{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Barycenter of MNIST Digits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "from mmot import MMOTSolver\n",
    "\n",
    "import numpy as np \n",
    "import matplotlib.pyplot as plt \n",
    "import itertools"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Download and open the MNIST dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "vscode": {
     "languageId": "markdown"
    }
   },
   "outputs": [],
   "source": [
    "import hashlib \n",
    "import os \n",
    "import requests \n",
    "import gzip\n",
    "\n",
    "#fetch data (adapted from https://github.com/geohot/ai-notebooks/blob/master/mnist_from_scratch.ipynb)\n",
    "path='./'\n",
    "def fetch(url):\n",
    "    fp = os.path.join(path, hashlib.md5(url.encode('utf-8')).hexdigest())\n",
    "    if os.path.isfile(fp):\n",
    "        with open(fp, \"rb\") as f:\n",
    "            data = f.read()\n",
    "    else:\n",
    "        with open(fp, \"wb\") as f:\n",
    "            data = requests.get(url).content\n",
    "            f.write(data)\n",
    "    return np.frombuffer(gzip.decompress(data), dtype=np.uint8).copy()\n",
    "\n",
    "digits = fetch(\"http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz\")[0x10:].reshape((-1, 28, 28))\n",
    "labels = fetch(\"http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz\")[8:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot a few samples of the digit we're interested in"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1800x360 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "desired_digit = 3\n",
    "inds = np.where(labels==desired_digit)[0]\n",
    "\n",
    "num_plot = 5\n",
    "fig,axs = plt.subplots(ncols=num_plot, sharey=True, figsize=(num_plot*5,5))\n",
    "for i in range(num_plot):\n",
    "    axs[i].imshow(digits[inds[i],:,:],cmap='Greys')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Extract digits with similar total measure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Grid of size n1 x n2\n",
    "n1 = digits.shape[1]   # x axis\n",
    "n2 = digits.shape[2]   # y axis\n",
    "\n",
    "x, y = np.meshgrid(np.linspace(0.5/n1,1-0.5/n1,n1), np.linspace(0.5/n2,1-0.5/n1,n2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "unroll_node = 0\n",
    "\n",
    "num_digits = 10 \n",
    "sums = np.array([np.sum(digits[i,:,:]) for i in inds])\n",
    "\n",
    "val = np.sum(digits[inds[0],:,:])\n",
    "\n",
    "sorted_inds = inds[np.argsort(np.abs(sums-val))]\n",
    "measures = [digits[sorted_inds[i],:,:]* (n1*n2/np.sum(digits[sorted_inds[i],:,:])) for i in range(num_digits)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the edge list for the barycenter problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "edge_list = []\n",
    "for i in range(num_digits):\n",
    "    for j in range(i+1,num_digits):\n",
    "        edge_list += [[i,j]]\n",
    "\n",
    "weights = np.ones(num_digits)/num_digits\n",
    "prob = MMOTSolver(measures, edge_list, x, y, unroll_node, weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solve the problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration, StepSize,        Cost,        Error,  Line Its\n",
      "next_root 0 =  0\n",
      "next_root 1 =  0\n",
      "next_root 2 =  0\n",
