Hellinger_distances_for_MDF.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-03-31T19:24:20.733106Z",
     "start_time": "2024-03-31T19:24:20.730879Z"
    }
   },
   "outputs": [],
   "source": [
    "## Created by Dr Oleg Bushuev and Dr Elijah Borodin ##\n",
    "## The University of Manchester, 2023-2024 ##\n",
    "\n",
    "# This jupyter (.ipynb) notebook is written as a tool for automatic detection and quantification of mesostructure (including shear bands) based on the measurement of the Hellinger distances between random and actual misorientation distribution function (MDF) experimentally obtained by EBSD or X-ray microscopy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [
    "# Set directory for Voronoi_PCC_Analyser code \n",
    "'/Users/user/Dropbox/OFFICE/my_science/Calculations/matgen'\n",
    "from importlib import reload\n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import os\n",
    "import seaborn as sns"
   ],
   "metadata": {
    "collapsed": false
   },
   "id": "66db69213fe192bd"
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [
    {
     "data": {
      "text/plain": "<module 'matgen.matutils' from '/Users/user/Dropbox/OFFICE/my_science/Calculations/matgen/matutils.py'>"
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reload(matutils)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-30T22:54:14.897778Z",
     "start_time": "2024-03-30T22:54:14.884129Z"
    }
   },
   "id": "38e617172f853946"
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "outputs": [],
   "source": [
    "from matgen import base, matutils\n",
    "from matgen.base import CellComplex"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-04-01T00:06:10.373547Z",
     "start_time": "2024-04-01T00:06:10.343864Z"
    }
   },
   "id": "d5ce158618947652"
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [],
   "source": [
    "## Settings"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-31T19:24:27.276646Z",
     "start_time": "2024-03-31T19:24:27.265143Z"
    }
   },
   "id": "cc0ff3eb76959395"
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [],
   "source": [
    "# Set number of bins for calculation Hellinger distance \n",
    "# bins = np.linspace(0, 64, 33) # 32 bins\n",
    "bins = [0, 15, 63] # 2 bins with the corresponding ranges of disorientation angles"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-31T19:24:31.179496Z",
     "start_time": "2024-03-31T19:24:31.165518Z"
    }
   },
   "id": "1f5091540e9d746"
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "outputs": [],
   "source": [
    "# Maximal order 'k' of the required for analysis grain 'k-neighbours'\n",
    "max_order = 8"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-31T19:24:31.982697Z",
     "start_time": "2024-03-31T19:24:31.971507Z"
    }
   },
   "id": "77ad08d22e640408"
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "outputs": [],
   "source": [
    "figsize = [8, 6]\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams[\"figure.figsize\"] = figsize"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-31T19:24:33.610787Z",
     "start_time": "2024-03-31T19:24:33.597016Z"
    }
   },
   "id": "4f5ca18a2d0b558d"
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-31T19:24:38.708077Z",
     "start_time": "2024-03-31T19:24:38.696797Z"
    }
   },
   "id": "14ca4453e8f8b00c"
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "outputs": [],
   "source": [
    "## Set Random (Mackenzie) distribution of grain disorientations - mandatory as a reference \n",
    "\n",
    "filename = '/Users/user/Dropbox/OFFICE/my_science/Calculations/random/disangles3.txt'\n",
    "random_distr = np.loadtxt(filename)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-31T19:24:39.118825Z",
     "start_time": "2024-03-31T19:24:39.107327Z"
    }
   },
   "id": "36fec0f8958e062d"
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 800x600 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Visualisation of the analytical (Mackenzie) MDF and the corresponding considered (with a specific number of bins) random distribution\n",
    "\n",
