From d63051d8b98aa0992a9a8277ab90cd261c53155f Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Fri, 24 Nov 2023 18:37:33 +0000 Subject: [PATCH] build based on 8798933 --- previews/PR154/.documenter-siteinfo.json | 1 + previews/PR154/about/index.html | 4 + previews/PR154/assets/aligned.css | 3 + previews/PR154/assets/documenter.js | 889 ++++++++++++++++++ previews/PR154/assets/logo.png | Bin 0 -> 20803 bytes previews/PR154/assets/readme_example.png | Bin 0 -> 17230 bytes .../PR154/assets/themes/documenter-dark.css | 7 + .../PR154/assets/themes/documenter-light.css | 9 + previews/PR154/assets/themeswap.js | 84 ++ previews/PR154/assets/warner.js | 52 + previews/PR154/index.html | 2 + previews/PR154/lib/methods/index.html | 15 + previews/PR154/lib/types/index.html | 24 + previews/PR154/search_index.js | 3 + previews/PR154/siteinfo.js | 1 + previews/PR154/tutorial-2d.png | Bin 0 -> 27998 bytes previews/PR154/tutorial-3d.png | Bin 0 -> 246783 bytes previews/PR154/tutorial/index.html | 34 + 18 files changed, 1128 insertions(+) create mode 100644 previews/PR154/.documenter-siteinfo.json create mode 100644 previews/PR154/about/index.html create mode 100644 previews/PR154/assets/aligned.css create mode 100644 previews/PR154/assets/documenter.js create mode 100644 previews/PR154/assets/logo.png create mode 100644 previews/PR154/assets/readme_example.png create mode 100644 previews/PR154/assets/themes/documenter-dark.css create mode 100644 previews/PR154/assets/themes/documenter-light.css create mode 100644 previews/PR154/assets/themeswap.js create mode 100644 previews/PR154/assets/warner.js create mode 100644 previews/PR154/index.html create mode 100644 previews/PR154/lib/methods/index.html create mode 100644 previews/PR154/lib/types/index.html create mode 100644 previews/PR154/search_index.js create mode 100644 previews/PR154/siteinfo.js create mode 100644 previews/PR154/tutorial-2d.png create mode 100644 previews/PR154/tutorial-3d.png create mode 100644 previews/PR154/tutorial/index.html diff --git a/previews/PR154/.documenter-siteinfo.json b/previews/PR154/.documenter-siteinfo.json new file mode 100644 index 00000000..7adf9b83 --- /dev/null +++ b/previews/PR154/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-11-24T18:37:28","documenter_version":"1.1.2"}} \ No newline at end of file diff --git a/previews/PR154/about/index.html b/previews/PR154/about/index.html new file mode 100644 index 00000000..4140636a --- /dev/null +++ b/previews/PR154/about/index.html @@ -0,0 +1,4 @@ + +About · RangeEnclosures.jl

About

This page contains some general information about this project, and recommendations about contributing.

Contributing

If you like this package, consider contributing! You can send bug reports (or fix them and send your code), add examples to the documentation, or propose new features.

Below some conventions that we follow when contributing to this package are detailed. For specific guidelines on documentation, see the Documentations Guidelines wiki.

Branches and pull requests (PR)

We use a standard pull request policy: You work in a private branch and eventually add a pull request, which is then reviewed by other programmers and merged into the master branch.

Each pull request should be pushed in a new branch with the name of the author followed by a descriptive name, e.g., mforets/my_feature. If the branch is associated to a previous discussion in one issue, we use the name of the issue for easier lookup, e.g., mforets/7.

Unit testing and continuous integration (CI)

This project is synchronized with GitHub Actions such that each PR gets tested before merging (and the build is automatically triggered after each new commit). For the maintainability of this project, it is important to make all unit tests pass.

To run the unit tests locally, you can do:

julia> using Pkg
+
+julia> Pkg.test("RangeEnclosures")

We also advise adding new unit tests when adding new features to ensure long-term support of your contributions.

Contributing to the documentation

New functions and types should be documented according to our guidelines directly in the source code.

You can view the source code documentation from inside the REPL by typing ? followed by the name of the type or function. For example, the following command will print the documentation of the enclose function:

julia> ?enclose

This documentation you are currently reading is written in Markdown, and it relies on Documenter.jl to produce the HTML layout. The sources for creating this documentation are found in docs/src. You can easily include the documentation that you wrote for your functions or types there (see the Documenter.jl guide or our sources for examples).

To generate the documentation locally, run make.jl, e.g., by executing the following command in the terminal:

$ julia --color=yes docs/make.jl

Credits

Core developers

The RangeEnclosures.jl library is maintained by (in alphabetic order):

Contributors

Huge thanks to all the contributors.

