelCase keys, so remove that. + key = key.map( camelCase ); + } else { + key = camelCase( key ); + + // If a key with the spaces exists, use it. + // Otherwise, create an array by matching non-whitespace + key = key in cache ? + [ key ] : + ( key.match( rnothtmlwhite ) || [] ); + } + + i = key.length; + + while ( i-- ) { + delete cache[ key[ i ] ]; + } + } + + // Remove the expando if there's no more data + if ( key === undefined || jQuery.isEmptyObject( cache ) ) { + + // Support: Chrome <=35 - 45 + // Webkit & Blink performance suffers when deleting properties + // from DOM nodes, so set to undefined instead + // https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted) + if ( owner.nodeType ) { + owner[ this.expando ] = undefined; + } else { + delete owner[ this.expando ]; + } + } + }, + hasData: function( owner ) { + var cache = owner[ this.expando ]; + return cache !== undefined && !jQuery.isEmptyObject( cache ); + } +}; +var dataPriv = new Data(); + +var dataUser = new Data(); + + + +// Implementation Summary +// +// 1. Enforce API surface and semantic compatibility with 1.9.x branch +// 2. Improve the module's maintainability by reducing the storage +// paths to a single mechanism. +// 3. Use the same single mechanism to support "private" and "user" data. +// 4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData) +// 5. Avoid exposing implementation details on user objects (eg. expando properties) +// 6. Provide a clear path for implementation upgrade to WeakMap in 2014 + +var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/, + rmultiDash = /[A-Z]/g; + +function getData( data ) { + if ( data === "true" ) { + return true; + } + + if ( data === "false" ) { + return false; + } + + if ( data === "null" ) { + return null; + } + + // Only convert to a number if it doesn't change the string + if ( data === +data + "" ) { + return +data; + } + + if ( rbrace.test( data ) ) { + return JSON.parse( data ); + } + + return data; +} + +function dataAttr( elem, key, data ) { + var name; + + // If nothing was found internally, try to fetch any + // data from the HTML5 data-* attribute + if ( data === undefined && elem.nodeType === 1 ) { + name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase(); + data = elem.getAttribute( name ); + + if ( typeof data === "string" ) { + try { + data = getData( data ); + } catch ( e ) {} + + // Make sure we set the data so it isn't changed later + dataUser.set( elem, key, data ); + } else { + data = undefined; + } + } + return data; +} + +jQuery.extend( { + hasData: function( elem ) { + return dataUser.hasData( elem ) || dataPriv.hasData( elem ); + }, + + data: function( elem, name, data ) { + return dataUser.access( elem, name, data ); + }, + + removeData: function( elem, name ) { + dataUser.remove( elem, name ); + }, + + // TODO: Now that all calls to _data and _removeData have been replaced + // with direct calls to dataPriv methods, these can be deprecated. + _data: function( elem, name, data ) { + return dataPriv.access( elem, name, data ); + }, + + _removeData: function( elem, name ) { + dataPriv.remove( elem, name ); + } +} ); + +jQuery.fn.extend( { + data: function( key, value ) { + var i, name, data, + elem = this[ 0 ], + attrs = elem && elem.attributes; + + // Gets all values + if ( key === undefined ) { + if ( this.length ) { + data = dataUser.get( elem ); + + if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) { + i = attrs.length; + while ( i-- ) { + + // Support: IE 11 only + // The attrs elements can be null (#14894) + if ( attrs[ i ] ) { + name = attrs[ i ].name; + if ( name.indexOf( "data-" ) === 0 ) { + name = camelCase( name.slice( 5 ) ); + dataAttr( elem, name, data[ name ] ); + } + } + } + dataPriv.set( elem, "hasDataAttrs", true ); + } + } + + return data; + } + + // Sets multiple values + if ( typeof key === "object" ) { + return this.each( function() { + dataUser.set( this, key ); + } ); + } + + return access( this, function( value ) { + var data; + + // The calling jQuery object (element matches) is not empty + // (and therefore has an element appears at this[ 0 ]) and the + // `value` parameter was not undefined. An empty jQuery object + // will result in `undefined` for elem = this[ 0 ] which will + // throw an exception if an attempt to read a data cache is made. + if ( elem && value === undefined ) { + + // Attempt to get data from the cache + // The key will always be camelCased in Data + data = dataUser.get( elem, key ); + if ( data !== undefined ) { + return data; + } + + // Attempt to "discover" the data in + // HTML5 custom data-* attrs + data = dataAttr( elem, key ); + if ( data !== undefined ) { + return data; + } + + // We tried really hard, but the data doesn't exist. + return; + } + + // Set the data... + this.each( function() { + + // We always store the camelCased key + dataUser.set( this, key, value ); + } ); + }, null, value, arguments.length > 1, null, true ); + }, + + removeData: function( key ) { + return this.each( function() { + dataUser.remove( this, key ); + } ); + } +} ); + + +jQuery.extend( { + queue: function( elem, type, data ) { + var queue; + + if ( elem ) { + type = ( type || "fx" ) + "queue"; + queue = dataPriv.get( elem, type ); + + // Speed up dequeue by getting out quickly if this is just a lookup + if ( data ) { + if ( !queue || Array.isArray( data ) ) { + queue = dataPriv.access( elem, type, jQuery.makeArray( data ) ); + } else { + queue.push( data ); + } + } + return queue || []; + } + }, + + dequeue: function( elem, type ) { + type = type || "fx"; + + var queue = jQuery.queue( elem, type ), + startLength = queue.length, + fn = queue.shift(), + hooks = jQuery._queueHooks( elem, type ), + next = function() { + jQuery.dequeue( elem, type ); + }; + + // If the fx queue is dequeued, always remove the progress sentinel + if ( fn === "inprogress" ) { + fn = queue.shift(); + startLength--; + } + + if ( fn ) { + + // Add a progress sentinel to prevent the fx queue from being + // automatically dequeued + if ( type === "fx" ) { + queue.unshift( "inprogress" ); + } + + // Clear up the last queue stop function + delete hooks.stop; + fn.call( elem, next, hooks ); + } + + if ( !startLength && hooks ) { + hooks.empty.fire(); + } + }, + + // Not public - generate a queueHooks object, or return the current one + _queueHooks: function( elem, type ) { + var key = type + "queueHooks"; + return dataPriv.get( elem, key ) || dataPriv.access( elem, key, { + empty: jQuery.Callbacks( "once memory" ).add( function() { + dataPriv.remove( elem, [ type + "queue", key ] ); + } ) + } ); + } +} ); + +jQuery.fn.extend( { + queue: function( type, data ) { + var setter = 2; + + if ( typeof type !== "string" ) { + data = type; + type = "fx"; + setter--; + } + + if ( arguments.length < setter ) { + return jQuery.queue( this[ 0 ], type ); + } + + return data === undefined ? + this : + this.each( function() { + var queue = jQuery.queue( this, type, data ); + + // Ensure a hooks for this queue + jQuery._queueHooks( this, type ); + + if ( type === "fx" && queue[ 0 ] !== "inprogress" ) { + jQuery.dequeue( this, type ); + } + } ); + }, + dequeue: function( type ) { + return this.each( function() { + jQuery.dequeue( this, type ); + } ); + }, + clearQueue: function( type ) { + return this.queue( type || "fx", [] ); + }, + + // Get a promise resolved when queues of a certain type + // are emptied (fx is the type by default) + promise: function( type, obj ) { + var tmp, + count = 1, + defer = jQuery.Deferred(), + elements = this, + i = this.length, + resolve = function() { + if ( !( --count ) ) { + defer.resolveWith( elements, [ elements ] ); + } + }; + + if ( typeof type !== "string" ) { + obj = type; + type = undefined; + } + type = type || "fx"; + + while ( i-- ) { + tmp = dataPriv.get( elements[ i ], type + "queueHooks" ); + if ( tmp && tmp.empty ) { + count++; + tmp.empty.add( resolve ); + } + } + resolve(); + return defer.promise( obj ); + } +} ); +var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source; + +var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" ); + + +var cssExpand = [ "Top", "Right", "Bottom", "Left" ]; + +var documentElement = document.documentElement; + + + + var isAttached = function( elem ) { + return jQuery.contains( elem.ownerDocument, elem ); + }, + composed = { composed: true }; + + // Support: IE 9 - 11+, Edge 12 - 18+, iOS 10.0 - 10.2 only + // Check attachment across shadow DOM boundaries when possible (gh-3504) + // Support: iOS 10.0-10.2 only + // Early iOS 10 versions support `attachShadow` but not `getRootNode`, + // leading to errors. We need to check for `getRootNode`. + if ( documentElement.getRootNode ) { + isAttached = function( elem ) { + return jQuery.contains( elem.ownerDocument, elem ) || + elem.getRootNode( composed ) === elem.ownerDocument; + }; + } +var isHiddenWithinTree = function( elem, el ) { + + // isHiddenWithinTree might be called from jQuery#filter function; + // in that case, element will be second argument + elem = el || elem; + + // Inline style trumps all + return elem.style.display === "none" || + elem.style.display === "" && + + // Otherwise, check computed style + // Support: Firefox <=43 - 45 + // Disconnected elements can have computed display: none, so first confirm that elem is + // in the document. + isAttached( elem ) && + + jQuery.css( elem, "display" ) === "none"; + }; + + + +function adjustCSS( elem, prop, valueParts, tween ) { + var adjusted, scale, + maxIterations = 20, + currentValue = tween ? + function() { + return tween.cur(); + } : + function() { + return jQuery.css( elem, prop, "" ); + }, + initial = currentValue(), + unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ), + + // Starting value computation is required for potential unit mismatches + initialInUnit = elem.nodeType && + ( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) && + rcssNum.exec( jQuery.css( elem, prop ) ); + + if ( initialInUnit && initialInUnit[ 3 ] !== unit ) { + + // Support: Firefox <=54 + // Halve the iteration target value to prevent interference from CSS upper bounds (gh-2144) + initial = initial / 2; + + // Trust units reported by jQuery.css + unit = unit || initialInUnit[ 3 ]; + + // Iteratively approximate from a nonzero starting point + initialInUnit = +initial || 1; + + while ( maxIterations-- ) { + + // Evaluate and update our best guess (doubling guesses that zero out). + // Finish if the scale equals or crosses 1 (making the old*new product non-positive). + jQuery.style( elem, prop, initialInUnit + unit ); + if ( ( 1 - scale ) * ( 1 - ( scale = currentValue() / initial || 0.5 ) ) <= 0 ) { + maxIterations = 0; + } + initialInUnit = initialInUnit / scale; + + } + + initialInUnit = initialInUnit * 2; + jQuery.style( elem, prop, initialInUnit + unit ); + + // Make sure we update the tween properties later on + valueParts = valueParts || []; + } + + if ( valueParts ) { + initialInUnit = +initialInUnit || +initial || 0; + + // Apply relative offset (+=/-=) if specified + adjusted = valueParts[ 1 ] ? + initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] : + +valueParts[ 2 ]; + if ( tween ) { + tween.unit = unit; + tween.start = initialInUnit; + tween.end = adjusted; + } + } + return adjusted; +} + + +var defaultDisplayMap = {}; + +function getDefaultDisplay( elem ) { + var temp, + doc = elem.ownerDocument, + nodeName = elem.nodeName, + display = defaultDisplayMap[ nodeName ]; + + if ( display ) { + return display; + } + + temp = doc.body.appendChild( doc.createElement( nodeName ) ); + display = jQuery.css( temp, "display" ); + + temp.parentNode.removeChild( temp ); + + if ( display === "none" ) { + display = "block"; + } + defaultDisplayMap[ nodeName ] = display; + + return display; +} + +function showHide( elements, show ) { + var display, elem, + values = [], + index = 0, + length = elements.length; + + // Determine new display value for elements that need to change + for ( ; index < length; index++ ) { + elem = elements[ index ]; + if ( !elem.style ) { + continue; + } + + display = elem.style.display; + if ( show ) { + + // Since we force visibility upon cascade-hidden elements, an immediate (and slow) + // check is required in this first loop unless we have a nonempty display value (either + // inline or about-to-be-restored) + if ( display === "none" ) { + values[ index ] = dataPriv.get( elem, "display" ) || null; + if ( !values[ index ] ) { + elem.style.display = ""; + } + } + if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) { + values[ index ] = getDefaultDisplay( elem ); + } + } else { + if ( display !== "none" ) { + values[ index ] = "none"; + + // Remember what we're overwriting + dataPriv.set( elem, "display", display ); + } + } + } + + // Set the display of the elements in a second loop to avoid constant reflow + for ( index = 0; index < length; index++ ) { + if ( values[ index ] != null ) { + elements[ index ].style.display = values[ index ]; + } + } + + return elements; +} + +jQuery.fn.extend( { + show: function() { + return showHide( this, true ); + }, + hide: function() { + return showHide( this ); + }, + toggle: function( state ) { + if ( typeof state === "boolean" ) { + return state ? this.show() : this.hide(); + } + + return this.each( function() { + if ( isHiddenWithinTree( this ) ) { + jQuery( this ).show(); + } else { + jQuery( this ).hide(); + } + } ); + } +} ); +var rcheckableType = ( /^(?:checkbox|radio)$/i ); + +var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]*)/i ); + +var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i ); + + + +( function() { + var fragment = document.createDocumentFragment(), + div = fragment.appendChild( document.createElement( "div" ) ), + input = document.createElement( "input" ); + + // Support: Android 4.0 - 4.3 only + // Check state lost if the name is set (#11217) + // Support: Windows Web Apps (WWA) + // `name` and `type` must use .setAttribute for WWA (#14901) + input.setAttribute( "type", "radio" ); + input.setAttribute( "checked", "checked" ); + input.setAttribute( "name", "t" ); + + div.appendChild( input ); + + // Support: Android <=4.1 only + // Older WebKit doesn't clone checked state correctly in fragments + support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked; + + // Support: IE <=11 only + // Make sure textarea (and checkbox) defaultValue is properly cloned + div.innerHTML = ""; + support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue; + + // Support: IE <=9 only + // IE <=9 replaces "; + support.option = !!div.lastChild; +} )(); + + +// We have to close these tags to support XHTML (#13200) +var wrapMap = { + + // XHTML parsers do not magically insert elements in the + // same way that tag soup parsers do. So we cannot shorten + // this by omitting or other required elements. + thead: [ 1, "", "
" ], + col: [ 2, "", "
" ], + tr: [ 2, "", "
" ], + td: [ 3, "", "
" ], + + _default: [ 0, "", "" ] +}; + +wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead; +wrapMap.th = wrapMap.td; + +// Support: IE <=9 only +if ( !support.option ) { + wrapMap.optgroup = wrapMap.option = [ 1, "" ]; +} + + +function getAll( context, tag ) { + + // Support: IE <=9 - 11 only + // Use typeof to avoid zero-argument method invocation on host objects (#15151) + var ret; + + if ( typeof context.getElementsByTagName !== "undefined" ) { + ret = context.getElementsByTagName( tag || "*" ); + + } else if ( typeof context.querySelectorAll !== "undefined" ) { + ret = context.querySelectorAll( tag || "*" ); + + } else { + ret = []; + } + + if ( tag === undefined || tag && nodeName( context, tag ) ) { + return jQuery.merge( [ context ], ret ); + } + + return ret; +} + + +// Mark scripts as having already been evaluated +function setGlobalEval( elems, refElements ) { + var i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + dataPriv.set( + elems[ i ], + "globalEval", + !refElements || dataPriv.get( refElements[ i ], "globalEval" ) + ); + } +} + + +var rhtml = /<|&#?\w+;/; + +function buildFragment( elems, context, scripts, selection, ignored ) { + var elem, tmp, tag, wrap, attached, j, + fragment = context.createDocumentFragment(), + nodes = [], + i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + elem = elems[ i ]; + + if ( elem || elem === 0 ) { + + // Add nodes directly + if ( toType( elem ) === "object" ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem ); + + // Convert non-html into a text node + } else if ( !rhtml.test( elem ) ) { + nodes.push( context.createTextNode( elem ) ); + + // Convert html into DOM nodes + } else { + tmp = tmp || fragment.appendChild( context.createElement( "div" ) ); + + // Deserialize a standard representation + tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase(); + wrap = wrapMap[ tag ] || wrapMap._default; + tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ]; + + // Descend through wrappers to the right content + j = wrap[ 0 ]; + while ( j-- ) { + tmp = tmp.lastChild; + } + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, tmp.childNodes ); + + // Remember the top-level container + tmp = fragment.firstChild; + + // Ensure the created nodes are orphaned (#12392) + tmp.textContent = ""; + } + } + } + + // Remove wrapper from fragment + fragment.textContent = ""; + + i = 0; + while ( ( elem = nodes[ i++ ] ) ) { + + // Skip elements already in the context collection (trac-4087) + if ( selection && jQuery.inArray( elem, selection ) > -1 ) { + if ( ignored ) { + ignored.push( elem ); + } + continue; + } + + attached = isAttached( elem ); + + // Append to fragment + tmp = getAll( fragment.appendChild( elem ), "script" ); + + // Preserve script evaluation history + if ( attached ) { + setGlobalEval( tmp ); + } + + // Capture executables + if ( scripts ) { + j = 0; + while ( ( elem = tmp[ j++ ] ) ) { + if ( rscriptType.test( elem.type || "" ) ) { + scripts.push( elem ); + } + } + } + } + + return fragment; +} + + +var + rkeyEvent = /^key/, + rmouseEvent = /^(?:mouse|pointer|contextmenu|drag|drop)|click/, + rtypenamespace = /^([^.]*)(?:\.(.+)|)/; + +function returnTrue() { + return true; +} + +function returnFalse() { + return false; +} + +// Support: IE <=9 - 11+ +// focus() and blur() are asynchronous, except when they are no-op. +// So expect focus to be synchronous when the element is already active, +// and blur to be synchronous when the element is not already active. +// (focus and blur are always synchronous in other supported browsers, +// this just defines when we can count on it). +function expectSync( elem, type ) { + return ( elem === safeActiveElement() ) === ( type === "focus" ); +} + +// Support: IE <=9 only +// Accessing document.activeElement can throw unexpectedly +// https://bugs.jquery.com/ticket/13393 +function safeActiveElement() { + try { + return document.activeElement; + } catch ( err ) { } +} + +function on( elem, types, selector, data, fn, one ) { + var origFn, type; + + // Types can be a map of types/handlers + if ( typeof types === "object" ) { + + // ( types-Object, selector, data ) + if ( typeof selector !== "string" ) { + + // ( types-Object, data ) + data = data || selector; + selector = undefined; + } + for ( type in types ) { + on( elem, type, selector, data, types[ type ], one ); + } + return elem; + } + + if ( data == null && fn == null ) { + + // ( types, fn ) + fn = selector; + data = selector = undefined; + } else if ( fn == null ) { + if ( typeof selector === "string" ) { + + // ( types, selector, fn ) + fn = data; + data = undefined; + } else { + + // ( types, data, fn ) + fn = data; + data = selector; + selector = undefined; + } + } + if ( fn === false ) { + fn = returnFalse; + } else if ( !fn ) { + return elem; + } + + if ( one === 1 ) { + origFn = fn; + fn = function( event ) { + + // Can use an empty set, since event contains the info + jQuery().off( event ); + return origFn.apply( this, arguments ); + }; + + // Use same guid so caller can remove using origFn + fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ ); + } + return elem.each( function() { + jQuery.event.add( this, types, fn, data, selector ); + } ); +} + +/* + * Helper functions for managing events -- not part of the public interface. + * Props to Dean Edwards' addEvent library for many of the ideas. + */ +jQuery.event = { + + global: {}, + + add: function( elem, types, handler, data, selector ) { + + var handleObjIn, eventHandle, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.get( elem ); + + // Only attach events to objects that accept data + if ( !acceptData( elem ) ) { + return; + } + + // Caller can pass in an object of custom data in lieu of the handler + if ( handler.handler ) { + handleObjIn = handler; + handler = handleObjIn.handler; + selector = handleObjIn.selector; + } + + // Ensure that invalid selectors throw exceptions at attach time + // Evaluate against documentElement in case elem is a non-element node (e.g., document) + if ( selector ) { + jQuery.find.matchesSelector( documentElement, selector ); + } + + // Make sure that the handler has a unique ID, used to find/remove it later + if ( !handler.guid ) { + handler.guid = jQuery.guid++; + } + + // Init the element's event structure and main handler, if this is the first + if ( !( events = elemData.events ) ) { + events = elemData.events = Object.create( null ); + } + if ( !( eventHandle = elemData.handle ) ) { + eventHandle = elemData.handle = function( e ) { + + // Discard the second event of a jQuery.event.trigger() and + // when an event is called after a page has unloaded + return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ? + jQuery.event.dispatch.apply( elem, arguments ) : undefined; + }; + } + + // Handle multiple events separated by a space + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // There *must* be a type, no attaching namespace-only handlers + if ( !type ) { + continue; + } + + // If event changes its type, use the special event handlers for the changed type + special = jQuery.event.special[ type ] || {}; + + // If selector defined, determine special event api type, otherwise given type + type = ( selector ? special.delegateType : special.bindType ) || type; + + // Update special based on newly reset type + special = jQuery.event.special[ type ] || {}; + + // handleObj is passed to all event handlers + handleObj = jQuery.extend( { + type: type, + origType: origType, + data: data, + handler: handler, + guid: handler.guid, + selector: selector, + needsContext: selector && jQuery.expr.match.needsContext.test( selector ), + namespace: namespaces.join( "." ) + }, handleObjIn ); + + // Init the event handler queue if we're the first + if ( !( handlers = events[ type ] ) ) { + handlers = events[ type ] = []; + handlers.delegateCount = 0; + + // Only use addEventListener if the special events handler returns false + if ( !special.setup || + special.setup.call( elem, data, namespaces, eventHandle ) === false ) { + + if ( elem.addEventListener ) { + elem.addEventListener( type, eventHandle ); + } + } + } + + if ( special.add ) { + special.add.call( elem, handleObj ); + + if ( !handleObj.handler.guid ) { + handleObj.handler.guid = handler.guid; + } + } + + // Add to the element's handler list, delegates in front + if ( selector ) { + handlers.splice( handlers.delegateCount++, 0, handleObj ); + } else { + handlers.push( handleObj ); + } + + // Keep track of which events have ever been used, for event optimization + jQuery.event.global[ type ] = true; + } + + }, + + // Detach an event or set of events from an element + remove: function( elem, types, handler, selector, mappedTypes ) { + + var j, origCount, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.hasData( elem ) && dataPriv.get( elem ); + + if ( !elemData || !( events = elemData.events ) ) { + return; + } + + // Once for each type.namespace in types; type may be omitted + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // Unbind all events (on this namespace, if provided) for the element + if ( !type ) { + for ( type in events ) { + jQuery.event.remove( elem, type + types[ t ], handler, selector, true ); + } + continue; + } + + special = jQuery.event.special[ type ] || {}; + type = ( selector ? special.delegateType : special.bindType ) || type; + handlers = events[ type ] || []; + tmp = tmp[ 2 ] && + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ); + + // Remove matching events + origCount = j = handlers.length; + while ( j-- ) { + handleObj = handlers[ j ]; + + if ( ( mappedTypes || origType === handleObj.origType ) && + ( !handler || handler.guid === handleObj.guid ) && + ( !tmp || tmp.test( handleObj.namespace ) ) && + ( !selector || selector === handleObj.selector || + selector === "**" && handleObj.selector ) ) { + handlers.splice( j, 1 ); + + if ( handleObj.selector ) { + handlers.delegateCount--; + } + if ( special.remove ) { + special.remove.call( elem, handleObj ); + } + } + } + + // Remove generic event handler if we removed something and no more handlers exist + // (avoids potential for endless recursion during removal of special event handlers) + if ( origCount && !handlers.length ) { + if ( !special.teardown || + special.teardown.call( elem, namespaces, elemData.handle ) === false ) { + + jQuery.removeEvent( elem, type, elemData.handle ); + } + + delete events[ type ]; + } + } + + // Remove data and the expando if it's no longer used + if ( jQuery.isEmptyObject( events ) ) { + dataPriv.remove( elem, "handle events" ); + } + }, + + dispatch: function( nativeEvent ) { + + var i, j, ret, matched, handleObj, handlerQueue, + args = new Array( arguments.length ), + + // Make a writable jQuery.Event from the native event object + event = jQuery.event.fix( nativeEvent ), + + handlers = ( + dataPriv.get( this, "events" ) || Object.create( null ) + )[ event.type ] || [], + special = jQuery.event.special[ event.type ] || {}; + + // Use the fix-ed jQuery.Event rather than the (read-only) native event + args[ 0 ] = event; + + for ( i = 1; i < arguments.length; i++ ) { + args[ i ] = arguments[ i ]; + } + + event.delegateTarget = this; + + // Call the preDispatch hook for the mapped type, and let it bail if desired + if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) { + return; + } + + // Determine handlers + handlerQueue = jQuery.event.handlers.call( this, event, handlers ); + + // Run delegates first; they may want to stop propagation beneath us + i = 0; + while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) { + event.currentTarget = matched.elem; + + j = 0; + while ( ( handleObj = matched.handlers[ j++ ] ) && + !event.isImmediatePropagationStopped() ) { + + // If the event is namespaced, then each handler is only invoked if it is + // specially universal or its namespaces are a superset of the event's. + if ( !event.rnamespace || handleObj.namespace === false || + event.rnamespace.test( handleObj.namespace ) ) { + + event.handleObj = handleObj; + event.data = handleObj.data; + + ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle || + handleObj.handler ).apply( matched.elem, args ); + + if ( ret !== undefined ) { + if ( ( event.result = ret ) === false ) { + event.preventDefault(); + event.stopPropagation(); + } + } + } + } + } + + // Call the postDispatch hook for the mapped type + if ( special.postDispatch ) { + special.postDispatch.call( this, event ); + } + + return event.result; + }, + + handlers: function( event, handlers ) { + var i, handleObj, sel, matchedHandlers, matchedSelectors, + handlerQueue = [], + delegateCount = handlers.delegateCount, + cur = event.target; + + // Find delegate handlers + if ( delegateCount && + + // Support: IE <=9 + // Black-hole SVG instance trees (trac-13180) + cur.nodeType && + + // Support: Firefox <=42 + // Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861) + // https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click + // Support: IE 11 only + // ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343) + !( event.type === "click" && event.button >= 1 ) ) { + + for ( ; cur !== this; cur = cur.parentNode || this ) { + + // Don't check non-elements (#13208) + // Don't process clicks on disabled elements (#6911, #8165, #11382, #11764) + if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) { + matchedHandlers = []; + matchedSelectors = {}; + for ( i = 0; i < delegateCount; i++ ) { + handleObj = handlers[ i ]; + + // Don't conflict with Object.prototype properties (#13203) + sel = handleObj.selector + " "; + + if ( matchedSelectors[ sel ] === undefined ) { + matchedSelectors[ sel ] = handleObj.needsContext ? + jQuery( sel, this ).index( cur ) > -1 : + jQuery.find( sel, this, null, [ cur ] ).length; + } + if ( matchedSelectors[ sel ] ) { + matchedHandlers.push( handleObj ); + } + } + if ( matchedHandlers.length ) { + handlerQueue.push( { elem: cur, handlers: matchedHandlers } ); + } + } + } + } + + // Add the remaining (directly-bound) handlers + cur = this; + if ( delegateCount < handlers.length ) { + handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } ); + } + + return handlerQueue; + }, + + addProp: function( name, hook ) { + Object.defineProperty( jQuery.Event.prototype, name, { + enumerable: true, + configurable: true, + + get: isFunction( hook ) ? + function() { + if ( this.originalEvent ) { + return hook( this.originalEvent ); + } + } : + function() { + if ( this.originalEvent ) { + return this.originalEvent[ name ]; + } + }, + + set: function( value ) { + Object.defineProperty( this, name, { + enumerable: true, + configurable: true, + writable: true, + value: value + } ); + } + } ); + }, + + fix: function( originalEvent ) { + return originalEvent[ jQuery.expando ] ? + originalEvent : + new jQuery.Event( originalEvent ); + }, + + special: { + load: { + + // Prevent triggered image.load events from bubbling to window.load + noBubble: true + }, + click: { + + // Utilize native event to ensure correct state for checkable inputs + setup: function( data ) { + + // For mutual compressibility with _default, replace `this` access with a local var. + // `|| data` is dead code meant only to preserve the variable through minification. + var el = this || data; + + // Claim the first handler + if ( rcheckableType.test( el.type ) && + el.click && nodeName( el, "input" ) ) { + + // dataPriv.set( el, "click", ... ) + leverageNative( el, "click", returnTrue ); + } + + // Return false to allow normal processing in the caller + return false; + }, + trigger: function( data ) { + + // For mutual compressibility with _default, replace `this` access with a local var. + // `|| data` is dead code meant only to preserve the variable through minification. + var el = this || data; + + // Force setup before triggering a click + if ( rcheckableType.test( el.type ) && + el.click && nodeName( el, "input" ) ) { + + leverageNative( el, "click" ); + } + + // Return non-false to allow normal event-path propagation + return true; + }, + + // For cross-browser consistency, suppress native .click() on links + // Also prevent it if we're currently inside a leveraged native-event stack + _default: function( event ) { + var target = event.target; + return rcheckableType.test( target.type ) && + target.click && nodeName( target, "input" ) && + dataPriv.get( target, "click" ) || + nodeName( target, "a" ); + } + }, + + beforeunload: { + postDispatch: function( event ) { + + // Support: Firefox 20+ + // Firefox doesn't alert if the returnValue field is not set. + if ( event.result !== undefined && event.originalEvent ) { + event.originalEvent.returnValue = event.result; + } + } + } + } +}; + +// Ensure the presence of an event listener that handles manually-triggered +// synthetic events by interrupting progress until reinvoked in response to +// *native* events that it fires directly, ensuring that state changes have +// already occurred before other listeners are invoked. +function leverageNative( el, type, expectSync ) { + + // Missing expectSync indicates a trigger call, which must force setup through jQuery.event.add + if ( !expectSync ) { + if ( dataPriv.get( el, type ) === undefined ) { + jQuery.event.add( el, type, returnTrue ); + } + return; + } + + // Register the controller as a special universal handler for all event namespaces + dataPriv.set( el, type, false ); + jQuery.event.add( el, type, { + namespace: false, + handler: function( event ) { + var notAsync, result, + saved = dataPriv.get( this, type ); + + if ( ( event.isTrigger & 1 ) && this[ type ] ) { + + // Interrupt processing of the outer synthetic .trigger()ed event + // Saved data should be false in such cases, but might be a leftover capture object + // from an async native handler (gh-4350) + if ( !saved.length ) { + + // Store arguments for use when handling the inner native event + // There will always be at least one argument (an event object), so this array + // will not be confused with a leftover capture object. + saved = slice.call( arguments ); + dataPriv.set( this, type, saved ); + + // Trigger the native event and capture its result + // Support: IE <=9 - 11+ + // focus() and blur() are asynchronous + notAsync = expectSync( this, type ); + this[ type ](); + result = dataPriv.get( this, type ); + if ( saved !== result || notAsync ) { + dataPriv.set( this, type, false ); + } else { + result = {}; + } + if ( saved !== result ) { + + // Cancel the outer synthetic event + event.stopImmediatePropagation(); + event.preventDefault(); + return result.value; + } + + // If this is an inner synthetic event for an event with a bubbling surrogate + // (focus or blur), assume that the surrogate already propagated from triggering the + // native event and prevent that from happening again here. + // This technically gets the ordering wrong w.r.t. to `.trigger()` (in which the + // bubbling surrogate propagates *after* the non-bubbling base), but that seems + // less bad than duplication. + } else if ( ( jQuery.event.special[ type ] || {} ).delegateType ) { + event.stopPropagation(); + } + + // If this is a native event triggered above, everything is now in order + // Fire an inner synthetic event with the original arguments + } else if ( saved.length ) { + + // ...and capture the result + dataPriv.set( this, type, { + value: jQuery.event.trigger( + + // Support: IE <=9 - 11+ + // Extend with the prototype to reset the above stopImmediatePropagation() + jQuery.extend( saved[ 0 ], jQuery.Event.prototype ), + saved.slice( 1 ), + this + ) + } ); + + // Abort handling of the native event + event.stopImmediatePropagation(); + } + } + } ); +} + +jQuery.removeEvent = function( elem, type, handle ) { + + // This "if" is needed for plain objects + if ( elem.removeEventListener ) { + elem.removeEventListener( type, handle ); + } +}; + +jQuery.Event = function( src, props ) { + + // Allow instantiation without the 'new' keyword + if ( !