experiment.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8e6811da-db35-4979-9b35-d7aaed6fa146",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from scipy import sparse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fda93f0a-6877-4c29-ae30-b059b4cebdcd",
   "metadata": {},
   "outputs": [],
   "source": [
    "from em import initialize, em, mle_em, em_bdct, mle_em_with_obj, mle_gd_with_obj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "70c1268b-5c1b-4993-b89c-02172f1b7404",
   "metadata": {},
   "outputs": [],
   "source": [
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8527831-80b0-4a2c-b03f-feb7d7943008",
   "metadata": {},
   "source": [
    "# image 10 by 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "04a57321-3f40-4ed0-be16-0b9f15924940",
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_init(max_step, threshold, sparse, ix=0):\n",
    "    np.random.seed(0)\n",
    "    start = time.time()\n",
    "    y_rand = np.random.poisson(Ax)\n",
    "    # x_initial = np.random.randn(len(x_flat))\n",
    "    print(f\"process: {ix: 2d}, y[:10]: {y_rand[:10]}\")\n",
    "    if sparse:\n",
    "        x_init =  np.linalg.inv((A.T@A).todense())@(A.T@y_rand)\n",
    "    else:\n",
    "        x_init =  np.linalg.inv((A.T@A))@(A.T@y_rand)\n",
    "    x_init = np.array(x_init).flatten()\n",
    "    x_init = np.array([v if v>0.1 else 10 for v in x_init])\n",
    "    x_et, diff, mse, objs, step = mle_em_with_obj(max_step, A, y_rand, x_true=x_flat, threshold=threshold, x_initial=x_init, sparse=sparse)\n",
    "    print(f\"process: {ix: 2d} finished. step: {step: 2d}, mse: {mse: 8.2f}, diff: {diff: 8.2f} time consuming: {time.time() - start: 8.1f} seconds\")\n",
    "    return x_et, diff, mse, objs, step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e965d3cf-e377-4552-a9f1-414f1d94cff4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def run(max_step, threshold, sparse, ix=0):\n",
    "    np.random.seed(0)\n",
    "    start = time.time()\n",
    "    y_rand = np.random.poisson(Ax)\n",
    "    # x_initial = np.random.randn(len(x_flat))\n",
    "    print(f\"process: {ix: 2d}, y[:10]: {y_rand[:10]}\")\n",
    "    x_et, diff, mse, objs, step = mle_em_with_obj(max_step, A, y_rand, x_true=x_flat, threshold=threshold, sparse=sparse)\n",
    "    print(f\"process: {ix: 2d} finished. step: {step: 2d}, mse: {mse: 8.2f}, diff: {diff: 8.2f} time consuming: {time.time() - start: 8.1f} seconds\")\n",
    "    return x_et, diff, mse, objs, step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b0d24b58-c87d-4b7c-a9af-879efb18dfd2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_gd(max_step, threshold, sparse, ix=0, alpha=0.01):\n",
    "    np.random.seed(0)\n",
    "    start = time.time()\n",
    "    y_rand = np.random.poisson(Ax)\n",
    "    # x_initial = np.random.randn(len(x_flat))\n",
    "    print(f\"process: {ix: 2d}, y[:10]: {y_rand[:10]}\")\n",
    "    x_et, diff, mse, objs, step = mle_gd_with_obj(max_step, A, y_rand, x_true=x_flat, threshold=threshold, sparse=sparse, alpha=alpha)\n",
    "    print(f\"process: {ix: 2d} finished. step: {step: 2d}, mse: {mse: 8.2f}, diff: {diff: 8.2f} time consuming: {time.time() - start: 8.1f} seconds\")\n",
    "    return x_et, diff, mse, objs, step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "8e08f665-dce8-4d10-a0fc-0ee3368e98c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_gd_init(max_step, threshold, sparse, ix=0, alpha=0.01):\n",
    "    np.random.seed(0)\n",
    "    start = time.time()\n",
    "    y_rand = np.random.poisson(Ax)\n",
    "    if sparse:\n",
    "        x_init =  np.linalg.inv((A.T@A).todense())@(A.T@y_rand)\n",
    "    else:\n",
    "        x_init =  np.linalg.inv((A.T@A))@(A.T@y_rand)\n",
    "    x_init = np.array(x_init).flatten()\n",
    "    x_init = np.array([v if v>0.1 else 10 for v in x_init])\n",
    "    print(f\"process: {ix: 2d}, y[:10]: {y_rand[:10]}\")\n",
    "    x_et, diff, mse, objs, step = mle_gd_with_obj(max_step, A, y_rand, x_true=x_flat, threshold=threshold, sparse=sparse, x_initial=x_init, alpha=alpha)\n",
    "    print(f\"process: {ix: 2d} finished. step: {step: 2d}, mse: {mse: 8.2f}, diff: {diff: 8.2f} time consuming: {time.time() - start: 8.1f} seconds\")\n",
    "    return x_et, diff, mse, objs, step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "586cc27b-b28a-4a38-b35f-a24da0c0ef48",
   "metadata": {},
   "outputs": [],
   "source": [
    "A_original = sparse.load_npz(\"data/simulated_large_A_23_10.npz\")\n",
    "x_flat = np.load(\"data/simulated_large_x_23_10.npy\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "28a7734b-b7f4-4462-ad78-ab4c6c4b0dba",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_flat[0] = 20\n",
    "x_flat[90] = 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "ef905842-6fa6-4937-b361-3e033c21ac7a",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = A_original*0.1\n",
    "Ax = A @ x_flat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "90e50c8f-7bd9-494c-8657-c01b62973919",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "process:  0, y[:10]: [  3  24  44  59  66  60  58 116 131  97]\n",
      "step:     0, lr:  1.0000, diff:  100.000000, mse:  308.879862:, obj: -143660.777382\n",
      "step:    20, lr:  1.0000, diff:  0.212950, mse:  307.376685:, obj: -143667.310007\n",
      "step:    40, lr:  1.0000, diff:  0.086493, mse:  305.886236:, obj: -143669.718442\n",
      "step:    60, lr:  1.0000, diff:  0.049351, mse:  304.384985:, obj: -143670.998269\n",
      "step:    80, lr:  1.0000, diff:  0.038498, mse:  302.922367:, obj: -143671.862021\n",
      "step:   100, lr:  1.0000, diff:  0.030656, mse:  301.588865:, obj: -143672.554118\n",
      "step:   120, lr:  1.0000, diff:  0.025598, mse:  300.322399:, obj: -143673.113163\n",
      "step:   140, lr:  1.0000, diff:  0.022279, mse:  299.114960:, obj: -143673.588917\n",
      "step:   160, lr:  1.0000, diff:  0.019644, mse:  297.989396:, obj: -143674.005875\n",
      "step:   180, lr:  1.0000, diff:  0.017500, mse:  296.937042:, obj: -143674.375542\n",
      "step:   200, lr:  1.0000, diff:  0.015720, mse:  295.950795:, obj: -143674.706323\n",