Acknowledgments

We are grateful to the following persons for enlightening discussions during the preparation of this package:

During Summer 2022, this project was financially supported by Google through the Google Summer of Code program. During Summer 2019, this project was financially supported by Julia through the Julia Season of Contributions program.

diff --git a/previews/PR154/assets/aligned.css b/previews/PR154/assets/aligned.css new file mode 100644 index 00000000..0078e6bb --- /dev/null +++ b/previews/PR154/assets/aligned.css @@ -0,0 +1,3 @@ +p { + text-align: justify +} diff --git a/previews/PR154/assets/documenter.js b/previews/PR154/assets/documenter.js new file mode 100644 index 00000000..f5311607 --- /dev/null +++ b/previews/PR154/assets/documenter.js @@ -0,0 +1,889 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'minisearch': 'https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function () { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'minisearch'], function($, minisearch) { + +// In general, most search related things will have "search" as a prefix. +// To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +let results = []; +let timer = undefined; + +let data = documenterSearchIndex["docs"].map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; +}); + +// list below is the lunr 2.1.3 list minus the intersect with names(Base) +// (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) +// ideally we'd just filter the original list but it's not available as a variable +const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", +]); + +let index = new minisearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with search results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + boost: { title: 100 }, + fuzzy: 2, + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + tokenize: (string) => string.split(/[\s\-\.]+/), + }, +}); + +index.addAll(data); + +let filters = [...new Set(data.map((x) => x.category))]; +var modal_filters = make_modal_body_filters(filters); +var filter_results = []; + +$(document).on("keyup", ".documenter-search-input", function (event) { + // Adding a debounce to prevent disruptions from super-speed typing! + debounce(() => update_search(filter_results), 300); +}); + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + $(this).removeClass("search-filter-selected"); + } else { + $(this).addClass("search-filter-selected"); + } + + // Adding a debounce to prevent disruptions from crazy clicking! + debounce(() => get_filters(), 300); +}); + +/** + * A debounce function, takes a function and an optional timeout in milliseconds + * + * @function callback + * @param {number} timeout + */ +function debounce(callback, timeout = 300) { + clearTimeout(timer); + timer = setTimeout(callback, timeout); +} + +/** + * Make/Update the search component + * + * @param {string[]} selected_filters + */ +function update_search(selected_filters = []) { + let initial_search_body = ` +
Type something to get started!
+ `; + + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + results = index.search(querystring, { + filter: (result) => { + // Filtering results + if (selected_filters.length === 0) { + return result.score >= 1; + } else { + return ( + result.score >= 1 && selected_filters.includes(result.category) + ); + } + }, + }); + + let search_result_container = ``; + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + results.forEach(function (result) { + if (result.location) { + // Checking for duplication of results for the same page + if (!links.includes(result.location)) { + search_results += make_search_result(result, querystring); + count++; + } + + links.push(result.location); + } + }); + + let result_count = `
${count} result(s)
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + filter_results = []; + modal_filters = make_modal_body_filters(filters, filter_results); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(initial_search_body); + } +} + +/** + * Make the modal filter html + * + * @param {string[]} filters + * @param {string[]} selected_filters + * @returns string + */ +function make_modal_body_filters(filters, selected_filters = []) { + let str = ``; + + filters.forEach((val) => { + if (selected_filters.includes(val)) { + str += `${val}`; + } else { + str += `${val}`; + } + }); + + let filter_html = ` +
+ Filters: + ${str} +
+ `; + + return filter_html; +} + +/** + * Make the result component given a minisearch result data object and the value of the search input as queryString. + * To view the result object structure, refer: https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ +function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`\\b${querystring}\\b`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`\\b${querystring}\\b`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${result.title}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+
+ ${search_divider} + `; + + return result_div; +} + +/** + * Get selected filters, remake the filter html and lastly update the search modal + */ +function get_filters() { + let ele = $(".search-filters .search-filter-selected").get(); + filter_results = ele.map((x) => $(x).text().toLowerCase()); + modal_filters = make_modal_body_filters(filters, filter_results); + update_search(filter_results); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let search_modal_header = ` + +`; + +let initial_search_body = ` +
Type something to get started!
+`; + +let search_modal_footer = ` + +`; + +$(document.body).append( + ` + + ` +); + +document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); +}); + +document.querySelector(".close-search-modal").addEventListener("click", () => { + closeModal(); +}); + +$(document).on("click", ".search-result-link", function () { + closeModal(); +}); + +document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; +}); + +// Functions to open and close a modal +function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); +} + +function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); +} + +document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/previews/PR154/assets/logo.png b/previews/PR154/assets/logo.png new file mode 100644 index 0000000000000000000000000000000000000000..b2a163b03af1ef1ee7eb3a22500eafa2d2d82207 GIT binary patch literal 20803 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.button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark 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.button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#232829;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(40,47,47,0.25)}html.theme--documenter-dark 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kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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.button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .content 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.button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#ad8100;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ad8100 #ad8100 !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-warning.is-light{background-color:#fffaeb;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:hover,html.theme--documenter-dark .button.is-warning.is-light.is-hovered{background-color:#fff7de;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-warning.is-light:active,html.theme--documenter-dark .button.is-warning.is-light.is-active{background-color:#fff3d1;border-color:transparent;color:#d19c00}html.theme--documenter-dark .button.is-danger{background-color:#9e1b0d;border-color:transparent;color:#fff}html.theme--documenter-dark 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.button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#9e1b0d;box-shadow:none;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--documenter-dark .icon.is-medium{height:2rem;width:2rem}html.theme--documenter-dark .icon.is-large{height:3rem;width:3rem}html.theme--documenter-dark .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--documenter-dark .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--documenter-dark .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--documenter-dark .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--documenter-dark div.icon-text{display:flex}html.theme--documenter-dark .image,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--documenter-dark .image img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--documenter-dark .image.is-5by4 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--documenter-dark .image.is-4by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--documenter-dark .image.is-4by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--documenter-dark .image.is-3by2 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--documenter-dark .image.is-3by2 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--documenter-dark .image.is-5by3 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--documenter-dark .image.is-5by3 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--documenter-dark .image.is-16by9 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-16by9 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+ Maintainer: @highlightjs/core-team + Website: https://highlightjs.org/ + License: see project LICENSE + Touched: 2021 +*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem} diff --git a/previews/PR154/assets/themeswap.js b/previews/PR154/assets/themeswap.js new file mode 100644 index 00000000..9f5eebe6 --- /dev/null +++ b/previews/PR154/assets/themeswap.js @@ -0,0 +1,84 @@ +// Small function to quickly swap out themes. Gets put into the tag.. +function set_theme_from_local_storage() { + // Initialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if (window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the users preference is for dark color scheme + var darkPreference = + window.matchMedia("(prefers-color-scheme: dark)").matches === true; + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; + var disabled = []; + var primaryLightTheme = null; + var primaryDarkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + if (ss.ownerNode.getAttribute("data-theme-primary") !== null) { + primaryLightTheme = themename; + } + // Check if the theme is primary dark theme so that we could store its name in darkTheme + if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) { + primaryDarkTheme = themename; + } + // If we find a matching theme (and it's not the default), we'll set active to non-null + if (themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if (themename !== theme) disabled.push(ss); + } + var activeTheme = null; + if (active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName("html")[0].className = "theme--" + theme; + activeTheme = theme; + } else { + // If we did _not_ find an active theme, then we need to fall back to the primary theme + // which can either be dark or light, depending on the user's OS preference. + var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme; + // In case it somehow happens that the relevant primary theme was not found in the + // preceding loop, we abort without doing anything. + if (activeTheme === null) { + console.error("Unable to determine primary theme."); + return; + } + // When switching to the primary light theme, then we must not have a class name + // for the tag. That's only for non-primary or the primary dark theme. + if (darkPreference) { + document.getElementsByTagName("html")[0].className = + "theme--" + activeTheme; + } else { + document.getElementsByTagName("html")[0].className = ""; + } + } + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // we'll disable all the stylesheets, except for the active one + ss.disabled = !(themename == activeTheme); + } +} +set_theme_from_local_storage(); diff --git a/previews/PR154/assets/warner.js b/previews/PR154/assets/warner.js new file mode 100644 index 00000000..3f6f5d00 --- /dev/null +++ b/previews/PR154/assets/warner.js @@ -0,0 +1,52 @@ +function maybeAddWarning() { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return; + } + + // Current version is not a version number, so we can't tell if it's the newest version. Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return; + } + + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return; + } + + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement("meta"); + meta.name = "robots"; + meta.content = "noindex"; + + document.getElementsByTagName("head")[0].appendChild(meta); + } + + const div = document.createElement("div"); + div.classList.add("outdated-warning-overlay"); + const closer = document.createElement("button"); + closer.classList.add("outdated-warning-closer", "delete"); + closer.addEventListener("click", function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE; + div.innerHTML = + 'This documentation is not for the latest stable release, but for either the development version or an older release.
Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", maybeAddWarning); +} else { + maybeAddWarning(); +} diff --git a/previews/PR154/index.html b/previews/PR154/index.html new file mode 100644 index 00000000..53de1631 --- /dev/null +++ b/previews/PR154/index.html @@ -0,0 +1,2 @@ + +Home · RangeEnclosures.jl