    "ax = sns.kdeplot(random_distr)\n",
    "ax.hist(random_distr, bins=bins, histtype='step', density=True)\n",
    "ax.set_title('Random distribution')\n",
    "plt.show()\n",
    "\n",
    "Q_random, _ = np.histogram(random_distr, bins=bins)\n",
    "Q_random = Q_random / Q_random.sum()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-31T19:24:40.197027Z",
     "start_time": "2024-03-31T19:24:39.711265Z"
    }
   },
   "id": "3fe96ced2e55745f"
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-31T19:24:42.022471Z",
     "start_time": "2024-03-31T19:24:42.010658Z"
    }
   },
   "id": "64ac138e03b85518"
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "outputs": [],
   "source": [
    " htp1.2"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-31T19:24:46.679964Z",
     "start_time": "2024-03-31T19:24:46.664568Z"
    }
   },
   "id": "ca395c33d8f63508"
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "20:24:47 Error reading theta from file /Users/user/Dropbox/OFFICE/my_science/PCCs/pass4.stedge\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class CellComplex> 2D\n",
      "20568 vertices\n",
      "30850 edges\n",
      "10283 faces\n"
     ]
    },
    {
     "data": {
      "text/plain": "0.3"
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Set the specific tessellation as a Neper output (*.tess file)\n",
    "\n",
    "filename = '/Users/user/Dropbox/OFFICE/my_science/PCCs/pass4.tess'\n",
    "cell_complex = CellComplex.from_tess_file(filename, with_theta=True)\n",
    "print(cell_complex)\n",
    "\n",
    "cell_complex.set_theta_from_ori()\n",
    "cell_complex.load_time"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-31T19:25:24.006198Z",
     "start_time": "2024-03-31T19:24:47.552945Z"
    }
   },
   "id": "62c7063a39f9bb76"
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10283/10283 [00:40<00:00, 250.95it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10283/10283 [01:28<00:00, 116.26it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10283/10283 [02:38<00:00, 64.77it/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10283/10283 [27:27<00:00,  6.24it/s]  \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10283/10283 [04:59<00:00, 34.36it/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10283/10283 [06:42<00:00, 25.55it/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10283/10283 [39:31<00:00,  4.34it/s]   \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10283/10283 [09:41<00:00, 17.68it/s] \n"
     ]
    }
   ],
   "source": [
    "## (!) Calculation of disorientation distributions for all the 'k-neighbours' of each grain in the range k = [1,max_order]\n",
    "\n",
    "disangles = {}\n",
    "\n",
    "for i in range(1, max_order + 1):    \n",
    "    print('Order of a grain neighbours k = ', i)\n",
    "    cell_complex.find_neighbors_of_order(i)\n",
    "    disangles[i] = cell_complex.get_neighbor_dis_angles(i)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-31T01:36:23.235130Z",
     "start_time": "2024-03-31T00:03:09.786578Z"
    }
   },
   "id": "4db9a1890f3fbcdb"
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'dirname' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m",
      "\u001B[0;31mNameError\u001B[0m                                 Traceback (most recent call last)",
      "Cell \u001B[0;32mIn[62], line 5\u001B[0m\n\u001B[1;32m      1\u001B[0m \u001B[38;5;66;03m#title = 'HPT2022/hpt1.2'\u001B[39;00m\n\u001B[1;32m      2\u001B[0m \u001B[38;5;66;03m#dirname = '/Users/user/Dropbox/OFFICE/my_science/Calculations/hpt1/'\u001B[39;00m\n\u001B[1;32m      4\u001B[0m \u001B[38;5;28;01mfor\u001B[39;00m i \u001B[38;5;129;01min\u001B[39;00m \u001B[38;5;28mrange\u001B[39m(\u001B[38;5;241m1\u001B[39m, max_order \u001B[38;5;241m+\u001B[39m \u001B[38;5;241m1\u001B[39m):\n\u001B[0;32m----> 5\u001B[0m     filename \u001B[38;5;241m=\u001B[39m os\u001B[38;5;241m.\u001B[39mpath\u001B[38;5;241m.\u001B[39mjoin(dirname, \u001B[38;5;124mf\u001B[39m\u001B[38;5;124m'\u001B[39m\u001B[38;5;124mdisangles\u001B[39m\u001B[38;5;132;01m{\u001B[39;00mi\u001B[38;5;132;01m}\u001B[39;00m\u001B[38;5;124m.txt\u001B[39m\u001B[38;5;124m'\u001B[39m)\n\u001B[1;32m      6\u001B[0m     disangles[i] \u001B[38;5;241m=\u001B[39m np\u001B[38;5;241m.\u001B[39mloadtxt(filename)\n",