      "step:   220, lr:  1.0000, diff:  0.014219, mse:  295.024706:, obj: -143675.004551\n",
      "step:   240, lr:  1.0000, diff:  0.012524, mse:  294.117624:, obj: -143675.268287\n",
      "step:   260, lr:  1.0000, diff:  0.011426, mse:  293.252734:, obj: -143675.506981\n",
      "step:   280, lr:  1.0000, diff:  0.010467, mse:  292.433911:, obj: -143675.725223\n",
      "step:   300, lr:  1.0000, diff:  0.009624, mse:  291.657795:, obj: -143675.925545\n",
      "step:   320, lr:  1.0000, diff:  0.008877, mse:  290.921391:, obj: -143676.110039\n",
      "step:   340, lr:  1.0000, diff:  0.008211, mse:  290.222014:, obj: -143676.280458\n",
      "step:   360, lr:  1.0000, diff:  0.007613, mse:  289.557237:, obj: -143676.438289\n",
      "step:   380, lr:  1.0000, diff:  0.007074, mse:  288.924857:, obj: -143676.584803\n",
      "step:   400, lr:  1.0000, diff:  0.006587, mse:  288.322862:, obj: -143676.721096\n",
      "step:   420, lr:  1.0000, diff:  0.006145, mse:  287.749413:, obj: -143676.848125\n",
      "step:   440, lr:  1.0000, diff:  0.005742, mse:  287.202813:, obj: -143676.966726\n",
      "step:   460, lr:  1.0000, diff:  0.005373, mse:  286.681500:, obj: -143677.077638\n",
      "step:   480, lr:  1.0000, diff:  0.005036, mse:  286.184029:, obj: -143677.181516\n",
      "step:   500, lr:  1.0000, diff:  0.004727, mse:  285.709058:, obj: -143677.278945\n",
      "step:   520, lr:  1.0000, diff:  0.004442, mse:  285.255341:, obj: -143677.370448\n",
      "step:   540, lr:  1.0000, diff:  0.004179, mse:  284.821718:, obj: -143677.456494\n",
      "step:   560, lr:  1.0000, diff:  0.003937, mse:  284.407105:, obj: -143677.537508\n",
      "step:   580, lr:  1.0000, diff:  0.003713, mse:  284.010492:, obj: -143677.613873\n",
      "step:   600, lr:  1.0000, diff:  0.003506, mse:  283.630932:, obj: -143677.685938\n",
      "step:   620, lr:  1.0000, diff:  0.003314, mse:  283.267541:, obj: -143677.754020\n",
      "step:   640, lr:  1.0000, diff:  0.003136, mse:  282.919486:, obj: -143677.818407\n",
      "step:   660, lr:  1.0000, diff:  0.002970, mse:  282.585989:, obj: -143677.879361\n",
      "step:   680, lr:  1.0000, diff:  0.002816, mse:  282.266318:, obj: -143677.937126\n",
      "step:   700, lr:  1.0000, diff:  0.002672, mse:  281.959785:, obj: -143677.991919\n",
      "step:   720, lr:  1.0000, diff:  0.002538, mse:  281.665742:, obj: -143678.043945\n",
      "step:   740, lr:  1.0000, diff:  0.002414, mse:  281.383580:, obj: -143678.093389\n",
      "step:   760, lr:  1.0000, diff:  0.002297, mse:  281.112724:, obj: -143678.140422\n",
      "step:   780, lr:  1.0000, diff:  0.002188, mse:  280.852634:, obj: -143678.185201\n",
      "step:   800, lr:  1.0000, diff:  0.002085, mse:  280.602798:, obj: -143678.227870\n",
      "step:   820, lr:  1.0000, diff:  0.001990, mse:  280.362736:, obj: -143678.268564\n",
      "step:   840, lr:  1.0000, diff:  0.001900, mse:  280.131992:, obj: -143678.307405\n",
      "step:   860, lr:  1.0000, diff:  0.001816, mse:  279.910137:, obj: -143678.344508\n",
      "step:   880, lr:  1.0000, diff:  0.001736, mse:  279.696764:, obj: -143678.379977\n",
      "step:   900, lr:  1.0000, diff:  0.001662, mse:  279.491489:, obj: -143678.413911\n",
      "step:   920, lr:  1.0000, diff:  0.001591, mse:  279.293948:, obj: -143678.446399\n",
      "step:   940, lr:  1.0000, diff:  0.001525, mse:  279.103798:, obj: -143678.477524\n",
      "step:   960, lr:  1.0000, diff:  0.001463, mse:  278.920712:, obj: -143678.507365\n",
      "step:   980, lr:  1.0000, diff:  0.001404, mse:  278.744382:, obj: -143678.535994\n",
      "step:  1000, lr:  1.0000, diff:  0.001348, mse:  278.574514:, obj: -143678.563477\n",
      "step:  1020, lr:  1.0000, diff:  0.001295, mse:  278.410832:, obj: -143678.589878\n",
      "step:  1040, lr:  1.0000, diff:  0.001245, mse:  278.253071:, obj: -143678.615253\n",
      "step:  1060, lr:  1.0000, diff:  0.001198, mse:  278.100981:, obj: -143678.639657\n",
      "step:  1080, lr:  1.0000, diff:  0.001153, mse:  277.954325:, obj: -143678.663141\n",
      "step:  1100, lr:  1.0000, diff:  0.001110, mse:  277.812877:, obj: -143678.685751\n",
      "step:  1120, lr:  1.0000, diff:  0.001070, mse:  277.676423:, obj: -143678.707532\n",
      "step:  1140, lr:  1.0000, diff:  0.001032, mse:  277.544757:, obj: -143678.728525\n",
      "step:  1160, lr:  1.0000, diff:  0.000995, mse:  277.417686:, obj: -143678.748768\n",
      "step:  1180, lr:  1.0000, diff:  0.000960, mse:  277.295026:, obj: -143678.768298\n",
      "step:  1200, lr:  1.0000, diff:  0.000927, mse:  277.176600:, obj: -143678.787149\n",
      "step:  1220, lr:  1.0000, diff:  0.000895, mse:  277.062240:, obj: -143678.805352\n",
      "step:  1240, lr:  1.0000, diff:  0.000865, mse:  276.951787:, obj: -143678.822937\n",
      "step:  1260, lr:  1.0000, diff:  0.000836, mse:  276.845089:, obj: -143678.839933\n",
      "step:  1280, lr:  1.0000, diff:  0.000809, mse:  276.741999:, obj: -143678.856366\n",
      "step:  1300, lr:  1.0000, diff:  0.000782, mse:  276.642380:, obj: -143678.872261\n",
      "step:  1320, lr:  1.0000, diff:  0.000757, mse:  276.546099:, obj: -143678.887641\n",
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      "step:  1400, lr:  1.0000, diff:  0.000667, mse:  276.191913:, obj: -143678.944445\n",
      "step:  1420, lr:  1.0000, diff:  0.000646, mse:  276.110537:, obj: -143678.957564\n",
      "step:  1440, lr:  1.0000, diff:  0.000627, mse:  276.031819:, obj: -143678.970285\n",
      "step:  1460, lr:  1.0000, diff:  0.000608, mse:  275.955665:, obj: -143678.982623\n",
      "step:  1480, lr:  1.0000, diff:  0.000590, mse:  275.881980:, obj: -143678.994595\n",
      "step:  1500, lr:  1.0000, diff:  0.000573, mse:  275.810678:, obj: -143679.006215\n",
      "step:  1520, lr:  1.0000, diff:  0.000556, mse:  275.741672:, obj: -143679.017496\n",
      "step:  1540, lr:  1.0000, diff:  0.000540, mse:  275.674883:, obj: -143679.028451\n",
      "step:  1560, lr:  1.0000, diff:  0.000525, mse:  275.610231:, obj: -143679.039093\n",
      "step:  1580, lr:  1.0000, diff:  0.000510, mse:  275.547643:, obj: -143679.049434\n",
      "step:  1600, lr:  1.0000, diff:  0.000496, mse:  275.487046:, obj: -143679.059484\n",