RangeEnclosures.jl

A Julia package to compute range enclosures of real-valued functions.

Features

  • Computation of lower and upper bounds of real-valued functions, either univariate or multivariate, over hyperrectangular (i.e. box shaped) domains.
  • The following solvers are always available (using the package IntervalArithmetic.jl):
    • NaturalEnclosure
    • MeanValueEnclosure
    • BranchAndBoundEnclosure
  • The following solvers are available upon loading other packages:

Quickstart

The package exports one single function, enclose, which receives a Julia function, a domain, and (optionally) a solver and additional options passed to the solver. See the README.md file for the basic usage, or consult the source code docstrings, either in the REPL or in the github repository source code

Library Outline

diff --git a/previews/PR154/lib/methods/index.html b/previews/PR154/lib/methods/index.html new file mode 100644 index 00000000..01387d19 --- /dev/null +++ b/previews/PR154/lib/methods/index.html @@ -0,0 +1,15 @@ + +Methods · RangeEnclosures.jl

Methods

This section describes systems methods implemented in RangeEnclosures.jl.

The enclose function

RangeEnclosures.encloseFunction
enclose(f, dom[, solver=NaturalEnclosure()]; kwargs...)

Return a range enclosure of a univariate or multivariate function on the given domain.

Input

  • f – function or AbstractPolynomialLike object
  • dom – hyperrectangular domain, either a unidimensional Interval or a multidimensional IntervalBox
  • solver – (optional, default: NaturalEnclosure()) choose one among the available solvers; you can get a list of available solvers with subtypes(AbstractEnclosureAlgorithm)
  • kwargs – optional keyword arguments passed to the solver; for available options see the documentation of each solver

Output

An interval enclosure of the range of f over dom.

Examples

julia> enclose(x -> 1 - x^4 + x^5, 0..1) # use default solver
+[0, 2]
+
+julia> enclose(x -> 1 - x^4 + x^5, 0..1, TaylorModelsEnclosure())
+[0.8125, 1.09375]

A vector of solvers can be passed in the solver options. Then, the result is obtained by intersecting the range enclosure of each solver.

julia> enclose(x -> 1 - x^4 + x^5, 0..1, [TaylorModelsEnclosure(), NaturalEnclosure()])
+[0.8125, 1.09375]
+
source

Utility functions

RangeEnclosures.relative_precisionFunction
relative_precision(x::Interval, xref::Interval)

Return the relative precision of an interval with respect to a reference interval.

