ms_hm_uniform.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1341,
   "id": "d96bc72e-6442-4225-9d70-92b01bdf60aa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Cython extension is already loaded. To reload it, use:\n",
      "  %reload_ext Cython\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "import numpy as np\n",
    "import scipy.integrate as integ\n",
    "import scipy.interpolate as interp\n",
    "from scipy import signal\n",
    "from scipy.ndimage import gaussian_filter1d\n",
    "import cProfile\n",
    "\n",
    "\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "mpl.rc('xtick', direction='in', top=True)\n",
    "mpl.rc('ytick', direction='in', right=True)\n",
    "mpl.rc('xtick.minor', visible=True)\n",
    "mpl.rc('ytick.minor', visible=True)\n",
    "import cython\n",
    "%load_ext Cython"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 518,
   "id": "fc396711-edd2-49b4-8414-ed692c2ebf27",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "In file included from /usr/local/lib/python3.8/dist-packages/numpy/core/include/numpy/ndarraytypes.h:1944,\n",
      "                 from /usr/local/lib/python3.8/dist-packages/numpy/core/include/numpy/ndarrayobject.h:12,\n",
      "                 from /usr/local/lib/python3.8/dist-packages/numpy/core/include/numpy/arrayobject.h:4,\n",
      "                 from /root/.cache/ipython/cython/_cython_magic_3d1c91796f657de279ef9f8ad58e8a70.c:646:\n",
      "/usr/local/lib/python3.8/dist-packages/numpy/core/include/numpy/npy_1_7_deprecated_api.h:17:2: warning: #warning \"Using deprecated NumPy API, disable it with \" \"#define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\" [-Wcpp]\n",
      "   17 | #warning \"Using deprecated NumPy API, disable it with \" \\\n",
      "      |  ^~~~~~~\n"
     ]
    }
   ],
   "source": [
    "%%cython\n",
    "\n",
    "import numpy as np\n",
    "import cython\n",
    "cimport numpy as np\n",
    "\n",
    "cimport cython\n",
    "ctypedef np.double_t DTYPE_t\n",
    "\n",
    "from libc.math cimport exp\n",
    "from libc.math cimport sqrt\n",
    "\n",
    "from cython.parallel import prange\n",
    "\n",
    "# first derivative\n",
    "@cython.boundscheck(False)  # Deactivate bounds checking\n",
    "cpdef smooth(np.ndarray arr, int order = 5):\n",
    "    cdef int size = arr.shape[0]\n",
    "    cdef double [:] f = arr\n",
    "    cdef double [:] res =  np.zeros(size, dtype=np.double)\n",
    "    cdef double f_sum = 0\n",
    "    cdef wid = int(order/2)\n",
    "    cdef i, j\n",
    "    for i in range(0, wid):\n",
    "        f_sum = 0\n",
    "        for j in range(0, 2 * i + 1):\n",
    "            f_sum += f[i] * V[i] \n",
    "            V_sum += V[i]\n",
    "        res[i] = f_sum / V_sum\n",
    "    \n",
    "    for i in range(wid + 1, size - wid):\n",
    "        f_sum -= f[i - wid - 1] * V[i - wid - 1]\n",
    "        V_sum -= V[i - wid - 1]\n",
    "        \n",
    "        \n",
    "    for i in range(size - 1, size - 1 - int(order / 2)):\n",
    "        f_sum = 0\n",
    "        V_sum = 0\n",
    "        for j in range(0, 2 * i + 1)):\n",
    "            f_sum += f[i] * V[i] \n",
    "            V_sum += V[i]\n",
    "        res[i] = f_sum / V_sum\n",
    "    \n",
    "\n",
    "# first derivative\n",
    "@cython.boundscheck(False)  # Deactivate bounds checking\n",
    "cpdef WENO_nuni_stg(np.ndarray arr, double [::1] V):\n",
    "    cdef int size = arr.shape[0]\n",
    "    cdef double [:] f = arr\n",
    "    cdef double [:] st_f =  np.zeros(size-1, dtype=np.double) # i+1/2 field\n",
    "    \n",
    "    cdef int i\n",
    "    cdef double b1, b2, b3, w1, w2, w3, ws, st_f1, st_f2, st_f3, w, uti, utip1, utim1, utim2, uttim1\n",
    "    for i in prange(2, size - 2,nogil=True):\n",
    "        w = V[i]  / (V[i] + V[i+1])\n",
    "        uti = (1 - w) * f[i] + w * f[i+1]\n",
    "        w = V[i+1] / (V[i+1] + V[i+2])\n",
    "        utip1 = (1 - w) * f[i+1] + w * f[i+2]\n",
    "        w = V[i-1] / (V[i-1] + V[i])\n",
    "        utim1 = (1 - w) * f[i-1] + w * f[i]\n",
    "        w = V[i-2] / (V[i-2] + V[i-1])\n",
    "        utim2 = (1 - w) * f[i-2] + w * f[i-1]\n",
    "        uttim1 = ((2 * V[i-1] + V[i-2]) * f[i-1] - V[i-1] * f[i-2]) / (V[i-2] + V[i-1])\n",
    "        \n",
    "        b1 = 13/ 12 * (2 * utim1 - 2 * uttim1) ** 2\\\n",
    "                + 1/4 * (4 * f[i] - 2 * utim1 - 2 * uttim1)**2 \n",
    "        b2 = 13/ 12 * (2 * utim1 - 4 * f[i] + 2 * uti) ** 2\\\n",
    "                + 1/4 * (-2 * utim1 + 2 * uti)**2\n",
    "        b3 = 13/ 12 * (2 * uti - 4 * f[i+1] + 2 * utip1) ** 2\\\n",
    "                + 1/4 * (-6 * uti + 8 * f[i+1] - 2 * utip1)**2\n",
    "        w1 = 1/10/(1e-6 + b1)**2\n",
    "        w2 = 6/10/(1e-6 + b2)**2\n",
    "        w3 = 3/10/(1e-6 + b3)**2\n",
    "        ws = w1 + w2 + w3\n",
    "        w1 = w1 / ws\n",
    "        w2 = w2 / ws\n",
    "        w3 = w3 / ws\n",
    "        st_f1 = 2 * f[i]  - 1 / 3 * utim1 - 2 / 3 * uttim1\n",
    "        st_f2 =  -1 / 3 * utim1 + 2 / 3 * f[i] + 2 / 3 * uti\n",
    "        st_f3 = 2/3 * uti + 2 / 3 * f[i+1] - 1/3 * utip1\n",
    "        st_f[i] = st_f1 * w1 + st_f2 * w2 + st_f3 * w3\n",
    "    \n",
    "    st_f[1] = (f[2] + f[1]) / 2\n",
    "    st_f[0] = (f[1] + f[0]) / 2\n",
    "    \n",
    "    st_f[size-2] = (f[size-1] + f[size-2]) / 2\n",
    "\n",
    "    \n",
    "    return np.asarray(st_f)\n",
    "\n",
    "@cython.boundscheck(False)  # Deactivate bounds checking\n",
    "cpdef WENO_nuni_dfdA(np.ndarray arr, double [::1] V,  double [::1] A, double bd=0):\n",
    "    cdef int size = arr.shape[0]\n",
    "    cdef double [:] f = arr\n",
    "    cdef double [:] st_f = WENO_nuni_stg(arr, V)\n",
    "    cdef double [:] res =  np.zeros(size, dtype=np.double)\n",
    "    cdef int i\n",
    "    for i in prange(1, size - 1,nogil=True):\n",
    "        res[i] = (st_f[i] - st_f[i-1]) / ((A[i+1] - A[i-1]) / 2)\n",
    "    \n",
    "    res[0] = (f[1] - f[0]) / (A[1] - A[0])\n",
    "    \n",
    "    i = size-1\n",
    "    res[size - 1] = (f[size-1] - f[size-2]) / (A[size-1] - A[size-2])\n",
    "\n",
    "    \n",
    "    return np.asarray(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1340,
   "id": "27c11657-b909-45b7-81b5-754d4bdc417c",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "In file included from /usr/local/lib/python3.8/dist-packages/numpy/core/include/numpy/ndarraytypes.h:1944,\n",
      "                 from /usr/local/lib/python3.8/dist-packages/numpy/core/include/numpy/ndarrayobject.h:12,\n",
      "                 from /usr/local/lib/python3.8/dist-packages/numpy/core/include/numpy/arrayobject.h:4,\n",
      "                 from /root/.cache/ipython/cython/_cython_magic_4a14fb61cd363bb28f40b06bade3cea1.c:652:\n",
      "/usr/local/lib/python3.8/dist-packages/numpy/core/include/numpy/npy_1_7_deprecated_api.h:17:2: warning: #warning \"Using deprecated NumPy API, disable it with \" \"#define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\" [-Wcpp]\n",
      "   17 | #warning \"Using deprecated NumPy API, disable it with \" \\\n",
      "      |  ^~~~~~~\n"
     ]
    }
   ],
   "source": [
    "%%cython\n",
    "\n",
    "import numpy as np\n",
    "import cython\n",
    "cimport numpy as np\n",
    "\n",
    "cimport cython\n",
    "ctypedef np.double_t DTYPE_t\n",
    "\n",
    "from libc.math cimport exp\n",
    "from libc.math cimport sqrt\n",
    "\n",
    "from cython.parallel import prange\n",
    "\n",
    "# first derivative\n",
    "@cython.boundscheck(False)  # Deactivate bounds checking\n",
    "cpdef dfdA(np.ndarray arr, double deltaL, double [::1] A, double bd = 0, int exec_pos = -1):\n",
    "    cdef int size = arr.shape[0]\n",
    "    cdef double [:] f = arr\n",
    "    cdef double [:] res =  np.zeros(size, dtype=np.double)\n",
    "    \n",
    "    cdef int i\n",
    "    for i in prange(exec_pos+2, size - 1,nogil=True):\n",
    "        res[i] = (f[i+1] - f[i-1]) / (A[i+1] - A[i-1])\n",
    "    if(exec_pos > -1):\n",
    "        res[exec_pos+1] = (f[exec_pos+2] - f[exec_pos+1]) / (A[exec_pos+2]-A[exec_pos+1]) \n",
    "    elif(bd < 1e99): # if bd value is valid, set 0th component to bd\n",
    "        res[0] = bd\n",
    "    else: # invalid bd value, so use one-side derivative\n",
    "        res[0] = (f[1] - f[0]) / (A[1] - A[0])\n",
    "        #res[0] = (-11 * f[0] / 6 + 3 * f[1] - 3 * f[2] / 2 + f[3] / 3) / (A[1] - A[0])\n",
    "    res[size - 1] = (f[-1] - f[-2]) / (A[size - 1] - A[size-2]) \n",
    "    return np.asarray(res)\n",
    "\n",
    "# first derivative\n",
    "@cython.boundscheck(False)  # Deactivate bounds checking\n",
    "cpdef stg_dfdA(np.ndarray arr, double [::1] A):\n",
    "    cdef int size = arr.shape[0]\n",
    "    cdef double [:] f = arr\n",
    "    cdef double [:] res =  np.zeros(size-1, dtype=np.double)\n",
    "    \n",
    "    cdef int i\n",
    "    for i in prange(0, size - 1,nogil=True):\n",
    "        res[i] = (f[i+1] - f[i]) / (A[i+1] - A[i])\n",
    "    \n",
    "    return np.asarray(res)\n",
    "\n",
    "# first derivative\n",
    "@cython.boundscheck(False)  # Deactivate bounds checking\n",
    "cpdef WENO_dfdA(np.ndarray arr, double deltaL, double [::1] A, double bd=0):\n",
    "    cdef int size = arr.shape[0]\n",
    "    cdef double [:] f = arr\n",
    "    cdef double [:] st_f =  np.zeros(size, dtype=np.double) # i+1/2 field\n",
    "    cdef double [:] res =  np.zeros(size, dtype=np.double)\n",
    "    \n",
    "    cdef int i\n",
    "    cdef double b1, b2, b3, w1, w2, w3, ws, st_f1, st_f2, st_f3\n",
    "    for i in prange(2, size - 2, nogil=True):\n",
    "        b1 = (4 * f[i-2]**2 - 19 * f[i-2] * f[i-1] + 25 * f[i-1]**2 + 11 * f[i-2] * f[i] - 31 * f[i-1] * f[i] + 10 * f[i]**2) / 3\n",
    "        b2 = (4 * f[i-1]**2 - 13 * f[i-1] * f[i] + 13 * f[i]**2 + 5 * f[i-1] * f[i+1] - 13 * f[i] * f[i+1] + 4 * f[i+1]**2) / 3\n",
    "        b3 = (10 * f[i]**2 - 31 * f[i] * f[i+1] + 25 * f[i+1]**2 + 11 *f[i] * f[i+2] - 19 * f[i+1] * f[i+2] + 4 * f[i+2]**2) / 3\n",
    "        w1 = 1/10/(1e-6 + b1)**2\n",
    "        w2 = 6/10/(1e-6 + b2)**2\n",
    "        w3 = 3/10/(1e-6 + b3)**2\n",
    "        ws = w1 + w2 + w3\n",
    "        w1 = w1 / ws\n",
    "        w2 = w2 / ws\n",
    "        w3 = w3 / ws\n",
    "        st_f1 = 3 * f[i-2] / 8 - 5 * f[i-1] / 4 + 15 * f[i] / 8\n",
    "        st_f2 = -f[i-1] / 8 + 3 * f[i] / 4 + 3 * f[i+1] / 8\n",
    "        st_f3 = 3 * f[i] / 8 + 3 * f[i+1] /4 - f[i+2] / 8\n",
    "        st_f[i] = st_f1 * w1 + st_f2 * w2 + st_f3 * w3\n",
    "        \n",
    "        \n",
    "    for i in prange(3, size - 2, nogil=True):\n",
    "        res[i] = (st_f[i] - st_f[i-1]) / ((A[i+1] - A[i-1]) / 2)\n",
    "    \n",
    "    res[2] = (f[3] - f[1]) / (A[3] - A[1])\n",
    "    res[1] = (f[2] - f[0]) / (A[2] - A[0])\n",
    "    res[0] = (f[1] - f[0]) / (A[1] - A[0])\n",
    "    \n",
    "    res[size - 1] = (f[size-1] - f[size-2]) / (A[size-1] - A[size-2])\n",
    "    res[size-2] = (f[size-1] - f[size-3]) / (A[size-1] - A[size-3])\n",
    "    \n",
    "    return np.asarray(res)\n",
    "\n",
    "\n",
    "@cython.boundscheck(False)  # Deactivate bounds checking\n",
    "cpdef WENO_to_stg(np.ndarray arr):\n",
    "    cdef int size = arr.shape[0]\n",
    "    cdef double [:] f = arr\n",
    "    cdef double [:] st_f =  np.zeros(size-1, dtype=np.double) # i+1/2 field\n",
    "    \n",
    "    cdef int i\n",
    "    cdef double b1, b2, b3, w1, w2, w3, ws, st_f1, st_f2, st_f3\n",
    "    for i in prange(2, size - 2,nogil=True):\n",
    "        b1 = (4 * f[i-2]**2 - 19 * f[i-2] * f[i-1] + 25 * f[i-1]**2 + 11 * f[i-2] * f[i] - 31 * f[i-1] * f[i] + 10 * f[i]**2) / 3\n",
    "        b2 = (4 * f[i-1]**2 - 13 * f[i-1] * f[i] + 13 * f[i]**2 + 5 * f[i-1] * f[i+1] - 13 * f[i] * f[i+1] + 4 * f[i+1]**2) / 3\n",
    "        b3 = (10 * f[i]**2 - 31 * f[i] * f[i+1] + 25 * f[i+1]**2 + 11 *f[i] * f[i+2] - 19 * f[i+1] * f[i+2] + 4 * f[i+2]**2) / 3\n",
    "        w1 = 1/10/(1e-6 + b1)**2\n",
    "        w2 = 6/10/(1e-6 + b2)**2\n",
    "        w3 = 3/10/(1e-6 + b3)**2\n",
    "        ws = w1 + w2 + w3\n",
    "        w1 = w1 / ws\n",
    "        w2 = w2 / ws\n",
    "        w3 = w3 / ws\n",
    "        st_f1 = 3 * f[i-2] / 8 - 5 * f[i-1] / 4 + 15 * f[i] / 8\n",
    "        st_f2 = -f[i-1] / 8 + 3 * f[i] / 4 + 3 * f[i+1] / 8\n",
    "        st_f3 = 3 * f[i] / 8 + 3 * f[i+1] /4 - f[i+2] / 8\n",
    "        st_f[i] = st_f1 * w1 + st_f2 * w2 + st_f3 * w3\n",
    "    \n",
    "    st_f[1] = (f[2] + f[1]) / 2\n",
    "    st_f[0] = (f[1] + f[0]) / 2\n",
    "    \n",
    "    st_f[size-2] = (f[size-1] + f[size-2]) / 2\n",
    "    \n",
    "    return np.asarray(st_f)\n",
    "\n",
    "@cython.boundscheck(False)  # Deactivate bounds checking\n",
    "cpdef inv_derv_phi(np.ndarray rho_in, double [:] P, double off_set=0, int exec_pos = -1):\n",
    "    cdef int size = rho_in.shape[0]\n",
    "    cdef double [:] rho = rho_in\n",
    "    cdef double [:] res =  np.zeros(size, dtype=np.double)\n",
    "    cdef int i\n",
    "    res[size - 1] = off_set\n",
    "    res[size - 2] =  (P[size-1] - P[size-2]) / (P[size-2] + rho[size-2]) + res[size-1]\n",
    "    for i in range(size-3, -1, -1):\n",
    "        res[i] = (P[i+2] - P[i]) / (P[i+1] + rho[i+1]) + res[i+2]\n",
    "    return np.asarray(res)\n",
    "\n",
    "@cython.boundscheck(False)  # Deactivate bounds checking\n",
    "# for exp(\\psi) in Eq. 165e\n",
    "cpdef derv_psi( np.ndarray xi, np.ndarray c, double off_set=0):\n",
    "    cdef int size = xi.shape[0]\n",
    "    cdef double [:] res =  np.zeros(size, dtype=np.double)\n",
    "    cdef int i\n",
    "    res[0] = off_set\n",
    "    res[1] = - (xi[2] - xi[1]) * c[0] + res[0]\n",
    "\n",
    "    for i in range(2, size):\n",
    "        res[i] = - (xi[i] - xi[i-2]) * c[i - 1] + res[i-2]\n",
    "    return np.asarray(res)\n",
    "\n",
    "@cython.boundscheck(False)  # Deactivate bounds checking\n",
    "# for exp(\\psi) in Eq. 165e\n",
    "cpdef inv_derv_psi( np.ndarray xi_in, double [::1] c, double off_set=0):\n",
    "    cdef int size = xi_in.shape[0]\n",
    "    cdef double [:] xi = xi_in\n",
    "    cdef double [:] res =  np.zeros(size, dtype=np.double)\n",
    "    cdef int i\n",
    "    res[size - 1] = off_set\n",
    "    res[size - 2] =  (xi[size-1] - xi[size-2]) * c[size-2] + res[size-1]\n",
    "    #for i in range(size-3, -1, -1):\n",
    "    #    res[i] = (xi[i+1] - xi[i]) * c[i] + res[i+1]\n",
    "    for i in range(size-3, -1, -1):\n",
    "        res[i] = (xi[i+2] - xi[i]) * c[i+1] + res[i+2]\n",
    "    return np.asarray(res)\n",
    "\n",
    "@cython.boundscheck(False)  # Deactivate bounds checking\n",
    "cpdef find_exec_pos(np.ndarray arr):\n",
    "    cdef int size = arr.shape[0]\n",
    "    cdef double [:] f = arr\n",
    "    \n",
    "    cdef int i\n",
    "    for i in range(size - 1, 1,-1):\n",
    "        if(arr[i] < 1 and arr[i-1] > 1): # found a horizon\n",
    "            return i-1\n",
    "    return -1\n",
    "\n",
    "@cython.boundscheck(False)  # Deactivate bounds checking\n",
    "cpdef ms_rho_term(np.ndarray R_in, double [:] m, double [:] A):\n",
    "    cdef int size = R_in.shape[0]\n",
    "    cdef double [:] res =  np.zeros(size, dtype=np.double)\n",
    "    cdef double [:] R = R_in\n",
    "    cdef int i\n",
    "    for i in prange(1, size - 1,nogil=True):\n",
    "        res[i] = A[i] * R[i] * (m[i+1] - m[i-1]) \\\n",
    "                / (3 * (A[i+1] * R[i+1] - A[i-1] * R[i-1]))\n",
    "    i = 0\n",
    "    res[i] = A[i] * R[i] * (m[i+1] - m[i]) \\\n",
    "                / (3 * (A[i+1] * R[i+1] - A[i] * R[i]))\n",
    "    i = size - 1\n",
    "    res[i] = A[i] * R[i] * (m[i] - m[i-1]) \\\n",
    "                / (3 * (A[i] * R[i] - A[i-1] * R[i-1]))\n",
    "    return np.asarray(res)\n",
    "\n",
    "@cython.boundscheck(False)  # Deactivate bounds checking\n",
    "cpdef ms_rho_term_stg(np.ndarray R_in, double [:] m, double [:] A,\n",
    "                     double [:] R_stg, double [:] A_stg):\n",
    "    cdef int size = R_in.shape[0]\n",
    "    cdef double [:] res =  np.zeros(size-1, dtype=np.double)\n",
    "    cdef double [:] R = R_in\n",
    "    cdef int i\n",
    "    for i in prange(0, size - 1,nogil=True):\n",
    "        res[i] = A_stg[i] * R_stg[i] * (m[i+1] - m[i]) \\\n",
    "                / (3 * (A[i+1] * R[i+1] - A[i] * R[i]))\n",
    "    return np.asarray(res)\n",
    "    \n",
    "@cython.boundscheck(False)  # Deactivate bounds checking\n",
    "cpdef hm_rho_term(np.ndarray R_in, double [:] m, double [:] A, double [:] xi,\n",
    "               double a):\n",
    "    cdef int size = R_in.shape[0]\n",
    "    cdef double [:] res =  np.zeros(size, dtype=np.double)\n",
    "    cdef double [:] R = R_in\n",
    "    cdef int i\n",
    "    for i in prange(1, size - 1,nogil=True):\n",
    "        res[i] = (m[i+1] - m[i-1] - 2 * m[i] * (xi[i+1] - xi[i-1])) \\\n",
    "                / (a * A[i] * R[i] * (xi[i+1] - xi[i-1]) + (A[i+1] * R[i+1] - A[i-1] * R[i-1]))\n",
    "        \n",
    "    i = 0\n",
    "    res[0] = (m[i+1] - m[i] - 2 * m[i] * (xi[i+1] - xi[i])) \\\n",
    "                / (a * A[i] * R[i] * (xi[i+1] - xi[i]) + (A[i+1] * R[i+1] - A[i] * R[i]))\n",
    "    i = size - 1\n",
    "    res[size-1] = (m[size-1] - m[i-1] - 2 * m[i] * (xi[size-1] - xi[i-1])) \\\n",
    "                / (a * A[i] * R[i] * (xi[size-1] - xi[i-1]) + (A[size-1] * R[size-1] - A[i-1] * R[i-1]))\n",
    "    return np.asarray(res)\n",
    "\n",
    "@cython.boundscheck(False)  # Deactivate bounds checking\n",
    "cpdef rho_term_stg(np.ndarray R_in, double [:] m, double [:] A, double [:] xi, \n",
    "               double [:] R_stg, double [:] m_stg, double [:] A_stg, double a):\n",
    "    cdef int size = R_in.shape[0]\n",
    "    cdef double [:] res =  np.zeros(size-1, dtype=np.double)\n",
    "    cdef double [:] R = R_in\n",
    "    cdef int i\n",
    "    for i in prange(0, size - 1,nogil=True):\n",
    "        res[i] = (m[i+1] - m[i] - 2 * m_stg[i] * (xi[i+1] - xi[i])) \\\n",
    "                / (a * A_stg[i] * R_stg[i] * (xi[i+1] - xi[i]) + (A[i+1] * R[i+1] - A[i] * R[i]))\n",
    "        \n",
    "    return np.asarray(res)\n",
    "\n",
    "@cython.boundscheck(False)  # Deactivate bounds checking\n",
    "cpdef ephi_term(np.ndarray R_in, double [:] U, double [:] A, double [:] xi, double [:] g,\n",
    "               double a):\n",
    "    cdef int size = R_in.shape[0]\n",
    "    cdef double [:] res =  np.zeros(size, dtype=np.double)\n",
    "    cdef double [:] R = R_in\n",
    "    cdef int i\n",
    "    for i in prange(1, size - 1,nogil=True):\n",
    "        res[i] = (a * (xi[i+1] - xi[i-1]) * A[i] * R[i] + (A[i+1] * R[i+1] - A[i-1] * R[i-1])) /\\\n",
    "                (a * (xi[i+1] - xi[i-1]) * (g[i] + A[i] * R[i] * U[i]))\n",
    "    \n",
    "    i = 0\n",
    "    res[0] = (a * (xi[i+1] - xi[i]) * A[i] * R[i] + (A[i+1] * R[i+1] - A[i] * R[i])) /\\\n",
    "                (a * (xi[i+1] - xi[i]) * (g[i] + A[i] * R[i] * U[i]))\n",
    "    i = size - 1\n",
    "    res[size-1] = (a * (xi[size-1] - xi[i-1]) * A[i] * R[i] + (A[size-1] * R[size-1] - A[i-1] * R[i-1])) /\\\n",
    "                (a * (xi[size-1] - xi[i-1]) * (g[i] + A[i] * R[i] * U[i]))\n",
    "    return np.asarray(res)\n",