( this instanceof jQuery.Event ) ) { + return new jQuery.Event( src, props ); + } + + // Event object + if ( src && src.type ) { + this.originalEvent = src; + this.type = src.type; + + // Events bubbling up the document may have been marked as prevented + // by a handler lower down the tree; reflect the correct value. + this.isDefaultPrevented = src.defaultPrevented || + src.defaultPrevented === undefined && + + // Support: Android <=2.3 only + src.returnValue === false ? + returnTrue : + returnFalse; + + // Create target properties + // Support: Safari <=6 - 7 only + // Target should not be a text node (#504, #13143) + this.target = ( src.target && src.target.nodeType === 3 ) ? + src.target.parentNode : + src.target; + + this.currentTarget = src.currentTarget; + this.relatedTarget = src.relatedTarget; + + // Event type + } else { + this.type = src; + } + + // Put explicitly provided properties onto the event object + if ( props ) { + jQuery.extend( this, props ); + } + + // Create a timestamp if incoming event doesn't have one + this.timeStamp = src && src.timeStamp || Date.now(); + + // Mark it as fixed + this[ jQuery.expando ] = true; +}; + +// jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding +// https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html +jQuery.Event.prototype = { + constructor: jQuery.Event, + isDefaultPrevented: returnFalse, + isPropagationStopped: returnFalse, + isImmediatePropagationStopped: returnFalse, + isSimulated: false, + + preventDefault: function() { + var e = this.originalEvent; + + this.isDefaultPrevented = returnTrue; + + if ( e && !this.isSimulated ) { + e.preventDefault(); + } + }, + stopPropagation: function() { + var e = this.originalEvent; + + this.isPropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopPropagation(); + } + }, + stopImmediatePropagation: function() { + var e = this.originalEvent; + + this.isImmediatePropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopImmediatePropagation(); + } + + this.stopPropagation(); + } +}; + +// Includes all common event props including KeyEvent and MouseEvent specific props +jQuery.each( { + altKey: true, + bubbles: true, + cancelable: true, + changedTouches: true, + ctrlKey: true, + detail: true, + eventPhase: true, + metaKey: true, + pageX: true, + pageY: true, + shiftKey: true, + view: true, + "char": true, + code: true, + charCode: true, + key: true, + keyCode: true, + button: true, + buttons: true, + clientX: true, + clientY: true, + offsetX: true, + offsetY: true, + pointerId: true, + pointerType: true, + screenX: true, + screenY: true, + targetTouches: true, + toElement: true, + touches: true, + + which: function( event ) { + var button = event.button; + + // Add which for key events + if ( event.which == null && rkeyEvent.test( event.type ) ) { + return event.charCode != null ? event.charCode : event.keyCode; + } + + // Add which for click: 1 === left; 2 === middle; 3 === right + if ( !event.which && button !== undefined && rmouseEvent.test( event.type ) ) { + if ( button & 1 ) { + return 1; + } + + if ( button & 2 ) { + return 3; + } + + if ( button & 4 ) { + return 2; + } + + return 0; + } + + return event.which; + } +}, jQuery.event.addProp ); + +jQuery.each( { focus: "focusin", blur: "focusout" }, function( type, delegateType ) { + jQuery.event.special[ type ] = { + + // Utilize native event if possible so blur/focus sequence is correct + setup: function() { + + // Claim the first handler + // dataPriv.set( this, "focus", ... ) + // dataPriv.set( this, "blur", ... ) + leverageNative( this, type, expectSync ); + + // Return false to allow normal processing in the caller + return false; + }, + trigger: function() { + + // Force setup before trigger + leverageNative( this, type ); + + // Return non-false to allow normal event-path propagation + return true; + }, + + delegateType: delegateType + }; +} ); + +// Create mouseenter/leave events using mouseover/out and event-time checks +// so that event delegation works in jQuery. +// Do the same for pointerenter/pointerleave and pointerover/pointerout +// +// Support: Safari 7 only +// Safari sends mouseenter too often; see: +// https://bugs.chromium.org/p/chromium/issues/detail?id=470258 +// for the description of the bug (it existed in older Chrome versions as well). +jQuery.each( { + mouseenter: "mouseover", + mouseleave: "mouseout", + pointerenter: "pointerover", + pointerleave: "pointerout" +}, function( orig, fix ) { + jQuery.event.special[ orig ] = { + delegateType: fix, + bindType: fix, + + handle: function( event ) { + var ret, + target = this, + related = event.relatedTarget, + handleObj = event.handleObj; + + // For mouseenter/leave call the handler if related is outside the target. + // NB: No relatedTarget if the mouse left/entered the browser window + if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) { + event.type = handleObj.origType; + ret = handleObj.handler.apply( this, arguments ); + event.type = fix; + } + return ret; + } + }; +} ); + +jQuery.fn.extend( { + + on: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn ); + }, + one: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn, 1 ); + }, + off: function( types, selector, fn ) { + var handleObj, type; + if ( types && types.preventDefault && types.handleObj ) { + + // ( event ) dispatched jQuery.Event + handleObj = types.handleObj; + jQuery( types.delegateTarget ).off( + handleObj.namespace ? + handleObj.origType + "." + handleObj.namespace : + handleObj.origType, + handleObj.selector, + handleObj.handler + ); + return this; + } + if ( typeof types === "object" ) { + + // ( types-object [, selector] ) + for ( type in types ) { + this.off( type, selector, types[ type ] ); + } + return this; + } + if ( selector === false || typeof selector === "function" ) { + + // ( types [, fn] ) + fn = selector; + selector = undefined; + } + if ( fn === false ) { + fn = returnFalse; + } + return this.each( function() { + jQuery.event.remove( this, types, fn, selector ); + } ); + } +} ); + + +var + + // Support: IE <=10 - 11, Edge 12 - 13 only + // In IE/Edge using regex groups here causes severe slowdowns. + // See https://connect.microsoft.com/IE/feedback/details/1736512/ + rnoInnerhtml = /\s*$/g; + +// Prefer a tbody over its parent table for containing new rows +function manipulationTarget( elem, content ) { + if ( nodeName( elem, "table" ) && + nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) { + + return jQuery( elem ).children( "tbody" )[ 0 ] || elem; + } + + return elem; +} + +// Replace/restore the type attribute of script elements for safe DOM manipulation +function disableScript( elem ) { + elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type; + return elem; +} +function restoreScript( elem ) { + if ( ( elem.type || "" ).slice( 0, 5 ) === "true/" ) { + elem.type = elem.type.slice( 5 ); + } else { + elem.removeAttribute( "type" ); + } + + return elem; +} + +function cloneCopyEvent( src, dest ) { + var i, l, type, pdataOld, udataOld, udataCur, events; + + if ( dest.nodeType !== 1 ) { + return; + } + + // 1. Copy private data: events, handlers, etc. + if ( dataPriv.hasData( src ) ) { + pdataOld = dataPriv.get( src ); + events = pdataOld.events; + + if ( events ) { + dataPriv.remove( dest, "handle events" ); + + for ( type in events ) { + for ( i = 0, l = events[ type ].length; i < l; i++ ) { + jQuery.event.add( dest, type, events[ type ][ i ] ); + } + } + } + } + + // 2. Copy user data + if ( dataUser.hasData( src ) ) { + udataOld = dataUser.access( src ); + udataCur = jQuery.extend( {}, udataOld ); + + dataUser.set( dest, udataCur ); + } +} + +// Fix IE bugs, see support tests +function fixInput( src, dest ) { + var nodeName = dest.nodeName.toLowerCase(); + + // Fails to persist the checked state of a cloned checkbox or radio button. + if ( nodeName === "input" && rcheckableType.test( src.type ) ) { + dest.checked = src.checked; + + // Fails to return the selected option to the default selected state when cloning options + } else if ( nodeName === "input" || nodeName === "textarea" ) { + dest.defaultValue = src.defaultValue; + } +} + +function domManip( collection, args, callback, ignored ) { + + // Flatten any nested arrays + args = flat( args ); + + var fragment, first, scripts, hasScripts, node, doc, + i = 0, + l = collection.length, + iNoClone = l - 1, + value = args[ 0 ], + valueIsFunction = isFunction( value ); + + // We can't cloneNode fragments that contain checked, in WebKit + if ( valueIsFunction || + ( l > 1 && typeof value === "string" && + !support.checkClone && rchecked.test( value ) ) ) { + return collection.each( function( index ) { + var self = collection.eq( index ); + if ( valueIsFunction ) { + args[ 0 ] = value.call( this, index, self.html() ); + } + domManip( self, args, callback, ignored ); + } ); + } + + if ( l ) { + fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored ); + first = fragment.firstChild; + + if ( fragment.childNodes.length === 1 ) { + fragment = first; + } + + // Require either new content or an interest in ignored elements to invoke the callback + if ( first || ignored ) { + scripts = jQuery.map( getAll( fragment, "script" ), disableScript ); + hasScripts = scripts.length; + + // Use the original fragment for the last item + // instead of the first because it can end up + // being emptied incorrectly in certain situations (#8070). + for ( ; i < l; i++ ) { + node = fragment; + + if ( i !== iNoClone ) { + node = jQuery.clone( node, true, true ); + + // Keep references to cloned scripts for later restoration + if ( hasScripts ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( scripts, getAll( node, "script" ) ); + } + } + + callback.call( collection[ i ], node, i ); + } + + if ( hasScripts ) { + doc = scripts[ scripts.length - 1 ].ownerDocument; + + // Reenable scripts + jQuery.map( scripts, restoreScript ); + + // Evaluate executable scripts on first document insertion + for ( i = 0; i < hasScripts; i++ ) { + node = scripts[ i ]; + if ( rscriptType.test( node.type || "" ) && + !dataPriv.access( node, "globalEval" ) && + jQuery.contains( doc, node ) ) { + + if ( node.src && ( node.type || "" ).toLowerCase() !== "module" ) { + + // Optional AJAX dependency, but won't run scripts if not present + if ( jQuery._evalUrl && !node.noModule ) { + jQuery._evalUrl( node.src, { + nonce: node.nonce || node.getAttribute( "nonce" ) + }, doc ); + } + } else { + DOMEval( node.textContent.replace( rcleanScript, "" ), node, doc ); + } + } + } + } + } + } + + return collection; +} + +function remove( elem, selector, keepData ) { + var node, + nodes = selector ? jQuery.filter( selector, elem ) : elem, + i = 0; + + for ( ; ( node = nodes[ i ] ) != null; i++ ) { + if ( !keepData && node.nodeType === 1 ) { + jQuery.cleanData( getAll( node ) ); + } + + if ( node.parentNode ) { + if ( keepData && isAttached( node ) ) { + setGlobalEval( getAll( node, "script" ) ); + } + node.parentNode.removeChild( node ); + } + } + + return elem; +} + +jQuery.extend( { + htmlPrefilter: function( html ) { + return html; + }, + + clone: function( elem, dataAndEvents, deepDataAndEvents ) { + var i, l, srcElements, destElements, + clone = elem.cloneNode( true ), + inPage = isAttached( elem ); + + // Fix IE cloning issues + if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) && + !jQuery.isXMLDoc( elem ) ) { + + // We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2 + destElements = getAll( clone ); + srcElements = getAll( elem ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + fixInput( srcElements[ i ], destElements[ i ] ); + } + } + + // Copy the events from the original to the clone + if ( dataAndEvents ) { + if ( deepDataAndEvents ) { + srcElements = srcElements || getAll( elem ); + destElements = destElements || getAll( clone ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + cloneCopyEvent( srcElements[ i ], destElements[ i ] ); + } + } else { + cloneCopyEvent( elem, clone ); + } + } + + // Preserve script evaluation history + destElements = getAll( clone, "script" ); + if ( destElements.length > 0 ) { + setGlobalEval( destElements, !inPage && getAll( elem, "script" ) ); + } + + // Return the cloned set + return clone; + }, + + cleanData: function( elems ) { + var data, elem, type, + special = jQuery.event.special, + i = 0; + + for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) { + if ( acceptData( elem ) ) { + if ( ( data = elem[ dataPriv.expando ] ) ) { + if ( data.events ) { + for ( type in data.events ) { + if ( special[ type ] ) { + jQuery.event.remove( elem, type ); + + // This is a shortcut to avoid jQuery.event.remove's overhead + } else { + jQuery.removeEvent( elem, type, data.handle ); + } + } + } + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataPriv.expando ] = undefined; + } + if ( elem[ dataUser.expando ] ) { + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataUser.expando ] = undefined; + } + } + } + } +} ); + +jQuery.fn.extend( { + detach: function( selector ) { + return remove( this, selector, true ); + }, + + remove: function( selector ) { + return remove( this, selector ); + }, + + text: function( value ) { + return access( this, function( value ) { + return value === undefined ? + jQuery.text( this ) : + this.empty().each( function() { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + this.textContent = value; + } + } ); + }, null, value, arguments.length ); + }, + + append: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.appendChild( elem ); + } + } ); + }, + + prepend: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.insertBefore( elem, target.firstChild ); + } + } ); + }, + + before: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this ); + } + } ); + }, + + after: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this.nextSibling ); + } + } ); + }, + + empty: function() { + var elem, + i = 0; + + for ( ; ( elem = this[ i ] ) != null; i++ ) { + if ( elem.nodeType === 1 ) { + + // Prevent memory leaks + jQuery.cleanData( getAll( elem, false ) ); + + // Remove any remaining nodes + elem.textContent = ""; + } + } + + return this; + }, + + clone: function( dataAndEvents, deepDataAndEvents ) { + dataAndEvents = dataAndEvents == null ? false : dataAndEvents; + deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents; + + return this.map( function() { + return jQuery.clone( this, dataAndEvents, deepDataAndEvents ); + } ); + }, + + html: function( value ) { + return access( this, function( value ) { + var elem = this[ 0 ] || {}, + i = 0, + l = this.length; + + if ( value === undefined && elem.nodeType === 1 ) { + return elem.innerHTML; + } + + // See if we can take a shortcut and just use innerHTML + if ( typeof value === "string" && !rnoInnerhtml.test( value ) && + !wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) { + + value = jQuery.htmlPrefilter( value ); + + try { + for ( ; i < l; i++ ) { + elem = this[ i ] || {}; + + // Remove element nodes and prevent memory leaks + if ( elem.nodeType === 1 ) { + jQuery.cleanData( getAll( elem, false ) ); + elem.innerHTML = value; + } + } + + elem = 0; + + // If using innerHTML throws an exception, use the fallback method + } catch ( e ) {} + } + + if ( elem ) { + this.empty().append( value ); + } + }, null, value, arguments.length ); + }, + + replaceWith: function() { + var ignored = []; + + // Make the changes, replacing each non-ignored context element with the new content + return domManip( this, arguments, function( elem ) { + var parent = this.parentNode; + + if ( jQuery.inArray( this, ignored ) < 0 ) { + jQuery.cleanData( getAll( this ) ); + if ( parent ) { + parent.replaceChild( elem, this ); + } + } + + // Force callback invocation + }, ignored ); + } +} ); + +jQuery.each( { + appendTo: "append", + prependTo: "prepend", + insertBefore: "before", + insertAfter: "after", + replaceAll: "replaceWith" +}, function( name, original ) { + jQuery.fn[ name ] = function( selector ) { + var elems, + ret = [], + insert = jQuery( selector ), + last = insert.length - 1, + i = 0; + + for ( ; i <= last; i++ ) { + elems = i === last ? this : this.clone( true ); + jQuery( insert[ i ] )[ original ]( elems ); + + // Support: Android <=4.0 only, PhantomJS 1 only + // .get() because push.apply(_, arraylike) throws on ancient WebKit + push.apply( ret, elems.get() ); + } + + return this.pushStack( ret ); + }; +} ); +var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" ); + +var getStyles = function( elem ) { + + // Support: IE <=11 only, Firefox <=30 (#15098, #14150) + // IE throws on elements created in popups + // FF meanwhile throws on frame elements through "defaultView.getComputedStyle" + var view = elem.ownerDocument.defaultView; + + if ( !view || !view.opener ) { + view = window; + } + + return view.getComputedStyle( elem ); + }; + +var swap = function( elem, options, callback ) { + var ret, name, + old = {}; + + // Remember the old values, and insert the new ones + for ( name in options ) { + old[ name ] = elem.style[ name ]; + elem.style[ name ] = options[ name ]; + } + + ret = callback.call( elem ); + + // Revert the old values + for ( name in options ) { + elem.style[ name ] = old[ name ]; + } + + return ret; +}; + + +var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" ); + + + +( function() { + + // Executing both pixelPosition & boxSizingReliable tests require only one layout + // so they're executed at the same time to save the second computation. + function computeStyleTests() { + + // This is a singleton, we need to execute it only once + if ( !div ) { + return; + } + + container.style.cssText = "position:absolute;left:-11111px;width:60px;" + + "margin-top:1px;padding:0;border:0"; + div.style.cssText = + "position:relative;display:block;box-sizing:border-box;overflow:scroll;" + + "margin:auto;border:1px;padding:1px;" + + "width:60%;top:1%"; + documentElement.appendChild( container ).appendChild( div ); + + var divStyle = window.getComputedStyle( div ); + pixelPositionVal = divStyle.top !== "1%"; + + // Support: Android 4.0 - 4.3 only, Firefox <=3 - 44 + reliableMarginLeftVal = roundPixelMeasures( divStyle.marginLeft ) === 12; + + // Support: Android 4.0 - 4.3 only, Safari <=9.1 - 10.1, iOS <=7.0 - 9.3 + // Some styles come back with percentage values, even though they shouldn't + div.style.right = "60%"; + pixelBoxStylesVal = roundPixelMeasures( divStyle.right ) === 36; + + // Support: IE 9 - 11 only + // Detect misreporting of content dimensions for box-sizing:border-box elements + boxSizingReliableVal = roundPixelMeasures( divStyle.width ) === 36; + + // Support: IE 9 only + // Detect overflow:scroll screwiness (gh-3699) + // Support: Chrome <=64 + // Don't get tricked when zoom affects offsetWidth (gh-4029) + div.style.position = "absolute"; + scrollboxSizeVal = roundPixelMeasures( div.offsetWidth / 3 ) === 12; + + documentElement.removeChild( container ); + + // Nullify the div so it wouldn't be stored in the memory and + // it will also be a sign that checks already performed + div = null; + } + + function roundPixelMeasures( measure ) { + return Math.round( parseFloat( measure ) ); + } + + var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal, + reliableTrDimensionsVal, reliableMarginLeftVal, + container = document.createElement( "div" ), + div = document.createElement( "div" ); + + // Finish early in limited (non-browser) environments + if ( !div.style ) { + return; + } + + // Support: IE <=9 - 11 only + // Style of cloned element affects source element cloned (#8908) + div.style.backgroundClip = "content-box"; + div.cloneNode( true ).style.backgroundClip = ""; + support.clearCloneStyle = div.style.backgroundClip === "content-box"; + + jQuery.extend( support, { + boxSizingReliable: function() { + computeStyleTests(); + return boxSizingReliableVal; + }, + pixelBoxStyles: function() { + computeStyleTests(); + return pixelBoxStylesVal; + }, + pixelPosition: function() { + computeStyleTests(); + return pixelPositionVal; + }, + reliableMarginLeft: function() { + computeStyleTests(); + return reliableMarginLeftVal; + }, + scrollboxSize: function() { + computeStyleTests(); + return scrollboxSizeVal; + }, + + // Support: IE 9 - 11+, Edge 15 - 18+ + // IE/Edge misreport `getComputedStyle` of table rows with width/height + // set in CSS while `offset*` properties report correct values. + // Behavior in IE 9 is more subtle than in newer versions & it passes + // some versions of this test; make sure not to make it pass there! + reliableTrDimensions: function() { + var table, tr, trChild, trStyle; + if ( reliableTrDimensionsVal == null ) { + table = document.createElement( "table" ); + tr = document.createElement( "tr" ); + trChild = document.createElement( "div" ); + + table.style.cssText = "position:absolute;left:-11111px"; + tr.style.height = "1px"; + trChild.style.height = "9px"; + + documentElement + .appendChild( table ) + .appendChild( tr ) + .appendChild( trChild ); + + trStyle = window.getComputedStyle( tr ); + reliableTrDimensionsVal = parseInt( trStyle.height ) > 3; + + documentElement.removeChild( table ); + } + return reliableTrDimensionsVal; + } + } ); +} )(); + + +function curCSS( elem, name, computed ) { + var width, minWidth, maxWidth, ret, + + // Support: Firefox 51+ + // Retrieving style before computed somehow + // fixes an issue with getting wrong values + // on detached elements + style = elem.style; + + computed = computed || getStyles( elem ); + + // getPropertyValue is needed for: + // .css('filter') (IE 9 only, #12537) + // .css('--customProperty) (#3144) + if ( computed ) { + ret = computed.getPropertyValue( name ) || computed[ name ]; + + if ( ret === "" && !isAttached( elem ) ) { + ret = jQuery.style( elem, name ); + } + + // A tribute to the "awesome hack by Dean Edwards" + // Android Browser returns percentage for some values, + // but width seems to be reliably pixels. + // This is against the CSSOM draft spec: + // https://drafts.csswg.org/cssom/#resolved-values + if ( !support.pixelBoxStyles() && rnumnonpx.test( ret ) && rboxStyle.test( name ) ) { + + // Remember the original values + width = style.width; + minWidth = style.minWidth; + maxWidth = style.maxWidth; + + // Put in the new values to get a computed value out + style.minWidth = style.maxWidth = style.width = ret; + ret = computed.width; + + // Revert the changed values + style.width = width; + style.minWidth = minWidth; + style.maxWidth = maxWidth; + } + } + + return ret !== undefined ? + + // Support: IE <=9 - 11 only + // IE returns zIndex value as an integer. + ret + "" : + ret; +} + + +function addGetHookIf( conditionFn, hookFn ) { + + // Define the hook, we'll check on the first run if it's really needed. + return { + get: function() { + if ( conditionFn() ) { + + // Hook not needed (or it's not possible to use it due + // to missing dependency), remove it. + delete this.get; + return; + } + + // Hook needed; redefine it so that the support test is not executed again. + return ( this.get = hookFn ).apply( this, arguments ); + } + }; +} + + +var cssPrefixes = [ "Webkit", "Moz", "ms" ], + emptyStyle = document.createElement( "div" ).style, + vendorProps = {}; + +// Return a vendor-prefixed property or undefined +function vendorPropName( name ) { + + // Check for vendor prefixed names + var capName = name[ 0 ].toUpperCase() + name.slice( 1 ), + i = cssPrefixes.length; + + while ( i-- ) { + name = cssPrefixes[ i ] + capName; + if ( name in emptyStyle ) { + return name; + } + } +} + +// Return a potentially-mapped jQuery.cssProps or vendor prefixed property +function finalPropName( name ) { + var final = jQuery.cssProps[ name ] || vendorProps[ name ]; + + if ( final ) { + return final; + } + if ( name in emptyStyle ) { + return name; + } + return vendorProps[ name ] = vendorPropName( name ) || name; +} + + +var + + // Swappable if display is none or starts with table + // except "table", "table-cell", or "table-caption" + // See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display + rdisplayswap = /^(none|table(?!-c[ea]).+)/, + rcustomProp = /^--/, + cssShow = { position: "absolute", visibility: "hidden", display: "block" }, + cssNormalTransform = { + letterSpacing: "0", + fontWeight: "400" + }; + +function setPositiveNumber( _elem, value, subtract ) { + + // Any relative (+/-) values have already been + // normalized at this point + var matches = rcssNum.exec( value ); + return matches ? + + // Guard against undefined "subtract", e.g., when used as in cssHooks + Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) : + value; +} + +function boxModelAdjustment( elem, dimension, box, isBorderBox, styles, computedVal ) { + var i = dimension === "width" ? 1 : 0, + extra = 0, + delta = 0; + + // Adjustment may not be necessary + if ( box === ( isBorderBox ? "border" : "content" ) ) { + return 0; + } + + for ( ; i < 4; i += 2 ) { + + // Both box models exclude margin + if ( box === "margin" ) { + delta += jQuery.css( elem, box + cssExpand[ i ], true, styles ); + } + + // If we get here with a content-box, we're seeking "padding" or "border" or "margin" + if ( !isBorderBox ) { + + // Add padding + delta += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + + // For "border" or "margin", add border + if ( box !== "padding" ) { + delta += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + + // But still keep track of it otherwise + } else { + extra += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + + // If we get here with a border-box (content + padding + border), we're seeking "content" or + // "padding" or "margin" + } else { + + // For "content", subtract padding + if ( box === "content" ) { + delta -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + } + + // For "content" or "padding", subtract border + if ( box !== "margin" ) { + delta -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + } + } + + // Account for positive content-box scroll gutter when requested by providing computedVal + if ( !isBorderBox && computedVal >= 0 ) { + + // offsetWidth/offsetHeight is a rounded sum of content, padding, scroll gutter, and border + // Assuming integer scroll gutter, subtract the rest and round down + delta += Math.max( 0, Math.ceil( + elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - + computedVal - + delta - + extra - + 0.5 + + // If offsetWidth/offsetHeight is unknown, then we can't determine content-box scroll gutter + // Use an explicit zero to avoid NaN (gh-3964) + ) ) || 0; + } + + return delta; +} + +function getWidthOrHeight( elem, dimension, extra ) { + + // Start with computed style + var styles = getStyles( elem ), + + // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-4322). + // Fake content-box until we know it's needed to know the true value. + boxSizingNeeded = !support.boxSizingReliable() || extra, + isBorderBox = boxSizingNeeded && + jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + valueIsBorderBox = isBorderBox, + + val = curCSS( elem, dimension, styles ), + offsetProp = "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ); + + // Support: Firefox <=54 + // Return a confounding non-pixel value or feign ignorance, as appropriate. + if ( rnumnonpx.test( val ) ) { + if ( !extra ) { + return val; + } + val = "auto"; + } + + + // Support: IE 9 - 11 only + // Use offsetWidth/offsetHeight for when box sizing is unreliable. + // In those cases, the computed value can be trusted to be border-box. + if ( ( !support.boxSizingReliable() && isBorderBox || + + // Support: IE 10 - 11+, Edge 15 - 18+ + // IE/Edge misreport `getComputedStyle` of table rows with width/height + // set in CSS while `offset*` properties report correct values. + // Interestingly, in some cases IE 9 doesn't suffer from this issue. + !support.reliableTrDimensions() && nodeName( elem, "tr" ) || + + // Fall back to offsetWidth/offsetHeight when value is "auto" + // This happens for inline elements with no explicit setting (gh-3571) + val === "auto" || + + // Support: Android <=4.1 - 4.3 only + // Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602) + !parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) && + + // Make sure the element is visible & connected + elem.getClientRects().length ) { + + isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box"; + + // Where available, offsetWidth/offsetHeight approximate border box dimensions. + // Where not available (e.g., SVG), assume unreliable box-sizing and interpret the + // retrieved value as a content box dimension. + valueIsBorderBox = offsetProp in elem; + if ( valueIsBorderBox ) { + val = elem[ offsetProp ]; + } + } + + // Normalize "" and auto + val = parseFloat( val ) || 0; + + // Adjust for the element's box model + return ( val + + boxModelAdjustment( + elem, + dimension, + extra || ( isBorderBox ? "border" : "content" ), + valueIsBorderBox, + styles, + + // Provide the current computed size to request scroll gutter calculation (gh-3589) + val + ) + ) + "px"; +} + +jQuery.extend( { + + // Add in style property hooks for overriding the default + // behavior of getting and setting a style property + cssHooks: { + opacity: { + get: function( elem, computed ) { + if ( computed ) { + + // We should always get a number back from opacity + var ret = curCSS( elem, "opacity" ); + return ret === "" ? "1" : ret; + } + } + } + }, + + // Don't automatically add "px" to these possibly-unitless properties + cssNumber: { + "animationIterationCount": true, + "columnCount": true, + "fillOpacity": true, + "flexGrow": true, + "flexShrink": true, + "fontWeight": true, + "gridArea": true, + "gridColumn": true, + "gridColumnEnd": true, + "gridColumnStart": true, + "gridRow": true, + "gridRowEnd": true, + "gridRowStart": true, + "lineHeight": true, + "opacity": true, + "order": true, + "orphans": true, + "widows": true, + "zIndex": true, + "zoom": true + }, + + // Add in properties whose names you wish to fix before + // setting or getting the value + cssProps: {}, + + // Get and set the style property on a DOM Node + style: function( elem, name, value, extra ) { + + // Don't set styles on text and comment nodes + if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) { + return; + } + + // Make sure that we're working with the right name + var ret, type, hooks, + origName = camelCase( name ), + isCustomProp = rcustomProp.test( name ), + style = elem.style; + + // Make sure that we're working with the right name. We don't + // want to query the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Gets hook for the prefixed version, then unprefixed version + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // Check if we're setting a value + if ( value !== undefined ) { + type = typeof value; + + // Convert "+=" or "-=" to relative numbers (#7345) + if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) { + value = adjustCSS( elem, name, ret ); + + // Fixes bug #9237 + type = "number"; + } + + // Make sure that null and NaN values aren't set (#7116) + if ( value == null || value !== value ) { + return; + } + + // If a number was passed in, add the unit (except for certain CSS properties) + // The isCustomProp check can be removed in jQuery 4.0 when we only auto-append + // "px" to a few hardcoded values. + if ( type === "number" && !isCustomProp ) { + value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" ); + } + + // background-* props affect original clone's values + if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) { + style[ name ] = "inherit"; + } + + // If a hook was provided, use that value, otherwise just set the specified value + if ( !hooks || !( "set" in hooks ) || + ( value = hooks.set( elem, value, extra ) ) !== undefined ) { + + if ( isCustomProp ) { + style.setProperty( name, value ); + } else { + style[ name ] = value; + } + } + + } else { + + // If a hook was provided get the non-computed value from there + if ( hooks && "get" in hooks && + ( ret = hooks.get( elem, false, extra ) ) !== undefined ) { + + return ret; + } + + // Otherwise just get the value from the style object + return style[ name ]; + } + }, + + css: function( elem, name, extra, styles ) { + var val, num, hooks, + origName = camelCase( name ), + isCustomProp = rcustomProp.test( name ); + + // Make sure that we're working with the right name. We don't + // want to modify the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Try prefixed name followed by the unprefixed name + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // If a hook was provided get the computed value from there + if ( hooks && "get" in hooks ) { + val = hooks.get( elem, true, extra ); + } + + // Otherwise, if a way to get the computed value exists, use that + if ( val === undefined ) { + val = curCSS( elem, name, styles ); + } + + // Convert "normal" to computed value + if ( val === "normal" && name in cssNormalTransform ) { + val = cssNormalTransform[ name ]; + } + + // Make numeric if forced or a qualifier was provided and val looks numeric + if ( extra === "" || extra ) { + num = parseFloat( val ); + return extra === true || isFinite( num ) ? num || 0 : val; + } + + return val; + } +} ); + +jQuery.each( [ "height", "width" ], function( _i, dimension ) { + jQuery.cssHooks[ dimension ] = { + get: function( elem, computed, extra ) { + if ( computed ) { + + // Certain elements can have dimension info if we invisibly show them + // but it must have a current display style that would benefit + return rdisplayswap.test( jQuery.css( elem, "display" ) ) && + + // Support: Safari 8+ + // Table columns in Safari have non-zero offsetWidth & zero + // getBoundingClientRect().width unless display is changed. + // Support: IE <=11 only + // Running getBoundingClientRect on a disconnected node + // in IE throws an error. + ( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ? + swap( elem, cssShow, function() { + return getWidthOrHeight( elem, dimension, extra ); + } ) : + getWidthOrHeight( elem, dimension, extra ); + } + }, + + set: function( elem, value, extra ) { + var matches, + styles = getStyles( elem ), + + // Only read styles.position if the test has a chance to fail + // to avoid forcing a reflow. + scrollboxSizeBuggy = !support.scrollboxSize() && + styles.position === "absolute", + + // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-3991) + boxSizingNeeded = scrollboxSizeBuggy || extra, + isBorderBox = boxSizingNeeded && + jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + subtract = extra ? + boxModelAdjustment( + elem, + dimension, + extra, + isBorderBox, + styles + ) : + 0; + + // Account for unreliable border-box dimensions by comparing offset* to computed and + // faking a content-box to get border and padding (gh-3699) + if ( isBorderBox && scrollboxSizeBuggy ) { + subtract -= Math.ceil( + elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - + parseFloat( styles[ dimension ] ) - + boxModelAdjustment( elem, dimension, "border", false, styles ) - + 0.5 + ); + } + + // Convert to pixels if value adjustment is needed + if ( subtract && ( matches = rcssNum.exec( value ) ) && + ( matches[ 3 ] || "px" ) !== "px" ) { + + elem.style[ dimension ] = value; + value = jQuery.css( elem, dimension ); + } + + return setPositiveNumber( elem, value, subtract ); + } + }; +} ); + +jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft, + function( elem, computed ) { + if ( computed ) { + return ( parseFloat( curCSS( elem, "marginLeft" ) ) || + elem.getBoundingClientRect().left - + swap( elem, { marginLeft: 0 }, function() { + return elem.getBoundingClientRect().left; + } ) + ) + "px"; + } + } +); + +// These hooks are used by animate to expand properties +jQuery.each( { + margin: "", + padding: "", + border: "Width" +}, function( prefix, suffix ) { + jQuery.cssHooks[ prefix + suffix ] = { + expand: function( value ) { + var i = 0, + expanded = {}, + + // Assumes a single number if not a string + parts = typeof value === "string" ? value.split( " " ) : [ value ]; + + for ( ; i < 4; i++ ) { + expanded[ prefix + cssExpand[ i ] + suffix ] = + parts[ i ] || parts[ i - 2 ] || parts[ 0 ]; + } + + return expanded; + } + }; + + if ( prefix !== "margin" ) { + jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber; + } +} ); + +jQuery.fn.extend( { + css: function( name, value ) { + return access( this, function( elem, name, value ) { + var styles, len, + map = {}, + i = 0; + + if ( Array.isArray( name ) ) { + styles = getStyles( elem ); + len = name.length; + + for ( ; i < len; i++ ) { + map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles ); + } + + return map; + } + + return value !