{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Computing Wasserstein and Bottleneck Distances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ripser import ripser\n",
    "from teaspoon.MakeData.PointCloud import Torus, Annulus\n",
    "import numpy as np\n",
    "from teaspoon.TDA.Distance import wassersteinDist, bottleneckDist\n",
    "numPts = 500\n",
    "seed = 0\n",
    "\n",
    "# Generate Torus\n",
    "t = Torus(N=numPts,seed = seed)\n",
    "\n",
    "# Generate Annulus\n",
    "a = Annulus(N=numPts,seed = seed)\n",
    "\n",
    "# Compute persistence diagrams\n",
    "PD1 = ripser(t,2)['dgms'][1]\n",
    "PD2 = ripser(a,1)['dgms'][1]\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8922819954736267"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wassersteinDist(PD1,PD2,p=2,q=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.6366934925317764,\n",
       " array([[ 0.00000000e+00, -1.00000000e+00,  4.00471091e-02],\n",
       "        [ 1.00000000e+00, -1.00000000e+00,  2.71813273e-02],\n",
       "        [ 2.00000000e+00, -1.00000000e+00,  1.37364864e-02],\n",
       "        [ 3.00000000e+00,  1.00000000e+00,  6.25133872e-01],\n",
       "        [ 4.00000000e+00,  4.00000000e+00,  6.24991775e-01],\n",
       "        [ 5.00000000e+00,  1.20000000e+01,  6.10377252e-01],\n",
       "        [ 6.00000000e+00,  2.40000000e+01,  6.14972815e-01],\n",
       "        [ 7.00000000e+00,  6.00000000e+00,  5.94342589e-01],\n",
       "        [ 8.00000000e+00,  2.30000000e+01,  5.70441499e-01],\n",
       "        [ 9.00000000e+00,  6.40000000e+01,  6.22471675e-01],\n",
       "        [ 1.00000000e+01,  3.70000000e+01,  5.74341476e-01],\n",
       "        [ 1.10000000e+01,  2.10000000e+01,  5.94332188e-01],\n",
       "        [ 1.20000000e+01,  7.90000000e+01,  6.01736724e-01],\n",
       "        [ 1.30000000e+01,  4.70000000e+01,  5.61174288e-01],\n",
       "        [ 1.40000000e+01,  6.80000000e+01,  6.19526848e-01],\n",
       "        [ 1.50000000e+01,  5.90000000e+01,  5.93475059e-01],\n",
       "        [ 1.60000000e+01,  1.40000000e+01,  6.12821907e-01],\n",
       "        [ 1.70000000e+01,  3.60000000e+01,  6.04333013e-01],\n",
       "        [ 1.80000000e+01,  5.80000000e+01,  5.69075733e-01],\n",
       "        [ 1.90000000e+01,  5.00000000e+00,  6.35556936e-01],\n",
       "        [ 2.00000000e+01,  2.80000000e+01,  5.91972291e-01],\n",
       "        [ 2.10000000e+01,  5.00000000e+01,  5.05411237e-01],\n",
       "        [ 2.20000000e+01,  5.20000000e+01,  4.91183102e-01],\n",
       "        [ 2.30000000e+01, -1.00000000e+00,  1.53810859e-01],\n",
       "        [ 2.40000000e+01,  8.60000000e+01,  5.02688169e-01],\n",
       "        [ 2.50000000e+01,  8.80000000e+01,  5.37646309e-01],\n",
       "        [ 2.60000000e+01,  4.10000000e+01,  4.85158443e-01],\n",
       "        [ 2.70000000e+01,  1.02000000e+02,  5.62547147e-01],\n",
       "        [ 2.80000000e+01,  7.40000000e+01,  4.81191859e-01],\n",
       "        [ 2.90000000e+01,  4.40000000e+01,  5.49388498e-01],\n",
       "        [ 3.00000000e+01,  1.70000000e+01,  4.69869703e-01],\n",
       "        [ 3.10000000e+01,  8.50000000e+01,  5.79165190e-01],\n",
       "        [ 3.20000000e+01,  0.00000000e+00,  3.45806956e-01],\n",