    "    \n",
    "@cython.boundscheck(False)  # Deactivate bounds checking\n",
    "cpdef rho_prime(np.ndarray R_in, double [:] m, double [:] A, double [:] xi,\n",
    "               double [:] Rp, double [:] mp, double [:] xip,\n",
    "               double [:] Rpp, double [:] mpp, double [:] xipp, double a):\n",
    "    cdef int size = R_in.shape[0]\n",
    "    cdef double [:] res =  np.zeros(size, dtype=np.double)\n",
    "    cdef double [:] R = R_in\n",
    "    cdef int i\n",
    "    for i in prange(0, size-1 ,nogil=True):\n",
    "        res[i] = ((R[i] + A[i] * Rp[i] + A[i] * a * R[i] * xip[i]  ) \n",
    "                  * (-2 * mp[i] * xip[i] + mpp[i] - 2 * m[i] * xipp[i]) \n",
    "                 - (mp[i] - 2 * m[i] * xip[i] ) * (Rp[i] * (2 + A[i] * a * xip[i]) \n",
    "                        + A[i] * Rpp[i] + a * R[i] * (xip[i] + A[i] * xipp[i])) ) \\\n",
    "                / (R[i] + A[i] * Rp[i] + A[i] * a * R[i] * xip[i])**2\n",
    "    return np.asarray(res)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1348,
   "id": "1d076c7c-8e53-49a0-b181-ec9def5094dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "class MS:\n",
    "    \n",
    "    def __init__(self, R, m, U, w, alpha, A, rho0, deltaL, L, trace_ray=False):\n",
    "        self.R = R\n",
    "        self.m = m\n",
    "        self.U = U\n",
    "        self.w = w\n",
    "        self.deltaL = deltaL\n",
    "        self.L = L\n",
    "        self.A = A\n",
    "        self.alpha = alpha\n",
    "        self.N = R.shape[0]\n",
    "        self.exec_pos = -1\n",
    "\n",
    "\n",
    "        self.t0 = self.alpha * np.sqrt(3 / (8*np.pi*rho0))\n",
    "        self.t = t0\n",
    "        self.xi = 0\n",
    "\n",
    "        self.RH = self.t0 / self.alpha\n",
    "        self.Abar = self.A / self.RH\n",
    "        self.Abar_stg = self.to_stg(self.Abar)\n",
    "        \n",
    "        self.q = 1\n",
    "        self.deltau_i = self.cfl_deltau(self.R, self.m, self.U) * 0.05\n",
    "        self.deltau_adap = self.deltau_i\n",
    "        \n",
    "        # initialize the poton\n",
    "        self.trace_ray = trace_ray\n",
    "        self.Abar_p = self.Abar[0]\n",
    "        self.U_p = self.U[0]\n",
    "        self.m_p = self.m[0]\n",
    "        self.R_p = self.R[0]\n",
    "        \n",
    "        self.U_hm = np.zeros(self.N-1)\n",
    "        self.m_hm = np.zeros(self.N-1)\n",
    "        self.R_hm = np.zeros(self.N-1)\n",
    "        self.xi_hm = np.zeros(self.N-1)\n",
    "        \n",
    "        self.U_hm[0] = self.U[0]\n",
    "        self.m_hm[0] = self.m[0]\n",
    "        self.R_hm[0] = self.R[0]\n",
    "        \n",
    "        self.xi_hm[0] = 0\n",
    "        self.r_old = 0\n",
    "        return\n",
    "    # convert to half grid\n",
    "    def to_stg(self,arr):\n",
    "        return (arr[0:-1] + arr[1:]) / 2\n",
    "    def to_cubic_stg(self,arr):\n",
    "        a1 = arr[0:-1] ** 3 \n",
    "        a2 = arr[1:] ** 3\n",
    "        return (a1 + a2) / (np.abs(a1 + a2)) * ( np.abs(a1 + a2)/ 2) **(1/3)\n",
    "    def to_idx(self, pos):\n",
    "        return np.searchsorted(self.Abar, pos, \"right\") - 1\n",
    "    def gamma(self, R, m, U): \n",
    "        return np.sqrt(np.exp(2 * (1 - self.alpha) * self.xi) \n",
    "                       + (self.Abar * R)**2 * (U**2 - m))\n",
    "    def P(self, rho) : \n",
    "        return self.w * rho\n",
    "    def rho(self, R, m):\n",
    "        return m + ms_rho_term(R, m, self.Abar)\n",
    "        return m + (dfdA(m, self.deltaL, self.Abar,0, self.exec_pos) * self.Abar * R)  \\\n",
    "            / (3* (self.Abar * dfdA(R, self.deltaL, self.Abar, 0, self.exec_pos) \n",
    "                  + R ))\n",
    "    def psi(self, rho, p, Pprime):\n",
    "        #return np.log(rho ** (-3 * self.alpha * self.w / 2))\n",
    "        offset = + np.log(rho[-1]**(-3 * self.alpha * self.w / 2))\n",
    "        return inv_derv_phi(rho, p, offset) \n",
    "    \n",
    "    def Pprime(self, R, m):\n",
    "        R_stg = self.to_stg(R)\n",
    "        m_stg = self.to_stg(m)\n",
    "        rho_stg = m_stg + ms_rho_term_stg(R, m, self.Abar, R_stg, self.Abar_stg)\n",
    "        return self.w * np.concatenate( ([0], stg_dfdA(rho_stg, self.Abar_stg) ,[0] ))\n",
    "        \n",
    "        mprime = dfdA(m, self.deltaL, self.Abar, 0, self.exec_pos)\n",
    "        Rprime = dfdA(R, self.deltaL, self.Abar, 0, self.exec_pos)\n",
    "        mpp = ddfddA(m, self.deltaL, self.Abar, 0, self.exec_pos)\n",
    "        Rpp = ddfddA(R, self.deltaL, self.Abar, 0, self.exec_pos)\n",
    "        return self.w * (4 * self.Abar**2 * mprime * Rprime**2 \n",
    "                + R**2 * (4 * mprime + self.Abar * mpp)\n",
    "               + self.Abar * R * (self.Abar * Rprime * mpp + mprime * (6 * Rprime - self.Abar * Rpp))) \\\n",
    "                / (3 * (R + self.Abar * Rprime)**2)\n",
    "    def k_coeffs(self, R, m, U, Abar_p) :\n",
    "        g = self.gamma(R, m, U)\n",
    "        r = self.rho(R, m)\n",
    "        p = self.P(r)\n",
    "        \n",
    "        Pprime = self.Pprime(R, m)\n",
    "        ep = np.exp(self.psi(r, p, Pprime))\n",
    "        #print(g,r,p,ep)\n",
    "        kR = self.alpha * R * (U * ep - 1)\n",
    "        km = 2 * m - 3 * self.alpha * U * ep * (p + m)\n",
    "        \n",
    "        AR_prime = R + self.Abar * dfdA(R, self.deltaL, self.Abar, 0, self.exec_pos)\n",
    "        \n",
    "        kU = U - self.alpha * ep * \\\n",
    "            (   g**2 * np.concatenate( ([self.w\n",
    "                            * ((m[1] + m[1] - 2 * m[0]) /( self.Abar[1]**2)) *  (1**2 * 5/3)] ,Pprime[1:] / \n",
    "             (self.Abar[1:]) ))  / (R * (AR_prime) * (r + p))  \n",
    "            + (2 * U**2 + m + 3 * p) / 2) \n",
    "\n",
    "        kA_p = self.alpha * interp.griddata(self.Abar, ep * g / AR_prime, \n",
    "                                            Abar_p, method='cubic') \n",
    "        #kA_p.fill(0)\n",
    "        return kR, km, kU, kA_p\n",
    "    \n",
    "\n",
    "    \n",
    "    def run_steps(self,n_steps, exc_intv=0) :\n",
    "        step = 0\n",
    "        \n",
    "        deltau = self.deltau_i\n",
    "        if(self.trace_ray == True):\n",
    "            print(\"Tracing ray is enabled and excision will be performed!\")\n",
    "        else:\n",
    "            print('Not Tracing ray and NO excision will be performed!')\n",
    "        while(step < n_steps) :\n",
    "            #if(step % 100 == 0):\n",
    "                #deltau = self.cfl_deltau(self.R, self.m, self.U) * 0.2\n",
    "            \n",
    "            if(self.to_idx(self.Abar_p) > 50 and self.to_idx(self.Abar_p) < self.N * 0.8):\n",
    "                self.exec_pos = np.max([self.exec_pos, self.to_idx(self.Abar_p) - 10])\n",
    "            exec_arr = np.concatenate(([0] * (self.exec_pos+1),[1] * (self.N - self.exec_pos - 1)))\n",
    "\n",
    "            kR1, km1, kU1, kA_p1 = self.k_coeffs(self.R, self.m, self.U, self.Abar_p)\n",
    "            kR2, km2, kU2, kA_p2 = self.k_coeffs(self.R + deltau/2*kR1, self.m + deltau/2*km1, \n",
    "                                                 self.U + deltau/2*kU1, self.Abar_p + deltau/2*kA_p1)\n",
    "            kR3, km3, kU3, kA_p3 = self.k_coeffs(self.R + deltau/2*kR2, self.m + deltau/2*km2, \n",
    "                                                 self.U + deltau/2*kU2, self.Abar_p + deltau/2*kA_p2)\n",
    "            kR4, km4, kU4, kA_p4 = self.k_coeffs(self.R + deltau*kR3, self.m + deltau*km3, \n",
    "                                                 self.U + deltau*kU3, self.Abar_p + deltau*kA_p3)\n",
    "            \n",
    "            self.R = self.R + (deltau/6*(kR1 + 2*kR2 + 2*kR3 + kR4)) * exec_arr\n",
    "            self.m = self.m + (deltau/6*(km1 + 2*km2 + 2*km3 + km4)) * exec_arr\n",
    "            self.U = self.U + (deltau/6*(kU1 + 2*kU2 + 2*kU3 + kU4)) * exec_arr\n",
    "            \n",
    "            if(self.trace_ray == True):\n",
    "                Abar_p_new = self.Abar_p + deltau/6*(kA_p1 + 2*kA_p2 + 2*kA_p3 + kA_p4)\n",
    "                idx_p_new = self.to_idx(Abar_p_new)\n",
    "                U_p_new = interp.griddata(self.Abar, self.U, Abar_p_new, method='cubic')\n",
    "                m_p_new = interp.griddata(self.Abar, self.m, Abar_p_new, method='cubic')\n",
    "                R_p_new = interp.griddata(self.Abar, self.R, Abar_p_new, method='cubic')\n",
    "\n",
    "                diff = idx_p_new - self.to_idx(self.Abar_p)\n",
    "                if (diff > 1): ##move across more than two grid pints!\n",
    "                    print('Warning!' + str(self.Abar_p) + ' ' + str(Abar_p_new))\n",
    "                    #break\n",
    "                if ( diff > 0): # move across one grid point            \n",
    "                    interp_w = (self.Abar[idx_p_new] - self.Abar_p) / (Abar_p_new - self.Abar_p)\n",
    "                    # linear interpolation\n",
    "                    self.U_hm[idx_p_new] = U_p_new * interp_w + self.U_p * (1 - interp_w)\n",
    "                    self.m_hm[idx_p_new] = m_p_new * interp_w + self.m_p * (1 - interp_w)\n",
    "                    self.R_hm[idx_p_new] = R_p_new * interp_w + self.R_p * (1 - interp_w)\n",
    "                    self.xi_hm[idx_p_new] = self.xi + deltau * interp_w\n",
    "\n",
    "                if(self.xi >= self.xi_hm[0]): #only start advancing photon when the system time is large enough\n",
    "                    self.Abar_p = Abar_p_new\n",
    "                    self.U_p = U_p_new\n",
    "                    self.m_p = m_p_new\n",
    "                    self.R_p = R_p_new\n",
    "                \n",
    "                if(idx_p_new == self.N-2): #going out of the boundary\n",
    "                    break\n",
    "                    \n",
    "            #r = self.rho(self.R, self.m)\n",
    "            #if(step %100 == 0):\n",
    "            #    print(deltau, (r - self.r_old).max())  \n",
    "            #self.r_old = r\n",
    "            \n",
    "            step+=1\n",
    "            self.xi += deltau\n",
    "            \n",
    "            if(step % 10 == 0):\n",
    "                if(find_exec_pos(self.R**2 * self.m * self.Abar**2 * np.exp(2 * (self.alpha-1) * self.xi)) > 0):\n",
    "                    break\n",
    "            \n",
    "        if step < n_steps:\n",
    "            print(\"Photon has gone out of the outter boundary or horizon is identified!\")\n",
    "  \n",
    "            \n",
    "    def adap_run_steps(self,n_steps, adjust_steps=100, tol=1e-7) :\n",
    "        step = 0\n",
    "        deltau = self.deltau_adap\n",
    "        \n",
    "        if(self.trace_ray == True):\n",
    "            print(\"Tracing ray is enabled and excision will be performed!\")\n",
    "        else:\n",
    "            print('Not Tracing ray and NO excision will be performed!')\n",
    "            \n",
    "        kR1, km1, kU1, kA_p1 = self.k_coeffs(self.R, self.m, self.U, self.Abar_p)\n",
    "        while(step < n_steps):\n",
    "            \n",
    "            if (deltau < 1e-9):\n",
    "                print(\"Warning, the time step is too small!\")\n",
    "                break\n",
    "            \n",
    "            if(self.to_idx(self.Abar_p) > 50 and self.to_idx(self.Abar_p) < self.N * 0.8):\n",
    "                self.exec_pos = np.max([self.exec_pos, self.to_idx(self.Abar_p) - 10])\n",
    "            exec_arr = np.concatenate(([0] * (self.exec_pos+1),[1] * (self.N - self.exec_pos - 1)))\n",
    "            \n",
    "            kR2, km2, kU2, kA_p2 = self.k_coeffs(self.R + deltau/2*kR1, self.m + deltau/2*km1, \n",
    "                                                 self.U + deltau/2*kU1, self.Abar_p + deltau/2*kA_p1)\n",
    "            \n",
    "            kR3, km3, kU3, kA_p3 = self.k_coeffs(self.R + 3/4*deltau*kR2, self.m + 3/4*deltau*km2, \n",
    "                                                 self.U + 3/4*deltau*kU2, self.Abar_p + 3/4*deltau*kA_p2)\n",
    "\n",
    "            \n",
    "            Abar_p_new = self.Abar_p + deltau/9*(2*kA_p1 + 3*kA_p2 + 4*kA_p3 )\n",
    "            R_new = self.R + deltau/9*(2*kR1 + 3*kR2 + 4*kR3 )\n",
    "            m_new = self.m + deltau/9*(2*km1 + 3*km2 + 4*km3 )\n",
    "            U_new = self.U + deltau/9*(2*kU1 + 3*kU2 + 4*kU3 )\n",
    "            \n",
    "            # calculating the difference of the photon position\n",
    "            # diff is always zero when tracing_ray is false\n",
    "            idx_p_new = self.to_idx(Abar_p_new)\n",
    "            diff = idx_p_new - self.to_idx(self.Abar_p)\n",
    "            \n",
    "            kR4, km4, kU4, kA_p4 = self.k_coeffs(R_new , m_new , U_new, Abar_p_new)\n",
    "            \n",
    "            E_R = np.max( np.abs((deltau * (-5*kR1/72 + kR2/12 + kR3/9 - kR4/8))))\n",
    "            E_m = np.max( np.abs(deltau * (-5*km1/72 + km2/12 + km3/9 - km4/8)))\n",
    "            E_U = np.max( np.abs(deltau * (-5*kU1/72 + kU2/12 + kU3/9 - kU4/8)))\n",
    "    \n",
    "            max_err_R = np.max(np.abs(self.R)) * tol\n",
    "            max_err_m = np.max(np.abs(self.m)) * tol\n",
    "            max_err_U = np.max(np.abs(self.U)) * tol\n",
    "            \n",
    "            if(diff <= 1 and E_R < max_err_R and E_m < max_err_m and E_U < max_err_U):\n",
    "                \n",
    "                self.R = R_new\n",
    "                self.m = m_new\n",
    "                self.U = U_new\n",
    "                \n",
    "                if(self.trace_ray == True):\n",
    "                    self.Abar_p = Abar_p_new\n",
    "                    U_p_new = interp.griddata(self.Abar, self.U, Abar_p_new, method='cubic')\n",
    "                    m_p_new = interp.griddata(self.Abar, self.m, Abar_p_new, method='cubic')\n",
    "                    R_p_new = interp.griddata(self.Abar, self.R, Abar_p_new, method='cubic')\n",
    "                    if ( diff > 0): # move across one grid point            \n",
    "                        interp_w = (self.Abar[idx_p_new] - self.Abar_p) / (Abar_p_new - self.Abar_p)\n",
    "                        # linear interpolation\n",
    "                        self.U_hm[idx_p_new] = U_p_new * interp_w + self.U_p * (1 - interp_w)\n",
    "                        self.m_hm[idx_p_new] = m_p_new * interp_w + self.m_p * (1 - interp_w)\n",
    "                        self.R_hm[idx_p_new] = R_p_new * interp_w + self.R_p * (1 - interp_w)\n",
    "                        self.xi_hm[idx_p_new] = self.xi + deltau * interp_w\n",
    "                \n",
    "                kR1 = kR4.copy()\n",
    "                km1 = km4.copy()\n",
    "                kU1 = kU4.copy()\n",
    "                \n",
    "                step+=1\n",
    "                self.xi += deltau\n",
    "            \n",
    "            if( diff <=1):\n",
    "                # Adjust step size.\n",
    "                self.q = 0.8*np.min((max_err_R/E_R, max_err_m/E_m, max_err_U/E_U) )**(1/3)   # conservative optimal step factor\n",
    "                self.q = min(self.q,10)               # limit stepsize growth\n",
    "                deltau *= self.q\n",
    "                #print(q, E_R, max_err_R)\n",
    "            else: \n",
    "                # reducing the deltau since diff is too large\n",
    "                deltau /= 2\n",
    "                \n",
    "            if(step % 10 == 0):\n",
    "                if(find_exec_pos(self.R**2 * self.m * self.Abar**2 * np.exp(2 * (self.alpha-1) * self.xi)) > 0):\n",
    "                    print(\"Horizon is found, code has been terminated!\")\n",
    "                    break\n",
    "            \n",
    "        if step < n_steps:\n",
    "            print(\"Photon has gone out of the outter boundary or horizon is identified!\")\n",
    "            \n",
    "    def cfl_deltau(self,R, m, U):\n",
    "        a = np.exp(self.alpha * self.xi)\n",
    "        H = np.exp(-self.xi) / self.RH\n",
    "        \n",
    "        g = self.gamma(R, m, U)\n",
    "        r = self.rho(R, m)\n",
    "        p = self.P(r)\n",
    "  \n",
    "        Pprime = self.Pprime(R, m)\n",
    "                           \n",
    "        ep = np.exp(self.psi(r, p, Pprime))\n",
    "        el =  (dfdA(a * self.A * self.R, self.deltaL, self.Abar, 1) / self.RH) /(a * H * self.RH * g) \n",
    "\n",
    "        return (np.log(1 + el / ep / np.exp(self.xi)  \n",
    "                       * self.alpha * np.concatenate( ([1e10],(self.Abar[1:] - self.Abar[0:-1])) ) / np.sqrt(self.w))).min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1312,
   "id": "a3bf354a-4894-4f0c-9f6c-39f8f9604aef",
   "metadata": {},
   "outputs": [],
   "source": [
    "class HM:\n",
    "    \n",
    "    def __init__(self, MS):\n",
    "        self.R = MS.R_hm\n",
    "        self.m = MS.m_hm\n",
    "        self.U = MS.U_hm\n",
    "        self.xi = MS.xi_hm\n",
    "        self.N = MS.R_hm.shape[0]\n",
    "        \n",
    "        self.w = MS.w\n",
    "        self.deltaL = MS.deltaL\n",
    "        self.L = MS.L\n",
    "        self.A = MS.A[:self.N]\n",
    "        self.alpha = MS.alpha\n",
    "\n",
    "\n",
    "        self.t0 = MS.t0\n",
    "        self.t = t0\n",
    "        self.u = 0\n",
    "\n",
    "        self.RH = self.t0 / self.alpha\n",
    "        self.Abar = MS.Abar[:self.N]\n",
    "        self.Abar_stg = self.to_stg(self.Abar)\n",
    "        #self.Abar_stg = WENO_to_stg(self.Abar)\n",
    "        self.Vbar = np.concatenate(\n",
    "            ([MS.Abar[1] ], (MS.Abar[2:] - MS.Abar[0:self.N-1]) / 2) )\n",
    "        \n",
    "        self.kappa = 2\n",
    "        self.Q = np.zeros(self.N)\n",
    "        self.Q_du = np.zeros(self.N)\n",
    "        self.Q_old = np.zeros(self.N)\n",
    "        self.Qprime = np.zeros(self.N)\n",
    "        \n",
    "        self.deltau_i = self.cfl_deltau(self.R, self.m, self.U, self.xi) * 0.05\n",
    "        self.deltau_adap = self.deltau_i\n",
    "\n",
    "        return\n",
    "    # convert to half grid\n",
    "    def to_stg(self,arr):\n",
    "        return (arr[0:-1] + arr[1:]) / 2\n",
    "    def to_cubic_stg(self,arr):\n",
    "        a1 = arr[0:-1] ** 3 \n",
    "        a2 = arr[1:] ** 3\n",
    "        return (a1 + a2) / (np.abs(a1 + a2)) * ( np.abs(a1 + a2)/ 2) **(1/3)\n",
    "    def gamma(self, R, m, U, xi): \n",
    "        return np.sqrt(np.exp(2 * (1 - self.alpha) * xi) \n",
    "                       + (self.Abar * R)**2 * (U**2 - m))\n",
    "    def P(self, rho) : \n",
    "        return self.w * rho\n",
    "    def rho(self, R, m, U, xi, g, xiprime, Rprime, mprime):\n",
    "        temp = (g + self.Abar * R * U) / (g - (self.w + self.Q ) * self.Abar * R * U ) \\\n",
    "            * (m + self.Abar * R * hm_rho_term(R, m, self.Abar, xi, self.alpha) / 3)\n",
    "        #temp = scipy.signal.savgol_filter(temp, 63, 3, mode='interp')\n",
    "        temp=gaussian_filter1d(temp, sigma = 5, mode='nearest')\n",
    "        return temp\n",
    "\n",
    "    def rho_stg(self, R, m, U, xi, g, xiprime, Rprime, mprime):\n",
    "        R_stg = self.to_stg(R)\n",
    "        m_stg = self.to_stg(m)\n",
    "        U_stg = self.to_stg(U)\n",