== undefined ? + jQuery.style( elem, name, value ) : + jQuery.css( elem, name ); + }, name, value, arguments.length > 1 ); + } +} ); + + +function Tween( elem, options, prop, end, easing ) { + return new Tween.prototype.init( elem, options, prop, end, easing ); +} +jQuery.Tween = Tween; + +Tween.prototype = { + constructor: Tween, + init: function( elem, options, prop, end, easing, unit ) { + this.elem = elem; + this.prop = prop; + this.easing = easing || jQuery.easing._default; + this.options = options; + this.start = this.now = this.cur(); + this.end = end; + this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" ); + }, + cur: function() { + var hooks = Tween.propHooks[ this.prop ]; + + return hooks && hooks.get ? + hooks.get( this ) : + Tween.propHooks._default.get( this ); + }, + run: function( percent ) { + var eased, + hooks = Tween.propHooks[ this.prop ]; + + if ( this.options.duration ) { + this.pos = eased = jQuery.easing[ this.easing ]( + percent, this.options.duration * percent, 0, 1, this.options.duration + ); + } else { + this.pos = eased = percent; + } + this.now = ( this.end - this.start ) * eased + this.start; + + if ( this.options.step ) { + this.options.step.call( this.elem, this.now, this ); + } + + if ( hooks && hooks.set ) { + hooks.set( this ); + } else { + Tween.propHooks._default.set( this ); + } + return this; + } +}; + +Tween.prototype.init.prototype = Tween.prototype; + +Tween.propHooks = { + _default: { + get: function( tween ) { + var result; + + // Use a property on the element directly when it is not a DOM element, + // or when there is no matching style property that exists. + if ( tween.elem.nodeType !== 1 || + tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) { + return tween.elem[ tween.prop ]; + } + + // Passing an empty string as a 3rd parameter to .css will automatically + // attempt a parseFloat and fallback to a string if the parse fails. + // Simple values such as "10px" are parsed to Float; + // complex values such as "rotate(1rad)" are returned as-is. + result = jQuery.css( tween.elem, tween.prop, "" ); + + // Empty strings, null, undefined and "auto" are converted to 0. + return !result || result === "auto" ? 0 : result; + }, + set: function( tween ) { + + // Use step hook for back compat. + // Use cssHook if its there. + // Use .style if available and use plain properties where available. + if ( jQuery.fx.step[ tween.prop ] ) { + jQuery.fx.step[ tween.prop ]( tween ); + } else if ( tween.elem.nodeType === 1 && ( + jQuery.cssHooks[ tween.prop ] || + tween.elem.style[ finalPropName( tween.prop ) ] != null ) ) { + jQuery.style( tween.elem, tween.prop, tween.now + tween.unit ); + } else { + tween.elem[ tween.prop ] = tween.now; + } + } + } +}; + +// Support: IE <=9 only +// Panic based approach to setting things on disconnected nodes +Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = { + set: function( tween ) { + if ( tween.elem.nodeType && tween.elem.parentNode ) { + tween.elem[ tween.prop ] = tween.now; + } + } +}; + +jQuery.easing = { + linear: function( p ) { + return p; + }, + swing: function( p ) { + return 0.5 - Math.cos( p * Math.PI ) / 2; + }, + _default: "swing" +}; + +jQuery.fx = Tween.prototype.init; + +// Back compat <1.8 extension point +jQuery.fx.step = {}; + + + + +var + fxNow, inProgress, + rfxtypes = /^(?:toggle|show|hide)$/, + rrun = /queueHooks$/; + +function schedule() { + if ( inProgress ) { + if ( document.hidden === false && window.requestAnimationFrame ) { + window.requestAnimationFrame( schedule ); + } else { + window.setTimeout( schedule, jQuery.fx.interval ); + } + + jQuery.fx.tick(); + } +} + +// Animations created synchronously will run synchronously +function createFxNow() { + window.setTimeout( function() { + fxNow = undefined; + } ); + return ( fxNow = Date.now() ); +} + +// Generate parameters to create a standard animation +function genFx( type, includeWidth ) { + var which, + i = 0, + attrs = { height: type }; + + // If we include width, step value is 1 to do all cssExpand values, + // otherwise step value is 2 to skip over Left and Right + includeWidth = includeWidth ? 1 : 0; + for ( ; i < 4; i += 2 - includeWidth ) { + which = cssExpand[ i ]; + attrs[ "margin" + which ] = attrs[ "padding" + which ] = type; + } + + if ( includeWidth ) { + attrs.opacity = attrs.width = type; + } + + return attrs; +} + +function createTween( value, prop, animation ) { + var tween, + collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ), + index = 0, + length = collection.length; + for ( ; index < length; index++ ) { + if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) { + + // We're done with this property + return tween; + } + } +} + +function defaultPrefilter( elem, props, opts ) { + var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display, + isBox = "width" in props || "height" in props, + anim = this, + orig = {}, + style = elem.style, + hidden = elem.nodeType && isHiddenWithinTree( elem ), + dataShow = dataPriv.get( elem, "fxshow" ); + + // Queue-skipping animations hijack the fx hooks + if ( !opts.queue ) { + hooks = jQuery._queueHooks( elem, "fx" ); + if ( hooks.unqueued == null ) { + hooks.unqueued = 0; + oldfire = hooks.empty.fire; + hooks.empty.fire = function() { + if ( !hooks.unqueued ) { + oldfire(); + } + }; + } + hooks.unqueued++; + + anim.always( function() { + + // Ensure the complete handler is called before this completes + anim.always( function() { + hooks.unqueued--; + if ( !jQuery.queue( elem, "fx" ).length ) { + hooks.empty.fire(); + } + } ); + } ); + } + + // Detect show/hide animations + for ( prop in props ) { + value = props[ prop ]; + if ( rfxtypes.test( value ) ) { + delete props[ prop ]; + toggle = toggle || value === "toggle"; + if ( value === ( hidden ? "hide" : "show" ) ) { + + // Pretend to be hidden if this is a "show" and + // there is still data from a stopped show/hide + if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) { + hidden = true; + + // Ignore all other no-op show/hide data + } else { + continue; + } + } + orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop ); + } + } + + // Bail out if this is a no-op like .hide().hide() + propTween = !jQuery.isEmptyObject( props ); + if ( !propTween && jQuery.isEmptyObject( orig ) ) { + return; + } + + // Restrict "overflow" and "display" styles during box animations + if ( isBox && elem.nodeType === 1 ) { + + // Support: IE <=9 - 11, Edge 12 - 15 + // Record all 3 overflow attributes because IE does not infer the shorthand + // from identically-valued overflowX and overflowY and Edge just mirrors + // the overflowX value there. + opts.overflow = [ style.overflow, style.overflowX, style.overflowY ]; + + // Identify a display type, preferring old show/hide data over the CSS cascade + restoreDisplay = dataShow && dataShow.display; + if ( restoreDisplay == null ) { + restoreDisplay = dataPriv.get( elem, "display" ); + } + display = jQuery.css( elem, "display" ); + if ( display === "none" ) { + if ( restoreDisplay ) { + display = restoreDisplay; + } else { + + // Get nonempty value(s) by temporarily forcing visibility + showHide( [ elem ], true ); + restoreDisplay = elem.style.display || restoreDisplay; + display = jQuery.css( elem, "display" ); + showHide( [ elem ] ); + } + } + + // Animate inline elements as inline-block + if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) { + if ( jQuery.css( elem, "float" ) === "none" ) { + + // Restore the original display value at the end of pure show/hide animations + if ( !propTween ) { + anim.done( function() { + style.display = restoreDisplay; + } ); + if ( restoreDisplay == null ) { + display = style.display; + restoreDisplay = display === "none" ? "" : display; + } + } + style.display = "inline-block"; + } + } + } + + if ( opts.overflow ) { + style.overflow = "hidden"; + anim.always( function() { + style.overflow = opts.overflow[ 0 ]; + style.overflowX = opts.overflow[ 1 ]; + style.overflowY = opts.overflow[ 2 ]; + } ); + } + + // Implement show/hide animations + propTween = false; + for ( prop in orig ) { + + // General show/hide setup for this element animation + if ( !propTween ) { + if ( dataShow ) { + if ( "hidden" in dataShow ) { + hidden = dataShow.hidden; + } + } else { + dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } ); + } + + // Store hidden/visible for toggle so `.stop().toggle()` "reverses" + if ( toggle ) { + dataShow.hidden = !hidden; + } + + // Show elements before animating them + if ( hidden ) { + showHide( [ elem ], true ); + } + + /* eslint-disable no-loop-func */ + + anim.done( function() { + + /* eslint-enable no-loop-func */ + + // The final step of a "hide" animation is actually hiding the element + if ( !hidden ) { + showHide( [ elem ] ); + } + dataPriv.remove( elem, "fxshow" ); + for ( prop in orig ) { + jQuery.style( elem, prop, orig[ prop ] ); + } + } ); + } + + // Per-property setup + propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim ); + if ( !( prop in dataShow ) ) { + dataShow[ prop ] = propTween.start; + if ( hidden ) { + propTween.end = propTween.start; + propTween.start = 0; + } + } + } +} + +function propFilter( props, specialEasing ) { + var index, name, easing, value, hooks; + + // camelCase, specialEasing and expand cssHook pass + for ( index in props ) { + name = camelCase( index ); + easing = specialEasing[ name ]; + value = props[ index ]; + if ( Array.isArray( value ) ) { + easing = value[ 1 ]; + value = props[ index ] = value[ 0 ]; + } + + if ( index !== name ) { + props[ name ] = value; + delete props[ index ]; + } + + hooks = jQuery.cssHooks[ name ]; + if ( hooks && "expand" in hooks ) { + value = hooks.expand( value ); + delete props[ name ]; + + // Not quite $.extend, this won't overwrite existing keys. + // Reusing 'index' because we have the correct "name" + for ( index in value ) { + if ( !( index in props ) ) { + props[ index ] = value[ index ]; + specialEasing[ index ] = easing; + } + } + } else { + specialEasing[ name ] = easing; + } + } +} + +function Animation( elem, properties, options ) { + var result, + stopped, + index = 0, + length = Animation.prefilters.length, + deferred = jQuery.Deferred().always( function() { + + // Don't match elem in the :animated selector + delete tick.elem; + } ), + tick = function() { + if ( stopped ) { + return false; + } + var currentTime = fxNow || createFxNow(), + remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ), + + // Support: Android 2.3 only + // Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497) + temp = remaining / animation.duration || 0, + percent = 1 - temp, + index = 0, + length = animation.tweens.length; + + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( percent ); + } + + deferred.notifyWith( elem, [ animation, percent, remaining ] ); + + // If there's more to do, yield + if ( percent < 1 && length ) { + return remaining; + } + + // If this was an empty animation, synthesize a final progress notification + if ( !length ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + } + + // Resolve the animation and report its conclusion + deferred.resolveWith( elem, [ animation ] ); + return false; + }, + animation = deferred.promise( { + elem: elem, + props: jQuery.extend( {}, properties ), + opts: jQuery.extend( true, { + specialEasing: {}, + easing: jQuery.easing._default + }, options ), + originalProperties: properties, + originalOptions: options, + startTime: fxNow || createFxNow(), + duration: options.duration, + tweens: [], + createTween: function( prop, end ) { + var tween = jQuery.Tween( elem, animation.opts, prop, end, + animation.opts.specialEasing[ prop ] || animation.opts.easing ); + animation.tweens.push( tween ); + return tween; + }, + stop: function( gotoEnd ) { + var index = 0, + + // If we are going to the end, we want to run all the tweens + // otherwise we skip this part + length = gotoEnd ? animation.tweens.length : 0; + if ( stopped ) { + return this; + } + stopped = true; + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( 1 ); + } + + // Resolve when we played the last frame; otherwise, reject + if ( gotoEnd ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + deferred.resolveWith( elem, [ animation, gotoEnd ] ); + } else { + deferred.rejectWith( elem, [ animation, gotoEnd ] ); + } + return this; + } + } ), + props = animation.props; + + propFilter( props, animation.opts.specialEasing ); + + for ( ; index < length; index++ ) { + result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts ); + if ( result ) { + if ( isFunction( result.stop ) ) { + jQuery._queueHooks( animation.elem, animation.opts.queue ).stop = + result.stop.bind( result ); + } + return result; + } + } + + jQuery.map( props, createTween, animation ); + + if ( isFunction( animation.opts.start ) ) { + animation.opts.start.call( elem, animation ); + } + + // Attach callbacks from options + animation + .progress( animation.opts.progress ) + .done( animation.opts.done, animation.opts.complete ) + .fail( animation.opts.fail ) + .always( animation.opts.always ); + + jQuery.fx.timer( + jQuery.extend( tick, { + elem: elem, + anim: animation, + queue: animation.opts.queue + } ) + ); + + return animation; +} + +jQuery.Animation = jQuery.extend( Animation, { + + tweeners: { + "*": [ function( prop, value ) { + var tween = this.createTween( prop, value ); + adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween ); + return tween; + } ] + }, + + tweener: function( props, callback ) { + if ( isFunction( props ) ) { + callback = props; + props = [ "*" ]; + } else { + props = props.match( rnothtmlwhite ); + } + + var prop, + index = 0, + length = props.length; + + for ( ; index < length; index++ ) { + prop = props[ index ]; + Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || []; + Animation.tweeners[ prop ].unshift( callback ); + } + }, + + prefilters: [ defaultPrefilter ], + + prefilter: function( callback, prepend ) { + if ( prepend ) { + Animation.prefilters.unshift( callback ); + } else { + Animation.prefilters.push( callback ); + } + } +} ); + +jQuery.speed = function( speed, easing, fn ) { + var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : { + complete: fn || !fn && easing || + isFunction( speed ) && speed, + duration: speed, + easing: fn && easing || easing && !isFunction( easing ) && easing + }; + + // Go to the end state if fx are off + if ( jQuery.fx.off ) { + opt.duration = 0; + + } else { + if ( typeof opt.duration !== "number" ) { + if ( opt.duration in jQuery.fx.speeds ) { + opt.duration = jQuery.fx.speeds[ opt.duration ]; + + } else { + opt.duration = jQuery.fx.speeds._default; + } + } + } + + // Normalize opt.queue - true/undefined/null -> "fx" + if ( opt.queue == null || opt.queue === true ) { + opt.queue = "fx"; + } + + // Queueing + opt.old = opt.complete; + + opt.complete = function() { + if ( isFunction( opt.old ) ) { + opt.old.call( this ); + } + + if ( opt.queue ) { + jQuery.dequeue( this, opt.queue ); + } + }; + + return opt; +}; + +jQuery.fn.extend( { + fadeTo: function( speed, to, easing, callback ) { + + // Show any hidden elements after setting opacity to 0 + return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show() + + // Animate to the value specified + .end().animate( { opacity: to }, speed, easing, callback ); + }, + animate: function( prop, speed, easing, callback ) { + var empty = jQuery.isEmptyObject( prop ), + optall = jQuery.speed( speed, easing, callback ), + doAnimation = function() { + + // Operate on a copy of prop so per-property easing won't be lost + var anim = Animation( this, jQuery.extend( {}, prop ), optall ); + + // Empty animations, or finishing resolves immediately + if ( empty || dataPriv.get( this, "finish" ) ) { + anim.stop( true ); + } + }; + doAnimation.finish = doAnimation; + + return empty || optall.queue === false ? + this.each( doAnimation ) : + this.queue( optall.queue, doAnimation ); + }, + stop: function( type, clearQueue, gotoEnd ) { + var stopQueue = function( hooks ) { + var stop = hooks.stop; + delete hooks.stop; + stop( gotoEnd ); + }; + + if ( typeof type !== "string" ) { + gotoEnd = clearQueue; + clearQueue = type; + type = undefined; + } + if ( clearQueue ) { + this.queue( type || "fx", [] ); + } + + return this.each( function() { + var dequeue = true, + index = type != null && type + "queueHooks", + timers = jQuery.timers, + data = dataPriv.get( this ); + + if ( index ) { + if ( data[ index ] && data[ index ].stop ) { + stopQueue( data[ index ] ); + } + } else { + for ( index in data ) { + if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) { + stopQueue( data[ index ] ); + } + } + } + + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && + ( type == null || timers[ index ].queue === type ) ) { + + timers[ index ].anim.stop( gotoEnd ); + dequeue = false; + timers.splice( index, 1 ); + } + } + + // Start the next in the queue if the last step wasn't forced. + // Timers currently will call their complete callbacks, which + // will dequeue but only if they were gotoEnd. + if ( dequeue || !gotoEnd ) { + jQuery.dequeue( this, type ); + } + } ); + }, + finish: function( type ) { + if ( type !== false ) { + type = type || "fx"; + } + return this.each( function() { + var index, + data = dataPriv.get( this ), + queue = data[ type + "queue" ], + hooks = data[ type + "queueHooks" ], + timers = jQuery.timers, + length = queue ? queue.length : 0; + + // Enable finishing flag on private data + data.finish = true; + + // Empty the queue first + jQuery.queue( this, type, [] ); + + if ( hooks && hooks.stop ) { + hooks.stop.call( this, true ); + } + + // Look for any active animations, and finish them + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && timers[ index ].queue === type ) { + timers[ index ].anim.stop( true ); + timers.splice( index, 1 ); + } + } + + // Look for any animations in the old queue and finish them + for ( index = 0; index < length; index++ ) { + if ( queue[ index ] && queue[ index ].finish ) { + queue[ index ].finish.call( this ); + } + } + + // Turn off finishing flag + delete data.finish; + } ); + } +} ); + +jQuery.each( [ "toggle", "show", "hide" ], function( _i, name ) { + var cssFn = jQuery.fn[ name ]; + jQuery.fn[ name ] = function( speed, easing, callback ) { + return speed == null || typeof speed === "boolean" ? + cssFn.apply( this, arguments ) : + this.animate( genFx( name, true ), speed, easing, callback ); + }; +} ); + +// Generate shortcuts for custom animations +jQuery.each( { + slideDown: genFx( "show" ), + slideUp: genFx( "hide" ), + slideToggle: genFx( "toggle" ), + fadeIn: { opacity: "show" }, + fadeOut: { opacity: "hide" }, + fadeToggle: { opacity: "toggle" } +}, function( name, props ) { + jQuery.fn[ name ] = function( speed, easing, callback ) { + return this.animate( props, speed, easing, callback ); + }; +} ); + +jQuery.timers = []; +jQuery.fx.tick = function() { + var timer, + i = 0, + timers = jQuery.timers; + + fxNow = Date.now(); + + for ( ; i < timers.length; i++ ) { + timer = timers[ i ]; + + // Run the timer and safely remove it when done (allowing for external removal) + if ( !timer() && timers[ i ] === timer ) { + timers.splice( i--, 1 ); + } + } + + if ( !timers.length ) { + jQuery.fx.stop(); + } + fxNow = undefined; +}; + +jQuery.fx.timer = function( timer ) { + jQuery.timers.push( timer ); + jQuery.fx.start(); +}; + +jQuery.fx.interval = 13; +jQuery.fx.start = function() { + if ( inProgress ) { + return; + } + + inProgress = true; + schedule(); +}; + +jQuery.fx.stop = function() { + inProgress = null; +}; + +jQuery.fx.speeds = { + slow: 600, + fast: 200, + + // Default speed + _default: 400 +}; + + +// Based off of the plugin by Clint Helfers, with permission. +// https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/ +jQuery.fn.delay = function( time, type ) { + time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time; + type = type || "fx"; + + return this.queue( type, function( next, hooks ) { + var timeout = window.setTimeout( next, time ); + hooks.stop = function() { + window.clearTimeout( timeout ); + }; + } ); +}; + + +( function() { + var input = document.createElement( "input" ), + select = document.createElement( "select" ), + opt = select.appendChild( document.createElement( "option" ) ); + + input.type = "checkbox"; + + // Support: Android <=4.3 only + // Default value for a checkbox should be "on" + support.checkOn = input.value !== ""; + + // Support: IE <=11 only + // Must access selectedIndex to make default options select + support.optSelected = opt.selected; + + // Support: IE <=11 only + // An input loses its value after becoming a radio + input = document.createElement( "input" ); + input.value = "t"; + input.type = "radio"; + support.radioValue = input.value === "t"; +} )(); + + +var boolHook, + attrHandle = jQuery.expr.attrHandle; + +jQuery.fn.extend( { + attr: function( name, value ) { + return access( this, jQuery.attr, name, value, arguments.length > 1 ); + }, + + removeAttr: function( name ) { + return this.each( function() { + jQuery.removeAttr( this, name ); + } ); + } +} ); + +jQuery.extend( { + attr: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set attributes on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + // Fallback to prop when attributes are not supported + if ( typeof elem.getAttribute === "undefined" ) { + return jQuery.prop( elem, name, value ); + } + + // Attribute hooks are determined by the lowercase version + // Grab necessary hook if one is defined + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + hooks = jQuery.attrHooks[ name.toLowerCase() ] || + ( jQuery.expr.match.bool.test( name ) ? boolHook : undefined ); + } + + if ( value !== undefined ) { + if ( value === null ) { + jQuery.removeAttr( elem, name ); + return; + } + + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + elem.setAttribute( name, value + "" ); + return value; + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + ret = jQuery.find.attr( elem, name ); + + // Non-existent attributes return null, we normalize to undefined + return ret == null ? undefined : ret; + }, + + attrHooks: { + type: { + set: function( elem, value ) { + if ( !support.radioValue && value === "radio" && + nodeName( elem, "input" ) ) { + var val = elem.value; + elem.setAttribute( "type", value ); + if ( val ) { + elem.value = val; + } + return value; + } + } + } + }, + + removeAttr: function( elem, value ) { + var name, + i = 0, + + // Attribute names can contain non-HTML whitespace characters + // https://html.spec.whatwg.org/multipage/syntax.html#attributes-2 + attrNames = value && value.match( rnothtmlwhite ); + + if ( attrNames && elem.nodeType === 1 ) { + while ( ( name = attrNames[ i++ ] ) ) { + elem.removeAttribute( name ); + } + } + } +} ); + +// Hooks for boolean attributes +boolHook = { + set: function( elem, value, name ) { + if ( value === false ) { + + // Remove boolean attributes when set to false + jQuery.removeAttr( elem, name ); + } else { + elem.setAttribute( name, name ); + } + return name; + } +}; + +jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( _i, name ) { + var getter = attrHandle[ name ] || jQuery.find.attr; + + attrHandle[ name ] = function( elem, name, isXML ) { + var ret, handle, + lowercaseName = name.toLowerCase(); + + if ( !isXML ) { + + // Avoid an infinite loop by temporarily removing this function from the getter + handle = attrHandle[ lowercaseName ]; + attrHandle[ lowercaseName ] = ret; + ret = getter( elem, name, isXML ) != null ? + lowercaseName : + null; + attrHandle[ lowercaseName ] = handle; + } + return ret; + }; +} ); + + + + +var rfocusable = /^(?:input|select|textarea|button)$/i, + rclickable = /^(?:a|area)$/i; + +jQuery.fn.extend( { + prop: function( name, value ) { + return access( this, jQuery.prop, name, value, arguments.length > 1 ); + }, + + removeProp: function( name ) { + return this.each( function() { + delete this[ jQuery.propFix[ name ] || name ]; + } ); + } +} ); + +jQuery.extend( { + prop: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set properties on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + + // Fix name and attach hooks + name = jQuery.propFix[ name ] || name; + hooks = jQuery.propHooks[ name ]; + } + + if ( value !== undefined ) { + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + return ( elem[ name ] = value ); + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + return elem[ name ]; + }, + + propHooks: { + tabIndex: { + get: function( elem ) { + + // Support: IE <=9 - 11 only + // elem.tabIndex doesn't always return the + // correct value when it hasn't been explicitly set + // https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/ + // Use proper attribute retrieval(#12072) + var tabindex = jQuery.find.attr( elem, "tabindex" ); + + if ( tabindex ) { + return parseInt( tabindex, 10 ); + } + + if ( + rfocusable.test( elem.nodeName ) || + rclickable.test( elem.nodeName ) && + elem.href + ) { + return 0; + } + + return -1; + } + } + }, + + propFix: { + "for": "htmlFor", + "class": "className" + } +} ); + +// Support: IE <=11 only +// Accessing the selectedIndex property +// forces the browser to respect setting selected +// on the option +// The getter ensures a default option is selected +// when in an optgroup +// eslint rule "no-unused-expressions" is disabled for this code +// since it considers such accessions noop +if ( !support.optSelected ) { + jQuery.propHooks.selected = { + get: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent && parent.parentNode ) { + parent.parentNode.selectedIndex; + } + return null; + }, + set: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent ) { + parent.selectedIndex; + + if ( parent.parentNode ) { + parent.parentNode.selectedIndex; + } + } + } + }; +} + +jQuery.each( [ + "tabIndex", + "readOnly", + "maxLength", + "cellSpacing", + "cellPadding", + "rowSpan", + "colSpan", + "useMap", + "frameBorder", + "contentEditable" +], function() { + jQuery.propFix[ this.toLowerCase() ] = this; +} ); + + + + + // Strip and collapse whitespace according to HTML spec + // https://infra.spec.whatwg.org/#strip-and-collapse-ascii-whitespace + function stripAndCollapse( value ) { + var tokens = value.match( rnothtmlwhite ) || []; + return tokens.join( " " ); + } + + +function getClass( elem ) { + return elem.getAttribute && elem.getAttribute( "class" ) || ""; +} + +function classesToArray( value ) { + if ( Array.isArray( value ) ) { + return value; + } + if ( typeof value === "string" ) { + return value.match( rnothtmlwhite ) || []; + } + return []; +} + +jQuery.fn.extend( { + addClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).addClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + classes = classesToArray( value ); + + if ( classes.length ) { + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + if ( cur.indexOf( " " + clazz + " " ) < 0 ) { + cur += clazz + " "; + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + removeClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + if ( !arguments.length ) { + return this.attr( "class", "" ); + } + + classes = classesToArray( value ); + + if ( classes.length ) { + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + + // This expression is here for better compressibility (see addClass) + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + + // Remove *all* instances + while ( cur.indexOf( " " + clazz + " " ) > -1 ) { + cur = cur.replace( " " + clazz + " ", " " ); + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + toggleClass: function( value, stateVal ) { + var type = typeof value, + isValidValue = type === "string" || Array.isArray( value ); + + if ( typeof stateVal === "boolean" && isValidValue ) { + return stateVal ? this.addClass( value ) : this.removeClass( value ); + } + + if ( isFunction( value ) ) { + return this.each( function( i ) { + jQuery( this ).toggleClass( + value.call( this, i, getClass( this ), stateVal ), + stateVal + ); + } ); + } + + return this.each( function() { + var className, i, self, classNames; + + if ( isValidValue ) { + + // Toggle individual class names + i = 0; + self = jQuery( this ); + classNames = classesToArray( value ); + + while ( ( className = classNames[ i++ ] ) ) { + + // Check each className given, space separated list + if ( self.hasClass( className ) ) { + self.removeClass( className ); + } else { + self.addClass( className ); + } + } + + // Toggle whole class name + } else if ( value === undefined || type === "boolean" ) { + className = getClass( this ); + if ( className ) { + + // Store className if set + dataPriv.set( this, "__className__", className ); + } + + // If the element has a class name or if we're passed `false`, + // then remove the whole classname (if there was one, the above saved it). + // Otherwise bring back whatever was previously saved (if anything), + // falling back to the empty string if nothing was stored. + if ( this.setAttribute ) { + this.setAttribute( "class", + className || value === false ? + "" : + dataPriv.get( this, "__className__" ) || "" + ); + } + } + } ); + }, + + hasClass: function( selector ) { + var className, elem, + i = 0; + + className = " " + selector + " "; + while ( ( elem = this[ i++ ] ) ) { + if ( elem.nodeType === 1 && + ( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) { + return true; + } + } + + return false; + } +} ); + + + + +var rreturn = /\r/g; + +jQuery.fn.extend( { + val: function( value ) { + var hooks, ret, valueIsFunction, + elem = this[ 0 ]; + + if ( !arguments.length ) { + if ( elem ) { + hooks = jQuery.valHooks[ elem.type ] || + jQuery.valHooks[ elem.nodeName.toLowerCase() ]; + + if ( hooks && + "get" in hooks && + ( ret = hooks.get( elem, "value" ) ) !== undefined + ) { + return ret; + } + + ret = elem.value; + + // Handle most common string cases + if ( typeof ret === "string" ) { + return ret.replace( rreturn, "" ); + } + + // Handle cases where value is null/undef or number + return ret == null ? "" : ret; + } + + return; + } + + valueIsFunction = isFunction( value ); + + return this.each( function( i ) { + var val; + + if ( this.nodeType !== 1 ) { + return; + } + + if ( valueIsFunction ) { + val = value.call( this, i, jQuery( this ).val() ); + } else { + val = value; + } + + // Treat null/undefined as ""; convert numbers to string + if ( val == null ) { + val = ""; + + } else if ( typeof val === "number" ) { + val += ""; + + } else if ( Array.isArray( val ) ) { + val = jQuery.map( val, function( value ) { + return value == null ? "" : value + ""; + } ); + } + + hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ]; + + // If set returns undefined, fall back to normal setting + if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) { + this.value = val; + } + } ); + } +} ); + +jQuery.extend( { + valHooks: { + option: { + get: function( elem ) { + + var val = jQuery.find.attr( elem, "value" ); + return val != null ? + val : + + // Support: IE <=10 - 11 only + // option.text throws exceptions (#14686, #14858) + // Strip and collapse whitespace + // https://html.spec.whatwg.org/#strip-and-collapse-whitespace + stripAndCollapse( jQuery.text( elem ) ); + } + }, + select: { + get: function( elem ) { + var value, option, i, + options = elem.options, + index = elem.selectedIndex, + one = elem.type === "select-one", + values = one ? null : [], + max = one ? index + 1 : options.length; + + if ( index < 0 ) { + i = max; + + } else { + i = one ? index : 0; + } + + // Loop through all the selected options + for ( ; i < max; i++ ) { + option = options[ i ]; + + // Support: IE <=9 only + // IE8-9 doesn't update selected after form reset (#2551) + if ( ( option.selected || i === index ) && + + // Don't return options that are disabled or in a disabled optgroup + !option.disabled && + ( !option.parentNode.disabled || + !nodeName( option.parentNode, "optgroup" ) ) ) { + + // Get the specific value for the option + value = jQuery( option ).val(); + + // We don't need an array for one selects + if ( one ) { + return value; + } + + // Multi-Selects return an array + values.push( value ); + } + } + + return values; + }, + + set: function( elem, value ) { + var optionSet, option, + options = elem.options, + values = jQuery.makeArray( value ), + i = options.length; + + while ( i-- ) { + option = options[ i ]; + + /* eslint-disable no-cond-assign */ + + if ( option.selected = + jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1 + ) { + optionSet = true; + } + + /* eslint-enable no-cond-assign */ + } + + // Force browsers to behave consistently when non-matching value is set + if ( !optionSet ) { + elem.selectedIndex = -1; + } + return values; + } + } + } +} ); + +// Radios and checkboxes getter/setter +jQuery.each( [ "radio", "checkbox" ], function() { + jQuery.valHooks[ this ] = { + set: function( elem, value ) { + if ( Array.isArray( value ) ) { + return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 ); + } + } + }; + if ( !support.checkOn ) { + jQuery.valHooks[ this ].get = function( elem ) { + return elem.getAttribute( "value" ) === null ? "on" : elem.value; + }; + } +} ); + + + + +// Return jQuery for attributes-only inclusion + + +support.focusin = "onfocusin" in window; + + +var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/, + stopPropagationCallback = function( e ) { + e.stopPropagation(); + }; + +jQuery.extend( jQuery.event, { + + trigger: function( event, data, elem, onlyHandlers ) { + + var i, cur, tmp, bubbleType, ontype, handle, special, lastElement, + eventPath = [ elem || document ], + type = hasOwn.call( event, "type" ) ? event.type : event, + namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : []; + + cur = lastElement = tmp = elem = elem || document; + + // Don't do events on text and comment nodes + if ( elem.nodeType === 3 || elem.nodeType === 8 ) { + return; + } + + // focus/blur morphs to focusin/out; ensure we're not firing them right now + if ( rfocusMorph.test( type + jQuery.event.triggered ) ) { + return; + } + + if ( type.indexOf( "." ) > -1 ) { + + // Namespaced trigger; create a regexp to match event type in handle() + namespaces = type.split( "." ); + type = namespaces.shift(); + namespaces.sort(); + } + ontype = type.indexOf( ":" ) < 0 && "on" + type; + + // Caller can pass in a jQuery.Event object, Object, or just an event type string + event = event[ jQuery.expando ] ? + event : + new jQuery.Event( type, typeof event === "object" && event ); + + // Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true) + event.isTrigger = onlyHandlers ? 