DAS_jeffrey_lyons.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dimension adaptive quadrature algorithm - latest version"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preamble"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Settings etc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import chaospy as ch\n",
    "from scipy import integrate\n",
    "import pandas as pd\n",
    "from mpl_toolkits import mplot3d\n",
    "import time\n",
    "import json\n",
    "import pickle\n",
    "from IPython.display import Image\n",
    "import pandas as pd\n",
    "import datetime\n",
    "import numpoly\n",
    "from itertools import product\n",
    "from collections import OrderedDict\n",
    "from os import PathLike\n",
    "import re\n",
    "import os\n",
    "\n",
    "##SALib\n",
    "from SALib.sample import saltelli\n",
    "from SALib.analyze import sobol\n",
    "from SALib.test_functions import Ishigami\n",
    "\n",
    "#Chaospy\n",
    "import chaospy as ch\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def c(s):\n",
    "    os.chdir(s)\n",
    "    \n",
    "def get():\n",
    "    return os.getcwd()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'C:\\\\Users\\\\jeffr\\\\OneDrive\\\\Documents\\\\Education\\\\Thesis\\\\Scripts\\\\Experiment 1 - LVM\\\\data\\\\new\\\\gt\\\\progression'"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c('progression')\n",
    "get()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "OneDrive/Documents/Education/Thesis/Scripts/Experiment 1 - LVM/data/new/gt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "gt_prey = pd.read_csv('pop_910_32800_2022-03-25.csv',index_col=['type','params']).loc['prey','ST']\n",
    "gt_norm = np.linalg.norm(gt_prey)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Settings etc\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "polynomial([1.0, q3-0.028999999999999998, q2-0.9299999999999999, q1-0.032,\n",
       "            q0-0.56, q3**2-0.057999999999999996*q3+0.0008273466666666665,\n",
       "            q2*q3-0.9299999999999999*q3-0.028999999999999998*q2+0.026969999999999997,\n",
       "            q2**2-1.8599999999999999*q2+0.8487666666666666,\n",
       "            q1*q3-0.032*q3-0.028999999999999998*q1+0.000928,\n",
       "            q1*q2-0.032*q2-0.9299999999999999*q1+0.029759999999999998,\n",
       "            q1**2-0.064*q1+0.000976,\n",
       "            q0*q3-0.56*q3-0.028999999999999998*q0+0.01624,\n",
       "            q0*q2-0.56*q2-0.9299999999999999*q0+0.5208,\n",
       "            q0*q1-0.56*q1-0.032*q0+0.017920000000000002,\n",
       "            q0**2-1.12*q0+0.3088])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "#Parameters & initial_conditions\n",
    "\n",
    "\n",
    "t = np.linspace(0., 30, 1000)\n",
    "\n",
    "#Model\n",
    "\n",
    "def lotka(X, t, alpha, beta, delta, gamma):\n",
    "    x, y = X\n",
    "    dotx = x * (alpha - beta * y)\n",
    "    doty = y * (-delta + gamma * x)\n",
    "    return np.array([dotx, doty])\n",
    "\n",
    "#Parameter space\n",
    "\n",
    "problem = {\n",
    "    'num_vars': 4,\n",
    "    'names': ['alpha','beta','delta','gamma'],\n",
    "    'bounds': [[0.44,0.68],\n",
    "               [0.02,0.044],\n",
    "               [0.71,1.15],\n",
    "               [0.0226,0.0354]]\n",
    "}\n",
    "\n",
    "##Parameters\n",
    "alpha = ch.Uniform(0.44, 0.68) #We choose uniform distributions to reflect our lack of knowledge about the relative likelihood functions\n",
    "beta = ch.Uniform(0.02, 0.044) #We take the same bounds as for the Sobol-Saltelli analysis\n",
    "delta = ch.Uniform(0.71, 1.15)\n",
    "gamma = ch.Uniform(0.0226, 0.0354)\n",
    "\n",
    "joint = ch.J(alpha,beta,delta,gamma) #The input paramter distributions are assumed to be independent so we may easily construct the joint input probability distribution.\n",
    "\n",
    "##Expansion\n",
    "expansion = ch.generate_expansion(2, joint) #Here we generate the polynomial expansion which is truncated a maximum mixed order of 2.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Grid and weight look-up table constructor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Uniform(lower=0.44, upper=0.68)\n",
      "Uniform(lower=0.02, upper=0.044)\n",
      "Uniform(lower=0.71, upper=1.15)\n",
      "Uniform(lower=0.0226, upper=0.0354)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
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       "   array([0.49071797, 0.62928203]),\n",
       "   array([0.4670484, 0.56     , 0.6529516]),\n",
       "   array([0.45666364, 0.51920227, 0.60079773, 0.66333636]),\n",
       "   array([0.45125842, 0.49538368, 0.56      , 0.62461632, 0.66874158]),\n",
       "   array([0.44810366, 0.48065487, 0.5313657 , 0.5886343 , 0.63934513,\n",
       "          0.67189634]),\n",
       "   array([0.44610705, 0.47101626, 0.51129858, 0.56      , 0.60870142,\n",
       "          0.64898374, 0.67389295]),\n",
       "   array([0.44476522, 0.46440002, 0.49693611, 0.53798784, 0.58201216,\n",
       "          0.62306389, 0.65559998, 0.67523478]),\n",
       "   array([0.44382077, 0.45967627, 0.48639543, 0.52108959, 0.56      ,\n",
       "          0.59891041, 0.63360457, 0.66032373, 0.67617923]),\n",
       "   array([0.44313122, 0.4561924 , 0.47847085, 0.50799255, 0.54213508,\n",
       "          0.57786492, 0.61200745, 0.64152915, 0.6638076 , 0.67686878]),\n",
       "   array([0.44261256, 0.45355249, 0.47238176, 0.49770846, 0.52765482,\n",
       "          0.56      , 0.59234518, 0.62229154, 0.64761824, 0.66644751,\n",
       "          0.67738744]),\n",
       "   array([0.44221272, 0.45150593, 0.46761168, 0.48952185, 0.51586022,\n",
       "          0.54497199, 0.57502801, 0.60413978, 0.63047815, 0.65238832,\n",
       "          0.66849407, 0.67778728]),\n",
       "   array([0.44189803, 0.44988819, 0.46381063, 0.48291808, 0.50618087,\n",
       "          0.532345  , 0.56      , 0.587655  , 0.61381913, 0.63708192,\n",
       "          0.65618937, 0.67011181, 0.67810197]),\n",
       "   array([0.44164594, 0.44858781, 0.46073584, 0.47752485, 0.49817016,\n",
       "          0.52170652, 0.54703341, 0.57296659, 0.59829348, 0.62182984,\n",
       "          0.64247515, 0.65926416, 0.67141219, 0.67835406]),\n",
       "   array([0.4414409 , 0.44752719, 0.45821521, 0.47306987, 0.49148334,\n",
       "          0.51270184, 0.53585671, 0.56      , 0.58414329, 0.60729816,\n",
       "          0.62851666, 0.64693013, 0.66178479, 0.67247281, 0.6785591 ]),\n",
       "   array([0.44127189, 0.446651  , 0.45612426, 0.46935147, 0.48585485,\n",
       "          0.50503799, 0.52620757, 0.5485985 , 0.5714015 , 0.59379243,\n",
       "          0.61496201, 0.63414515, 0.65064853, 0.66387574, 0.673349  ,\n",
       "          0.67872811]),\n",
       "   array([0.44113094, 0.44591894, 0.4543713 , 0.46621832, 0.48107946,\n",
       "          0.49847714, 0.51785219, 0.5385819 , 0.56      , 0.5814181 ,\n",
       "          0.60214781, 0.62152286, 0.63892054, 0.65378168, 0.6656287 ,\n",
       "          0.67408106, 0.67886906]),\n",
       "   array([0.44101218, 0.44530113, 0.4528877 , 0.4635554 , 0.47699755,\n",
       "          0.4928275 , 0.51058986, 0.52977365, 0.549827  , 0.570173  ,\n",
       "          0.59022635, 0.60941014, 0.6271725 , 0.64300245, 0.6564446 ,\n",
       "          0.6671123 , 0.67469887, 0.67898782]),\n",
       "   array([0.44091118, 0.44477502, 0.45162129, 0.46127424, 0.47348406,\n",
       "          0.48793456, 0.50425151, 0.52201231, 0.54075696, 0.56      ,\n",
       "          0.57924304, 0.59798769, 0.61574849, 0.63206544, 0.64651594,\n",
       "          0.65872576, 0.66837871, 0.67522498, 0.67908882]),\n",
       "   array([0.44082457, 0.44432337, 0.45053187, 0.45930596, 0.47044017,\n",
       "          0.48367356, 0.49869596, 0.51515527, 0.5326657 , 0.55081682,\n",
       "          0.56918318, 0.5873343 , 0.60484473, 0.62130404, 0.63632644,\n",