    "        g_stg = self.to_stg(g)\n",
    "        #R_stg = WENO_to_stg(R)\n",
    "        #m_stg = WENO_to_stg(m)\n",
    "        #U_stg = WENO_to_stg(U)\n",
    "        #g_stg = WENO_to_stg(g)\n",
    "        A_stg = self.Abar_stg\n",
    "        \n",
    "        if self.Q.shape[0] > 1:\n",
    "            Q_stg = self.to_stg(self.Q)\n",
    "        else:\n",
    "            Q_stg = self.Q\n",
    "        \n",
    "        temp = (g_stg + A_stg * R_stg * U_stg) / (g_stg - (self.w + Q_stg ) * A_stg * R_stg * U_stg ) \\\n",
    "            * (m_stg + A_stg * R_stg * rho_term_stg(R, m, self.Abar, xi, R_stg, m_stg, A_stg, self.alpha) / 3)\n",
    "        #temp = scipy.signal.savgol_filter(temp, 31, 3, mode='interp')\n",
    "        return temp\n",
    "        \n",
    "    def ephi(self, R, U, g, xi, xiprime, Rprime):\n",
    "        return ephi_term(R, U, self.Abar, xi, g, self.alpha)\n",
    "    \n",
    "    def elambda(self, ephi, exi, xiprime):\n",
    "        return self.alpha * ephi * exi * xiprime\n",
    "    \n",
    "    def epsi(self, R, U, g, xi, rho, ephi):\n",
    "        c = self.alpha - 1 + ephi * self.Abar * R * rho * (1 + self.w + self.Q) /\\\n",
    "            ((g + self.Abar * R * U) * (1+self.w))\n",
    "        offset = np.log(1/ephi[-1] * (g[-1] + self.Abar[-1] * R[-1] * U[-1])) \n",
    "        temp = inv_derv_psi(xi, c, offset)\n",
    "        return  (g + self.Abar * R * U) / np.exp(temp)\n",
    "    \n",
    "    def drho(self, R, m, U, g, xi, Rp, mp, xip):\n",
    "        rho_stg = self.rho_stg(R, m, U, xi, g, xip, Rp, mp)\n",
    "        return np.concatenate( ([0], stg_dfdA(rho_stg, self.to_stg(self.Abar)) ,[0]) )\n",
    "        \n",
    "        \n",
    "    \n",
    "            \n",
    "    def k_coeffs(self, R, m, U, xi) :\n",
    "        xiprime = WENO_dfdA(xi, self.deltaL, self.Abar, 1e100)\n",
    "        Rprime = WENO_dfdA(R, self.deltaL, self.Abar, 1e100)\n",
    "        mprime = WENO_dfdA(m, self.deltaL, self.Abar, 1e100)\n",
    "        Uprime = WENO_dfdA(U, self.deltaL, self.Abar, 1e100)\n",
    "        \n",
    "        #xiprime = WENO_nuni_dfdA(xi, self.Vbar, self.Abar, 1e100)\n",
    "        #Rprime = WENO_nuni_dfdA(R, self.Vbar, self.Abar, 1e100)\n",
    "        #mprime = WENO_nuni_dfdA(m, self.Vbar, self.Abar, 1e100)\n",
    "        #Uprime = WENO_nuni_dfdA(U, self.Vbar, self.Abar, 1e100)\n",
    "        \n",
    "        g = self.gamma(R, m, U, xi)\n",
    "        r = self.rho(R, m, U, xi, g, xiprime, Rprime, mprime)\n",
    "        p = self.P(r)\n",
    "                \n",
    "        exi = np.exp(xi)\n",
    "        ephi = self.ephi(R, U, g, xi, xiprime, Rprime)\n",
    "        elambda = self.elambda(ephi, exi, xiprime)\n",
    "        epsi = self.epsi(R, U, g, xi, r, ephi)\n",
    "        \n",
    "\n",
    "        drho = self.drho(R, m, U, g, xi, Rprime, mprime, xiprime)\n",
    "        #drho  = dfdA(r, self.deltaL, self.Abar, 1e100)\n",
    "        drho[0] = 3 * elambda[0] / exi[0] * ((1 + self.w) * r[0] / ephi[0] - (r[0] + p[0]) * U[0])\n",
    "        drho[-1] = 0\n",
    "        \n",
    "        kxi = epsi / ephi / np.exp(xi) / self.alpha\n",
    "        \n",
    "        kR = epsi / exi * R * (U - 1/ephi)\n",
    "        \n",
    "        km = 3 * epsi / exi * (1/ephi * m * (1+self.w) - U * (p +m)) \n",
    "                \n",
    "        kU = - epsi / exi / (1 - self.w - self.Q) * (\n",
    "            (m + 3 * p) / 2 + U**2 - U / self.alpha / ephi \n",
    "        + (self.w + self.Q) * exi / elambda * Uprime + g * (self.w + self.Q) / ( np.concatenate( ([1], self.Abar[1:]) ) \\\n",
    "                                                                                * R * (1+self.w + self.Q)) * (\n",
    "            3 * self.Q * U + exi * (self.Qprime / elambda - self.Q_du / epsi) / (self.w + self.Q)\n",
    "         + 3 * (1 + self.w) * (U - 1 / ephi) + exi / elambda * drho / r) )\n",
    "        \n",
    "        # boundary conditions \n",
    "        kxi[0] = epsi[0] / elambda[0] * (xi[1] - xi[0]) / ( (self.Abar[1] - self.Abar[0]) )\n",
    "        kR[0] = epsi[0] / elambda[0] * (R[1] - R[0]) / ( (self.Abar[1] - self.Abar[0]) )\n",
    "        km[0] = epsi[0] / elambda[0] * (m[1] - m[0]) / ( (self.Abar[1] - self.Abar[0]) )\n",
    "        kU[0] = epsi[0] / elambda[0] * (U[1] - U[0]) / ( (self.Abar[1] - self.Abar[0]) )\n",
    "        \n",
    "        return kxi, kR, km, kU\n",
    "    \n",
    "    def adap_run_steps(self,n_steps, adj_intv=-1, tol=1e-7) :\n",
    "        step = 0\n",
    "        deltau = self.deltau_adap\n",
    "        kxi1, kR1, km1, kU1 = self.k_coeffs(self.R, self.m, self.U,  self.xi)\n",
    "        while(step < n_steps) :\n",
    "\n",
    "            if (deltau < 1e-9):\n",
    "                print(\"Warning, the time step is too small!\")\n",
    "                break\n",
    "            kxi2, kR2, km2, kU2 = self.k_coeffs(self.R + deltau/2*kR1, self.m + deltau/2*km1, \n",
    "                                                 self.U + deltau/2*kU1, self.xi + deltau/2*kxi1)\n",
    "            kxi3, kR3, km3, kU3 = self.k_coeffs(self.R + 3*deltau/4*kR2, self.m + 3*deltau/4*km2, \n",
    "                                                 self.U + 3*deltau/4*kU2, self.xi + 3*deltau/4*kxi2)\n",
    "            \n",
    "            \n",
    "            \n",
    "            xi_new = self.xi + deltau/9*(2*kxi1 + 3*kxi2 + 4*kxi3 )\n",
    "            R_new = self.R + deltau/9*(2*kR1 + 3*kR2 + 4*kR3 )\n",
    "            m_new = self.m + deltau/9*(2*km1 + 3*km2 + 4*km3 )\n",
    "            U_new = self.U + deltau/9*(2*kU1 + 3*kU2 + 4*kU3 )\n",
    "            \n",
    "            kxi4, kR4, km4, kU4 = self.k_coeffs(R_new , m_new , U_new, xi_new)\n",
    "\n",
    "            E_xi = np.max( np.abs(deltau * (-5*kxi1/72 + kxi2/12 + kxi3/9 - kxi4/8)))\n",
    "            E_R = np.max( np.abs((deltau * (-5*kR1/72 + kR2/12 + kR3/9 - kR4/8))))\n",
    "            E_m = np.max( np.abs(deltau * (-5*km1/72 + km2/12 + km3/9 - km4/8)))\n",
    "            E_U = np.max( np.abs(deltau * (-5*kU1/72 + kU2/12 + kU3/9 - kU4/8)))\n",
    "    \n",
    "            max_err_xi = np.max(np.abs(self.xi)) * tol\n",
    "            max_err_R = np.max(np.abs(self.R)) * tol\n",
    "            max_err_m = np.max(np.abs(self.m)) * tol\n",
    "            max_err_U = np.max(np.abs(self.U)) * tol\n",
    "            \n",
    "            if(E_xi < max_err_xi and E_R < max_err_R and E_m < max_err_m and E_U < max_err_U):\n",
    "                self.xi = xi_new\n",
    "                self.R = R_new\n",
    "                self.m = m_new\n",
    "                self.U = U_new\n",
    "                \n",
    "                kxi1 = np.copy(kxi4)\n",
    "                kR1 = np.copy(kR4)\n",
    "                km1 = np.copy(km4)\n",
    "                kU1 = np.copy(kU4)\n",
    "                \n",
    "                step+=1\n",
    "                self.u += deltau\n",
    "                \n",
    "            \n",
    "            # Adjust step size.\n",
    "            self.q = 0.8*np.min((max_err_xi/E_xi, max_err_R/E_R, max_err_m/E_m, max_err_U/E_U) )**(1/3)   # conservative optimal step factor\n",
    "            self.q = min(self.q,10)               # limit stepsize growth\n",
    "            deltau *= self.q\n",
    "            self.deltau_adap = deltau\n",
    "            #print(self.q, E_R, max_err_R, kR1.max(), kR2.max(), kR3.max(), kR4.max())\n",
    "    \n",
    "    def run_steps(self,n_steps, adj_intv=-1) :\n",
    "        step = 0\n",
    "        \n",
    "        deltau = self.deltau_i\n",
    "        while(step < n_steps) :\n",
    "            if(adj_intv > 0 and step % adj_intv == 0):\n",
    "                deltau = self.cfl_deltau(self.R, self.m, self.U, self.xi) * 0.05\n",
    "            \n",
    "            #der_U = dfdA(np.exp(self.xi * (self.alpha-1)) * self.Abar * self.R * self.U , self.deltaL, self.Abar, 1e100)\n",
    "            \n",
    "            #self.Q = self.kappa * (self.Abar[1])**2 * der_U**2\n",
    "            #self.Qprime = dfdA(self.Q , self.deltaL, self.Abar, 1e100)\n",
    "            #self.Q_du = (self.Q - self.Q_old) / deltau\n",
    "            \n",
    "            #self.Q[der_U > 0] = 0\n",
    "            #self.Qprime[der_U>0] = 0\n",
    "            #self.Q_du[der_U>0] = 0\n",
    "            \n",
    "            kxi1, kR1, km1, kU1 = self.k_coeffs(self.R, self.m, self.U,  self.xi)\n",
    "            kxi2, kR2, km2, kU2 = self.k_coeffs(self.R + deltau/2*kR1, self.m + deltau/2*km1, \n",
    "                                                 self.U + deltau/2*kU1, self.xi + deltau/2*kxi1)\n",
    "            kxi3, kR3, km3, kU3 = self.k_coeffs(self.R + deltau/2*kR2, self.m + deltau/2*km2, \n",
    "                                                 self.U + deltau/2*kU2, self.xi + deltau/2*kxi2)\n",
    "            kxi4, kR4, km4, kU4 = self.k_coeffs(self.R + deltau*kR3, self.m + deltau*km3, \n",
    "                                                 self.U + deltau*kU3,  self.xi + deltau*kxi3)\n",
    "            \n",
    "            self.xi = self.xi + (deltau/6*(kxi1 + 2*kxi2 + 2*kxi3 + kxi4)) \n",
    "            self.R = self.R + (deltau/6*(kR1 + 2*kR2 + 2*kR3 + kR4)) \n",
    "            self.m = self.m + (deltau/6*(km1 + 2*km2 + 2*km3 + km4))\n",
    "            self.U = self.U + (deltau/6*(kU1 + 2*kU2 + 2*kU3 + kU4))\n",
    "            \n",
    "            self.Q_old = self.Q\n",
    "            \n",
    "            step+=1\n",
    "            self.u += deltau\n",
    "\n",
    "              \n",
    "    def cfl_deltau(self,R, m, U, xi):\n",
    "        xiprime = dfdA(xi, self.deltaL, self.Abar, 1e100)\n",
    "        Rprime = dfdA(R, self.deltaL, self.Abar, 1e100)\n",
    "        mprime = dfdA(m, self.deltaL, self.Abar, 1e100)\n",
    "        \n",
    "        g = self.gamma(R, m, U, xi)\n",
    "        r = self.rho(R, m, U, xi, g, xiprime, Rprime, mprime)\n",
    "        #p = self.P(r)\n",
    "        exi = np.exp(xi)\n",
    "        ephi = self.ephi(R, U, g, xi, xiprime, Rprime)\n",
    "        elambda = self.elambda(ephi, exi, xiprime)\n",
    "        epsi = self.epsi(R, U, g, xi, r, ephi)\n",
    "        return ((1 / np.sqrt(self.w) - 1)  * (self.Abar[1] - self.Abar[0]) * elambda / epsi).min()\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "784229b7-83fd-410a-889a-a70588230cfb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# creating a mix of uniform and logarithmic grids\n",
    "def mix_grid(left, right, n):\n",
    "    A = np.exp(np.linspace(left, right, n))\n",
    "    dA = A[1] - A[0]\n",
    "    A = np.concatenate( (np.linspace(0, A[0],int(np.ceil(A[0] / dA)), endpoint=False), A))\n",
    "    return A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "14cad629-84aa-4355-80c2-558f0c32f84b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# creating uniform grids\n",
    "def uni_grid( right, n):\n",
    "    A = np.linspace(0, np.exp(right), n)\n",
    "    return A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1385,
   "id": "ac69a6c1-bcfb-4f4b-8f48-05d5888680f3",
   "metadata": {},
   "outputs": [],
   "source": [
    "n=1500\n",
    "\n",
    "lower = 1\n",
    "lower = -0.15\n",
    "upper = 2.2\n",
    "#L = np.linspace(-6, 1.5, n)\n",
    "#A = np.exp(L)\n",
    "#A = np.linspace(0, np.exp(1.5), n)\n",
    "A = mix_grid(lower,upper,n)\n",
    "#A = uni_grid(upper, n)\n",
    "\n",
    "w = 1 / 3\n",
    "alpha = 1/2 # alpha = 1/2 for w = 1/3\n",
    "\n",
    "\n",
    "rho0 = 1\n",
    "t0 = alpha * np.sqrt(3 / (8*np.pi*rho0))\n",
    "RH = t0 / alpha\n",
    "Abar = A / RH\n",
    "\n",
    "deltaL = 0\n",
    "\n",
    "L = Abar[-1]\n",
    "deltaA = Abar[1] - Abar[0]\n",
    "\n",
    "amp = 0.3\n",
    "delta0 = amp * np.exp(-Abar**2 / 2 /(1.6)**2)\n",
    "delta0P = amp * delta0 * 2 * (-1 / 2 / (1.6)**2 ) * Abar\n",
    "\n",
    "\n",
    "#delta0 = amp * (1 - Abar**2 / (Abar[-1] * RH)**2) *  np.exp(-3 * Abar**2 / 2 / (Abar[-1] * RH)**2)\n",
    "#delta0P = amp * delta0 * 2 * (-2 / (Abar[-1] * RH)**2 ) * Abar\n",
    "\n",
    "m = 1 + delta0 \n",
    "U = 1 - alpha * delta0 / 2\n",
    "R = 1 - alpha / 2 * (delta0 + w * Abar * delta0P / (1 + 3 * w) )\n",
    "\n",
    "\n",
    "ms = MS(R,m,U,w,alpha,A,rho0, deltaL,L, trace_ray=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1370,
   "id": "1dec5579-76df-4139-a7cc-f933dd13b9b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.1, 10000.0)"
      ]
     },
     "execution_count": 1370,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot((ms.Abar*ms.R * np.exp((ms.alpha-1) * ms.xi)), ms.rho(ms.R,ms.m))\n",
    "plt.xlim(0,1)\n",
    "plt.yscale('log')\n",
    "plt.ylim(1e-1,1e4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 883,
   "id": "aa612fa1-3fc2-4318-932a-2b3cf2fc3c2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f3a5bc8f700>]"
      ]
     },
     "execution_count": 883,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ms.Abar[0:ms.N-1], ms.U_hm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1357,
   "id": "6e50acf4-5c4a-41a6-99a1-f07f5b416686",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f3a309b7f40>]"
      ]
     },
     "execution_count": 1357,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ms.Abar, ms.U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1386,
   "id": "12d5711d-e94c-4b26-a412-16fa53944425",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tracing ray is enabled and excision will be performed!\n",
      "CPU times: user 28.9 ms, sys: 4 ms, total: 32.9 ms\n",
      "Wall time: 30.8 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "ms.adap_run_steps(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1356,
   "id": "cb0932dd-8815-452f-94ef-fe75c38fa818",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Not Tracing ray and NO excision will be performed!\n",
      "Photon has gone out of the outter boundary or horizon is identified!\n"
     ]
    }
   ],
   "source": [
    "ms.run_steps(53000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1359,
   "id": "a84b32d6-bc31-4f4b-966f-b25dc03d47b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "ms_std=copy.copy(ms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1366,
   "id": "9dcf1141-63f0-4be3-a96a-cbfbbeb37dc5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.8863530526193597"
      ]
     },
     "execution_count": 1366,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ms_std.xi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1164,
   "id": "540040b1-486c-40f7-a8c7-3f918d98dad9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import copy\n",
    "ms_mix2 = copy.copy(ms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 873,
   "id": "09e9a9bc-a63c-4990-838f-a76ee7679064",
   "metadata": {},
   "outputs": [],
   "source": [
    "import copy\n",
    "ms_mix = copy.copy(ms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 875,
   "id": "fd2949ba-fd64-43b8-ac5a-79982cc5161d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import copy\n",
    "ms_uni = copy.copy(ms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1313,
   "id": "96114c0d-c2a9-4c9e-96e1-1150b856c4fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "hm_uni = HM(ms_uni)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1342,
   "id": "8af668c9-c4e0-4dd1-8464-f3d494e11409",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "hm_mix = HM(ms_mix2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1123,
   "id": "61783ba8-da38-4dea-a31d-ead61691975e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_2413/1207476646.py:89: RuntimeWarning: overflow encountered in exp\n",
      "  return  (g + self.Abar * R * U) / np.exp(temp)\n",
      "/tmp/ipykernel_2413/1207476646.py:133: RuntimeWarning: invalid value encountered in true_divide\n",
      "  3 * self.Q * U + exi * (self.Qprime / elambda - self.Q_du / epsi) / (self.w + self.Q)\n"
     ]
    }
   ],
   "source": [
    "hm_mix.run_steps(333537)\n",
    "hm=hm_mix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1335,
   "id": "ed950331-88d9-4ca3-a3e1-c277d77986c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "U_bak = hm_mix.U.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1337,
   "id": "93960f26-68ce-4855-a7b0-2e70389578b6",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         741485 function calls in 23.707 seconds\n",
      "\n",
      "   Ordered by: standard name\n",
      "\n",
      "   ncalls  tottime  percall  cumtime  percall filename:lineno(function)\n",
      "        1    1.887    1.887   23.707   23.707 2697303776.py:145(adap_run_steps)\n",
      "    39606    0.955    0.000    0.955    0.000 2697303776.py:39(to_stg)\n",
      "     6601    0.831    0.000    0.831    0.000 2697303776.py:45(gamma)\n",
      "     6601    0.068    0.000    0.068    0.000 2697303776.py:48(P)\n",
      "     6601    0.726    0.000    3.517    0.001 2697303776.py:50(rho)\n",
      "     6601    0.763    0.000    2.072    0.000 2697303776.py:57(rho_stg)\n",
      "     6601    0.027    0.000    0.534    0.000 2697303776.py:78(ephi)\n",
      "     6601    0.145    0.000    0.145    0.000 2697303776.py:81(elambda)\n",
      "     6601    1.224    0.000    1.480    0.000 2697303776.py:84(epsi)\n",
      "     6601    0.114    0.000    2.814    0.000 2697303776.py:91(drho)\n",
      "     6601    4.417    0.001   20.794    0.003 2697303776.py:98(k_coeffs)\n",
      "    17600    0.096    0.000    0.709    0.000 <__array_function__ internals>:2(amax)\n",
      "     2200    0.012    0.000    0.111    0.000 <__array_function__ internals>:2(amin)\n",
      "    13202    0.086    0.000    0.323    0.000 <__array_function__ internals>:2(concatenate)\n",
      "     8800    0.045    0.000    0.196    0.000 <__array_function__ internals>:2(copy)\n",
      "        1    0.000    0.000   23.707   23.707 <string>:1(<module>)\n",
      "    79212    0.282    0.000    0.645    0.000 _asarray.py:23(asarray)\n",
      "     6601    0.015    0.000    0.015    0.000 _dtype.py:24(_kind_name)\n",
      "     6601    0.036    0.000    0.177    0.000 _dtype.py:307(_name_includes_bit_suffix)\n",
      "     6601    0.084    0.000    0.309    0.000 _dtype.py:321(_name_get)\n",
      "     6601    0.024    0.000    0.138    0.000 _methods.py:45(_sum)\n",
      "     6601    0.011    0.000    0.011    0.000 _ni_support.py:36(_extend_mode_to_code)\n",
      "     6601    0.100    0.000    0.471    0.000 _ni_support.py:73(_get_output)\n",
      "     6601    0.189    0.000    0.421    0.000 filters.py:179(_gaussian_kernel1d)\n",
      "     6601    0.078    0.000    2.306    0.000 filters.py:210(gaussian_filter1d)\n",
      "     6601    0.017    0.000    0.017    0.000 filters.py:50(_invalid_origin)\n",
      "     6601    0.189    0.000    1.807    0.000 filters.py:83(correlate1d)\n",
      "    17600    0.027    0.000    0.027    0.000 fromnumeric.py:2612(_amax_dispatcher)\n",
      "    17600    0.095    0.000    0.513    0.000 fromnumeric.py:2617(amax)\n",
      "     2200    0.003    0.000    0.003    0.000 fromnumeric.py:2737(_amin_dispatcher)\n",
      "     2200    0.011    0.000    0.087    0.000 fromnumeric.py:2742(amin)\n",
      "    19800    0.181    0.000    0.494    0.000 fromnumeric.py:70(_wrapreduction)\n",
      "    19800    0.048    0.000    0.048    0.000 fromnumeric.py:71(<dictcomp>)\n",