2 : 3; + event.namespace = namespaces.join( "." ); + event.rnamespace = event.namespace ? + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) : + null; + + // Clean up the event in case it is being reused + event.result = undefined; + if ( !event.target ) { + event.target = elem; + } + + // Clone any incoming data and prepend the event, creating the handler arg list + data = data == null ? + [ event ] : + jQuery.makeArray( data, [ event ] ); + + // Allow special events to draw outside the lines + special = jQuery.event.special[ type ] || {}; + if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) { + return; + } + + // Determine event propagation path in advance, per W3C events spec (#9951) + // Bubble up to document, then to window; watch for a global ownerDocument var (#9724) + if ( !onlyHandlers && !special.noBubble && !isWindow( elem ) ) { + + bubbleType = special.delegateType || type; + if ( !rfocusMorph.test( bubbleType + type ) ) { + cur = cur.parentNode; + } + for ( ; cur; cur = cur.parentNode ) { + eventPath.push( cur ); + tmp = cur; + } + + // Only add window if we got to document (e.g., not plain obj or detached DOM) + if ( tmp === ( elem.ownerDocument || document ) ) { + eventPath.push( tmp.defaultView || tmp.parentWindow || window ); + } + } + + // Fire handlers on the event path + i = 0; + while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) { + lastElement = cur; + event.type = i > 1 ? + bubbleType : + special.bindType || type; + + // jQuery handler + handle = ( + dataPriv.get( cur, "events" ) || Object.create( null ) + )[ event.type ] && + dataPriv.get( cur, "handle" ); + if ( handle ) { + handle.apply( cur, data ); + } + + // Native handler + handle = ontype && cur[ ontype ]; + if ( handle && handle.apply && acceptData( cur ) ) { + event.result = handle.apply( cur, data ); + if ( event.result === false ) { + event.preventDefault(); + } + } + } + event.type = type; + + // If nobody prevented the default action, do it now + if ( !onlyHandlers && !event.isDefaultPrevented() ) { + + if ( ( !special._default || + special._default.apply( eventPath.pop(), data ) === false ) && + acceptData( elem ) ) { + + // Call a native DOM method on the target with the same name as the event. + // Don't do default actions on window, that's where global variables be (#6170) + if ( ontype && isFunction( elem[ type ] ) && !isWindow( elem ) ) { + + // Don't re-trigger an onFOO event when we call its FOO() method + tmp = elem[ ontype ]; + + if ( tmp ) { + elem[ ontype ] = null; + } + + // Prevent re-triggering of the same event, since we already bubbled it above + jQuery.event.triggered = type; + + if ( event.isPropagationStopped() ) { + lastElement.addEventListener( type, stopPropagationCallback ); + } + + elem[ type ](); + + if ( event.isPropagationStopped() ) { + lastElement.removeEventListener( type, stopPropagationCallback ); + } + + jQuery.event.triggered = undefined; + + if ( tmp ) { + elem[ ontype ] = tmp; + } + } + } + } + + return event.result; + }, + + // Piggyback on a donor event to simulate a different one + // Used only for `focus(in | out)` events + simulate: function( type, elem, event ) { + var e = jQuery.extend( + new jQuery.Event(), + event, + { + type: type, + isSimulated: true + } + ); + + jQuery.event.trigger( e, null, elem ); + } + +} ); + +jQuery.fn.extend( { + + trigger: function( type, data ) { + return this.each( function() { + jQuery.event.trigger( type, data, this ); + } ); + }, + triggerHandler: function( type, data ) { + var elem = this[ 0 ]; + if ( elem ) { + return jQuery.event.trigger( type, data, elem, true ); + } + } +} ); + + +// Support: Firefox <=44 +// Firefox doesn't have focus(in | out) events +// Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787 +// +// Support: Chrome <=48 - 49, Safari <=9.0 - 9.1 +// focus(in | out) events fire after focus & blur events, +// which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order +// Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857 +if ( !support.focusin ) { + jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) { + + // Attach a single capturing handler on the document while someone wants focusin/focusout + var handler = function( event ) { + jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) ); + }; + + jQuery.event.special[ fix ] = { + setup: function() { + + // Handle: regular nodes (via `this.ownerDocument`), window + // (via `this.document`) & document (via `this`). + var doc = this.ownerDocument || this.document || this, + attaches = dataPriv.access( doc, fix ); + + if ( !attaches ) { + doc.addEventListener( orig, handler, true ); + } + dataPriv.access( doc, fix, ( attaches || 0 ) + 1 ); + }, + teardown: function() { + var doc = this.ownerDocument || this.document || this, + attaches = dataPriv.access( doc, fix ) - 1; + + if ( !attaches ) { + doc.removeEventListener( orig, handler, true ); + dataPriv.remove( doc, fix ); + + } else { + dataPriv.access( doc, fix, attaches ); + } + } + }; + } ); +} +var location = window.location; + +var nonce = { guid: Date.now() }; + +var rquery = ( /\?/ ); + + + +// Cross-browser xml parsing +jQuery.parseXML = function( data ) { + var xml; + if ( !data || typeof data !== "string" ) { + return null; + } + + // Support: IE 9 - 11 only + // IE throws on parseFromString with invalid input. + try { + xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" ); + } catch ( e ) { + xml = undefined; + } + + if ( !xml || xml.getElementsByTagName( "parsererror" ).length ) { + jQuery.error( "Invalid XML: " + data ); + } + return xml; +}; + + +var + rbracket = /\[\]$/, + rCRLF = /\r?\n/g, + rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i, + rsubmittable = /^(?:input|select|textarea|keygen)/i; + +function buildParams( prefix, obj, traditional, add ) { + var name; + + if ( Array.isArray( obj ) ) { + + // Serialize array item. + jQuery.each( obj, function( i, v ) { + if ( traditional || rbracket.test( prefix ) ) { + + // Treat each array item as a scalar. + add( prefix, v ); + + } else { + + // Item is non-scalar (array or object), encode its numeric index. + buildParams( + prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]", + v, + traditional, + add + ); + } + } ); + + } else if ( !traditional && toType( obj ) === "object" ) { + + // Serialize object item. + for ( name in obj ) { + buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add ); + } + + } else { + + // Serialize scalar item. + add( prefix, obj ); + } +} + +// Serialize an array of form elements or a set of +// key/values into a query string +jQuery.param = function( a, traditional ) { + var prefix, + s = [], + add = function( key, valueOrFunction ) { + + // If value is a function, invoke it and use its return value + var value = isFunction( valueOrFunction ) ? + valueOrFunction() : + valueOrFunction; + + s[ s.length ] = encodeURIComponent( key ) + "=" + + encodeURIComponent( value == null ? "" : value ); + }; + + if ( a == null ) { + return ""; + } + + // If an array was passed in, assume that it is an array of form elements. + if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) { + + // Serialize the form elements + jQuery.each( a, function() { + add( this.name, this.value ); + } ); + + } else { + + // If traditional, encode the "old" way (the way 1.3.2 or older + // did it), otherwise encode params recursively. + for ( prefix in a ) { + buildParams( prefix, a[ prefix ], traditional, add ); + } + } + + // Return the resulting serialization + return s.join( "&" ); +}; + +jQuery.fn.extend( { + serialize: function() { + return jQuery.param( this.serializeArray() ); + }, + serializeArray: function() { + return this.map( function() { + + // Can add propHook for "elements" to filter or add form elements + var elements = jQuery.prop( this, "elements" ); + return elements ? jQuery.makeArray( elements ) : this; + } ) + .filter( function() { + var type = this.type; + + // Use .is( ":disabled" ) so that fieldset[disabled] works + return this.name && !jQuery( this ).is( ":disabled" ) && + rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) && + ( this.checked || !rcheckableType.test( type ) ); + } ) + .map( function( _i, elem ) { + var val = jQuery( this ).val(); + + if ( val == null ) { + return null; + } + + if ( Array.isArray( val ) ) { + return jQuery.map( val, function( val ) { + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ); + } + + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ).get(); + } +} ); + + +var + r20 = /%20/g, + rhash = /#.*$/, + rantiCache = /([?&])_=[^&]*/, + rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg, + + // #7653, #8125, #8152: local protocol detection + rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/, + rnoContent = /^(?:GET|HEAD)$/, + rprotocol = /^\/\//, + + /* Prefilters + * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example) + * 2) These are called: + * - BEFORE asking for a transport + * - AFTER param serialization (s.data is a string if s.processData is true) + * 3) key is the dataType + * 4) the catchall symbol "*" can be used + * 5) execution will start with transport dataType and THEN continue down to "*" if needed + */ + prefilters = {}, + + /* Transports bindings + * 1) key is the dataType + * 2) the catchall symbol "*" can be used + * 3) selection will start with transport dataType and THEN go to "*" if needed + */ + transports = {}, + + // Avoid comment-prolog char sequence (#10098); must appease lint and evade compression + allTypes = "*/".concat( "*" ), + + // Anchor tag for parsing the document origin + originAnchor = document.createElement( "a" ); + originAnchor.href = location.href; + +// Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport +function addToPrefiltersOrTransports( structure ) { + + // dataTypeExpression is optional and defaults to "*" + return function( dataTypeExpression, func ) { + + if ( typeof dataTypeExpression !== "string" ) { + func = dataTypeExpression; + dataTypeExpression = "*"; + } + + var dataType, + i = 0, + dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || []; + + if ( isFunction( func ) ) { + + // For each dataType in the dataTypeExpression + while ( ( dataType = dataTypes[ i++ ] ) ) { + + // Prepend if requested + if ( dataType[ 0 ] === "+" ) { + dataType = dataType.slice( 1 ) || "*"; + ( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func ); + + // Otherwise append + } else { + ( structure[ dataType ] = structure[ dataType ] || [] ).push( func ); + } + } + } + }; +} + +// Base inspection function for prefilters and transports +function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) { + + var inspected = {}, + seekingTransport = ( structure === transports ); + + function inspect( dataType ) { + var selected; + inspected[ dataType ] = true; + jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) { + var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR ); + if ( typeof dataTypeOrTransport === "string" && + !seekingTransport && !inspected[ dataTypeOrTransport ] ) { + + options.dataTypes.unshift( dataTypeOrTransport ); + inspect( dataTypeOrTransport ); + return false; + } else if ( seekingTransport ) { + return !( selected = dataTypeOrTransport ); + } + } ); + return selected; + } + + return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" ); +} + +// A special extend for ajax options +// that takes "flat" options (not to be deep extended) +// Fixes #9887 +function ajaxExtend( target, src ) { + var key, deep, + flatOptions = jQuery.ajaxSettings.flatOptions || {}; + + for ( key in src ) { + if ( src[ key ] !== undefined ) { + ( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ]; + } + } + if ( deep ) { + jQuery.extend( true, target, deep ); + } + + return target; +} + +/* Handles responses to an ajax request: + * - finds the right dataType (mediates between content-type and expected dataType) + * - returns the corresponding response + */ +function ajaxHandleResponses( s, jqXHR, responses ) { + + var ct, type, finalDataType, firstDataType, + contents = s.contents, + dataTypes = s.dataTypes; + + // Remove auto dataType and get content-type in the process + while ( dataTypes[ 0 ] === "*" ) { + dataTypes.shift(); + if ( ct === undefined ) { + ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" ); + } + } + + // Check if we're dealing with a known content-type + if ( ct ) { + for ( type in contents ) { + if ( contents[ type ] && contents[ type ].test( ct ) ) { + dataTypes.unshift( type ); + break; + } + } + } + + // Check to see if we have a response for the expected dataType + if ( dataTypes[ 0 ] in responses ) { + finalDataType = dataTypes[ 0 ]; + } else { + + // Try convertible dataTypes + for ( type in responses ) { + if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) { + finalDataType = type; + break; + } + if ( !firstDataType ) { + firstDataType = type; + } + } + + // Or just use first one + finalDataType = finalDataType || firstDataType; + } + + // If we found a dataType + // We add the dataType to the list if needed + // and return the corresponding response + if ( finalDataType ) { + if ( finalDataType !== dataTypes[ 0 ] ) { + dataTypes.unshift( finalDataType ); + } + return responses[ finalDataType ]; + } +} + +/* Chain conversions given the request and the original response + * Also sets the responseXXX fields on the jqXHR instance + */ +function ajaxConvert( s, response, jqXHR, isSuccess ) { + var conv2, current, conv, tmp, prev, + converters = {}, + + // Work with a copy of dataTypes in case we need to modify it for conversion + dataTypes = s.dataTypes.slice(); + + // Create converters map with lowercased keys + if ( dataTypes[ 1 ] ) { + for ( conv in s.converters ) { + converters[ conv.toLowerCase() ] = s.converters[ conv ]; + } + } + + current = dataTypes.shift(); + + // Convert to each sequential dataType + while ( current ) { + + if ( s.responseFields[ current ] ) { + jqXHR[ s.responseFields[ current ] ] = response; + } + + // Apply the dataFilter if provided + if ( !prev && isSuccess && s.dataFilter ) { + response = s.dataFilter( response, s.dataType ); + } + + prev = current; + current = dataTypes.shift(); + + if ( current ) { + + // There's only work to do if current dataType is non-auto + if ( current === "*" ) { + + current = prev; + + // Convert response if prev dataType is non-auto and differs from current + } else if ( prev !== "*" && prev !== current ) { + + // Seek a direct converter + conv = converters[ prev + " " + current ] || converters[ "* " + current ]; + + // If none found, seek a pair + if ( !conv ) { + for ( conv2 in converters ) { + + // If conv2 outputs current + tmp = conv2.split( " " ); + if ( tmp[ 1 ] === current ) { + + // If prev can be converted to accepted input + conv = converters[ prev + " " + tmp[ 0 ] ] || + converters[ "* " + tmp[ 0 ] ]; + if ( conv ) { + + // Condense equivalence converters + if ( conv === true ) { + conv = converters[ conv2 ]; + + // Otherwise, insert the intermediate dataType + } else if ( converters[ conv2 ] !== true ) { + current = tmp[ 0 ]; + dataTypes.unshift( tmp[ 1 ] ); + } + break; + } + } + } + } + + // Apply converter (if not an equivalence) + if ( conv !== true ) { + + // Unless errors are allowed to bubble, catch and return them + if ( conv && s.throws ) { + response = conv( response ); + } else { + try { + response = conv( response ); + } catch ( e ) { + return { + state: "parsererror", + error: conv ? e : "No conversion from " + prev + " to " + current + }; + } + } + } + } + } + } + + return { state: "success", data: response }; +} + +jQuery.extend( { + + // Counter for holding the number of active queries + active: 0, + + // Last-Modified header cache for next request + lastModified: {}, + etag: {}, + + ajaxSettings: { + url: location.href, + type: "GET", + isLocal: rlocalProtocol.test( location.protocol ), + global: true, + processData: true, + async: true, + contentType: "application/x-www-form-urlencoded; charset=UTF-8", + + /* + timeout: 0, + data: null, + dataType: null, + username: null, + password: null, + cache: null, + throws: false, + traditional: false, + headers: {}, + */ + + accepts: { + "*": allTypes, + text: "text/plain", + html: "text/html", + xml: "application/xml, text/xml", + json: "application/json, text/javascript" + }, + + contents: { + xml: /\bxml\b/, + html: /\bhtml/, + json: /\bjson\b/ + }, + + responseFields: { + xml: "responseXML", + text: "responseText", + json: "responseJSON" + }, + + // Data converters + // Keys separate source (or catchall "*") and destination types with a single space + converters: { + + // Convert anything to text + "* text": String, + + // Text to html (true = no transformation) + "text html": true, + + // Evaluate text as a json expression + "text json": JSON.parse, + + // Parse text as xml + "text xml": jQuery.parseXML + }, + + // For options that shouldn't be deep extended: + // you can add your own custom options here if + // and when you create one that shouldn't be + // deep extended (see ajaxExtend) + flatOptions: { + url: true, + context: true + } + }, + + // Creates a full fledged settings object into target + // with both ajaxSettings and settings fields. + // If target is omitted, writes into ajaxSettings. + ajaxSetup: function( target, settings ) { + return settings ? + + // Building a settings object + ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) : + + // Extending ajaxSettings + ajaxExtend( jQuery.ajaxSettings, target ); + }, + + ajaxPrefilter: addToPrefiltersOrTransports( prefilters ), + ajaxTransport: addToPrefiltersOrTransports( transports ), + + // Main method + ajax: function( url, options ) { + + // If url is an object, simulate pre-1.5 signature + if ( typeof url === "object" ) { + options = url; + url = undefined; + } + + // Force options to be an object + options = options || {}; + + var transport, + + // URL without anti-cache param + cacheURL, + + // Response headers + responseHeadersString, + responseHeaders, + + // timeout handle + timeoutTimer, + + // Url cleanup var + urlAnchor, + + // Request state (becomes false upon send and true upon completion) + completed, + + // To know if global events are to be dispatched + fireGlobals, + + // Loop variable + i, + + // uncached part of the url + uncached, + + // Create the final options object + s = jQuery.ajaxSetup( {}, options ), + + // Callbacks context + callbackContext = s.context || s, + + // Context for global events is callbackContext if it is a DOM node or jQuery collection + globalEventContext = s.context && + ( callbackContext.nodeType || callbackContext.jquery ) ? + jQuery( callbackContext ) : + jQuery.event, + + // Deferreds + deferred = jQuery.Deferred(), + completeDeferred = jQuery.Callbacks( "once memory" ), + + // Status-dependent callbacks + statusCode = s.statusCode || {}, + + // Headers (they are sent all at once) + requestHeaders = {}, + requestHeadersNames = {}, + + // Default abort message + strAbort = "canceled", + + // Fake xhr + jqXHR = { + readyState: 0, + + // Builds headers hashtable if needed + getResponseHeader: function( key ) { + var match; + if ( completed ) { + if ( !responseHeaders ) { + responseHeaders = {}; + while ( ( match = rheaders.exec( responseHeadersString ) ) ) { + responseHeaders[ match[ 1 ].toLowerCase() + " " ] = + ( responseHeaders[ match[ 1 ].toLowerCase() + " " ] || [] ) + .concat( match[ 2 ] ); + } + } + match = responseHeaders[ key.toLowerCase() + " " ]; + } + return match == null ? null : match.join( ", " ); + }, + + // Raw string + getAllResponseHeaders: function() { + return completed ? responseHeadersString : null; + }, + + // Caches the header + setRequestHeader: function( name, value ) { + if ( completed == null ) { + name = requestHeadersNames[ name.toLowerCase() ] = + requestHeadersNames[ name.toLowerCase() ] || name; + requestHeaders[ name ] = value; + } + return this; + }, + + // Overrides response content-type header + overrideMimeType: function( type ) { + if ( completed == null ) { + s.mimeType = type; + } + return this; + }, + + // Status-dependent callbacks + statusCode: function( map ) { + var code; + if ( map ) { + if ( completed ) { + + // Execute the appropriate callbacks + jqXHR.always( map[ jqXHR.status ] ); + } else { + + // Lazy-add the new callbacks in a way that preserves old ones + for ( code in map ) { + statusCode[ code ] = [ statusCode[ code ], map[ code ] ]; + } + } + } + return this; + }, + + // Cancel the request + abort: function( statusText ) { + var finalText = statusText || strAbort; + if ( transport ) { + transport.abort( finalText ); + } + done( 0, finalText ); + return this; + } + }; + + // Attach deferreds + deferred.promise( jqXHR ); + + // Add protocol if not provided (prefilters might expect it) + // Handle falsy url in the settings object (#10093: consistency with old signature) + // We also use the url parameter if available + s.url = ( ( url || s.url || location.href ) + "" ) + .replace( rprotocol, location.protocol + "//" ); + + // Alias method option to type as per ticket #12004 + s.type = options.method || options.type || s.method || s.type; + + // Extract dataTypes list + s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ]; + + // A cross-domain request is in order when the origin doesn't match the current origin. + if ( s.crossDomain == null ) { + urlAnchor = document.createElement( "a" ); + + // Support: IE <=8 - 11, Edge 12 - 15 + // IE throws exception on accessing the href property if url is malformed, + // e.g. http://example.com:80x/ + try { + urlAnchor.href = s.url; + + // Support: IE <=8 - 11 only + // Anchor's host property isn't correctly set when s.url is relative + urlAnchor.href = urlAnchor.href; + s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !== + urlAnchor.protocol + "//" + urlAnchor.host; + } catch ( e ) { + + // If there is an error parsing the URL, assume it is crossDomain, + // it can be rejected by the transport if it is invalid + s.crossDomain = true; + } + } + + // Convert data if not already a string + if ( s.data && s.processData && typeof s.data !== "string" ) { + s.data = jQuery.param( s.data, s.traditional ); + } + + // Apply prefilters + inspectPrefiltersOrTransports( prefilters, s, options, jqXHR ); + + // If request was aborted inside a prefilter, stop there + if ( completed ) { + return jqXHR; + } + + // We can fire global events as of now if asked to + // Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118) + fireGlobals = jQuery.event && s.global; + + // Watch for a new set of requests + if ( fireGlobals && jQuery.active++ === 0 ) { + jQuery.event.trigger( "ajaxStart" ); + } + + // Uppercase the type + s.type = s.type.toUpperCase(); + + // Determine if request has content + s.hasContent = !rnoContent.test( s.type ); + + // Save the URL in case we're toying with the If-Modified-Since + // and/or If-None-Match header later on + // Remove hash to simplify url manipulation + cacheURL = s.url.replace( rhash, "" ); + + // More options handling for requests with no content + if ( !s.hasContent ) { + + // Remember the hash so we can put it back + uncached = s.url.slice( cacheURL.length ); + + // If data is available and should be processed, append data to url + if ( s.data && ( s.processData || typeof s.data === "string" ) ) { + cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data; + + // #9682: remove data so that it's not used in an eventual retry + delete s.data; + } + + // Add or update anti-cache param if needed + if ( s.cache === false ) { + cacheURL = cacheURL.replace( rantiCache, "$1" ); + uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce.guid++ ) + + uncached; + } + + // Put hash and anti-cache on the URL that will be requested (gh-1732) + s.url = cacheURL + uncached; + + // Change '%20' to '+' if this is encoded form body content (gh-2658) + } else if ( s.data && s.processData && + ( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) { + s.data = s.data.replace( r20, "+" ); + } + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + if ( jQuery.lastModified[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] ); + } + if ( jQuery.etag[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] ); + } + } + + // Set the correct header, if data is being sent + if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) { + jqXHR.setRequestHeader( "Content-Type", s.contentType ); + } + + // Set the Accepts header for the server, depending on the dataType + jqXHR.setRequestHeader( + "Accept", + s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ? + s.accepts[ s.dataTypes[ 0 ] ] + + ( s.dataTypes[ 0 ] !== "*" ? ", " + allTypes + "; q=0.01" : "" ) : + s.accepts[ "*" ] + ); + + // Check for headers option + for ( i in s.headers ) { + jqXHR.setRequestHeader( i, s.headers[ i ] ); + } + + // Allow custom headers/mimetypes and early abort + if ( s.beforeSend && + ( s.beforeSend.call( callbackContext, jqXHR, s ) === false || completed ) ) { + + // Abort if not done already and return + return jqXHR.abort(); + } + + // Aborting is no longer a cancellation + strAbort = "abort"; + + // Install callbacks on deferreds + completeDeferred.add( s.complete ); + jqXHR.done( s.success ); + jqXHR.fail( s.error ); + + // Get transport + transport = inspectPrefiltersOrTransports( transports, s, options, jqXHR ); + + // If no transport, we auto-abort + if ( !transport ) { + done( -1, "No Transport" ); + } else { + jqXHR.readyState = 1; + + // Send global event + if ( fireGlobals ) { + globalEventContext.trigger( "ajaxSend", [ jqXHR, s ] ); + } + + // If request was aborted inside ajaxSend, stop there + if ( completed ) { + return jqXHR; + } + + // Timeout + if ( s.async && s.timeout > 0 ) { + timeoutTimer = window.setTimeout( function() { + jqXHR.abort( "timeout" ); + }, s.timeout ); + } + + try { + completed = false; + transport.send( requestHeaders, done ); + } catch ( e ) { + + // Rethrow post-completion exceptions + if ( completed ) { + throw e; + } + + // Propagate others as results + done( -1, e ); + } + } + + // Callback for when everything is done + function done( status, nativeStatusText, responses, headers ) { + var isSuccess, success, error, response, modified, + statusText = nativeStatusText; + + // Ignore repeat invocations + if ( completed ) { + return; + } + + completed = true; + + // Clear timeout if it exists + if ( timeoutTimer ) { + window.clearTimeout( timeoutTimer ); + } + + // Dereference transport for early garbage collection + // (no matter how long the jqXHR object will be used) + transport = undefined; + + // Cache response headers + responseHeadersString = headers || ""; + + // Set readyState + jqXHR.readyState = status > 0 ? 4 : 0; + + // Determine if successful + isSuccess = status >= 200 && status < 300 || status === 304; + + // Get response data + if ( responses ) { + response = ajaxHandleResponses( s, jqXHR, responses ); + } + + // Use a noop converter for missing script + if ( !isSuccess && jQuery.inArray( "script", s.dataTypes ) > -1 ) { + s.converters[ "text script" ] = function() {}; + } + + // Convert no matter what (that way responseXXX fields are always set) + response = ajaxConvert( s, response, jqXHR, isSuccess ); + + // If successful, handle type chaining + if ( isSuccess ) { + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + modified = jqXHR.getResponseHeader( "Last-Modified" ); + if ( modified ) { + jQuery.lastModified[ cacheURL ] = modified; + } + modified = jqXHR.getResponseHeader( "etag" ); + if ( modified ) { + jQuery.etag[ cacheURL ] = modified; + } + } + + // if no content + if ( status === 204 || s.type === "HEAD" ) { + statusText = "nocontent"; + + // if not modified + } else if ( status === 304 ) { + statusText = "notmodified"; + + // If we have data, let's convert it + } else { + statusText = response.state; + success = response.data; + error = response.error; + isSuccess = !error; + } + } else { + + // Extract error from statusText and normalize for non-aborts + error = statusText; + if ( status || !statusText ) { + statusText = "error"; + if ( status < 0 ) { + status = 0; + } + } + } + + // Set data for the fake xhr object + jqXHR.status = status; + jqXHR.statusText = ( nativeStatusText || statusText ) + ""; + + // Success/Error + if ( isSuccess ) { + deferred.resolveWith( callbackContext, [ success, statusText, jqXHR ] ); + } else { + deferred.rejectWith( callbackContext, [ jqXHR, statusText, error ] ); + } + + // Status-dependent callbacks + jqXHR.statusCode( statusCode ); + statusCode = undefined; + + if ( fireGlobals ) { + globalEventContext.trigger( isSuccess ? "ajaxSuccess" : "ajaxError", + [ jqXHR, s, isSuccess ? success : error ] ); + } + + // Complete + completeDeferred.fireWith( callbackContext, [ jqXHR, statusText ] ); + + if ( fireGlobals ) { + globalEventContext.trigger( "ajaxComplete", [ jqXHR, s ] ); + + // Handle the global AJAX counter + if ( !( --jQuery.active ) ) { + jQuery.event.trigger( "ajaxStop" ); + } + } + } + + return jqXHR; + }, + + getJSON: function( url, data, callback ) { + return jQuery.get( url, data, callback, "json" ); + }, + + getScript: function( url, callback ) { + return jQuery.get( url, undefined, callback, "script" ); + } +} ); + +jQuery.each( [ "get", "post" ], function( _i, method ) { + jQuery[ method ] = function( url, data, callback, type ) { + + // Shift arguments if data argument was omitted + if ( isFunction( data ) ) { + type = type || callback; + callback = data; + data = undefined; + } + + // The url can be an options object (which then must have .url) + return jQuery.ajax( jQuery.extend( { + url: url, + type: method, + dataType: type, + data: data, + success: callback + }, jQuery.isPlainObject( url ) && url ) ); + }; +} ); + +jQuery.ajaxPrefilter( function( s ) { + var i; + for ( i in s.headers ) { + if ( i.toLowerCase() === "content-type" ) { + s.contentType = s.headers[ i ] || ""; + } + } +} ); + + +jQuery._evalUrl = function( url, options, doc ) { + return jQuery.ajax( { + url: url, + + // Make this explicit, since user can override this through ajaxSetup (#11264) + type: "GET", + dataType: "script", + cache: true, + async: false, + global: false, + + // Only evaluate the response if it is successful (gh-4126) + // dataFilter is not invoked for failure responses, so using it instead + // of the default converter is kludgy but it works. + converters: { + "text script": function() {} + }, + dataFilter: function( response ) { + jQuery.globalEval( response, options, doc ); + } + } ); +}; + + +jQuery.fn.extend( { + wrapAll: function( html ) { + var wrap; + + if ( this[ 0 ] ) { + if ( isFunction( html ) ) { + html = html.call( this[ 0 ] ); + } + + // The elements to wrap the target around + wrap = jQuery( html, this[ 0 ].ownerDocument ).eq( 0 ).clone( true ); + + if ( this[ 0 ].parentNode ) { + wrap.insertBefore( this[ 0 ] ); + } + + wrap.map( function() { + var elem = this; + + while ( elem.firstElementChild ) { + elem = elem.firstElementChild; + } + + return elem; + } ).append( this ); + } + + return this; + }, + + wrapInner: function( html ) { + if ( isFunction( html ) ) { + return this.each( function( i ) { + jQuery( this ).wrapInner( html.call( this, i ) ); + } ); + } + + return this.each( function() { + var self = jQuery( this ), + contents = self.contents(); + + if ( contents.length ) { + contents.wrapAll( html ); + + } else { + self.append( html ); + } + } ); + }, + + wrap: function( html ) { + var htmlIsFunction = isFunction( html ); + + return this.each( function( i ) { + jQuery( this ).wrapAll( htmlIsFunction ? html.call( this, i ) : html ); + } ); + }, + + unwrap: function( selector ) { + this.parent( selector ).not( "body" ).each( function() { + jQuery( this ).replaceWith( this.childNodes ); + } ); + return this; + } +} ); + + +jQuery.expr.pseudos.hidden = function( elem ) { + return !jQuery.expr.pseudos.visible( elem ); +}; +jQuery.expr.pseudos.visible = function( elem ) { + return !!( elem.offsetWidth || elem.offsetHeight || elem.getClientRects().length ); +}; + + + + +jQuery.ajaxSettings.xhr = function() { + try { + return new window.XMLHttpRequest(); + } catch ( e ) {} +}; + +var xhrSuccessStatus = { + + // File protocol always yields status code 0, assume 200 + 0: 200, + + // Support: IE <=9 only + // #1450: sometimes IE returns 1223 when it should be 204 + 1223: 204 + }, + xhrSupported = jQuery.ajaxSettings.xhr(); + +support.cors = !!xhrSupported && ( "withCredentials" in xhrSupported ); +support.ajax = xhrSupported = !!xhrSupported; + +jQuery.ajaxTransport( function( options ) { + var callback, errorCallback; + + // Cross domain only allowed if supported through XMLHttpRequest + if ( support.cors || xhrSupported && !options.crossDomain ) { + return { + send: function( headers, complete ) { + var i, + xhr = options.xhr(); + + xhr.open( + options.type, + options.url, + options.async, + options.username, + options.password + ); + + // Apply custom fields if provided + if ( options.xhrFields ) { + for ( i in options.xhrFields ) { + xhr[ i ] = options.xhrFields[ i ]; + } + } + + // Override mime type if needed + if ( options.mimeType && xhr.overrideMimeType ) { + xhr.overrideMimeType( options.mimeType ); + } + + // X-Requested-With header + // For cross-domain requests, seeing as conditions for a preflight are + // akin to a jigsaw puzzle, we simply never set it to be sure. + // (it can always be set on a per-request basis or even using ajaxSetup) + // For same-domain requests, won't change header if already provided. + if ( !options.crossDomain && !headers[ "X-Requested-With" ] ) { + headers[ "X-Requested-With" ] = "XMLHttpRequest"; + } + + // Set headers + for ( i in headers ) { + xhr.setRequestHeader( i, headers[ i ] ); + } + + // Callback + callback = function( type ) { + return function() { + if ( callback ) { + callback = errorCallback = xhr.onload = + xhr.onerror = xhr.onabort = xhr.ontimeout = + xhr.onreadystatechange = null; + + if ( type === "abort" ) { + xhr.abort(); + } else if ( type === "error" ) { + + // Support: IE <=9 only + // On a manual native abort, IE9 throws + // errors on any property access that is not readyState + if ( typeof xhr.status !== "number" ) { + complete( 0, "error" ); + } else { + complete( + + // File: protocol always yields status 0; see #8605, #14207 + xhr.status, + xhr.statusText + ); + } + } else { + complete( + xhrSuccessStatus[ xhr.status ] || xhr.status, + xhr.statusText, + + // Support: IE <=9 only + // IE9 has no XHR2 but throws on binary (trac-11426) + // For XHR2 non-text, let the caller handle it (gh-2498) + ( xhr.responseType || "text" ) !== "text" || + typeof xhr.responseText !== "string" ? + { binary: xhr.response } : + { text: xhr.responseText }, + xhr.getAllResponseHeaders() + ); + } + } + }; + }; + + // Listen to events + xhr.onload = callback(); + errorCallback = xhr.onerror = xhr.ontimeout = callback( "error" ); + + // Support: IE 9 only + // Use onreadystatechange to replace onabort + // to handle uncaught aborts + if ( xhr.onabort !== undefined ) { + xhr.onabort = errorCallback; + } else { + xhr.onreadystatechange = function() { + + // Check readyState before timeout as it changes + if ( xhr.readyState === 4 ) { + + // Allow onerror to be called first, + // but that will not handle a native abort + // Also, save errorCallback to a variable + // as xhr.onerror cannot be accessed + window.setTimeout( function() { + if ( callback ) { + errorCallback(); + } + } ); + } + }; + } + + // Create the abort callback + callback = callback( "abort" ); + + try { + + // Do send the request (this may raise an exception) + xhr.send( options.hasContent && options.data || null ); + } catch ( e ) { + + // #14683: Only rethrow if this hasn't been notified as an error yet + if ( callback ) { + throw e; + } + } + }, + + abort: function() { + if ( callback ) { + callback(); + } + } + }; + } +} ); + + + + +// Prevent auto-execution of scripts when no explicit dataType was provided (See gh-2432) +jQuery.ajaxPrefilter( function( s ) { + if ( s.crossDomain ) { + s.contents.script = false; + } +} ); + +// Install script dataType +jQuery.ajaxSetup( { + accepts: { + script: "text/javascript, application/javascript, " + + "application/ecmascript, application/x-ecmascript" + }, + contents: { + script: /\b(?:java|ecma)script\b/ + }, + converters: { + "text script": function( text ) { + jQuery.globalEval( text ); + return text; + } + } +} ); + +// Handle cache's special case and crossDomain +jQuery.ajaxPrefilter( "script", function( s ) { + if ( s.cache === undefined ) { + s.cache = false; + } + if ( s.crossDomain ) { + s.type = "GET"; + } +} ); + +// Bind script tag hack transport +jQuery.ajaxTransport( "script", function( s ) { + + // This transport only deals with cross domain or forced-by-attrs requests + if ( s.crossDomain || s.scriptAttrs ) { + var script, callback; + return { + send: function( _, complete ) { + script = jQuery( " +{% endmacro %} \ No newline at end of file diff --git a/docs/source/_build/html/extra/adpeps.ipeps.ctm.html b/docs/source/_build/html/extra/adpeps.ipeps.ctm.html new file mode 100644 index 0000000..2d91dd3 --- /dev/null +++ b/docs/source/_build/html/extra/adpeps.ipeps.ctm.html @@ -0,0 +1,606 @@ + + + + + + + + adpeps.ipeps.ctm — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.ipeps.ctm