      "next_root 3 =  0\n",
      "next_root 4 =  0\n",
      "next_root 5 =  0\n",
      "next_root 6 =  0\n",
      "next_root 7 =  0\n",
      "next_root 8 =  0\n",
      "        0,   0.0008,  1.2998e-04,   1.0349e+00,         8\n",
      "next_root 0 =  1\n",
      "next_root 0 =  2\n",
      "next_root 0 =  3\n",
      "next_root 0 =  4\n",
      "next_root 0 =  5\n",
      "next_root 0 =  6\n",
      "next_root 0 =  7\n",
      "next_root 0 =  8\n",
      "next_root 0 =  9\n",
      "next_root 1 =  9\n",
      "next_root 0 =  10\n",
      "next_root 1 =  10\n",
      "       10,   0.0012,  1.2499e-03,   1.5150e-01,         1\n",
      "next_root 0 =  11\n",
      "next_root 0 =  12\n",
      "next_root 0 =  13\n",
      "next_root 0 =  14\n",
      "next_root 0 =  15\n",
      "next_root 0 =  16\n",
      "next_root 0 =  17\n",
      "next_root 1 =  17\n",
      "next_root 2 =  17\n",
      "next_root 0 =  18\n",
      "next_root 0 =  19\n",
      "next_root 0 =  20\n",
      "next_root 1 =  20\n",
      "       20,   0.0009,  1.4826e-03,   4.6731e-02,         1\n",
      "next_root 0 =  21\n",
      "next_root 0 =  22\n",
      "next_root 0 =  23\n",
      "next_root 1 =  23\n",
      "next_root 0 =  24\n",
      "next_root 0 =  25\n",
      "next_root 0 =  26\n",
      "next_root 1 =  26\n",
      "next_root 0 =  27\n",
      "next_root 0 =  28\n",
      "next_root 0 =  29\n",
      "next_root 1 =  29\n",
      "next_root 0 =  30\n",
      "       30,   0.0007,  1.5566e-03,   4.0157e-02,         0\n",
      "next_root 0 =  31\n",
      "next_root 0 =  32\n",
      "next_root 1 =  32\n",
      "next_root 0 =  33\n",
      "next_root 0 =  34\n",
      "next_root 0 =  35\n",
      "next_root 0 =  36\n",
      "next_root 1 =  36\n",
      "next_root 0 =  37\n",
      "next_root 0 =  38\n",
      "next_root 0 =  39\n",
      "next_root 1 =  39\n",
      "next_root 0 =  40\n",
      "       40,   0.0006,  1.6275e-03,   4.0973e-02,         0\n",
      "next_root 0 =  41\n",
      "next_root 0 =  42\n",
      "next_root 1 =  42\n",
      "next_root 0 =  43\n",
      "next_root 0 =  44\n",
      "next_root 0 =  45\n",
      "next_root 0 =  0\n",
      "next_root 0 =  1\n",
      "next_root 0 =  2\n",
      "next_root 0 =  3\n",
      "next_root 1 =  3\n",
      "next_root 0 =  4\n",
      "       50,   0.0009,  1.7358e-03,   3.2187e-02,         0\n",
      "next_root 0 =  5\n",
      "next_root 1 =  5\n",
      "next_root 0 =  6\n",
      "next_root 0 =  7\n",
      "next_root 1 =  7\n",
      "next_root 0 =  8\n",
      "next_root 0 =  9\n",
      "next_root 0 =  10\n",
      "next_root 0 =  11\n",
      "next_root 1 =  11\n",
      "next_root 0 =  12\n",
      "next_root 0 =  13\n",
      "next_root 1 =  13\n",
      "next_root 0 =  14\n",
      "       60,   0.0003,  1.7963e-03,   2.8782e-02,         0\n",
      "next_root 0 =  15\n",
      "next_root 0 =  16\n",
      "next_root 0 =  17\n",
      "next_root 0 =  18\n",
      "next_root 0 =  19\n",
      "next_root 1 =  19\n",
      "next_root 0 =  20\n",
      "next_root 0 =  21\n",
      "next_root 0 =  22\n",
      "next_root 1 =  22\n",
      "next_root 0 =  23\n",
      "next_root 0 =  24\n",
      "       70,   0.0005,  1.8271e-03,   2.7783e-02,         0\n",
      "next_root 0 =  25\n",
      "next_root 0 =  26\n",