       "        [ 3.30000000e+01,  8.30000000e+01,  4.90191489e-01],\n",
       "        [ 3.40000000e+01,  7.00000000e+00,  5.50218254e-01],\n",
       "        [ 3.50000000e+01,  4.90000000e+01,  5.08215398e-01],\n",
       "        [ 3.60000000e+01,  4.00000000e+01,  4.91077721e-01],\n",
       "        [ 3.70000000e+01,  9.40000000e+01,  6.36319071e-01],\n",
       "        [ 3.80000000e+01,  8.40000000e+01,  4.37877417e-01],\n",
       "        [ 3.90000000e+01,  1.11000000e+02,  5.28377473e-01],\n",
       "        [ 4.00000000e+01,  2.00000000e+00,  4.88982797e-01],\n",
       "        [ 4.10000000e+01,  2.20000000e+01,  4.26122889e-01],\n",
       "        [ 4.20000000e+01, -1.00000000e+00,  2.01255441e-01],\n",
       "        [ 4.30000000e+01,  1.08000000e+02,  4.98728067e-01],\n",
       "        [ 4.40000000e+01,  2.60000000e+01,  6.21646851e-01],\n",
       "        [ 4.50000000e+01, -1.00000000e+00,  2.30730712e-01],\n",
       "        [ 4.60000000e+01,  8.00000000e+01,  5.58013529e-01],\n",
       "        [ 4.70000000e+01,  7.50000000e+01,  4.05672327e-01],\n",
       "        [ 4.80000000e+01,  1.00000000e+02,  5.63187107e-01],\n",
       "        [ 4.90000000e+01, -1.00000000e+00,  1.55224830e-01],\n",
       "        [ 5.00000000e+01,  4.50000000e+01,  6.23585433e-01],\n",
       "        [ 5.10000000e+01,  9.00000000e+00,  6.30193621e-01],\n",
       "        [ 5.20000000e+01,  5.40000000e+01,  3.58591825e-01],\n",
       "        [ 5.30000000e+01,  1.30000000e+01,  5.82507074e-01],\n",
       "        [ 5.40000000e+01,  1.50000000e+01,  2.93366134e-01],\n",
       "        [ 5.50000000e+01, -1.00000000e+00,  1.84884369e-02],\n",
       "        [ 5.60000000e+01, -1.00000000e+00,  8.92637074e-02],\n",
       "        [ 5.70000000e+01,  1.00000000e+01,  5.54640710e-01],\n",
       "        [ 5.80000000e+01,  4.20000000e+01,  3.44508752e-01],\n",
       "        [ 5.90000000e+01, -1.00000000e+00,  1.84549183e-01],\n",
       "        [ 6.00000000e+01,  6.20000000e+01,  6.24789238e-01],\n",
       "        [ 6.10000000e+01, -1.00000000e+00,  1.89112216e-01],\n",
       "        [ 6.20000000e+01, -1.00000000e+00,  9.76866484e-03],\n",
       "        [ 6.30000000e+01, -1.00000000e+00,  3.27083468e-03],\n",
       "        [ 6.40000000e+01, -1.00000000e+00,  3.15819949e-01],\n",
       "        [ 6.50000000e+01,  8.90000000e+01,  4.51657131e-01],\n",
       "        [ 6.60000000e+01, -1.00000000e+00,  2.99509466e-02],\n",
       "        [ 6.70000000e+01,  1.60000000e+01,  3.92686695e-01],\n",
       "        [ 6.80000000e+01, -1.00000000e+00,  5.61060607e-02],\n",
       "        [ 6.90000000e+01,  3.50000000e+01,  5.68416148e-01],\n",
       "        [ 7.00000000e+01,  1.10000000e+01,  3.08061302e-01],\n",
       "        [ 7.10000000e+01,  2.70000000e+01,  3.48432913e-01],\n",
       "        [ 7.20000000e+01, -1.00000000e+00,  2.18237072e-01],\n",
       "        [ 7.30000000e+01, -1.00000000e+00,  2.49618351e-01],\n",
       "        [ 7.40000000e+01,  1.07000000e+02,  4.26221788e-01],\n",
       "        [ 7.50000000e+01,  1.04000000e+02,  5.78848407e-01],\n",
       "        [ 7.60000000e+01, -1.00000000e+00,  1.54110909e-01],\n",
       "        [ 7.70000000e+01,  2.90000000e+01,  2.80739784e-01],\n",