+

Main CTM code

+

The individual site and boundary tensors come in a +special list-type object (TList), which has extra +indexing features, such as periodic boundary +conditions and shift contexts

+

All ncon contractions are defined in contractions.yaml

+
+
+class CTM(tensors, chi, conv_fun=None)[source]
+

CTM class

+
+
Parameters
+
+
+
+
+
+property converged
+

Check convergence with supplied convergence function

+
+ +
+
+show_progress()[source]
+

Print out the current progress

+
+ +
+
+update()[source]
+

Perform an update of all boundary tensors

+
+ +
+ +
+
+do_bottom(ts, chi)[source]
+

Perform bottom CTM move

+
+
Parameters
+
+
+
Returns
+

updated tensors

+
+
Return type
+

ts

+
+
Return type
+

CTMTensors

+
+
+
+ +
+
+do_left(ts, chi)[source]
+

Perform left CTM move

+
+
Parameters
+
+
+
Returns
+

A tuple containing

+
    +

  • tensors (CTMTensors): updated tensors

    • +

  • sl (np.ndarray): singular values of C1 (for convergence)

    • +
+

+
+
Return type
+

Tuple[CTMTensors, ndarray]

+
+
+
+ +
+
+do_right(ts, chi)[source]
+

Perform right CTM move

+
+
Parameters
+
+
+
Returns
+

updated tensors

+
+
Return type
+

ts

+
+
Return type
+

CTMTensors

+
+
+
+ +
+
+do_top(ts, chi)[source]
+

Perform top CTM move

+
+
Parameters
+
+
+
Returns
+

updated tensors

+
+
Return type
+

ts

+
+
Return type
+

CTMTensors

+
+
+
+ +
+
+get_projectors(T1, T2, chi)[source]
+

Contracts the corners together and computes the +projectors by performing an svd

+
+
Parameters
+

T1 (int) –

+
+
+
+ +
+
+get_projectors_bottom(ts, chi)[source]
+

Returns the bottom projectors

+
+
Return type
+

Tuple[ndarray, ndarray, ndarray]

+
+
Parameters
+
+
+
+
+ +
+
+get_projectors_left(ts, chi)[source]
+

Returns the left projectors

+
+
Return type
+

Tuple[ndarray, ndarray, ndarray]

+
+
Parameters
+
+
+
+
+ +
+
+get_projectors_right(ts, chi)[source]
+

Returns the right projectors

+
+
Return type
+

Tuple[ndarray, ndarray, ndarray]

+
+
Parameters
+
+
+
+
+ +
+
+get_projectors_top(ts, chi)[source]
+

Returns the top projectors

+
+
Return type
+

Tuple[ndarray, ndarray, ndarray]

+
+
Parameters
+
+
+
+
+ +
+
+renorm_left(ts, Pl, Plb)[source]
+
+
Return type
+

Tuple[Nested, Nested, Nested]

+
+
Parameters
+
+
+
+
+ +
+
+renormalize(tensors, chi)[source]
+

Performs a CTM iteration +Updates all sites in the unit cell

+
+
Parameters
+
+
+
Returns
+

A tuple containing

+
    +

  • tensors (CTMTensors): updated tensors

    • +

  • S (np.ndarray): singular values of C1 (for convergence)

    • +
+

+
+
Return type
+

Tuple[CTMTensors, ndarray]

+
+
+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/extra/adpeps.ipeps.ipeps.html b/docs/source/_build/html/extra/adpeps.ipeps.ipeps.html new file mode 100644 index 0000000..ba660c5 --- /dev/null +++ b/docs/source/_build/html/extra/adpeps.ipeps.ipeps.html @@ -0,0 +1,552 @@ + + + + + + + + adpeps.ipeps.ipeps — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ +
+ On this page +
+ + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.ipeps.ipeps

+

iPEPS module for optimization with CTM

+

For an example of how to run a simulation see adpeps.simulation.run_ipeps_gs

+

The module is initialized from one of the specific +model files, which return the initial boundary and +site tensors

+

The list of parameters is set to the elements of the +individual site tensors

+

Conventions for indices:

+
+
    +

  • Site tensors:

    +
    A: [phys, right, top, left, bottom]
+
    +
    +
    • +

  • Boundary tensors:

    +
    C1: [right, bottom]
+C2: [left,  bottom]
+C3: [top,   left]
+C4: [right, top]
+T1: [right, left, ket, bra]
+T2: [top,   bottom, ket, bra]
+T3: [right, left, ket, bra]
+T4: [top,   bottom, ket, bra]
+
    +
    +
    • +
+
+

Order of boundary tensors:

+
C1 - T1 - C2
+|    |    |
+T4 - A  - T2
+|    |    |
+C4 - T3 - C3
+
+
+
+
+class iPEPS[source]
+

Initialize the iPEPS based on the settings in +adpeps.ipeps.config

+
+
+converge_boundaries()[source]
+

Performs CTM on the boundary tensors until convergence, +without gradient tracking

+
+ +
+
+fill(A)[source]
+

Fill the site tensors with the elements +The elements can be specified either as a list of (d,D,D,D,D)-dimensional +arrays or one 1-dimensional array of all elements concatenated

+
+ +
+
+numel()[source]
+

Number of variational parameters

+
+ +
+
+parse_elements(elements)[source]
+

Returns site tensors filled with the input elements

+
+ +
+
+run(params)[source]
+

Run the simulation

+
+
Parameters
+

params (jax._src.numpy.lax_numpy.ndarray) – variational parameters

+
+
Returns
+

energy of iPEPS

+
+
Return type
+

ndarray

+
+
+
+ +
+ +
+
+class iPEPS_exci[source]
+

Excited-state variant of the iPEPS class

+
+
+fill(B)[source]
+

Fill the site tensors with the elements +The elements can be specified either as a list of (d,D,D,D,D)-dimensional +arrays or one 1-dimensional array of all elements concatenated

+
+ +
+ +
+
+init_A_tensor(d, D, pattern)[source]
+

The elements will be randomized based on sim_config.seed

+
+ +
+
+init_ctm_tensors(A, Ad)[source]
+

Returns initital boundary T-tensors based on the unit cell tensors and +empty trivial boundary C-tensors

+
+ +
+

iPEPS

+
+
+class iPEPS[source]
+

Initialize the iPEPS based on the settings in +adpeps.ipeps.config

+
+
+run(params)[source]
+

Run the simulation

+
+
Parameters
+

params (jax._src.numpy.lax_numpy.ndarray) – variational parameters

+
+
Returns
+

energy of iPEPS

+
+
Return type
+

ndarray

+
+
+
+ +
+
+converge_boundaries()[source]
+

Performs CTM on the boundary tensors until convergence, +without gradient tracking

+
+ +
+
+numel()[source]
+

Number of variational parameters

+
+ +
+
+parse_elements(elements)[source]
+

Returns site tensors filled with the input elements

+
+ +
+
+fill(A)[source]
+

Fill the site tensors with the elements +The elements can be specified either as a list of (d,D,D,D,D)-dimensional +arrays or one 1-dimensional array of all elements concatenated

+
+ +
+ +
+
+

iPEPS_exci

+
+
+class iPEPS_exci[source]
+

Excited-state variant of the iPEPS class

+
+
+fill(B)[source]
+

Fill the site tensors with the elements +The elements can be specified either as a list of (d,D,D,D,D)-dimensional +arrays or one 1-dimensional array of all elements concatenated

+
+ +
+ +
+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/extra/ipeps.ipeps.html b/docs/source/_build/html/extra/ipeps.ipeps.html new file mode 100644 index 0000000..be03447 --- /dev/null +++ b/docs/source/_build/html/extra/ipeps.ipeps.html @@ -0,0 +1,340 @@ + + + + + + + + iPEPSS — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

iPEPSS

+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/generated/adpeps.ipeps.config.html b/docs/source/_build/html/generated/adpeps.ipeps.config.html new file mode 100644 index 0000000..5532291 --- /dev/null +++ b/docs/source/_build/html/generated/adpeps.ipeps.config.html @@ -0,0 +1,492 @@ + + + + + + + + adpeps.ipeps.config — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.ipeps.config

+

Configuration module for iPEPS simulations

+

These settings will be loaded from a configuration file .yml file +via the from_dict() function

+
+
+from_dict(cfg)[source]
+

Import config from configuration (.yml) file

+
+ +
+
+D: int = None
+

iPEPS bond dimension

+
+ +
+
+base_sim: Optional[str] = None
+

Base simulation

+
+ +
+
+chi: int = None
+

CTM boundary bond dimension

+
+ +
+
+ctm_conv_tol: float = 1e-10
+

CTM convergence criterium (singular values norm difference)

+
+ +
+
+ctm_max_iter: int = 20
+

Maximal number of CTM steps

+
+ +
+
+ctm_min_iter: int = 5
+

Minimal number of CTM steps

+
+ +
+
+disp_level: int = 1
+

no output)

+
+
Type
+

Display level (0

+
+
+
+ +
+
+flush_output: bool = False
+

Passes the flush    = True argument to the builtin print function +when calling the adpeps.utils.printing.print() function

+

Useful when deploying the code to computing clusters and capturing the output +into text files

+
+ +
+
+load_sim: bool = None
+

Load previous (Python) simulation

+
+ +
+
+max_iterations: int = 100
+

Maximum number of optimizer iterations

+
+ +
+
+method: str = None
+

Optimization method

+
+ +
+
+model: str = None
+

Model

+
+ +
+
+model_params: dict = None
+

Model parameters

+
+ +
+
+momentum_path: str = 'Bril1'
+

Momentum path through the BZ

+
+ +
+
+out_prefix: str = ''
+

Optional prefix for the output file of the simulation

+

Example

+

.../{model}_D{D}_X{chi}.npz

+

becomes

+

.../{out_prefix}_{model}_D{D}_X{chi}.npz

+
+ +
+
+pattern: Optional[Iterable] = None
+

Unit cell configuration +Defined as a 2-D array of integers that label the unique sites in the unit +cell.

+

Example

+

A 2x2 unit cell with a [AB, BA]-type pattern is defined by

+
pattern            = [
+    [0, 1],
+    [1, 0]
+]
+
+
+
+ +
+
+resume: bool = False
+

Resume earlier simulation if found

+
+ +
+
+seed: int = 1
+

Random seed for initial state

+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/generated/adpeps.ipeps.ctm.html b/docs/source/_build/html/generated/adpeps.ipeps.ctm.html new file mode 100644 index 0000000..5673031 --- /dev/null +++ b/docs/source/_build/html/generated/adpeps.ipeps.ctm.html @@ -0,0 +1,608 @@ + + + + + + + + adpeps.ipeps.ctm — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.ipeps.ctm

+

Main CTM code

+

The individual site and boundary tensors come in a +special list-type object (TList), which has extra +indexing features, such as periodic boundary +conditions and shift contexts

+

All ncon contractions are defined in contractions.yaml

+
+
+class CTM(tensors, chi, conv_fun=None)[source]
+

CTM class

+
+
Parameters
+
+
+
+
+
+show_progress()[source]
+

Print out the current progress

+
+ +
+
+update()[source]
+

Perform an update of all boundary tensors

+
+ +
+
+property converged
+

Check convergence with supplied convergence function

+
+ +
+ +
+
+do_bottom(ts, chi)[source]
+

Perform bottom CTM move

+
+
Parameters
+
+
+
Returns
+

updated tensors

+
+
Return type
+

ts

+
+
Return type
+

CTMTensors

+
+
+
+ +
+
+do_left(ts, chi)[source]
+

Perform left CTM move

+
+
Parameters
+
+
+
Returns
+

A tuple containing

+
    +

  • tensors (CTMTensors): updated tensors

    • +

  • sl (np.ndarray): singular values of C1 (for convergence)

    • +
+

+
+
Return type
+

Tuple[CTMTensors, ndarray]

+
+
+
+ +
+
+do_right(ts, chi)[source]
+

Perform right CTM move

+
+
Parameters
+
+
+
Returns
+

updated tensors

+
+
Return type
+

ts

+
+
Return type
+

CTMTensors

+
+
+
+ +
+
+do_top(ts, chi)[source]
+

Perform top CTM move

+
+
Parameters
+
+
+
Returns
+

updated tensors

+
+
Return type
+

ts

+
+
Return type
+

CTMTensors

+
+
+
+ +
+
+get_projectors(T1, T2, chi)[source]
+

Contracts the corners together and computes the +projectors by performing an svd

+
+
Parameters
+

T1 (int) –

+
+
+
+ +
+
+get_projectors_bottom(ts, chi)[source]
+

Returns the bottom projectors

+
+
Return type
+

Tuple[ndarray, ndarray, ndarray]

+
+
Parameters
+
+
+
+
+ +
+
+get_projectors_left(ts, chi)[source]
+

Returns the left projectors

+
+
Return type
+

Tuple[ndarray, ndarray, ndarray]

+
+
Parameters
+
+
+
+
+ +
+
+get_projectors_right(ts, chi)[source]
+

Returns the right projectors

+
+
Return type
+

Tuple[ndarray, ndarray, ndarray]

+
+
Parameters
+
+
+
+
+ +
+
+get_projectors_top(ts, chi)[source]
+

Returns the top projectors

+
+
Return type
+

Tuple[ndarray, ndarray, ndarray]

+
+
Parameters
+
+
+
+
+ +
+
+renorm_left(ts, Pl, Plb)[source]
+
+
Return type
+

Tuple[Nested, Nested, Nested]

+
+
Parameters
+
+
+
+
+ +
+
+renormalize(tensors, chi)[source]
+

Performs a CTM iteration +Updates all sites in the unit cell

+
+
Parameters
+
+
+
Returns
+

A tuple containing

+
    +

  • tensors (CTMTensors): updated tensors

    • +

  • S (np.ndarray): singular values of C1 (for convergence)

    • +
+

+
+
Return type
+

Tuple[CTMTensors, ndarray]

+
+
+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/generated/adpeps.ipeps.ipeps.evaluation.html b/docs/source/_build/html/generated/adpeps.ipeps.ipeps.evaluation.html new file mode 100644 index 0000000..aa14e80 --- /dev/null +++ b/docs/source/_build/html/generated/adpeps.ipeps.ipeps.evaluation.html @@ -0,0 +1,364 @@ + + + + + + + + adpeps.ipeps.ipeps.evaluation — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.ipeps.ipeps.evaluation

+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/generated/adpeps.ipeps.ipeps.html b/docs/source/_build/html/generated/adpeps.ipeps.ipeps.html new file mode 100644 index 0000000..3c40ce7 --- /dev/null +++ b/docs/source/_build/html/generated/adpeps.ipeps.ipeps.html @@ -0,0 +1,468 @@ + + + + + + + + adpeps.ipeps.ipeps — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.ipeps.ipeps

+

iPEPS module for optimization with CTM

+

For an example of how to run a simulation see adpeps.simulation.run_ipeps_gs

+

The module is initialized from one of the specific +model files, which return the initial boundary and +site tensors

+

The list of parameters is set to the elements of the +individual site tensors

+

Conventions for indices:

+
+
    +

  • Site tensors:

    +
    A: [phys, right, top, left, bottom]
+
    +
    +
    • +

  • Boundary tensors:

    +
    C1: [right, bottom]
+C2: [left,  bottom]
+C3: [top,   left]
+C4: [right, top]
+T1: [right, left, ket, bra]
+T2: [top,   bottom, ket, bra]
+T3: [right, left, ket, bra]
+T4: [top,   bottom, ket, bra]
+
    +
    +
    • +
+
+

Order of boundary tensors:

+
C1 - T1 - C2
+|    |    |
+T4 - A  - T2
+|    |    |
+C4 - T3 - C3
+
+
+
+
+class iPEPS[source]
+

Initialize the iPEPS based on the settings in +adpeps.ipeps.config

+
+
+converge_boundaries()[source]
+

Performs CTM on the boundary tensors until convergence, +without gradient tracking

+
+ +
+
+fill(A)[source]
+

Fill the site tensors with the elements +The elements can be specified either as a list of (d,D,D,D,D)-dimensional +arrays or one 1-dimensional array of all elements concatenated

+
+ +
+
+numel()[source]
+

Number of variational parameters

+
+ +
+
+parse_elements(elements)[source]
+

Returns site tensors filled with the input elements

+
+ +
+
+run(params)[source]
+

Run the simulation

+
+
Parameters
+

params (jax._src.numpy.lax_numpy.ndarray) – variational parameters

+
+
Returns
+

energy of iPEPS

+
+
Return type
+

ndarray

+
+
+
+ +
+ +
+
+class iPEPS_exci[source]
+

Excited-state variant of the iPEPS class

+
+
+fill(B)[source]
+

Fill the site tensors with the elements +The elements can be specified either as a list of (d,D,D,D,D)-dimensional +arrays or one 1-dimensional array of all elements concatenated

+
+ +
+ +
+
+init_A_tensor(d, D, pattern)[source]
+

The elements will be randomized based on sim_config.seed

+
+ +
+
+init_ctm_tensors(A, Ad)[source]
+

Returns initital boundary T-tensors based on the unit cell tensors and +empty trivial boundary C-tensors

+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/generated/adpeps.ipeps.models.common.html b/docs/source/_build/html/generated/adpeps.ipeps.models.common.html new file mode 100644 index 0000000..52a83e8 --- /dev/null +++ b/docs/source/_build/html/generated/adpeps.ipeps.models.common.html @@ -0,0 +1,342 @@ + + + + + + + + adpeps.ipeps.models.common — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.ipeps.models.common

+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/generated/adpeps.ipeps.models.heisenberg.html b/docs/source/_build/html/generated/adpeps.ipeps.models.heisenberg.html new file mode 100644 index 0000000..e542042 --- /dev/null +++ b/docs/source/_build/html/generated/adpeps.ipeps.models.heisenberg.html @@ -0,0 +1,366 @@ + + + + + + + + adpeps.ipeps.models.heisenberg — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.ipeps.models.heisenberg

+

2D Heisenberg model

+
+
+make_hamiltonian(J=1)[source]
+

Heisenberg model

+
+ +
+
+setup()[source]
+

Returns the Hamiltonian

+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/generated/adpeps.ipeps.models.html b/docs/source/_build/html/generated/adpeps.ipeps.models.html new file mode 100644 index 0000000..9e9cec9 --- /dev/null +++ b/docs/source/_build/html/generated/adpeps.ipeps.models.html @@ -0,0 +1,381 @@ + + + + + + + + adpeps.ipeps.models — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ +
+ On this page +
+ + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.ipeps.models

+
+

Modules

+

Contains all models defined by Hamiltonians as part of this module

+ ++++ + + + + + + + + +

adpeps.ipeps.models.common

adpeps.ipeps.models.heisenberg

2D Heisenberg model

+
+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/generated/adpeps.simulation.html b/docs/source/_build/html/generated/adpeps.simulation.html new file mode 100644 index 0000000..3723b3c --- /dev/null +++ b/docs/source/_build/html/generated/adpeps.simulation.html @@ -0,0 +1,387 @@ + + + + + + + + adpeps.simulation — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ +
+ On this page +
+ + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.simulation

+
+

Modules

+

Module with executable scripts for running the simulations

+
+

Note

+

The simulations are intended to be used by calling the package +directly via python -m adpeps ..., as described in +Getting Started

+
+ ++++ + + + + + + + + +

adpeps.simulation.run_ipeps_exci

Main excited-state executable script

adpeps.simulation.run_ipeps_gs

Main ground-state executable script

+
+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/generated/adpeps.simulation.run_ipeps_exci.html b/docs/source/_build/html/generated/adpeps.simulation.run_ipeps_exci.html new file mode 100644 index 0000000..00a2a35 --- /dev/null +++ b/docs/source/_build/html/generated/adpeps.simulation.run_ipeps_exci.html @@ -0,0 +1,381 @@ + + + + + + + + adpeps.simulation.run_ipeps_exci — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.simulation.run_ipeps_exci

+

Main excited-state executable script

+
+

Note

+

The simulations are intended to be used by calling the package +directly via python -m adpeps ..., as described in +Getting Started

+
+
+
+class iPEPSExciSimulation(config_file, momentum_ix)[source]
+

Simulation class for the excited-state simulation

+

Call an instance of this class directly to start the simulation

+
+ +
+
+run(config_file, momentum_ix)[source]
+

Start the simulation

+
+
Parameters
+
    +

  • config_file (str) – filename of the configuration file

    • +

  • momentum_ix (int) – index of the point in momentum space

    • +
+
+
+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/generated/adpeps.simulation.run_ipeps_gs.html b/docs/source/_build/html/generated/adpeps.simulation.run_ipeps_gs.html new file mode 100644 index 0000000..ead30ae --- /dev/null +++ b/docs/source/_build/html/generated/adpeps.simulation.run_ipeps_gs.html @@ -0,0 +1,440 @@ + + + + + + + + adpeps.simulation.run_ipeps_gs — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.simulation.run_ipeps_gs

+

Main ground-state executable script

+
+

Note

+

The simulations are intended to be used by calling the package +directly via python -m adpeps ..., as described in +Getting Started

+
+
+
+class Objective(peps)[source]
+

Class containing the objective function for the optimizer

+
+
Parameters
+

peps (adpeps.ipeps.ipeps.iPEPS) – iPEPS object to be optimized

+
+
+
+
+jac(v)[source]
+

Computes the vector-Jacobian product (gradient) of the +iPEPS at the current point v in parameter space

+

This function is designed to work with optimizers that make separate +calls to the objective function and the gradient, by caching both.

+
+
Parameters
+

v (jax._src.numpy.lax_numpy.ndarray) – input variational parameters for the site tensors of +the iPEPS

+
+
Returns
+

gradient of the iPEPS with respect to the input parameters v

+
+
Return type
+

ndarray

+
+
+
+ +
+
+out(v)[source]
+

Computes the objective function (energy) of the iPEPS

+

Since many optimizers make separate calls to the objective function +and the gradient, but usually require both results for any given +parameter vector v, this function calls the gradient as well.

+
+
Parameters
+

v – input variational parameters for the site tensors of +the iPEPS

+
+
Returns
+

energy of the iPEPS at the point v in parameter space

+
+
+
+ +
+
+fun
+

Objective function - CTM iterations until convergence +followed by the evaluation of the energy

+
+ +
+
+property gradnrm
+

Norm of the gradient

+
+ +
+
+peps
+

iPEPS object

+
+ +
+ +
+
+run(config_file)[source]
+

Start the simulation

+
+
Parameters
+

config_file (str) – filename of the configuration file

+
+
+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/generated/adpeps.utils.ctmtensors.html b/docs/source/_build/html/generated/adpeps.utils.ctmtensors.html new file mode 100644 index 0000000..14279de --- /dev/null +++ b/docs/source/_build/html/generated/adpeps.utils.ctmtensors.html @@ -0,0 +1,397 @@ + + + + + + + + adpeps.utils.ctmtensors — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.utils.ctmtensors

+

Contains utility class that contains all iPEPS tensors

+
+
+class CTMTensors(A, Ad, Cs=<factory>, Ts=<factory>, B=None, Bd=None, B_Cs=None, B_Ts=None, Bd_Cs=None, Bd_Ts=None, BB_Cs=None, BB_Ts=None, Pl=None, Pr=None, Pt=None, Pb=None, Plb=None, Prb=None, Ptb=None, Pbb=None, observables=<factory>)[source]
+

This is a utility class that contains all tensors related to an iPEPS. +In effect, this forms a representation of the full state, including +the site tensors with variational parameters, the boundary tensors +generated by CTM and the projectors.

+

There are several fields of this dataclass that are generated +automatically, which provide convenient wrappers for the tensors.