Input

  • x – test interval
  • xref – reference interval

Output

Left and right relative precision (in %) computed as

  • rleft = (inf(xref) - inf(x)) / diam(xref) * 100%
  • rright = (sup(x) - sup(xright)) / diam(xref) * 100%

Examples

julia> xref = interval(-1.2, 4.6)
+[-1.2, 4.6]
+
+julia> x = interval(-1.25, 7.45)
+[-1.25, 7.45001]
+
+julia> relative_precision(x, xref)
+(0.8620689655172422, 49.13793103448277)

Algorithm

This function measures the relative precision of the result in a more informative way than taking the scalar overestimation because it evaluates the precision of the lower and the upper bounds separately (cf. Eq. (20) in [1]).

[1] Althoff, Matthias, Dmitry Grebenyuk, and Niklas Kochdumper. Implementation of Taylor models in CORA 2018. Proc. of the 5th International Workshop on Applied Verification for Continuous and Hybrid Systems. 2018.

source
diff --git a/previews/PR154/lib/types/index.html b/previews/PR154/lib/types/index.html new file mode 100644 index 00000000..7095ae18 --- /dev/null +++ b/previews/PR154/lib/types/index.html @@ -0,0 +1,24 @@ + +Types · RangeEnclosures.jl

Types

This section describes systems types implemented in RangeEnclosures.jl.

RangeEnclosures.AffineArithmeticEnclosureType
AffineArithmeticEnclosure <: AbstractDirectRangeAlgorithm

Data type to bound the range of f over X using affine arithmetic. See AffineArithmetic.jl for more details.

Notes

To use this algorithm, you need to load AffineArithmetic.jl. Note also that AffineArithmetic.jl currently supports only arithmetic operations.

source
RangeEnclosures.BranchAndBoundEnclosureType
BranchAndBoundEnclosure <: AbstractIterativeRangeAlgorithm

Data type to bound the range of f over X using the branch and bound algorithm.

Fields

  • maxdepth (default 10): maximum depth of the search tree
  • tol (default 1e-3): tolerance to compute the range of the function

Algorithm

The algorithm evaluates a function f over an interval X. If the maximum depth is reached or the width of f(X) is below the tolerance, the algorithm returns the computed range; otherwise it bisects the interval/interval box.

The algorithm also looks at the sign of the derivative / gradient to see if the range can be computed directly. By default, the derivative / gradient is computed using ForwardDiff.jl, but a custom value can be passed via the df keyword argument to enclose.

Examples

julia> enclose(x -> -x^3/6 + 5x, 1..4, BranchAndBoundEnclosure())
+[4.83333, 10.5709]
+
+julia> enclose(x -> -x^3/6 + 5x, 1..4, BranchAndBoundEnclosure(tol=1e-2); df=x->-x^2/2+5)
+[4.83333, 10.5709]
source
RangeEnclosures.NaturalEnclosureType

NaturalEnclosure <: AbstractDirectRangeAlgorithm

Data type to bound the range of f over X using natural enclosure, i.e., to evaluate f(X) with interval arithmetic.

Examples

julia> enclose(x -> 1 - x^4 + x^5, 0..1, NaturalEnclosure())
+[0, 2]
source
RangeEnclosures.MeanValueEnclosureType
MeanValueEnclosure

Data type to bound the range of f over X using the mean value form, that is the range is bounded by the expression $f(Xc) + f'(X) * (X - Xc)$, where Xc is the midpoint of X and f' is the derivative of f (gradient in the multivariate case).

source
RangeEnclosures.MooreSkelboeEnclosureType
MooreSkelboeEnclosure{T} <: AbstractIterativeRangeAlgorithm

Data type to bound the range of f over X using the Moore-Skelboe algorithm, which rigorously computes the global minimum and maximum of the function. See IntervalOptimisation.jl for more details.

Fields

  • structure – (default: HeapedVector) the way in which vector elements are kept arranged; possible options are HeapedVector and SortedVector
  • tol – (default 1e-3) tolerance to which the optima are computed

Notes

To use this algorithm, you need to load IntervalOptimisation.jl.

Examples

julia> using IntervalOptimisation
+
+julia> enclose(x -> 1 - x^4 + x^5, 0..1, MooreSkelboeEnclosure()) # default parameters
+[0.916034, 1.00213]
+
+julia> enclose(x -> 1 - x^4 + x^5, 0..1, MooreSkelboeEnclosure(; tol=1e-2))
+[0.900812, 1.0326]
source
RangeEnclosures.SumOfSquaresEnclosureType
SumOfSquaresEnclosure{T} <: AbstractIterativeRangeAlgorithm

Data type to bound the range of f over X using sum-of-squares optimization. See SumOfSquares.jl for more details

Fields

  • backend – backend used to solve the optimization problem; a list of available backends can be found here
  • order – (default 5), maximum degree of the SDP relaxation

Notes

To use this solver, you need to load SumOfSquares.jl and a backend.

Since the optimization problem is solved numerically and not with interval arithmetic, the result of this algorithm is not rigorous.