       "          0.64955983, 0.66069404, 0.66946813, 0.67567663, 0.67917543]),\n",
       "   array([0.44074974, 0.44393278, 0.44958808, 0.4575964 , 0.4677872 ,\n",
       "          0.47994334, 0.49380574, 0.50907895, 0.52543744, 0.54253258,\n",
       "          0.56      , 0.57746742, 0.59456256, 0.61092105, 0.62619426,\n",
       "          0.64005666, 0.6522128 , 0.6624036 , 0.67041192, 0.67606722,\n",
       "          0.67925026])],\n",
       "  [array([0.032]),\n",
       "   array([0.0250718, 0.0389282]),\n",
       "   array([0.02270484, 0.032     , 0.04129516]),\n",
       "   array([0.02166636, 0.02792023, 0.03607977, 0.04233364]),\n",
       "   array([0.02112584, 0.02553837, 0.032     , 0.03846163, 0.04287416]),\n",
       "   array([0.02081037, 0.02406549, 0.02913657, 0.03486343, 0.03993451,\n",
       "          0.04318963]),\n",
       "   array([0.02061071, 0.02310163, 0.02712986, 0.032     , 0.03687014,\n",
       "          0.04089837, 0.04338929]),\n",
       "   array([0.02047652, 0.02244   , 0.02569361, 0.02979878, 0.03420122,\n",
       "          0.03830639, 0.04156   , 0.04352348]),\n",
       "   array([0.02038208, 0.02196763, 0.02463954, 0.02810896, 0.032     ,\n",
       "          0.03589104, 0.03936046, 0.04203237, 0.04361792]),\n",
       "   array([0.02031312, 0.02161924, 0.02384709, 0.02679926, 0.03021351,\n",
       "          0.03378649, 0.03720074, 0.04015291, 0.04238076, 0.04368688]),\n",
       "   array([0.02026126, 0.02135525, 0.02323818, 0.02577085, 0.02876548,\n",
       "          0.032     , 0.03523452, 0.03822915, 0.04076182, 0.04264475,\n",
       "          0.04373874]),\n",
       "   array([0.02022127, 0.02115059, 0.02276117, 0.02495218, 0.02758602,\n",
       "          0.0304972 , 0.0335028 , 0.03641398, 0.03904782, 0.04123883,\n",
       "          0.04284941, 0.04377873]),\n",
       "   array([0.0201898 , 0.02098882, 0.02238106, 0.02429181, 0.02661809,\n",
       "          0.0292345 , 0.032     , 0.0347655 , 0.03738191, 0.03970819,\n",
       "          0.04161894, 0.04301118, 0.0438102 ]),\n",
       "   array([0.02016459, 0.02085878, 0.02207358, 0.02375249, 0.02581702,\n",
       "          0.02817065, 0.03070334, 0.03329666, 0.03582935, 0.03818298,\n",
       "          0.04024751, 0.04192642, 0.04314122, 0.04383541]),\n",
       "   array([0.02014409, 0.02075272, 0.02182152, 0.02330699, 0.02514833,\n",
       "          0.02727018, 0.02958567, 0.032     , 0.03441433, 0.03672982,\n",
       "          0.03885167, 0.04069301, 0.04217848, 0.04324728, 0.04385591]),\n",
       "   array([0.02012719, 0.0206651 , 0.02161243, 0.02293515, 0.02458549,\n",
       "          0.0265038 , 0.02862076, 0.03085985, 0.03314015, 0.03537924,\n",
       "          0.0374962 , 0.03941451, 0.04106485, 0.04238757, 0.0433349 ,\n",
       "          0.04387281]),\n",
       "   array([0.02011309, 0.02059189, 0.02143713, 0.02262183, 0.02410795,\n",
       "          0.02584771, 0.02778522, 0.02985819, 0.032     , 0.03414181,\n",
       "          0.03621478, 0.03815229, 0.03989205, 0.04137817, 0.04256287,\n",
       "          0.04340811, 0.04388691]),\n",
       "   array([0.02010122, 0.02053011, 0.02128877, 0.02235554, 0.02369976,\n",
       "          0.02528275, 0.02705899, 0.02897737, 0.0309827 , 0.0330173 ,\n",
       "          0.03502263, 0.03694101, 0.03871725, 0.04030024, 0.04164446,\n",
       "          0.04271123, 0.04346989, 0.04389878]),\n",
       "   array([0.02009112, 0.0204775 , 0.02116213, 0.02212742, 0.02334841,\n",
       "          0.02479346, 0.02642515, 0.02820123, 0.0300757 , 0.032     ,\n",
       "          0.0339243 , 0.03579877, 0.03757485, 0.03920654, 0.04065159,\n",
       "          0.04187258, 0.04283787, 0.0435225 , 0.04390888]),\n",
       "   array([0.02008246, 0.02043234, 0.02105319, 0.0219306 , 0.02304402,\n",
       "          0.02436736, 0.0258696 , 0.02751553, 0.02926657, 0.03108168,\n",
       "          0.03291832, 0.03473343, 0.03648447, 0.0381304 , 0.03963264,\n",
       "          0.04095598, 0.0420694 , 0.04294681, 0.04356766, 0.04391754]),\n",
       "   array([0.02007497, 0.02039328, 0.02095881, 0.02175964, 0.02277872,\n",
       "          0.02399433, 0.02538057, 0.02690789, 0.02854374, 0.03025326,\n",
       "          0.032     , 0.03374674, 0.03545626, 0.03709211, 0.03861943,\n",
       "          0.04000567, 0.04122128, 0.04224036, 0.04304119, 0.04360672,\n",
       "          0.04392503])],\n",
       "  [array([0.93]),\n",
       "   array([0.80298294, 1.05701706]),\n",
       "   array([0.75958873, 0.93      , 1.10041127]),\n",
       "   array([0.74055001, 0.85520417, 1.00479583, 1.11944999]),\n",
       "   array([0.73064043, 0.81153675, 0.93      , 1.04846325, 1.12935957]),\n",
       "   array([0.72485671, 0.78453393, 0.87750378, 0.98249622, 1.07546607,\n",
       "          1.13514329]),\n",
       "   array([0.72119626, 0.76686314, 0.84071407, 0.93      , 1.01928593,\n",
       "          1.09313686, 1.13880374]),\n",
       "   array([0.71873623, 0.75473337, 0.81438287, 0.88964438, 0.97035562,\n",
       "          1.04561713, 1.10526663, 1.14126377]),\n",
       "   array([0.71700475, 0.74607316, 0.79505828, 0.85866425, 0.93      ,\n",
       "          1.00133575, 1.06494172, 1.11392684, 1.14299525]),\n",
       "   array([0.71574056, 0.73968606, 0.78052989, 0.83465301, 0.89724765,\n",
       "          0.96275235, 1.02534699, 1.07947011, 1.12031394, 1.14425944]),\n",
       "   array([0.7147897 , 0.73484623, 0.76936656, 0.81579885, 0.87070051,\n",
       "          0.93      , 0.98929949, 1.04420115, 1.09063344, 1.12515377,\n",
       "          1.1452103 ]),\n",
       "   array([0.71405666, 0.7310942 , 0.76062141, 0.80079005, 0.84907707,\n",
       "          0.90244865, 0.95755135, 1.01092293, 1.05920995, 1.09937859,\n",
       "          1.1289058 , 1.14594334]),\n",
       "   array([0.71347973, 0.72812835, 0.75365282, 0.78868315, 0.83133159,\n",
       "          0.87929917, 0.93      , 0.98070083, 1.02866841, 1.07131685,\n",
       "          1.10634718, 1.13187165, 1.14652027]),\n",
       "   array([0.71301756, 0.72574433, 0.74801571, 0.77879556, 0.8166453 ,\n",
       "          0.85979528, 0.90622791, 0.95377209, 1.00020472, 1.0433547 ,\n",
       "          1.08120444, 1.11198429, 1.13425567, 1.14698244]),\n",
       "   array([0.71264165, 0.72379985, 0.74339455, 0.7706281 , 0.80438612,\n",
       "          0.8432867 , 0.8857373 , 0.93      , 0.9742627 , 1.0167133 ,\n",
       "          1.05561388, 1.0893719 , 1.11660545, 1.13620015, 1.14735835]),\n",
       "   array([0.71233179, 0.72219349, 0.73956114, 0.76381103, 0.79406723,\n",
       "          0.82923631, 0.86804722, 0.90909725, 0.95090275, 0.99195278,\n",
       "          1.03076369, 1.06593277, 1.09618897, 1.12043886, 1.13780651,\n",
       "          1.14766821]),\n",
       "   array([0.7120734 , 0.72085139, 0.73634739, 0.75806692, 0.78531234,\n",
       "          0.81720808, 0.85272901, 0.89073348, 0.93      , 0.96926652,\n",
       "          1.00727099, 1.04279192, 1.07468766, 1.10193308, 1.12365261,\n",
       "          1.13914861, 1.1479266 ]),\n",
       "   array([0.71185566, 0.71971873, 0.73362746, 0.75318491, 0.77782885,\n",
       "          0.80685042, 0.83941474, 0.87458503, 0.9113495 , 0.9486505 ,\n",
       "          0.98541497, 1.02058526, 1.05314958, 1.08217115, 1.10681509,\n",
       "          1.12637254, 1.14028127, 1.14814434]),\n",
       "   array([0.71167049, 0.71875421, 0.7313057 , 0.74900278, 0.77138744,\n",
       "          0.79788003, 0.82779444, 0.8603559 , 0.8947211 , 0.93      ,\n",
       "          0.9652789 , 0.9996441 , 1.03220556, 1.06211997, 1.08861256,\n",
       "          1.11099722, 1.1286943 , 1.14124579, 1.14832951]),\n",
       "   array([0.71151171, 0.71792618, 0.72930843, 0.74539427, 0.76580698,\n",
       "          0.79006819, 0.81760926, 0.84778466, 0.87988711, 0.91316417,\n",
       "          0.94683583, 0.98011289, 1.01221534, 1.04239074, 1.06993181,\n",