+

For example, the CTMTensors.A field returns the site tensors +(contained in a adpeps.utils.tlist.TList)

+
+
Parameters
+
    +

  • A (adpeps.utils.tlist.TList) –

    • +

  • Ad (adpeps.utils.tlist.TList) –

    • +

  • Cs (List[adpeps.utils.tlist.TList]) –

    • +

  • Ts (List[adpeps.utils.tlist.TList]) –

    • +

  • B (adpeps.utils.tlist.TList) –

    • +

  • Bd (adpeps.utils.tlist.TList) –

    • +

  • B_Cs (List[adpeps.utils.tlist.TList]) –

    • +

  • B_Ts (List[adpeps.utils.tlist.TList]) –

    • +

  • Bd_Cs (List[adpeps.utils.tlist.TList]) –

    • +

  • Bd_Ts (List[adpeps.utils.tlist.TList]) –

    • +

  • BB_Cs (List[adpeps.utils.tlist.TList]) –

    • +

  • BB_Ts (List[adpeps.utils.tlist.TList]) –

    • +

  • Pl (adpeps.utils.tlist.TList) –

    • +

  • Pr (adpeps.utils.tlist.TList) –

    • +

  • Pt (adpeps.utils.tlist.TList) –

    • +

  • Pb (adpeps.utils.tlist.TList) –

    • +

  • Plb (adpeps.utils.tlist.TList) –

    • +

  • Prb (adpeps.utils.tlist.TList) –

    • +

  • Ptb (adpeps.utils.tlist.TList) –

    • +

  • Pbb (adpeps.utils.tlist.TList) –

    • +

  • observables (List) –

    • +
+
+
Return type
+

None

+
+
+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/generated/adpeps.utils.empty_tensor.html b/docs/source/_build/html/generated/adpeps.utils.empty_tensor.html new file mode 100644 index 0000000..6efd574 --- /dev/null +++ b/docs/source/_build/html/generated/adpeps.utils.empty_tensor.html @@ -0,0 +1,354 @@ + + + + + + + + adpeps.utils.empty_tensor — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.utils.empty_tensor

+

Contains utility class that represents a ‘zero’ (empty) tensor object

+
+
+class EmptyT[source]
+

Empty tensor utility class, which can be used to represent a +‘zero’ tensor.

+

The operations involving this type of tensor will return the expected +results, such as (Tensor * EmptyT -> EmptyT), removing the need for +checking if a tensor is empty in the part of the code where the +operation is called.

+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/generated/adpeps.utils.html b/docs/source/_build/html/generated/adpeps.utils.html new file mode 100644 index 0000000..461583c --- /dev/null +++ b/docs/source/_build/html/generated/adpeps.utils.html @@ -0,0 +1,394 @@ + + + + + + + + adpeps.utils — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ +
+ On this page +
+ + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.utils

+
+

Modules

+

Utilities module with several convenience functions and classes +used during the simulations

+ ++++ + + + + + + + + + + + + + + + + + + + + +

adpeps.utils.ctmtensors

Contains utility class that contains all iPEPS tensors

adpeps.utils.empty_tensor

Contains utility class that represents a ‘zero’ (empty) tensor object

adpeps.utils.io

IO module with convenience function for forming the localized filenames and foldernames of the relevant configuration files and data files.

adpeps.utils.nested

Contains utility class that represents a collection of tensors of different types, with operations that can be applied to all contained tensors at once

adpeps.utils.printing

Utility module for printing output depending on the verbosity setting adpeps.ipeps.config.disp_level in the configuration file.

adpeps.utils.tlist

List object with additional features, used for storing the iPEPS tensors

+
+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/generated/adpeps.utils.io.html b/docs/source/_build/html/generated/adpeps.utils.io.html new file mode 100644 index 0000000..77201ad --- /dev/null +++ b/docs/source/_build/html/generated/adpeps.utils.io.html @@ -0,0 +1,357 @@ + + + + + + + + adpeps.utils.io — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.utils.io

+

IO module with convenience function for forming the localized filenames +and foldernames of the relevant configuration files and data files.

+
+

Note

+

The input configuration file location can be set via the +CONFIGDIR variable. If it is not set, the default +input folder will be the examples subfolder of the package +root directory

+
+
+

Note

+

The output data location can be set via the DATADIR +variable. If it is not set, the default output folder will be +in the simulations subfolder of the package root directory.

+
+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/generated/adpeps.utils.nested.html b/docs/source/_build/html/generated/adpeps.utils.nested.html new file mode 100644 index 0000000..892d7d2 --- /dev/null +++ b/docs/source/_build/html/generated/adpeps.utils.nested.html @@ -0,0 +1,419 @@ + + + + + + + + adpeps.utils.nested — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.utils.nested

+

Contains utility class that represents a collection of tensors of +different types, with operations that can be applied to all +contained tensors at once

+
+
+class Nested(tensors)[source]
+

This is a helper class for the efficient contraction of variants of tensors, +used in the energy evaluation of excited states

+

A Nested tensor contains the following variants (some may be empty):

+
+
    +

  • tensors[0]: regular tensor (no B or Bd)

    • +

  • tensors[1]: (terms with) a single B tensor

    • +

  • tensors[2]: (terms with) a single Bd tensor

    • +

  • tensors[3]: (terms with) both a B and a Bd tensor

    • +
+
+

When two Nested tensors x,y are contracted, all combinations are taken into account +and the result is again a Nested tensor, filled with the following variants:

+
+
    +

  • tensors[0]: x[0] * y[0]

    • +

  • tensors[1]: x[1] * y[0] + x[0] * y[1]

    • +

  • tensors[2]: x[2] * y[0] + x[0] * y[2]

    • +

  • tensors[3]: x[3] * y[0] + x[2] * y[1] + x[1] * y[2] + x[0] * y[3]

    • +
+
+

By using Nested tensors in a (large) contraction, the many different terms are +resummed on the fly, leading to a potentially reduced computational cost

+
+

Note

+

Most implented functions act as wrappers for the corresponding numpy functions +on the individual tensors

+
+
+
+mult(other, *args)[source]
+
+
Parameters
+
    +

  • other (Union[np.ndarray, Nested, EmptyT]) – other tensor-like object to contract with

    • +

  • *args – arguments to be passed to the contraction method +(np.tensordot)

    • +
+
+
Returns
+

result of the contraction

+
+
Return type
+

res

+
+
Return type
+

Nested

+
+
+
+ +
+
+normalize()[source]
+

Normalize the contained tensors by the largest value +of the first element of self.tensors

+
+ +
+
+transpose(*args)[source]
+

Applies transpose to each contained tensor

+
+
Return type
+

Nested

+
+
+
+ +
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/generated/adpeps.utils.printing.html b/docs/source/_build/html/generated/adpeps.utils.printing.html new file mode 100644 index 0000000..9d2114f --- /dev/null +++ b/docs/source/_build/html/generated/adpeps.utils.printing.html @@ -0,0 +1,361 @@ + + + + + + + + adpeps.utils.printing — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.utils.printing

+

Utility module for printing output depending on the verbosity setting +adpeps.ipeps.config.disp_level in the configuration file.

+
+
+print(*args, level=None, **kwargs)[source]
+

Print output using builtin print if level +<= adpeps.ipeps.config.disp_level

+
+
Parameters
+
    +

  • *args – arbitraty arguments to be passed to builtin print

    • +

  • level (Optional[int]) – verbosity level, determining at which verbosity setting this +should be printed

    • +

  • **kwargs – arbitraty keyword arguments for builtin print

    • +
+
+
+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/generated/adpeps.utils.tlist.html b/docs/source/_build/html/generated/adpeps.utils.tlist.html new file mode 100644 index 0000000..1b7d9a5 --- /dev/null +++ b/docs/source/_build/html/generated/adpeps.utils.tlist.html @@ -0,0 +1,421 @@ + + + + + + + + adpeps.utils.tlist — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.utils.tlist

+

List object with additional features, used for storing +the iPEPS tensors

+

Items in the list can be accessed by either a linear index +or a (i,j) double index, where i and j will be automatically +taken modulo the unit cell size (i.e. i = i % n_x)

+

Additionally, convenience functions that work on tensors can +be defined for the whole list, e.g. conj()

+
+
+cur_loc(*loc)[source]
+

Shift the locations of the tensors relative to a +new zero (loc) while in this context

+
+
Parameters
+

loc (int) – shifts (x,y)

+
+
+

Example

+
>>> l = TList([[1,2], [3,4]])
+>>> l[0,0]
+1
+>>> with cur_loc(1,0):
+>>>     l[0,0]
+2
+>>>     l[0,1]
+4
+>>> l[0,0]
+1
+
+
+

Note that this applies to ALL TList objects while +inside the context

+
+ +
+
+hold_write(*lists)[source]
+

Hold off on writing to the list while +inside the context

+
+
Parameters
+

lists (adpeps.utils.tlist.TList) – one or more TList objects that should have the writing +action delayed until the context is disabled

+
+
+

Example

+
>>> l = TList([[1,2], [3,4]])
+>>> with hold_write(l):
+>>>    l[0,0] = 100
+>>>    l[0,0]
+1
+>>> l[0,0]
+100
+
+
+
+ +
+
+set_pattern(pattern)[source]
+

Set pattern for all new TLists that are created while +the context is active

+
+
Parameters
+

pattern –

+
+
+
+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/genindex.html b/docs/source/_build/html/genindex.html new file mode 100644 index 0000000..9b475ca --- /dev/null +++ b/docs/source/_build/html/genindex.html @@ -0,0 +1,816 @@ + + + + + + + + Index — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ + +

Index

+ +
+ A + | B + | C + | D + | E + | F + | G + | H + | I + | J + | L + | M + | N + | O + | P + | R + | S + | T + | U + +
+

A

+ + + +
    +
  • + adpeps.ipeps.config + +
    • +
  • + adpeps.ipeps.ctm + +
    • +
  • + adpeps.ipeps.ipeps + +
    • +
  • + adpeps.ipeps.ipeps.evaluation + +
    • +
  • + adpeps.ipeps.models + +
    • +
  • + adpeps.ipeps.models.common + +
    • +
  • + adpeps.ipeps.models.heisenberg + +
    • +
  • + adpeps.simulation + +
    • +
  • + adpeps.simulation.run_ipeps_exci + +
    • +
    +
  • + adpeps.simulation.run_ipeps_gs + +
    • +
  • + adpeps.utils + +
    • +
  • + adpeps.utils.ctmtensors + +
    • +
  • + adpeps.utils.empty_tensor + +
    • +
  • + adpeps.utils.io + +
    • +
  • + adpeps.utils.nested + +
    • +
  • + adpeps.utils.printing + +
    • +
  • + adpeps.utils.tlist + +
    • +
+ +

B

+ + +
+ +

C

+ + + +
+ +

D

+ + + +
+ +

E

+ + +
+ +

F

+ + + +
+ +

G

+ + + +
+ +

H

+ + +
+ +

I

+ + + +
+ +

J

+ + +
+ +

L

+ + +
+ +

M

+ + + +
+ +

N

+ + + +
+ +

O

+ + + +
+ +

P

+ + + +
+ +

R

+ + + +
+ +

S

+ + + +
+ +

T

+ + +
+ +

U

+ + +
+ + + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/index.html b/docs/source/_build/html/index.html new file mode 100644 index 0000000..1cac0da --- /dev/null +++ b/docs/source/_build/html/index.html @@ -0,0 +1,438 @@ + + + + + + + + AD-PEPS’s documentation — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ +
+ On this page +
+ + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

AD-PEPS’s documentation

+

The AD-PEPS Python package is intended as a example of an implementation of iPEPS ground-state and excited-state algorithms using Automatic Differentiation, as described in <paper> +As such, the code is meant to illustrate the workings of the algorithms described the paper. +For real applications, this code would likely need to be further adapted and optimized, however the package is a complete implementation and can directly be used for simple calculations.

+
+ +
+
+

Reference

+ ++++ + + + + + + + + + + + + + + + + + + + + +

ipeps.ipeps

iPEPS module for optimization with CTM

ipeps.config

Configuration module for iPEPS simulations

ipeps.ctm

Main CTM code

ipeps.models

Contains all models defined by Hamiltonians as part of this module

simulation

Module with executable scripts for running the simulations

utils

Utilities module with several convenience functions and classes used during the simulations

+
+
+
+

Indices and tables

+ +
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/ipeps.html b/docs/source/_build/html/ipeps.html new file mode 100644 index 0000000..d2bb43e --- /dev/null +++ b/docs/source/_build/html/ipeps.html @@ -0,0 +1,364 @@ + + + + + + + + adpeps.ipeps — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

adpeps.ipeps

+
+
+ ++++ + + + + + +

adpeps.ipeps.config

Configuration module for iPEPS simulations

+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
+

+Created using Sphinx 3.5.4.
+

+
+ +
+
+ + \ No newline at end of file diff --git a/docs/source/_build/html/notes/example.html b/docs/source/_build/html/notes/example.html new file mode 100644 index 0000000..ed9e92a --- /dev/null +++ b/docs/source/_build/html/notes/example.html @@ -0,0 +1,469 @@ + + + + + + + + Example: ground state — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
+
+ + + + +
+ + +
+ + + +
+ +
+ +
+ + +
+ + + + + + +
+ +
+ +
+

Example: ground state

+

The package includes an example configuration for a ground-state simulation of the 2D Heisenberg model, defined by the Hamiltonian

+
+\[H = J \sum_i S_i \cdot S_{i+1}~.\]
+

The configuration file examples/heis_D2.yaml contains the following:

+
# Base configuration file for iPEPS simulation
+# See the individual config modules for more information
+
+# Simulation options
+# -> ipeps/config.py
+D:             2
+chi:           41
+model:         'heisenberg'
+
+# (Ground state) Optimizer
+method:        'L-BFGS-B'
+
+# If an existing state is loaded in the model initialization, 
+# the seed controls the random (small) noise that is added to 
+# the site tensors
+seed:          1
+
+# Prefix for output file
+out_prefix:
+
+# Resume earlier simulation if found
+resume:        True
+
+model_params:
+  J:           1
+
+# Set to 0 to suppress all output besides printing each step
+disp_level:    2
+
+# CTM convergence criterium (singular values norm difference)
+ctm_conv_tol:  1.e-6
+
+# Minimal number of CTM steps
+ctm_min_iter:  4
+
+# Maximal number of CTM steps
+ctm_max_iter:  8
+
+# Flush output (prints with print(*args, flush=True))
+flush_output:  True
+
+# Unit cell pattern (Neel order)
+pattern:
+  [
+    [0,1],
+    [1,0],
+  ]
+
+
+

This configures a simulation with bond dimension D=2 and boundary bond dimension chi=40, using the model defined in adpeps.ipeps.models.heisenberg.

+

Now the simulation can be started by calling the adpeps module with the name of this configuration file:

+
>>> python -m adpeps gs 'heis_D2'
+WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)
+Namespace(config_file='heis_D2', sim_mode='gs', version=False)
+Running ground-state sim
+...
+
+
+

The simulation will continue to run and you should see output similar to this:

+
...
+Performing CTM pre-steps without tracking
+  | CTM step 1 conv: 4.935e-03 time: 3.17 obj: -0.658758
+  | CTM step 2 conv: 7.918e-04 time: 3.74 obj: -0.659550
+  | CTM step 3 conv: 1.234e-05 time: 6.42 obj: -0.659562
+Performing CTM
+  | CTM step 1 conv: 3.171e-07 time: 8.8 obj: -0.659563
+  | CTM step 2 conv: 2.108e-08 time: 4.07 obj: -0.659563
+  | CTM step 3 conv: 8.173e-09 time: 2.93 obj: -0.659563
+Energy: -0.6595625579862193
+...
+
+
+

The first cycle of iterations are not taken into account in the gradient computation, but make sure that the CTM iterations with gradient tracking start from some reasonably converged boundary tensors in order to avoid instabilities with initial CTM steps.

+
+

Note

+

The convergence rate of the CTM depends on the variational parameters of the iPEPS and the settings of the simulation. +Generally the convergence improves as the simulation approaches the optimum.

+
+

Whenever a step in the optimization has completed (this could take more than one cycle of CTM iterations depending on the type of optimizer), the module will output a summary of the steps so far:

+
...
+# ======================== #
+#      Step completed      #
+# ======================== #
+
+Step   0  E: -0.376468389894  |grad|: 1.2103482
+Step   1  E: -0.505252956403  |grad|: 0.19064889
+Step   2  E: -0.517432085607  |grad|: 0.10910666
+Step   3  E: -0.578045570568  |grad|: 0.081472534
+Step   4  E: -0.589074339197  |grad|: 0.089438567
+Step   5  E: -0.597590746400  |grad|: 0.15282526
+Step   6  E: -0.612205652457  |grad|: 0.076385807
+Step   7  E: -0.628079118387  |grad|: 0.0684857
+Step   8  E: -0.642200026835  |grad|: 0.097849544
+Step   9  E: -0.649553574703  |grad|: 0.066648727
+Step  10  E: -0.653909263824  |grad|: 0.0264237
+Step  11  E: -0.655389076620  |grad|: 0.016836624
+Step  12  E: -0.656585389308  |grad|: 0.016954703
+Step  13  E: -0.657797020335  |grad|: 0.020011479
+Step  14  E: -0.658174755217  |grad|: 0.033691114
+Step  15  E: -0.659083649568  |grad|: 0.012202327
+Step  16  E: -0.659365377610  |grad|: 0.0064214407
+Step  17  E: -0.659562557986  |grad|: 0.007503111
+...
+
+
+

The simulation will continue until adpeps.ipeps.config.max_iterations has been reached. +At any point the simulation can be stopped and continued later by restarting the module.

+
+

Note

+

In case you would like the simulation to continue from an earlier saved simulation with the same configuration file, make sure to set adpeps.ipeps.config.resume = True

+
+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
+

+ © Copyright 2021, Boris Ponsioen.
+

+
+ +
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+Created using Sphinx 3.5.4.
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+ + \ No newline at end of file diff --git a/docs/source/_build/html/notes/example2.html b/docs/source/_build/html/notes/example2.html new file mode 100644 index 0000000..92c1eec --- /dev/null +++ b/docs/source/_build/html/notes/example2.html @@ -0,0 +1,485 @@ + + + + + + + + Example: excitations — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + +
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+ + + + +
+ + +
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+ +
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+ + +
+ + + + + + +
+ +
+ +
+

Example: excitations

+
+

Note

+

This example continues from the ground-state example and requires an optimized ground state to start from.

+
+

Here we demonstrates how to use the adpeps package for computing excited states of the 2D Heisenberg model.

+

The configuration file examples/heis_D2_exci.yaml contains the following settings:

+
# Base configuration file for iPEPS simulation
+# See the individual config modules for more information
+
+# Simulation options
+# -> ipeps/config.py
+D:             2
+chi:           40
+model:         'heisenberg'
+
+# Prefix for output file
+out_prefix:
+
+# Resume earlier simulation if found
+resume:        True
+
+model_params:
+  J:           1
+
+# Set to 0 to suppress all output besides printing each step
+disp_level:    1
+
+# CTM convergence criterium (singular values norm difference)
+ctm_conv_tol:  1.e-6
+
+# Minimal number of CTM steps
+ctm_min_iter:  4
+
+# Maximal number of CTM steps
+ctm_max_iter:  20
+
+# Flush output (prints with print(*args, flush=True))
+flush_output:  True
+
+# Unit cell pattern (Neel order)
+pattern:
+  [
+    [0,1],
+    [1,0],
+  ]
+
+# Excitations
+momentum_path: 'Bril1'
+
+
+

Note that many of the options are the same as for the ground-state simulation, with the addition of the adpeps.ipeps.config.momentum_path setting, which controls which path through the Brillouin zone will be taken.

+

In the configuration for excited states you do not explicitly set the momentum, but choose a preset path of points in momentum space and pass the index for each simulation.

+

If we now start the simulation, we get the following response:

+
>>> python -m adpeps exci 'heis_D2_exci' --p_ix=1
+...
+Running excited-state sim
+...
+Base file .../exci/heisenberg_D2_X40.base.npz not found.
+Prepare the simulation first by running with option '-i'
+
+
+

What happened is that we first need to make some preparations for the simulation. +For excited-state simulations, we require the following:

+
+
    +

  1. Well-converged CTM boundary tensors

    2. +

  2. A basis for the excited-state tensors, orthogonal to the ground state

    3. +
+
+

The preparations for the simulation need to be performed only once, resulting in a base simulation file that will be used by the simulations for every momentum.

+
>>> python -m adpeps exci 'heis_D2_exci' -i
+...
+Running excited-state sim
+...
+  | CTM step 1 conv: 1.036e-01 time: 3.64 obj: -0.665574
+  | CTM step 2 conv: 3.137e-03 time: 4.23 obj: -0.662436
+  | CTM step 3 conv: 7.887e-05 time: 4.0 obj: -0.662515
+  | CTM step 4 conv: 1.388e-06 time: 2.2 obj: -0.662514
+  | CTM step 5 conv: 2.455e-07 time: 1.35 obj: -0.662514
+  | CTM step 6 conv: 3.044e-08 time: 1.35 obj: -0.662514
+  | CTM step 7 conv: 4.673e-09 time: 1.37 obj: -0.662514
+  | CTM step 8 conv: 4.467e-10 time: 1.36 obj: -0.662514
+  | CTM step 9 conv: 5.029e-11 time: 1.35 obj: -0.662514
+  | CTM step 10 conv: 5.612e-11 time: 1.38 obj: -0.662514
+  | CTM step 11 conv: 2.801e-11 time: 1.36 obj: -0.662514
+  | CTM step 12 conv: 1.204e-11 time: 1.65 obj: -0.662514
+  | CTM step 13 conv: 4.936e-12 time: 1.42 obj: -0.662514
+  | CTM step 14 conv: 1.989e-12 time: 1.39 obj: -0.662514
+GS norm 3.5890188873039093
+GS norm 1.0
+Substracting -0.33125703308289145 from Hamiltonian
+
+
+

Several steps have been performed: first a full CTM contraction of the ground-state network, followed by a normalization of the ground-state tensors. +Then the Hamiltonian is shifted by the ground-state energy expectation value, in order for the excitations to have energies relative to the ground state. +Finally, the basis is prepared and we have everything to get started.

+
>>> python -m adpeps exci 'heis_D2_exci' --p_ix=0
+...
+Running excited-state sim
+...
+Starting simulation of basis vector 1/62
+Performing CTM
+  | CTM step 1 conv: 4.236e+00 time: 3.19 obj: 5.173629
+  | CTM step 2 conv: 3.539e-02 time: 1.38 obj: 5.138237
+  | CTM step 3 conv: 6.139e-03 time: 1.27 obj: 5.132099
+  | CTM step 4 conv: 2.116e-04 time: 1.24 obj: 5.132310
+  | CTM step 5 conv: 6.148e-05 time: 1.28 obj: 5.132249
+  | CTM step 6 conv: 3.704e-04 time: 1.25 obj: 5.131879
+  | CTM step 7 conv: 2.493e-04 time: 1.25 obj: 5.131629
+Energies: 0.04418993415167889 1.5450126399606245e-10
+Norm: 0.008611083119254162
+==========
+Finished basis vector 1/62
+-
+Starting simulation of basis vector 2/62
+Performing CTM
+  | CTM step 1 conv: 2.004e+00 time: 0.99 obj: 3.335621
+  | CTM step 2 conv: 6.150e-02 time: 1.26 obj: 3.397117
+  | CTM step 3 conv: 2.017e-02 time: 1.28 obj: 3.376950
+  | CTM step 4 conv: 3.838e-03 time: 1.26 obj: 3.380788
+  | CTM step 5 conv: 3.650e-04 time: 1.3 obj: 3.380423
+  | CTM step 6 conv: 1.246e-03 time: 1.29 obj: 3.381669
+  | CTM step 7 conv: 1.288e-03 time: 1.31 obj: 3.380380
+Energies: 0.4285335373465171 1.5450126399606245e-10
+Norm: 0.12679967208649232
+==========
+Finished basis vector 2/62
+...
+
+
+

In this version of the algorithm, the full energy and norm overlap matrices will be computed. +Each of the basis vectors, as seen in the output above, is used as input in a separate CTM summation and the program will continue to run until all basis vectors have been used.

+
+ + +
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+ © Copyright 2021, Boris Ponsioen.
+

+
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+Created using Sphinx 3.5.4.
+

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+ + \ No newline at end of file diff --git a/docs/source/_build/html/notes/install.html b/docs/source/_build/html/notes/install.html new file mode 100644 index 0000000..3282054 --- /dev/null +++ b/docs/source/_build/html/notes/install.html @@ -0,0 +1,388 @@ + + + + + + + + Installation — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+ On this page +
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Installation

+

The quickest way of installing the adpeps package is to clone the repository

+
git clone <repo>
+
+
+ +
+

Method 2: pip

+

The package can also be installed via pip:

+
cd ad-peps
+pip install -e .
+
+
+
+
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+ © Copyright 2021, Boris Ponsioen.
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+Created using Sphinx 3.5.4.
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+ + \ No newline at end of file diff --git a/docs/source/_build/html/notes/start.html b/docs/source/_build/html/notes/start.html new file mode 100644 index 0000000..6eeb332 --- /dev/null +++ b/docs/source/_build/html/notes/start.html @@ -0,0 +1,453 @@ + + + + + + + + Getting Started — AD-PEPS documentation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+ On this page +
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+ +
+

Getting Started

+
+

General

+

The main starting point for running simulations with the adpeps package is by loading the module directly via python -m adpeps.

+

For both ground-state and excited-state simulations the configuration can be set via configuration .yaml files. +Each option in the configuration file corresponds to an attribute of the adpeps.ipeps.config module.

+

The first argument for the module is the simulation mode (ground-state or excited-state):

+
python -m adpeps {gs,exci} ...
+
+
+
+

Note

+

The input configuration file location can be set via the +CONFIGDIR variable. If it is not set, the default +input folder will be the examples subfolder of the package +root directory

+
+
+

Note

+

The output data location can be set via the DATADIR +variable. If it is not set, the default output folder will be +in the simulations subfolder of the package root directory.

+
+
+
+

Ground states

+

For ground-state simulations, the only required argument is the configuration file.

+
usage: python -m adpeps gs [-h] config_file
+
+
+
+

Positional Arguments

+
+
config_file
+

Configuration (.yml) file for the simulation options

+
+
+
+
+
+

Excited states

+

For excited-state simulations, the first argument is again the name of a configuration file (note that the relevant options are different for excited-state simulations), and furthermore the momentum index -p is required.

+

The momentum index refers to a point in momentum space \((k_x, k_y)\) defined in a specific path through the Brillouin zone. +The corresponding momentum path can be set via the adpeps.ipeps.config.momentum_path option. +By default, the ‘Bril1’ path is taken, which follows the cut along high symmetry points \((\pi,0) - (\pi,\pi) - (\pi/2,\pi/2) - (0,0) - (\pi,0) - (\pi/2,\pi/2)\)

+
usage: python -m adpeps exci [-h] [-p MOMENTUM_IX] [-e] [-i]
+                             config_file
+
+
+
+