      "\u001B[0;31mNameError\u001B[0m: name 'dirname' is not defined"
     ]
    }
   ],
   "source": [
    "# Alternative scheme (if the disorientation are already computed and can be read from file)\n",
    "\n",
    "#title = 'HPT2022/hpt1.2'\n",
    "#dirname = '/Users/user/Dropbox/OFFICE/my_science/Calculations/hpt1/'\n",
    "\n",
    "for i in range(1, max_order + 1):\n",
    "    filename = os.path.join(dirname, f'disangles{i}.txt')\n",
    "    disangles[i] = np.loadtxt(filename)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-31T09:59:39.184785Z",
     "start_time": "2024-03-31T09:59:39.160418Z"
    }
   },
   "id": "53b4dd80fdf37177"
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'disangles' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m",
      "\u001B[0;31mNameError\u001B[0m                                 Traceback (most recent call last)",
      "Cell \u001B[0;32mIn[13], line 2\u001B[0m\n\u001B[1;32m      1\u001B[0m \u001B[38;5;28;01mfor\u001B[39;00m i \u001B[38;5;129;01min\u001B[39;00m \u001B[38;5;28mrange\u001B[39m(\u001B[38;5;241m1\u001B[39m, max_order \u001B[38;5;241m+\u001B[39m \u001B[38;5;241m1\u001B[39m):\n\u001B[0;32m----> 2\u001B[0m     plt\u001B[38;5;241m.\u001B[39mhist(disangles[i], bins\u001B[38;5;241m=\u001B[39mbins, density\u001B[38;5;241m=\u001B[39m\u001B[38;5;28;01mTrue\u001B[39;00m, histtype\u001B[38;5;241m=\u001B[39m\u001B[38;5;124m'\u001B[39m\u001B[38;5;124mstep\u001B[39m\u001B[38;5;124m'\u001B[39m, label\u001B[38;5;241m=\u001B[39m\u001B[38;5;28mstr\u001B[39m(i))\n\u001B[1;32m      3\u001B[0m plt\u001B[38;5;241m.\u001B[39mhist(random_distr, bins\u001B[38;5;241m=\u001B[39mbins, density\u001B[38;5;241m=\u001B[39m\u001B[38;5;28;01mTrue\u001B[39;00m, histtype\u001B[38;5;241m=\u001B[39m\u001B[38;5;124m'\u001B[39m\u001B[38;5;124mstep\u001B[39m\u001B[38;5;124m'\u001B[39m, label\u001B[38;5;241m=\u001B[39m\u001B[38;5;124m'\u001B[39m\u001B[38;5;124mbaseline\u001B[39m\u001B[38;5;124m'\u001B[39m)\n\u001B[1;32m      4\u001B[0m plt\u001B[38;5;241m.\u001B[39mlegend()\n",
      "\u001B[0;31mNameError\u001B[0m: name 'disangles' is not defined"
     ]
    }
   ],
   "source": [
    "## Visualisation of the MDF for all the computed grain k-neighbours in the range k = [1,max_order] for a given number of 'bins'\n",
    "\n",
    "for i in range(1, max_order + 1):\n",
    "    plt.hist(disangles[i], bins=bins, density=True, histtype='step', label=str(i))\n",
    "plt.hist(random_distr, bins=bins, density=True, histtype='step', label='baseline')\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-31T19:25:24.409850Z",
     "start_time": "2024-03-31T19:25:24.008696Z"
    }
   },
   "id": "4abd6597fab5069a"
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Is difference from random significant?\n",
      "1 30537 0.0 True\n",
      "2 69582 0.0 True\n",
      "3 119255 0.0 True\n",
      "4 177434 0.0 True\n",
      "5 242649 0.0 True\n",
      "6 313747 0.0 True\n",
      "7 388590 1.0 False\n",
      "8 465535 1.0 False\n"
     ]
    }
   ],
   "source": [
    "## Check of statistical significance of the deviations from the random distribution (MDF)\n",
    "\n",
    "print('Is difference from random significant?')\n",
    "for i in range(1, max_order + 1):\n",
    "    ns, _ = np.histogram(disangles[i], bins=bins)\n",
    "    ms, _ = np.histogram(random_distr, bins=bins)\n",
    "    _, pvalue = matutils._check_chi2(ns, ms)\n",
    "    print(i, len(disangles[i]), pvalue, pvalue < 0.001)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-31T10:00:31.362168Z",
     "start_time": "2024-03-31T10:00:31.146214Z"
    }
   },
   "id": "7d59d7f8191ae534"
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 0.378\n",
      "2 0.288\n",
      "3 0.221\n",
      "4 0.179\n",
      "5 0.146\n",
      "6 0.123\n",
      "7 0.108\n",
      "8 0.095\n"
     ]
    }
   ],
   "source": [
    "## (!) Calculation of the Hellinger distances of the considered experimental distribution (MDF) for k-order neighbours from the random distriburion \n",