      "     8800    0.013    0.000    0.013    0.000 function_base.py:711(_copy_dispatcher)\n",
      "     8800    0.028    0.000    0.106    0.000 function_base.py:715(copy)\n",
      "    13202    0.022    0.000    0.022    0.000 multiarray.py:143(concatenate)\n",
      "    13202    0.053    0.000    0.080    0.000 numerictypes.py:285(issubclass_)\n",
      "     6601    0.051    0.000    0.140    0.000 numerictypes.py:359(issubdtype)\n",
      "    26404    6.600    0.000    6.834    0.000 {built-in method _cython_magic_151f6b3046fa84f4ff2ea51ca9fc42d7.WENO_dfdA}\n",
      "     6601    0.444    0.000    0.507    0.000 {built-in method _cython_magic_151f6b3046fa84f4ff2ea51ca9fc42d7.ephi_term}\n",
      "     6601    0.428    0.000    0.486    0.000 {built-in method _cython_magic_151f6b3046fa84f4ff2ea51ca9fc42d7.hm_rho_term}\n",
      "     6601    0.198    0.000    0.256    0.000 {built-in method _cython_magic_151f6b3046fa84f4ff2ea51ca9fc42d7.inv_derv_psi}\n",
      "     6601    0.454    0.000    0.515    0.000 {built-in method _cython_magic_151f6b3046fa84f4ff2ea51ca9fc42d7.rho_term_stg}\n",
      "     6601    0.243    0.000    0.299    0.000 {built-in method _cython_magic_151f6b3046fa84f4ff2ea51ca9fc42d7.stg_dfdA}\n",
      "        1    0.000    0.000   23.707   23.707 {built-in method builtins.exec}\n",
      "     2200    0.008    0.000    0.008    0.000 {built-in method builtins.getattr}\n",
      "    26404    0.047    0.000    0.047    0.000 {built-in method builtins.issubclass}\n",
      "     6601    0.011    0.000    0.011    0.000 {built-in method builtins.len}\n",
      "     2200    0.010    0.000    0.010    0.000 {built-in method builtins.min}\n",
      "    13202    0.063    0.000    0.063    0.000 {built-in method numpy.arange}\n",
      "    88012    0.441    0.000    0.441    0.000 {built-in method numpy.array}\n",
      "    41802    0.329    0.000    1.035    0.000 {built-in method numpy.core._multiarray_umath.implement_array_function}\n",
      "     6601    0.014    0.000    0.014    0.000 {built-in method numpy.core._multiarray_umath.normalize_axis_index}\n",
      "     6601    0.062    0.000    0.062    0.000 {built-in method numpy.zeros}\n",
      "     6601    0.952    0.000    0.952    0.000 {built-in method scipy.ndimage._nd_image.correlate1d}\n",
      "     6601    0.025    0.000    0.025    0.000 {method 'copy' of 'numpy.ndarray' objects}\n",
      "        1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}\n",
      "     6601    0.023    0.000    0.023    0.000 {method 'format' of 'str' objects}\n",
      "    19800    0.031    0.000    0.031    0.000 {method 'items' of 'dict' objects}\n",
      "    26401    0.340    0.000    0.340    0.000 {method 'reduce' of 'numpy.ufunc' objects}\n",
      "     6601    0.032    0.000    0.169    0.000 {method 'sum' of 'numpy.ndarray' objects}\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "cProfile.run('hm_mix.adap_run_steps(2200)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1343,
   "id": "bbd71fd7-1695-4d5d-8e65-50249024cf52",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 21.7 s, sys: 8 ms, total: 21.7 s\n",
      "Wall time: 21.7 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "hm_mix.adap_run_steps(2200)\n",
    "hm=hm_mix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1310,
   "id": "6fcc680b-8ac0-4e22-9dfc-ebc012600c8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "272695.2368164876"
      ]
     },
     "execution_count": 1310,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hm.u / hm.deltau_i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1323,
   "id": "3c0fbcbd-ad48-4cf8-852d-36f7dc7da99a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning, the time step is too small!\n"
     ]
    }
   ],
   "source": [
    "hm_uni.adap_run_steps(200)\n",
    "hm=hm_uni"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1324,
   "id": "023ac11c-9ce7-47dc-b33f-3c5aec3290a8",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f3a47984400>]"
      ]
     },
     "execution_count": 1324,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot((hm.Abar), hm.U)\n",
    "#plt.plot((hm.Abar), hm_mix_adp_bak.U)\n",
    "\n",
    "\n",
    "\n",
    "#plt.xlim(20,28)\n",
    "#plt.ylim(-0.95,1.2)\n",
    "#plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1281,
   "id": "a8e62d80-d4b2-4e11-b097-b2fba47e43f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f3a4a643940>]"
      ]
     },
     "execution_count": 1281,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot((hm.Abar), hm.U)\n",
    "#plt.plot((hm.Abar), hm_mix_adp_bak.U)\n",
    "\n",
    "\n",
    "\n",
    "#plt.xlim(20,28)\n",
    "#plt.ylim(-0.95,1.2)\n",
    "#plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1267,
   "id": "069a0b65-82b6-477c-90f1-e7212ce8af04",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f3a56921f70>]"
      ]
     },
     "execution_count": 1267,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot((hm_mix_high_bak.Abar), hm_mix_high_bak.U)\n",
    "\n",
    "\n",
    "plt.plot((hm.Abar), hm.U)\n",
    "\n",
    "\n",
    "#plt.xlim(20,28)\n",
    "#plt.ylim(-0.95,1.2)\n",
    "#plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 862,
   "id": "7ae6eaae-4b7e-4187-9495-7e5bbe44b6cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "hm_mix_high_bak=copy.copy(hm_mix)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 920,
   "id": "a5a6f50e-2a03-41ff-b074-2e9207b93736",
   "metadata": {},
   "outputs": [],
   "source": [
    "hm_uni_high_bak=copy.copy(hm_uni)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 963,
   "id": "8d6d969f-6987-429c-aefe-757084ae6b53",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         124404 function calls (120404 primitive calls) in 2.014 seconds\n",
      "\n",
      "   Ordered by: standard name\n",
      "\n",
      "   ncalls  tottime  percall  cumtime  percall filename:lineno(function)\n",
      "        1    0.045    0.045    2.014    2.014 2625552801.py:147(run_steps)\n",
      "     2400    0.060    0.000    0.060    0.000 2625552801.py:39(to_stg)\n",
      "      400    0.051    0.000    0.051    0.000 2625552801.py:45(gamma)\n",
      "      400    0.005    0.000    0.005    0.000 2625552801.py:48(P)\n",
      "      400    0.046    0.000    0.886    0.002 2625552801.py:50(rho)\n",
      "      400    0.048    0.000    0.130    0.000 2625552801.py:56(rho_stg)\n",
      "      400    0.002    0.000    0.035    0.000 2625552801.py:77(ephi)\n",
      "      400    0.010    0.000    0.010    0.000 2625552801.py:80(elambda)\n",
      "      400    0.077    0.000    0.094    0.000 2625552801.py:83(epsi)\n",
      "      400    0.007    0.000    0.176    0.000 2625552801.py:92(drho)\n",
      "      400    0.275    0.001    1.969    0.005 2625552801.py:99(k_coeffs)\n",
      "      800    0.005    0.000    0.020    0.000 <__array_function__ internals>:2(concatenate)\n",
      "      800    0.005    0.000    0.010    0.000 <__array_function__ internals>:2(copyto)\n",
      "      800    0.005    0.000    0.010    0.000 <__array_function__ internals>:2(empty_like)\n",
      "      800    0.005    0.000    0.182    0.000 <__array_function__ internals>:2(lstsq)\n",
      "      800    0.005    0.000    0.336    0.000 <__array_function__ internals>:2(polyfit)\n",
      "      800    0.004    0.000    0.103    0.000 <__array_function__ internals>:2(polyval)\n",
      "      800    0.005    0.000    0.051    0.000 <__array_function__ internals>:2(vander)\n",
      "      800    0.004    0.000    0.041    0.000 <__array_function__ internals>:2(zeros_like)\n",
      "        1    0.000    0.000    2.014    2.014 <string>:1(<module>)\n",
      "     1600    0.008    0.000    0.008    0.000 _arraytools.py:7(axis_slice)\n",
      "      800    0.003    0.000    0.004    0.000 _asarray.py:110(asanyarray)\n",
      "    11600    0.039    0.000    0.080    0.000 _asarray.py:23(asarray)\n",
      "      400    0.001    0.000    0.001    0.000 _dtype.py:24(_kind_name)\n",
      "      400    0.002    0.000    0.011    0.000 _dtype.py:307(_name_includes_bit_suffix)\n",
      "      400    0.005    0.000    0.019    0.000 _dtype.py:321(_name_get)\n",
      "      800    0.003    0.000    0.018    0.000 _methods.py:45(_sum)\n",
      "      800    0.003    0.000    0.011    0.000 _methods.py:59(_all)\n",
      "      400    0.001    0.000    0.001    0.000 _ni_support.py:36(_extend_mode_to_code)\n",
      "      400    0.006    0.000    0.029    0.000 _ni_support.py:73(_get_output)\n",
      "      800    0.030    0.000    0.494    0.001 _savitzky_golay.py:166(_fit_edge)\n",
      "      400    0.004    0.000    0.498    0.001 _savitzky_golay.py:210(_fit_edges_polyfit)\n",
      "      400    0.008    0.000    0.811    0.002 _savitzky_golay.py:225(savgol_filter)\n",
      "      400    0.024    0.000    0.165    0.000 _savitzky_golay.py:8(savgol_coeffs)\n",
      "      400    0.002    0.000    0.003    0.000 _util.py:147(float_factorial)\n",
      "      800    0.011    0.000    0.048    0.000 _util.py:216(_asarray_validated)\n",
      "      800    0.003    0.000    0.004    0.000 base.py:1205(isspmatrix)\n",
      "      400    0.044    0.000    0.129    0.000 basic.py:1031(lstsq)\n",
      "      400    0.003    0.000    0.004    0.000 blas.py:382(getter)\n",
      "      800    0.002    0.000    0.004    0.000 core.py:6371(isMaskedArray)\n",
      "      400    0.005    0.000    0.138    0.000 filters.py:138(convolve1d)\n",
      "      400    0.001    0.000    0.001    0.000 filters.py:50(_invalid_origin)\n",
      "      400    0.011    0.000    0.131    0.000 filters.py:83(correlate1d)\n",
      "      800    0.010    0.000    0.029    0.000 function_base.py:422(asarray_chkfinite)\n",
      "     1200    0.006    0.000    0.008    0.000 getlimits.py:382(__new__)\n",
      "     1200    0.004    0.000    0.007    0.000 lapack.py:1013(<genexpr>)\n",
      "      800    0.003    0.000    0.003    0.000 lapack.py:1017(_check_work_float)\n",
      "      400    0.009    0.000    0.018    0.000 lapack.py:982(_compute_lwork)\n",
      "      800    0.002    0.000    0.002    0.000 linalg.py:102(get_linalg_error_extobj)\n",
      "     1600    0.008    0.000    0.019    0.000 linalg.py:107(_makearray)\n",
      "     2400    0.007    0.000    0.011    0.000 linalg.py:112(isComplexType)\n",
      "     2400    0.008    0.000    0.011    0.000 linalg.py:125(_realType)\n",
      "      800    0.001    0.000    0.001    0.000 linalg.py:131(_linalgRealType)\n",
      "      800    0.012    0.000    0.029    0.000 linalg.py:135(_commonType)\n",
      "      800    0.002    0.000    0.002    0.000 linalg.py:187(_assert_2d)\n",
      "      800    0.001    0.000    0.001    0.000 linalg.py:2165(_lstsq_dispatcher)\n",
      "      800    0.098    0.000    0.172    0.000 linalg.py:2169(lstsq)\n",
      "      800    0.002    0.000    0.003    0.000 misc.py:182(_datacopied)\n",
      "      800    0.001    0.000    0.001    0.000 multiarray.py:1054(copyto)\n",
      "      800    0.001    0.000    0.001    0.000 multiarray.py:143(concatenate)\n",
      "      800    0.001    0.000    0.001    0.000 multiarray.py:75(empty_like)\n",
      "      800    0.001    0.000    0.001    0.000 numeric.py:71(_zeros_like_dispatcher)\n",
      "      800    0.008    0.000    0.032    0.000 numeric.py:75(zeros_like)\n",
      "      800    0.003    0.000    0.005    0.000 numerictypes.py:285(issubclass_)\n",
      "      400    0.003    0.000    0.009    0.000 numerictypes.py:359(issubdtype)\n",
      "      800    0.001    0.000    0.001    0.000 polynomial.py:449(_polyfit_dispatcher)\n",
      "      800    0.055    0.000    0.325    0.000 polynomial.py:453(polyfit)\n",
      "      800    0.001    0.000    0.001    0.000 polynomial.py:692(_polyval_dispatcher)\n",
      "      800    0.041    0.000    0.093    0.000 polynomial.py:696(polyval)\n",
      "      800    0.001    0.000    0.001    0.000 twodim_base.py:499(_vander_dispatcher)\n",
      "      800    0.019    0.000    0.042    0.000 twodim_base.py:504(vander)\n",
      "     1600    0.412    0.000    0.427    0.000 {built-in method _cython_magic_3c884615fe871d54dba3bc94a06cc110.WENO_dfdA}\n",
      "      400    0.029    0.000    0.033    0.000 {built-in method _cython_magic_3c884615fe871d54dba3bc94a06cc110.ephi_term}\n",
      "      400    0.026    0.000    0.030    0.000 {built-in method _cython_magic_3c884615fe871d54dba3bc94a06cc110.hm_rho_term}\n",
      "      400    0.012    0.000    0.016    0.000 {built-in method _cython_magic_3c884615fe871d54dba3bc94a06cc110.inv_derv_psi}\n",
      "      400    0.028    0.000    0.032    0.000 {built-in method _cython_magic_3c884615fe871d54dba3bc94a06cc110.rho_term_stg}\n",
      "      400    0.015    0.000    0.018    0.000 {built-in method _cython_magic_3c884615fe871d54dba3bc94a06cc110.stg_dfdA}\n",
      "      400    0.001    0.000    0.001    0.000 {built-in method builtins.divmod}\n",
      "        1    0.000    0.000    2.014    2.014 {built-in method builtins.exec}\n",
      "     2400    0.004    0.000    0.004    0.000 {built-in method builtins.getattr}\n",
      "     2800    0.005    0.000    0.005    0.000 {built-in method builtins.isinstance}\n",
      "     5600    0.009    0.000    0.009    0.000 {built-in method builtins.issubclass}\n",
      "     4800    0.007    0.000    0.007    0.000 {built-in method builtins.len}\n",
      "      400    0.001    0.000    0.001    0.000 {built-in method math.factorial}\n",
      "     2400    0.014    0.000    0.014    0.000 {built-in method numpy.arange}\n",
      "    12400    0.043    0.000    0.043    0.000 {built-in method numpy.array}\n",
      "6400/2400    0.040    0.000    0.441    0.000 {built-in method numpy.core._multiarray_umath.implement_array_function}\n",
      "      400    0.001    0.000    0.001    0.000 {built-in method numpy.core._multiarray_umath.normalize_axis_index}\n",
      "      800    0.004    0.000    0.004    0.000 {built-in method numpy.empty}\n",
      "      800    0.002    0.000    0.002    0.000 {built-in method numpy.promote_types}\n",
      "     2000    0.012    0.000    0.012    0.000 {built-in method numpy.zeros}\n",
      "      400    0.080    0.000    0.080    0.000 {built-in method scipy.ndimage._nd_image.correlate1d}\n",
      "     1600    0.003    0.000    0.003    0.000 {method '__array_prepare__' of 'numpy.ndarray' objects}\n",
      "      800    0.013    0.000    0.013    0.000 {method 'accumulate' of 'numpy.ufunc' objects}\n",
      "      800    0.003    0.000    0.015    0.000 {method 'all' of 'numpy.ndarray' objects}\n",
      "     2400    0.010    0.000    0.010    0.000 {method 'astype' of 'numpy.ndarray' objects}\n",
      "      400    0.002    0.000    0.002    0.000 {method 'copy' of 'numpy.ndarray' objects}\n",
      "        1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}\n",
      "      400    0.001    0.000    0.001    0.000 {method 'format' of 'str' objects}\n",
      "     4000    0.007    0.000    0.007    0.000 {method 'get' of 'dict' objects}\n",
      "     1600    0.023    0.000    0.023    0.000 {method 'reduce' of 'numpy.ufunc' objects}\n",
      "     2800    0.010    0.000    0.010    0.000 {method 'reshape' of 'numpy.ndarray' objects}\n",
      "      800    0.004    0.000    0.022    0.000 {method 'sum' of 'numpy.ndarray' objects}\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import cProfile\n",
    "cProfile.run('hm_mix_bak.run_steps(100)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 916,
   "id": "5ffc8fd0-400d-4077-ac5a-9349605df1ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "hm_uni=copy.copy(hm_uni_high_bak)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 598,
   "id": "d7539671-ee1d-4b90-9847-0a3821f5c7c4",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_2413/1599527816.py:154: RuntimeWarning: overflow encountered in exp\n",
      "  der_U = dfdA(np.exp(self.xi * (self.alpha-1)) * self.Abar * self.R * self.U , self.deltaL, self.Abar, 1e100)\n",
      "/tmp/ipykernel_2413/1599527816.py:45: RuntimeWarning: overflow encountered in exp\n",
      "  return np.sqrt(np.exp(2 * (1 - self.alpha) * self.xi)\n",
      "/tmp/ipykernel_2413/1599527816.py:50: RuntimeWarning: invalid value encountered in true_divide\n",
      "  temp = (g + self.Abar * R * U) / (g - (self.w + self.Q ) * self.Abar * R * U ) \\\n",
      "/tmp/ipykernel_2413/1599527816.py:113: RuntimeWarning: overflow encountered in exp\n",
      "  exi = np.exp(xi)\n",
      "/tmp/ipykernel_2413/1599527816.py:80: RuntimeWarning: invalid value encountered in multiply\n",
      "  return self.alpha * ephi * exi * xiprime\n",
      "/tmp/ipykernel_2413/1599527816.py:89: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  return  (g + self.Abar * R * U) / np.exp(temp)\n",
      "/tmp/ipykernel_2413/1599527816.py:124: RuntimeWarning: overflow encountered in exp\n",
      "  kxi = epsi / ephi / np.exp(xi) / self.alpha\n",
      "/tmp/ipykernel_2413/1599527816.py:126: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  kR = epsi / exi * R * (U - 1/ephi)\n",
      "/tmp/ipykernel_2413/1599527816.py:128: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  km = 3 * epsi / exi * (1/ephi * m * (1+w) - U * (p +m))\n",
      "/tmp/ipykernel_2413/1599527816.py:131: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  (m + 3 * p) / 2 + U**2 - U / self.alpha / ephi\n",
      "/tmp/ipykernel_2413/1599527816.py:132: RuntimeWarning: invalid value encountered in true_divide\n",
      "  + (w + self.Q) * exi / elambda * Uprime + g * (w + self.Q) / ( np.concatenate( ([1], self.Abar[1:]) ) * R * (1+w + self.Q)) * (\n",
      "/tmp/ipykernel_2413/1599527816.py:133: RuntimeWarning: invalid value encountered in true_divide\n",
      "  3 * self.Q * U + exi * (self.Qprime / elambda - self.Q_du / epsi) / (self.w + self.Q)\n",
      "/tmp/ipykernel_2413/1599527816.py:134: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  + 3 * (1 + w) * (U - 1 / ephi) + exi / elambda * drho / r) )\n",
      "/tmp/ipykernel_2413/1599527816.py:134: RuntimeWarning: invalid value encountered in true_divide\n",
      "  + 3 * (1 + w) * (U - 1 / ephi) + exi / elambda * drho / r) )\n"
     ]
    },
    {
     "ename": "ZeroDivisionError",
     "evalue": "float division",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mZeroDivisionError\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_2413/3915526147.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m#hm_mix.deltau_i*= 10\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mhm_mix\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_steps\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m12000\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mhm\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mhm_mix\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_2413/1599527816.py\u001b[0m in \u001b[0;36mrun_steps\u001b[0;34m(self, n_steps, exc_intv)\u001b[0m\n\u001b[1;32m    163\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    164\u001b[0m             \u001b[0mkxi1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkR1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkm1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkU1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mk_coeffs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mR\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mU\u001b[0m\u001b[0;34m,\u001b[0m  \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 165\u001b[0;31m             kxi2, kR2, km2, kU2 = self.k_coeffs(self.R + deltau/2*kR1, self.m + deltau/2*km1, \n\u001b[0m\u001b[1;32m    166\u001b[0m                                                  self.U + deltau/2*kU1, self.xi)\n\u001b[1;32m    167\u001b[0m             kxi3, kR3, km3, kU3 = self.k_coeffs(self.R + deltau/2*kR2, self.m + deltau/2*km2, \n",