Examples

julia> using SumOfSquares, SDPA, DynamicPolynomials
+
+julia> backend = SDPA.Optimizer;
+
+julia> @polyvar x;
+
+julia> enclose(-x^3/6 + 5x, 1..4, SumOfSquaresEnclosure(; backend=backend))
+[4.83333, 10.541]
source
RangeEnclosures.TaylorModelsEnclosureType
TaylorModelsEnclosure <: AbstractDirectRangeAlgorithm

Data type to bound the range of f over X using Taylor models. See TaylorModels.jl for more details.

Fields

  • order – (default: 10) order of the Taylor model used to compute an enclosure of f over dom
  • normalize – (default: true) if true, normalize the Taylor model on the unit symmetric box around the origin

Notes

To use this solver, you need to load TaylorModels.jl and a backend.

Examples

julia> enclose(x -> 1 - x^4 + x^5, 0..1, TaylorModelsEnclosure()) # default parameters
+[0.8125, 1.09375]
+
+julia> enclose(x -> 1 - x^4 + x^5, 0..1, TaylorModelsEnclosure(; order=4))
+[0.78125, 1.125]
source
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Sanders","category":"page"},{"location":"about/","page":"About","title":"About","text":"During Summer 2022, this project was financially supported by Google through the Google Summer of Code program. 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Next, we will discuss in more detail how to use the package in different scenarios (1D, higher dimension, using algorithms from external libraries, etc.).","category":"page"},{"location":"tutorial/#Setup","page":"Tutorial","title":"Setup","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Assuming you have installed Julia, you can install the package from the Julia REPL with the following lines.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using Pkg\nPkg.add(\"RangeEnclosures\")","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Then you can load the package in the standard way.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using RangeEnclosures","category":"page"},{"location":"tutorial/#Overview","page":"Tutorial","title":"Overview","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"RangeEnclosures is used to bound the range of a given function f. The main function provided by this package is enclose, and its basic usage is the following.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"enclose(f, D, solver; kwargs...)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"where","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"f is the function whose range we want to bound,\nD is the domain over which we want to compute the range,\nsolver is the solver used to compute the range (which is optional; if not specified, the package will default to the NaturalEnclosure solver), and\nkwargs... are possible keyword arguments used by the solver.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"The solvers can be divided into two families: direct solvers, which compute the range enclosure over the whole domain, and iterative solvers, which recursively split the domain into smaller subdomains to get a more accurate estimate. A detailed list of available solvers can be found here.","category":"page"},{"location":"tutorial/#Usage-Examples","page":"Tutorial","title":"Usage Examples","text":"","category":"section"},{"location":"tutorial/#A-one-dimensional-example","page":"Tutorial","title":"A one-dimensional example","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Suppose we want to compute the range of the function","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"f(x) = -sum_k=1^5kxsinleft(frack(x-3)3right)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"over the domain D = -10 10.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"If we call enclose without specifying the solver, it will evaluate f(D) using plain interval arithmetic (this is called natural enclosure), as the following example shows.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"f(x) = -sum(k*x*sin(k*(x-3)/3) for k in 1:5)\nD = -10..10\nR = enclose(f, D)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Generally, using natural enclosures leads to unpleasantly large overestimates, which is due to the dependency problem. To overcome this, you may want to use some other solvers in your application. The next example bounds the range using the BranchAndBoundEnclosure solver.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Rbb = enclose(f, D, BranchAndBoundEnclosure())","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As you can see, the result is much tighter now, while still being rigorous! The results can be visualized using Plots.jl.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using Plots\nplot(xlabel=\"x\", ylabel=\"f(x)\", legendfontsize=12, tickfontsize=12,\n xguidefont=font(15, \"Times\"), yguidefont=font(15, \"Times\"))\nplot!(IntervalBox(D, R), label=\"natural enclosure\")\nplot!(IntervalBox(D, Rbb), label=\"branch and bound\", alpha=1)\nplot!(f, -10, 10, lw=2, c=:black, label=\"f\")\nsavefig(\"tutorial-2d.png\"); nothing # hide","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"(Image: )","category":"page"},{"location":"tutorial/#Tuning-parameters","page":"Tutorial","title":"Tuning parameters","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Some solvers have parameters that can be tuned. For example, looking at the BranchAndBoundEnclosure documentation, we can see that it has two parameters, tol and maxdepth. If you want to use different values from the default ones, you can pass the parameters as keyword arguments to the solver constructor. For example, you can limit the depth of the search tree to 6 the following way:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"enclose(f, D, BranchAndBoundEnclosure(maxdepth=6))","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Generally, tuning parameters can be a good idea to achieve the desired accuracy tradeoff in your application.","category":"page"},{"location":"tutorial/#Combining-different-solvers","page":"Tutorial","title":"Combining different solvers","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Sometimes there is no strictly \"best\" solver, as one solver might give a tighter estimate of the range's upper bound and another solver might give a tighter estimate on the lower bound. In this case, the results can be combined by taking the intersection. For example, let us consider the function g(x) = x^2 - 2x + 1, which we want to bound over the domain D_g = 0 4. Let us first use plain interval arithmetic:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"g(x) = x^2 - 2*x + 1\nDg = 0..4\nenclose(g, Dg, NaturalEnclosure()) # this is equivalent to enclose(g, Dg)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Now let us bound the range using the MeanValueEnclosure solver, which uses the mean-value form of the function:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"enclose(g, Dg, MeanValueEnclosure())","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"As you can see, there is no clear winner and a better enclosure could be obtained by taking the intersection of the two results. This can be easily done in one command by passing a vector of solvers to enclose:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"enclose(g, Dg, [NaturalEnclosure(), MeanValueEnclosure()])","category":"page"},{"location":"tutorial/#Using-solvers-based-on-external-libraries","page":"Tutorial","title":"Using solvers based on external libraries","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Some of the available solvers are implemented in external libraries. To keep the start-up time of RangeEnclosures.jl low, these libraries are not imported by default. To use more solvers, these libraries need to be manually loaded. For example, suppose we want to bound the previous function using the Moore-Skelboe algorithm. Trying the following will fail:","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"enclose(f, D, MooreSkelboeEnclosure())","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"ERROR: AssertionError: package 'IntervalOptimisation' not loaded (it is required for executing `enclose`)\n...","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"This is because the algorithm is implemented in IntervalOptimisation.jl and to use it you need to load that package first (note that you need to have it installed before loading it). Let us fix our example.