       "        [ 7.80000000e+01, -1.00000000e+00,  2.31105447e-01],\n",
       "        [ 7.90000000e+01,  1.80000000e+01,  2.53880560e-01],\n",
       "        [ 8.00000000e+01, -1.00000000e+00,  1.22905701e-01],\n",
       "        [ 8.10000000e+01, -1.00000000e+00,  2.65246928e-02],\n",
       "        [ 8.20000000e+01, -1.00000000e+00,  1.52449235e-01],\n",
       "        [ 8.30000000e+01,  1.06000000e+02,  3.73621762e-01],\n",
       "        [ 8.40000000e+01,  3.00000000e+00,  5.06627142e-01],\n",
       "        [ 8.50000000e+01,  4.60000000e+01,  4.36542779e-01],\n",
       "        [ 8.60000000e+01, -1.00000000e+00,  2.92968094e-01],\n",
       "        [ 8.70000000e+01,  9.30000000e+01,  3.54303300e-01],\n",
       "        [ 8.80000000e+01,  8.00000000e+00,  5.84330589e-01],\n",
       "        [ 8.90000000e+01, -1.00000000e+00,  2.52512455e-01],\n",
       "        [ 9.00000000e+01, -1.00000000e+00,  2.74253979e-01],\n",
       "        [ 9.10000000e+01, -1.00000000e+00,  6.36693493e-01],\n",
       "        [ 9.20000000e+01, -1.00000000e+00,  7.14935958e-02],\n",
       "        [ 9.30000000e+01, -1.00000000e+00,  1.20996982e-02],\n",
       "        [ 9.40000000e+01, -1.00000000e+00,  2.99180150e-02],\n",
       "        [ 9.50000000e+01, -1.00000000e+00,  3.11482698e-02],\n",
       "        [ 9.60000000e+01,  6.50000000e+01,  2.65198678e-01],\n",
       "        [ 9.70000000e+01,  1.16000000e+02,  3.37533318e-01],\n",
       "        [ 9.80000000e+01,  1.12000000e+02,  3.94425884e-01],\n",
       "        [ 9.90000000e+01,  5.70000000e+01,  4.30781990e-01],\n",
       "        [ 1.00000000e+02, -1.00000000e+00,  1.36743784e-02],\n",
       "        [ 1.01000000e+02,  3.00000000e+01,  3.20468366e-01],\n",
       "        [ 1.02000000e+02,  1.01000000e+02,  4.99496475e-01],\n",
       "        [ 1.03000000e+02, -1.00000000e+00,  1.21596754e-02],\n",
       "        [ 1.04000000e+02, -1.00000000e+00,  1.41060799e-02],\n",
       "        [ 1.05000000e+02,  2.50000000e+01,  1.75237477e-01],\n",
       "        [ 1.06000000e+02, -1.00000000e+00,  6.92397356e-02],\n",
       "        [ 1.07000000e+02,  8.20000000e+01,  5.11952758e-01],\n",
       "        [ 1.08000000e+02,  5.60000000e+01,  2.13363960e-01],\n",
       "        [ 1.09000000e+02, -1.00000000e+00,  6.39622211e-02],\n",
       "        [ 1.10000000e+02, -1.00000000e+00,  3.37317288e-02],\n",
       "        [ 1.11000000e+02,  1.17000000e+02,  4.30798046e-01],\n",
       "        [ 1.12000000e+02, -1.00000000e+00,  7.26116598e-02],\n",
       "        [ 1.13000000e+02,  7.70000000e+01,  2.68923864e-01],\n",
       "        [ 1.14000000e+02,  2.00000000e+01,  1.49338126e-01],\n",
       "        [ 1.15000000e+02, -1.00000000e+00,  1.34231299e-02],\n",
       "        [ 1.16000000e+02,  1.13000000e+02,  2.79534213e-01],\n",
       "        [ 1.17000000e+02,  5.50000000e+01,  2.12662250e-01],\n",
       "        [ 1.18000000e+02,  3.30000000e+01,  1.71612278e-01],\n",
       "        [ 1.19000000e+02,  4.30000000e+01,  2.26397738e-01],\n",
       "        [ 1.20000000e+02,  6.70000000e+01,  2.63867706e-01],\n",
       "        [ 1.21000000e+02,  1.90000000e+01,  1.80421382e-01],\n",
       "        [ 1.22000000e+02, -1.00000000e+00,  2.56633759e-02],\n",