      "step:  1620, lr:  1.0000, diff:  0.000482, mse:  275.428373:, obj: -143679.069255\n",
      "step:  1640, lr:  1.0000, diff:  0.000469, mse:  275.371557:, obj: -143679.078757\n",
      "step:  1660, lr:  1.0000, diff:  0.000456, mse:  275.316534:, obj: -143679.087999\n",
      "step:  1680, lr:  1.0000, diff:  0.000444, mse:  275.263245:, obj: -143679.096990\n",
      "step:  1700, lr:  1.0000, diff:  0.000432, mse:  275.211630:, obj: -143679.105740\n",
      "step:  1720, lr:  1.0000, diff:  0.000420, mse:  275.161634:, obj: -143679.114257\n",
      "step:  1740, lr:  1.0000, diff:  0.000409, mse:  275.113203:, obj: -143679.122550\n",
      "step:  1760, lr:  1.0000, diff:  0.000399, mse:  275.066284:, obj: -143679.130625\n",
      "step:  1780, lr:  1.0000, diff:  0.000388, mse:  275.020828:, obj: -143679.138490\n",
      "step:  1800, lr:  1.0000, diff:  0.000378, mse:  274.976787:, obj: -143679.146153\n",
      "step:  1820, lr:  1.0000, diff:  0.000369, mse:  274.934115:, obj: -143679.153620\n",
      "step:  1840, lr:  1.0000, diff:  0.000359, mse:  274.892767:, obj: -143679.160898\n",
      "step:  1860, lr:  1.0000, diff:  0.000350, mse:  274.852701:, obj: -143679.167992\n",
      "step:  1880, lr:  1.0000, diff:  0.000342, mse:  274.813875:, obj: -143679.174910\n",
      "step:  1900, lr:  1.0000, diff:  0.000333, mse:  274.776250:, obj: -143679.181656\n",
      "step:  1920, lr:  1.0000, diff:  0.000325, mse:  274.739788:, obj: -143679.188237\n",
      "step:  1940, lr:  1.0000, diff:  0.000317, mse:  274.704452:, obj: -143679.194657\n",
      "step:  1960, lr:  1.0000, diff:  0.000310, mse:  274.670205:, obj: -143679.200922\n",
      "step:  1980, lr:  1.0000, diff:  0.000302, mse:  274.637015:, obj: -143679.207036\n",
      "step:  2000, lr:  1.0000, diff:  0.000295, mse:  274.604848:, obj: -143679.213004\n",
      "step:  2020, lr:  1.0000, diff:  0.000288, mse:  274.573673:, obj: -143679.218831\n",
      "step:  2040, lr:  1.0000, diff:  0.000281, mse:  274.543458:, obj: -143679.224521\n",
      "step:  2060, lr:  1.0000, diff:  0.000275, mse:  274.514174:, obj: -143679.230079\n",
      "step:  2080, lr:  1.0000, diff:  0.000268, mse:  274.485792:, obj: -143679.235507\n",
      "step:  2100, lr:  1.0000, diff:  0.000262, mse:  274.458285:, obj: -143679.240811\n",
      "step:  2120, lr:  1.0000, diff:  0.000256, mse:  274.431626:, obj: -143679.245993\n",
      "step:  2140, lr:  1.0000, diff:  0.000250, mse:  274.405790:, obj: -143679.251058\n",
      "step:  2160, lr:  1.0000, diff:  0.000245, mse:  274.380751:, obj: -143679.256008\n",
      "step:  2180, lr:  1.0000, diff:  0.000239, mse:  274.356486:, obj: -143679.260848\n",
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      "step:  2860, lr:  1.0000, diff:  0.000120, mse:  273.862603:, obj: -143679.377072\n",
      "step:  2880, lr:  1.0000, diff:  0.000118, mse:  273.854966:, obj: -143679.379453\n",
      "step:  2900, lr:  1.0000, diff:  0.000116, mse:  273.847600:, obj: -143679.381790\n",
      "step:  2920, lr:  1.0000, diff:  0.000114, mse:  273.840499:, obj: -143679.384086\n",
      "step:  2940, lr:  1.0000, diff:  0.000112, mse:  273.833655:, obj: -143679.386340\n",
      "step:  2960, lr:  1.0000, diff:  0.000110, mse:  273.827061:, obj: -143679.388554\n",
      "step:  2980, lr:  1.0000, diff:  0.000108, mse:  273.820710:, obj: -143679.390729\n",
      "step:  3000, lr:  1.0000, diff:  0.000106, mse:  273.814596:, obj: -143679.392865\n",
      "step:  3020, lr:  1.0000, diff:  0.000104, mse:  273.808711:, obj: -143679.394964\n",
      "step:  3040, lr:  1.0000, diff:  0.000102, mse:  273.803049:, obj: -143679.397026\n",
      "step:  3060, lr:  1.0000, diff:  0.000100, mse:  273.797605:, obj: -143679.399052\n",
      "process:  0 finished. step:  3066, mse:   273.80, diff:     0.00 time consuming:      1.0 seconds\n"
     ]
    }
   ],
   "source": [
    "result_gd_init = run_gd_init(10000, 0.0001, True, alpha=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "ea25a312-645a-40d3-a91c-c85a9e34e472",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "process:  0, y[:10]: [  3  24  44  59  66  60  58 116 131  97]\n",
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      "step:  8280, lr:  1.0000, diff:  0.000107, mse:  268.556838:, obj: -143679.233638\n",
      "step:  8300, lr:  1.0000, diff:  0.000106, mse:  268.558073:, obj: -143679.235775\n",
      "step:  8320, lr:  1.0000, diff:  0.000106, mse:  268.559391:, obj: -143679.237895\n",
      "step:  8340, lr:  1.0000, diff:  0.000105, mse:  268.560790:, obj: -143679.239998\n",
      "step:  8360, lr:  1.0000, diff:  0.000104, mse:  268.562271:, obj: -143679.242085\n",
      "step:  8380, lr:  1.0000, diff:  0.000103, mse:  268.563832:, obj: -143679.244155\n",
      "step:  8400, lr:  1.0000, diff:  0.000102, mse:  268.565473:, obj: -143679.246209\n",
      "step:  8420, lr:  1.0000, diff:  0.000102, mse:  268.567193:, obj: -143679.248247\n",
      "step:  8440, lr:  1.0000, diff:  0.000101, mse:  268.568991:, obj: -143679.250270\n",
      "process:  0 finished. step:  8459, mse:   268.57, diff:     0.00 time consuming:      2.4 seconds\n"
     ]
    }
   ],
   "source": [
    "result_gd = run_gd(10000, 0.0001, True, alpha=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "e601136b-b0f4-4cd9-acce-b70922ce69f3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "process:  0, y[:10]: [  3  24  44  59  66  60  58 116 131  97]\n",
      "step:     0, diff:  100.000000, mse:  773.637465:, obj: -142515.463644\n",
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      "step:   360, diff:  0.001598, mse:  278.637879:, obj: -143680.662980\n",
      "step:   380, diff:  0.001309, mse:  278.911564:, obj: -143680.691800\n",
      "step:   400, diff:  0.001079, mse:  279.148422:, obj: -143680.715482\n",
      "step:   420, diff:  0.000893, mse:  279.353417:, obj: -143680.735038\n",
      "step:   440, diff:  0.000742, mse:  279.530896:, obj: -143680.751254\n",
      "step:   460, diff:  0.000618, mse:  279.684634:, obj: -143680.764753\n",
      "step:   480, diff:  0.000517, mse:  279.817901:, obj: -143680.776027\n",