      "next_root 1 =  26\n",
      "next_root 0 =  27\n",
      "next_root 0 =  28\n",
      "next_root 0 =  29\n",
      "next_root 1 =  29\n",
      "next_root 0 =  30\n",
      "next_root 0 =  31\n",
      "next_root 0 =  32\n",
      "next_root 1 =  32\n",
      "next_root 0 =  33\n",
      "next_root 1 =  33\n",
      "next_root 0 =  34\n",
      "       80,   0.0002,  1.8805e-03,   2.8257e-02,         0\n",
      "next_root 0 =  35\n",
      "next_root 0 =  36\n",
      "next_root 0 =  37\n",
      "next_root 0 =  38\n",
      "next_root 1 =  38\n",
      "next_root 0 =  39\n",
      "next_root 0 =  40\n",
      "next_root 0 =  41\n",
      "next_root 0 =  42\n",
      "next_root 1 =  42\n",
      "next_root 0 =  43\n",
      "next_root 0 =  44\n",
      "       90,   0.0003,  1.9226e-03,   2.9543e-02,         0\n",
      "next_root 0 =  45\n",
      "next_root 0 =  0\n",
      "next_root 1 =  0\n",
      "next_root 0 =  1\n",
      "next_root 1 =  1\n",
      "next_root 0 =  2\n",
      "next_root 0 =  3\n",
      "next_root 0 =  4\n",
      "next_root 0 =  5\n",
      "next_root 1 =  5\n",
      "next_root 0 =  6\n",
      "next_root 0 =  7\n",
      "next_root 1 =  7\n",
      "next_root 0 =  8\n",
      "      100,   0.0001,  1.9420e-03,   2.8192e-02,         0\n",
      "next_root 0 =  9\n",
      "next_root 0 =  10\n",
      "next_root 0 =  11\n",
      "next_root 0 =  12\n",
      "next_root 0 =  13\n",
      "next_root 1 =  13\n",
      "next_root 0 =  14\n",
      "next_root 0 =  15\n",
      "next_root 0 =  16\n",
      "next_root 0 =  17\n",
      "next_root 1 =  17\n",
      "next_root 0 =  18\n",
      "      110,   0.0002,  1.9607e-03,   2.6876e-02,         0\n",
      "next_root 0 =  19\n",
      "next_root 0 =  20\n",
      "next_root 1 =  20\n",
      "next_root 0 =  21\n",
      "next_root 0 =  22\n",
      "next_root 0 =  23\n",
      "next_root 0 =  24\n",
      "next_root 1 =  24\n",
      "next_root 0 =  25\n",
      "next_root 0 =  26\n",
      "next_root 0 =  27\n",
      "next_root 0 =  28\n",
      "next_root 1 =  28\n",
      "      120,   0.0001,  1.9792e-03,   2.6153e-02,         1\n",
      "next_root 0 =  29\n",
      "next_root 0 =  30\n",
      "next_root 0 =  31\n",
      "next_root 0 =  32\n",
      "next_root 1 =  32\n",
      "next_root 0 =  33\n",
      "next_root 1 =  33\n",
      "next_root 0 =  34\n",
      "next_root 0 =  35\n",
      "next_root 0 =  36\n",
      "next_root 0 =  37\n",
      "next_root 0 =  38\n",
      "next_root 1 =  38\n",
      "      130,   0.0001,  1.9903e-03,   2.7401e-02,         1\n",
      "next_root 0 =  39\n",
      "next_root 0 =  40\n",
      "next_root 0 =  41\n",
      "next_root 0 =  42\n",
      "next_root 1 =  42\n",
      "next_root 0 =  43\n",
      "next_root 0 =  44\n",
      "next_root 0 =  45\n",
      "next_root 0 =  0\n",
      "next_root 1 =  0\n",
      "next_root 0 =  1\n",
      "next_root 1 =  1\n",
      "next_root 0 =  2\n",
      "next_root 1 =  2\n",
      "      140,   0.0000,  2.0004e-03,   2.7720e-02,         1\n",
      "next_root 0 =  3\n",
      "next_root 0 =  4\n",
      "next_root 0 =  5\n",
      "next_root 0 =  6\n",
      "next_root 0 =  7\n",
      "next_root 1 =  7\n",
      "next_root 0 =  8\n",
      "next_root 0 =  9\n",
      "next_root 0 =  10\n",
      "next_root 0 =  11\n",