      "\u001b[0;32m/tmp/ipykernel_2413/1599527816.py\u001b[0m in \u001b[0;36mk_coeffs\u001b[0;34m(self, R, m, U, xi)\u001b[0m\n\u001b[1;32m    112\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    113\u001b[0m         \u001b[0mexi\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 114\u001b[0;31m         \u001b[0mephi\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mephi\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mR\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mU\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxiprime\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mRprime\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    115\u001b[0m         \u001b[0melambda\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0melambda\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mephi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxiprime\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    116\u001b[0m         \u001b[0mepsi\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mepsi\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mR\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mU\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mephi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/tmp/ipykernel_2413/1599527816.py\u001b[0m in \u001b[0;36mephi\u001b[0;34m(self, R, U, g, xi, xiprime, Rprime)\u001b[0m\n\u001b[1;32m     75\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     76\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mephi\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mR\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mU\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxiprime\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mRprime\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 77\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mephi_term\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mR\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mU\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mAbar\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     78\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     79\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0melambda\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mephi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxiprime\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m_cython_magic_6fe1f93bc6ccb0ed02b1f05de6b21e93.pyx\u001b[0m in \u001b[0;36m_cython_magic_6fe1f93bc6ccb0ed02b1f05de6b21e93.ephi_term\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32m_cython_magic_6fe1f93bc6ccb0ed02b1f05de6b21e93.pyx\u001b[0m in \u001b[0;36m_cython_magic_6fe1f93bc6ccb0ed02b1f05de6b21e93.ephi_term\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;31mZeroDivisionError\u001b[0m: float division"
     ]
    }
   ],
   "source": [
    "#hm_mix.deltau_i*= 10\n",
    "hm_mix.run_steps(12000)\n",
    "hm=hm_mix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1124,
   "id": "6bd4d41a-0ece-45d1-a56e-c2fc3ae1c7f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03940933898531598"
      ]
     },
     "execution_count": 1124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(hm_mix_adp_bak.u - hm_mix.u) / hm_mix.deltau_i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1119,
   "id": "bd58b146-0d22-4f64-ad95-ab08c9452245",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-5536.950510792765"
      ]
     },
     "execution_count": 1119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(hm_mix_high_bak.u - hm_mix.u) / hm_mix.deltau_i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "5ea302c0-4e7c-4b8b-9cac-be2ece93e3f3",
   "metadata": {},
   "outputs": [],
   "source": [
    "hm_uni=copy.copy(hm_uni_bak)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "7ff7951e-ffb2-4372-90dc-9c7a38fb1bfa",
   "metadata": {},
   "outputs": [],
   "source": [
    "hm_uni_bak=copy.copy(hm_uni)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 958,
   "id": "f7cd0826-0791-442d-b119-d4b302af2986",
   "metadata": {},
   "outputs": [],
   "source": [
    "hm_mix_bak=copy.copy(hm_mix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "id": "7fcde445-f758-4f9d-820f-58a4d03637f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "hm_mix = copy.copy(hm_mix_bak)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1269,
   "id": "7049c575-cc39-4e55-ba58-9c6eccc7deab",
   "metadata": {},
   "outputs": [],
   "source": [
    "hm_mix_adp_bak=copy.copy(hm_mix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 477,
   "id": "20d58ff8-e617-4153-a1aa-92a1b1b68a4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "hm_mix_bak2=copy.copy(hm_mix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 323,
   "id": "166c1f21-ee7c-4b21-a30c-4cf77a187845",
   "metadata": {},
   "outputs": [],
   "source": [
    "hm_mix = copy.copy(hm_mix_adp_bak)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1264,
   "id": "29c9fc06-59f5-4df6-a502-fe3c35ec289d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 10.0)"
      ]
     },
     "execution_count": 1264,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = np.exp(hm.alpha * hm.xi)\n",
    "H = np.exp(-hm.xi) / hm.RH\n",
    "rho_b = a**(1+hm.w)\n",
    "Rb = a * hm.A\n",
    "plt.plot(hm.R * Rb ,  (np.exp(-hm.xi/2) * hm.R **3 * hm.Abar**3 * hm.m ) / 2 )\n",
    "plt.plot(hm.R * Rb ,  np.array([5] * hm.N) )\n",
    "plt.xlim(0,10)\n",
    "plt.ylim(0,10)\n",
    "#plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1334,
   "id": "cc90c76d-e2aa-4ce5-ab62-911cd86bd6c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "206"
      ]
     },
     "execution_count": 1334,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hm_mix.U.argmin()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 672,
   "id": "687027ad-8d9c-4871-8560-46c1e900dd53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f3a6fea44c0>]"
      ]
     },
     "execution_count": 672,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot((hm.Abar), hm.U)\n",
    "#plt.plot((hm_uni.Abar), hm_uni.U)\n",
    "\n",
    "\n",
    "\n",
    "#plt.xlim(20,28)\n",
    "#plt.ylim(-0.95,1.2)\n",
    "#plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 543,
   "id": "bb2c94f1-5d11-46c0-9ac4-84395b6ba6f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f3a81567430>]"
      ]
     },
     "execution_count": 543,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot((hm_mix_bak.Abar), hm_mix_bak.U)\n",
    "#plt.plot((hm_uni.Abar), hm_uni.U)\n",
    "\n",
    "\n",
    "\n",
    "#plt.xlim(20,28)\n",
    "#plt.ylim(-0.95,1.2)\n",
    "#plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 653,
   "id": "e8e4e4e1-5f98-406c-8fcc-dd534c28a724",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f3a8e05d7f0>]"
      ]
     },
     "execution_count": 653,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot((hm_uni.Abar), hm_uni.U)\n",
    "#plt.plot((hm_uni.Abar), hm_uni.U)\n",
    "\n",
    "\n",
    "\n",
    "#plt.xlim(0,5)\n",
    "#plt.ylim(-60,10)\n",
    "#plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 540,
   "id": "828ed535-cb7e-4553-929a-2298cfb45797",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-30.0, -10.0)"
      ]
     },
     "execution_count": 540,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot((hm_mix.Abar), hm_mix.U)\n",
    "#plt.plot((hm_uni.Abar), hm_uni.U)\n",
    "\n",
    "\n",
    "\n",
    "plt.xlim(0,5)\n",
    "plt.ylim(-30,-10)\n",
    "#plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 537,
   "id": "7b05ad90-91fe-40e7-86af-53ef44843ef1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f3a839483d0>]"
      ]
     },
     "execution_count": 537,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot((hm_mix.Abar), hm_mix.U)\n",
    "#plt.plot((hm_uni.Abar), hm_uni.U)\n",
    "\n",
    "\n",
    "\n",
    "#plt.xlim(8,10)\n",
    "#plt.ylim(-0.9,1.1)\n",
    "#plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 597,
   "id": "749c3544-ad6a-41b8-9609-1310395f3517",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f3a7c0d51c0>]"
      ]
     },
     "execution_count": 597,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot((hm_mix.Abar), hm_mix.U)\n",
    "#plt.plot((hm_uni.Abar), hm_uni.U)\n",
    "\n",
    "\n",
    "\n",
    "#plt.xlim(8,10)\n",
    "#plt.ylim(-0.9,1.1)\n",
    "#plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 628,
   "id": "f32662fe-e899-4d47-b68c-11a448749e07",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-60.0, 10.0)"
      ]
     },
     "execution_count": 628,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZTUDqBJbBvFFzgo/d9QKTc9J4+MZ3kpcx9m7MNVEdb2nnr9V1XtNOHXUt4dshnzslm4vnFnPxnGIqZuSr0zaOxkIn8GDWAv/XzH5IuBN4DvBSlNYlE9T8khzuvq6C6+59iZvu38T9n7uQRHUaRkVndw+b9jfw/O7wAX/bkSacg/yMZC6aU8zFc4q4eG4xk3PUjj+RRJQAzOxq4CdAMfBHM9vsnLvcOfe6mT0EbAe6gJtVASSjsWJWIf/r6nfw9d9t4UdP7+Lrl8+Ld0gTRm/n7Z+9ztsWr/N26fQ8/uv753Lx3GLOm5qrpDuBRVoF9AjwyCDT7gDuiGT5IgB/t2waG/fVc+f6apaV5+sagVE61dnNS2/W89zOEH/eVdt3AdbUvHRWLS7lkrlFvOucInL0ew2BoZvBybhw+1UL2Xqoia89tJk/fvk96hQeoX11rTy3szb8LX/vcU519pCSlMCFMwv4xIXlXKLO20CL+60gdC8gGal9da2s+slfmTUpi9994Z2kJEXvB7fHq5Md3WzYe7zvoL/veBsAMwozuHTeJC6ZW8yKWYW6Bfc4pnsBSWD957Yabrx/E59+1wxuv2phvMOJO+cce0Jvfct/8c16Orp6SEtO4F2zi7h0XrhiZ0ZRZrxDFZ+N5SogkahYeV4Jn71oJvf89U0umFEQyB+a7+5xvLj3OI9vq2H9jhCHG08CcM6kLK5bUc4l88K3W1CJpgxHCUDGnVuuOJdXDzTwjYe3cG5JNrOLs+IdUtQ559h0oJF1W47wx9dqCDW3k5GSyEXnFPHFy2Zzydxi/aiOnDUlABl3khMTuPMTS/nQj//CF+/fxB9ufveEbNPuvQJ33ZYa1m05wuHGk6QkJfDeeZO4akkpl82bNCE/t8SOEoCMS6V56fzvNefz6f/zEv/j0W18/6OL4x2Sb/aEWli7+Qjrth5hb6iVpATjPXOK+McPzuUDCyaTrTJN8UncE0BTUxOVlZWqApKzdsncYv7hvXP48bO7WVyWx7UryuMd0qgdrG/jsa3hb/rba05gBitmFvK5i2ax8rwpFGTqNhgS1lsFBORGuixVAcm41t3j+NyvXmb9zhDfueYdrFk+Pd4hjYhzjt21LazfUcuTrx9l04FGAM6fnseqRaV8aFGJbrsgQ1IVkAReYoLx808to/LXr3DbH7YxvySHxWV58Q5rQCc7uvnbnjrW76x9W/XOgpIcvrFyHqsWlVJWoI5ciR2dAciE0NTWycp/e570lEQe+eK7x8y96Pcfb2X9jlrW7wxfidvR1UNGSiLvPqeI9547iUvnFVOSq6ua5ezpDEDEk5uRzA8+uphr732JK//tL9z5ifM5f3p+zOPo6XFsOtDAE9uOsn5nLXu9++3MKsrkUxeW895zJ3HBzHxSk1S9I/GnMwCZUDYdaODLD7xKU1snD98Uu18T23m0mUc3H+bRzW+Va66YVchl84q5bN4kXYkrvvPjDEAJQCacI40n+chP/x/JiQncde0yFpbmROVmZ4cbT7JuyxH+8OphdhxtJjHBuOicIlYvKeWDC6eQlaoTbImeCZEAdDM4iYZth5tYU7WBlvYu5k7O4pYrzuW9504e9fKcc9Q0nWJPqIVdx1p48vWjvPRmPRCu3Fm9uJQPLSqlODvVr48gMiDdDE5kBOpbO3j8tRrue2Efu4618MkLp/O1D8wlOSF8F9GstKQBf+yktb2LTQca2HygkepQC3tCLewNtdLW8dZvGs0qzuQjS6ayekkp5YVq3pHYmxBnAEoAEm3tXd384KldVD2/923jM1ISWVCSw3lTczlnUhZ7Q61s3F/P60dO0N0T/r+Ylp/O7OKs8GNSJrOLs5hVnElxVqruoS9xpQQgchZe2d/Aqwca+g7cB+vbeP1IE68fOUFbRzcpSQksKctj+YwCLphZwNLpebrtgoxZKgMVOQvLyvNZVn5maWh3j+NI40km5aSqPFMCRQlAAi8xwXQFrgRS3H9Tr/dmcN7NjUREZAjr1q2jsrISdDM4EZFg8qMPIKIzADP7npntMLOtZvaImeX1m3armVWb2U4zuzyS9YiIiP8ibQJ6GjjPObcI2AXcCmBmC4A1wEJgJfAzM1PvmojIGBJRAnDOPeWc6/IGNwDTvNergQedc+3OuTeBamB5JOsSERF/+dkJfAPwhPd6KnCw37RD3jgRERkjhi0DNbNngCkDTLrNOfeoN89tQBfwm7MNIBQKUVHxVj9GZWVlbw+3iIj0U1VVRVVVVe9gUaTLi7gKyMw+DXwBeJ9zrs0bdyuAc+7b3vCTwO3OuRdOf7+qgEREzt5YqAJaCXwDuKr34O9ZC6wxs1QzmwnMAV6KZF0iIuKvSK8EvhNIBZ727q+ywTl3o3PudTN7CNhOuGnoZudc9xDLERGRGIsoATjnzhli2h3AHZEsX0REoifut4IQEZH4iHsC0L2ARERGTvcCEhEJuLhXAYmIyPilBCAiElBKACIiAaUEICISUHFPAKoCEhEZOVUBiYgEnKqARERk1JQAREQCSglARCSglABERAJKCUBEJKDingBUBioiMnIqAxURCTiVgYqIyKgpAYiIBJQSgIhIQCkBiIgEVNwTgKqARERGTlVAIiIBF/cqIDP7FzPbamabzewpMyv1xpuZ/djMqr3pSyNZj4iI+C/SJqDvOecWOeeWAI8B3/TGXwHM8R6VwM8jXI+IiPgsogTgnDvRbzAT6G1PWg3c58I2AHlmVhLJukRExF9JkS7AzO4ArgOagMu80VOBg/1mO+SNq4l0fSIi4o9hzwDM7Bkz2zbAYzWAc+4251wZ8BvgS2cbQCgUoqKiou9RVVV19p9CRCQAqqqq+o6VQFGky/OtCsjMpgOPO+fOM7O7gOeccw9403YClzrnzjgDUBWQiMjZGwtVQHP6Da4Gdniv1wLXedVAK4CmgQ7+IiISP5H2AXzHzOYBPcB+4EZv/OPAlUA10AZ8JsL1iIiIzyJKAM65/zLIeAfcHMmyRUQkuuJ+KwgREYmPuCcA3QtIRGTkdC8gEZGAi3sVkIiIjF9KACIiAaUEICISUEoAIiIBpQQgIhJQcU8AKgMVERk5lYGKiAScykBFRGTUlABERAJKCUBEJKCUAEREAiruCUBVQCIiI6cqIBGRgFMVkIiIjJoSgIhIQCkBiIgElBKAiEhAxT0BqApIRGTkVAUkIhJwqgISEZFR8yUBmNk/mpkzsyJv2Mzsx2ZWbWZbzWypH+sRERH/RJwAzKwM+CBwoN/oK4A53qMS+Hmk6xEREX/5cQbwI+AbQP/OhNXAfS5sA5BnZiU+rEtERHwSUQIws9XAYefcltMmTQUO9hs+5I07QygUoqKiou9RVVUVSUgiIhNWVVVV37ESKIp0eUnDzWBmzwBTBph0G/BPhJt/Rq24uBhVAYmIDK+ysrK3BBQzq4t0ecMmAOfc+wcab2bvAGYCW8wMYBqwycyWA4eBsn6zT/PGiYjIGDHqJiDn3GvOuUnOuRnOuRmEm3mWOueOAmuB67xqoBVAk3Ouxp+QRUTED8OeAYzS48CVQDXQBnwmSusREZFR8i0BeGcBva8dcLNfyxYREf/F/Upg3QtIRGTkdC8gEZGA072ARERk1JQAREQCSglARCSglABERAJKCUBEJKDingBUBioiMnIqAxURCTiVgYqIyKgpAYiIBJQSgIhIQCkBiIgEVNwTgKqARERGTlVAIiIBpyogEREZNSUAEZGAUgIQEQkoJQARkYCKewJQFZCIyMipCkhEJOBUBSQiIqMWUQIws9vN7LCZbfYeV/abdquZVZvZTjO7PPJQRUTET0k+LONHzrnv9x9hZguANcBCoBR4xszmOue6fVifiIj4IFpNQKuBB51z7c65N4FqYHmU1iUiIqPgRwL4kpltNbN7zSzfGzcVONhvnkPeuDOEQiEqKir6HlVVVT6EJCIy8VRVVfUdK4GiSJc3bBWQmT0DTBlg0m3ABqAOcMC/ACXOuRvM7E5gg3Pufm8Z9wBPOOcePn0hqgISETl7flQBDdsH4Jx7/wiDuRt4zBs8DJT1mzzNGyciImNEpFVAJf0Grwa2ea/XAmvMLNXMZgJzgJciWZeIiPgr0iqg75rZEsJNQPuALwA45143s4eA7UAXcLMqgERExpaIEoBz7tohpt0B3BHJ8kVEJHrifiWw7gUkIjJyuheQiEjA6V5AIiIyakoAIiIBpQQgIhJQSgAiIgGlBCAiElBxTwAqAxURGTmVgYqIBJzKQEVEZNSUAEREAkoJQEQkoJQAREQCKu4JQFVAIiIjpyogEZGAUxWQiIiMmhKAiEhAKQGIiASUEoCISEDFPQGoCkhEZORUBSQiEnCqAhIRkVGLOAGY2T+Y2Q4ze93Mvttv/K1mVm1mO83s8sHeHwqFIg0hJqqqquIdwrDGQ4ygOP2mOP01XuIEiiJegnNu1A/gMuAZINUbnuQ9LwC2AKnATGAPkDjQMjIyMtxQ1q5dG9F0v5axbNmyqK8j0mUMF6Mf6/BjGbGI04/PEenffCTzTJQ4Y/E/5EccE+V/3TnngFYXwfHbORfxGcBNwHecc+1eMqn1xq8GHnTOtTvn3gSqgeWjWcFwncMj6Tz2YxmxWIfi9G8dfnwOP94flDhj8Tf3I46xsG/6tQw/RNQJbGabgUeBlcAp4OvOuZfN7E5gg3Pufm++e4AnnHMPD7CMU0B3v1EhoK7fcC7QNEQYw033axlFp8UVjXVEuozhYvRjHX4sIxZx+vE5Iv2bj2SeiRJnLP6H/IhjvP+vFwHF3utE51zaMOsZUtJwM5jZM8CUASbd5r2/AFgBXAA8ZGazziaASD+AiIiMzrAJwDn3/sGmmdlNwO+99qiXzKyHcIY6DJT1m3WaN05ERMaISPsA/kC4IxgzmwukED51WgusMbNUM5sJzAFeinBdIiLio0gTwL3ALDPbBjwIXO91UL8OPARsB/7Tm2+7VxZ6y+kL8RLFb73pL5rZjAjjOmtmVmZm681su1fS+pUB5rnUzJrMbLP3+Gas4/Ti2Gdmr3kxnHEVnYX92NueW81saRxinNdvO202sxNm9tXT5onL9jSze82s1ttve8cVmNnTZrbbe84f5L3Xe/PsNrPr4xDn97yy661m9oiZ5Q3y3iH3kRjEebuZHe73t71ykPeu9ErFBzw2xCDO3/aLcZ/XrznQe2OyPQc7DkVt/4y0jGi4B5BIuAx0FuEzhC3AgtPm+SLwC+/1GuC30Y5rgDhLgKXe62xg1wBxXgo8FuvYBoh1H1A0xPQrgScAI9w/82Kc400EjgLlY2F7AhcDS4Ft/cZ9F7jFe30L8K8DvK8A2Os953uv82Mc5weBJO/1vw4U50j2kRjEeTvhopDh9oshjw3RjvO06T8AvhnP7TnYcSha+2csrgReDlQ75/Y65zoInymsPm2e1cCvvNcPA+8zM4tBbH2cczXOuU3e62bgDWBqLGPw0WrgPhe2Acgzs5I4xvM+YI9zbn8cY+jjnHseqD9tdP998FfARwZ46+XA0865eudcA/A04Qq4mMXpnHvKOdflDW4g3L8WV4Nsz5EYybHBN0PF6R1vPgY8EK31j8QQx6Go7J+xSABTgYP9hg9x5oG1bx5v524CCmMQ24C8JqjzgRcHmPxOM9tiZk+Y2cLYRtbHAU+Z2StmVjnA9JFs81haw+D/WGNhewJMds7VeK+PApMHmGesbdcbCJ/pDWS4fSQWvuQ1Vd07SJPFWNqe7wGOOed2DzI95tvztONQVPZP3QvoNGaWBfwH8FXn3InTJm8i3IyxGPgJ4U7weLjIObcUuAK42cwujlMcwzKzFOAq4HcDTB4r2/NtXPh8Or53SRyGmd0GdAG/GWSWeO8jPwdmA0uAGsLNK2PZxxn6239Mt+dQxyE/989YJICRlIT2zWNmSYQvgjgeg9jexsySCW/03zjnfn/6dOfcCedci/f6cSDZzCK/H8dZcs4d9p5rgUc48yrrsVSGewWwyTl37PQJY2V7eo71NpN5z7UDzDMmtquZfRr4MPBJ72BwhhHsI1HlnDvmnOt2zvUAdw+y/rGyPZOAa4DfDjZPLLfnIMehqOyfsUgALwNzzGym921wDeEy0f7WAr091n8H/GmwHTtavDbAe4A3nHM/HGSeKb19E2a2nPD2i2miMrNMM8vufU24U3DbabOtBa6zsBVAU7/Tx1gb9JvVWNie/fTfB68nfIX76Z4EPmhm+V6Txge9cTFjZiuBbwBXOefaBplnJPtIVJ3W53T1IOsfybEhFt4P7HDOHRpoYiy35xDHoejsn9Hu1faO41cS7s3eA9zmjftnwjsxQBrhJoJqwtcLzIpFXKfFeBHh06qtwGbvcSVwI3CjN8+XgNcJVytsAN4Vhzhneevf4sXSuz37x2nAT73t/RpQEes4vTgyCR/Qc/uNi/v2JJyQaoBOwu2knyXc5/QssJvwDQ4LvHkrgF/2e+8N3n5aDXwmDnFWE27n7d1He6vnSoHHh9pHYhznr719byvhg1fJ6XF6w2ccG2IZpzf+33v3yX7zxmV7DnEcisr+GfcfhBERkfhQJ7CISEApAYiIBJQSgIhIQCkBiIgElBKAiEhAKQGIiASUEoCISEApAYiIBNT/Bw4WT51FPHioAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot((hm.Abar*hm.R * np.exp((hm.alpha) * hm.xi)), hm.U)\n",
    "#plt.plot((hm_uni.Abar), hm_uni.U)\n",
    "\n",
    "\n",
    "\n",
    "plt.xlim(0,20)\n",
    "plt.ylim(-60,10)\n",
    "#plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 544,
   "id": "57f6186a-6a1c-4655-bd9c-07906b030713",
   "metadata": {},
   "outputs": [],
   "source": [
    "hm=hm_mix_bak"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2116,
   "id": "0373f1bb-99b9-4f5e-8005-4e0bfafa18ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "31.831053572039675"
      ]
     },
     "execution_count": 2116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hm_mix_bak_low.Abar[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2123,
   "id": "1e95a2f2-40ce-4879-a8e5-122a6b5fc7c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 54.0)"
      ]
     },
     "execution_count": 2123,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot((hm_mix.Abar*hm_mix.R * np.exp((hm_mix.alpha) * hm_mix.xi))*hm_mix.RH, hm_mix.U)\n",
    "#plt.plot((hm_uni.Abar), hm_uni.U)\n",
    "\n",
    "\n",
    "\n",
    "plt.xlim(0,54)\n",
    "#plt.ylim(-60,10)\n",
    "#plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1490,
   "id": "b628acdf-cbe5-484a-984b-93caf262211a",
   "metadata": {},
   "outputs": [],
   "source": [
    "ms=ms_mix_cubic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1614,