      "step:   500, diff:  0.000434, mse:  279.933521:, obj: -143680.785475\n",
      "step:   520, diff:  0.000365, mse:  280.033926:, obj: -143680.793415\n",
      "step:   540, diff:  0.000309, mse:  280.121213:, obj: -143680.800109\n",
      "step:   560, diff:  0.000261, mse:  280.197190:, obj: -143680.805769\n",
      "step:   580, diff:  0.000222, mse:  280.263410:, obj: -143680.810570\n",
      "step:   600, diff:  0.000189, mse:  280.321214:, obj: -143680.814654\n",
      "step:   620, diff:  0.000162, mse:  280.371756:, obj: -143680.818139\n",
      "step:   640, diff:  0.000139, mse:  280.416028:, obj: -143680.821124\n",
      "step:   660, diff:  0.000119, mse:  280.454886:, obj: -143680.823689\n",
      "step:   680, diff:  0.000103, mse:  280.489067:, obj: -143680.825901\n",
      "process:  0 finished. step:  685, mse:   280.50, diff:     0.00 time consuming:      0.5 seconds\n"
     ]
    }
   ],
   "source": [
    "result_em = run(2000, 0.0001, True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "08a7ac72-8752-4741-a9c5-4e34b77c6bc0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "process:  0, y[:10]: [  3  24  44  59  66  60  58 116 131  97]\n",
      "step:     0, diff:  100.000000, mse:  291.073713:, obj: -143670.096581\n",
      "step:    20, diff:  0.093480, mse:  270.631432:, obj: -143678.222643\n",
      "step:    40, diff:  0.036955, mse:  272.639229:, obj: -143679.378168\n",
      "step:    60, diff:  0.018554, mse:  274.529636:, obj: -143679.895461\n",
      "step:    80, diff:  0.010811, mse:  275.856164:, obj: -143680.175359\n",
      "step:   100, diff:  0.006993, mse:  276.789455:, obj: -143680.347502\n",
      "step:   120, diff:  0.004851, mse:  277.472362:, obj: -143680.463031\n",
      "step:   140, diff:  0.003522, mse:  277.993342:, obj: -143680.545130\n",
      "step:   160, diff:  0.002636, mse:  278.405435:, obj: -143680.605705\n",
      "step:   180, diff:  0.002015, mse:  278.740849:, obj: -143680.651555\n",
      "step:   200, diff:  0.001565, mse:  279.019667:, obj: -143680.686903\n",
      "step:   220, diff:  0.001231, mse:  279.254868:, obj: -143680.714538\n",
      "step:   240, diff:  0.000978, mse:  279.455212:, obj: -143680.736388\n",
      "step:   260, diff:  0.000784, mse:  279.626913:, obj: -143680.753831\n",
      "step:   280, diff:  0.000634, mse:  279.774608:, obj: -143680.767873\n",
      "step:   300, diff:  0.000516, mse:  279.901919:, obj: -143680.779267\n",
      "step:   320, diff:  0.000423, mse:  280.011784:, obj: -143680.788576\n",
      "step:   340, diff:  0.000349, mse:  280.106653:, obj: -143680.796236\n",
      "step:   360, diff:  0.000290, mse:  280.188610:, obj: -143680.802580\n",
      "step:   380, diff:  0.000243, mse:  280.259442:, obj: -143680.807866\n",
      "step:   400, diff:  0.000204, mse:  280.320697:, obj: -143680.812300\n",
      "step:   420, diff:  0.000173, mse:  280.373713:, obj: -143680.816040\n",
      "step:   440, diff:  0.000147, mse:  280.419653:, obj: -143680.819214\n",
      "step:   460, diff:  0.000126, mse:  280.459519:, obj: -143680.821924\n",
      "step:   480, diff:  0.000108, mse:  280.494180:, obj: -143680.824251\n",
      "process:  0 finished. step:  491, mse:   280.51, diff:     0.00 time consuming:      0.3 seconds\n"
     ]
    }
   ],
   "source": [
    "result_em_init = run_init(2000, 0.0001, True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "3c6041bb-e048-40da-ae92-16ac36c2a0b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x1152 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "fig.set_size_inches(16, 16)\n",
    "\n",
    "plt.subplot(2, 2, 1)\n",
    "plt.plot(result_gd[-2][10:2000])\n",
    "plt.plot(result_gd_init[-2][10:2000])\n",
    "plt.legend([\"GD\", \"GD+\"])\n",
    "plt.xlabel(\"iteration\")\n",
    "plt.ylabel(\"objective\")\n",
    "\n",
    "plt.subplot(2, 2, 2)\n",
    "plt.plot(result_em[-2][10:2000])\n",
    "plt.plot(result_em_init[-2][10:2000])\n",
    "plt.legend([\"EM\", \"EM+\"])\n",
    "plt.xlabel(\"iteration\")\n",
    "plt.ylabel(\"objective\")\n",
    "\n",
    "plt.subplot(2, 2, 3)\n",
    "plt.plot(result_gd[-2][10:2000])\n",
    "plt.plot(result_em[-2][10:2000])\n",
    "plt.legend([\"GD\", \"EM\"])\n",
    "plt.xlabel(\"iteration\")\n",
    "plt.ylabel(\"objective\")\n",
    "\n",
    "plt.subplot(2, 2, 4)\n",
    "plt.plot(result_gd_init[-2][10:2000])\n",
    "plt.plot(result_em_init[-2][10:2000])\n",
    "plt.legend([\"GD+\", \"EM+\"])\n",
    "plt.xlabel(\"iteration\")\n",
    "plt.ylabel(\"objective\")\n",
    "plt.savefig(\"itr_obj.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "870bfcf3-1311-4a26-ba0c-58ffed60b20b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'objective')"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "plt.plot(result_gd[-2][10:2000])\n",
    "plt.plot(result_gd_init[-2][10:2000])\n",
    "plt.legend([\"GD\", \"GD+\"])\n",
    "plt.xlabel(\"iteration\")\n",
    "plt.ylabel(\"objective\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "ebd486e5-52af-4818-a662-6918ed915134",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'objective')"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "plt.plot(result_em[-2][10:2000])\n",
    "plt.plot(result_em_init[-2][10:2000])\n",
    "plt.legend([\"EM\", \"EM+\"])\n",
    "plt.xlabel(\"iteration\")\n",
    "plt.ylabel(\"objective\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "618f9dcb-ec41-4eb0-842c-7dd9bb39eb26",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'objective')"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "plt.plot(result_gd_init[-2][10:2000])\n",
    "plt.plot(result_em_init[-2][10:2000])\n",
    "plt.legend([\"GD+\", \"EM+\"])\n",
    "plt.xlabel(\"iteration\")\n",
    "plt.ylabel(\"objective\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "d2c42830-4095-46ae-8d46-83324c4334c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'objective')"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "plt.plot(result_gd[-2][10:2000])\n",
    "plt.plot(result_em[-2][10:2000])\n",
    "plt.legend([\"GD\", \"EM\"])\n",
    "plt.xlabel(\"iteration\")\n",
    "plt.ylabel(\"objective\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "791966a3-cc00-433c-8cb9-7e9f511650e2",