       "          1.09419302, 1.11460573, 1.13069157, 1.14207382, 1.14848829]),\n",
       "   array([0.71137452, 0.7172101 , 0.72757815, 0.74226006, 0.76094321,\n",
       "          0.78322946, 0.80864386, 0.83664473, 0.86663531, 0.89797639,\n",
       "          0.93      , 0.96202361, 0.99336469, 1.02335527, 1.05135614,\n",
       "          1.07677054, 1.09905679, 1.11773994, 1.13242185, 1.1427899 ,\n",
       "          1.14862548])],\n",
       "  [array([0.029]),\n",
       "   array([0.02530496, 0.03269504]),\n",
       "   array([0.02404258, 0.029     , 0.03395742]),\n",
       "   array([0.02348873, 0.02682412, 0.03117588, 0.03451127]),\n",
       "   array([0.02320045, 0.0255538 , 0.029     , 0.0324462 , 0.03479955]),\n",
       "   array([0.0230322 , 0.02476826, 0.02747284, 0.03052716, 0.03323174,\n",
       "          0.0349678 ]),\n",
       "   array([0.02292571, 0.0242542 , 0.02640259, 0.029     , 0.03159741,\n",
       "          0.0337458 , 0.03507429]),\n",
       "   array([0.02285414, 0.02390133, 0.02563659, 0.02782602, 0.03017398,\n",
       "          0.03236341, 0.03409867, 0.03514586]),\n",
       "   array([0.02280377, 0.0236494 , 0.02507442, 0.02692478, 0.029     ,\n",
       "          0.03107522, 0.03292558, 0.0343506 , 0.03519623]),\n",
       "   array([0.022767  , 0.02346359, 0.02465178, 0.02622627, 0.0280472 ,\n",
       "          0.0299528 , 0.03177373, 0.03334822, 0.03453641, 0.035233  ]),\n",
       "   array([0.02273934, 0.0233228 , 0.02432703, 0.02567778, 0.02727492,\n",
       "          0.029     , 0.03072508, 0.03232222, 0.03367297, 0.0346772 ,\n",
       "          0.03526066]),\n",
       "   array([0.02271801, 0.02321365, 0.02407262, 0.02524117, 0.02664588,\n",
       "          0.02819851, 0.02980149, 0.03135412, 0.03275883, 0.03392738,\n",
       "          0.03478635, 0.03528199]),\n",
       "   array([0.02270123, 0.02312737, 0.0238699 , 0.02488896, 0.02612965,\n",
       "          0.02752507, 0.029     , 0.03047493, 0.03187035, 0.03311104,\n",
       "          0.0341301 , 0.03487263, 0.03529877]),\n",
       "   array([0.02268778, 0.02305802, 0.02370591, 0.02460133, 0.02570241,\n",
       "          0.02695768, 0.02830845, 0.02969155, 0.03104232, 0.03229759,\n",
       "          0.03339867, 0.03429409, 0.03494198, 0.03531222]),\n",
       "   array([0.02267685, 0.02300145, 0.02357148, 0.02436373, 0.02534578,\n",
       "          0.02647743, 0.02771236, 0.029     , 0.03028764, 0.03152257,\n",
       "          0.03265422, 0.03363627, 0.03442852, 0.03499855, 0.03532315]),\n",
       "   array([0.02266783, 0.02295472, 0.02345996, 0.02416541, 0.02504559,\n",
       "          0.02606869, 0.02719774, 0.02839192, 0.02960808, 0.03080226,\n",
       "          0.03193131, 0.03295441, 0.03383459, 0.03454004, 0.03504528,\n",
       "          0.03533217]),\n",
       "   array([0.02266032, 0.02291568, 0.02336647, 0.02399831, 0.0247909 ,\n",
       "          0.02571878, 0.02675212, 0.0278577 , 0.029     , 0.0301423 ,\n",
       "          0.03124788, 0.03228122, 0.0332091 , 0.03400169, 0.03463353,\n",
       "          0.03508432, 0.03533968]),\n",
       "   array([0.02265398, 0.02288273, 0.02328734, 0.02385629, 0.0245732 ,\n",
       "          0.02541747, 0.02636479, 0.02738793, 0.02845744, 0.02954256,\n",
       "          0.03061207, 0.03163521, 0.03258253, 0.0334268 , 0.03414371,\n",
       "          0.03471266, 0.03511727, 0.03534602]),\n",
       "   array([0.0226486 , 0.02285467, 0.0232198 , 0.02373463, 0.02438582,\n",
       "          0.02515651, 0.02602675, 0.02697399, 0.0279737 , 0.029     ,\n",
       "          0.0300263 , 0.03102601, 0.03197325, 0.03284349, 0.03361418,\n",
       "          0.03426537, 0.0347802 , 0.03514533, 0.0353514 ]),\n",
       "   array([0.02264398, 0.02283058, 0.0231617 , 0.02362965, 0.02422348,\n",
       "          0.02492926, 0.02573045, 0.02660828, 0.02754217, 0.02851023,\n",
       "          0.02948977, 0.03045783, 0.03139172, 0.03226955, 0.03307074,\n",
       "          0.03377652, 0.03437035, 0.0348383 , 0.03516942, 0.03535602]),\n",
       "   array([0.02263999, 0.02280975, 0.02311136, 0.02353847, 0.02408198,\n",
       "          0.02473031, 0.02546964, 0.02628421, 0.02715666, 0.0280684 ,\n",
       "          0.029     , 0.0299316 , 0.03084334, 0.03171579, 0.03253036,\n",
       "          0.03326969, 0.03391802, 0.03446153, 0.03488864, 0.03519025,\n",
       "          0.03536001])]],\n",
       " [[array([1.]),\n",
       "   array([0.5, 0.5]),\n",
       "   array([0.27777778, 0.44444444, 0.27777778]),\n",
       "   array([0.17392742, 0.32607258, 0.32607258, 0.17392742]),\n",
       "   array([0.11846344, 0.23931434, 0.28444444, 0.23931434, 0.11846344]),\n",
       "   array([0.08566225, 0.18038079, 0.23395697, 0.23395697, 0.18038079,\n",
       "          0.08566225]),\n",
       "   array([0.06474248, 0.1398527 , 0.19091503, 0.20897959, 0.19091503,\n",
       "          0.1398527 , 0.06474248]),\n",
       "   array([0.05061427, 0.11119052, 0.15685332, 0.18134189, 0.18134189,\n",
       "          0.15685332, 0.11119052, 0.05061427]),\n",
       "   array([0.04063719, 0.09032408, 0.13030535, 0.15617354, 0.16511968,\n",
       "          0.15617354, 0.13030535, 0.09032408, 0.04063719]),\n",
       "   array([0.03333567, 0.07472567, 0.10954318, 0.13463336, 0.14776211,\n",
       "          0.14776211, 0.13463336, 0.10954318, 0.07472567, 0.03333567]),\n",
       "   array([0.02783428, 0.06279018, 0.09314511, 0.11659688, 0.13140227,\n",
       "          0.13646254, 0.13140227, 0.11659688, 0.09314511, 0.06279018,\n",
       "          0.02783428]),\n",
       "   array([0.02358767, 0.05346966, 0.08003916, 0.10158371, 0.11674627,\n",
       "          0.12457352, 0.12457352, 0.11674627, 0.10158371, 0.08003916,\n",
       "          0.05346966, 0.02358767]),\n",
       "   array([0.020242  , 0.04606075, 0.06943676, 0.08907299, 0.10390802,\n",
       "          0.11314159, 0.11627578, 0.11314159, 0.10390802, 0.08907299,\n",
       "          0.06943676, 0.04606075, 0.020242  ]),\n",
       "   array([0.01755973, 0.04007904, 0.06075929, 0.07860158, 0.0927692 ,\n",
       "          0.10259923, 0.10763193, 0.10763193, 0.10259923, 0.0927692 ,\n",
       "          0.07860158, 0.06075929, 0.04007904, 0.01755973]),\n",
       "   array([0.01537662, 0.03518302, 0.05357961, 0.06978534, 0.0831346 ,\n",
       "          0.0930805 , 0.09921574, 0.10128912, 0.09921574, 0.0930805 ,\n",
       "          0.0831346 , 0.06978534, 0.05357961, 0.03518302, 0.01537662]),\n",
       "   array([0.01357623, 0.03112676, 0.04757926, 0.06231449, 0.07479799,\n",
       "          0.08457826, 0.09130171, 0.09472531, 0.09472531, 0.09130171,\n",
       "          0.08457826, 0.07479799, 0.06231449, 0.04757926, 0.03112676,\n",
       "          0.01357623]),\n",
       "   array([0.01207415, 0.02772976, 0.04251807, 0.05594192, 0.06756818,\n",
       "          0.07702288, 0.08400205, 0.08828135, 0.08972324, 0.08828135,\n",
       "          0.08400205, 0.07702288, 0.06756818, 0.05594192, 0.04251807,\n",
       "          0.02772976, 0.01207415]),\n",
       "   array([0.01080801, 0.02485727, 0.03821287, 0.05047102, 0.0612776 ,\n",
       "          0.07032146, 0.07734234, 0.08213824, 0.08457119, 0.08457119,\n",
       "          0.08213824, 0.07734234, 0.07032146, 0.0612776 , 0.05047102,\n",
       "          0.03821287, 0.02485727, 0.01080801]),\n",
       "   array([0.00973089, 0.02240711, 0.03452227, 0.04574501, 0.05578332,\n",
       "          0.06437698, 0.07130335, 0.07638302, 0.07948442, 0.08052722,\n",
       "          0.07948442, 0.07638302, 0.07130335, 0.06437698, 0.05578332,\n",
       "          0.04574501, 0.03452227, 0.02240711, 0.00973089]),\n",
       "   array([0.008807  , 0.02030071, 0.03133602, 0.04163837, 0.05096506,\n",
       "          0.05909727, 0.06584432, 0.07104805, 0.07458649, 0.07637669,\n",
       "          0.07637669, 0.07458649, 0.07104805, 0.06584432, 0.05909727,\n",