      "next_root 1 =  11\n",
      "next_root 0 =  12\n",
      "      150,   0.0001,  2.0087e-03,   2.7586e-02,         0\n",
      "next_root 0 =  13\n",
      "next_root 0 =  14\n",
      "next_root 0 =  15\n",
      "next_root 1 =  15\n",
      "next_root 0 =  16\n",
      "next_root 0 =  17\n",
      "next_root 0 =  18\n",
      "next_root 0 =  19\n",
      "next_root 0 =  20\n",
      "next_root 1 =  20\n",
      "next_root 0 =  21\n",
      "next_root 0 =  22\n",
      "      160,   0.0001,  2.0155e-03,   2.7085e-02,         0\n",
      "next_root 0 =  23\n",
      "next_root 0 =  24\n",
      "next_root 1 =  24\n",
      "next_root 0 =  25\n",
      "next_root 0 =  26\n",
      "next_root 0 =  27\n",
      "next_root 0 =  28\n",
      "next_root 1 =  28\n",
      "next_root 0 =  29\n",
      "next_root 0 =  30\n",
      "next_root 0 =  31\n",
      "next_root 0 =  32\n",
      "next_root 1 =  32\n",
      "      170,   0.0001,  2.0205e-03,   2.7040e-02,         1\n",
      "next_root 0 =  33\n",
      "next_root 1 =  33\n",
      "next_root 0 =  34\n",
      "next_root 0 =  35\n",
      "next_root 0 =  36\n",
      "next_root 0 =  37\n",
      "next_root 1 =  37\n",
      "next_root 0 =  38\n",
      "next_root 0 =  39\n",
      "next_root 0 =  40\n",
      "next_root 0 =  41\n",
      "next_root 0 =  42\n",
      "next_root 1 =  42\n",
      "      180,   0.0001,  2.0259e-03,   2.7703e-02,         1\n",
      "next_root 0 =  43\n",
      "next_root 0 =  44\n",
      "next_root 0 =  45\n",
      "next_root 0 =  0\n",
      "next_root 1 =  0\n",
      "next_root 0 =  1\n",
      "next_root 1 =  1\n",
      "next_root 0 =  2\n",
      "next_root 1 =  2\n",
      "next_root 0 =  3\n",
      "next_root 0 =  4\n",
      "next_root 0 =  5\n",
      "next_root 1 =  5\n",
      "next_root 0 =  6\n",
      "      190,   0.0000,  2.0300e-03,   2.7548e-02,         0\n",
      "next_root 0 =  7\n",
      "next_root 0 =  8\n",
      "next_root 0 =  9\n",
      "next_root 0 =  10\n",
      "next_root 0 =  11\n",
      "next_root 1 =  11\n",
      "next_root 0 =  12\n",
      "next_root 0 =  13\n",
      "next_root 1 =  13\n",
      "next_root 0 =  14\n",
      "next_root 0 =  15\n",
      "next_root 0 =  16\n",
      "      200,   0.0000,  2.0350e-03,   2.7808e-02,         0\n",
      "next_root 0 =  17\n",
      "next_root 0 =  18\n",
      "next_root 0 =  19\n",
      "next_root 1 =  19\n",
      "next_root 0 =  20\n",
      "next_root 0 =  21\n",
      "next_root 0 =  22\n",
      "next_root 0 =  23\n",
      "next_root 0 =  24\n",
      "next_root 1 =  24\n",
      "next_root 0 =  25\n",
      "next_root 0 =  26\n",
      "next_root 1 =  26\n",
      "      210,   0.0000,  2.0386e-03,   2.7053e-02,         1\n",
      "next_root 0 =  27\n",
      "next_root 0 =  28\n",
      "next_root 0 =  29\n",
      "next_root 1 =  29\n",
      "next_root 0 =  30\n",
      "next_root 0 =  31\n",
      "next_root 0 =  32\n",
      "next_root 1 =  32\n",
      "next_root 0 =  33\n",
      "next_root 0 =  34\n",
      "next_root 0 =  35\n",
      "next_root 0 =  36\n",
      "      220,   0.0000,  2.0425e-03,   2.7091e-02,         0\n",
      "next_root 0 =  37\n",
      "next_root 1 =  37\n",
      "next_root 0 =  38\n",
      "next_root 0 =  39\n",
      "next_root 0 =  40\n",
      "next_root 1 =  40\n",