   "metadata": {},
   "source": [
    "# Image 100 by 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "a4f630d6-18f8-425e-908e-eb976581d5df",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Image vector x is of shape (10000,)\n",
      "Mixing matrix A is of shape (33362, 10000)\n"
     ]
    }
   ],
   "source": [
    "A = sparse.load_npz(\"data/simulated_large_A_117_100.npz\")\n",
    "x_flat = np.load(\"data/simulated_large_x_117_100.npy\")\n",
    "Ax = A@x_flat\n",
    "# y = np.random.poisson(Ax)\n",
    "print(\"Image vector x is of shape {}\".format(np.shape(x_flat)))\n",
    "print(\"Mixing matrix A is of shape {}\".format(np.shape(A)))\n",
    "# print(\"Observation matrix Y is of shape {}\".format(np.shape(y)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "c75667e5-0b3a-426b-b805-d74b6f41d1b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# x_et, diff, mse, objs, step = run_init(1000, 0.1, True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8460712-17e3-4f1f-b61f-e675cfe10a8b",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Image 50 by 50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "c807c654-9a9b-4c52-b947-7b4e7237c04e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Image vector x is of shape (2500,)\n",
      "Mixing matrix A is of shape (3108, 2500)\n"
     ]
    }
   ],
   "source": [
    "A = np.load(\"simulated_large_A.npy\")\n",
    "x_flat = np.load(\"simulated_large_x.npy\")\n",
    "Ax = A@x_flat\n",
    "print(\"Image vector x is of shape {}\".format(np.shape(x_flat)))\n",
    "print(\"Mixing matrix A is of shape {}\".format(np.shape(A)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "0f13d0b3-b570-4100-8450-5a628b20b02e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "process:  0, y[:10]: [  2   1   9   0   8   9  11  28 600 811]\n",
      "step:     0, diff:  100.000000, mse:  2889.664090:, obj: -22172085.856553\n",
      "step:    20, diff:  72.291757, mse:  2711.458246:, obj: -22203029.836827\n",
      "step:    40, diff:  20.073959, mse:  2662.408212:, obj: -22203769.786324\n",
      "step:    60, diff:  9.137955, mse:  2634.982122:, obj: -22204035.090214\n",
      "step:    80, diff:  5.290779, mse:  2614.991839:, obj: -22204171.900099\n",
      "step:   100, diff:  3.530588, mse:  2598.630061:, obj: -22204257.258813\n",
      "step:   120, diff:  2.576803, mse:  2584.459032:, obj: -22204316.998193\n",
      "step:   140, diff:  1.995295, mse:  2571.798732:, obj: -22204361.999263\n",
      "step:   160, diff:  1.609065, mse:  2560.268698:, obj: -22204397.610848\n",
      "step:   180, diff:  1.335737, mse:  2549.628121:, obj: -22204426.777582\n",
      "step:   200, diff:  1.132908, mse:  2539.711115:, obj: -22204451.268951\n",
      "step:   220, diff:  0.976919, mse:  2530.396878:, obj: -22204472.225157\n",
      "step:   240, diff:  0.853637, mse:  2521.594162:, obj: -22204490.423289\n",
      "step:   260, diff:  0.754113, mse:  2513.232309:, obj: -22204506.417172\n",
      "step:   280, diff:  0.672390, mse:  2505.255602:, obj: -22204520.615630\n",
      "step:   300, diff:  0.604327, mse:  2497.619494:, obj: -22204533.328824\n",
      "step:   320, diff:  0.546949, mse:  2490.287945:, obj: -22204544.797158\n",
      "step:   340, diff:  0.498058, mse:  2483.231491:, obj: -22204555.210183\n",
      "step:   360, diff:  0.455997, mse:  2476.425795:, obj: -22204564.719497\n",
      "step:   380, diff:  0.419496, mse:  2469.850543:, obj: -22204573.447827\n",
      "step:   400, diff:  0.387570, mse:  2463.488595:, obj: -22204581.495623\n",
      "step:   420, diff:  0.359442, mse:  2457.325322:, obj: -22204588.945921\n",
      "step:   440, diff:  0.334498, mse:  2451.348095:, obj: -22204595.868000\n",
      "step:   460, diff:  0.312243, mse:  2445.545881:, obj: -22204602.320165\n",
      "step:   480, diff:  0.292279, mse:  2439.908936:, obj: -22204608.351888\n",
      "step:   500, diff:  0.274281, mse:  2434.428561:, obj: -22204614.005462\n",
      "step:   520, diff:  0.257981, mse:  2429.096911:, obj: -22204619.317308\n",
      "step:   540, diff:  0.243158, mse:  2423.906853:, obj: -22204624.318994\n",
      "step:   560, diff:  0.229626, mse:  2418.851846:, obj: -22204629.038056\n",
      "step:   580, diff:  0.217230, mse:  2413.925857:, obj: -22204633.498651\n",
      "step:   600, diff:  0.205839, mse:  2409.123283:, obj: -22204637.722084\n",
      "step:   620, diff:  0.195341, mse:  2404.438901:, obj: -22204641.727240\n",
      "step:   640, diff:  0.185639, mse:  2399.867819:, obj: -22204645.530936\n",
      "step:   660, diff:  0.176651, mse:  2395.405440:, obj: -22204649.148216\n",
      "step:   680, diff:  0.168305, mse:  2391.047430:, obj: -22204652.592586\n",
      "step:   700, diff:  0.160539, mse:  2386.789698:, obj: -22204655.876225\n",
      "step:   720, diff:  0.153299, mse:  2382.628369:, obj: -22204659.010148\n",
      "step:   740, diff:  0.146536, mse:  2378.559769:, obj: -22204662.004357\n",
      "step:   760, diff:  0.140210, mse:  2374.580406:, obj: -22204664.867960\n",
      "step:   780, diff:  0.134282, mse:  2370.686961:, obj: -22204667.609276\n",
      "step:   800, diff:  0.128720, mse:  2366.876269:, obj: -22204670.235927\n",
      "step:   820, diff:  0.123494, mse:  2363.145316:, obj: -22204672.754915\n",
      "step:   840, diff:  0.118578, mse:  2359.491220:, obj: -22204675.172684\n",
      "step:   860, diff:  0.113949, mse:  2355.911229:, obj: -22204677.495184\n",
      "step:   880, diff:  0.109585, mse:  2352.402712:, obj: -22204679.727920\n",
      "step:   900, diff:  0.105467, mse:  2348.963146:, obj: -22204681.875989\n",
      "step:   920, diff:  0.101578, mse:  2345.590119:, obj: -22204683.944125\n",
      "step:   940, diff:  0.097901, mse:  2342.281315:, obj: -22204685.936730\n",
      "step:   960, diff:  0.094422, mse:  2339.034515:, obj: -22204687.857900\n",
      "step:   980, diff:  0.091128, mse:  2335.847590:, obj: -22204689.711454\n",
      "process:  0 finished. step:  1000, mse:  2332.87, diff:     0.09 time consuming:    277.0 seconds\n"
     ]
    }
   ],
   "source": [