       "          0.05096506, 0.04163837, 0.03133602, 0.02030071, 0.008807  ]),\n",
       "   array([0.00800861, 0.01847689, 0.02856721, 0.03805006, 0.04672221,\n",
       "          0.05439865, 0.06091571, 0.06613447, 0.0699437 , 0.0722622 ,\n",
       "          0.07304057, 0.0722622 , 0.0699437 , 0.06613447, 0.06091571,\n",
       "          0.05439865, 0.04672221, 0.03805006, 0.02856721, 0.01847689,\n",
       "          0.00800861])],\n",
       "  [array([1.]),\n",
       "   array([0.5, 0.5]),\n",
       "   array([0.27777778, 0.44444444, 0.27777778]),\n",
       "   array([0.17392742, 0.32607258, 0.32607258, 0.17392742]),\n",
       "   array([0.11846344, 0.23931434, 0.28444444, 0.23931434, 0.11846344]),\n",
       "   array([0.08566225, 0.18038079, 0.23395697, 0.23395697, 0.18038079,\n",
       "          0.08566225]),\n",
       "   array([0.06474248, 0.1398527 , 0.19091503, 0.20897959, 0.19091503,\n",
       "          0.1398527 , 0.06474248]),\n",
       "   array([0.05061427, 0.11119052, 0.15685332, 0.18134189, 0.18134189,\n",
       "          0.15685332, 0.11119052, 0.05061427]),\n",
       "   array([0.04063719, 0.09032408, 0.13030535, 0.15617354, 0.16511968,\n",
       "          0.15617354, 0.13030535, 0.09032408, 0.04063719]),\n",
       "   array([0.03333567, 0.07472567, 0.10954318, 0.13463336, 0.14776211,\n",
       "          0.14776211, 0.13463336, 0.10954318, 0.07472567, 0.03333567]),\n",
       "   array([0.02783428, 0.06279018, 0.09314511, 0.11659688, 0.13140227,\n",
       "          0.13646254, 0.13140227, 0.11659688, 0.09314511, 0.06279018,\n",
       "          0.02783428]),\n",
       "   array([0.02358767, 0.05346966, 0.08003916, 0.10158371, 0.11674627,\n",
       "          0.12457352, 0.12457352, 0.11674627, 0.10158371, 0.08003916,\n",
       "          0.05346966, 0.02358767]),\n",
       "   array([0.020242  , 0.04606075, 0.06943676, 0.08907299, 0.10390802,\n",
       "          0.11314159, 0.11627578, 0.11314159, 0.10390802, 0.08907299,\n",
       "          0.06943676, 0.04606075, 0.020242  ]),\n",
       "   array([0.01755973, 0.04007904, 0.06075929, 0.07860158, 0.0927692 ,\n",
       "          0.10259923, 0.10763193, 0.10763193, 0.10259923, 0.0927692 ,\n",
       "          0.07860158, 0.06075929, 0.04007904, 0.01755973]),\n",
       "   array([0.01537662, 0.03518302, 0.05357961, 0.06978534, 0.0831346 ,\n",
       "          0.0930805 , 0.09921574, 0.10128912, 0.09921574, 0.0930805 ,\n",
       "          0.0831346 , 0.06978534, 0.05357961, 0.03518302, 0.01537662]),\n",
       "   array([0.01357623, 0.03112676, 0.04757926, 0.06231449, 0.07479799,\n",
       "          0.08457826, 0.09130171, 0.09472531, 0.09472531, 0.09130171,\n",
       "          0.08457826, 0.07479799, 0.06231449, 0.04757926, 0.03112676,\n",
       "          0.01357623]),\n",
       "   array([0.01207415, 0.02772976, 0.04251807, 0.05594192, 0.06756818,\n",
       "          0.07702288, 0.08400205, 0.08828135, 0.08972324, 0.08828135,\n",
       "          0.08400205, 0.07702288, 0.06756818, 0.05594192, 0.04251807,\n",
       "          0.02772976, 0.01207415]),\n",
       "   array([0.01080801, 0.02485727, 0.03821287, 0.05047102, 0.0612776 ,\n",
       "          0.07032146, 0.07734234, 0.08213824, 0.08457119, 0.08457119,\n",
       "          0.08213824, 0.07734234, 0.07032146, 0.0612776 , 0.05047102,\n",
       "          0.03821287, 0.02485727, 0.01080801]),\n",
       "   array([0.00973089, 0.02240711, 0.03452227, 0.04574501, 0.05578332,\n",
       "          0.06437698, 0.07130335, 0.07638302, 0.07948442, 0.08052722,\n",
       "          0.07948442, 0.07638302, 0.07130335, 0.06437698, 0.05578332,\n",
       "          0.04574501, 0.03452227, 0.02240711, 0.00973089]),\n",
       "   array([0.008807  , 0.02030071, 0.03133602, 0.04163837, 0.05096506,\n",
       "          0.05909727, 0.06584432, 0.07104805, 0.07458649, 0.07637669,\n",
       "          0.07637669, 0.07458649, 0.07104805, 0.06584432, 0.05909727,\n",
       "          0.05096506, 0.04163837, 0.03133602, 0.02030071, 0.008807  ]),\n",
       "   array([0.00800861, 0.01847689, 0.02856721, 0.03805006, 0.04672221,\n",
       "          0.05439865, 0.06091571, 0.06613447, 0.0699437 , 0.0722622 ,\n",
       "          0.07304057, 0.0722622 , 0.0699437 , 0.06613447, 0.06091571,\n",
       "          0.05439865, 0.04672221, 0.03805006, 0.02856721, 0.01847689,\n",
       "          0.00800861])],\n",
       "  [array([1.]),\n",
       "   array([0.5, 0.5]),\n",
       "   array([0.27777778, 0.44444444, 0.27777778]),\n",
       "   array([0.17392742, 0.32607258, 0.32607258, 0.17392742]),\n",
       "   array([0.11846344, 0.23931434, 0.28444444, 0.23931434, 0.11846344]),\n",
       "   array([0.08566225, 0.18038079, 0.23395697, 0.23395697, 0.18038079,\n",
       "          0.08566225]),\n",
       "   array([0.06474248, 0.1398527 , 0.19091503, 0.20897959, 0.19091503,\n",
       "          0.1398527 , 0.06474248]),\n",
       "   array([0.05061427, 0.11119052, 0.15685332, 0.18134189, 0.18134189,\n",
       "          0.15685332, 0.11119052, 0.05061427]),\n",
       "   array([0.04063719, 0.09032408, 0.13030535, 0.15617354, 0.16511968,\n",
       "          0.15617354, 0.13030535, 0.09032408, 0.04063719]),\n",
       "   array([0.03333567, 0.07472567, 0.10954318, 0.13463336, 0.14776211,\n",
       "          0.14776211, 0.13463336, 0.10954318, 0.07472567, 0.03333567]),\n",
       "   array([0.02783428, 0.06279018, 0.09314511, 0.11659688, 0.13140227,\n",
       "          0.13646254, 0.13140227, 0.11659688, 0.09314511, 0.06279018,\n",
       "          0.02783428]),\n",
       "   array([0.02358767, 0.05346966, 0.08003916, 0.10158371, 0.11674627,\n",
       "          0.12457352, 0.12457352, 0.11674627, 0.10158371, 0.08003916,\n",
       "          0.05346966, 0.02358767]),\n",
       "   array([0.020242  , 0.04606075, 0.06943676, 0.08907299, 0.10390802,\n",
       "          0.11314159, 0.11627578, 0.11314159, 0.10390802, 0.08907299,\n",
       "          0.06943676, 0.04606075, 0.020242  ]),\n",
       "   array([0.01755973, 0.04007904, 0.06075929, 0.07860158, 0.0927692 ,\n",
       "          0.10259923, 0.10763193, 0.10763193, 0.10259923, 0.0927692 ,\n",
       "          0.07860158, 0.06075929, 0.04007904, 0.01755973]),\n",
       "   array([0.01537662, 0.03518302, 0.05357961, 0.06978534, 0.0831346 ,\n",
       "          0.0930805 , 0.09921574, 0.10128912, 0.09921574, 0.0930805 ,\n",
       "          0.0831346 , 0.06978534, 0.05357961, 0.03518302, 0.01537662]),\n",
       "   array([0.01357623, 0.03112676, 0.04757926, 0.06231449, 0.07479799,\n",
       "          0.08457826, 0.09130171, 0.09472531, 0.09472531, 0.09130171,\n",
       "          0.08457826, 0.07479799, 0.06231449, 0.04757926, 0.03112676,\n",
       "          0.01357623]),\n",
       "   array([0.01207415, 0.02772976, 0.04251807, 0.05594192, 0.06756818,\n",
       "          0.07702288, 0.08400205, 0.08828135, 0.08972324, 0.08828135,\n",
       "          0.08400205, 0.07702288, 0.06756818, 0.05594192, 0.04251807,\n",
       "          0.02772976, 0.01207415]),\n",
       "   array([0.01080801, 0.02485727, 0.03821287, 0.05047102, 0.0612776 ,\n",
       "          0.07032146, 0.07734234, 0.08213824, 0.08457119, 0.08457119,\n",
       "          0.08213824, 0.07734234, 0.07032146, 0.0612776 , 0.05047102,\n",
       "          0.03821287, 0.02485727, 0.01080801]),\n",
       "   array([0.00973089, 0.02240711, 0.03452227, 0.04574501, 0.05578332,\n",
       "          0.06437698, 0.07130335, 0.07638302, 0.07948442, 0.08052722,\n",
       "          0.07948442, 0.07638302, 0.07130335, 0.06437698, 0.05578332,\n",
       "          0.04574501, 0.03452227, 0.02240711, 0.00973089]),\n",
       "   array([0.008807  , 0.02030071, 0.03133602, 0.04163837, 0.05096506,\n",
       "          0.05909727, 0.06584432, 0.07104805, 0.07458649, 0.07637669,\n",
       "          0.07637669, 0.07458649, 0.07104805, 0.06584432, 0.05909727,\n",
       "          0.05096506, 0.04163837, 0.03133602, 0.02030071, 0.008807  ]),\n",