       "        [ 1.23000000e+02, -1.00000000e+00,  3.68491560e-02],\n",
       "        [ 1.24000000e+02, -1.00000000e+00,  2.47931331e-02],\n",
       "        [ 1.25000000e+02, -1.00000000e+00,  1.76113844e-03],\n",
       "        [ 1.26000000e+02, -1.00000000e+00,  6.34832680e-03],\n",
       "        [ 1.27000000e+02,  6.10000000e+01,  1.50503203e-01],\n",
       "        [ 1.28000000e+02, -1.00000000e+00,  2.19387710e-02],\n",
       "        [ 1.29000000e+02,  5.30000000e+01,  1.59247160e-01],\n",
       "        [ 1.30000000e+02, -1.00000000e+00,  1.22604668e-02],\n",
       "        [ 1.31000000e+02,  4.80000000e+01,  1.00676760e-01],\n",
       "        [ 1.32000000e+02,  3.40000000e+01,  5.09298742e-02],\n",
       "        [ 1.33000000e+02,  3.80000000e+01,  6.54186010e-02],\n",
       "        [ 1.34000000e+02,  6.90000000e+01,  7.37212300e-02],\n",
       "        [ 1.35000000e+02,  3.10000000e+01,  4.78426814e-02],\n",
       "        [-1.00000000e+00,  3.20000000e+01,  8.66083801e-03],\n",
       "        [-1.00000000e+00,  3.90000000e+01,  3.12919617e-02],\n",
       "        [-1.00000000e+00,  5.10000000e+01,  4.13046703e-02],\n",
       "        [-1.00000000e+00,  6.00000000e+01,  3.59383970e-02],\n",
       "        [-1.00000000e+00,  6.30000000e+01,  6.48078173e-02],\n",
       "        [-1.00000000e+00,  6.60000000e+01,  4.32454273e-02],\n",
       "        [-1.00000000e+00,  7.00000000e+01,  4.45385501e-02],\n",
       "        [-1.00000000e+00,  7.10000000e+01,  2.49823928e-03],\n",
       "        [-1.00000000e+00,  7.20000000e+01,  7.58492127e-02],\n",
       "        [-1.00000000e+00,  7.30000000e+01,  5.37747145e-03],\n",
       "        [-1.00000000e+00,  7.60000000e+01,  4.18755412e-03],\n",
       "        [-1.00000000e+00,  7.80000000e+01,  2.83078104e-03],\n",
       "        [-1.00000000e+00,  8.10000000e+01,  5.16147166e-03],\n",
       "        [-1.00000000e+00,  8.70000000e+01,  6.52091205e-03],\n",
       "        [-1.00000000e+00,  9.00000000e+01,  1.11295059e-02],\n",
       "        [-1.00000000e+00,  9.10000000e+01,  1.12642422e-02],\n",
       "        [-1.00000000e+00,  9.20000000e+01,  2.80567855e-02],\n",
       "        [-1.00000000e+00,  9.50000000e+01,  1.24959499e-02],\n",
       "        [-1.00000000e+00,  9.60000000e+01,  2.50186846e-02],\n",
       "        [-1.00000000e+00,  9.70000000e+01,  4.74356934e-02],\n",
       "        [-1.00000000e+00,  9.80000000e+01,  8.76357406e-03],\n",
       "        [-1.00000000e+00,  9.90000000e+01,  9.97943431e-03],\n",
       "        [-1.00000000e+00,  1.03000000e+02,  3.08658928e-03],\n",
       "        [-1.00000000e+00,  1.05000000e+02,  8.10882449e-03],\n",
       "        [-1.00000000e+00,  1.09000000e+02,  9.55005363e-03],\n",
       "        [-1.00000000e+00,  1.10000000e+02,  8.60956684e-03],\n",
       "        [-1.00000000e+00,  1.14000000e+02,  1.03326328e-02],\n",
       "        [-1.00000000e+00,  1.15000000e+02,  1.48827359e-02]]))"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bottleneckDist(PD1, PD2, matching = True, plot = True)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "env",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "11b1644334321e87102cd5694058ba8626a3907e9e14dc84c97fba2485a83109"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}