    "x_et, diff, mse, objs, step = run_init(1000, 0.01, False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "4163ffef-94ed-4b5a-bace-d9e610a2294c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "size = int(np.sqrt(A.shape[1]))\n",
    "\n",
    "plt.figure()\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.imshow(x_et.reshape(size, size), cmap='gray')\n",
    "plt.title('Reconstructed Image')\n",
    "plt.axis('off')\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.imshow(x_flat.reshape(size, size), cmap='gray')\n",
    "plt.axis('off')\n",
    "plt.title('Original Image')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7f14218e-47de-4fb5-94af-fff887f60c0e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "size = int(np.sqrt(A.shape[1]))\n",
    "\n",
    "plt.figure()\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.imshow(x_et.reshape(size, size), cmap='gray')\n",
    "plt.title('Reconstructed Image')\n",
    "plt.axis('off')\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.imshow(x_flat.reshape(size, size), cmap='gray')\n",
    "plt.axis('off')\n",
    "plt.title('Original Image')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1148127e-1c5b-4b07-af4c-a4203c2cdf66",
   "metadata": {},
   "source": [
    "# Image 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "82c85f69-81a6-4f33-ab54-d8165f245ebc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Image vector x is of shape (2500,)\n",
      "Mixing matrix A is of shape (2777, 2500)\n",
      "Observation matrix Y is of shape (2777,)\n"
     ]
    }
   ],
   "source": [
    "A = sparse.load_npz('/nfs/stak/users/zhoutian/Downloads/simulated_large_A_20_50.npz')\n",
    "x_flat = np.load(\"/nfs/stak/users/zhoutian/Downloads/simulated_large_x_20_50.npy\")\n",
    "Ax = A@x_flat\n",
    "y = np.random.poisson(Ax)\n",
    "print(\"Image vector x is of shape {}\".format(np.shape(x_flat)))\n",
    "print(\"Mixing matrix A is of shape {}\".format(np.shape(A)))\n",
    "print(\"Observation matrix Y is of shape {}\".format(np.shape(y)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "ec0354fd-3bc8-4505-83c0-a4e196ccd206",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mc_run(n, max_step=500, threshold=2, sparse=True):\n",
    "    etms = []\n",
    "    for i in range(n):\n",
    "        print(f\"{i}th run start =>\")\n",
    "        y = np.random.poisson(Ax)\n",
    "        x_et, diff, mse, step = mle_em(max_step, A, y, x_true=x_flat, threshold=threshold, x_initial=None, sparse=sparse)\n",
    "        etms.append([x_et, diff, mse, step])\n",
    "    return etms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "aebdf99d-7857-4475-978d-f262840afeb8",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_aver = np.mean([e[0] for e in etms ], axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "09307ee0-6235-49fc-9588-2507dca42f03",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([112.61630754, 150.40308926, 245.56907365, ..., 111.88822054,\n",
       "       123.6858849 , 125.4410671 ])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_aver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "fa583712-e101-4884-bafb-c80ba655f2fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "size = int(np.sqrt(A.shape[1]))\n",
    "\n",
    "fig = plt.figure()\n",
    "fig.set_size_inches(10,5)\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.imshow(x_aver.reshape(size, size), cmap='gray')\n",
    "plt.title('Reconstructed Image')\n",
    "plt.axis('off')\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.imshow(x_flat.reshape(size, ssparse, cmap='gray')\n",
    "plt.axis('off')\n",
    "plt.title('Original Image')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "2d7a7fa6-b3bb-4a0d-aaf8-94ea6b365e31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "fig.set_size_inches(20,10)\n",
    "for i in range(10):\n",
    "    plt.subplot(2, 5, i+1)\n",
    "    plt.imshow(etms[i][0].reshape(size, size), cmap='gray')\n",
    "    plt.title(f'Reconstructed Image {i}')\n",
    "    plt.axis('off')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8915a396-a5c6-45e4-8f96-5b5bd74c7e33",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dWlKwO+/sPzKKlIC0ix4FDEpg+R55pHN2QlIQ1oE7+ZQdSJU8iifVKRypGj8nreGuM+UCthm9HUaPHt3xt9/97neTzfBoelrQ84E76JQ7JGnYsGHJphM8wfYjtaOXC6WX3MujF6DsRFDWIX1lu3g71xybObzAB5aDNNqTFDheWCb2M+ebF77sSQocz/wt75l/x7nOevIZHBd8hhd2z/BzjkGOI86Ru+66K9kcj16ovFSfP4sWLUq2FxbN/qXNtvDek0SsdAOBQKBFxEs3EAgEWkSjvEDqxGU2Y7K5zCZNIbUgzeR98lhoLuv5m5EjRyabVIY7i/Q0IAVhgIMX200Kwt1H7kqSEnmyC3eipbq0QarK37DOpD+sD2ULejJQamCww7JlyzqWie3NQAnS1FzyoScEx8OoUaM6/p7tRJsSCe/ZK3AscAx7Mf+UBNiX/G2THMffe1JTN5nsaJ9yyikdy03vAI5nShae0z8pPn+bz1Uvz4SXpY11471Yz8033zzZzHxHeXHChAnJphcV++Skk05K9uWXX96xPlLdI4u5S/bff/9k/+QnP+n4PI55vj9y759OiJVuIBAItIh46QYCgUCLaJQX6NxPqsV8BqSNXiq/XXfdNdlPPfVUsvMdZFInPpteB6Q1pO9c1nNnniDF4Y4wvSZIibwEy5Q+KAOQpuXXkW6y3N4uOqUa0iLSQqadY/0ZrEC5gP1G6eTggw9O9oMPPlgrB+UPPpu7/KSU7EOmhaQs4qVGbBOe0zypL9vUi+33Ps+lJuYM4dxgu7CfGSjAMTlx4sSO5fZyFXjBFxyP3k48x2buBdGNXMJ6cm7QpmTF+ULPIXoUTZ48OdlHHHFEsplulpLi8ccfn+xLL720Vgd6PzBA6IYbbki2Jx2wDl77eYiVbiAQCLSIeOkGAoFAi+g6OIJ0nB4IzENAmk6awRSRpFNNTvKkTt7ZRqRLc+bMSTYDJTwqy2CCJg+EPpBqeVQ5j0/3AjlI7SkR5DvEfSCtYW4DSjCUASiF0FOAAR5so+nTpyebXg2ST0+92H3WjVID82fcdNNN6jVIX70+Zx1Jp9kfXsrH/OQI7zuOC84fSmSky156QfYN78PP2Tdeefg565+fMOPlZeDnvBfB6/lslpu0nm1POWLu3LnJZi6VQw89NNnM1fL973+/Vo6LL7442ZR/vvjFLyabc5jeRZ6XU+ReCAQCgQGGeOkGAoFAi2iUF+gMTCngySefTDZpN9MrkrKRNpCa5w7k3KX0dk5JeSgR5Cce9MFzGufuO3dNmYeAtIG0no7R3kF5Up1G0SZ1Yh0I0hTel3klKG2wrGxj72hqSg1f//rXk02ZRpK23XbbZJNiMoUfKR/HDHM98KQCelH0CuxDL0eAt/vueTWwX/OxzXHLoB72Fcck01/SiZ/l4D0539gfrKdXt09z0KaXqpRl4njjNWwbjgXOJX7OurFMDBriHOazGNxwxRVX1Oqw4447JpuBRuxTykeetwjlVs9zioiVbiAQCLSIeOkGAoFAi4iXbiAQCLSIRk2X+gQTQlADYpIKaiHUbRgVxWQsef5R5rf0jgChXkO9li5QdO2gJkM9iFon9WAvCo96M/VWlpO6ag5qd147UcemFke3MrrPUKPj52wjanfU2Nh2Dz/8cLKZXEiq6/F0/Rs8eHCy6a5D7Z+Jh6iZ5adA9wJsd46L3DWq0+f8LduXdc91Uq9/qJVy7N18883J9vRkL3cr+5bP9aLCPC2V4zmPtuSzWQfufTAikS5Z3rFG/JyuqJ7mTA2dc4rj8ZZbbkk2T9KW6to396k4HtgGbBvOBbrT5tp3J8RKNxAIBFpEvHQDgUCgRXSdecTLuUlqzs/pOrR06dJkb7HFFv0Pz2gDr6MMQbclXkPpgFKIF7VD2sVnUzogPWDeYLo/0VWFbiQ8MViqR4OxHF756HpCVzLScV7vJcKh2w7pHikRy83755SV0gMjffh70kLKLew3loNUrlfwoqU8uuvRcc8VqsnFilIF+5njk2OMz6NM5eXy5bM4znnNuHHjkn3fffclm66EHGtjx46t1YeSH9uG88RzXaMkQ9mJbcZyUzogWH/v2CxGP3I8SvUkN