       "   array([0.00800861, 0.01847689, 0.02856721, 0.03805006, 0.04672221,\n",
       "          0.05439865, 0.06091571, 0.06613447, 0.0699437 , 0.0722622 ,\n",
       "          0.07304057, 0.0722622 , 0.0699437 , 0.06613447, 0.06091571,\n",
       "          0.05439865, 0.04672221, 0.03805006, 0.02856721, 0.01847689,\n",
       "          0.00800861])],\n",
       "  [array([1.]),\n",
       "   array([0.5, 0.5]),\n",
       "   array([0.27777778, 0.44444444, 0.27777778]),\n",
       "   array([0.17392742, 0.32607258, 0.32607258, 0.17392742]),\n",
       "   array([0.11846344, 0.23931434, 0.28444444, 0.23931434, 0.11846344]),\n",
       "   array([0.08566225, 0.18038079, 0.23395697, 0.23395697, 0.18038079,\n",
       "          0.08566225]),\n",
       "   array([0.06474248, 0.1398527 , 0.19091503, 0.20897959, 0.19091503,\n",
       "          0.1398527 , 0.06474248]),\n",
       "   array([0.05061427, 0.11119052, 0.15685332, 0.18134189, 0.18134189,\n",
       "          0.15685332, 0.11119052, 0.05061427]),\n",
       "   array([0.04063719, 0.09032408, 0.13030535, 0.15617354, 0.16511968,\n",
       "          0.15617354, 0.13030535, 0.09032408, 0.04063719]),\n",
       "   array([0.03333567, 0.07472567, 0.10954318, 0.13463336, 0.14776211,\n",
       "          0.14776211, 0.13463336, 0.10954318, 0.07472567, 0.03333567]),\n",
       "   array([0.02783428, 0.06279018, 0.09314511, 0.11659688, 0.13140227,\n",
       "          0.13646254, 0.13140227, 0.11659688, 0.09314511, 0.06279018,\n",
       "          0.02783428]),\n",
       "   array([0.02358767, 0.05346966, 0.08003916, 0.10158371, 0.11674627,\n",
       "          0.12457352, 0.12457352, 0.11674627, 0.10158371, 0.08003916,\n",
       "          0.05346966, 0.02358767]),\n",
       "   array([0.020242  , 0.04606075, 0.06943676, 0.08907299, 0.10390802,\n",
       "          0.11314159, 0.11627578, 0.11314159, 0.10390802, 0.08907299,\n",
       "          0.06943676, 0.04606075, 0.020242  ]),\n",
       "   array([0.01755973, 0.04007904, 0.06075929, 0.07860158, 0.0927692 ,\n",
       "          0.10259923, 0.10763193, 0.10763193, 0.10259923, 0.0927692 ,\n",
       "          0.07860158, 0.06075929, 0.04007904, 0.01755973]),\n",
       "   array([0.01537662, 0.03518302, 0.05357961, 0.06978534, 0.0831346 ,\n",
       "          0.0930805 , 0.09921574, 0.10128912, 0.09921574, 0.0930805 ,\n",
       "          0.0831346 , 0.06978534, 0.05357961, 0.03518302, 0.01537662]),\n",
       "   array([0.01357623, 0.03112676, 0.04757926, 0.06231449, 0.07479799,\n",
       "          0.08457826, 0.09130171, 0.09472531, 0.09472531, 0.09130171,\n",
       "          0.08457826, 0.07479799, 0.06231449, 0.04757926, 0.03112676,\n",
       "          0.01357623]),\n",
       "   array([0.01207415, 0.02772976, 0.04251807, 0.05594192, 0.06756818,\n",
       "          0.07702288, 0.08400205, 0.08828135, 0.08972324, 0.08828135,\n",
       "          0.08400205, 0.07702288, 0.06756818, 0.05594192, 0.04251807,\n",
       "          0.02772976, 0.01207415]),\n",
       "   array([0.01080801, 0.02485727, 0.03821287, 0.05047102, 0.0612776 ,\n",
       "          0.07032146, 0.07734234, 0.08213824, 0.08457119, 0.08457119,\n",
       "          0.08213824, 0.07734234, 0.07032146, 0.0612776 , 0.05047102,\n",
       "          0.03821287, 0.02485727, 0.01080801]),\n",
       "   array([0.00973089, 0.02240711, 0.03452227, 0.04574501, 0.05578332,\n",
       "          0.06437698, 0.07130335, 0.07638302, 0.07948442, 0.08052722,\n",
       "          0.07948442, 0.07638302, 0.07130335, 0.06437698, 0.05578332,\n",
       "          0.04574501, 0.03452227, 0.02240711, 0.00973089]),\n",
       "   array([0.008807  , 0.02030071, 0.03133602, 0.04163837, 0.05096506,\n",
       "          0.05909727, 0.06584432, 0.07104805, 0.07458649, 0.07637669,\n",
       "          0.07637669, 0.07458649, 0.07104805, 0.06584432, 0.05909727,\n",
       "          0.05096506, 0.04163837, 0.03133602, 0.02030071, 0.008807  ]),\n",
       "   array([0.00800861, 0.01847689, 0.02856721, 0.03805006, 0.04672221,\n",
       "          0.05439865, 0.06091571, 0.06613447, 0.0699437 , 0.0722622 ,\n",
       "          0.07304057, 0.0722622 , 0.0699437 , 0.06613447, 0.06091571,\n",
       "          0.05439865, 0.04672221, 0.03805006, 0.02856721, 0.01847689,\n",
       "          0.00800861])]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#alpha = ch.Uniform(0,1) #We choose uniform distributions to reflect our lack of knowledge about the relative likelihood functions\n",
    "#beta = ch.Uniform(0,1) #We take the same bounds as for the Sobol-Saltelli analysis\n",
    "#delta = ch.Uniform(0,1)\n",
    "#gamma = ch.Uniform(0,1)\n",
    "#joint = ch.J(alpha,beta,delta,gamma)\n",
    "\n",
    "\n",
    "growth=None\n",
    "recurrence_algorithm='stieltjes'\n",
    "rule='g'\n",
    "tolerance=1e-10\n",
    "scaling=3\n",
    "n_max=50000\n",
    "\n",
    "def _construct_lookup(\n",
    "        orders,\n",
    "        dists,\n",
    "        growth,\n",
    "        recurrence_algorithm,\n",
    "        rules,\n",
    "        tolerance,\n",
    "        scaling,\n",
    "        n_max,\n",
    "):\n",
    "    \"\"\"\n",
    "    Create abscissas and weights look-up table so values do not need to be\n",
    "    re-calculatated on the fly.\n",
    "    \"\"\"\n",
    "    x_lookup = []\n",
    "    w_lookup = []\n",
    "\n",
    "    for order, dist in zip(max_order_vector, dists):\n",
    "        print(dist)\n",
    "        x_lookup.append([])\n",
    "        w_lookup.append([])\n",
    "        for orderr in range(max_order+1):\n",
    "            (abscissas,), weights = ch.generate_quadrature(\n",
    "                order=orderr,\n",
    "                dist=dist,\n",
    "                growth=growth,\n",
    "                recurrence_algorithm=recurrence_algorithm,\n",
    "                rule=rule,\n",
    "                tolerance=tolerance,\n",
    "                scaling=scaling,\n",
    "                n_max=n_max,\n",
    "            )\n",
    "            x_lookup[-1].append(abscissas)\n",
    "            w_lookup[-1].append(weights)\n",
    "    return x_lookup, w_lookup\n",
    "\n",
    "\n",
    "def construct_wrapper(maxx):\n",
    "    global max_order_vector,max_order\n",
    "    global x_lookup,w_lookup\n",
    "    \n",
    "    max_order = maxx\n",
    "    max_order_vector = max_order*np.ones(len(joint), dtype=int)\n",
    "    #print(max_order_vector)\n",
    "    \n",
    "    \n",
    "    x_lookup, w_lookup = _construct_lookup(\n",
    "        orders=max_order_vector,\n",
    "        dists=joint,\n",
    "        growth=growth,\n",
    "        recurrence_algorithm=recurrence_algorithm,\n",
    "        rules=rule,\n",
    "        tolerance=tolerance,\n",
    "        scaling=scaling,\n",
    "        n_max=5000)\n",
    "    \n",
    "    \n",
    "    return x_lookup,w_lookup\n",
    "    \n",
    "    \n",
    "construct_wrapper(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Grid and weight constructor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "def grid_constructor(current_index):\n",
    "    \n",
    "    nodestack = []\n",
    "    \n",
    "    if (type(current_index) == tuple):\n",
    "        current_index = current_index[0]\n",
    "    else:\n",
    "        current_index = current_index\n",
    "        \n",
    "    if np.any([ i >= (len(x_lookup[0]) - 1) for i in current_index] ):\n",
    "        construct_wrapper(len(x_lookup[0]) + 10)\n",
    "        \n",
    "    \n",
    "    for index,element in enumerate(current_index):\n",
    "        nodestack.append([])\n",
    "        nodestack[index] = list(x_lookup[index][element])\n",
    "    \n",
    "    global master,final_nodes\n",
    "    master = []\n",
    "    nodes = nodestack[0]\n",
    "    \n",
    "    for i in range(1,len(nodestack)):\n",
    "        nodes = product(nodes,nodestack[i])\n",
    "    \n",