      "next_root 0 =  41\n",
      "next_root 0 =  42\n",
      "next_root 0 =  43\n",
      "next_root 0 =  44\n",
      "next_root 0 =  45\n",
      "next_root 0 =  0\n",
      "next_root 1 =  0\n",
      "      230,   0.0000,  2.0447e-03,   2.7168e-02,         1\n",
      "next_root 0 =  1\n",
      "next_root 1 =  1\n",
      "next_root 2 =  1\n",
      "next_root 0 =  2\n",
      "next_root 1 =  2\n",
      "next_root 0 =  3\n",
      "next_root 1 =  3\n",
      "next_root 0 =  4\n",
      "next_root 0 =  5\n",
      "next_root 1 =  5\n",
      "next_root 0 =  6\n",
      "next_root 0 =  7\n",
      "next_root 1 =  7\n",
      "next_root 0 =  8\n",
      "next_root 0 =  9\n",
      "next_root 0 =  10\n",
      "      240,   0.0000,  2.0456e-03,   2.7954e-02,         0\n",
      "next_root 0 =  11\n",
      "next_root 1 =  11\n",
      "next_root 0 =  12\n",
      "next_root 0 =  13\n",
      "next_root 1 =  13\n",
      "next_root 0 =  14\n",
      "next_root 0 =  15\n",
      "next_root 1 =  15\n",
      "next_root 0 =  16\n",
      "next_root 0 =  17\n",
      "next_root 0 =  18\n",
      "next_root 0 =  19\n",
      "next_root 1 =  19\n",
      "next_root 0 =  20\n",
      "      250,   0.0000,  2.0472e-03,   2.7679e-02,         0\n",
      "next_root 0 =  21\n",
      "next_root 0 =  22\n",
      "next_root 0 =  23\n",
      "next_root 1 =  23\n",
      "next_root 0 =  24\n",
      "next_root 1 =  24\n",
      "next_root 0 =  25\n",
      "next_root 0 =  26\n",
      "next_root 0 =  27\n",
      "next_root 0 =  28\n",
      "next_root 1 =  28\n",
      "next_root 0 =  29\n",
      "next_root 0 =  30\n",
      "      260,   0.0000,  2.0484e-03,   2.7547e-02,         0\n",
      "next_root 0 =  31\n",
      "next_root 0 =  32\n",
      "next_root 1 =  32\n",
      "next_root 0 =  33\n",
      "next_root 1 =  33\n",
      "next_root 0 =  34\n",
      "next_root 0 =  35\n",
      "next_root 1 =  35\n",
      "next_root 0 =  36\n",
      "next_root 0 =  37\n",
      "next_root 0 =  38\n",
      "next_root 1 =  38\n",
      "next_root 0 =  39\n",
      "next_root 0 =  40\n",
      "      270,   0.0000,  2.0494e-03,   2.7256e-02,         0\n",
      "next_root 0 =  41\n",
      "next_root 0 =  42\n",
      "next_root 1 =  42\n",
      "next_root 0 =  43\n",
      "next_root 0 =  44\n",
      "next_root 0 =  45\n",
      "next_root 0 =  0\n",
      "next_root 1 =  0\n",
      "next_root 0 =  1\n",
      "next_root 1 =  1\n",
      "next_root 2 =  1\n",
      "next_root 0 =  2\n",
      "next_root 1 =  2\n",
      "next_root 2 =  2\n",
      "next_root 0 =  3\n",
      "next_root 1 =  3\n",
      "next_root 0 =  4\n",
      "next_root 1 =  4\n",
      "      280,   0.0000,  2.0503e-03,   2.7424e-02,         1\n",
      "next_root 0 =  5\n",
      "next_root 1 =  5\n",
      "next_root 2 =  5\n",
      "next_root 0 =  6\n",
      "next_root 1 =  6\n",
      "next_root 0 =  7\n",
      "next_root 1 =  7\n",
      "next_root 2 =  7\n",
      "next_root 0 =  8\n",
      "next_root 1 =  8\n",
      "next_root 0 =  9\n",
      "next_root 1 =  9\n",
      "next_root 0 =  10\n",
      "next_root 1 =  10\n",
      "next_root 0 =  11\n",
      "next_root 1 =  11\n",
      "next_root 0 =  12\n",
      "next_root 1 =  12\n",
      "next_root 0 =  13\n",
      "next_root 1 =  13\n",