Positional Arguments

+
+
config_file
+

config file of excited-state simulation

+
+
+
+
+

Named Arguments

+
+
-p, --p_ix
+

momentum index

+
+
-e, --eval
+

Prepare excitation base

+
+
-i, --init
+

Prepare excitation base

+
+
+
+
+
+ + +
+ + +
+ + +
+
+ + + + +
+
+ +
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+ © Copyright 2021, Boris Ponsioen.
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+Created using Sphinx 3.5.4.
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currentmodule:: {{ fullname }} + +.. autoclass:: {{ fullname }} + :members: + :member-order: bysource + +.. .. autoclass:: {{ fullname }} + +.. {% if methods %} +.. .. rubric:: Methods + +.. .. autosummary:: +.. :toctree: + +.. {% for method in methods %} +.. {{ method }} +.. {% endfor %} + +.. {% endif %} + +.. {% if attributes %} +.. .. rubric:: Attributes + +.. .. autosummary:: +.. :toctree: + +.. {% for attribute in attributes %} +.. {{ attribute }} +.. {% endfor %} + +.. {% endif %} + diff --git a/docs/source/_templates/autosummary/module.rst b/docs/source/_templates/autosummary/module.rst new file mode 100644 index 0000000..d0c8575 --- /dev/null +++ b/docs/source/_templates/autosummary/module.rst @@ -0,0 +1,27 @@ +{{ fullname | escape | underline }} + +.. currentmodule:: {{ fullname }} + +.. module:: {{ fullname }} + +{% if modules %} +Modules +------- + +.. automodule:: {{ fullname }} + +.. autosummary:: + :toctree: + + {% for module in modules %} + {{ module }} + {% endfor %} + +{% else %} + +.. automodule:: {{ fullname }} + :members: + :member-order: groupwise + +{% endif %} + diff --git a/docs/source/_templates/autosummary/module2.rst b/docs/source/_templates/autosummary/module2.rst new file mode 100644 index 0000000..7f8ea09 --- /dev/null +++ b/docs/source/_templates/autosummary/module2.rst @@ -0,0 +1,59 @@ +{{ fullname | escape | underline }} + +Description +-------------- + +.. currentmodule:: {{ fullname | escape }} + +.. automodule:: {{ fullname | escape }} + + {% if attributes %} + Attributes + ----------- + + .. autosummary:: + :toctree: + + {% for attribute in attributes %} + {{ attribute }} + {% endfor %} + + {% endif %} + + {% if modules %} + Modules + ------- + + .. autosummary:: + :toctree: + + {% for module in modules %} + {{ module }} + {% endfor %} + + {% endif %} + + {% if classes %} + Classes + ------- + .. autosummary:: + :toctree: + :nosignatures: + + {% for class in classes %} + {{ class }} + {% endfor %} + + {% endif %} + + {% if functions %} + Functions + --------- + .. autosummary:: + :toctree: + + {% for function in functions %} + {{ function }} + {% endfor %} + + {% endif %} diff --git a/docs/source/_templates/autosummary/module_o.rst b/docs/source/_templates/autosummary/module_o.rst new file mode 100644 index 0000000..8ab96bc --- /dev/null +++ b/docs/source/_templates/autosummary/module_o.rst @@ -0,0 +1,58 @@ +{{ fullname | escape | underline }} + +.. currentmodule:: {{ fullname | escape }} + +.. automodule:: {{ fullname }} + :members: + +{% if modules %} +Modules +------- + +.. autosummary:: + :toctree: + + {% for module in modules %} + {{ module }} + {% endfor %} + +{% else %} + +{% if classes %} +Classes +------- +{% for class in classes %} +{{ class | escape | underline }} + .. autoclass:: {{ class }} + :members: + :member-order: bysource +{% endfor %} +{% endif %} + +{% if attributes %} +Attributes +----------- + +{% for attribute in attributes %} +.. autoattribute:: {{ attribute }} +{% endfor %} + +{% endif %} + +{% if functions %} +Functions +--------- + +.. .. automodule:: {{ fullname}} +.. :members: + +{% for function in functions %} +.. autofunction:: {{ function }} + +.. {% endfor %} + +{% endif %} + + +{% endif %} + diff --git a/docs/source/_templates/autosummary/modules.rst b/docs/source/_templates/autosummary/modules.rst new file mode 100644 index 0000000..f58896e --- /dev/null +++ b/docs/source/_templates/autosummary/modules.rst @@ -0,0 +1,58 @@ +{{ fullname | escape | underline }} + +Description +----------- + +.. currentmodule:: {{ fullname | escape }} + +.. automodule:: {{ fullname | escape }} + + {% if attributes %} + Attributes + ------- + + .. autosummary:: + :toctree: generated + + {% for attribute in attributes %} + {{ attribute }} + {% endfor %} + + {% endif %} + + {% if modules %} + Modules + ------- + + .. autosummary:: + :toctree: generated + + {% for module in modules %} + {{ module }} + {% endfor %} + + {% endif %} + + {% if classes %} + Classes + ------- + .. autosummary:: + :toctree: generated + + {% for class in classes %} + {{ class }} + {% endfor %} + + {% endif %} + + {% if functions %} + Functions + --------- + .. autosummary:: + :toctree: generated + + {% for function in functions %} + {{ function }} + {% endfor %} + + {% endif %} diff --git a/docs/source/_templates/sidebar-nav-bs.html b/docs/source/_templates/sidebar-nav-bs.html new file mode 100644 index 0000000..7514049 --- /dev/null +++ b/docs/source/_templates/sidebar-nav-bs.html @@ -0,0 +1,10 @@ + diff --git a/docs/source/conf.py b/docs/source/conf.py new file mode 100644 index 0000000..44cf9a0 --- /dev/null +++ b/docs/source/conf.py @@ -0,0 +1,90 @@ +# Configuration file for the Sphinx documentation builder. +# +# This file only contains a selection of the most common options. For a full +# list see the documentation: +# https://www.sphinx-doc.org/en/master/usage/configuration.html + +# import sphinx_readable_theme +# import sphinx_bootstrap_theme +# import sphinx_rtd_theme + +# -- Path setup -------------------------------------------------------------- + +# If extensions (or modules to document with autodoc) are in another directory, +# add these directories to sys.path here. If the directory is relative to the +# documentation root, use os.path.abspath to make it absolute, like shown here. +# +import os +import sys +sys.path.insert(0, os.path.abspath('..')) + + +# -- Project information ----------------------------------------------------- + +project = 'AD-PEPS' +copyright = '2021, Boris Ponsioen' +author = 'Boris Ponsioen' + + +# -- General configuration --------------------------------------------------- + +# Add any Sphinx extension module names here, as strings. They can be +# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom +# ones. +extensions = [ + 'sphinx.ext.autodoc', + 'sphinx.ext.autosummary', + 'sphinx_autodoc_typehints', + 'sphinxarg.ext', + 'sphinx.ext.viewcode', + 'sphinx.ext.napoleon', + # 'sphinx_autodoc_typehints', + # 'sphinx_autodoc_napoleon_typehints', + # 'sphinx_rtd_theme', +] + +# Add any paths that contain templates here, relative to this directory. +templates_path = ['_templates'] + +# List of patterns, relative to source directory, that match files and +# directories to ignore when looking for source files. +# This pattern also affects html_static_path and html_extra_path. +exclude_patterns = ['_build', 'Thumbs.db', '.DS_Store'] + +autosummary_generate = True +autoclass_content = "both" +add_module_names = False +napoleon_attr_annotations = True + +autodoc_typehints = "description" + +autodoc_type_aliases = {'Tensor_like': 'adpeps.types.TensorType'} + +# -- Options for HTML output ------------------------------------------------- + +# html_theme_path = [sphinx_readable_theme.get_html_theme_path()] +# html_theme_path = sphinx_bootstrap_theme.get_html_theme_path() + +# The theme to use for HTML and HTML Help pages. See the documentation for +# a list of builtin themes. +# +# html_theme = 'alabaster' +# html_theme = 'readable' +# html_theme = 'bootstrap' +# html_theme = "sphinx_rtd_theme" +# html_theme = 'sphinx_material' +# # Material theme options (see theme.conf for more information) +# html_theme_options = { +# 'globaltoc_collapse': False, +# # If True, show hidden TOC entries +# 'globaltoc_includehidden': True, +# } +html_theme = "pydata_sphinx_theme" +html_theme_options = { + "show_prev_next": False +} + +# Add any paths that contain custom static files (such as style sheets) here, +# relative to this directory. They are copied after the builtin static files, +# so a file named "default.css" will overwrite the builtin "default.css". +html_static_path = ['_static'] diff --git a/docs/source/example.ipynb b/docs/source/example.ipynb new file mode 100644 index 0000000..8d1980d --- /dev/null +++ b/docs/source/example.ipynb @@ -0,0 +1,1002 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import sym_tensor\n", + "import torch\n", + "import numpy as np\n", + "import sym_tensor.ops as st_ops" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Contents\n", + "(Links work only when you run the notebook)\n", + "- [Tensor basics](#Tensor-basics)\n", + "- [U(1) symmetry](#U(1)-symmetry)\n", + "- [Differentiable programming](#Differentiable-programming)\n", + "- [Gradient descent demo](#Gradient-descent-demo) (new)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Tensor basics\n", + "A symmetric tensor is defined by its elements, quantum numbers (`charges`) and symmetry group (`ZN`). \n", + "To initialize a `Z2`-symmetric matrix, run" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2-D SymTensor (4, 4):\n", + "| Free elements: 8 / 16 (50% of total) in 2 blocks \n", + "| ZN: 2 \n", + "| Totalcharge: 0 \n", + "| Readorder: [0, 1] \n", + " \n", + "Quantum numbers on each leg:\n", + " +-----+\n", + "( 0): [ 0, 1 ] --| |-- ( 1): [ 0, 1 ]\n", + " +-----+\n", + "\n" + ] + } + ], + "source": [ + "charges = [\n", + " [\n", + " [0,2],\n", + " [1,2]\n", + " ],[\n", + " [0,2],\n", + " [1,2]\n", + " ]\n", + "]\n", + "\n", + "# Use elements=None to initialize with random elements\n", + "T = sym_tensor.newtensor(elements=None, charges=charges, ZN=2)\n", + "print(T)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A `Z2`-symmetric matrix can be represented in block-diagonal form; in this case by two 2x2 blocks. Every symmetric tensor can be reshaped to a block-diagonal matrix by fusing indices together:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "tensor([[0.8911, 0.0553],\n", + " [0.0132, 0.3870]])\n", + "tensor([[0.9066, 0.0323],\n", + " [0.6183, 0.6328]])\n", + "tensor([[0.8911, 0.0553, 0.0000, 0.0000],\n", + " [0.0132, 0.3870, 0.0000, 0.0000],\n", + " [0.0000, 0.0000, 0.9066, 0.0323],\n", + " [0.0000, 0.0000, 0.6183, 0.6328]])\n" + ] + } + ], + "source": [ + "# Choose [0] as the left index, [1] as the right index and 'n' (irrelevant for Z2)\n", + "blocks, *meta = T.get_blocks(left_legs=[0], right_legs=[1], side='n') # The metadata is necessary to reverse the reshaping\n", + "for b in blocks:\n", + " print(b)\n", + "T_full = T.to_full() # Embed the blocks in a matrix (only Z2 matrices for now supported)\n", + "print(T_full)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To multiply tensors together, there are several options:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "tensor([[0.7947, 0.0707, 0.0000, 0.0000],\n", + " [0.0169, 0.1505, 0.0000, 0.0000],\n", + " [0.0000, 0.0000, 0.8420, 0.0497],\n", + " [0.0000, 0.0000, 0.9518, 0.4204]])\n", + "tensor([[0.7947, 0.0707, 0.0000, 0.0000],\n", + " [0.0169, 0.1505, 0.0000, 0.0000],\n", + " [0.0000, 0.0000, 0.8420, 0.0497],\n", + " [0.0000, 0.0000, 0.9518, 0.4204]])\n", + "tensor([[0.7947, 0.0707, 0.0000, 0.0000],\n", + " [0.0169, 0.1505, 0.0000, 0.0000],\n", + " [0.0000, 0.0000, 0.8420, 0.0497],\n", + " [0.0000, 0.0000, 0.9518, 0.4204]])\n", + "tensor([[0.7947, 0.0707, 0.0000, 0.0000],\n", + " [0.0169, 0.1505, 0.0000, 0.0000],\n", + " [0.0000, 0.0000, 0.8420, 0.0497],\n", + " [0.0000, 0.0000, 0.9518, 0.4204]])\n" + ] + } + ], + "source": [ + "T2 = T.copy() # No shared memory\n", + "\n", + "# Ncon\n", + "res = st_ops.ncon([T,T2], ([-1,1],[1,-2]))\n", + "print(res.to_full())\n", + "\n", + "# Mult (arguments are the legs to be contracted on each tensor)\n", + "res = T.mult(T2, [1], [0])\n", + "print(res.to_full())\n", + "\n", + "# Matrix product (in general: contract over last index of T and first index of T2)\n", + "res = T @ T2\n", + "print(res.to_full())\n", + "\n", + "# Full result\n", + "print(T_full @ T_full)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "tensor([[0.8911, 0.0553, 0.0000, 0.0000],\n", + " [0.0132, 0.3870, 0.0000, 0.0000],\n", + " [0.0000, 0.0000, 0.9066, 0.0323],\n", + " [0.0000, 0.0000, 0.6183, 0.6328]])\n", + "True\n" + ] + } + ], + "source": [ + "# SVD (left_legs, right_legs, number of singular values to keep, absorb s left/right/not)\n", + "u,s,v = T.svd([0], [1], n=np.inf, absorb='n')\n", + "print((u@s@v.t()).to_full()) # Equal to T itself\n", + "print(T.allclose(u@s@v.t()))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## U(1) symmetry\n", + "The continuous `U(1)` symmetry can be approximated by a `ZN` symmetry with large enough `N`. Initialize a tensor like:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3-D SymTensor (2, 3, 3):\n", + "| Free elements: 4 / 18 (22% of total) in 4 blocks \n", + "| ZN: 36 \n", + "| Totalcharge: 0 \n", + "| Readorder: [0, 1, 2] \n", + " \n", + "Quantum numbers on each leg:\n", + " +-----+\n", + "( 0): [ 1, 35 ] --| |-- ( 2): [ 0, 1, 35 ]\n", + "( 1): [ 0, 1, 35 ] --| |\n", + " +-----+\n", + "\n" + ] + } + ], + "source": [ + "charges = [\n", + " [\n", + " [1,1],\n", + " [35,1]\n", + " ],[\n", + " [0,1],\n", + " [1,1],\n", + " [35,1]\n", + " ],[\n", + " [0,1],\n", + " [1,1],\n", + " [35,1]\n", + " ]\n", + "]\n", + "\n", + "# Use elements=None to initialize with random elements\n", + "T = sym_tensor.newtensor(elements=None, charges=charges, ZN=36)\n", + "print(T)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Quantum number: 0\n", + "tensor([[0.6956],\n", + " [0.9434]])\n", + "Quantum number: 1\n", + "tensor([[0.0927]])\n", + "Quantum number: 35\n", + "tensor([[0.7140]])\n" + ] + } + ], + "source": [ + "blocks, *meta = T.get_blocks(left_legs=[0,1], right_legs=[2], side='n') # The metadata is necessary to reverse the reshaping\n", + "for i,b in enumerate(blocks):\n", + " if b.numel() > 0:\n", + " print(\"Quantum number: \", i)\n", + " print(b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The same information can be obtained by" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Matrix block structure with combined indices (0, 1) x (2,)\n", + " 0: Size (2, 1) block with quantum numbers [0, 0] (2 elements)\n", + " 1: Size (1, 1) block with quantum numbers [1, 1] (1 elements)\n", + " 2: Size (1, 1) block with quantum numbers [35, 35] (1 elements)\n", + "----> 4 elements in total\n", + "Tensor block structure (4 blocks)\n", + " 0 ( 3): Size (1, 1, 1) block with quantum numbers [35, 1, 0] (1 elements)\n", + " 1 ( 4): Size (1, 1, 1) block with quantum numbers [1, 35, 0] (1 elements)\n", + " 2 ( 7): Size (1, 1, 1) block with quantum numbers [35, 0, 1] (1 elements)\n", + " 3 ( 12): Size (1, 1, 1) block with quantum numbers [1, 0, 35] (1 elements)\n", + "----> 4 elements in total\n" + ] + } + ], + "source": [ + "# Reshaped as matrix with indices 0 and 1 fused\n", + "T.show_block_structure([0,1], [2])\n", + "\n", + "# As tensor\n", + "T.show_block_structure()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Hamiltonian initizalization (automatic)\n", + "For the automatic conversion of a Hamiltonian (or other operators) in full array format to a symmetric tensor, we can use the `symmetrize_operator` function:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Elements of H: tensor([ 0.2500, 0.5000, -0.2500, -0.2500, 0.5000, 0.2500])\n", + "4-D SymTensor (2, 2, 2, 2):\n", + "| Free elements: 6 / 16 (37% of total) in 6 blocks \n", + "| ZN: 36 \n", + "| Totalcharge: 0 \n", + "| Readorder: [0, 1, 2, 3] \n", + " \n", + "Quantum numbers on each leg:\n", + " +-----+\n", + "( 0): [ 1, 35 ] --| |-- ( 2): [ 1, 35 ]\n", + "( 1): [ 1, 35 ] --| |-- ( 3): [ 1, 35 ]\n", + " +-----+\n", + "\n", + "Tensor block structure (6 blocks)\n", + " 0 ( 3): Size (1, 1, 1, 1) block with quantum numbers [35, 35, 1, 1] (1 elements)\n", + " 1 ( 5): Size (1, 1, 1, 1) block with quantum numbers [35, 1, 35, 1] (1 elements)\n", + " 2 ( 6): Size (1, 1, 1, 1) block with quantum numbers [1, 35, 35, 1] (1 elements)\n", + " 3 ( 9): Size (1, 1, 1, 1) block with quantum numbers [35, 1, 1, 35] (1 elements)\n", + " 4 ( 10): Size (1, 1, 1, 1) block with quantum numbers [1, 35, 1, 35] (1 elements)\n", + " 5 ( 12): Size (1, 1, 1, 1) block with quantum numbers [1, 1, 35, 35] (1 elements)\n", + "----> 6 elements in total\n", + "\n", + "Elements of H: tensor([ 0.2500, 0.5000, -0.2500, -0.2500, 0.5000, 0.2500])\n", + "4-D SymTensor (2, 2, 2, 2):\n", + "| Free elements: 6 / 16 (37% of total) in 6 blocks \n", + "| ZN: 36 \n", + "| Totalcharge: 0 \n", + "| Readorder: [0, 1, 2, 3] \n", + " \n", + "Quantum numbers on each leg:\n", + " +-----+\n", + "( 0): [ 1, 35 ] --| |-- ( 2): [ 1, 35 ]\n", + "( 1): [ 1, 35 ] --| |-- ( 3): [ 1, 35 ]\n", + " +-----+\n", + "\n" + ] + } + ], + "source": [ + "H_Heis = np.array([\n", + " [0.25, 0, 0, 0],\n", + " [0, -0.25, 0.5, 0],\n", + " [0, 0.5, -0.25, 0],\n", + " [0, 0, 0, 0.25]\n", + "])\n", + "\n", + "# These represent the quantum numbers on each physical index\n", + "# For a spin-1/2 system with U(1) symmetry (approximated by Z36), the \n", + "# basis states (up,down) correspond to quantum numbers (1,-1) mod ZN = (1,35)\n", + "phys_charges = [1,35]\n", + "\n", + "# Either give the operator in matrix-form (bra indices, ket indices):\n", + "H_Heis_symmetric = sym_tensor.symmetrize_operator(op=H_Heis, phys_charges=phys_charges, ZN=36)\n", + "print('Elements of H: ', H_Heis_symmetric.data)\n", + "print(H_Heis_symmetric)\n", + "H_Heis_symmetric.show_block_structure()\n", + "\n", + "# Or in tensor format, with an index for each physical leg:\n", + "H_Heis = np.reshape(H_Heis, [2,2,2,2])\n", + "H_Heis_symmetric = sym_tensor.symmetrize_operator(op=H_Heis, phys_charges=phys_charges, ZN=36)\n", + "print('\\nElements of H: ', H_Heis_symmetric.data)\n", + "print(H_Heis_symmetric)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Covariant tensors\n", + "If you want to, for example, write a spin-flip operator as SymTensor, it will not be possible with a `U(1)`-invariant tensor, since it contains exactly the elements that are not allowed by the symmetry.\n", + "In order to still make such a SymTensor, you can attach an extra index to the tensor that carries a nontrivial quantum number, such that the total charge `Q_in - Q_out` is still conserved:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "S+ operator:\n", + "[[0 1]\n", + " [0 0]]\n" + ] + } + ], + "source": [ + "Splus = np.array([[0,1],[0,0]])\n", + "print(\"S+ operator:\")\n", + "print(Splus)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The SymTensor will have only two elements that are allowed to be nonzero:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "General operator:\n", + "[[1 2]\n", + " [3 4]]\n", + "\n", + "2-D SymTensor (2, 2):\n", + "| Free elements: 2 / 4 (50% of total) in 2 blocks \n", + "| ZN: 36 \n", + "| Totalcharge: 0 \n", + "| Readorder: [0, 1] \n", + " \n", + "Quantum numbers on each leg:\n", + " +-----+\n", + "( 0): [ 1, 35 ] --| |-- ( 1): [ 1, 35 ]\n", + " +-----+\n", + "\n", + "tensor([1., 4.])\n", + "\n" + ] + } + ], + "source": [ + "operator_el = np.array([[1,2],[3,4]])\n", + "print(\"General operator:\")\n", + "print(operator_el)\n", + "print(\"\")\n", + "\n", + "op = sym_tensor.symmetrize_operator(operator_el, phys_charges=[1,35], ZN=36)\n", + "# Tensor with 2 allowed nonzero elements, namely the diagonal elements\n", + "# of the operator in matrix form\n", + "print(op)\n", + "print(op.data) # [1, 4]\n", + "print(\"\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now make a new tensor with an additional index with quantum number +2 or -2\n", + "Why ±2? Because in the code there are no fractional quantum numbers, so spin-up corresponds to +1 (not +1/2). The S+ operator changes spin-down (-1) to spin-up (+1), so the difference is +2." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3-D SymTensor (2, 2, 1):\n", + "| Free elements: 1 / 4 (25% of total) in 1 blocks \n", + "| ZN: 36 \n", + "| Totalcharge: 0 \n", + "| Readorder: [0, 1, 2] \n", + " \n", + "Quantum numbers on each leg:\n", + " +-----+\n", + "( 0): [ 1, 35 ] --| |-- ( 2): [ 2 ]\n", + "( 1): [ 1, 35 ] --| |\n", + " +-----+\n", + "\n" + ] + } + ], + "source": [ + "charges_with_extra_leg = [[[1,1],[35,1]], [[1,1],[35,1]], [[2,1]]]\n", + "op = sym_tensor.newtensor(charges=charges_with_extra_leg, ZN=36)\n", + "\n", + "# Note that now there's only a single allowed nonzero element - just like the \n", + "# the S+ operator\n", + "print(op)\n", + "\n", + "# Make it S+:\n", + "op.data[0] = 1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The other way of doing this is by using the `totalcharge` property, which can be set to ±2 for this example. However this property is not yet fully supported in the code so that may cause some problems." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Hamiltonian initialization (manual)\n", + "When building a Hamiltonian by hand with a nontrivial symmetry, the blocks of the tensor have be matched with the right elements of the Hamiltonian.\n", + "Here we use a Heisenberg Hamiltonian as an example. The basis is the standard spin basis {(up,up), (up,down), (down,up), (down,down)}, which can be identified with the set of quantum numbers {(1,1), (1,-1), (-1,1), (-1,-1)}.\n", + "The 4x4 (2-site) Hamiltonian can be reshaped to tensor form 2x2x2x2 where each index connects to a physical index of a tensor network. Each index then runs over the quantum numbers (1,-1) and will be given a `charge` of [[1,1],[35,1]] when we approximate the `U(1)` symmetry by `Z36`. " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0.25 0. 0. 0. ]\n", + " [ 0. -0.25 0.5 0. ]\n", + " [ 0. 0.5 -0.25 0. ]\n", + " [ 0. 0. 0. 0.25]]\n" + ] + } + ], + "source": [ + "H_Heis = np.array([\n", + " [0.25, 0, 0, 0],\n", + " [0, -0.25, 0.5, 0],\n", + " [0, 0.5, -0.25, 0],\n", + " [0, 0, 0, 0.25]\n", + "])\n", + "print(H_Heis)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we need to identify all elements with the right quantum numbers. The top-left element maps an (up, up) state to an (up, up) state, corresponding to quantum numbers ( (1,1), (1,1) ).\n", + "The element on its bottom right corner (-0.25) maps (up,down) -> (up,down), so quantum numbers ( (1, -1), (1, -1) ).\n", + "Let's make a SymTensor with (±1) charges on each leg and inspect the nonzero blocks:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Tensor block structure (6 blocks)\n", + " 0 ( 3): Size (1, 1, 1, 1) block with quantum numbers [35, 35, 1, 1] (1 elements)\n", + " 1 ( 5): Size (1, 1, 1, 1) block with quantum numbers [35, 1, 35, 1] (1 elements)\n", + " 2 ( 6): Size (1, 1, 1, 1) block with quantum numbers [1, 35, 35, 1] (1 elements)\n", + " 3 ( 9): Size (1, 1, 1, 1) block with quantum numbers [35, 1, 1, 35] (1 elements)\n", + " 4 ( 10): Size (1, 1, 1, 1) block with quantum numbers [1, 35, 1, 35] (1 elements)\n", + " 5 ( 12): Size (1, 1, 1, 1) block with quantum numbers [1, 1, 35, 35] (1 elements)\n", + "----> 6 elements in total\n" + ] + } + ], + "source": [ + "H = sym_tensor.newtensor(charges=4*[[[1,1],[35,1]]], ZN=36)\n", + "H.show_block_structure()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that there are 6 blocks of size 1. One important remark is that the charges on the outgoing indices [2,3] are *conjugated* (in the code the 'arrows' are always pointed inwards), so in the first block [35,35,1,1] corresponds to ( (-1, -1), (-1, -1) ), which is the element that maps (down,down)->(down,down) - the element on the bottom right of the Hamiltonian (0.25).\n", + "We can then identify each block with a matrix element:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Elements of H: tensor([ 0.2500, 0.5000, -0.2500, -0.2500, 0.5000, 0.2500])\n", + "Matrix block structure with combined indices (0, 1) x (2, 3)\n", + " 0: Size (2, 2) block with quantum numbers [0, 0] (4 elements)\n", + " 1: Size (1, 1) block with quantum numbers [2, 2] (1 elements)\n", + " 2: Size (1, 1) block with quantum numbers [34, 34] (1 elements)\n", + "----> 6 elements in total\n" + ] + } + ], + "source": [ + "data = torch.zeros(6)\n", + "data[0] = H_Heis[3,3] # (down,down) -> (down,down)\n", + "data[1] = H_Heis[2,1] # (up,down) -> (down,up)\n", + "data[2] = H_Heis[1,1] # (up,down) -> (up,down)\n", + "data[3] = H_Heis[2,2] # (down,up) -> (down,up)\n", + "data[4] = H_Heis[1,2] # (down,up) -> (up,down)\n", + "data[5] = H_Heis[0,0] # (up,up) -> (up,up)\n", + "H.data = data\n", + "print('Elements of H: ', H.data)\n", + "H.show_block_structure(left_legs=[0,1], right_legs=[2,3])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Differentiable programming\n", + "Within Torch, all tensor operations should be differentiable in order to obtain gradients. Turn on the tracking of gradients:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3-D SymTensor (2, 3, 3):\n", + "| Free elements: 4 / 18 (22% of total) in 4 blocks \n", + "| ZN: 36 \n", + "| Totalcharge: 0 \n", + "| Readorder: [0, 1, 2] \n", + "| Requires gradient: True \n", + " \n", + "Quantum numbers on each leg:\n", + " +-----+\n", + "( 0): [ 1, 35 ] --| |-- ( 2): [ 0, 1, 35 ]\n", + "( 1): [ 0, 1, 35 ] --| |\n", + " +-----+\n", + "\n" + ] + } + ], + "source": [ + "T.requires_grad = True\n", + "print(T) # Note that now the gradient will be tracked" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1-D SymTensor (1,):\n", + "| Free elements: 1 / 1 (100% of total) in 1 blocks \n", + "| ZN: 36 \n", + "| Totalcharge: 0 \n", + "| Readorder: [0] \n", + "| Requires gradient: True \n", + "| Gradient function: \n", + " \n", + "Quantum numbers on each leg:\n", + " +-----+\n", + "( 0): [ 0 ] --| |\n", + " +-----+\n", + "\n" + ] + } + ], + "source": [ + "T2 = sym_tensor.newtensor(elements=None, charges=charges, ZN=36)\n", + "T2 = T2.conj() # Take the hermitian conjugate\n", + "nrm = T.mult(T2, [0,1,2], [0,1,2]) # Full contraction to a scalar\n", + "print(nrm) # Note that now the gradient function has been stored" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "tensor([0.9855, 0.4243, 0.9606, 0.6537])\n" + ] + } + ], + "source": [ + "# Backpropagation is the same as with regular torch Tensors\n", + "nrm.backward()\n", + "print(T.grad) # The gradient will be stored as a raw torch Tensor" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The methods defined for SymTensor objects automatically determine whether they should be wrapped into a Torch autograd function (defined in `ops.py`) by checking the `T.requires_grad` property.\n", + "A method which is differentiable follows this general structure:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [], + "source": [ + "%%script false --no-raise-error\n", + "# tensors.py\n", + "# wrap_grad decorator wraps function in autograd operation if necessary \n", + "# ('Max' in ops.py in this case)\n", + "# The decorator can be bypassed by adding the nograd=True keyword argument \n", + "# T.max(nograd = True)\n", + "# or by calling the equivalent underscore variant:\n", + "# T.max_()\n", + "# When the tensor does not have the property requireds_grad==True, the gradient\n", + "# is never computed, so the explicit bypass is almost never necessary.\n", + "@_Decorators.wrap_grad(st_ops.Max)\n", + "def max(self): # Implementation on tensor level\n", + " \"\"\" Largest element \"\"\"\n", + " max_el = self.data.max().unsqueeze(0).detach().clone()\n", + " T = newtensor(elements=None, charges=[[[0,1]]], ZN=self.ZN, totalcharge=self.totalcharge)\n", + " T.data = max_el\n", + " return T\n", + "\n", + "# ops.py\n", + "class Max(torch.autograd.Function):\n", + " @staticmethod\n", + " def forward(ctx, tensor):\n", + " res = tensor.max_() # Basic operation on tensor (note the underscore)\n", + " \n", + " # Save information for backward pass\n", + " ctx.intermediate_results = (tensor, res)\n", + " \n", + " # In some operations, only the metadata of the SymTensor needs to \n", + " # be saved, since Torch already saves the elements of the output.\n", + " # res.meta contains all information of the resulting SymTensor \n", + " # (except the elements) that can be used to reconstruct a SymTensor\n", + " # in the backward pass\n", + " # Saving the information would then be something like:\n", + " # ctx.intermediate_results = (res.meta)\n", + " \n", + " return res\n", + "\n", + " @staticmethod\n", + " def backward(ctx, grad_output):\n", + " # Backward pass, which receives the grad_output in the form of a \n", + " # regular Torch Tensor. If necessary, we cast the grad_output back\n", + " # to a SymTensor like this:\n", + " # (meta) = ctx.intermediate_results\n", + " # tensor = tensors.from_meta(meta, elements=grad_output)\n", + " (tensor, res) = ctx.intermediate_results\n", + " tensor = tensor.copy()\n", + " new_data = torch.zeros_like(tensor.data)\n", + " tensor.data = new_data.masked_fill(tensor.data == res.data, grad_output.squeeze())\n", + " return res" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Most of the elementwise functions can be simply be implemented by calling the equivalent Torch function on the elements:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + "def __add__(self, other):\n", + " return self._elem_function(torch.Tensor.__add__, other)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`T._elem_function` makes sure the elements are in the correct order, then calls the corresponding torch.Tensor function (here `torch.Tensor.__add__`) on the elements and finally calls `T.fill_data` to reconstruct the SymTensor from the elements." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Gradient descent demo\n", + "We can put the SymTensors to work in a simple 2-site Heisenberg chain example. \n", + "In this case, there are two variable tensors, for which we construct (1) a torch.nn.Parameter with the elements and (2) a corresponding SymTensor that is filled with the elements and used in the rest of the code.\n", + "Note that since `T.fill_data` is differentiable, the gradient on the SymTensors are automatically propagated to the Parameter objects." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "# models.py\n", + "from torch import nn\n", + "class TwoSiteHeis(nn.Module):\n", + " def __init__(self, elems_A=None, elems_B=None):\n", + " super(TwoSiteHeis, self).