    "    master = [(a,b,c,d) for (((a,b),c),d) in nodes]\n",
    "    \n",
    "    final_nodes = np.array([element for element in master]).T\n",
    "    \n",
    "    return final_nodes\n",
    "\n",
    "def weight_constructor(current_index):\n",
    "    \n",
    "    global new_nodes\n",
    "    \n",
    "    nodestack = []\n",
    "    new_nodes = []\n",
    "    \n",
    "    \n",
    "    if(type(current_index) == tuple):\n",
    "        current_index = current_index[0]\n",
    "    else:\n",
    "        current_index = current_index\n",
    "        \n",
    "    for index,element in enumerate(current_index):\n",
    "        nodestack.append([])\n",
    "        nodestack[index] = list(w_lookup[index][element])\n",
    "    \n",
    "    global master_1,final_weights,weights\n",
    "    master_1 = []\n",
    "    weights = nodestack[0]\n",
    "    \n",
    "    for i in range(1,len(nodestack)):\n",
    "        weights = product(weights,nodestack[i])\n",
    "    \n",
    "    \n",
    "    master_1 = [(a,b,c,d) for (((a,b),c),d) in weights]\n",
    "    \n",
    "    for i,el in enumerate(master_1):\n",
    "        psum = 1\n",
    "        for ex in el:\n",
    "            psum *= ex\n",
    "        new_nodes.append(psum)\n",
    "    \n",
    "    final_weights = new_nodes\n",
    "    return final_weights\n",
    "\n",
    "    \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def new_solver(final_nodes,final_weights,P):\n",
    "    \n",
    "    global expansion,algorithm_evals\n",
    "    \n",
    "    expansion = ch.generate_expansion(P, joint)\n",
    "    \n",
    "    start_time = time.perf_counter()\n",
    "    \n",
    "    global Y,fitter_prey,solution,prey\n",
    "                                                                         #Choose 1000 parameter samples at which to solve for coefficients\n",
    "    Y = np.zeros((2, len(final_weights)))\n",
    "     \n",
    "    x0 = 33                                                               #Initial conditions same as before\n",
    "    y0 = 6.2                       \n",
    "    X = [x0,y0]\n",
    "    t = np.linspace(0., 30, 1000)\n",
    "    \n",
    "    for i,ex in enumerate(final_nodes.T):\n",
    "        a,b,d,g = ex\n",
    "        solution = integrate.odeint(lotka, X, t, args = (a,b,d,g))\n",
    "        Y[0][i] =  solution.T[0][910]\n",
    "        Y[1][i] =  solution.T[1][910]\n",
    "    \n",
    "    prey = Y[0]\n",
    "    \n",
    "    fitter_prey = ch.fit_quadrature(expansion,final_nodes,final_weights,prey)\n",
    "\n",
    "    return fitter_prey\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "36\n",
      "Global error >>> 0.6608124633355859\n",
      "Step time >>> 5.23735459999989 seconds\n",
      "Chosen index >>> [2 2 1 1]\n",
      "Global error >>> 0.6608124633496135\n",
      "Step time >>> 13.525167499999952 seconds\n",
      "Chosen index >>> [2 2 2 1]\n",
      "Global error >>> 1.2981023671057872\n",
      "Step time >>> 24.4788681 seconds\n",
      "Chosen index >>> [2 2 3 1]\n",
      "Global error >>> 1.297734084575294\n",
      "Step time >>> 36.769545399999515 seconds\n",
      "Chosen index >>> [2 2 1 2]\n",
      "Global error >>> 1.3871915663443222\n",
      "Step time >>> 50.759039599999596 seconds\n",
      "Chosen index >>> [2 2 1 3]\n",
      "Global error >>> 1.387171863131299\n",
      "Step time >>> 67.05051479999929 seconds\n",
      "Chosen index >>> [2 3 2 1]\n",
      "Global error >>> 1.079176810578499\n",
      "Step time >>> 81.54243319999932 seconds\n",
      "Chosen index >>> [2 3 1 3]\n",
      "Global error >>> 1.079176812239542\n",
      "Step time >>> 96.46294499999931 seconds\n",
      "Chosen index >>> [3 2 3 1]\n",
      "Global error >>> 0.18173992920861262\n",
      "Step time >>> 110.83349910000015 seconds\n"
     ]
    }
   ],
   "source": [
    "\n",
    "def algorithm(P):\n",
    "    \n",
    "    global old, active, poly, indices_list, global_errors, points,p\n",
    "    global old_node_set, old_weight_set, step, vectors, df\n",
    "    \n",
    "    '''Initialise'''\n",
    "    \n",
    "    seed = (np.array([2,2,1,1], dtype = 'int'),0)\n",
    "    vectors = np.identity(len(joint), dtype='int')\n",
    "    date_today = datetime.date.today()\n",
    "    start_time = time.perf_counter()\n",
    "    samples = saltelli.sample(problem, 512)\n",
    "    step = 0\n",
    "    points = 0\n",
    "    \n",
    "    old = []\n",
    "    active = []\n",
    "    poly = []\n",
    "    local_errors = []\n",
    "    global_errors = []\n",
    "    p = []\n",
    "    \n",
    "    old_node_set = np.array([])\n",
    "    old_weight_set = np.array([])\n",
    "    \n",
    "    df = pd.DataFrame(columns=['chosen_index','local_error','global_error','run_time'])\n",
    "    df_indices = pd.DataFrame(columns=['alpha','beta','delta','gamma'])\n",
    "    \n",
    "    \n",
    "    # Temporary data saving\n",
    "    active_indices = {}\n",
    "    \n",
    "    \n",
    "    '''Execute zeroth step'''\n",
    "    \n",
    "    active.append(seed)\n",
    "    active_indices[step] = active\n",
    "    old_node_set = grid_constructor(seed)\n",
    "    old_weight_set = weight_constructor(seed)\n",
    "    print(len(old_weight_set))\n",
    "    points += len(old_weight_set)\n",
    "    p.append(points)\n",
    "    \n",
    "    poly.append(new_solver(old_node_set, old_weight_set, P))\n",
    "    \n",
    "    st = ch.Sens_t(poly[-1],joint)\n",
    "    df_indices = df_indices.append({'alpha' : st[0], 'beta': st[1], 'delta': st[2], 'gamma': st[3] },ignore_index = True )\n",
    "\n",
    "    \n",
    "    global_errors.append(sobol_error(st))\n",
    "    global_errors.append(sobol_error(st))\n",
    "    \n",
    "    \n",
    "    print('Global error >>>', global_errors[-1])\n",
    "    print('Step time >>>', time.perf_counter() - start_time, 'seconds')\n",
    "    \n",
    "    '''Main loop'''\n",
    "    \n",
    "    while (global_errors[-1] > 0.2) and len(active) > 0:\n",
    "        \n",
    "        if len(active) > 1000000000:\n",
    "            return\n",
    "\n",
    "        \n",
    "        else:\n",
    "            \n",
    "            active_indices[step] = active\n",
    "            chosen_index = active[-1][0]\n",
    "            local_errors.append(active[-1][1])\n",
    "            active.pop()\n",
    "            print('Chosen index >>>', chosen_index)\n",
    "\n",
    "            old.append(tuple(chosen_index))\n",
    "            generate_candidates(chosen_index,P)\n",
    "\n",
    "            stripped_active = [i[0] for i in active] + [j for j in candidates]\n",
    "            assign_errors(stripped_active)\n",
    "\n",
    "            old_node_set = np.concatenate((old_node_set, grid_constructor(chosen_index)), axis = 1)\n",
    "            old_weight_set = np.concatenate((old_weight_set, weight_constructor(chosen_index)))\n",
    "            points += len(old_weight_set)\n",
    "            p.append(points)\n",
    "\n",
    "                        \n",
    "\n",
    "\n",
    "            poly.append(new_solver(old_node_set, old_weight_set,P))\n",
    "            st = ch.Sens_t(poly[-1], joint)\n",
    "            df_indices = df_indices.append({'alpha': st[0], 'beta': st[1], 'delta': st[2], 'gamma': st[3] }, ignore_index=True)\n",
    "\n",
    "            global_errors.append(sobol_error(st))\n",
    "\n",
    "            print('Global error >>>', global_errors[-1])\n",
    "\n",
    "            '''Save data'''\n",
    "\n",
    "            numpoly.savez(f'{date_today}_step{step}.npz',*poly)\n",
    "            run_time = time.perf_counter() - start_time\n",
    "            df = df.append({'chosen_index': old[-1],'local_error':local_errors[-1],'global_error':global_errors[-1], 'run_time':run_time}, ignore_index=True)\n",
    "            df.to_csv(f'comma_file_{date_today}.csv')\n",
    "            df_indices.to_csv('total_order_indices.csv')\n",
    "\n",