    "\n",
    "distance = []\n",
    "x = []\n",
    "\n",
    "Q = Q_random\n",
    "\n",
    "for i in range(1, max_order + 1):\n",
    "    P, _ = np.histogram(disangles[i], bins=bins)\n",
    "    P = P / P.sum()\n",
    "    d = matutils._hellinger(P, Q)\n",
    "    x.append(i)\n",
    "    distance.append(d)\n",
    "    print(i, round(d, 3))\n",
    "\n",
    "distance1 = distance"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-31T10:00:34.378437Z",
     "start_time": "2024-03-31T10:00:34.222059Z"
    }
   },
   "id": "bebd160da88678c0"
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 800x600 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Graph of the Hellinger distances as function of a neighbour order 'k'\n",
    "\n",
    "plt.plot(x, distance)\n",
    "# plt.title(title + ', Hellinger distance from random')\n",
    "plt.xlabel('neighbour order')\n",
    "plt.ylabel('distance')\n",
    "plt.xticks(x)\n",
    "# plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-31T10:00:50.095860Z",
     "start_time": "2024-03-31T10:00:50.028137Z"
    }
   },
   "id": "3968626565baef88"
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "outputs": [],
   "source": [
    "## hpt3"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-22T09:49:47.056726Z",
     "start_time": "2024-03-22T09:49:47.046468Z"
    }
   },
   "id": "25fb33ef5ee42e45"
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 800x600 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "title = 'HPT2022/hpt3'\n",
    "dirname = '/Users/user/Dropbox/OFFICE/my_science/Calculations/hpt3/'\n",
    "\n",
    "disangles = {}\n",
    "for i in range(1, max_order + 1):\n",
    "    filename = os.path.join(dirname, f'disangles{i}.txt')\n",
    "    disangles[i] = np.loadtxt(filename)\n",
    "\n",
    "for i in range(1, max_order + 1):\n",
    "    plt.hist(disangles[i], bins=bins, density=True, histtype='step', label=str(i))\n",
    "plt.hist(random_distr, bins=bins, density=True, histtype='step', label='baseline')\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-22T09:49:48.066949Z",
     "start_time": "2024-03-22T09:49:47.495494Z"
    }
   },
   "id": "ac577bb74f90e31b"
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Is difference from random significant?\n",
      "1 102851 0.0 True\n",
      "2 225697 0.0 True\n",
      "3 364050 0.0 True\n",
      "4 510261 0.0 True\n",
      "5 659600 0.0 True\n",
      "6 810239 0.0 True\n",
      "7 961060 0.0 True\n",
      "8 1111434 0.0 True\n"
     ]
    }
   ],
   "source": [
    "print('Is difference from random significant?')\n",
    "for i in range(1, max_order + 1):\n",
    "    ns, _ = np.histogram(disangles[i], bins=bins)\n",
    "    ms, _ = np.histogram(random_distr, bins=bins)\n",
    "    _, pvalue = matutils._check_chi2(ns, ms)\n",
    "    print(i, len(disangles[i]), pvalue, pvalue < 0.001)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-22T09:49:48.908492Z",
     "start_time": "2024-03-22T09:49:48.564736Z"
    }
   },
   "id": "e423599f43b7f9e9"
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 0.038\n",
      "2 0.032\n",
      "3 0.024\n",
      "4 0.022\n",
      "5 0.022\n",
      "6 0.02\n",
      "7 0.021\n",
      "8 0.02\n"
     ]
    }
   ],
   "source": [
    "distance = []\n",
    "x = []\n",
    "\n",
    "Q = Q_random\n",
    "\n",
    "for i in range(1, max_order + 1):\n",
    "    P, _ = np.histogram(disangles[i], bins=bins)\n",
    "    P = P / P.sum()\n",
    "    d = matutils._hellinger(P, Q)\n",
    "    x.append(i)\n",
    "    distance.append(d)\n",
    "    print(i, round(d, 3))\n",
    "\n",
    "distance3 = distance"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-22T09:49:50.837518Z",
     "start_time": "2024-03-22T09:49:50.550057Z"
    }
   },
   "id": "896c61a25bd675af"
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 800x600 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, distance)\n",
    "plt.title(title + ', Hellinger distance from random')\n",
    "plt.xlabel('neighbour order')\n",