   "id": "9888d9e4-b195-4a6c-9c5f-8952d3c219e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAD7CAYAAACMlyg3AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAWXklEQVR4nO3df2zc933f8ef77ihSpCRSFuValhRLzhIjmrMsjWCny9ZmcLMpaRQXXZbFbrOlUK0lm/vHNgzLsAEbNgxbMXTAgnjwuMRwM2x2vPxRWK4Lb9gaGE1sz968tP5Ru7KS2JTsmLQk6gfFn/feH3ckz7IkHu+o44nf5wM43Pf7ve+Pjz463oufH/dlZCaSpGIqrXUBJElrxxCQpAIzBCSpwAwBSSowQ0CSCswQkKQCMwQkqcAMAUkqsI6GQEQMRMRzEfHZTl5XknRpbYVARDwQEW9HxAsXbT8QEa9ExNGI+FrDS/8IeKSda0qSVk+0c9uIiPh54Bzw7cy8tb6tDLwKfAoYBZ4F7gJ2AtuAPmA8Mx9rr+iSpHZV2jk4M5+MiD0Xbb4NOJqZxwAi4mHgTmATMADsAy5ExOOZWW3n+pKk9rQVApexE3ijYX0UuD0z7wWIiC9Tawm8JwD6+vqyXC4vrg8PD7N9+/YVXXxiYoLBwcEWir1651iNMoyNja343341ymFdrN45rIvVLUPR62JsbIzx8XEAJicnpzOzr6UCZGZbD2AP8ELD+ueBbzasfwn4RjPn6u/vz3bdc889a36O1SjDxz72sbbPYV2sbjmsi9U7h3WxumUAzmeLn+FXY3bQcWB3w/qu+rZlzc/Pc/jwYY4cOdLyxQ8ePNjysat1jtUow2qwLpZYF0usiyXXel0cOXKEw4cPA5SX2/dy2hoYBqiPCTyWSwPDFWoDw3dQ+/B/Frg7M19c7lwDAwN5/vz5tsqzXuzfv5/nnnturYvRFayLJdbFEutiSURMZuZAK8e2O0X0IeAp4JaIGI2IQ5k5B9wLPAG8DDzSTAAADAwMtN0SWC/q6S6si0bWxRLr4l0tgZZ/e267JbCa9u/fnya7JK1MRPyfzNzfyrHeNkKSCqyrQmBiYsLuIElqUkN3UMtzVO0OkqRrnN1BkqSWdFUI2B0kSc2zO0iSZHeQJKk1XRUCdgdJUvPsDpIk2R0kSWqNISBJBdZVIeCYgCQ1zzEBSZJjApKk1hgCklRghoAkFZghIEkF1lUh4OwgSWqes4MkSc4OkiS1xhCQpAIzBCSpwAwBSSowQ0CSCqyrQsApopLUPKeISpKcIipJao0hIEkFZghIUoEZApJUYIaAJBWYISBJBWYISFKBdSwEIuJDEXF/RHw3Ir7aqetKki6vrRCIiAci4u2IeOGi7Qci4pWIOBoRXwPIzJcz8yvAF4BPtHNdSdLqaLcl8CBwoHFDRJSB+4BPA/uAuyJiX/21zwG/Bzze5nUlSaugrRDIzCeBkxdtvg04mpnHMnMGeBi4s77/o5n5aeBX27muJGl1VK7COXcCbzSsjwK3R8QngV8BerlMS2BsbIz9+5duf3H48OGFmyNJkhqMjIwwMjKysDrc6nmuRghcUmZ+D/jelfbZvn073kBOkpbX+EtyRIy3ep6rMTvoOLC7YX1XfduyvJW0JDWvK24lHRF7gMcy89b6egV4FbiD2of/s8DdmfnicufyVtKStHJrdivpiHgIeAq4JSJGI+JQZs4B9wJPAC8DjzQTAJKkzmtrTCAz77rM9sdpYRroQnfQwYMHOXjwYDtFk6R178iRIwvd5/5lMUkqqnXzl8UcGJak5nXFwPBqsiUgSSu3bloCkqTO6qoQsDtIkppnd5Akye4gSVJruioE7A6SpObZHSRJsjtIktQaQ0CSCswQkKQC66oQcGBYkprnwLAkyYFhSVJrDAFJKjBDQJIKrKtCwIFhSWqeA8OSJAeGJUmtMQQkqcAMAUkqMENAkgrMEJCkAjMEJKnAuioE/J6AJDXP7wlIkvyegCSpNYaAJBWYISBJBWYISFKBGQKSVGCGgCQVmCEgSQVW6dSFIuKXgV8CtgDfysz/3qlrS5Iura2WQEQ8EBFvR8QLF20/EBGvRMTRiPgaQGb+bmbeA3wF+BvtXFeStDra7Q56EDjQuCEiysB9wKeBfcBdEbGvYZd/Wn9dkrTG2gqBzHwSOHnR5tuAo5l5LDNngIeBO6Pmt4Dfz8z/2851JUmr42qMCewE3mhYHwVuB34T+EVgMCL+TGbef/GBY2Nj7N+/dPuLw4cPL9wcSZLUYGRkhJGRkYXV4VbP07GB4cz8OvD1K+2zfft2vIGcJC2v8ZfkiBhv9TxXY4rocWB3w/qu+rZleStpSWpeV9xKOiL2AI9l5q319QrwKnAHtQ//Z4G7M/PF5c7lraQlaeXW7FbSEfEQ8BRwS0SMRsShzJwD7gWeAF4GHmkmAMCWgCStRFe0BFaTLQFJWjn/qIwkqSVdFQJ2B0lS8+wOkiStn+4gWwKS1DxbApKk9dMSkCR1liEgSQXWVSHgmIAkNc8xAUmSYwKSpNYYApJUYF0VAo4JSFLzHBOQJDkmIElqjSEgSQVmCEhSgRkCklRgXRUCzg6SpOY5O0iS5OwgSVJrDAFJKjBDQJIKzBCQpAIzBCSpwLoqBJwiKknNc4qoJMkpopKk1hgCklRghoAkFZghIEkFZghIUoEZApJUYIaAJBVYx0IgIm6OiG9FxHc7dU1J0pW1FQIR8UBEvB0RL1y0/UBEvBIRRyPiawCZeSwzD7VzPUnS6mq3JfAgcKBxQ0SUgfuATwP7gLsiYl+b15EkXQVthUBmPgmcvGjzbcDR+m/+M8DDwJ3tXEeSdHVcjTGBncAbDeujwM6I2BYR9wMfjYh/fKkDx8bG2L9//+JjZGTkKhRPkq59IyMji5+VwHCr56msXpGuLDPfAb5ypX22b9+ON5CTpOUdPnx44Q6iRMR4q+e5Gi2B48DuhvVd9W3L8lbSktS8rriVdETsAR7LzFvr6xXgVeAOah/+zwJ3Z+aLy53LW0lL0sqt2a2kI+Ih4CnglogYjYhDmTkH3As8AbwMPNJMAEiSOq+tMYHMvOsy2x8HHl/p+Ra6gw4ePMjBgwfbKZokrXtHjhxZ6D73L4tJUlGtm78s5sCwJDWvKwaGV5MtAUlauXXTEpAkdVZXhYDdQZLUPLuDJEl2B0mSWtNVIWB3kCQ1z+4gSZLdQZKk1hgCklRghoAkFVhXhYADw5LUPAeGJUkODEuSWmMISFKBGQKSVGBdFQIODEtS8xwYliQ5MCxJao0hIEkFZghIUoEZApJUYIaAJBWYISBJBdZVIbCevydQrSYTk7O8NTHFyfMznJ+eY26+utbFknQN83sCXeLCzDx/8tYZXhs7z+snJxk9Ocn4+RkmJmc4fWGWifrjUlVdLgW9lVL9Uaa3Z2l5y8YKw5t6Gd7Uy/bNS8/Xb+7lxsGNbNlYISI6/w+W1FXa+Z5AZbULs96NnZ3mhRMTvPzmGV46cYaX3zzDj8bPU61/wEfAji19bN/cy2D/Bm7aNsBQfw9DG3vYsrGH/g0VZuerTM/NMz1bZXquvjxXra/Xlqdm5zkzNcfzr59m7Ow0F2bn31OWgQ1ldgxt5Mahjewc6mPH4EZ2Dm1k19aN7Lqunxu29FEuGRKSLs8QuILM5LWx8/zvH53kuR+f5LmfnOL1k5OLr+/aupF9O7bw2T93I/tu3MIHrt/Ezq0b6a2UV70s56fnGD83zdjZaX56Zpo3Jy5w4vQUJ05f4MTEBV46cYbxc9PvOqZSCnYM9bFrqL8WDFtrzzu31oLihi19VMpd1SMoqcMMgQaZyU/emeT7r43zg9fe4ZljJxc/WIc3beBjN23lSx+/iQ/vGuRDO7YwuLGnY2Ub6K0w0Fvhpm0Dl91nanaeNyemGD01yeipCw3PF3jyT8f46Zl3h0S5FNywpa8WCvUWxM6tG9k51M8Ng33cONRH/wbfItJ6Vvif8BOnL/D0sXf4wWvv8IOj45yYmALghi19/KUPDHP73uu4be917B0e6Pr+976eMnuHB9g7fOmgWAiJ4/WAOH66FhDHT9Xq4K0zU4vdWgu29FXYMbiRHUN97BisdTndMLi0vGOwj4Hewr+NpGtW4X56Fz70a4+Ti907W/t7+Ln3b+Or7x/mE+/fdk186K/UciExO1/lrYlaF9ObE1O8OTHFWxMXODExxVsTU7xwfILxczPvOW5Tb6U+cL2B7Zt72d4wmN04oD28qZcNFbufpG6y7kPg+OkLPHOJD/3BjT3cvvc6vvwX9nD7zdfxoRu2UCr4IGpPucTu6/rZfV3/ZfeZnpvnpxO1MYk3J6Y4MXGBsbO1sYrxc9O88tZZ/vDsOGem5i55/ODGnsWg2LZpA1v7N9QGzvs3MLSxp768tD64scdxC+kqWlchMDU7z4snJnj+9dP8cHSC518/xeipCwAM9dc+9H/9E3v4+M3buOVnNhf+Q78VvZUy79vWz/u2XT4ooPZ/8c75mVo4nJ1m7NxSUCyExgvHJxan0F5ppvLm3gpDAz0MbawFxmA9LLb2b2CwPutqU33MZFNvuTZ+sqGyuM3Wh3R5HQuBiBgA/gMwA3wvM/9LO+e7MDPP0bfP8fJbZ/jhG6f54ehp/uTNs8zVO7VvHOzjI7uHOPQX9/qhvwb6esrsHKpNWV1OtZqcnZrj9IUZTk3OcnpyhokLs5w6X/uexenJWlCcmpzh9OQso6cuLO5z8RjGpWwolxjoLbOp793hUHsuNyzXHpvrz309Jfp6yvRWas999e9x9DV8n2O9dRmqeNoKgYh4APgs8HZm3tqw/QDw74Ey8M3M/DfArwDfzcwjEfEd4D0hcH56ju8fHWe+mouPuWpSzWRqdp5jY+d55adn+dOfnuUnJycXf3vc3FvhI7uH+Nu/cDMf2TXEn989xPVb+tr5p6mDSqVgsL+Hwf4ebtrW/HHVanJmapazU3Ocm57j/PTC83zD8hznZurPU3Ocq792anKGN05Ncn5h/5m5K7ZGLmcxIHpqX/BbCI6loLjEaw3rG8oleiolekolKuWgp1yip/5cKZfoKQU9lRKV0sJrtf021J8rpdLi8sKxBpNWot2WwIPAN4BvL2yIiDJwH/ApYBR4NiIeBXYBf1zf7b3ffAKOjZ/nV7/5zGUvVi4Fe4cH+LM3DvLLH93JLT+zmQ/esJm92wb8Lb+ASqWojR30b2j7XNVqcmF2/l1BMjU3z9TsPFP1L/FNzda+xLfwZb7phuWp2SpT9S8ALhx3bnqO8XMzF+03z9RclflmmjAtKpeiFiTvCpZaQFTKtUCplINyBKVSUIqFZWrL9W2loGG5vr0UlKO2X235UscF5dJF+wS1b1K2K5MEdl/Xz1//2C4DbxW0FQKZ+WRE7Llo823A0cw8BhARDwN3UguEXcD/4zL3LNo7PMDvHP44lXLtjVQplSiXYvFNfbW+iCWVSrHYHXR9B643N19laq7K9Ow8c9Vkdr7K3HzteXY+matWF5cv/drC9ioz88ncfJW5ajIzV2WuWtt/5grnXGhpV7P2mK8m1SrMZZX5TKrVpJq8d5+kYf/6Pov7X2KfXDrPanvgD3+0ON5zcSvu0Xs/YUA06WqMCewE3mhYHwVuB74OfCMifgm45B3iLpw5xd/9wl9dXD98+PDCzZGkdaVSLrGpXGKT37FYsWo1+e3/8QovnTjzru2NH/qZq9Pw6GYjIyOMjIwsrA63ep62byBXbwk8tjAmEBGfBw5k5m/U178E3J6Z9y53rmv1BnKStJa67Q/NHwd2N6zvqm9b1nq+lbQkrbauuJX0JVoCFeBV4A5qH/7PAndn5ovLncuWgCSt3Jq1BCLiIeAp4JaIGI2IQ5k5B9wLPAG8DDzSTACALQFJWomuaAmsJlsCkrRy3TYmIEm6RnRVCNgdJEnNsztIkrR+uoNsCUhS82wJSJLWT0tAktRZhoAkFVhXhYBjApLUPMcEJEmOCUiSWmMISFKBdVUIOCYgSc1zTECS5JiAJKk1hoAkFZghIEkFZghIUoF1VQg4O0iSmufsIEmSs4MkSa0xBCSpwAwBSSowQ0CSCswQkKQC66oQcIqoJDXPKaKSJKeISpJaYwhIUoEZApJUYIaAJBWYISBJBWYISFKBGQKSVGAdC4GIuDkivhUR3+3UNSVJV9ZUCETEAxHxdkS8cNH2AxHxSkQcjYivXekcmXksMw9daZ+xsbFmilMIIyMja12ErmFdLLEullgX7zLc6oHNtgQeBA40boiIMnAf8GlgH3BXROyLiA9HxGMXPa5v5iLj4+MrKPqlrcYtJ9o9x2qUYTXe4NbF6pbDuli9c1gXq1sGYHurBzYVApn5JHDyos23AUfrv+HPAA8Dd2bmH2fmZy96vN1qAVdqHf2nts26WGJdLLEullgXK7h3UETsAR7LzFvr658HDmTmb9TXvwTcnpn3Xub4bcC/Aj4FfDMz//Ul9pkC5hs2jQErbR4MAhMrPGa1z7EaZRhm5f/2q1EO62L1zmFdrG4Zil4Xwyy1AMqZ2dfKxSutHNSKzHwH+Moy+7T0j5Aktaad2UHHgd0N67vq2yRJ14h2QuBZ4AMRsTciNgBfBB5dnWJJkjqh2SmiDwFPAbdExGhEHMrMOeBe4AngZeCRzHyxyfNdcWppRPRGxHfqrz9TH49Yl5qoi78fES9FxB9FxP+MiJvWopyd0OyU44j4axGREdHS/dOvBc3URUR8of7eeDEi/muny9gpTfyMvC8i/iAinq//nHxmLcp5tV1uqn7D6xERX6/X0x9FxM82deLM7OgDKAOvATcDG4AfAvsu2ufvAPfXl78IfKfT5eyiuvjLQH99+atFrov6fpuBJ4Gngf1rXe41fF98AHge2Fpfv36ty72GdTECfLW+vA/48VqX+yrVxc8DPwu8cJnXPwP8PhDAx4FnmjnvWtw24pJTSy/a507gd+rL3wXuiIjoYBk7Zdm6yMw/yMzJ+urT1MZe1qNm3hcA/xL4LWCqk4XrsGbq4h7gvsw8BZAdnIbdYc3URQJb6suDwIkOlq9j8tJT9RvdCXw7a54GhiJix3LnXYsQ2Am80bA+Wt92yX2y1u00AWzrSOk6q5m6aHSIWtKvR8vWRb15uzszf6+TBVsDzbwvPgh8MCK+HxFPR8QB1qdm6uKfA78WEaPA48BvdqZoXWelnydAB6eIqj0R8WvAfuAX1rosayEiSsC/A768xkXpFhVqXUKfpNY6fDIiPpyZp9eyUGvkLuDBzPztiPg54D9HxK2ZWV3rgl0L1qIl0MzU0sV9IqJCrYn3TkdK11lNTbONiF8E/gnwucyc7lDZOm25utgM3Ap8LyJ+TK3P89F1OjjczPtiFHg0M2cz80fAq9RCYb1ppi4OAY8AZOZTQB9t3EvnGtbStP21CIFmppY+Cvyt+vLngf+V9ZGPdWbZuoiIjwL/kVoArNd+X1imLjJzIjOHM3NPZu6hNj7yucx8bm2Ke1U18zPyu9RaAUTEMLXuoWMdLGOnNFMXrwN3AETEh6iFQBHvRvko8Dfrs4Q+Dkxk5pvLHdTx7qDMnIuIhamlZeCBzHwxIv4F8FxmPgp8i1qT7ii1gZAvdrqcndBkXfxbYBPw3+pj469n5ufWrNBXSZN1UQhN1sUTwF+JiJeo3WrlH2btW/nrSpN18Q+A/xQRf4/aIPGX1+MvjfWp+p8EhuvjH/8M6AHIzPupjYd8BjgKTAK/3tR512FdSZKa5F8Wk6QCMwQkqcAMAUkqMENAkgrMEJCkAjMEJKnADAFJKjBDQJIK7P8DoqlzbYM/AS0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot((ms.Abar*ms.R * np.exp((ms.alpha-1) * ms.xi)), ms.rho(ms.R,ms.m))\n",
    "\n",
    "plt.ylim(1e-1,1e4)\n",
    "plt.xlim(0,1)\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1896,
   "id": "7aadaad0-ee42-476e-8279-7c9858cbcac8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f59f095db50>]"
      ]
     },
     "execution_count": 1896,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot((hm_mix.Abar*hm_mix.R * np.exp((hm_mix.alpha-1) * hm_mix.xi)))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2692,
   "id": "0c613e7d-61b7-4899-b720-c0f71b93020b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1470.0, 1500.0)"
      ]
     },
     "execution_count": 2692,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(np.arange(hm.N), r)\n",
    "\n",
    "#plt.ylim(0.5,1)\n",
    "plt.xlim(1470,1500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2563,
   "id": "f817fcbf-47fc-4482-a02b-a16d95609d2b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 30.0)"
      ]
     },
     "execution_count": 2563,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(np.arange(hm.N), WENO_dfdA(r, hm.deltaL, hm.Abar, 1e100)[:])\n",
    "\n",
    "#plt.ylim(0.5,1)\n",
    "plt.xlim(0,30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2876,
   "id": "f673c3e1-8d52-41ef-8bcf-a7341372415a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 30.0)"
      ]
     },
     "execution_count": 2876,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD1CAYAAABEDd6nAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAWR0lEQVR4nO3dfZAc9Xng8e/DgspCcJJzUnJYUoKc2pBTGceYLRzKqQvizCHiW8mxUy5xlcTkhc1doZx9TqhId6mE09UVOpMXUxeVcyNMBVfFVgjhuJ0yV4orkHLixI6wMSaCIt6THSSZmMVYSnhJsOTn/pgeMV7t7kyvpmdnmu+naovpnqd7fr9p9HTP7+mXyEwkSfVx3nI3QJLUXyZ2SaoZE7sk1YyJXZJqxsQuSTVjYpekmjl/kB+2cuXKvOiii1izZg2rV69eNPbkyZNdY4YpdnZ2lnXr1vUUW2U7hqF/VbWhynUPQ/+q/C5GrX9lv4s69u/kyZOcOHGC55577h8zc2VPK27LzIH9XXjhhdmrm2++eaRir7zyyp5jq2zHMPSvqjZUue5h6F+V38Wo9a/sd1Hn/gEvZslcO7RDMZOTkyMVW9YwtLmq/lXZhjr3r8rvoqr1DkNsWcPQ5ir7BxA5wCtPV61alS+++OLAPm+QJiYmeOSRR5a7GZWxf6PN/o2uiHgpM1eVWWagR+xr164d5McN1NTU1HI3oVL2b7TZv5E2W3aBgR6xj4+P55YtW5icnKz8p4gkjbJms0mz2WT//v0zmTleZtmuiT0i7gb+LfBsZr5pnvcDuBP4MeAl4KbM/MJ865qYmMi6/lySpCpExOczc6LMMr0MxfwesHWR928Axou/KeAjZRogSeqvrok9Mz8NPL9IyHbgY8WZOZ8F1kTEJf1qoCSpnH4UT9cDRzumjxXzJEnLYKBXns7OzjIx8epQ0dTUVN2r2ZJUWqPRoNFotCdLn07Yj8R+HNjYMb2hmHeWdevW1fZcU0nql86D3oh4ruzy/RiKmQZ+Olp+GDiZmc/0Yb2SpCXoesQeEZ8ArgHWRsQx4NeBCwAy83eBB2md6jhD63THn6mqsZKk7rom9sy8scv7CdzStxZJks7JQG8pcPLkSaampmg2m4P8WEkaOc1msz3O3vv9iwsDvaWAV55KUjlVXXkqSRohJnZJqhnH2CVpCDnGLkk15Ri7JMnELkl1Y2KXpJqxeCpJQ8jiqSTVlMVTSZKJXZLqxsQuSTVj8VSShtC5FE97SuwRsTUinoqImYjYNc/73xcRfxIRX4qIP42IDfOt5+kX4PAbd3B6w1sX/KwHHj3O2/c+xKZdn+Ttex/igUfnfcqeJNXa5ORk+7mnJ8su2zWxR8QYsA+4AdgM3BgRm+eE/Qbwscx8M7AHuH2h9R0/8TK773983oT9wKPH2X3/4xw/8TLZJVaSNL9ejtivAmYy80hmvgIcALbPidkMPFS8fnie97/Dy986zR0Hnzpr/h0Hn+Llb53uKRY8upek+fSS2NcDRzumjxXzOj0GvLt4/ePAxRHxzxdb6ddOvNzTvIXme3QvSfPr+szTHv0y8DsRcRPwaeA4cHpu0OmXTvLMPR8A4IKx82i88Xi7OADAG9as5Pg8SfwNa1aeNW+xo/t3XTF3v1POA48e546DT/G1Ey/zhjUrufX6yxZcZ5lYSepFo9Foj68DrC27fC+J/TiwsWN6QzHvjMz8GsURe0RcBLwnM0/MXdHYhau55H0fZuUFY9z+7svPSoC3Xn8Zu+9//DsS9soLxrj1+svOalSZo/sy2r8E2m1o/xIAzmpvmdiltsWdhvTaMzU1deagNyKeK7t8L0Mxh4DxiNgUESuAHcB0Z0BErI2I9rp2A3cvtLL1a1bOm9ShlQxvf/flrF+zkugSO99R/GLzex2PLzPOX7YmUIZDTZKWqusRe2aeioidwEFgDLg7Mw9HxB7gkcycBq4Bbo+IpDUUc8t867p8/Wo+s+vaRT/vXVes7+motMzRfZkj6zK/BKr61QDVDjVJqreextgz80HgwTnzfq3j9X3Aff1t2uLaya2XoYoySbLMOH+Z2LZeh1fK7jSsC0hq61fxtCftK08nJyeZnJw85/X1enRfJkmW+SVQJhbK/XIos9Oosi7gDkNaHs1ms32VfjVXnvbL6tWraTQafUnqZZQZjy8zzl8mFsqNyd96/WWsvGDsO+YttNOoqi5QZpy/bE3AaxCkxZ3LlacDPWJfLmWPrHv9JVA2tswvhzJDTVXVBcoMYZWJXcrZRP5ykHr3mkjsZZJklcqOyfe606iqLjAMOwwYnqEmaVS8Zm7b+64r1vOZXdfylb3v5DO7rl2Wf7xlhleqWm+Z2DJDWGViyxaGh2GoqR3f6/CRQ01aTt62d4DKjslXsd4yscOww4Dl+eUwl/UGDZrPPFVlqhjbnjtcAix4NTLA2/c+NO/w0fo1K8+6LqJM7KZdn2S+//sD+Mredw6kDWW/i/YyDh+9dizlmaeviTF2LV0VheSyNY+qTkGte72hHW/R+bXHxK5lUXaHAb3tCMrEVrUTqGqHAdWdfWTRuV5M7BoJy/3LYRh+NcBonq7qTmDwRvrKU+lcVbETqGqHAaM3fFT1TqDOO41zufLU4qm0zMqOg/dabB21onPZQvJS4kdxJ2DxVBpBVdUbhmH4qMpC8jD9chg2JnZpxIzS8FGVheRRHD4a1A7DMXapxkap6Fy2kDwMvxyqPPPov3z49/jox+/j/DWXXDlv4xcx0MTevrujpNG23DuBsvHDsBMou8O4/xv/gtdd+x847+gH5m3PYnpK7BGxFbiT1hOU7srMvXPe/17gHmBNEbOreDiHpNe4qi5cG4ZfDoM886iMrok9IsaAfcB1wDHgUERMZ+YTHWG/CtybmR+JiM20nrZ06ZJbJek1qczQUZn4YdgJ9GOH0atejtivAmYy8whARBwAtgOdiT2Bf1a8Xg187ZxaJUl9ttw7gX7sMHrVS2JfDxztmD4GvG1OzG3AH0fELwKrgHfMt6LZ2VkmJl49HXNqaqp99zJJGhrLfebRD71wiC987KN8O5PTL5V+gFL3C5Qi4ieArZn588X0TwFvy8ydHTEfLNb1mxFxNfBR4E2Z+e3OdXmBkiT1pn1q5CN3/gL/9MyXo8yyvdyP/TiwsWN6QzGv088B9wJk5l8CrwPWlmmIJOlV7YcDvfJ3M58vu2wvif0QMB4RmyJiBbADmJ4T8zTwrwEi4l/SSuyzZRsjSTp3XRN7Zp4CdgIHgSdpnf1yOCL2RMS2IuyXgJsj4jHgE8BNOcib0EiSzhjoTcDGx8dzy5YtXnkqSV207+64f//+mcwcL7Osd3eUpCG2lLs7DvRh1pKk6pnYJalmTOySVDMDTezt2/YWj3uSJC2g2Wy2r8z30XiSVCcWTyVJJnZJqhsTuyTVjMVTSRpCFk8lqaYsnkqSTOySVDcmdkmqGYunkjSEKi+eRsRW4E5gDLgrM/fOef+3gS3F5IXAd2fmmrnrsXgqSeUspXh6fg8rHQP2AdcBx4BDETGdmU+0YzLzP3XE/yJwRZlGSJL6p5ehmKuAmcw8kpmvAAeA7YvE30jr8XiSpGXQS2JfDxztmD5WzDtLRHwfsAl46NybJklaiq5DMSXtAO7LzNPzvTk7O8vExKtDRVNTU+3igCSp0Gg0aDQa7cm1ZZfvWjyNiKuB2zLz+mJ6N0Bm3j5P7KPALZn5F/Oty+KpJJVT1ZWnh4DxiNgUEStoHZVPz/PhPwi8HvjLMg2QJPVX18SemaeAncBB4Eng3sw8HBF7ImJbR+gO4EAO8uYzkqSzDPQmYOPj47llyxYmJyeZnJwc2OdK0qhpNps0m032798/k5njZZb17o6SNMS8u6MkycQuSXVjYpekmvHujpI0hHw0niTVlMVTSZKJXZLqxsQuSTVj8VSShpDFU0mqKYunkiQTuyTVjYldkmrG4qkkDaHKi6cRsRW4ExgD7srMvfPEvBe4DUjgscz8d3NjLJ5KUjlLKZ52fZh1RIwB+4DrgGPAoYiYzswnOmLGgd3A2zPzmxHx3eWaLknql16GYq4CZjLzSGa+AhwAts+JuRnYl5nfBMjMZ/vbTElSr3pJ7OuBox3Tx4p5nX4A+IGI+ExEfLYYupEkLYOuQzEl1jMOXANsAD4dEZdn5onOoNnZWSYmXh0qmpqaahcHJEmFRqNBo9FoT64tu3wvif04sLFjekMxr9Mx4HOZ+S3gKxHxN7QS/aHOoHXr1mHxVJIW13nQGxHPlV2+l6GYQ8B4RGyKiBXADmB6TswDtI7WiYi1tIZmjpRtjCTp3HVN7Jl5CtgJHASeBO7NzMMRsScithVhB4FvRMQTwMPArZn5jaoaLUlamDcBk6QhNvQ3AfPKU0nqjbftlaSaGvojdklS9UzsklQzJnZJqhmLp5I0hCyeSlJNWTyVJJnYJaluHGOXpCHkGLsk1ZRj7JIkE7sk1Y2JXZJqxuKpJA2hyounxcOp7wTGgLsyc++c928C7uDVR+b9TmbeNXc9Fk8lqZylFE+7PvM0IsaAfcB1tJ5teigipjPziTmhf5CZO8t8uCSp/3oZirkKmMnMI5n5CnAA2F5tsyRJS9VLYl8PHO2YPlbMm+s9EfGliLgvIjb2pXWSpNL6VTxtApdm5puBTwH3zBc0OzvLxMTEmb9Go9Gnj5ek+mg0GmfyJLC27PJdi6cRcTVwW2ZeX0zvBsjM2xeIHwOez8yzKrkWTyWpnKquPD0EjEfEpohYAewApud88CUdk9uAJ8s0QpLUP13PisnMUxGxEzhI63THuzPzcETsAR7JzGngP0bENuAU8DxwU4VtliQtwpuASdIQG/qbgHnlqST1xtv2SlJNDf0RuySpeiZ2SaoZE7sk1YzFU0kaQhZPJammLJ5KkkzsklQ3JnZJqhmLp5I0hCyeSlJNWTyVJJnYJaluHGOXpCHkGLsk1VRlY+wRsTUinoqImYjYtUjceyIiI6JUIyRJ/dM1sRcPp94H3ABsBm6MiM3zxF0MvB/4XL8bKUnqXS9H7FcBM5l5JDNfAQ4A2+eJ+2/A/wD+sY/tkySV1EtiXw8c7Zg+Vsw7IyLeCmzMzE8utqLZ2VkmJibO/DUajdINlqS6azQaZ/IksLbs8uefawMi4jzgt4CbusWuW7cOi6eStLipqan2GTFExHNll+/liP04sLFjekMxr+1i4E3An0bEV4EfBqYtoErS8uglsR8CxiNiU0SsAHYA0+03M/NkZq7NzEsz81Lgs8C2zPTQXJKWQdfEnpmngJ3AQeBJ4N7MPBwReyJiW9UNlCSVM9ALlMbHx3PLli1MTk4yOTk5sM+VpFHTbDZpNpvs379/JjPHyyzrlaeSNMS8u6MkycQuSXVjYpekmvG2vZI0hLxtryTVlMVTSZKJXZLqxsQuSTVj8VSShpDFU0mqKYunkiQTuyTVjYldkmrG4qkkDaHKi6cRsRW4ExgD7srMvXPe//fALcBp4AVgKjOfmLsei6eSVE4lxdOIGAP2ATcAm4EbI2LznLCPZ+blmfkW4EO0Hm4tSVoGvQzFXAXMZOaRzHwFOABs7wzIzL/vmFwFDO4cSknSdzi/h5j1wNGO6WPA2+YGRcQtwAeBFcC1fWmdJKm0vhVPM3NfZn4/8CvAr84XMzs7y8TExJm/RqPRr4+XpNpoNBpn8iSwtuzyXYunEXE1cFtmXl9M7wbIzNsXiD8P+GZmnlXJtXgqSeVUdeXpIWA8IjZFxApgBzA954M7n6D9TuDLZRohSeqfrmPsmXkqInYCB2md7nh3Zh6OiD3AI5k5DeyMiHcA3wK+CbyvykZLkhY20JuAjY+P55YtW5icnGRycnJgnytJo6bZbNJsNtm/f/9MZo53X+JV3t1RkoaYd3eUJJnYJaluTOySVDPe3VGShpCPxpOkmrJ4KkkysUtS3ZjYJalmLJ5K0hCyeCpJNWXxVJJkYpekujGxS1LNWDyVpCFUefE0IrYCd9J60MZdmbl3zvsfBH4eOAXMAj+bmX87dz0WTyWpnEqKpxExBuwDbgA2AzdGxOY5YY8CE5n5ZuA+4ENlGiFJ6p9ehmKuAmYy80hmvgIcALZ3BmTmw5n5UjH5WWBDf5spSepVL4l9PXC0Y/pYMW8hPwf833NplCRp6bo+zLqMiPhJYAL40fnen52dZWLi1aGiqampdnFAklRoNBo0Go325Nqyy3ctnkbE1cBtmXl9Mb0bIDNvnxP3DuB/Aj+amc/Oty6Lp5JUTlVXnh4CxiNiU0SsAHYA03M++ArgfwHbFkrqkqTB6JrYM/MUsBM4CDwJ3JuZhyNiT0RsK8LuAC4C/jAivhgR0wusTpJUsZ7G2DPzQeDBOfN+reP1O/rcLknSEnnlqSQNIW/bK0k15W17JUkmdkmqGxO7JNXMQBP7008/XdviacdVYrVk/0ab/Rs9HcXT7y29cGYO7O/CCy/MXk1PT49U7JVXXtlzbJXtGIb+VdWGKtc9DP2r8rsYtf6V/S7q3D/gxSyZa4d2KKbMUf0wxJY1DG2uqn9VtqHO/avyu6hqvcMQW9YwtLnqUYuBnu4YEf8APNVj+Grg5AjFrgWe6zG2ynYMQ/+qakOV6x6G/lX5XYxa/8p+F3Xu32WZeXGPscCAE7skqXpDOxQjSVoaE7sk1cxAEntEbI2IpyJiJiJ2DeIzBykivhoRjxd3thz5eyZExN0R8WxE/HXHvO+KiE9FxJeL/75+Odt4Lhbo320RcbzYhl+MiB9bzjYuVURsjIiHI+KJiDgcEe8v5tdi+y3Sv7psv9dFxF9FxGNF//5rMX9TRHyuyKF/UNxCfeH1VD3GXjwM+2+A62g9Vu8QcGNmPlHpBw9QRHyV1sO8yxRPh1ZE/CvgBeBjmfmmYt6HgOczc2+xc359Zv7KcrZzqRbo323AC5n5G8vZtnMVEZcAl2TmFyLiYuDzwLuAm6jB9lukf++lHtsvgFWZ+UJEXAD8OfB+4IPA/Zl5ICJ+F3gsMz+y0HoGccTe9WHYGi6Z+Wng+TmztwP3FK/vofWPaSQt0L9ayMxnMvMLxet/oPUMhfXUZPst0r9aKE5df6GYvKD4S+Ba4L5iftftN4jEXvZh2KMogT+OiM9HRF0f4vo9mflM8frvgO9ZzsZUZGdEfKkYqhnJoYpOEXEpcAXwOWq4/eb0D2qy/SJiLCK+CDwLfAr4f8CJbD30CHrIoRZP++NHMvOtwA3ALcVP/doqroar23myHwG+H3gL8Azwm8vamnMUERcBfwR8IDP/vvO9Omy/efpXm+2Xmacz8y3ABlojHj9Ydh2DSOzHgY0d0xuKebWRmceL/z4L/G9aG6Nuvl6Mb7bHOWv1bNvM/HrxD+rbwH5GeBsWY7N/BPx+Zt5fzK7N9puvf3Xafm2ZeQJ4GLgaWBMR7Sfedc2hg0jsXR+GPcoiYlVRxCEiVgH/BvjrxZcaSdPA+4rX7wP+zzK2pe/aSa/w44zoNiyKbx8FnszM3+p4qxbbb6H+1Wj7rYuINcXrlbROOnmSVoL/iSKs6/YbyJWnxalHHwbGgLsz879X/qEDEhFvpHWUDq1nyH581PsXEZ8ArqF1mfbXgV8HHgDupXWnub8F3puZI1mAXKB/19D6GZ/AV4Ff6BiTHhkR8SPAnwGPA98uZv9nWuPQI7/9FunfjdRj+72ZVnF0jNaB972ZuafIMweA7wIeBX4yM/9pwfV4SwFJqheLp5JUMyZ2SaoZE7sk1YyJXZJqxsQuSTVjYpekmjGxS1LNmNglqWb+P5rpBSp1FkxHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(np.arange(hm.N), hm.U)\n",
    "\n",
    "#plt.ylim(0.5,1)\n",
    "plt.xlim(0,30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c5918b0d-9a04-4329-8697-d8c2c3d8fd2e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 2560,
   "id": "9b89b0f4-97f2-4fff-979d-fabd168dd9a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f59cdd1b850>]"
      ]
     },
     "execution_count": 2560,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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0DSIc1bRpE4BrehNR7nFJ2GMIxGdXTq4qHfUa76ZDRFZmi+Bt1jjv1q7UE3SAoS1vpk2IyHosH7zNHOedmF2ZaqhgDVveRGRhNuiwNE9rmqnxwJAOS+a8iSjHCqjD0py8ycHOflSXulBRMvo0JNb07mTwJqIcK4gOSzNnxx840o/ptWWp98s1vYnIwiwfvM20r6MfM9IEbyC2pjc7LInIioo6573/SD9mTBojeLPlTURZ+OEf3sc9v0t5g7Ex5ew2aMeS7W3QzBgq2DUQQvdAOG3aBOCysESUnQdf2YmHN+zJ+H25vA2aacwaKnjgSD8AjJ02KeMNGYho4iJRxd+cNdeUsi0fvM2yvyMWvNnyJiKzhCJRuJ3mhFlbBG8z0iY7Ar0AgHkNFWm3Yc6biCYqHIkiqoDHZePgnU2HpZg0WHB7aw/qKzyYVOFJu01NmRsDoSiC4YgpdSCiwhWKxFqdE2l5F0yHpRk+CvRg/uTKMbepLk3MsmTem4gyk7iRy0Ra3jnrsBSR1SLyvohsF5HbjCjTbB8FejDfe4zgneP1TV7Z3obN+2PXSlWx/0j/mPuORBUbd7Vjb3sfeoOj/8GEI1HeCYgoT4KR2Cd2j9Oc7EHW0+NFxAngAQAXANgH4A0R+b2qbs227AQ1eHp8W08QHX0hzPemz3cD5qzpraro7A9h2XefRZnbia3fvRAigqv8r+HVHYcBABvvWgXffc8l33Pf5Utw2bLpqCo9+s9k054juObB14eV/dB1p+K8RZMRiSqe3XoIX/lVS/K1U2bV4tpPzsHSxlrMHSPPf6hrAP2DETyz9WM8vGEPdh/uQ4XHibpKD+orSvCPly3BkhnVkCHDgKLR2D+aZ7cewvotH+P1ne0o9zixeFo1TplZi0VTq7C0sRb1lR6UuByoLHENe3+m528gFEXfYBg9wTBau4Po6B1Ea3cQO9t6UeFxIhRVRKIKj9OB2fXlGAhHsayxFlOqS1BX4YHTIePefySqOHCkP/a9sx8723rhdjhQWerCYDiKwUgU+zv6UVvuRigSRX1FCXoHw1g4pQoNlR70DUZQ7nGhssQFp0NQVeqCyyEZ1SGfVBUiAlVN9j2Fo4qoKhwiGIxEEVXFYDgKVaC9dxAOAVxOB0pcDnT2h9ATDCPQHUT/YARVpS70DobRNxhBfUVJvBFVgY8CvXA5BFOqSyECDIRiga+ixIVwRLGnvQ+VJS7UVXjQNRDC9JoyhKNRzKwrj+9TML22DC6HwOWMnV+HCEpcjuT3XJ/zRNrErJy3EWubnAZgu6ruAAAR+TWAywAYErzNONfvxlu3J05Pm04CYMzddA529uO5rYfwwaEeXLG8EZc98Erytf5QBNc8+DpObqxNBm4AwwI3ANz135vxnbVb8M9fWIZIVHHLf21K2Yl73UNvpK3HW3uO4K09m5KPLzlpGk6ZVQuPywG304GXPgzgxQ/a0JOiBd87GEFvez/2tvej6f++nHz+smXT8btNB1Lur28wgpbdHWjZ3ZG2TrPqyhFVxRXLG+F2xv64nBL7w3M5BXsO9+EXf9mFkxpr8NaeI2nLyVZ1qQtXnz4bf9x2CB+29pi2n2Mp9zhR7nFhSnUJSlwOTKstw6Y9R3DxSVMRiQLtvUHMaagYdu2H/n2M7B8SiXX27+vow9Sa2Jr12w52Y3Z9OTbsPIxJ5R68ubsDNWVuHOgcyMUh2tLpc+uwaGoVyj0uiAAOiZ3HV7a3ITiOT7Z1FebcRlE0y6EcInIFgNWq+rfxx18GcLqqfi2xzezZs9Xr9SbfM/TW9scy57anAAA7v3+xYf8173/uA/zkjx/i3XsvRGWKRakSPjzUjQv++UX8n6tOwWdOnp7RPjp6B3HDf7Tg9V3t2VaXiCzAE+94HIxklop8/Y6VmFw9+oYv6fj9/uRCfi0tLbtVdU6q7XKyqqDX68XGjRuzKuP8H72AhVMqccK0Gpw2tw7LZ0+a8MeRt/YcwYLJlWMGbgCoi49EaY/fcWc8dh/uxQPPb8dvNu6bUN3SaT57Hj7va4RDBH9+P4DvPpn6g82qxVPw7v4jONQ1us6z6sqx4rh6nLNwMk6cXo2acjdC4ShCEcWOth70BSM40NmPx9/cj7f3HklbF4/TgZtXLcB1K+ageyCMK/2vYWdb75j1n11fjhOnV2NeQyVm15djSnUppteWQQSYXlMGp0MQiSrC0SiiUSAcjWIgHEVXfwiTq0pwqCuILQc6EYkq6io8eGvvEewM9GLX4V6893H3qP1VlbrQneYT06RyN85a4MWqxZNx0owaTK0pRbnHhYFQBB8c6sYr2w/jjV3taNndYciqkucs9KInGMY5C70IhiNQBc6YV49QJIpwVDGjNnb8pW4nnBL71OFxOeBxOdDVH8Kkck+yhe12OpKjF0Y2vIY+HNkkC0WiKHE5EIynNzr6BlFX4UFrVxAVJU609w6i1O3EQCiCj7sG4HI40Nk/iNn1FegJhtHVH4JqLOU4f3IlOvtC6OgbRCii2NvRh487B9AbDCfTGxFVhCOKnW29KT/N5cqJ06ux5UAXSlyOZB/X/MmVOHNePfa09+GE6dUIhaOoKHFicnUpasvciCowraYUDhG4nbH0i8NxtOGYOO+J9FFXfxgelwMDoQi2HOhEQ2UJdgR64XY6cPFJUzNudA5t3IpIW7rtjAje+wHMHPK4Mf6coeZ7K/D+x914ZushqAINlSW48tSZuOr0WWPOkhxpIBTBhp2HceWps4657aTyWH60rWfwmNtGo4pvPf4OHm3JLGjf23QCrl0xF777nkNb/J/E9z97Eu584l1E43+Br9x2/rBjnOetxHUr5uDJdw7i64+8lXz+2b87GwumVAGIdciu/NELydce/+onsXz2pLT1SHysBoBrzpwDIDac8tKfvoSBUKylcfFJU/EvX1w+7H3lHhee/+a5yX1+f9023LRyAda+fQALJlfhwhOnoqbcncEZcQ57lDju+soSnDC9Ovn8p0+cOmy7cCSK/lAEr350GKfOqUsOAX1zTweqS104bnLVMfdc6nZiaWMtljbW4quYP+r1nmAYW/Z34uSZtRiMRLFlfxeOm1yJ2nI3Xt/ZjiXTa1BZ6oIAw/7Ys5Hod0llZFAYK0Y4HbHzWuqOfS/zxM7rrPpyALHzm5D4HTJbbzCMwXAUgZ4gFk6pwgsfBNA9EMKqxVOS9QSAlt3t2Ly/C5cvm4FgJILWriAWT6vGYDiKMo8T0fgfilHn/FgS590d74j0VsXqWlPmxpR4C3tpY6359TAgbeIC8AGAlYgF7TcAXK2qWxLb+Hw+nWjLO5E22fWDSwAA3QMhvLL9MB5r2Ys/vtcKAXD+8VPwpTNm4ewF3mNewD+/34prH3oDD117Ks47fvIx93/a957DeYsm439dsXTM7b7ws1exYWf6FMlbd18Ap1Ow6kcvYMmMGvzpvVYAR9NBm/YeweXxfHjiWEORKLa39mDxtOq05d766Nt4tGVfytTOz174CP/+6m6su+lTGQZQIrICEWlRVV+q17JueatqWES+BuAPiDWbHhwauI1WVerG6iVTsXrJVOzr6MMjr+/Bf72xF89tO4TZ9eX48hmzcfXps1DuSX1oj7+5HzVlbpw5v35c+/NWlSRvVJzOz1/akTJw11d4cOuFi/A530w44/9UXr9zFYDYsECHHO39XjazFv/vS59I3t0HiH1EHitwA8A/fe5k/NPnTk752g3nzMcN54xuQRKR/RmS81bVdQDWpXs9McMycXcIozROKsetFx6Pm1cuxPotH+NXr+7GfU9twwPPb8d1K+bimjNno7b86AzKHYEerN98EF88ffawj2Vj8VaVJO91mcrbe4/gvqe2JR///msrsLSxFnsO96GmzJ22xbviuIZRz61eMm1cdSKiwrZ27drEjPS0Q+KyTpuMRzZpkzd2tWNyVQlm1489JjuhZXc7Hnj+I/zpvVaUe5y4+rRZuMLXiEhUceuj72BPex/+9M1zMLlqfL2/tz76Nl7e3oZXb1856jVVxdzbj/7P+vHnT8ZnP9E4vgMjIjoGU9MmZjt1Tl1G2y+fXYcHr63DtoNd+NkLH+Ghv+zCz1/eCQCoLHHhp1efMu7ADcRa3m09QUSjOiqf/p21R0d8fPH0WQzcRJQzlg/eE7V4WjXuv/IUfOPTi/Dmng4MhqNYcVzDmEvApuKtKkEoEpsVOXQRq4FQBL/4y67k49suOt6oqhMRHVPBBu+EmXXlmFlXPuH3e6tiQ6gOdQ8MC95PvXMw+fNjXzkzOXWdiCgXLL8kbL7NnBQL/HsO9w17/huPvg0AuHTpNPgyTO0QEY1lPEvC5qTlnVgS1o7mxDtKdw8J3us3H211/zDNMD0ioolKjMxbs2aNfe9hmW815W5MKndj1+Gj07+f2XIIAPClM2aNe8ghEZGRGLzHYXZ9RfK2aV0DITz5zkHMqivHdz6zJM81I6JixeA9Dstm1qJlTwd6gmHc9+RWDEai+MFnT0rOmiQiyjV2WI7DxSdNw2A4ivuf/QC/2bgPZW7nuKfXExFlajwdlpafYWkFkaji1O89h/be2OqC/3jZifhyfOU9IiKzjDXDkmmTcXA6BDedf1zy8RXLZ46xNRGR+Qp+ko5Rrl0xF1f4ZsLjdJh2TzoiovFi8M7Ase68Q0SUK+ywJCKyGNM7LEXkcwDuBbAYwGmqmrJX0u4dlkRE+WBmh+VmAJ8F8GKW5RARUQaySuKq6jZg9I1QiYjIXJYfNmHXBa0moliOlcdZeIrlWK10nMcM3iLynIhsTvF12Xh3EggE4PP5kl833njjuCuY6cnKtFM0k+3NLBvI7FjNrouZ58XMa2ql88Lf3fzUxe6/u36/PxkrAYy+2W3cMYO3qq5S1SUpvn433kp5vV5s3Lgx+RUKhcb71oxZ6UKbObrGzn8AmbLSNbLrNS2W48x0eyv+7jY3NydjJYC2dNsbMj1eRP4M4JvpRpuISADA7iFP1QBIu07tCA0Y4wBSyKTsTLc3s2wgs2M1uy5mnhczr6mVzgt/d/NTl0L63Z2tqt5UG2c7VPCvAPwUgBfAEQCbVPXCCRdIRETjkpOFqYiIyFiWH21CRESjWTp4i8hqEXlfRLaLyG35ro9ZRGSXiLwrIptEpKCmoorIgyLSKiKbhzxXJyLPisiH8e+T8llHI6Q5zntFZH/8um4SkYvzWUcjiMhMEXleRLaKyBYRuTn+fCFe03THaonratm0iYg4AXwA4AIA+wC8AeAqVd2a14qZQER2AfCpaiYdIbYgImcD6AHw76q6JP7c/wbQrqo/iP9TnqSq38pnPbOV5jjvBdCjqj/MZ92MJCLTAExT1TdFpApAC4DLAVyLwrum6Y7187DAdbVyy/s0ANtVdYeqDgL4NYBxjy0na1DVFwG0j3j6MgC/jP/8S8T+IGwtzXEWHFU9qKpvxn/uBrANwAwU5jVNd6yWYOXgPQPA3iGP98FCJ85gCuAZEWkRkeZ8VyYHpqjqwfjPHwOYks/KmOxrIvJOPK1i+1TCUCIyB8ApADagwK/piGMFLHBdrRy8i8lZqvoJABcBuDH+EbwoaCxvZ83cXfb+FcB8AMsAHATwo7zWxkAiUgngcQC3qGrX0NcK7ZqmOFZLXFcrB+/9AIbeb6wx/lzBUdX98e+tAJ5ALGVUyA7F84mJvGJrnutjClU9pKoRVY0CWIMCua4i4kYsmD2sqr+NP12Q1zTVsVrlulo5eL8BYIGIzBURD4ArAfw+z3UynIhUxDtDICIVAD6N2FK7hez3AP46/vNfAxj3Ugt2kghmcX+FAriuEltC9N8AbFPVHw95qeCuabpjtcp1texoEwCID8G5H4ATwIOq+r381sh4IjIPsdY2EFui9z8L6ThF5BEA5yI2rfgQgHsA/DeA3wCYhdiyCZ9XVVt39qU5znMR+2itAHYBuGFIXtiWROQsAC8BeBdANP70HYjlggvtmqY71qtggetq6eBNRESpWTltQkREaTB4ExHZEIM3EZENMXgTEdkQgzcRkQ0xeBMR2RCDNxGRDTF4ExHZ0P8Hnxi4BaxZVeUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "        xiprime = dfdA(hm.xi, hm.deltaL, hm.Abar, 1e100)\n",