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using IntervalOptimisation\nenclose(f, D, MooreSkelboeEnclosure())","category":"page"},{"location":"tutorial/#Bounding-multivariate-functions","page":"Tutorial","title":"Bounding multivariate functions","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"While our previous examples were in one dimension, the techniques generalize to multivariate functions mathbbR^nrightarrowmathbbR, the only difference is that the domain, instead of being an interval, should be an IntervalBox. For example, consider the function","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"h(x_1 x_2) = sin(x_1) - cos(x_2) - sin(x_1)cos(x_1)","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"over the domain D_h = -5 5 times -5 5. An enclosure can be computed as follows.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"h(x) = sin(x[1]) - cos(x[2]) - sin(x[1]) * cos(x[1])\nDh = IntervalBox(-5..5, -5..5)\nRh = enclose(h, Dh, BranchAndBoundEnclosure())","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"We can visualize the result with the following script. For this we use the API of IntervalArithmetic, which must be loaded first.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using IntervalArithmetic\n\nx = y = -5:0.1:5\nf(x, y) = h([x, y])\nplot(legend=:none, size=(800, 800), xlabel=\"x\", ylabel=\"y\", zlabel=\"h(x,y)\",\n tickfontsize=18, guidefont=font(22, \"Times\"), zticks=[-2, 0, 2])\nsurface!(x, y, [inf(Rh) for _ in x, _ in y], α=0.4)\nsurface!(x, y, f.(x', y), zlims=(-4, 4))\nsurface!(x, y, [sup(Rh) for _ in x, _ in y], α=0.4)\nsavefig(\"tutorial-3d.png\"); nothing # hide","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"(Image: )","category":"page"},{"location":"tutorial/#Adding-a-new-enclosure-algorithm","page":"Tutorial","title":"Adding a new enclosure algorithm","text":"","category":"section"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"To add a new enclosure algorithm, or solver, just add a corresponding struct (let us call it MyEnclosure) and extend the method enclose, as the following code snippet demonstrates.","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"using RangeEnclosures\nimport RangeEnclosures: enclose\nusing IntervalArithmetic: Interval\n\nstruct MyEnclosure end\n\nfunction enclose(f::Function,\n D::Union{Interval,IntervalBox},\n solver::MyEnclosure; kwargs...)\n # solver-specific implementation\nend\nnothing # hide","category":"page"},{"location":"tutorial/","page":"Tutorial","title":"Tutorial","text":"Note that the domain D can be of type Interval for univariate (n = 1) functions or of type IntervalBox for multivariate (n 1) functions.","category":"page"},{"location":"lib/methods/#Methods","page":"Methods","title":"Methods","text":"","category":"section"},{"location":"lib/methods/","page":"Methods","title":"Methods","text":"This section describes systems methods implemented in RangeEnclosures.jl.","category":"page"},{"location":"lib/methods/","page":"Methods","title":"Methods","text":"Pages = [\"methods.md\"]\nDepth = 3","category":"page"},{"location":"lib/methods/","page":"Methods","title":"Methods","text":"CurrentModule = RangeEnclosures","category":"page"},{"location":"lib/methods/#The-enclose-function","page":"Methods","title":"The enclose function","text":"","category":"section"},{"location":"lib/methods/","page":"Methods","title":"Methods","text":"enclose","category":"page"},{"location":"lib/methods/#RangeEnclosures.enclose","page":"Methods","title":"RangeEnclosures.enclose","text":"enclose(f, dom[, solver=NaturalEnclosure()]; kwargs...)\n\nReturn a range enclosure of a univariate or multivariate function on the given domain.\n\nInput\n\nf – function or AbstractPolynomialLike object\ndom – hyperrectangular domain, either a unidimensional Interval or a multidimensional IntervalBox\nsolver – (optional, default: NaturalEnclosure()) choose one among the available solvers; you can get a list of available solvers with subtypes(AbstractEnclosureAlgorithm)\nkwargs – optional keyword arguments passed to the solver; for available options see the documentation of each solver\n\nOutput\n\nAn interval enclosure of the range of f over dom.\n\nExamples\n\njulia> enclose(x -> 1 - x^4 + x^5, 0..1) # use default solver\n[0, 2]\n\njulia> enclose(x -> 1 - x^4 + x^5, 0..1, TaylorModelsEnclosure())\n[0.8125, 1.09375]\n\nA vector of solvers can be passed in the solver options. Then, the result is obtained by intersecting the range enclosure of each solver.\n\njulia> enclose(x -> 1 - x^4 + x^5, 0..1, [TaylorModelsEnclosure(), NaturalEnclosure()])\n[0.8125, 1.09375]\n\n\n\n\n\n\n","category":"function"},{"location":"lib/methods/#Utility-functions","page":"Methods","title":"Utility functions","text":"","category":"section"},{"location":"lib/methods/","page":"Methods","title":"Methods","text":"relative_precision","category":"page"},{"location":"lib/methods/#RangeEnclosures.relative_precision","page":"Methods","title":"RangeEnclosures.relative_precision","text":"relative_precision(x::Interval, xref::Interval)\n\nReturn the relative precision of an interval with respect to a reference interval.\n\nInput\n\nx – test interval\nxref – reference interval\n\nOutput\n\nLeft and right relative precision (in %) computed as\n\nrleft = (inf(xref) - inf(x)) / diam(xref) * 100%\nrright = (sup(x) - sup(xright)) / diam(xref) * 100%\n\nExamples\n\njulia> xref = interval(-1.2, 4.6)\n[-1.2, 4.6]\n\njulia> x = interval(-1.25, 7.45)\n[-1.25, 7.45001]\n\njulia> relative_precision(x, xref)\n(0.8620689655172422, 49.13793103448277)\n\nAlgorithm\n\nThis function measures the relative precision of the result in a more informative way than taking the scalar overestimation because it evaluates the precision of the lower and the upper bounds separately (cf. Eq. (20) in [1]).\n\n[1] Althoff, Matthias, Dmitry Grebenyuk, and Niklas Kochdumper. Implementation of Taylor models in CORA 2018. Proc. of the 5th International Workshop on Applied Verification for Continuous and Hybrid Systems. 2018.\n\n\n\n\n\n","category":"function"}] +} diff --git a/previews/PR154/siteinfo.js b/previews/PR154/siteinfo.js new file mode 100644 index 00000000..857ad3d7 --- /dev/null +++ b/previews/PR154/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR154"; diff --git a/previews/PR154/tutorial-2d.png b/previews/PR154/tutorial-2d.png new file mode 100644 index 0000000000000000000000000000000000000000..ee069a537549db955a455ac47ce172354583b487 GIT binary patch literal 27998 zcmb@uWmr{f*foj*ihz^?N|&^Nbfb$y`j`J7%}lSguU;?Jb$ zg=fUhZEZG1j{bdgwd)pH65tn22!v1mP>;#JaeZ$n{b=5JC@8;w-ui$4g&O&tLPSeT zYdnOuLWhkm^&SgbM92J2imtym_GW(hj*D=4%jLU67 ztVA-!btt`eV!C{USk=gIZg1vmyyGXs@ul6+!ZxC*YsAC2fr5f2+WPso2i}ddP1jRG2a`m}-W{(dEKaq;@agS8R$Tpgw_5u&1^iHV8a zByzEiw_!>mjIu04n_qwS_0`tUSRXAAmzK`RYLu0eOSteFA0PjyKG5GE&Z_y^)HEU@ zqSd6RCr;?-^k7XjOHKM8Io!byuEHUj6s3%VgM-nYbcKY?#r&Q5R_BA&yt>Qw*9F}P 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zA|fJc7z#UjG^RAe1A&dpL`2S>ot>plu@DGNJ2J(CCB!8pfDj#*@wL*Nug^8NsGjE^QD~I*IQ)@7-K1v+tV%q#d`+^YGG8PPOz6I^k74QMPv;g z#3OOxxy@YxTRlBJ^Ap{yJd&2+8qn_@i-@8wPdCh;vT8M5)M*rU!RxU;3m-kol|Faw z9NsRJCV~6ZD)&a^TpY72>N(m*R7#zmo<67~a`0fi&o3LKbdn}8;XC67LNKsTQw&`s z@DtGC`mYHYh=wcZ<*Z25J`!SMMQ#t_@0g#TnPuS6(^A)0D +Tutorial · RangeEnclosures.jl