    "            print('Step time >>>', time.perf_counter() - start_time, 'seconds')\n",
    "\n",
    "            step += 1\n",
    "        \n",
    "def assign_errors(param):\n",
    "    \n",
    "    global active_errors,active,candidates,current_errors,new\n",
    "    active_errors = []\n",
    "    \n",
    "\n",
    "    for multi_index in param:\n",
    "        nodes = grid_constructor(multi_index)\n",
    "        current_errors = []\n",
    "        \n",
    "        for node in nodes.T:\n",
    "            a,b,d,g = node\n",
    "            solution = integrate.odeint(lotka, (33,6.2), t, args = (a,b,d,g)).T[0][910]\n",
    "            current_errors.append(abs(solution - poly[-1](a,b,d,g)))\n",
    "        \n",
    "        active_errors.append(np.mean(current_errors))\n",
    "           \n",
    "    \n",
    "    active = sorted(list(zip(param,active_errors)),key = lambda x: x[1])\n",
    "    active = [i for i in OrderedDict((tuple(x[0]), x) for x in active).values()]\n",
    "    #print(active)\n",
    "    \n",
    "    \n",
    "def calculate_global_error(polynomial,samples):\n",
    "    \n",
    "    global global_error\n",
    "    \n",
    "    current_errors = []\n",
    "    \n",
    "    for idx,node in enumerate(samples):\n",
    "        a,b,d,g = node\n",
    "        current_errors.append(abs(evals[idx] - polynomial(a,b,d,g)))\n",
    "    \n",
    "    global_error = np.mean(current_errors)\n",
    "    \n",
    "    return global_error   \n",
    "\n",
    "def sobol_error(vec):\n",
    "    \n",
    "    return np.linalg.norm(gt_prey - vec) / gt_norm\n",
    "    \n",
    "def model_evals(samples):\n",
    "    \n",
    "    evals_list = []\n",
    "    \n",
    "    for idx,node in enumerate(samples):\n",
    "        a,b,d,g = node\n",
    "        solution = integrate.odeint(lotka, (33,6.2), t, args = (a,b,d,g)).T[0][910]\n",
    "        evals_list.append(solution)\n",
    "        \n",
    "    evals = np.array(evals_list)\n",
    "    \n",
    "    return evals\n",
    "\n",
    "def generate_candidates(index_set,P):\n",
    "    global candidates,pre_candidates,back_neighbours\n",
    "    \n",
    "    pre_candidates = []\n",
    "    candidates = []\n",
    "    new = []\n",
    "    \n",
    "    for j in range(0,len(joint)):\n",
    "        pre_candidates.append(index_set + vectors[j])\n",
    "    \n",
    "    for candidate in pre_candidates:\n",
    "        back_neighbours = []\n",
    "        for j in range(0,len(joint)):\n",
    "            back_neighbour = candidate-vectors[j]\n",
    "            if np.all((back_neighbour > 1)):\n",
    "                back_neighbours.append(tuple(back_neighbour))\n",
    "    \n",
    "        if np.all([neighbour in old for neighbour in back_neighbours]):    \n",
    "            candidates.append(candidate)\n",
    "            \n",
    "        for multi_index in candidates:\n",
    "            if np.all([i<P+1 for i in multi_index]):\n",
    "                new.append(multi_index)\n",
    "                \n",
    "                \n",
    "    candidates = new\n",
    "                \n",
    "    \n",
    "    \n",
    "        \n",
    "\n",
    "algorithm(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2484"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(old_weight_set)\n",
    "points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "j = ch.J(alpha,beta)a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "29\n"
     ]
    }
   ],
   "source": [
    "nodes,weights = ch.generate_quadrature(3,j,sparse=True)\n",
    "print(len(weights))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.6608124633355859,\n",
       " 0.6608124633496135,\n",
       " 1.2981023671057872,\n",
       " 1.297734084575294,\n",
       " 1.3871915663443222,\n",
       " 1.387171863131299,\n",
       " 1.079176810578499,\n",
       " 1.079176812239542,\n",
       " 0.18173992920861262]"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "global_errors \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(figsize=(10,6))\n",
    "xs = p \n",
    "ax.plot(p,global_errors,marker='o',linestyle = ':',color='cornflowerblue')\n",
    "labels = p\n",
    "ax.set_xlabel('Points in grid',fontsize='x-large')\n",
    "ax.set_ylabel(r'Global error - $ \\mathbf{S}_{T} $',fontsize='x-large')\n",
    "ax.set_title('Global error during dimension adaptive integration')\n",
    "x = [i for i in p]\n",
    "ax.set_xticks(x)\n",
    "plt.savefig('DAS_error.jpg',bbox_inches='tight',dpi=200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.4670484 , 0.4670484 , 0.4670484 , ..., 0.66333636, 0.66333636,\n",
       "        0.66333636],\n",
       "       [0.02270484, 0.02270484, 0.02270484, ..., 0.04129516, 0.04129516,\n",
       "        0.04129516],\n",
       "       [0.80298294, 0.80298294, 1.05701706, ..., 1.00479583, 1.11944999,\n",
       "        1.11944999],\n",
       "       [0.02530496, 0.03269504, 0.02530496, ..., 0.03269504, 0.02530496,\n",
       "        0.03269504]])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "old_node_set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 588)"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "one.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "one = old_node_set[0:2]\n",
    "two = old_node_set[2:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'C:\\\\Users\\\\jeffr\\\\OneDrive\\\\Documents\\\\Education\\\\Thesis\\\\Scripts\\\\midterm_meeting_figures'"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c('midterm_meeting_figures')\n",
    "get()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.80298294, 0.80298294, 1.05701706, 1.05701706, 0.80298294,\n",
       "       0.80298294, 1.05701706, 1.05701706, 0.80298294, 0.80298294,\n",
       "       1.05701706, 1.05701706, 0.80298294, 0.80298294, 1.05701706,\n",
       "       1.05701706, 0.80298294, 0.80298294, 1.05701706, 1.05701706,\n",
       "       0.80298294, 0.80298294, 1.05701706, 1.05701706, 0.80298294,\n",
       "       0.80298294, 1.05701706, 1.05701706, 0.80298294, 0.80298294,\n",
       "       1.05701706, 1.05701706, 0.80298294, 0.80298294, 1.05701706,\n",
       "       1.05701706, 0.80298294, 0.80298294, 1.05701706, 1.05701706,\n",
       "       0.80298294, 0.80298294, 1.05701706, 1.05701706, 0.80298294,\n",
       "       0.80298294, 1.05701706, 1.05701706, 0.80298294, 0.80298294,\n",
       "       1.05701706, 1.05701706, 0.80298294, 0.80298294, 1.05701706,\n",
       "       1.05701706, 0.80298294, 0.80298294, 1.05701706, 1.05701706,\n",
       "       0.80298294, 0.80298294, 1.05701706, 1.05701706, 0.80298294,\n",
       "       0.80298294, 1.05701706, 1.05701706, 0.80298294, 0.80298294,\n",
       "       1.05701706, 1.05701706, 0.75958873, 0.75958873, 0.93      ,\n",
       "       0.93      , 1.10041127, 1.10041127, 0.75958873, 0.75958873,\n",
       "       0.93      , 0.93      , 1.10041127, 1.10041127, 0.75958873,\n",
       "       0.75958873, 0.93      , 0.93      , 1.10041127, 1.10041127,\n",
       "       0.75958873, 0.75958873, 0.93      , 0.93      , 1.10041127,\n",
       "       1.10041127, 0.75958873, 0.75958873, 0.93      , 0.93      ,\n",
       "       1.10041127, 1.10041127, 0.75958873, 0.75958873, 0.93      ,\n",
       "       0.93      , 1.10041127, 1.10041127, 0.75958873, 0.75958873,\n",
       "       0.93      , 0.93      , 1.10041127, 1.10041127, 0.75958873,\n",
       "       0.75958873, 0.93      , 0.93      , 1.10041127, 1.10041127,\n",
       "       0.75958873, 0.75958873, 0.93      , 0.93      , 1.10041127,\n",
       "       1.10041127, 0.74055001, 0.74055001, 0.85520417, 0.85520417,\n",
       "       1.00479583, 1.00479583, 1.11944999, 1.11944999, 0.74055001,\n",
       "       0.74055001, 0.85520417, 0.85520417, 1.00479583, 1.00479583,\n",
       "       1.11944999, 1.11944999, 0.74055001, 0.74055001, 0.85520417,\n",
       "       0.85520417, 1.00479583, 1.00479583, 1.11944999, 1.11944999,\n",
       "       0.74055001, 0.74055001, 0.85520417, 0.85520417, 1.00479583,\n",