    "plt.ylabel('distance')\n",
    "plt.xticks(x)\n",
    "# plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-22T09:47:29.009285Z",
     "start_time": "2024-03-22T09:47:28.936452Z"
    }
   },
   "id": "d329d735752b595e"
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 800x600 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.show()\n",
    "plt.plot(x + [8], distance1, label='hpt1.2')\n",
    "plt.plot(x, distance3, label='hpt3')\n",
    "plt.title('HPT2022' + ', Hellinger distance from random')\n",
    "plt.xlabel('order')\n",
    "plt.ylabel('distance')\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-22T09:47:30.844138Z",
     "start_time": "2024-03-22T09:47:30.764825Z"
    }
   },
   "id": "7c9fdeca4c074170"
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "outputs": [],
   "source": [
    "## 01Cr-01Zr Pass4"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-21T23:08:28.282055Z",
     "start_time": "2024-03-21T23:08:28.271172Z"
    }
   },
   "id": "2a56867353d91f4d"
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 800x600 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "title = 'new ECAP2022/Cu_01Cr_01Zr/pass4'\n",
    "dirname = '/Users/user/Dropbox/OFFICE/my_science/Calculations/Cu01Cr01Zr_Pass4/'\n",
    "\n",
    "disangles = {}\n",
    "for i in range(1, max_order + 1):\n",
    "    filename = os.path.join(dirname, f'disangles{i}.txt')\n",
    "    disangles[i] = np.loadtxt(filename)\n",
    "\n",
    "for i in range(1, max_order + 1):\n",
    "    plt.hist(disangles[i], bins=bins, density=True, histtype='step', label=str(i))\n",
    "plt.hist(random_distr, bins=bins, density=True, histtype='step', label='baseline')\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-21T23:08:29.157420Z",
     "start_time": "2024-03-21T23:08:28.959143Z"
    }
   },
   "id": "aa89518a934844dd"
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Is difference from random significant?\n",
      "1 0.0 True\n",
      "2 0.0 True\n",
      "3 1.8607402285653052e-09 True\n",
      "4 3.548528137997664e-11 True\n",
      "5 2.6022204993370046e-05 True\n",
      "6 3.2193339860597803e-06 True\n",
      "7 0.0044890111021357315 False\n",
      "8 0.25573100171424434 False\n"
     ]
    }
   ],
   "source": [
    "print('Is difference from random significant?')\n",
    "for i in range(1, max_order + 1):\n",
    "    ns, _ = np.histogram(disangles[i], bins=bins)\n",
    "    ms, _ = np.histogram(random_distr, bins=bins)\n",
    "    _, pvalue = matutils._check_chi2(ns, ms)\n",
    "    print(i, pvalue, pvalue < 0.001)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-21T23:08:31.553632Z",
     "start_time": "2024-03-21T23:08:31.489018Z"
    }
   },
   "id": "cdac1aee78721e12"
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 0.1\n",
      "2 0.043\n",
      "3 0.026\n",
      "4 0.025\n",
      "5 0.015\n",
      "6 0.015\n",
      "7 0.009\n",
      "8 0.004\n"
     ]
    }
   ],
   "source": [
    "distance = []\n",
    "x = []\n",
    "\n",
    "Q = Q_random\n",
    "\n",
    "for i in range(1, max_order + 1):\n",
    "    P, _ = np.histogram(disangles[i], bins=bins)\n",
    "    P = P / P.sum()\n",
    "    d = matutils._hellinger(P, Q)\n",
    "    x.append(i)\n",
    "    distance.append(d)\n",
    "    print(i, round(d, 3))\n",
    "\n",
    "distance4 = distance"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-21T23:08:47.757963Z",
     "start_time": "2024-03-21T23:08:47.744086Z"
    }
   },
   "id": "38e034d708894519"
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 800x600 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, distance)\n",
    "plt.title(title + ', Hellinger distance from random')\n",
    "plt.xlabel('neighbour order')\n",
    "plt.ylabel('distance')\n",
    "plt.xticks(x)\n",
    "# plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-03-21T23:08:34.705872Z",
     "start_time": "2024-03-21T23:08:34.643633Z"
    }
   },
   "id": "d1b0bf36830aaf00"
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false
   },
   "id": "a763509ca725406f"
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}