Tutorial

This tutorial will teach you how to use RangeEnclosures. First, we will give a basic overview of the package and its functionalities. Next, we will discuss in more detail how to use the package in different scenarios (1D, higher dimension, using algorithms from external libraries, etc.).

Setup

Assuming you have installed Julia, you can install the package from the Julia REPL with the following lines.

using Pkg
+Pkg.add("RangeEnclosures")

Then you can load the package in the standard way.

using RangeEnclosures

Overview

RangeEnclosures is used to bound the range of a given function f. The main function provided by this package is enclose, and its basic usage is the following.

enclose(f, D, solver; kwargs...)

where

  • f is the function whose range we want to bound,
  • D is the domain over which we want to compute the range,
  • solver is the solver used to compute the range (which is optional; if not specified, the package will default to the NaturalEnclosure solver), and
  • kwargs... are possible keyword arguments used by the solver.

The solvers can be divided into two families: direct solvers, which compute the range enclosure over the whole domain, and iterative solvers, which recursively split the domain into smaller subdomains to get a more accurate estimate. A detailed list of available solvers can be found here.

Usage Examples

A one-dimensional example

Suppose we want to compute the range of the function

\[f(x) = -\sum_{k=1}^5kx\sin\left(\frac{k(x-3)}{3}\right)\]

over the domain $D = [-10, 10]$.