      "next_root 0 =  14\n",
      "next_root 1 =  14\n",
      "      290,   0.0000,  2.0511e-03,   2.7508e-02,         1\n",
      "next_root 0 =  15\n",
      "next_root 1 =  15\n",
      "next_root 0 =  16\n",
      "next_root 1 =  16\n",
      "next_root 0 =  17\n",
      "next_root 1 =  17\n",
      "next_root 0 =  18\n",
      "next_root 1 =  18\n",
      "next_root 0 =  19\n",
      "next_root 1 =  19\n",
      "next_root 0 =  20\n",
      "next_root 1 =  20\n",
      "next_root 0 =  21\n",
      "next_root 1 =  21\n",
      "next_root 0 =  22\n",
      "next_root 1 =  22\n",
      "next_root 0 =  23\n",
      "next_root 0 =  24\n",
      "next_root 1 =  24\n",
      "      300,   0.0000,  2.0520e-03,   2.7258e-02,         1\n",
      "next_root 0 =  25\n",
      "next_root 0 =  26\n",
      "next_root 1 =  26\n",
      "next_root 0 =  27\n",
      "next_root 1 =  27\n",
      "next_root 0 =  28\n",
      "next_root 1 =  28\n",
      "next_root 0 =  29\n",
      "next_root 1 =  29\n",
      "next_root 0 =  30\n",
      "next_root 1 =  30\n",
      "next_root 0 =  31\n",
      "next_root 0 =  32\n",
      "next_root 1 =  32\n",
      "next_root 2 =  32\n",
      "next_root 0 =  33\n",
      "next_root 1 =  33\n",
      "next_root 2 =  33\n",
      "next_root 0 =  34\n",
      "next_root 1 =  34\n",
      "      310,   0.0000,  2.0527e-03,   2.7769e-02,         1\n",
      "next_root 0 =  35\n",
      "next_root 1 =  35\n",
      "next_root 0 =  36\n",
      "next_root 1 =  36\n",
      "next_root 0 =  37\n",
      "next_root 1 =  37\n",
      "next_root 0 =  38\n",
      "next_root 1 =  38\n",
      "next_root 0 =  39\n",
      "next_root 1 =  39\n",
      "next_root 0 =  40\n",
      "next_root 1 =  40\n",
      "next_root 0 =  41\n",
      "next_root 1 =  41\n",
      "next_root 0 =  42\n",
      "next_root 1 =  42\n",
      "next_root 0 =  43\n",
      "next_root 1 =  43\n",
      "next_root 0 =  44\n",
      "next_root 1 =  44\n",
      "      320,   0.0000,  2.0535e-03,   2.7419e-02,         1\n",
      "next_root 0 =  45\n",
      "next_root 1 =  45\n",
      "next_root 0 =  0\n",
      "next_root 1 =  0\n",
      "next_root 2 =  0\n",
      "next_root 0 =  1\n",
      "next_root 1 =  1\n",
      "next_root 2 =  1\n",
      "next_root 0 =  2\n",
      "next_root 1 =  2\n",
      "next_root 2 =  2\n",
      "next_root 3 =  2\n",
      "next_root 0 =  3\n",
      "next_root 1 =  3\n",
      "next_root 2 =  3\n",
      "next_root 0 =  4\n",
      "next_root 1 =  4\n",
      "next_root 2 =  4\n",
      "next_root 0 =  5\n",
      "next_root 1 =  5\n",
      "next_root 2 =  5\n",
      "next_root 3 =  5\n",
      "next_root 0 =  6\n",
      "next_root 1 =  6\n",
      "next_root 2 =  6\n",
      "next_root 0 =  7\n",
      "next_root 1 =  7\n",
      "next_root 2 =  7\n",
      "next_root 3 =  7\n",
      "next_root 0 =  8\n",
      "next_root 1 =  8\n",
      "next_root 2 =  8\n",
      "      330,   0.0000,  2.0539e-03,   2.7790e-02,         2\n",
      "next_root 0 =  9\n",
      "next_root 1 =  9\n",
      "next_root 2 =  9\n",
      "next_root 0 =  10\n",
      "next_root 1 =  10\n",
      "next_root 2 =  10\n",
      "next_root 0 =  11\n",
      "next_root 1 =  11\n",
      "next_root 2 =  11\n",
      "next_root 0 =  12\n",
      "next_root 1 =  12\n",