2wb3suLKvXcafNToDshVrqBQCDQIuKlGwgEAi2i64Q3jKIhHWVyCHoQkMpy951UhLuPkr/zzZM6WSZSM0oNngcCf0uaxvuQ4lDKYB285+anAfNe3OHk7qrngeAlEaGcw/bi/emlsGTJkmSTErGN6JmS14HfsX+ZbIR9SkmFET/cjc5Plu01vLbuJpmNl+All87Yz17O1VmzZiWb1JxRiF4kGKU9L8KOuOaaa5LtedBwrM2cObP2e/Y56+qNZ0+28U7MZpk49/juoWeBl7ObkgBPDJakMWPGJJt5iq+++upkM0rQO8qIz4h8uoFAIDDAEC/dQCAQaBGN8gJpAJ2yvXyT3Lnmbrq3y5hjxIgRyeauI+kon0EK5h2lQepDWcDb+aWMwrKyDN7xLjlIr3hfPo/lI40kpfJOq6U8w/vzuZRRSH0oNZCyMWmRVKfefDbLRDmDY4M703SOp5dGr8A+ICX26LGXc5b34fX5uCA1zYOC+uC1L9uL17CspLgsK8vE37JfWR8vmCj39mC9KXNxbrB8lAJYJi8pDp/N8cly81k8DZv3JxYsWFD7+9hjj+1Yh25yDfNdwrHt9S0RK91AIBBoEfHSDQQCgRbRKC/ssssuySZdIsVnDD4pLgMLSHG5RM9pAHOuknbwuB4GIFBS8Og/Ax9InTzaTUrk0WAGYvC3++yzT+065qaljEDZwvOuIB2ljED64uVWpUzBXVZe71FkBkNI0lFHHZVsejLcfffdyWYbcLeXdWOZmnJU9AKeRMQxxTp6R8nw+jzIhG3vncTL8Un66u2I89lsd2+3n2OQ/c/fet4RebAH60MvB+a1ZTn233//ZM+bNy/ZnNseTWdgBevM+vBoKAY9ELlEwt/T+4fzm8FcBK/3gjc8xEo3EAgEWkS8dAOBQKBFNMoLTzzxRLLp6D5kyJBk09Gf1J+5E3jCLCWI/Hgbz+uAO+qPP/54sklNmHaNO5ykKZQOSLu8HVdSGdImUnZSxTynwKBBg5Lt5UZg+VhntgV3Vvm55yHinUjaTUrJnE6xLdkGw4YNSzblJi8HAKWGgeC94AUrsPzesS0EJYUmzxzmnmB+AqZGZUAR4c0Lz+a8YM4EBgewrBxHrDPnRR7swTFMuYj3pfx3//33J5vjmTIfx5GXMpPXc37yt6xD02ndlD8YUEGpgu+r7bffvmOZvKPFPMRKNxAIBFpEvHQDgUCgRTTKC6Q1BxxwQLIfeuihZJN2kbLT+4C7j6QcPOFBqtMCxupTOuBynzSay33vhF6Wgzuu3qnCpE2kJqQ13okAUr2u3O1k3gPSNO+kCrYx78my8resp5faj23tta9Urx/T/pHCeqkKSVuZt6Gb7PqrGqw/y+9Rec9xn3WkF0AOjnXel+OTXhGULfhslptjh/3BccETKDhfvNOA8xMiOj1LqrcBpROWjx4rHGP8La9n6kVKLQyC8lJysh84vjhf8jwUzDPCOcmysg6cG+wfLz+Dh1jpBgKBQIuIl24gEAi0iEZ5gXSH6RUZt89lPekrbS7RSX3p1SDVJQXuUjLNI2UELve9OHQvLpz0itSJ9Jh1IMX3PBz4W6kuKXjeC6QmbCcGIrBdSLUoQbCvvMAPUkfu3PK5ebpNemSwrKSwpHMsK53dWY5uKNiqBuvPMcm+8ZzeeY1HfXOaTo8N1p/t650i0Y3nBPuN/eSdfODlcPByUuRloBTA39Azg/ONz6aXE3MmMKiBz+vmRIluDpOk11X+bD7PO1GCfco25tzu5tDVWOkGAoFAi4iXbiAQCLSIRnmBlIjOx6S1zNjOz0nBaHMZz91wqb67yljtGTNmJJs7jryXJyOQ/pEe0NGf9yF9IYUgBfUCF/JdedaH1NE7+I7l5m4qaRSvp8xDesVrPO8KtiNTauap6dgejElnu3pBF92k5+sVpk6dmuyvfOUryeZYZTlJtXkNd8fZJqScku9FwjnmBZZ43hUcRywrPRk4tvlbSlD0rKBsRPkul4R4L44LPo+/Yf0pQXnSiTcP2d6UEVge72QPBnhJ9f569tlnO5aD7eQFNbHtuxnbsdINBAKBFhEv3UAgEGgRjfICaQed25nO0TtkkbTJCzjIHa5JqbirS2rP3AB8NmPYSc1pe2kHvRwB3iGFLDd36POUcswZwaz1lDbYZpQLWGfKDpQL2JZe4IOX58CjQfS4kOrUkW1DeYLlY5uRCnopLHsFeuMceuihySZNZd+QsnpSFscRd83z+/I7jhnel9d4B60SbHfvBAvPM4P1pKTAe+bP3WuvvZJ9/fXXJ5teEfQQ4ZindECvC44LSpWUajgvKN+xznzfjBs3LtkM4pDqY4BtQ88hthMlMtatm3wLRKx0A4FAoEXESzcQCARaRKO8QAdoz+GaadC4a7p06dJkk7Lynnm6ODork2owReIjjzySbFITj76QanA3lWXi9c8991yyu8m3QLpDyiFJc+fO7fgbUlVSJFI7UiEvD4MXyEFa76XgI4Xy0tpJ9XR2bD96sxAcG16f8PDKXsELcPB2x3kN24H9yrrnOQI8eYLtwrHAcUVq7+VG8E5kIfXl/b0xRdvz3pCkKVOmJJvBDpQCKIt4kgfbknOV/UAPApbPS7154IEHdiwP3095OTjuWSbe15v3lII4TjzESjcQCARaRLx0A4FAoEU0ygv0UuBhctyx95z46U1AGkzKxt1DSdpvv/2STc8J3pcyB3dKSYVIqUjlKEfQC4I7yF7dSC14H9Kg/CQMlpu2d5ghPQ24U0o6zrYkDermtAzen5INZYA8wIOx9PyOVNDLUTB8+PBkk8rlJ2z0AqTst912W7K//OUvJ5uSjTeOSOspFeQ72uwfL+iA44fjgmB/eqdfkBIfdthhyebYvu6665LNMcV+4j1zbwzWgUFObAOOFy9PAtuF44XyFeeYJ+ccd9xxyabMx9+yDyU/hwzL7c1VtiXfaXlQTCfESjcQCARaRLx0A4FAoEU0ygs8TI50jLIDaXC+O9gHLrlJ5fNDEElzvfh2UjCWiUt8T14gxSElYjkYF87nXnHFFcn+8Y9/nGwGD+TwdmlHjRqVbFIkUnnWYcmSJcn2DsRj8ArpFSUFxpc/9thjyWb9c4mEu7o8DeTKK69M9i677JJsel14VJP17BXY7myLMWPGJNtzevdO+2hK7ch54uWk8HJ9eMEkLAf7kLv39NJhmSZMmJBszgtKP/Rqyak55SUvvat3QgTBMt17773J5jjkPRnIwrHNfvBOJqFUkJfPO7XFO3iUEo53sKmHWOkGAoFAi4iXbiAQCLSIRnmBlJV0nJSINMOjY3RuJm3IKRglAuZV2G233ZL9+OOPJ5s7n3wGvQ4YBECPCj6bdJ8p/3iyxVlnndWxnNzJzncu+R2pEOk1HdZpkxZ6ORZIR+ntwQz5Xv4M/pYyAGmtJC1btizZ3O2lxLTzzjsnmwEhw4YN6/i8PACjF/ByFXBMcYxQavJSBxJ5KkRv1539zHFI2Yrl4FgYPXp0stnWHGv8LU8IYfnomcD0h9tss02yOTZzUBa85ZZbkk0PGe8QTY++02OH89DrE44vtjXHJt9VUl1K4dyldEAvBV6fe3P0Ic8n0wmx0g0EAoEWES/dQCAQaBGN8sKXvvSlZNOZmmfSk2pxB9U7pYAyQO4ATjrOXWTSEVIWOmjzGlIC0iU6XLMc06ZNSzZ3/hlH7d2fdcvrQ8rD3VvmM6DU4OWSoCxAGsT2pkTA3VfKALyeVJPIJZ+RI0cmmzTv1ltvTTbzYZCGsj6UhfIUe72Ad5Apy0wZzTvhgOO8aefaO8GA84dlIrXnuD3yyCOTzXFIas76UC7y0pN6gR+85sILL/zjSlWgXHLGGWck++abb+74bEqMzMVy0EEHdbye8iLfPZQRPE8mShB5/gieTsMAGfYJxwAlBbYZnxHeC4FAIDDAEC/dQCAQaBFdp3bkzh+X2aS73Cnn7iiX3KQsu+++e+15pKYMouCzmXqREgFpNKkJd9OZgo6UYOjQockmrffisbnDzbLRayK/F+kIPSq408zgAz6blIp94p3ewKz+pP6kV55TPnfEJWnmzJnJ9vJssP2465471Pch39nvBdgWrD/LRqmF45a/5dgmzc5PWmBeEXqEeLH9PCyUMh/L5B1YSomAEhnHLT/nOCU4ppoOXGQdOPe++c1vJptzlXObz+A4okRGKcyTKbxcDbwP55ck3XXXXcnuJsUqn8E6sL3zg107IVa6gUAg0CLipRsIBAItolFeuPHGG5NN6sOlOB3muRSfP39+sr30gvluP2kBr+OuOykud45Jf7z7cAeZzyb1IWWn4zqpDL0JSEfz0wLoUUAq6Dmp5ydp9IG7upRX2C6kuaRBzIswe/bsZB988MEdn8UUnlI9kMHbCWa+CtKrxYsXJ7ubjPptwvOiYb28tI3eKQ1NO9eUBSjtULbgfUmF2abeCS5eoIAnkbA+fBZlEcpDzDci1ecJqTbHOduY9+K8otTGuc2ysp7eqQ6UtbwgqNtvv71WB3pFsB9ZJo5t3ovvA5bVO9mDiJVuIBAItIh46QYCgUCLiJduIBAItIhGTZcuVtQhqVtQY6QmxQQcjz76aLLpjsHIEclPhMJEE3TRousNwWczcY53vA3rwKgrRvyw/rNmzUo2NW1qWFJdH2RkELVvtiV/z7Zh+ains0x0MfJc1eiSM2fOnGQzCi/vAz6D2t8TTzyRbOrm1AqpfdPNkDpZr0Adjjbbl/3nHRlD8Jo8EQ41R88Vy4sYy93POv3WO96Hro50Q/ROIeY1HJuct1Jdo+fYo6brHSHFsnpuhXTDYjm8iEG2EfuB5dxjjz1qz6Ar5j777JPsq6++uuOz+e6hfs86e7l8iVjpBgKBQIuIl24gEAi0iEZ5ga5HTPhCNyS6p5CKUpogteRSPHevoDzBI1R23XXXZHv0j9Ft/C2pBn/LpDOkKZQyFi5cmGzSGt6H9ydNl+rH7PA3eeRaH0hbPTpLdxue4sqjlRi1xjrwtFUvQQoTCuXX0Z2MMszll1+e7AMOOCDZlDNYjoHgPublKCb1ZR94FJ8yQFPUFucPxwn7kPINxyTnhefexjHi5e6lrEEZwZtTHPM5OGb4e7aB53JHUGpikh+Wm1Fl7BPKV3zfeEfv5MdEMXKTyXkol7F/KRHyvUc5z6snESvdQCAQaBHx0g0EAoEWYXmOSWLrrbdOX1IK4LLeS5ZBqsREOB5Nk+o7pKQa3BEkrSFdIF0iBd9hhx2SzdNNSYNIj0jNKEEwSuX0009P9s9//vNkM2es5HsUnHvuucn+2te+lmzSd+8kXdJ/L4ENZSHu2PI0YF7P/K45PSItZt+RanlH1rB8pLYcGzNnzuzsCrCKsfbaa6fCsf+/853vdLyeVNkbj9zdzqUG0lH2IeUCetdcdNFFyaYUQomISXR4H+8IKdaTnhK83vPwyaVA/s05w3aiROB5SPB5bCMvQRTLyjHIZ/H+PK4nP06LMh/bj3KTF+npnQzMeX7++ed3HNux0g0EAoEWES/dQCAQaBGNW2177713shlkwGU9j7z45S9/mWzuytLmbuIDDzxQe94xxxyTbO5GMqEGTwnlcp9UlvaDDz6YbO84IUoQPCaIFO+hhx5K9rXXXptsUos8T+wdd9yRbLbZNddck2zuZN90003J/tGPfpRsJg+ipEJaTw8R0nfKBXwW6RHvk8s/THRy3nnndXwef+MlGKJHSZPE1BZInceOHdvxGlLLPJlRJ5CiMmgm/85LWkSKTEmBO+hLly5N9oIFC5I9YcKEjtd7ARTeMUPsmybpkc/g7zneujlZmdfwPTFjxoxkH3LIIcnmmKL8R5mHYD7pcePG1b7jnOTcZTIfetp47UR5JYIjAoFAYIAhXrqBQCDQIhrlhaeffjrZ3IlnAMH06dOTzeU3KUR+TEYfclrHJbsX20xaQzrCnWOCu52UNk477bRkX3/99cmmjMC8nKSEpByUJugdINV3XVk3SjWsJ+kP6fsll1yS7O9973vJJl0kHWU9vVyfpGmkRJRsJOnkk09ONscAPVgofxDeSapNTvdtgdSZkhW9Ndg3vN47GsfL6SzVKSh38pnDgn3ieR3Q5g4/xzD7nLmYGazCa+g1RC+TJqrsyQLe773cv5T/vFPGKcfxuQzQoe3lHL7vvvtqdeCc4VxizhXWjc/2chN3cxRVrHQDgUCgRcRLNxAIBFpEo7wwfvz4ZDM1HZfTnpOwt6PnURmpnl6Np9DyvvR4IOWjozNp2tFHH53sG264Idk//elPk02aRumANMjbraWkkFNz/k2pgnILKT89NijhTJw4UZ3A69k/LDdj20nBmF6SeRGYO0Gqn5hKLxLm2WCbsU/pKM4+9OSmNkEKShnE81jwToMmSFfz/BLsZ96LY5ife8fB8Ble+ViHe+65J9l33nlnsinHkVpTghg5cmTH66V6G7CsnPeUSDgOmerVawuC85n3ZzAS24jlZhvldfAkAv6GdaNU4R0nFN4LgUAgMMAQL91AIBBoEY3ywr333ptsUnBSJdJmLq2Z54AnIpAe5HRi2rRpyWbuBd7LkzPyuOo+MODAo76sA6m552XAXBJ0gmdggOSn4eOONcvEdqIUQOmA9+HJGZ7jNtM8MtXk8uXLk02Z4uGHH67VgVIA+4SO+d6prwQpYh440AuceOKJHT/3ZABvfHleIPnYZruwzzneKJFR/qAkR+rrpWSkt493SoVHoTlGKDvlp6IQrDcDDvg56Ti9A1hnT7ZhG7OeHPP0tKJHCfOKUBKT/FwiuezZB44Nz0OCtodY6QYCgUCLiJduIBAItIhGeYGOwXT0X7RoUbJJqUmDSEtJM0gtSQmkOs0ldeCuI52PKRFwt5hUkMt9OujTCZ4Uz8uI7wUZMBAhPzmC8gJj7ClPeBSRkgpBSYX0iPSVbUSPA2/HlZJPHuDB8u22227J5gGW7Cv2IfuB5e4mj8GqBvuQbeGdqOFRZVJi0uCcouapEfvA+UPJhuPKkwg4P1k+Pot14PjyrvGQyyUcM/TSIbVne9Dm3PO8C9jGXvk4v9gulAV5yo0nEUn1cc7nUUbgGOaYYdvEyRGBQCAwwBAv3UAgEGgRjWthLtnp0MzdftJ671A73of0lfQgvxd3Gj0HZV5PSk0a4HkjcAeVMgVpE6kmy0BKxB39nJqT8nOXlidbsNzerjbbkjIF0zyS4nsp9WhzN9qTaaQ6vWJsPMtKSYESE+kiy5fvIvcC7EMvzSXbkePOc9b3xml+L1Jn9i3HJ2kq78XP2aYsE/uW9fQCfLzTIph3Y/LkybX68DccMzzNgv3MejLdIuvGMvFzzmdKKl4wBX/LMuQpRSkpeKkaCc5htjHb1fstESvdQCAQaBHx0g0EAoEW0Sgv0PmeXgeUFxi3TsoxZMiQZNPbgUtxxnlL9V1N0hE+g7u63GUkdaZs4cWk81mkCqRvpDIsN3ecuXN7xBFH1OrDdHuk3fQCYBvTQZuUjbTGq7O3a8r2oqTCz+lAnnsWsK7MqE8qPWfOnGRTbmGZdt1112QzB0CvwLajDMSxwLb2gk9Ixzn+83YkFaZkw7FKSYnt6wUH0OZ4Ib32duK5k8+2YH0uu+wyeSDlZ/vxxAfSd8LLT0CZy/NkILwcMJwvTMk6evTojveR6nOP5ebnnAssE/uB7eIhVrqBQCDQIuKlGwgEAi2iUV4gHSUlYNw+Aw54zf33359sBkqQ7uROz6TzXOJzR5QpH0ntSYv4W+9UBFIFpssjreFOJOmEF3zBPA9SXSIhheNJC6QjDDggLWKZSKlIRykXsM5sC5aVh44yEIOeCPl9KclQPho+fHiySWE5TiivUM7oFTzvBVJlth1lAI/u8/Mc7H+2BdvOO52C9+V9OIZJgzlGOMc4zj2vC54IQi+D/LQPlonfUV6irOgF9bA+fDalLLYLf+sFLHkHefIQXcnPk8AxwLZkO/EdwM/j5IhAIBAYYIiXbiAQCLSIRnmB9GDYsGHJJlVgbD+X4jyTnqkJeWIB46KluvM9aSpTTJLykXZ7dIw26RgpBOkLKTt/u/POOyebtJk7rvmJCF5G+UGDBiWbDvHMycAACtJCUjl+TtpF2zuZ4LHHHut4z5xGUm7gfUmR2e+UIxjIwcARL4VfmyAl9JzsKUF4gQjePUn3pboMR8rPABe2F/OSeN4OHHuk1LyGY947ZHGPPfZI9uzZs5PteWnkz+PhrCy35y2TH9rZB0pePPDW89jw5D+Oc3oysL2kuseH53XA+cBysxych5F7IRAIBAYY4qUbCAQCLaJxLUxKzV1J7mKTQnD3nQENpKjcleTSX6pTai7TuZQnbSPloVxA2sHrPS8AL+Ud70naRRmBFCzfufQcyEm1vbhtUkHvgEfek/SVtJg2aS2fxb7K82Gwr9nelIkoi9DThG1Get6UYq8teCehsH3ZN56k4OW2yNuR7c2xR3mOzvuk6RzD3mGUHMOe1xHLQMmPAQ3eIZN5gAJpN09C8U6w8Gg658xtt92WbI4X1oH199rUS+ean+zCv3kQrBfsQBnBS/vKueQhVrqBQCDQIuKlGwgEAi2iUV7oJus8l9ykSqQQXOKTKtMZWvIPfyQN4AkWDMAgfaGMQFrIe5IqUyJgmVg3L10kaWq+8+/lKmD5eI23W+6l6iONpDeBd4Aey82dW94z36VmezBgg3XtJladu9cDAewPSgFeHgL2M+kuqSx/m6cRJEiFvaAeti/lGEpbXsAOy8qAIM/DpZvUiXnKz1w+6QPnOscCr/cOquU4ZP35HvICP1huthHHYF4HSgGeZxOfwXZiubvJgULESjcQCARaRLx0A4FAoEU0roVJTbzdZ9J9LvHp6M0lOg9vZErA/DvvID9SKtJl7+BDb7eTdIKyw+LFi5PtxZfT64L3zHe4SUM9Okb6z3YiHWfbE6RplCmYhpNlogcK68zP81MdSEP5PFJHL46fVJO0K8/v0At0c+oA290bj+xjtnXe3/zbO5jTC8DwpC2C7UupiZIFPQU8zwS2i7dDn/9NuYzj1pMzvJwHlAUoa3mHtLK9aLONxowZk2y+z6S63MDysX/4m8GDByeb45wePnFyRCAQCAwwxEs3EAgEWkSjvEBHd1Jq0kaPNpPucslN6pPvlJNGkbJwie/RaOZD4PNI/xh8QYmEzyXFJ80gvSQdZ31Iv6W63EL6QqnCC/ZgmTxHcUoElHPYV7zPCy+80PFZvCf7VvIDJ9j2pIX0TmF7ULagY36vQHpMau7JV+wDXkOq7KUdzJ/hpXAkZR03blyyp06dmmz2AcvEfuZYZf+xP7yDHylrcI7kc9VLVckyefPHk/zY3gy4oJcOr2FbePk86IlA+TL/zvPyYIAYA1a23XbbZLNunmxFxEo3EAgEWkS8dAOBQKBFxEs3EAgEWkSjpks9yDuegolPqHl4rhMjRoxINrUgyXc5Y4IY6pjUyeh6Rc2I2rAXaULXGGrG1IBYNkZmUcNpSnZBrcuLcuHvWSZPD/SOMaFNvZY6lHdsEnVvqa5X0R2IOVR5ojHbj9fwcyZG6hW8PMPUBqkfcjx7pwR795fqGi/7h1GPvIZudSwTNXfqshyrdGFi+aiBcnxx3Hl5ZfPPPRcwjjEelcM65Md09cGLBuS+h+fexn2FCRMmJJvvgrxP+B3dx3haN/cf2GbMg01XvKYjm/oQK91AIBBoEfHSDQQCgRbRKC+Q4pOaUGqgGxKpvOcWRTqVL8UpVZCysBykIHSNonvbvHnzks2lP2k6bV5D2kTa5UkWHh3L68Byk2p7dISUl7KIl3+X9/Tom+fO4p3OKtXzjG6++ebJZpQQZQfWmdSM7UepplfwogW9RDAsfzenBOeJTyjJ8V78jSdhnHrqqcmePHlysjkWPHfApjL1gdKc5xqXu4aynzmnKb15J/R65eM89OQIXs9rDjvssI7loRxDaVKq15tSJ8c2XVFZH74DKcl50XZErHQDgUCgRcRLNxAIBFpEo7xw5513Jnvo0KHJJt0nrSH9JOXkMp4JZfIIES9pBSkfKSuT1tDDgTu/3mmg3K0kVWDdlixZkmzujrJslCByjw3SedaV9/IiiRghQ6mG0Tl8Nukb78/IMZbby9HLvpLqu9H8DZ/B35Misj95n5zm9QKe9EOQpnbzW9L3XDaipOIl0uF9SZ3ZvhMnTkz2ZZdd1vE+XmSjd0wO5xev4T3z+lBi806rJrUnfadcwDpzrHr5i1m+o48+uuOzOA851vh+kur123HHHZPN9wpPa/aSP+XRhytCrHQDgUCgRcRLNxAIBFpEo7zAJTuX9dyJpaM7dzj5Wzprk2aTcub3ZYIUSgSUBbjE57NZJsoc3g4y6+Yl9iHdoU2anVNzSgSkUZ50wvsyTzGpGaUQ0hpSM7bxoEGDkk1phuWhZJF7PowdOzbZPB7pmWeeSTYpLGUeL5ev513RJrrJdewFpbBe3mnAObwkTN4JwqTv7POddtop2d/+9reTPWXKlGR7dN9L4MPPvUCRHJRLKD0yUIa/Z5k4Z9gurKd3dBHlFZbBO1qL8yL3LJg0aVKyL7roomRTAmV7EF7+3fBeCAQCgQGGeOkGAoFAi7Cm/I8nnnhi+pJOz6TRdB728tuSTniUQKrTXO40UlIgZSGV9fJ1kprTq+Hxxx9PtndqL69fuHBhshnEwcCP3Omf8gd3REnBmJ+AcgTbhnIBaQ0/p6TCOlAuIfVhu7CtuaudP4+Ul9Sb9eZ9KX+QknOcTJ8+fcXnm6wCTJo0KY1tjhcvtyxBSuzRyTwQgePTc6b3cvNSdmIfcB6yTU8//fRksw88WcfLT0BqndeHfc7vvFwP3unTLBPn1QEHHJBsSlNsI96ffcLyUDrhXJPqc5dtzFPNKW1041HBfvvhD3/YcWzHSjcQCARaRLx0A4FAoEU0ei8wNRt3Fr0YcVIO0gku9+mETAlC8uO++WzeixSctIvlIJXjPUnNeH9+Ts8HSg0sJ5+V52HgfelFQKmhGxmBv+UpqWxjtiX7hM/ydtq9vBL5vUg9KcnwN7Tnzp2bbHpjsF16BdbLOzLGi/PvxmMhl+14HYN02LeEd8KyN+aZavC8885L9lVXXZXs+fPnJ5tzgVSZ5ea4yD086F1Ays/56bUNjyLaa6+9OpaJoCcTy9TNac0EJVLJD/Dw3kN8N3iBSd3kFYmVbiAQCLSIeOkGAoFAi2iUF7ic5u44d8RrNwO14M6gt/TPd0RJHSgLMH7aC0wg3SX14fWUCPgsfk6Q4pO+0ZNhzz33TDapvFSnHfRYYFsedNBBySaN8mQbT3ZhX7GsXurNwYMHd7ye9FqqtyWfx/ZjfPqQIUOSTe8N9icDK3oFL/DBCyDgOGK9PAmC7SPV6bmX5pNtTUnBO1WawS70QKEHCfMT8EQEPpc5Rtg3HIPcxZfq/czgiFGjRiX7iCOOSDbHNk/6Za4TBt+wXb2TsdkWbF8vwCOXfPiO4r34OcEx4J3Qzft4iJVuIBAItIh46QYCgUCLaJQXuJzmkpsUjEt2BjdwJ55eEF6WfqlOqUiLubNIOkJayzwJpHakkY888kjHZ/Ma1oFUftiwYckmPWQs/LRp02r1IbUjdWTbsP3Y3gxS8Jzm+VtSTea08A7NYyAG+4RO9lK9bTyPBUobpKd8nhd73yt4O+60PZrK8dXN5/nzSE05rzwvAu8UBd6Tc4Eyl+elwTE4evToZO+9997JZj/lc5WUn9ID5yfHwqOPPppsylkMUmKZOF4or9Dbg/OF7cU6UzrMZS1PwqB8xP7hPPHyuHgH8hKx0g0EAoEWES/dQCAQaBGNuRcCgUAgsHIRK91AIBBoEfHSDQQCgRYRL91AIBBoEfHSDQQCgRYRL91AIBBoEfHSDQQCgRbx/wC4tB+H1FJCzQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "size = int(np.sqrt(A.shape[1]))\n",
    "\n",
    "plt.figure()\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.imshow(x_et.reshape(size, size), cmap='gray')\n",
    "plt.title('Reconstructed Image')\n",
    "plt.axis('off')\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.imshow(x_flat.reshape(size, size), cmap='gray')\n",
    "plt.axis('off')\n",
    "plt.title('Original Image')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cd0de633-736b-42c0-9763-83f0d6a31521",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}