If we call enclose without specifying the solver, it will evaluate $f(D)$ using plain interval arithmetic (this is called natural enclosure), as the following example shows.

f(x) = -sum(k*x*sin(k*(x-3)/3) for k in 1:5)
+D = -10..10
+R = enclose(f, D)
[-150, 150]

Generally, using natural enclosures leads to unpleasantly large overestimates, which is due to the dependency problem. To overcome this, you may want to use some other solvers in your application. The next example bounds the range using the BranchAndBoundEnclosure solver.

Rbb = enclose(f, D, BranchAndBoundEnclosure())
[-56.4232, 34.9988]

As you can see, the result is much tighter now, while still being rigorous! The results can be visualized using Plots.jl.

using Plots
+plot(xlabel="x", ylabel="f(x)", legendfontsize=12, tickfontsize=12,
+     xguidefont=font(15, "Times"), yguidefont=font(15, "Times"))
+plot!(IntervalBox(D, R), label="natural enclosure")
+plot!(IntervalBox(D, Rbb), label="branch and bound", alpha=1)
+plot!(f, -10, 10, lw=2, c=:black, label="f")

Tuning parameters

Some solvers have parameters that can be tuned. For example, looking at the BranchAndBoundEnclosure documentation, we can see that it has two parameters, tol and maxdepth. If you want to use different values from the default ones, you can pass the parameters as keyword arguments to the solver constructor. For example, you can limit the depth of the search tree to 6 the following way:

enclose(f, D, BranchAndBoundEnclosure(maxdepth=6))
[-67.4124, 57.9244]

Generally, tuning parameters can be a good idea to achieve the desired accuracy tradeoff in your application.

Combining different solvers

Sometimes there is no strictly "best" solver, as one solver might give a tighter estimate of the range's upper bound and another solver might give a tighter estimate on the lower bound. In this case, the results can be combined by taking the intersection. For example, let us consider the function $g(x) = x^2 - 2x + 1$, which we want to bound over the domain $D_g = [0, 4]$. Let us first use plain interval arithmetic:

g(x) = x^2 - 2*x + 1
+Dg = 0..4
+enclose(g, Dg, NaturalEnclosure()) # this is equivalent to enclose(g, Dg)
[-7, 17]

Now let us bound the range using the MeanValueEnclosure solver, which uses the mean-value form of the function:

enclose(g, Dg, MeanValueEnclosure())
[-11, 13]

As you can see, there is no clear winner and a better enclosure could be obtained by taking the intersection of the two results. This can be easily done in one command by passing a vector of solvers to enclose:

enclose(g, Dg, [NaturalEnclosure(), MeanValueEnclosure()])
[-7, 13]

Using solvers based on external libraries

Some of the available solvers are implemented in external libraries. To keep the start-up time of RangeEnclosures.jl low, these libraries are not imported by default. To use more solvers, these libraries need to be manually loaded. For example, suppose we want to bound the previous function using the Moore-Skelboe algorithm. Trying the following will fail:

enclose(f, D, MooreSkelboeEnclosure())
ERROR: AssertionError: package 'IntervalOptimisation' not loaded (it is required for executing `enclose`)
+...

This is because the algorithm is implemented in IntervalOptimisation.jl and to use it you need to load that package first (note that you need to have it installed before loading it). Let us fix our example.

using IntervalOptimisation
+enclose(f, D, MooreSkelboeEnclosure())
[-55.6016, 33.4161]

Bounding multivariate functions

While our previous examples were in one dimension, the techniques generalize to multivariate functions $\mathbb{R}^n\rightarrow\mathbb{R}$, the only difference is that the domain, instead of being an interval, should be an IntervalBox. For example, consider the function

\[h(x_1, x_2) = \sin(x_1) - \cos(x_2) - \sin(x_1)\cos(x_1)\]

over the domain $D_h = [-5, 5] \times [-5, 5]$. An enclosure can be computed as follows.

h(x) = sin(x[1]) - cos(x[2]) - sin(x[1]) * cos(x[1])
+Dh = IntervalBox(-5..5, -5..5)
+Rh = enclose(h, Dh, BranchAndBoundEnclosure())
[-2.71068, 2.71313]

We can visualize the result with the following script. For this we use the API of IntervalArithmetic, which must be loaded first.

using IntervalArithmetic
+
+x = y = -5:0.1:5
+f(x, y) = h([x, y])
+plot(legend=:none, size=(800, 800), xlabel="x", ylabel="y", zlabel="h(x,y)",
+     tickfontsize=18, guidefont=font(22, "Times"), zticks=[-2, 0, 2])
+surface!(x, y, [inf(Rh) for _ in x, _ in y], α=0.4)
+surface!(x, y, f.(x', y), zlims=(-4, 4))
+surface!(x, y, [sup(Rh) for _ in x, _ in y], α=0.4)

Adding a new enclosure algorithm

To add a new enclosure algorithm, or solver, just add a corresponding struct (let us call it MyEnclosure) and extend the method enclose, as the following code snippet demonstrates.

using RangeEnclosures
+import RangeEnclosures: enclose
+using IntervalArithmetic: Interval
+
+struct MyEnclosure end
+
+function enclose(f::Function,
+                 D::Union{Interval,IntervalBox},
+                 solver::MyEnclosure; kwargs...)
+    # solver-specific implementation
+end

Note that the domain D can be of type Interval for univariate ($n = 1$) functions or of type IntervalBox for multivariate ($n > 1$) functions.