       "       1.00479583, 1.11944999, 1.11944999, 0.74055001, 0.74055001,\n",
       "       0.85520417, 0.85520417, 1.00479583, 1.00479583, 1.11944999,\n",
       "       1.11944999, 0.74055001, 0.74055001, 0.85520417, 0.85520417,\n",
       "       1.00479583, 1.00479583, 1.11944999, 1.11944999, 0.74055001,\n",
       "       0.74055001, 0.85520417, 0.85520417, 1.00479583, 1.00479583,\n",
       "       1.11944999, 1.11944999, 0.74055001, 0.74055001, 0.85520417,\n",
       "       0.85520417, 1.00479583, 1.00479583, 1.11944999, 1.11944999,\n",
       "       0.74055001, 0.74055001, 0.85520417, 0.85520417, 1.00479583,\n",
       "       1.00479583, 1.11944999, 1.11944999, 0.80298294, 0.80298294,\n",
       "       0.80298294, 1.05701706, 1.05701706, 1.05701706, 0.80298294,\n",
       "       0.80298294, 0.80298294, 1.05701706, 1.05701706, 1.05701706,\n",
       "       0.80298294, 0.80298294, 0.80298294, 1.05701706, 1.05701706,\n",
       "       1.05701706, 0.80298294, 0.80298294, 0.80298294, 1.05701706,\n",
       "       1.05701706, 1.05701706, 0.80298294, 0.80298294, 0.80298294,\n",
       "       1.05701706, 1.05701706, 1.05701706, 0.80298294, 0.80298294,\n",
       "       0.80298294, 1.05701706, 1.05701706, 1.05701706, 0.80298294,\n",
       "       0.80298294, 0.80298294, 1.05701706, 1.05701706, 1.05701706,\n",
       "       0.80298294, 0.80298294, 0.80298294, 1.05701706, 1.05701706,\n",
       "       1.05701706, 0.80298294, 0.80298294, 0.80298294, 1.05701706,\n",
       "       1.05701706, 1.05701706, 0.80298294, 0.80298294, 0.80298294,\n",
       "       0.80298294, 1.05701706, 1.05701706, 1.05701706, 1.05701706,\n",
       "       0.80298294, 0.80298294, 0.80298294, 0.80298294, 1.05701706,\n",
       "       1.05701706, 1.05701706, 1.05701706, 0.80298294, 0.80298294,\n",
       "       0.80298294, 0.80298294, 1.05701706, 1.05701706, 1.05701706,\n",
       "       1.05701706, 0.80298294, 0.80298294, 0.80298294, 0.80298294,\n",
       "       1.05701706, 1.05701706, 1.05701706, 1.05701706, 0.80298294,\n",
       "       0.80298294, 0.80298294, 0.80298294, 1.05701706, 1.05701706,\n",
       "       1.05701706, 1.05701706, 0.80298294, 0.80298294, 0.80298294,\n",
       "       0.80298294, 1.05701706, 1.05701706, 1.05701706, 1.05701706,\n",
       "       0.80298294, 0.80298294, 0.80298294, 0.80298294, 1.05701706,\n",
       "       1.05701706, 1.05701706, 1.05701706, 0.80298294, 0.80298294,\n",
       "       0.80298294, 0.80298294, 1.05701706, 1.05701706, 1.05701706,\n",
       "       1.05701706, 0.80298294, 0.80298294, 0.80298294, 0.80298294,\n",
       "       1.05701706, 1.05701706, 1.05701706, 1.05701706, 0.75958873,\n",
       "       0.75958873, 0.93      , 0.93      , 1.10041127, 1.10041127,\n",
       "       0.75958873, 0.75958873, 0.93      , 0.93      , 1.10041127,\n",
       "       1.10041127, 0.75958873, 0.75958873, 0.93      , 0.93      ,\n",
       "       1.10041127, 1.10041127, 0.75958873, 0.75958873, 0.93      ,\n",
       "       0.93      , 1.10041127, 1.10041127, 0.75958873, 0.75958873,\n",
       "       0.93      , 0.93      , 1.10041127, 1.10041127, 0.75958873,\n",
       "       0.75958873, 0.93      , 0.93      , 1.10041127, 1.10041127,\n",
       "       0.75958873, 0.75958873, 0.93      , 0.93      , 1.10041127,\n",
       "       1.10041127, 0.75958873, 0.75958873, 0.93      , 0.93      ,\n",
       "       1.10041127, 1.10041127, 0.75958873, 0.75958873, 0.93      ,\n",
       "       0.93      , 1.10041127, 1.10041127, 0.75958873, 0.75958873,\n",
       "       0.93      , 0.93      , 1.10041127, 1.10041127, 0.75958873,\n",
       "       0.75958873, 0.93      , 0.93      , 1.10041127, 1.10041127,\n",
       "       0.75958873, 0.75958873, 0.93      , 0.93      , 1.10041127,\n",
       "       1.10041127, 0.80298294, 0.80298294, 0.80298294, 0.80298294,\n",
       "       1.05701706, 1.05701706, 1.05701706, 1.05701706, 0.80298294,\n",
       "       0.80298294, 0.80298294, 0.80298294, 1.05701706, 1.05701706,\n",
       "       1.05701706, 1.05701706, 0.80298294, 0.80298294, 0.80298294,\n",
       "       0.80298294, 1.05701706, 1.05701706, 1.05701706, 1.05701706,\n",
       "       0.80298294, 0.80298294, 0.80298294, 0.80298294, 1.05701706,\n",
       "       1.05701706, 1.05701706, 1.05701706, 0.80298294, 0.80298294,\n",
       "       0.80298294, 0.80298294, 1.05701706, 1.05701706, 1.05701706,\n",
       "       1.05701706, 0.80298294, 0.80298294, 0.80298294, 0.80298294,\n",
       "       1.05701706, 1.05701706, 1.05701706, 1.05701706, 0.80298294,\n",
       "       0.80298294, 0.80298294, 0.80298294, 1.05701706, 1.05701706,\n",
       "       1.05701706, 1.05701706, 0.80298294, 0.80298294, 0.80298294,\n",
       "       0.80298294, 1.05701706, 1.05701706, 1.05701706, 1.05701706,\n",
       "       0.80298294, 0.80298294, 0.80298294, 0.80298294, 1.05701706,\n",
       "       1.05701706, 1.05701706, 1.05701706, 0.80298294, 0.80298294,\n",
       "       0.80298294, 0.80298294, 1.05701706, 1.05701706, 1.05701706,\n",
       "       1.05701706, 0.80298294, 0.80298294, 0.80298294, 0.80298294,\n",
       "       1.05701706, 1.05701706, 1.05701706, 1.05701706, 0.80298294,\n",
       "       0.80298294, 0.80298294, 0.80298294, 1.05701706, 1.05701706,\n",
       "       1.05701706, 1.05701706, 0.74055001, 0.74055001, 0.85520417,\n",
       "       0.85520417, 1.00479583, 1.00479583, 1.11944999, 1.11944999,\n",
       "       0.74055001, 0.74055001, 0.85520417, 0.85520417, 1.00479583,\n",
       "       1.00479583, 1.11944999, 1.11944999, 0.74055001, 0.74055001,\n",
       "       0.85520417, 0.85520417, 1.00479583, 1.00479583, 1.11944999,\n",
       "       1.11944999, 0.74055001, 0.74055001, 0.85520417, 0.85520417,\n",
       "       1.00479583, 1.00479583, 1.11944999, 1.11944999, 0.74055001,\n",
       "       0.74055001, 0.85520417, 0.85520417, 1.00479583, 1.00479583,\n",
       "       1.11944999, 1.11944999, 0.74055001, 0.74055001, 0.85520417,\n",
       "       0.85520417, 1.00479583, 1.00479583, 1.11944999, 1.11944999,\n",
       "       0.74055001, 0.74055001, 0.85520417, 0.85520417, 1.00479583,\n",
       "       1.00479583, 1.11944999, 1.11944999, 0.74055001, 0.74055001,\n",
       "       0.85520417, 0.85520417, 1.00479583, 1.00479583, 1.11944999,\n",
       "       1.11944999, 0.74055001, 0.74055001, 0.85520417, 0.85520417,\n",
       "       1.00479583, 1.00479583, 1.11944999, 1.11944999, 0.74055001,\n",
       "       0.74055001, 0.85520417, 0.85520417, 1.00479583, 1.00479583,\n",
       "       1.11944999, 1.11944999, 0.74055001, 0.74055001, 0.85520417,\n",
       "       0.85520417, 1.00479583, 1.00479583, 1.11944999, 1.11944999,\n",
       "       0.74055001, 0.74055001, 0.85520417, 0.85520417, 1.00479583,\n",
       "       1.00479583, 1.11944999, 1.11944999])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "two[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axs = plt.subplots(1,2,figsize=(15,7))\n",
    "\n",
    "one = old_node_set[0:2]\n",
    "two = old_node_set[2:4]\n",
    "\n",
    "\n",
    "axs[0].scatter(one[0],one[1], marker = 's', color='plum',linewidth=2)\n",
    "axs[1].scatter(two[0],two[1],marker = 's', color='paleturquoise',linewidth=2)\n",
    "\n",
    "axs[0].set_ylabel(r'$ \\alpha $', fontsize='xx-large')\n",
    "axs[1].set_ylabel(r'$ \\delta $', fontsize='xx-large')\n",
    "\n",
    "axs[0].set_xlabel(r'$ \\beta $', fontsize='xx-large')\n",
    "axs[1].set_xlabel(r'$ \\gamma $', fontsize='xx-large')\n",
    "\n",
    "fig.suptitle(r'Grid after halting for p=3 in $ \\mathbf{R}^{4}$ - 2,484 nodes',fontsize = 'xx-large')\n",
    "plt.savefig('DAS_grid_graph.jpg', bbox_inches = 'tight', dpi=200 )\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'C:\\\\Users\\\\jeffr\\\\OneDrive\\\\Documents\\\\Education\\\\Thesis\\\\Scripts\\\\midterm_meeting_figures'"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get()"
   ]
  }
 ],
 "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}