      "next_root 2 =  12\n",
      "next_root 0 =  13\n",
      "next_root 1 =  13\n",
      "next_root 2 =  13\n",
      "next_root 0 =  14\n",
      "next_root 1 =  14\n",
      "next_root 2 =  14\n",
      "next_root 0 =  15\n",
      "next_root 1 =  15\n",
      "next_root 2 =  15\n",
      "next_root 0 =  16\n",
      "next_root 1 =  16\n",
      "next_root 2 =  16\n",
      "next_root 0 =  17\n",
      "next_root 1 =  17\n",
      "next_root 2 =  17\n",
      "next_root 0 =  18\n",
      "next_root 1 =  18\n",
      "next_root 2 =  18\n",
      "      340,   0.0000,  2.0544e-03,   2.7167e-02,         2\n",
      "next_root 0 =  19\n",
      "next_root 1 =  19\n",
      "next_root 2 =  19\n",
      "next_root 0 =  20\n",
      "next_root 1 =  20\n",
      "next_root 2 =  20\n",
      "next_root 0 =  21\n",
      "next_root 1 =  21\n",
      "next_root 2 =  21\n",
      "next_root 0 =  22\n",
      "next_root 1 =  22\n",
      "next_root 2 =  22\n",
      "next_root 0 =  23\n",
      "next_root 1 =  23\n",
      "next_root 2 =  23\n",
      "next_root 0 =  24\n",
      "next_root 1 =  24\n",
      "next_root 2 =  24\n",
      "next_root 0 =  25\n",
      "next_root 1 =  25\n",
      "      347,   0.0000,  2.0548e-03,   2.7386e-02,         1\n",
      "Terminating due to small change in objective.\n"
     ]
    }
   ],
   "source": [
    "res = prob.Solve(max_its=10000, step_size=0.2, ftol_abs=1e-9, gtol_abs=1e-3)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1152x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "    \n",
    "fig, axs = plt.subplots(ncols=4,sharex=True,figsize=(16,4))\n",
    "axs[0].plot(res.costs)\n",
    "axs[0].set_title('Dual Objective')\n",
    "axs[0].set_xlabel('Iteration')\n",
    "\n",
    "axs[1].semilogy(res.grad_sq_norms)\n",
    "axs[1].set_title('Squared Norm of Gradient')\n",
    "axs[1].set_xlabel('Iteration')\n",
    "\n",
    "axs[2].semilogy(res.step_sizes)\n",
    "axs[2].set_title('Step Size (after line search)')\n",
    "axs[2].set_xlabel('Iteration')\n",
    "\n",
    "axs[3].plot(res.line_its)\n",
    "axs[3].set_title('Line Search Iterations')\n",
    "axs[3].set_xlabel('Iteration')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute the Barycenter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "bary = prob.Barycenter(res.dual_vars)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the images used and the barycenter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Barycenter')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3168x288 with 11 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "vmax = np.max([np.max(m) for m in measures])\n",
    "fig, axs = plt.subplots(1, num_digits+1, figsize=((num_digits+1)*4,4))\n",
    "for i in range(num_digits):\n",
    "    axs[i].imshow(measures[i], origin='lower', extent=(0,1,0,1), vmin=0, vmax=vmax, cmap='Greys')\n",
    "    axs[i].set_title(\"$\\\\mu_{{ {:0d} }}$\".format(i))\n",
    "    \n",
    "axs[-1].imshow(bary, origin='lower', extent=(0,1,0,1), vmin=0, vmax=vmax, cmap='Greys')\n",
    "axs[-1].set_title('Barycenter')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "545e036c4b32438aced1f6b3c8d38ca151d9c36189e05839cb0aa568fda70ddd"
  },
  "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": "3.10.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}