    "        Rprime = dfdA(hm.R, hm.deltaL, hm.Abar, 1e100)\n",
    "        mprime = dfdA(hm.m, hm.deltaL, hm.Abar, 1e100)\n",
    "\n",
    "\n",
    "        \n",
    "        #xiprime.fill(1)\n",
    "        \n",
    "        g = hm.gamma(hm.R, hm.m, hm.U)\n",
    "        r = hm.rho(hm.R, hm.m, hm.U, hm.xi, g, xiprime, Rprime, mprime)\n",
    "        drho = hm.drho(hm.R, hm.m, hm.U, g, hm.xi, Rprime, mprime, xiprime)\n",
    "        exi = np.exp(hm.xi)\n",
    "        ephi = hm.ephi(hm.R, hm.U, g, hm.xi, xiprime, Rprime)\n",
    "        elambda = hm.elambda(ephi, exi, xiprime)\n",
    "        epsi = hm.epsi(hm.R, hm.U, g, hm.xi, r, ephi)\n",
    "        \n",
    "        plt.plot(hm.Abar[2:], ddfddA(hm.U, hm.deltaL, hm.Abar, 0)[2:])\n",
    "        #plt.plot(np.arange(hm.N), dfdA(r, hm.deltaL, hm.Abar, 1e100))\n",
    "        #plt.plot((hm_mix.Abar*hm_mix.R * np.exp((hm_mix.alpha) * hm_mix.xi)), r* (np.exp((hm_mix.alpha) * hm_mix.xi))**(-3*(1+w)))\n",
    "        #plt.plot(np.arange(hm.N), ephi)\n",
    "        #plt.plot(np.arange(hm.N), epsi)\n",
    "        #plt.plot(np.arange(hm.N),elambda / epsi)\n",
    "        #plt.xlim(0.1,3)\n",
    "        #plt.ylim(-0.1,0)\n",
    "        #plt.yscale('log')\n",
    "#plt.ylim(0.915,0.93)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2083,
   "id": "55968d85-75a1-43d9-b98a-43fe4b48901d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-6.108149663452625e-06"
      ]
     },
     "execution_count": 2083,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " epsi[0] / elambda[0] * (hm.U[1] - hm.U[0]) / ( (hm.Abar[1] - hm.Abar[0]) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2197,
   "id": "4683f728-32bd-4d32-a080-980b93af1c18",
   "metadata": {},
   "outputs": [],
   "source": [
    "hm=hm_mix_bak\n",
    "hm_mix = hm_mix_bak"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2200,
   "id": "9dcadba3-ab66-43a7-82a7-585cc088b1f8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "        xiprime = dfdA(hm.xi, hm.deltaL, hm.Abar, 1e100)\n",
    "        Rprime = dfdA(hm.R, hm.deltaL, hm.Abar, 1e100)\n",
    "        mprime = dfdA(hm.m, hm.deltaL, hm.Abar, 1e100)\n",
    "\n",
    "\n",
    "        \n",
    "        #xiprime.fill(1)\n",
    "        \n",
    "        g = hm.gamma(hm.R, hm.m, hm.U)\n",
    "        r = hm.rho(hm.R, hm.m, hm.U, hm.xi, g, xiprime, Rprime, mprime)\n",
    "        drho = hm.drho(hm.R, hm.m, hm.U, g, hm.xi, Rprime, mprime, xiprime)\n",
    "        exi = np.exp(hm.xi)\n",
    "        ephi = hm.ephi(hm.R, hm.U, g, hm.xi, xiprime, Rprime)\n",
    "        elambda = hm.elambda(ephi, exi, xiprime)\n",
    "        epsi = hm.epsi(hm.R, hm.U, g, hm.xi, r, ephi)\n",
    "        \n",
    "        #plt.plot(np.arange(hm.N-1), ddfddA(hm.U, hm.deltaL, hm.Abar, 0)[1:])\n",
    "        #plt.plot(np.arange(hm.N), dfdA(r, hm.deltaL, hm.Abar, 1e100))\n",
    "        plt.plot((hm_mix.Abar*hm_mix.R * np.exp((hm_mix.alpha) * hm_mix.xi)), r* (np.exp((hm_mix.alpha) * hm_mix.xi))**(-3*(1+w)))\n",
    "        #plt.plot(np.arange(hm.N), ephi)\n",
    "        #plt.plot(np.arange(hm.N), epsi)\n",
    "        #plt.plot(np.arange(hm.N),elambda / epsi)\n",
    "        plt.xlim(0,15)\n",
    "        plt.ylim(1e-8,1)\n",
    "        plt.yscale('log')\n",
    "#plt.ylim(0.915,0.93)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2084,
   "id": "6464e79a-3dc6-445b-ba42-429896714dce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "        xiprime = dfdA(hm.xi, hm.deltaL, hm.Abar, 1e100)\n",
    "        Rprime = dfdA(hm.R, hm.deltaL, hm.Abar, 1e100)\n",
    "        mprime = dfdA(hm.m, hm.deltaL, hm.Abar, 1e100)\n",
    "\n",
    "\n",
    "        \n",
    "        #xiprime.fill(1)\n",
    "        \n",
    "        g = hm.gamma(hm.R, hm.m, hm.U)\n",
    "        r = hm.rho(hm.R, hm.m, hm.U, hm.xi, g, xiprime, Rprime, mprime)\n",
    "        drho = hm.drho(hm.R, hm.m, hm.U, g, hm.xi, Rprime, mprime, xiprime)\n",
    "        exi = np.exp(hm.xi)\n",
    "        ephi = hm.ephi(hm.R, hm.U, g, hm.xi, xiprime, Rprime)\n",
    "        elambda = hm.elambda(ephi, exi, xiprime)\n",
    "        epsi = hm.epsi(hm.R, hm.U, g, hm.xi, r, ephi)\n",
    "        \n",
    "        #plt.plot(np.arange(hm.N-1), ddfddA(hm.U, hm.deltaL, hm.Abar, 0)[1:])\n",
    "        #plt.plot(np.arange(hm.N), dfdA(r, hm.deltaL, hm.Abar, 1e100))\n",
    "        plt.plot((hm_mix.Abar*hm_mix.R * np.exp((hm_mix.alpha) * hm_mix.xi)), r* (np.exp((hm_mix.alpha) * hm_mix.xi))**(-3*(1+w)))\n",
    "        #plt.plot(np.arange(hm.N), ephi)\n",
    "        #plt.plot(np.arange(hm.N), epsi)\n",
    "        #plt.plot(np.arange(hm.N),elambda / epsi)\n",
    "        plt.xlim(0,25)\n",
    "        plt.ylim(1e-8,1)\n",
    "        plt.yscale('log')\n",
    "#plt.ylim(0.915,0.93)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 546,
   "id": "508157a7-f911-457d-94af-50bce60144c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "        xiprime = dfdA(hm.xi, hm.deltaL, hm.Abar, 1e100)\n",
    "        Rprime = dfdA(hm.R, hm.deltaL, hm.Abar, 1e100)\n",
    "        mprime = dfdA(hm.m, hm.deltaL, hm.Abar, 1e100)\n",
    "\n",
    "\n",
    "        \n",
    "        #xiprime.fill(1)\n",
    "        \n",
    "        g = hm.gamma(hm.R, hm.m, hm.U)\n",
    "        r = hm.rho(hm.R, hm.m, hm.U, hm.xi, g, xiprime, Rprime, mprime)\n",
    "        drho = hm.drho(hm.R, hm.m, hm.U, g, hm.xi, Rprime, mprime, xiprime)\n",
    "        exi = np.exp(hm.xi)\n",
    "        ephi = hm.ephi(hm.R, hm.U, g, hm.xi, xiprime, Rprime)\n",
    "        elambda = hm.elambda(ephi, exi, xiprime)\n",
    "        epsi = hm.epsi(hm.R, hm.U, g, hm.xi, r, ephi)\n",
    "        \n",
    "        #plt.plot(np.arange(hm.N-1), ddfddA(hm.U, hm.deltaL, hm.Abar, 0)[1:])\n",
    "        #plt.plot(np.arange(hm.N), dfdA(r, hm.deltaL, hm.Abar, 1e100))\n",
    "        plt.plot(hm.Abar, epsi)\n",
    "        plt.plot(hm.Abar, ephi)\n",
    "        #plt.plot(np.arange(hm.N), ephi)\n",
    "        #plt.plot(np.arange(hm.N), epsi)\n",
    "        #plt.plot(np.arange(hm.N),elambda / epsi)\n",
    "        #plt.xlim(0,25)\n",
    "        #plt.ylim(1e-8,1)\n",
    "        plt.yscale('log')\n",
    "#plt.ylim(0.915,0.93)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1258,
   "id": "77c45a70-908c-4046-bd34-516296db8100",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "        xiprime = dfdA(hm.xi, hm.deltaL, hm.Abar, 1e100)\n",
    "        Rprime = dfdA(hm.R, hm.deltaL, hm.Abar, 1e100)\n",
    "        mprime = dfdA(hm.m, hm.deltaL, hm.Abar, 1e100)\n",
    "\n",
    "\n",
    "        \n",
    "        #xiprime.fill(1)\n",
    "        \n",
    "        g = hm.gamma(hm.R, hm.m, hm.U, hm.xi)\n",
    "        r = hm.rho(hm.R, hm.m, hm.U, hm.xi, g, xiprime, Rprime, mprime)\n",
    "        drho = hm.drho(hm.R, hm.m, hm.U, g, hm.xi, Rprime, mprime, xiprime)\n",
    "        exi = np.exp(hm.xi)\n",
    "        ephi = hm.ephi(hm.R, hm.U, g, hm.xi, xiprime, Rprime)\n",
    "        elambda = hm.elambda(ephi, exi, xiprime)\n",
    "        epsi = hm.epsi(hm.R, hm.U, g, hm.xi, r, ephi)\n",
    "        \n",
    "        #plt.plot(np.arange(hm.N-1), ddfddA(hm.U, hm.deltaL, hm.Abar, 0)[1:])\n",
    "        #plt.plot(np.arange(hm.N), dfdA(r, hm.deltaL, hm.Abar, 1e100))\n",
    "        plt.plot((hm.Abar*hm.R * np.exp((hm.alpha) * hm.xi)), epsi)\n",
    "        #plt.plot(np.arange(hm.N), ephi)\n",
    "        #plt.plot(np.arange(hm.N), epsi)\n",
    "        #plt.plot(np.arange(hm.N),elambda / epsi)\n",
    "        plt.xlim(0,25)\n",
    "        #plt.ylim(1e-8,1)\n",
    "        plt.yscale('log')\n",
    "#plt.ylim(0.915,0.93)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 779,
   "id": "ccb79e79-0028-4171-9162-bb0630958f3d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "759.1217309588485"
      ]
     },
     "execution_count": 779,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hm_uni.u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1295,
   "id": "d3dc854b-da6c-4ab4-b121-1a3e6090c24b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "392.8628124890612"
      ]
     },
     "execution_count": 1295,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hm_mix.u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1261,
   "id": "c1f710f9-e77f-4e66-959a-857530094a9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9905349489198917"
      ]
     },
     "execution_count": 1261,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(hm.R**2 * hm.m * hm.Abar**2 * np.exp(2*(hm.alpha-1)*hm.xi)).max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 840,
   "id": "e897cfdc-a660-4f70-b6ec-2783a1f43176",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 1.0)"
      ]
     },
     "execution_count": 840,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot((hm.Abar*hm.R * np.exp((hm.alpha) * hm.xi)), hm.R**2 * hm.m * hm.Abar**2 * np.exp(2*(hm.alpha-1)*hm.xi))\n",
    "#plt.plot(hm.Abar, hm_bak.R**2 * hm_bak.m * hm_bak.Abar**2 * np.exp(2*(hm_bak.alpha-1)*(hm_bak.xi)))\n",
    "\n",
    "plt.xlim(0,60)\n",
    "plt.ylim(0.,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "id": "c53340c6-2530-4a65-9cbe-11a3667379d0",
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "ephi() missing 1 required positional argument: 'Rprime'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_2413/1194290693.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0mp\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mhm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mP\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0mexi\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0mephi\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mhm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mephi\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mR\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mU\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxiprime\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mRprime\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     11\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     12\u001b[0m \u001b[0mepsi\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mhm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mepsi\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mR\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mU\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mephi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mTypeError\u001b[0m: ephi() missing 1 required positional argument: 'Rprime'"
     ]
    }
   ],
   "source": [
    "        xiprime = dfdA(hm.xi, hm.deltaL, hm.Abar, 0)\n",
    "        Rprime = dfdA(hm.R, hm.deltaL, hm.Abar, 0)\n",
    "        mprime = dfdA(hm.m, hm.deltaL, hm.Abar, 0)\n",
    "        Uprime = dfdA(hm.U, hm.deltaL, hm.Abar, 0)\n",
    "        #print((xiprime ))\n",
    "        g = hm.gamma(hm.R, hm.m, hm.U)\n",
    "        r = hm.rho(hm.R, hm.m, hm.U, hm.xi, g, xiprime, Rprime, mprime)\n",
    "        p = hm.P(r)\n",
    "        exi = np.exp(hm.xi)\n",
    "        ephi = hm.ephi(hm.R, hm.U, g, xiprime, Rprime)\n",
    "        \n",
    "        epsi = hm.epsi(hm.R, hm.U, g, hm.xi, r, ephi)\n",
    "        plt.plot(hm.Abar, epsi)\n",
    "        plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1652,
   "id": "6e462a28-d677-4874-b0cb-3bd20fbf7449",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f5a07428f10>]"
      ]
     },
     "execution_count": 1652,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ms.Abar, ms_bak.R**2 * ms_bak.m * ms_bak.Abar**2 * np.exp(2 * (ms_bak.alpha-1) * ms_bak.xi))\n",
    "plt.plot(ms.Abar, np.array([1]*ms.N))\n",
    "#plt.xlim(0,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "id": "78bd45c5-4ecc-4061-98f7-4664bac9b075",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f5a4f7dacd0>"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(Abar[:], ms.U[:])\n",
    "#plt.xlim(0,30)\n",
    "#plt.ylim(0,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 707,
   "id": "49842670-8707-4a3d-9587-b0430c3ecc59",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f5a400f9580>]"
      ]
     },
     "execution_count": 707,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ms_mix.Abar[:ms_mix.N-1], ms_mix.U_hm[:ms_mix.N-1])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 811,
   "id": "bda0946a-4807-4409-9351-7300c1242068",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f5a3da46d60>]"
      ]
     },
     "execution_count": 811,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ms.Abar[:ms.N-1], ms.U_hm[:ms.N-1])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "id": "c43fd32c-8fe1-4687-ba68-ca2f0b069452",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.038651819295227194"
      ]
     },
     "execution_count": 194,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hm.deltau_i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bee8ed1c-593f-4f4d-8c95-3a30dc25008a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 618,
   "id": "49c9bf92-257b-4fe8-a8a5-fd70d6ac2efc",
   "metadata": {},
   "outputs": [],
   "source": [
    "import copy\n",
    "ms_std = copy.copy(ms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 665,
   "id": "5c4004b6-26b3-4517-b4fa-a205f8583619",
   "metadata": {},
   "outputs": [],
   "source": [
    "ms = copy.copy(ms_std)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1026,
   "id": "0cf3b195-a0ad-4d1b-b0a7-04dede8550b0",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "hm = HM(ms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "32adfb3b-0580-48c8-96fe-d26418fac5b3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'hm' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_1959/4170168912.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mhm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_steps\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2000\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'hm' is not defined"
     ]
    }
   ],
   "source": [
    "hm.run_steps(2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 820,
   "id": "f7023f12-4166-4750-a808-e7c1441b6d63",
   "metadata": {},
   "outputs": [],
   "source": [
    "import copy\n",
    "hm_bak = copy.copy(hm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 933,
   "id": "49845c7a-e181-49a6-ac70-f0ea7a4eea01",
   "metadata": {},
   "outputs": [],
   "source": [
    "import copy\n",
    "hm_bak2 = copy.copy(hm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1009,
   "id": "e0d18735-c561-474b-becd-c40aed8ba34d",
   "metadata": {},
   "outputs": [],
   "source": [
    "hm = copy.copy(hm_bak2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 977,
   "id": "89c29619-90c6-4634-acbc-e1c1a36d6e78",
   "metadata": {},
   "outputs": [],
   "source": [
    "import copy\n",
    "hm_bak3 = copy.copy(hm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 953,
   "id": "7c57577f-8e67-47b3-8079-90e4434fdee3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "142219.99999575678"
      ]
     },
     "execution_count": 953,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hm.u / hm.deltau_i / 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1024,
   "id": "b8246cf2-65fc-4ccb-ae35-3b7ad8706496",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 10.0)"
      ]
     },