__init__()\n", + " H_Heis = np.array([\n", + " [0.25, 0, 0, 0],\n", + " [0, -0.25, 0.5, 0],\n", + " [0, 0.5, -0.25, 0],\n", + " [0, 0, 0, 0.25]\n", + " ])\n", + " phys_charges = [1,35]\n", + " self.H = sym_tensor.symmetrize_operator(op=H_Heis, phys_charges=phys_charges, ZN=36)\n", + " \n", + " # A and B are simple U(1) MPS tensors that form a two-site chain\n", + " ch_A = ch_B = [[[1,1],[35,1]], [[0,1],[1,1],[35,1]]]\n", + " self.A = sym_tensor.newtensor(elements=elems_A, charges=ch_A, ZN=36)\n", + " self.B = sym_tensor.newtensor(elements=elems_B, charges=ch_B, ZN=36)\n", + "\n", + " if elems_A is None:\n", + " self.elems_A = nn.Parameter(self.A.data)\n", + " if elems_B is None:\n", + " self.elems_B = nn.Parameter(self.B.data)\n", + "\n", + " def forward(self, elems_A=None, elems_B=None):\n", + " # The elements can be given as optional arguments so that the gradient \n", + " # of the full forward pass can be checked numerically\n", + " # Normally, just take the tensors that are stored in the model\n", + " if elems_A is not None:\n", + " self.elems_A = elems_A\n", + " if elems_B is not None:\n", + " self.elems_B = elems_B\n", + "\n", + " # This is an important step: it copies the elements into the SymTensor \n", + " # in such a way that the operation remains differentiable\n", + " # In the backward step, the gradient of A (SymTensor) will be propagated \n", + " # back to the gradient of elems_A (regular Torch Tensor)\n", + " A = self.A.fill_data(self.elems_A)\n", + " B = self.B.fill_data(self.elems_B)\n", + "\n", + " A_c = A.conj()\n", + " B_c = B.conj()\n", + " E = st_ops.ncon([A, B, self.H, A_c, B_c], ([1,2],[3,2],[1,3,4,5],[4,6],[5,6]))\n", + " nrm = st_ops.ncon([A, B, A_c, B_c], ([1,2],[3,2],[1,4],[3,4]))\n", + " E_normalized = E / nrm\n", + " return E_normalized" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Check if everything works:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Starting energy: tensor([-0.1177])\n", + "Gradient of A: tensor([ 0.2022, -0.2456])\n", + "Gradient of SymTensor m.A: None\n", + "Gradient check: True\n" + ] + } + ], + "source": [ + "m = TwoSiteHeis()\n", + "\n", + "# Check the forward pass with two random initial tensors\n", + "elems_A = torch.nn.Parameter(torch.rand(m.A.numel(), requires_grad=True))\n", + "elems_B = torch.nn.Parameter(torch.rand(m.B.numel(), requires_grad=False))\n", + "E = m.forward(elems_A, elems_B) # Returns the energy in a SymTensor\n", + "print(\"Starting energy:\", E.data)\n", + "\n", + "# Notice that now the gradient of the SymTensor that is stored \n", + "# on the model (m.A) is propagated to the Parameter object (elems_A)\n", + "E.backward()\n", + "print(\"Gradient of A:\", elems_A.grad)\n", + "# Since the SymTensor is not a leaf in the graph, its gradient will be\n", + "# deleted, unless you set m.A.retain_grad()\n", + "print(\"Gradient of SymTensor m.A:\", m.A.grad) # None\n", + "\n", + "# Check the gradient of the full computation against a numerical gradient\n", + "print(\"Gradient check:\", torch.autograd.gradcheck(m, (elems_A, elems_B)))" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Model Parameters:\n", + "[Parameter containing:\n", + "tensor([0.1730, 0.4866], requires_grad=True), Parameter containing:\n", + "tensor([0.2344, 0.4912], requires_grad=True)]\n", + "Step 0 energy tensor([0.2291])\n", + "Step 1 energy tensor([-0.7500])\n", + "Step 2 energy tensor([-0.7500])\n", + "Step 3 energy tensor([-0.7500])\n", + "Step 4 energy tensor([-0.7500])\n", + "Step 5 energy tensor([-0.7500])\n", + "Step 6 energy tensor([-0.7500])\n", + "Step 7 energy tensor([-0.7500])\n", + "Step 8 energy tensor([-0.7500])\n", + "Step 9 energy tensor([-0.7500])\n", + "Final energy: tensor([-0.7500]) error: tensor([2.3562e-12])\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# main simulation script\n", + "m = TwoSiteHeis()\n", + "print(\"Model Parameters:\")\n", + "print(list(m.parameters()))\n", + "\n", + "learning_rate = 1\n", + "\n", + "optimizer = torch.optim.LBFGS(m.parameters(), max_iter=10, lr=learning_rate)\n", + "\n", + "def closure():\n", + " optimizer.zero_grad()\n", + " loss = m.forward()\n", + " loss.backward()\n", + " return loss\n", + "\n", + "energies = []\n", + "for epoch in range(10):\n", + " loss = optimizer.step(closure)\n", + " print(\"Step\", epoch, \"energy\", loss.data)\n", + " energies.append(loss)\n", + "\n", + "print(\"Final energy:\", energies[-1].data, \"error:\", energies[-1].data--0.75)\n", + "import matplotlib.pyplot as plt\n", + "plt.plot(energies, '-+');" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/docs/source/extra/adpeps.ipeps.ctm.rst b/docs/source/extra/adpeps.ipeps.ctm.rst new file mode 100644 index 0000000..c011e15 --- /dev/null +++ b/docs/source/extra/adpeps.ipeps.ctm.rst @@ -0,0 +1,10 @@ +adpeps.ipeps.ctm +================ + +.. currentmodule:: adpeps.ipeps.ctm + +.. .. toctree:: +.. :maxdepth: 2 + +.. automodule:: adpeps.ipeps.ctm + :members: diff --git a/docs/source/extra/adpeps.ipeps.ipeps.rst b/docs/source/extra/adpeps.ipeps.ipeps.rst new file mode 100644 index 0000000..3323f55 --- /dev/null +++ b/docs/source/extra/adpeps.ipeps.ipeps.rst @@ -0,0 +1,35 @@ +adpeps.ipeps.ipeps +================== + +.. currentmodule:: adpeps.ipeps.ipeps + +.. .. toctree:: +.. :maxdepth: 2 + +.. automodule:: adpeps.ipeps.ipeps + :members: + + +iPEPS +----------- + +.. autoclass:: iPEPS + :members: + :member-order: bysource + +iPEPS_exci +----------- + +.. autoclass:: iPEPS_exci + :members: + :member-order: bysource + + +.. .. autosummary:: +.. :toctree: generated +.. :caption: Section 1 +.. :nosignatures: + +.. iPEPS +.. iPEPS_exci + diff --git a/docs/source/extra/ipeps.ipeps.rst b/docs/source/extra/ipeps.ipeps.rst new file mode 100644 index 0000000..193f163 --- /dev/null +++ b/docs/source/extra/ipeps.ipeps.rst @@ -0,0 +1,19 @@ +iPEPSS +====== + +.. :noindex: + +.. .. currentmodule:: adpeps.ipeps.ipeps + +.. .. toctree:: +.. :maxdepth: 2 + +.. .. automodule:: adpeps.ipeps.ipeps + +.. .. autosummary:: + :toctree: generated + :nosignatures: + :caption: Classes + + iPEPS + iPEPS_exci diff --git a/docs/source/generated/adpeps.ipeps.config.rst b/docs/source/generated/adpeps.ipeps.config.rst new file mode 100644 index 0000000..eafaa88 --- /dev/null +++ b/docs/source/generated/adpeps.ipeps.config.rst @@ -0,0 +1,14 @@ +adpeps.ipeps.config +=================== + +.. currentmodule:: adpeps.ipeps.config + +.. module:: adpeps.ipeps.config + + + +.. automodule:: adpeps.ipeps.config + :members: + :member-order: groupwise + + diff --git a/docs/source/generated/adpeps.ipeps.ctm.rst b/docs/source/generated/adpeps.ipeps.ctm.rst new file mode 100644 index 0000000..25af8d5 --- /dev/null +++ b/docs/source/generated/adpeps.ipeps.ctm.rst @@ -0,0 +1,14 @@ +adpeps.ipeps.ctm +================ + +.. currentmodule:: adpeps.ipeps.ctm + +.. module:: adpeps.ipeps.ctm + + + +.. automodule:: adpeps.ipeps.ctm + :members: + :member-order: groupwise + + diff --git a/docs/source/generated/adpeps.ipeps.ipeps.evaluation.rst b/docs/source/generated/adpeps.ipeps.ipeps.evaluation.rst new file mode 100644 index 0000000..9134e28 --- /dev/null +++ b/docs/source/generated/adpeps.ipeps.ipeps.evaluation.rst @@ -0,0 +1,14 @@ +adpeps.ipeps.ipeps.evaluation +============================= + +.. currentmodule:: adpeps.ipeps.ipeps.evaluation + +.. module:: adpeps.ipeps.ipeps.evaluation + + + +.. automodule:: adpeps.ipeps.ipeps.evaluation + :members: + :member-order: groupwise + + diff --git a/docs/source/generated/adpeps.ipeps.ipeps.rst b/docs/source/generated/adpeps.ipeps.ipeps.rst new file mode 100644 index 0000000..e4ac247 --- /dev/null +++ b/docs/source/generated/adpeps.ipeps.ipeps.rst @@ -0,0 +1,14 @@ +adpeps.ipeps.ipeps +================== + +.. currentmodule:: adpeps.ipeps.ipeps + +.. module:: adpeps.ipeps.ipeps + + + +.. automodule:: adpeps.ipeps.ipeps + :members: + :member-order: groupwise + + diff --git a/docs/source/generated/adpeps.ipeps.models.common.rst b/docs/source/generated/adpeps.ipeps.models.common.rst new file mode 100644 index 0000000..617b7fb --- /dev/null +++ b/docs/source/generated/adpeps.ipeps.models.common.rst @@ -0,0 +1,14 @@ +adpeps.ipeps.models.common +========================== + +.. currentmodule:: adpeps.ipeps.models.common + +.. module:: adpeps.ipeps.models.common + + + +.. automodule:: adpeps.ipeps.models.common + :members: + :member-order: groupwise + + diff --git a/docs/source/generated/adpeps.ipeps.models.heisenberg.rst b/docs/source/generated/adpeps.ipeps.models.heisenberg.rst new file mode 100644 index 0000000..fb407e7 --- /dev/null +++ b/docs/source/generated/adpeps.ipeps.models.heisenberg.rst @@ -0,0 +1,14 @@ +adpeps.ipeps.models.heisenberg +============================== + +.. currentmodule:: adpeps.ipeps.models.heisenberg + +.. module:: adpeps.ipeps.models.heisenberg + + + +.. automodule:: adpeps.ipeps.models.heisenberg + :members: + :member-order: groupwise + + diff --git a/docs/source/generated/adpeps.ipeps.models.rst b/docs/source/generated/adpeps.ipeps.models.rst new file mode 100644 index 0000000..886d6cb --- /dev/null +++ b/docs/source/generated/adpeps.ipeps.models.rst @@ -0,0 +1,23 @@ +adpeps.ipeps.models +=================== + +.. currentmodule:: adpeps.ipeps.models + +.. module:: adpeps.ipeps.models + + +Modules +------- + +.. automodule:: adpeps.ipeps.models + +.. autosummary:: + :toctree: + + + adpeps.ipeps.models.common + + adpeps.ipeps.models.heisenberg + + + diff --git a/docs/source/generated/adpeps.simulation.rst b/docs/source/generated/adpeps.simulation.rst new file mode 100644 index 0000000..d2c6305 --- /dev/null +++ b/docs/source/generated/adpeps.simulation.rst @@ -0,0 +1,23 @@ +adpeps.simulation +================= + +.. currentmodule:: adpeps.simulation + +.. module:: adpeps.simulation + + +Modules +------- + +.. automodule:: adpeps.simulation + +.. autosummary:: + :toctree: + + + adpeps.simulation.run_ipeps_exci + + adpeps.simulation.run_ipeps_gs + + + diff --git a/docs/source/generated/adpeps.simulation.run_ipeps_exci.rst b/docs/source/generated/adpeps.simulation.run_ipeps_exci.rst new file mode 100644 index 0000000..70250d6 --- /dev/null +++ b/docs/source/generated/adpeps.simulation.run_ipeps_exci.rst @@ -0,0 +1,14 @@ +adpeps.simulation.run\_ipeps\_exci +================================== + +.. currentmodule:: adpeps.simulation.run_ipeps_exci + +.. module:: adpeps.simulation.run_ipeps_exci + + + +.. automodule:: adpeps.simulation.run_ipeps_exci + :members: + :member-order: groupwise + + diff --git a/docs/source/generated/adpeps.simulation.run_ipeps_gs.rst b/docs/source/generated/adpeps.simulation.run_ipeps_gs.rst new file mode 100644 index 0000000..276e16a --- /dev/null +++ b/docs/source/generated/adpeps.simulation.run_ipeps_gs.rst @@ -0,0 +1,14 @@ +adpeps.simulation.run\_ipeps\_gs +================================ + +.. currentmodule:: adpeps.simulation.run_ipeps_gs + +.. module:: adpeps.simulation.run_ipeps_gs + + + +.. automodule:: adpeps.simulation.run_ipeps_gs + :members: + :member-order: groupwise + + diff --git a/docs/source/generated/adpeps.utils.ctmtensors.rst b/docs/source/generated/adpeps.utils.ctmtensors.rst new file mode 100644 index 0000000..fc3a665 --- /dev/null +++ b/docs/source/generated/adpeps.utils.ctmtensors.rst @@ -0,0 +1,14 @@ +adpeps.utils.ctmtensors +======================= + +.. currentmodule:: adpeps.utils.ctmtensors + +.. module:: adpeps.utils.ctmtensors + + + +.. automodule:: adpeps.utils.ctmtensors + :members: + :member-order: groupwise + + diff --git a/docs/source/generated/adpeps.utils.empty_tensor.rst b/docs/source/generated/adpeps.utils.empty_tensor.rst new file mode 100644 index 0000000..634791b --- /dev/null +++ b/docs/source/generated/adpeps.utils.empty_tensor.rst @@ -0,0 +1,14 @@ +adpeps.utils.empty\_tensor +========================== + +.. currentmodule:: adpeps.utils.empty_tensor + +.. module:: adpeps.utils.empty_tensor + + + +.. automodule:: adpeps.utils.empty_tensor + :members: + :member-order: groupwise + + diff --git a/docs/source/generated/adpeps.utils.io.rst b/docs/source/generated/adpeps.utils.io.rst new file mode 100644 index 0000000..d73ab43 --- /dev/null +++ b/docs/source/generated/adpeps.utils.io.rst @@ -0,0 +1,14 @@ +adpeps.utils.io +=============== + +.. currentmodule:: adpeps.utils.io + +.. module:: adpeps.utils.io + + + +.. automodule:: adpeps.utils.io + :members: + :member-order: groupwise + + diff --git a/docs/source/generated/adpeps.utils.nested.rst b/docs/source/generated/adpeps.utils.nested.rst new file mode 100644 index 0000000..4d807d9 --- /dev/null +++ b/docs/source/generated/adpeps.utils.nested.rst @@ -0,0 +1,14 @@ +adpeps.utils.nested +=================== + +.. currentmodule:: adpeps.utils.nested + +.. module:: adpeps.utils.nested + + + +.. automodule:: adpeps.utils.nested + :members: + :member-order: groupwise + + diff --git a/docs/source/generated/adpeps.utils.printing.rst b/docs/source/generated/adpeps.utils.printing.rst new file mode 100644 index 0000000..a54b81a --- /dev/null +++ b/docs/source/generated/adpeps.utils.printing.rst @@ -0,0 +1,14 @@ +adpeps.utils.printing +===================== + +.. currentmodule:: adpeps.utils.printing + +.. module:: adpeps.utils.printing + + + +.. automodule:: adpeps.utils.printing + :members: + :member-order: groupwise + + diff --git a/docs/source/generated/adpeps.utils.rst b/docs/source/generated/adpeps.utils.rst new file mode 100644 index 0000000..dc43a5c --- /dev/null +++ b/docs/source/generated/adpeps.utils.rst @@ -0,0 +1,31 @@ +adpeps.utils +============ + +.. currentmodule:: adpeps.utils + +.. module:: adpeps.utils + + +Modules +------- + +.. automodule:: adpeps.utils + +.. autosummary:: + :toctree: + + + adpeps.utils.ctmtensors + + adpeps.utils.empty_tensor + + adpeps.utils.io + + adpeps.utils.nested + + adpeps.utils.printing + + adpeps.utils.tlist + + + diff --git a/docs/source/generated/adpeps.utils.tlist.rst b/docs/source/generated/adpeps.utils.tlist.rst new file mode 100644 index 0000000..8698206 --- /dev/null +++ b/docs/source/generated/adpeps.utils.tlist.rst @@ -0,0 +1,14 @@ +adpeps.utils.tlist +================== + +.. currentmodule:: adpeps.utils.tlist + +.. module:: adpeps.utils.tlist + + + +.. automodule:: adpeps.utils.tlist + :members: + :member-order: groupwise + + diff --git a/docs/source/index.rst b/docs/source/index.rst new file mode 100644 index 0000000..78614ef --- /dev/null +++ b/docs/source/index.rst @@ -0,0 +1,48 @@ +.. AD-PEPS documentation master file, created by + sphinx-quickstart on Mon Apr 12 16:13:24 2021. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +AD-PEPS's documentation +=================================== + +The AD-PEPS Python package is intended as a example of an implementation of iPEPS ground-state and excited-state algorithms using Automatic Differentiation, as described in +As such, the code is meant to illustrate the workings of the algorithms described the paper. +For real applications, this code would likely need to be further adapted and optimized, however the package is a complete implementation and can directly be used for simple calculations. + +.. toctree:: + + notes/install + notes/start + notes/example + notes/example2 + + +Reference +-------------- + +.. .. toctree:: +.. :maxdepth: 2 + +.. ipeps + +.. currentmodule:: adpeps + +.. autosummary:: + :toctree: generated + :recursive: + + ipeps.ipeps + ipeps.config + ipeps.ctm + ipeps.models + simulation + utils + + +Indices and tables +================== + +* :ref:`genindex` +* :ref:`modindex` +* :ref:`search` diff --git a/docs/source/ipeps.rst b/docs/source/ipeps.rst new file mode 100644 index 0000000..e94d9b0 --- /dev/null +++ b/docs/source/ipeps.rst @@ -0,0 +1,17 @@ +adpeps.ipeps +============ + +.. currentmodule:: adpeps.ipeps + +.. toctree:: + :maxdepth: 2 + :caption: Contents + + adpeps.ipeps.ipeps + adpeps.ipeps.ctm + +.. autosummary:: + :toctree: generated + :nosignatures: + + adpeps.ipeps.config diff --git a/docs/source/make.bat b/docs/source/make.bat new file mode 100644 index 0000000..2119f51 --- /dev/null +++ b/docs/source/make.bat @@ -0,0 +1,35 @@ +@ECHO OFF + +pushd %~dp0 + +REM Command file for Sphinx documentation + +if "%SPHINXBUILD%" == "" ( + set SPHINXBUILD=sphinx-build +) +set SOURCEDIR=. +set BUILDDIR=_build + +if "%1" == "" goto help + +%SPHINXBUILD% >NUL 2>NUL +if errorlevel 9009 ( + echo. + echo.The 'sphinx-build' command was not found. Make sure you have Sphinx + echo.installed, then set the SPHINXBUILD environment variable to point + echo.to the full path of the 'sphinx-build' executable. Alternatively you + echo.may add the Sphinx directory to PATH. + echo. + echo.If you don't have Sphinx installed, grab it from + echo.http://sphinx-doc.org/ + exit /b 1 +) + +%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O% +goto end + +:help +%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O% + +:end +popd diff --git a/docs/source/notes/example.rst b/docs/source/notes/example.rst new file mode 100644 index 0000000..480ca94 --- /dev/null +++ b/docs/source/notes/example.rst @@ -0,0 +1,81 @@ +.. _notes/example: + +Example: ground state +=========================================== + +The package includes an example configuration for a ground-state simulation of the 2D Heisenberg model, defined by the Hamiltonian + +.. math:: + + H = J \sum_i S_i \cdot S_{i+1}~. + +The configuration file `examples/heis_D2.yaml` contains the following: + +.. literalinclude:: ../../../examples/heis_D2.yaml + +This configures a simulation with bond dimension :code:`D=2` and boundary bond dimension :code:`chi=40`, using the model defined in :mod:`adpeps.ipeps.models.heisenberg`. + +Now the simulation can be started by calling the :code:`adpeps` module with the name of this configuration file: + + >>> python -m adpeps gs 'heis_D2' + WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.) + Namespace(config_file='heis_D2', sim_mode='gs', version=False) + Running ground-state sim + ... + +The simulation will continue to run and you should see output similar to this: + +.. code-block:: + + ... + Performing CTM pre-steps without tracking + | CTM step 1 conv: 4.935e-03 time: 3.17 obj: -0.658758 + | CTM step 2 conv: 7.918e-04 time: 3.74 obj: -0.659550 + | CTM step 3 conv: 1.234e-05 time: 6.42 obj: -0.659562 + Performing CTM + | CTM step 1 conv: 3.171e-07 time: 8.8 obj: -0.659563 + | CTM step 2 conv: 2.108e-08 time: 4.07 obj: -0.659563 + | CTM step 3 conv: 8.173e-09 time: 2.93 obj: -0.659563 + Energy: -0.6595625579862193 + ... + +The first cycle of iterations are not taken into account in the gradient computation, but make sure that the CTM iterations with gradient tracking start from some reasonably converged boundary tensors in order to avoid instabilities with initial CTM steps. + +.. note:: + The convergence rate of the CTM depends on the variational parameters of the iPEPS and the settings of the simulation. + Generally the convergence improves as the simulation approaches the optimum. + +Whenever a step in the optimization has completed (this could take more than one cycle of CTM iterations depending on the type of optimizer), the module will output a summary of the steps so far: + +.. code-block:: + + ... + # ======================== # + # Step completed # + # ======================== # + + Step 0 E: -0.376468389894 |grad|: 1.2103482 + Step 1 E: -0.505252956403 |grad|: 0.19064889 + Step 2 E: -0.517432085607 |grad|: 0.10910666 + Step 3 E: -0.578045570568 |grad|: 0.081472534 + Step 4 E: -0.589074339197 |grad|: 0.089438567 + Step 5 E: -0.597590746400 |grad|: 0.15282526 + Step 6 E: -0.612205652457 |grad|: 0.076385807 + Step 7 E: -0.628079118387 |grad|: 0.0684857 + Step 8 E: -0.642200026835 |grad|: 0.097849544 + Step 9 E: -0.649553574703 |grad|: 0.066648727 + Step 10 E: -0.653909263824 |grad|: 0.0264237 + Step 11 E: -0.655389076620 |grad|: 0.016836624 + Step 12 E: -0.656585389308 |grad|: 0.016954703 + Step 13 E: -0.657797020335 |grad|: 0.020011479 + Step 14 E: -0.658174755217 |grad|: 0.033691114 + Step 15 E: -0.659083649568 |grad|: 0.012202327 + Step 16 E: -0.659365377610 |grad|: 0.0064214407 + Step 17 E: -0.659562557986 |grad|: 0.007503111 + ... + +The simulation will continue until :attr:`adpeps.ipeps.config.max_iterations` has been reached. +At any point the simulation can be stopped and continued later by restarting the module. + +.. note:: + In case you would like the simulation to continue from an earlier saved simulation with the same configuration file, make sure to set :attr:`adpeps.ipeps.config.resume` :code:`= True` diff --git a/docs/source/notes/example2.rst b/docs/source/notes/example2.rst new file mode 100644 index 0000000..d894348 --- /dev/null +++ b/docs/source/notes/example2.rst @@ -0,0 +1,96 @@ +.. _notes/example2: + +Example: excitations +========================================= + +.. note:: + This example continues from :ref:`the ground-state example` and requires an optimized ground state to start from. + +Here we demonstrates how to use the :mod:`adpeps` package for computing excited states of the 2D Heisenberg model. + +The configuration file `examples/heis_D2_exci.yaml` contains the following settings: + +.. literalinclude:: ../../../examples/heis_D2_exci.yaml + +Note that many of the options are the same as for the ground-state simulation, with the addition of the :attr:`adpeps.ipeps.config.momentum_path` setting, which controls which path through the Brillouin zone will be taken. + +In the configuration for excited states you do not explicitly set the momentum, but choose a preset path of points in momentum space and pass the index for each simulation. + +If we now start the simulation, we get the following response: + + >>> python -m adpeps exci 'heis_D2_exci' --p_ix=1 + ... + Running excited-state sim + ... + Base file .../exci/heisenberg_D2_X40.base.npz not found. + Prepare the simulation first by running with option '-i' + +What happened is that we first need to make some preparations for the simulation. +For excited-state simulations, we require the following: + + 1. Well-converged CTM boundary tensors + 2. A basis for the excited-state tensors, orthogonal to the ground state + +The preparations for the simulation need to be performed only once, resulting in a `base` simulation file that will be used by the simulations for every momentum. + + >>> python -m adpeps exci 'heis_D2_exci' -i + ... + Running excited-state sim + ... + | CTM step 1 conv: 1.036e-01 time: 3.64 obj: -0.665574 + | CTM step 2 conv: 3.137e-03 time: 4.23 obj: -0.662436 + | CTM step 3 conv: 7.887e-05 time: 4.0 obj: -0.662515 + | CTM step 4 conv: 1.388e-06 time: 2.2 obj: -0.662514 + | CTM step 5 conv: 2.455e-07 time: 1.35 obj: -0.662514 + | CTM step 6 conv: 3.044e-08 time: 1.35 obj: -0.662514 + | CTM step 7 conv: 4.673e-09 time: 1.37 obj: -0.662514 + | CTM step 8 conv: 4.467e-10 time: 1.36 obj: -0.662514 + | CTM step 9 conv: 5.029e-11 time: 1.35 obj: -0.662514 + | CTM step 10 conv: 5.612e-11 time: 1.38 obj: -0.662514 + | CTM step 11 conv: 2.801e-11 time: 1.36 obj: -0.662514 + | CTM step 12 conv: 1.204e-11 time: 1.65 obj: -0.662514 + | CTM step 13 conv: 4.936e-12 time: 1.42 obj: -0.662514 + | CTM step 14 conv: 1.989e-12 time: 1.39 obj: -0.662514 + GS norm 3.5890188873039093 + GS norm 1.0 + Substracting -0.33125703308289145 from Hamiltonian + +Several steps have been performed: first a full CTM contraction of the ground-state network, followed by a normalization of the ground-state tensors. +Then the Hamiltonian is shifted by the ground-state energy expectation value, in order for the excitations to have energies relative to the ground state. +Finally, the basis is prepared and we have everything to get started. + + >>> python -m adpeps exci 'heis_D2_exci' --p_ix=0 + ... + Running excited-state sim + ... + Starting simulation of basis vector 1/62 + Performing CTM + | CTM step 1 conv: 4.236e+00 time: 3.19 obj: 5.173629 + | CTM step 2 conv: 3.539e-02 time: 1.38 obj: 5.138237 + | CTM step 3 conv: 6.139e-03 time: 1.27 obj: 5.132099 + | CTM step 4 conv: 2.116e-04 time: 1.24 obj: 5.132310 + | CTM step 5 conv: 6.148e-05 time: 1.28 obj: 5.132249 + | CTM step 6 conv: 3.704e-04 time: 1.25 obj: 5.131879 + | CTM step 7 conv: 2.493e-04 time: 1.25 obj: 5.131629 + Energies: 0.04418993415167889 1.5450126399606245e-10 + Norm: 0.008611083119254162 + ========== + Finished basis vector 1/62 + - + Starting simulation of basis vector 2/62 + Performing CTM + | CTM step 1 conv: 2.004e+00 time: 0.99 obj: 3.335621 + | CTM step 2 conv: 6.150e-02 time: 1.26 obj: 3.397117 + | CTM step 3 conv: 2.017e-02 time: 1.28 obj: 3.376950 + | CTM step 4 conv: 3.838e-03 time: 1.26 obj: 3.380788 + | CTM step 5 conv: 3.650e-04 time: 1.3 obj: 3.380423 + | CTM step 6 conv: 1.246e-03 time: 1.29 obj: 3.381669 + | CTM step 7 conv: 1.288e-03 time: 1.31 obj: 3.380380 + Energies: 0.4285335373465171 1.5450126399606245e-10 + Norm: 0.12679967208649232 + ========== + Finished basis vector 2/62 + ... + +In this version of the algorithm, the full energy and norm overlap matrices will be computed. +Each of the basis vectors, as seen in the output above, is used as input in a separate CTM summation and the program will continue to run until all basis vectors have been used. diff --git a/docs/source/notes/install.rst b/docs/source/notes/install.rst new file mode 100644 index 0000000..b668de6 --- /dev/null +++ b/docs/source/notes/install.rst @@ -0,0 +1,36 @@ +Installation +=================================== + +The quickest way of installing the :code:`adpeps` package is to clone the repository + +.. code-block:: bash + + git clone + + +Method 1 (recommended): `conda` +------------------------------------------ + +The repository comes with an included :code:`environment.yml` file, which automatically installs a Python environment with all required packages, which can be used as follows + +.. code-block:: bash + + cd ad-peps + conda env create -f environment.yml + conda activate adpeps + +When the installation finishes, you can check that the package is working + +.. code-block:: bash + + python -m adpeps -v + +Method 2: `pip` +------------------------------------------ + +The package can also be installed via `pip`: + +.. code-block:: bash + + cd ad-peps + pip install -e . diff --git a/docs/source/notes/start.rst b/docs/source/notes/start.rst new file mode 100644 index 0000000..08534e4 --- /dev/null +++ b/docs/source/notes/start.rst @@ -0,0 +1,57 @@ +.. _notes/start: + +Getting Started +=================================== + +General +-------------- + +The main starting point for running simulations with the `adpeps` package is by loading the module directly via :code:`python -m adpeps`. + +For both ground-state and excited-state simulations the configuration can be set via configuration :code:`.yaml` files. +Each option in the configuration file corresponds to an attribute of the :mod:`adpeps.ipeps.config` module. + +The first argument for the module is the simulation mode (ground-state or excited-state): + +.. code-block:: bash + + python -m adpeps {gs,exci} ... + +.. note:: + The input configuration file location can be set via the + :envvar:`CONFIGDIR` variable. If it is not set, the default + input folder will be the `examples` subfolder of the package + root directory + +.. note:: + The output data location can be set via the :envvar:`DATADIR` + variable. If it is not set, the default output folder will be + in the `simulations` subfolder of the package root directory. + + +Ground states +-------------- + +For ground-state simulations, the only required argument is the configuration file. + +.. argparse:: + :ref: adpeps.__main__.get_parser + :prog: python -m adpeps + :path: gs + + +Excited states +-------------- + +For excited-state simulations, the first argument is again the name of a configuration file (note that the relevant options are different for excited-state simulations), and furthermore the `momentum index` :code:`-p` is required. + +The momentum index refers to a point in momentum space :math:`(k_x, k_y)` defined in a specific path through the Brillouin zone. +The corresponding momentum path can be set via the :attr:`adpeps.ipeps.config.momentum_path` option. +By default, the `'Bril1'` path is taken, which follows the cut along high symmetry points :math:`(\pi,0) - (\pi,\pi) - (\pi/2,\pi/2) - (0,0) - (\pi,0) - (\pi/2,\pi/2)` + +.. argparse:: + :ref: adpeps.__main__.get_parser + :prog: python -m adpeps + :nodefault: + :path: exci + diff --git a/docs/source/tmpmod.rst_bak b/docs/source/tmpmod.rst_bak new file mode 100644 index 0000000..408b838 --- /dev/null +++ b/docs/source/tmpmod.rst_bak @@ -0,0 +1,45 @@ +{{ fullname | escape | underline }} + +Description +----------- + +.. currentmodule:: {{ fullname | escape }} + +.. automodule:: {{ fullname | escape }} + + {% if modules %} + Modules + ------- + + .. autosummary:: + :toctree: generated + + {% for module in modules %} + {{ module }} + {% endfor %} + + {% endif %} + + {% if classes %} + Classes + ------- + .. autosummary:: + :toctree: generated + + {% for class in classes %} + {{ class }} + {% endfor %} + + {% endif %} + + {% if functions %} + Functions + --------- + .. autosummary:: + :toctree: generated + + {% for function in functions %} + {{ function }} + {% endfor %} + + {% endif %} diff --git a/environment.yml b/environment.yml new file mode 100644 index 0000000..4adab83 --- /dev/null +++ b/environment.yml @@ -0,0 +1,17 @@ +name: adpeps +channels: + - defaults +dependencies: + - pip=21.0.1=py38hecd8cb5_0 + - python=3.8.8=h88f2d9e_4 + - pip: + - absl-py==0.12.0 + - flatbuffers==1.12 + - jax==0.2.12 + - jaxlib==0.1.65 + - numpy==1.20.2 + - opt-einsum==3.3.0 + - pyyaml==5.4.1 + - scipy==1.6.2 + - six==1.15.0 + - git+ssh://git@github.com/b1592/ad-peps.git#egg=adpeps diff --git a/examples/heis_D2.yaml b/examples/heis_D2.yaml new file mode 100644 index 0000000..9fe2e6c --- /dev/null +++ b/examples/heis_D2.yaml @@ -0,0 +1,47 @@ +# Base configuration file for iPEPS simulation +# See the individual config modules for more information + +# Simulation options +# -> ipeps/config.py +D: 2 +chi: 41 +model: 'heisenberg' + +# (Ground state) Optimizer +method: 'L-BFGS-B' + +# If an existing state is loaded in the model initialization, +# the seed controls the random (small) noise that is added to +# the site tensors +seed: 1 + +# Prefix for output file +out_prefix: + +# Resume earlier simulation if found +resume: True + +model_params: + J: 1 + +# Set to 0 to suppress all output besides printing each step +disp_level: 2 + +# CTM convergence criterium (singular values norm difference) +ctm_conv_tol: 1.e-6 + +# Minimal number of CTM steps +ctm_min_iter: 4 + +# Maximal number of CTM steps +ctm_max_iter: 8 + +# Flush output (prints with print(*args, flush=True)) +flush_output: True + +# Unit cell pattern (Neel order) +pattern: + [ + [0,1], + [1,0], + ] diff --git a/examples/heis_D2_exci.yaml b/examples/heis_D2_exci.yaml new file mode 100644 index 0000000..11ce49f --- /dev/null +++ b/examples/heis_D2_exci.yaml @@ -0,0 +1,42 @@ +# Base configuration file for iPEPS simulation +# See the individual config modules for more information + +# Simulation options +# -> ipeps/config.py +D: 2 +chi: 40 +model: 'heisenberg' + +# Prefix for output file +out_prefix: + +# Resume earlier simulation if found +resume: True + +model_params: + J: 1 + +# Set to 0 to suppress all output besides printing each step +disp_level: 1 + +# CTM convergence criterium (singular values norm difference) +ctm_conv_tol: 1.e-6 + +# Minimal number of CTM steps +ctm_min_iter: 4 + +# Maximal number of CTM steps +ctm_max_iter: 20 + +# Flush output (prints with print(*args, flush=True)) +flush_output: True + +# Unit cell pattern (Neel order) +pattern: + [ + [0,1], + [1,0], + ] + +# Excitations +momentum_path: 'Bril1' diff --git a/setup.cfg b/setup.cfg new file mode 100644 index 0000000..2b928cc --- /dev/null +++ b/setup.cfg @@ -0,0 +1,11 @@ + +# See the docstring in versioneer.py for instructions. Note that you must +# re-run 'versioneer.py setup' after changing this section, and commit the +# resulting files. + +[versioneer] +VCS = git +style = pep440 +versionfile_source = adpeps/_version.py +versionfile_build = adpeps/_version.py +tag_prefix = diff --git a/setup.py b/setup.py new file mode 100644 index 0000000..e3bf9e9 --- /dev/null +++ b/setup.py @@ -0,0 +1,31 @@ +# -*- coding: utf-8 -*- + +from setuptools import setup, find_packages + +import versioneer + +with open('README.md') as f: + readme = f.read() + +with open('LICENSE') as f: + license = f.read() + +setup( + name='adpeps', + version=versioneer.get_version(), + description='Basic AD iPEPS code for ground states and excitations', + long_description=readme, + author='Boris Ponsioen', + author_email='b.g.t.ponsioen@uva.nl', + url='https://github.com/b1592/ad-peps', + license=license, + packages=find_packages(exclude=('tests', 'docs')), + include_package_data=True, + install_requires=[ + 'jax>=0.2.12', + 'jaxlib>=0.1.65', 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