     "execution_count": 1024,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW0AAAD5CAYAAADsgWTDAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAaX0lEQVR4nO3deXzV9Z3v8deHhOwJCQk7CAoIglaBWLFatWo7uKBzp51qx/qwTq/Y2rp0uqhtbzuPcdqxU0fb2l7nZrTVuVpri0uB67gUddrOqC2LC4iAC7JDAmQhIfvn/nFOQgg5JCfnnPzO7+T9fDzyyFl++Z03eSRvvvme3/f3M3dHRETCYUTQAUREZOBU2iIiIaLSFhEJEZW2iEiIqLRFREJEpS0iEiL9lraZ/dzM9prZuh6PjTaz581sc/RzWWpjiogIDGyk/SCwqNdjtwEr3X0msDJ6X0REUswGsrjGzKYBK9z95Oj9jcB57r7LzCYAL7n7rJQmFRGRQc9pj3P3XdHbu4FxScojIiLHkJ3oDtzdzazP4XpeXp5nZWV136+oqGDMmDF97qeuro5Ro0YN+HXj2T6ebaurq2NmHKoM8X4vwpY5VXnj3T4dMuvn4rB0yBvv9snMXF1dTU1NDQBNTU3N7p7f54bu3u8HMA1Y1+P+RmBC9PYEYGNfX1dQUOADdd111w1423i3j2fbBQsWBJ4h3u9F2DKnKm+826dDZv1cHJYOeePdPlWZgWqP0ceDnR5ZBlwTvX0N8NtB7qfb4sWLU7Z9vPsOOkOq8qYyRzp8j+PdPh0yp0PeVOYI2/d4MNunaL+1MZ+J1eZ+eFT9KLALaAO2A58HyokcNbIZ+B0wuq+vjWeknS7i+Z8zXYQtc9jyuivzUAhbXvfUZQZWeYxO7ndO290/E+OpC/r72oqKiv42STtLliwJOkLcwpY5bHlBmYdC2PJCMJkHdMjfYFVWVvqqVatStn8RkUxkZqvdvbKv57SMXUQkRFTaIiIhotIWEQkRlbaISIiotEVEQiSlpV1XV8eSJUtYvnx5Kl9GRCQjLF++vOswwpjr3XXIn4hImtEhfyIiGUKlLSISIiptEZEQUWmLiISISltEJERU2iIiIaLSFhEJEZW2iEiIqLRFREJEy9hFRNKElrGLiISQlrGLiGQIlbaISIiotEVEQkSlLSISIiptEZEQUWmLiISISltEJERU2iIiIaIVkSIiaUIrIkVEQkgrIkVEMoRKW0QkRFTaIiIhotIWEQkRlbaISIiotEVEQiSh0jazr5jZejNbZ2aPmllesoKJiMjRBl3aZjYJuAmodPeTgSzgymQFExGRoyU6PZIN5JtZNlAA7Ew8koiIxDLo0nb3HcBdwFZgF1Dn7s/13Ka6uprKysruj6qqqsTSiohkqKqqqu6uBCpibTfoZexmVgY8DlwB1AK/AZa6+8Nd22gZu4hI/FK1jP1C4H13r3b3NuAJ4CMJ7E9ERPqRSGlvBRaaWYGZGXABsCE5sUREpC+JzGm/CiwF1gBvRvelSWsRkRTKTuSL3f27wHeTlEVERPqhFZEiIiGi0hYRCRGVtohIiKi0RURCRKUtIhIiuhq7iEia0NXYRURCSFdjFxHJECptEZEQUWmLiISISltEJERU2iIiIaLSFhEJEZW2iEiIqLRFREJEpS0iEiJaxi4ikia0jF1EJIS0jF1EJEOotEVEQkSlLSISIiptEZEQUWmLiISISltEJERU2iIiIaLSFhEJEZW2iEiIaBm7iEia0DJ2EZEQ0jJ2EZEModIWEQkRlbaISIiotEVEQkSlLSISIgmVtpmVmtlSM3vbzDaY2ZnJCiYiIkfLTvDrfww84+6fMrMcoCAJmUREJIZBl7aZjQLOAT4H4O6tQGtyYomISF8SmR45HqgGfmFma83sfjMrTFIuERHpQyKlnQ3MB+5z93lAI3Bbzw2qq6uprKzs/qiqqkrg5UREMldVVVV3VwIVsbYb9DJ2MxsPvOLu06L3Pwrc5u6XdG2jZewiIvFLyTJ2d98NbDOzWdGHLgDeGuz+RESkf4kePXIj8Ej0yJH3gGsTjyQiIrEkVNru/hrQ5xBeRESSTysiRURCRKUtIhIiKm0RkRBJ9I1IERGJg7tTd6iN6oYWqhta2Bv9XH2wpfuxY1Fpi4gkQXNbx1Hl213I0cdrordbOzqP+vrc7BGMLcllTFHuMV9HpS0iEkNbRyf7DrZSc/BwGdccbKGmIfLY3obm7lKub24/6uvNoLwwh4qiXMYU5zJjTBFjiiO3x0Y/d30U52ZjZpGv+1LsTCkt7a6rsS9evJjFixen8qVERAakpb2ju4i7CviIQj7YQk30+dqmtj73UZCTFSnbolxmjS/m7BkVPco4r/t2eWEO2VkDf+tw+fLlLF++HHQ1dhHJZM1tHYfLtkf5Roo4Uso10emJvkbEAEW52VQURUbFFUW5VBT3uF2Uy5ge9wtzUztJcaxl7JoeEZG04+7UH2qnprGFfQdb2XewhZrG6OeDLT1GypGSbmjpu4iL87IZEy3a2eOLqZhR0aOIc6iIjpYrinLJz8ka4n/l4Ki0RWRINLd1sC9avF2lu6+7iFu7y3hfYwv7G1tp6+h7FqCsYCTlRZGphzkTS6Kl23OEfPh+3shwFHE8VNoiMigdnU5tUyv7GnsUbrSIaw72GBU3trLvYCsHY4yGc7NHdJfthFF5nDyppLuUK4pyKS/KobwwUsRlhTmMjGOOOBOptEWkW2NLe2QU3Ni7hA+PgrtGyfsbW+nsYzA8wmB0YbRoi3M4tayU8ujIt7wwJ1LIRTlUFEY+F+RkdR81If1TaYtksPaOTvY3tVLTcGThHjFN0eP2obaOPvdTlJsdHfHmMGV0AfOOK6Mier+7hKOlXFqQQ9YIlXCqqLRFQsTdaYiOhvf1ODyt9yi4q5QPxDhkLXuEdU87lBflcEJFYaSEe09LRO9n4txwWKm0RQLW0ekcaGo9YtFGzRFvzh35Rl1fq+kARuWP7J52mDm2iIUnjI5OUeRS0WtaoiQ/W1MSIaXSFkmBlvYO9je2dpdw9RGHqR152FqsueGRWdY9L1xRlMuJ44q7j4oo7/W5rCCHnOzh/QbdcKHSFhmgxpb2I0bANb2LuCHyBt6xFnAU5GR1F21kbrj0iAUcXc+NKdJoWPqmZewybHWdbe2IIm44fLREdUPX/HCkkGO9STcqf2T3fPBJ40uomBG53bWAozxawhXFORTkaJwksWkZuww7vY+WOHIEfOQIeV9jS58LOCKHrPVcsJHTfRxxeeHhVXRdb+RpWkKSTcvYJdRa2ju6lyt3jXpjzRHvb2qlr3FITtaI7mXLY4tzmTOhJLpy7sjVdOVFOZTpkDVJYyptCcyh1g72NjSzt6GFPfXN7K2PnH94b0PX7chzsc60VpiT1V28x1cUUjltdHQ++MjpiYpep70UCTOVtiSVu3OwpT1SvvVHF/De+hb2NDRTXd/3SX5GZln3qS2nlRdyxvHl3ecd7vlGXZhO8COSTCptGbC2jk521TazvbaJ3XU9RsgNLVRHi3lPfUufb9h1XZVjXHEes8cXc87MMYwpzmVcSR5ji3MZWxI5D3FZwUiNiEWOQaUt3VraOyKlfOAQO2qb2H7gUPSjiR0HDrG7vvmo44kLc7IYWxIZGZ8yuZQLonPGXSU8riSXMcV5lORpekIkGVTaw0hzWwc7ag+xo2cZ1x6+vbeh5Yg38UYYTBiVz6SyfBZOL2dyaT6TywqYXJbP+FF5jC3JoyjFJ4MXkSPpNy4DtXV0smFXPWs+OMDr2+t4v6aRHbWHjrrKc/YIY0JpHpNLC/jozDFMLouU8qTS/O5iHu6nwRRJNyrtDLC3vpk1Ww+wdmsta7Ye4I3tdbS0R85PMbY4l5njijh/1lgml0VGzV2j5XEleTq0TSRktCIyZFrbO1m/s667oNdurWVH7SEgcizy3EklfHbhVOYdV8r848qYMCpPc8kiIaEVkRli2/4mlq7ezh82V7NuZz2t0VH0xFF5zJtaxrwppcyfWsbciSXkZuswOJGw04rIEGpu6+DZ9bv59apt/Nc7+zCDeVNKuebMqcw/rox5x5UxflRe0DFFZIiptNPMuh11/HrVNp5au4P65nYmlebzlQtP5JMLJjG5rCDoeCISMJV2GmhqbWfp6u089udtrN9ZT072CBbNHc+nK6fwkenljNCbhSISpdIO2H9uquZbT77J9gOHmDuxhH+4fC6XnTqR0oKcoKOJSBpSaQek5mALd6x4i9++tpPpYwr51ZKFLDyhPOhYIpLmVNpDzN15fM0O/vH/vUVjSzu3XDiTL543XUd9iMiAJFzaZpYFrAJ2uPuliUfKXHVNbXz50TX8YXMNlVPLuPOTpzBjbHHQsUQkRJIx0r4Z2ACUJGFfGWtX3SGu+fmf2FLTxB2Xz+WqM6bqDUYRiVtCJ5Yws8nAJcD9yYmTmd7Z28An//d/s7O2mQevPZ2rz5ymwhaRQUl0pP0j4BtAn3/jV1dXU1l5eFHPkiVLWLJkSYIvGS6rPzjA5x/6M9kjRvCrJQs5eVLM1akiMoxVVVVRVVXVdbci1naDXsZuZpcCF7v7DWZ2HvC13nPaw30Z+/qddfz1v77M2OJc/v1vz+C4ci2OEZH+pWoZ+1nAZWZ2MZAHlJjZw+7+2QT2mTH2NjRz3UOrKMkbyWPXn8m4Ei05F5HEDXpO291vd/fJ7j4NuBJ4QYUd0dzWwfX/dzX7m1q5/5pKFbaIJI2O004yd+ebT77J2q213HfVfM1hi0hSJaW03f0l4KVk7Cvslq7ezhNrdnDLhTO56JQJQccRkQyja0kl0Qf7Gvn7Zes54/jR3Hj+zKDjiEgGUmknSXtHJ7c89hpZI4x7rjhNl/ESkZTQnHaS/OzFd1m7tZZ7PzOPiaX5QccRkQylkXYSbNrTwE9f3Mxlp05k8akTg44jIhlMpZ2gjk7n1sffoCg3m+8unhN0HBHJcCkt7a6rsUevLpyRHn7lA9ZureU7i+dQXpQbdBwRCbHly5d3nepDV2NPhT31zZx/10ssmDaah649HTO9+SgiiTvWMnZNjyTgn57eQFuHc8flc1XYIjIkVNqD9Op7+3jqtZ1cf+4JTC0vDDqOiAwTKu1BaO/o5LvL1jOpNJ8bzpsRdBwRGUZU2oPwyKtbeXt3A9++5CTyc3RtRxEZOirtONUcbOFfntvI2TMqWHTy+KDjiMgwo9KO0w+f2UhTawd/f9kcvfkoIkNOpR2HN7bX8tiqbVx71jRdRV1EAqHSHiB35x9XbKC8MIebLtAZ/EQkGCrtAXp2/R7+tGU/X/n4iRTnjQw6jogMU1rGPgCt7Z3c+R8bmDm2iCtPnxJ0HBHJUFrGniQP/PF97ljxFr+49nQ+Nmts0HFEJMNpGXsCapta+cnKzXx0ZgXnnTgm6DgiMsyptPtx7wvvUN/cxjcvPkmH+IlI4FTax7B1XxP//vIWPr1gCidNKAk6joiISvtY7vndJkaY8XefODHoKCIigEo7prd31/PUazv43FnTGFeSF3QcERFApR3TXc9upCg3my+eOz3oKCIi3VTafVj9wX5+t2EvXzh3OqUFOUHHERHpptLuxd35wTMbqSjK5dqzpgUdR0TkCCrtXv5zUzV/en8/N18wg4Kc7KDjiIgcQcvYe+jsdP75mY1MGZ3PFacfF3QcERlmtIw9Tste38lNj67lR1ecxl/OmxR0HBEZprSMfQDaOjq5+7mNzB5fzGWnTgw6johIn1TaUb9etY0t+5r4+l/MYsQILVcXkfSk0gYOtXbwk5WbWTC1jPNn6yx+IpK+VNrAQy9vYU99C7cumq2TQolIWhv2pV13qI37XnqX82aN4cPHjw46jojIMQ26tM1sipm9aGZvmdl6M7s5mcGGStXv36XuUBtf/4tZQUcREelXIqtH2oGvuvsaMysGVpvZ8+7+VpKypdzehmZ+/sctXHbqROZOjHlYpIhI2hj0SNvdd7n7mujtBmADEKqDm3/6wju0dXTydx/XqVdFJBySMqdtZtOAecCrydjfUNi6r4lfvrqVK06fwrSKwqDjiIgMSMIn1zCzIuBx4BZ3r+/5XHV1NZWVhxf1LFmypGuJZuDu+d0msrOMmy6YGXQUERGqqqqoqqrqulsRa7uElrGb2UhgBfCsu9/d+/l0Xca+YVc9F//kD1x/znRuu2h20HFERI6QkmXsFjmg+QFgQ1+Fnc50gQMRCatE5rTPAq4Gzjez16IfFycpV8qs2rKflW9HLnAwqmBk0HFEROIy6Dltd/8jEKrlg+6RU6/qAgciElbDakXkS5uq+dMWXeBARMJr2JS2LnAgIplg2JT2std3smFXPV/7xCxysofNP1tEMsywaK+W9g7uem4jcyeWsPhDusCBiITXsCjtR17ZyvYDh7jtotm6wIGIhFrGl3Z9cxv3vrCZs2dU8NGZY4KOIyKSkIy/Gvu//f49DjS1cesirXwUkfQ27K/Gvre+mXN/+BIXzhnHvZ+ZF1gOEZF4DNursf945WbaOjr52id06lURyQwZW9rvVR/kV3/exlVnHMfUcp16VUQyQ8aW9j8/s5G87BHcqFOvikgGycjSfvndfTyzfjc3fGwGFUW5QccREUmajCvtjk7nH1a8xaTSfD5/9vFBxxERSaqMK+3frNrGhl313H7xbPJGZgUdR0QkqTKqtBua27jruY2cPq2MS06ZEHQcEZGky6jS/ukL77CvsZXvXDqXyIV1REQyS8aU9qY9DTzwx/f51PzJnDI55mIiEZFQy4hl7O7Ot59aR1FeNrdffFJKX0tEJFWGzTL2pau387XfvM6df3UKV35YFzgQkXDL6GXstU2tfP/pDcw/rpRPV04JOo6ISEqFvrTvWLGBukNtfO9/nKJzZYtIxgt1ab/w9h4eX7OdG86bzkkTSoKOIyKScqEt7bqmNm57/E1mjy/mxvN1fhERGR6ygw4wWN9dto59ja08cM3pulCviAwboWy7x1dv56nXdvLlj83QMdkiMqyErrTfqz7I//rtOj58/GhuPH9G0HFERIZUqEq7qbWdL/1yLbnZI/jxlaeRnRWq+CIiCQvNikh35+u/eYO3d9dz9xWnMWFUfhISioikj4xaEfmTlZu5+/lN3HbRbL5w7vSk7FNEJB2FfkXkI69+wN3Pb+Kv5k3i+nNOCDqOiEhg0r60l7++k28/tY7zZ4/lB5/6kE65KiLDWlqX9hNrtnPLY69x+tTR/Oxv5jNSbzyKyDCXlotr3J37//A+33t6Ax+ZXs7/uXoB+Tm6dJiISNqV9sGWdm57/A1WvLGLi08Zzz1XnEZutgpbRATSrLT/650avvXkm2zd38Q3Fs3iC+dM15n7RER6SGiS2MwWmdlGM3vHzG7r/Xx1dfWA9rN+Zx1ffHg1V93/Kg788rqF3HDejEAKu6qqashfM1Fhyxy2vKDMQyFseSGgzO4+qA8gC3gXOAHIAV4H5vTcpqCgwGPZtr/RH35li//1ff/tU29d4bO+udzveX6jH2ptj/k1PS1btmxA28W77YIFC1Ky31Rt6x6+zKnKG+/26ZBZPxeHpUPeeLdPVWZgs8fo3kRG2h8G3nH399y9FfgVcHnPDTpzirh35Wb+5bmN/NPTG7h16Rv8zb+9wsLvr+TsH7zIt55cx/6mVr6xaBZn1jzNLReeSN7Igc1fx7PKMlXXqExVhlReUzNsmePdb9gyp0PeVOYI2/d4MNunaL+lsZ4Y9IpIM/sUsMjd/2f0/tXAGe7+5R7bNAMdPb6sGqiJsctRQF0cEeLZPp5tK4idcagyxPu9CFvmVOWNd/t0yKyfi8PSIW+82yczcwUwJnp7hLv3ea6OlL4R6e55qdy/iMhwk8j0yA6g55V0J0cfExGRFEmktP8MzDSz480sB7gSWJacWCIi0pdBl7a7twNfBp4FNgC/dvf1Xc/3dzhgujGzKWb2opm9ZWbrzezmoDMNhJllmdlaM1sRdJaBMLNSM1tqZm+b2QYzOzPoTMdiZl+J/jysM7NHzSztpvzM7OdmttfM1vV4bLSZPW9mm6Ofy4LM2FuMzD+M/ly8YWZPmllpgBGP0lfmHs991czczCpSnSOh47Td/Wl3P9Hdp7v797oeN7Ms4GfARcAc4DNmNiexqCnXDnzV3ecAC4EvhSAzwM1E/tMMix8Dz7j7bOBU0ji7mU0CbgIq3f1kIoe5Xhlsqj49CCzq9dhtwEp3nwmsjN5PJw9ydObngZPd/UPAJuD2oQ7Vjwc5OjNmNgX4BLB1KEKk6gxM/R4OmG7cfZe7r4nebiBSJpOCTXVsZjYZuAS4P+gsA2Fmo4BzgAcA3L3V3WsDDdW/bCDfzLKBAmBnwHmO4u6/B/b3evhy4KHo7YeAvxzKTP3pK7O7Pxf9Cx7gFSLvk6WNGN9ngHuAbwCpuzhBD6kq7UnAth73t5PmBdiTmU0D5gGvBhylPz8i8sPSGXCOgTqeyGGfv4hO6dxvZoVBh4rF3XcAdxEZQe0C6tz9uWBTDdg4d98Vvb0bGBdkmEH4W+A/gg7RHzO7HNjh7q8P1WvqXKe9mFkR8Dhwi7vXB50nFjO7FNjr7quDzhKHbGA+cJ+7zwMaSb8/27tF54EvJ/KfzUSg0Mw+G2yq+EVX2A3JKDAZzOxbRKYrHwk6y7GYWQHwTeA7Q/m6qSrtUB4OaGYjiRT2I+7+RNB5+nEWcJmZbSEy/XS+mT0cbKR+bQe2u3vXXzBLiZR4uroQeN/dq929DXgC+EjAmQZqj5lNAIh+3htwngExs88BlwJX+WBX/g2d6UT+Q389+ns4GVhjZuNT+aKpKu3QHQ5okUviPABscPe7g87TH3e/3d0nu/s0It/fF9w9rUeB7r4b2GZms6IPXQC8FWCk/mwFFppZQfTn4wLS+I3TXpYB10RvXwP8NsAsA2Jmi4hM913m7k1B5+mPu7/p7mPdfVr093A7MD/6c54yKSnt/g4HTFNnAVcTGbG+Fv24OOhQGehG4BEzewM4Dfh+sHFii/5FsBRYA7xJ5Pcl7U5FZ2aPAi8Ds8xsu5l9HrgT+LiZbSbyF8OdQWbsLUbmnwLFwPPR379/DTRkLzEyD32O9P8LREREuuiNSBGREFFpi4iEiEpbRCREVNoiIiGi0hYRCRGVtohIiKi0RURCRKUtIhIi/x/kypbmiLdCpwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = np.exp(hm.alpha * hm.xi)\n",
    "H = np.exp(-hm.xi) / hm.RH\n",
    "rho_b = a**(1+hm.w)\n",
    "Rb = a * hm.A\n",
    "plt.plot(hm.R * Rb ,  (np.exp(-hm.xi/2) * hm.R **3 * hm.Abar**3 * hm.m ) / 2 )\n",
    "plt.xlim(0,15)\n",
    "plt.ylim(0,10)\n",
    "#plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5765dc5b-a7ed-4c8a-ab2b-716533ba4774",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(hm.Abar, hm.m)\n",
    "plt.plot(hm_bak.Abar, hm_bak.m)\n",
    "\n",
    "\n",
    "#plt.xlim(0,300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 784,
   "id": "fe212c9a-1757-437c-98eb-aaa5df2babd7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 300.0)"
      ]
     },
     "execution_count": 784,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "        xiprime = dfdA(hm.xi, hm.deltaL, hm.Abar, 0)\n",
    "        Rprime = dfdA(hm.R, hm.deltaL, hm.Abar, 0)\n",
    "        mprime = dfdA(hm.m, hm.deltaL, hm.Abar, 0)\n",
    "\n",
    "\n",
    "        \n",
    "        #xiprime.fill(1)\n",
    "        \n",
    "        g = hm.gamma(hm.R, hm.m, hm.U)\n",
    "        r = hm.rho(hm.R, hm.m, hm.U, hm.xi, g, xiprime, Rprime, mprime)\n",
    "        exi = np.exp(hm.xi)\n",
    "        ephi = hm.ephi(hm.R, hm.U, g, xiprime, Rprime)\n",
    "        elambda = hm.elambda(ephi, exi, xiprime)\n",
    "        epsi = hm.epsi(hm.R, hm.U, g, hm.xi, r, ephi)\n",
    "        plt.scatter(np.arange(hm.N), ephi)\n",
    "        plt.scatter(np.arange(hm.N), epsi)\n",
    "        plt.xlim(0,300)\n",
    "#plt.ylim(0.915,0.93)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 832,
   "id": "44cfa2c9-6ea5-4c87-a998-9bcc16427538",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f01e28be040>]"
      ]
     },
     "execution_count": 832,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(hm.Abar,  hm.xi-0)\n",
    "\n",
    "\n",
    "#plt.xlim(0,300)\n",
    "#plt.ylim(0.915,0.93)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1012,
   "id": "eeb8e9d7-c7b2-4d5e-93ee-dfc1f62de63c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9326803234148633"
      ]
     },
     "execution_count": 1012,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "( hm.R**2 * hm.m * hm.Abar**2 * np.exp(2*(hm.alpha-1)*hm.xi)).max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1011,
   "id": "b87799e9-6ebd-4466-96df-c2da44e053c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 1.0)"
      ]
     },
     "execution_count": 1011,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(hm.Abar, hm.R**2 * hm.m * hm.Abar**2 * np.exp(2*(hm.alpha-1)*hm.xi))\n",
    "plt.plot(hm.Abar, hm_bak.R**2 * hm_bak.m * hm_bak.Abar**2 * np.exp(2*(hm_bak.alpha-1)*(hm_bak.xi)))\n",
    "\n",
    "\n",
    "#plt.xlim(0,300)\n",
    "plt.ylim(0.,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0720c75d-9845-40cb-86b2-7a1a0b14711e",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(hm.Abar, hm.R**2 * hm.m * hm.A**2 * np.exp(2*(hm.alpha-1)*hm.xi))\n",
    "plt.plot(hm.Abar, hm_bak.R**2 * hm_bak.m * hm_bak.A**2 * np.exp(2*(hm_bak.alpha-1)*hm_bak.xi))\n",
    "\n",
    "\n",
    "#plt.xlim(0,300)\n",
    "#plt.ylim(0.915,0.93)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1010,
   "id": "0aa0cc8c-7fee-4b5e-ac83-c00ff194147c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f01cc3115b0>]"
      ]
     },
     "execution_count": 1010,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "        xiprime = dfdA(hm.xi, hm.deltaL, hm.Abar, 0)\n",
    "        Rprime = dfdA(hm.R, hm.deltaL, hm.Abar, 0)\n",
    "        mprime = dfdA(hm.m, hm.deltaL, hm.Abar, 0)\n",
    "        Uprime = dfdA(hm.U, hm.deltaL, hm.Abar, 0)\n",
    "        #print((xiprime ))\n",
    "        g = hm.gamma(hm.R, hm.m, hm.U)\n",
    "        r = hm.rho(hm.R, hm.m, hm.U, hm.xi, g, xiprime, Rprime, mprime)\n",
    "        p = hm.P(r)\n",
    "        exi = np.exp(hm.xi)\n",
    "        ephi = hm.ephi(hm.R, hm.U, g, xiprime, Rprime)\n",
    "        \n",
    "        epsi = hm.epsi(hm.R, hm.U, g, hm.xi, r, ephi)\n",
    "        plt.plot(hm.Abar, epsi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f7207ca3-68af-4a10-aae2-77f81a47e4a4",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 763,
   "id": "d0c1f703-5420-4041-a05b-935fb1c3f31f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f01db1333a0>"
      ]
     },
     "execution_count": 763,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(hm.Abar, hm.U[:])\n",
    "#plt.xlim(0,30)\n",
    "#plt.ylim(0,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 884,
   "id": "14cd4dd8-d103-43c1-a9bf-bbe30a883087",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f01d3f8fc10>"
      ]
     },
     "execution_count": 884,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(Abar[:n-1], ms.xi_hm[:])\n",
    "#plt.xlim(0,30)\n",
    "#plt.ylim(0,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 883,
   "id": "3f537ad8-4ccd-40b3-8fab-5b67e483742b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f01d608cf10>"
      ]
     },
     "execution_count": 883,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWcAAAD1CAYAAACMYTRxAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAU/klEQVR4nO3df5BddXnH8c+TzQoLSlYmqZUFG+owcfihxOw42LSdAlWoEMzQH+gIY1uH/ae14Cg2GTMCjpXMhFKcaUd7QdQZU6sF3LIoBEZ0HB2hBTYSQ0i1liIXLJfRBIQMJOHpH3vvstm959e95/d5v2Z22N177tln+fHhm+c853vM3QUAKJdlRRcAAFiKcAaAEiKcAaCECGcAKCHCGQBKiHAGgBJansZJjjvuOD/qqKM0Pj4uSVqxYkXs93Y6Ha1atSr28fv37090/qyPp/50jx/kPWX7Hai/2HqqUP/+/fu1b98+Pfvss8+5e/+TufvQH+vWrfOeyy+/3JNY+N44kp4/6+OpP93jB3lP2X4H6k/3/HWuX9KDHpCrqbc1NmzYkPYphzp/1scnRf3ZvCfL8zftnwH1p3v+gesJSu2FH5LGJd0q6TFJeyS90wNWzkkN894yoP7iVf13oP5iFVm/QlbOcXvOn5V0t7v/iZm9RtIxg/2vYKmpqam0TlUI6i9e1X8H6i9WWes3j9hbw8xWSNop6bc94ODJyUl/8MEH068OAGrMzB5y98l+r8XpOZ8sqSPpi2Y2a2Y3m9mxqVYIADhCnHBeLuntkj7n7mslvSBp08IDOp2OJicn5z9arVYGpQJAeUzPtrV+6306edM3tX7rfZqebcd6X6vVms9KSSuDjovT1vhNSfe7++ru178naZO7X9A7hrYGgLqZnm1r2469emrfAZ0wPqarzlujjWsn5l/bfPsuHTh4eP74sdERXXfxGfPHxDFUW8PdfyHp52a2pvutcyU9GvunA0BJBa1+e+Hb3ndALqm974A2375r/vVtO/YeEcySdODgYW3bsTe12uJOa3xY0vbupMbPJP1FahUAQIaCVsCLV7+9AJbCw3fj2gk9te9A358V9P1BxApnd98pqe/SGwCKlnYAR4XvCeNjavc55oTxsdR+p1T21gCArOUZwFHhe9V5a/r2nK86b82S9wwqldu39+/fr6mpKc3MzKRxOgANNUgPeJgA7qcX/GOjI0d8f2H4blw7oesuPkMT42MySRPjY4kuBs7MzPRufgncQSlyWiMOpjUADCtsAmLbjr19V7IT42N6qhvYi5mC2w8T3QAOm7gIm9ZIS9i0Bm0NALnrF3xZtCDC2g+9oA0K4I1rJ1IP4yRYOQPIRNwesTQXmIuDuacKK+BBsXIGkJl+4Scp8UW6ETMd7rNYrPoKeFCsnAHEEieEpbnQPHp0mX714sEl5wjrEffeW8UV8KDCVs6EM4AjpBHCQeK0KOoWwGEyD+dTTjnFzz77bG3YsCHzpxAASM/iID77Lat020PtoUM4SJwecRPMzMxoZmZGN91000/d/ZR+x7ByBhog7mrYpMCWQxLjY6N66dArjWpRDIK2BtAQWbYk+gkLYSn4Ih3mEM5ADeXZkiCEs8EoHVAz/faT2H7/E0taEgcOHg6cHw6yuLUxNjqiay46TVL4uBrSRTgDFbB4lfziy4eWhG7SPwMHrYb/eN2EvvNYhxAuGOEMlExUu6LfGFqYoBCOWg2jWIzSAQWK0zdOMkHRryVBX7h8GKUDSiTtIF4sqiWB8uGCIFCAhWG8YmxUL7x8SAcPz0Vv0AW8JME8PjaqY49aThDXFOEMpCBqVbzvwNJRtiRBHDRBQRjXF+EMJBTngl2/VXFc/YKYdkXzEM5AhCzbEwQxgqQSzr1nCDKtgToIC+Nh2xMLEcTN1ZvWEM8QBIKFhfEwFq+KR5eZXnv0cu178SBBDElMawBHSLoyjoP2BNIWK5zN7HFJz0s6LOlQUNIDZZRFGC9EECMLSVbOZ7v7s5lVAqQk6zCmPYE80NZA5RHGqKO44eyS7jEzl/TP7t7KsCYgUi+Q2/sOHNHvJYxRF3HD+XfdvW1mvyHpXjN7zN2/13ux0+locvLVNvTU1JSmpqZSLhVNFrY6HnaugjBGnlqtllqt+fXtyqDjEo/Smdk1kn7t7tf3vscoHbIQtDoeFmGMshhqlM7MjpW0zN2f737+bkmfSrlGILPVMWGMKorT1niDpG+YWe/4f3H3uzOtCo2RRe+YMEYdRIazu/9M0ttyqAUNERTIw6yOe+eZIIxRE4zSIRdpBzKrY9Qd4YzMpB3IrI7RJOxKh1SlGcisjlFX7EqHXKQ58sbqGE3CrnRIXZorZAIZWIpwRmLTs21tvn3X/GOZCGQgfYQzYlu4Wh4EgQzERzgj1LD9ZAIZGAzhjL6mZ9u65o7dR9ypl/ShpQQyMDhG6TBvmFUygQzExygdYum3Sk6CQAYGwygdlkhjNnlsdETXXXwGoQxkgHBumGF6yRLtCyAvhHMDpHUH3+uPGdXVG04jkIEcEM41N8wNI6ySgeIwrVFj07NtffTrP9LhAS76skoGssO0RkMNMn3BKhnIH9MaDTHoSByrZKB8COeaWNxbDsMqGSg/wrkGkvSWR8z093/2NgIZKDnCucKStjG4aQSoDsK5opK0MST6ykDVMEpXQUnaGIQyUD6M0tVQ3BUzvWWg/Bilq4m4K2Z6y0D1xQ5nMxuR9KCktrtfmF1JWCzJhT/aGEA9JFk5XyFpj6TjMqoFfdDGAJppWZyDzOxESRdIujnbcrBQr40RFcxjoyMEM1AzscJZ0o2SPi7plexKwUK9FXNUf3nEjP4yUEOR4WxmF0p6xt0fCjqm0+locnJy/qPVaqVaZNOwYgbqq9VqzWelpJVBx0WO0pnZdZIuk3RI0tGa6znf7u6X9o5hlC49cXvMXPgDqm+oUTp33yxpc/dEfyDpYwuDGenatmNvaDBz4Q9ohrg9Z+Rgerat9r4Dga/TxgCaI9FNKO7+XUnfzaSShuu1M4Jw4Q9oFlbOJXHtzO7AdgYrZqB5Ugnn3sZH3Y08kND0bFu/ejH47j9WzEC9zMzMaGpqSmLjo/KK2i9jYnxMP9h0Ts5VAchD2LQGbY0CxbnR5Krz1uRYEYCyIJwLFDU2Nz42SjsDaCjCuSBxxuauuei0HCsCUCaEcwEYmwMQhXAuAGNzAKIwSpczxuYAMEpXQuu33hfYa2ZsDmgWRulKIuoiIGNzAHoI55xEXQRkbA7AQoRzTsJmmhmbA7AY4ZyTsHYGFwEBLEY452B6ti0LeG1ifIxgBrAEo3Q52LZjr/rNxJi4CAg0EaN0JTA929aVX9sZ+PrjWy/IrxgApcIoXUGiJjQmxsdyrAZAlRDOGYq6TZuWBoAghHNGuE0bwDAI54xs27E38DUmNABEYVojA9ymDSAM0xoF6F0EDOo1j4+NaufV7865KgBlxLRGjrhNG0AaIsPZzI42s/8wsx+Z2W4zuzaPwqqK27QBpGF5jGNeknSOu//azEYlfd/M7nL3+zOurXJ6t2n3axRxERBAEpHh7HNN6V93vxztfgzfqK6ha2d2c5s2gFTE6jmb2YiZ7ZT0jKR73f2BTKuqoLC5ZpdYNQNIJFY4u/thdz9T0omS3mFmpy98vdPpaHJycv6j1WplUGq5Rc01A4AktVqt+ayUtDLouMSjdGb2SUkvuvv1ve81fZQuanOjGy85k5UzgCWGGqUzs1VmNt79fEzSuyQ9lmqFFcbjpwBkIc60xhslfdnMRjQX5l939zuzLas6ojY3Yq4ZwCDiTGs8ImltDrVUDpsbAcgKdwgOgc2NAGSFcB4CmxsByAq70g0o7KGtXAQEEIZd6TK09lP39O03m6R/YHQOQAzsSpcy7gYEkDXCeQDXzuwOfI27AQGkgXBOKGp8jguBANJAOCcUNj7HhUAAaWFaI4GoZwNyNyCAOJjWSBHPBgSQNqY1UsAeGgDyRDjHwB4aAPJGOMcQNTpHMANIG+EcYcv0LkbnAOSOcA4xPdvW9vufCHyd0TkAWWGULkTQ07R7uAgIYBCM0g0h6rmAjM4BGBajdAMIuwhoYtUMIFuEcx9Ro3MfOOtN9JoBZIpw7iNs1Tw+NqpPbzwjx2oANBHhvEjUqpl2BoA8EM6LRK2aaWcAyAOjdAtE3XDCqhlAGhilS2B6tq2PfG1n4Fwzo3MA0sYoXQzccAKgTCLD2cxOMrPvmNmjZrbbzK7Io7A8RbUz6DUDyNvyGMcckvRRd3/YzF4n6SEzu9fdH824tlxE7Z/BDScAihC5cnb3p9394e7nz0vaI6k2y8iodgY3nAAoQqKes5mtlrRW0gOZVJOzqJlmbjgBUJQ4bQ1Jkpm9VtJtkq509+cWvtbpdDQ5+eoFx6mpqd6YSKmxfwaAvLVaLbVard6XK4OOizVKZ2ajku6UtMPdb1j8elVH6VZv+mbga5ee9SZWzQAyNdQonZmZpC9I2tMvmKtqy/Su0NcJZgBFitNzXi/pMknnmNnO7sd7Mq4rU1umd+krEU84AYAiRfac3f37mmvB1kLU6JxErxlA8Rp3h2DU6Bw3nAAog0ZtfBQ1OseEBoA8sPHRIqd98m698PLhwNeZ0ACQJzY+0txFQIIZQFU0IpynZ9uh0xkSo3MAyqUR4fyJb4TPNDM6B6Bsah/O07Pt0HaGxEVAAOVT+3AO2z9Dmus1MzoHoGxqPUoXNTo3NrqMXjOA3DV+lC5qdO7GS85k1QygMI0cpYszOkcwAyirWoYzo3MAqq6W4czoHICqq104MzoHoA5qF85Rq2Z6zQCqoFajdFEXARmdA1AGjRqli3q6icToHIByqf0oXZzpjLHRZQQzgMqoRThH9Zkl6bqL35pDJQCQjsqHc5zpDC4CAqiayodz1KqZi4AAqqjS0xpxVs20MwCUTe2nNdZsuUsvHXol8HUePQWgzGo5rTE92w4NZtoZAKosMpzN7BYze8bMfpxHQXH97W2PhL5OOwNAlcVZOX9J0vkZ15HIluldoatmSUxnAKi0yHB29+9J+mUOtcS2PeKGk0vPelNOlQBANirXc94yvUthlzBHl7FXM4DqW57GSTqdjiYnX73gODU11RsTSVWc27S3/emZqf9cAEhLq9VSq9Xqfbky6LhYo3RmtlrSne5+er/X8xqlixqdG10m/eQzF2ReBwCkoRajdFGjcxKrZgD1EWeU7quSfihpjZk9aWYfyr6spaJG59h1DkCdRPac3f39eRQSJs6qmblmAHVSibZG1Kp5/ZuPZ9UMoFZKH85xVs3bL39nTtUAQD5Kvyvdx/7tR6Gvc8MJgKqp/K50cZ4L+PhWRucAVFNlR+niPBcQAOqotOm2ZZrnAgJortKGc9SqmQkNAHVWynCenm1HHsOEBoA6K+W0BhMaAOqsktMa07NtXfm1naHHMKEBoA4qNa0RtWpmQgNAE5Qq6aZn2zr0SvhKngkNAE1QqnCOWjUvE88GBNAMpQnnOKvmGy45M59iAKBgpQnnqJ3nJFbNAJqjNKN0UTvPMT4HoC4qM0r3gZt+qB/89y9Dj2F8DkDdlH6ULiqYWTUDaJrCwznOBkef3nhGDpUAQHkUHs5RGxwVXiAAFKD02cf4HIAmKjSc33r13ZHHMD4HoIkKHaV77qXDoa+vf/Pxw5QFAKVU6lE6xucANF0pR+mighkAmixWOJvZ+Wa218x+amabsi5Kkm7kQiCABosMZzMbkfRPkv5I0qmS3m9mpw7zQ1dv+mbkMVwIBNBkcVbO75D0U3f/mbu/LOlfJb03y6KOHrEsTw8ApRcnnCck/XzB1092vzev0+locnJy/qPVag1V1GN/956h3g8AZdVqteazUtLKoOOWp/HDVq1apbSeIQgAdTY1NdUbo5OZPRt0XJyVc1vSSQu+PrH7PQBARuKE839KOsXMTjaz10h6n6Q7hvmhYfPLzDYDQIy2hrsfMrO/lrRD0oikW9x997A/mBAGgGCxes7u/i1J38q4FgBAV+l3pQOAJir8GYLDjt0VjfqLV/XfgfqLVUT9cTY+krsP/bFu3TrvueOOOzyJhe+NI+n5sz6e+tM9fpD3lO13oP50z1/n+iU96AG5mnpbY5gncGdx/qyPT4r6s3lPludv2j8D6k/3/IPWk8qWoWbWkfS/3S9XSNqf4O0rJQUOYveR9PxZH0/96R4/yHvK9jtQf7H1VKn+33L3Vf1eSCWcAQDpYloDAEqIcAaAEio0nIvYxD8tZnaSmX3HzB41s91mdkXRNQ3CzEbMbNbM7iy6lqTMbNzMbjWzx8xsj5m9s+iakjCzj3T/3fmxmX3VzI4uuqYoZnaLmT1jZj9e8L3jzexeM/tJ96+vL7LGMAH1b+v+O/SImX3DzMYLLHFeYeGcxSb+OTsk6aPufqqksyT9VcXq77lC0p6iixjQZyXd7e5vkfQ2Vej3MLMJSX8jadLdT9fc1gjvK7aqWL4k6fxF39sk6dvufoqkb3e/LqsvaWn990o63d3fKum/JG3Ou6h+ilw5576Jf5rc/Wl3f7j7+fOaC4ZKPb7FzE6UdIGkm4uuJSkzWyHp9yV9QZLc/WV331doUcktlzRmZsslHSPpqYLrieTu35O0+AGg75X05e7nX5a0Mc+akuhXv7vf4+6Hul/er7mdNwtXZDhHbuJfFWa2WtJaSQ8UXEpSN0r6uKRXCq5jECdL6kj6Yrctc7OZHVt0UXG5e1vS9ZKekPS0pP3ufk+xVQ3sDe7+dPfzX0h6Q5HFDOkvJd1VdBESFwSHZmavlXSbpCvd/bmi64nLzC6U9Iy7P1R0LQNaLuntkj7n7mslvaBy/3H6CN2+7Hs19z+ZEyQda2aXFlvV8Lp3vVVyPtfMPqG5duX2omuRig3nym/ib2ajmgvm7e5+e9H1JLRe0kVm9rjmWkrnmNlXii0pkSclPenuvT+t3Kq5sK6KP5T0P+7ecfeDkm6X9DsF1zSo/zOzN0pS96/PFFxPYmb255IulPQBL8nNH0WGc+qb+OfJzExz/c497n5D0fUk5e6b3f1Ed1+tub/397l7ZVZu7v4LST83szXdb50r6dECS0rqCUlnmdkx3X+XzlWFLmgucoekD3Y//6Ckfy+wlsTM7HzNtfcucvcXi66np7Bw7jbge5v475H0dU9hE/8crZd0meZWnDu7HzyZNl8flrTdzB6RdKakzxRbTnzdFf+tkh6WtEtz/y2Wfns3M/uqpB9KWmNmT5rZhyRtlfQuM/uJ5v5EsLXIGsME1P+Pkl4n6d7uf8efL7TILm7fBoAS4oIgAJQQ4QwAJUQ4A0AJEc4AUEKEMwCUEOEMACVEOANACRHOAFBC/w/qmIYBli4hLQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(Abar[:n-1], ms_std.xi_hm[:])\n",
    "#plt.xlim(0,30)\n",
    "#plt.ylim(0,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b475e83a-49cd-4de1-82a3-d0119cf6cebb",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}