test_rfft.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import torch.nn.functional as F\n",
    "import numpy as np\n",
    "import torchvision.transforms as transforms\n",
    "import torchvision\n",
    "import torch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = torch.linspace(0, 255, 256)\n",
    "b = torch.tensor([[0, 1, 2], [1, 2, 3]], dtype=torch.int32)\n",
    "c = a[b]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0., 1., 2.],\n",
       "        [1., 2., 3.]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_data = torchvision.datasets.MNIST(\"./\", train=True, transform=transforms.ToTensor(), download=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = train_data[0][0].view(1, 1, 28, 28)\n",
    "x = F.interpolate(x, size=36, mode=\"bicubic\")\n",
    "x = x[0, 0]\n",
    "plt.imshow(x, cmap=\"gray\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [],
   "source": [
    "h, w = x.size()\n",
    "\n",
    "f = torch.fft.rfft2(x, s=(h, w), norm='ortho')\n",
    "f_l = f.clone()\n",
    "f[..., :h//4+1, :w//4+1] = 0\n",
    "f[..., -h//4:, :w//4+1] = 0\n",
    "f_l[..., h//4+1:-h//4, :] = 0\n",
    "f_l[..., w//4+1:] = 0\n",
    "x_recon = torch.fft.irfft2(f, s=(h, w), norm='ortho')\n",
    "x_recon_l = torch.fft.irfft2(f_l, s=(h, w), norm='ortho')\n",
    "x_r = x_recon + x_recon_l\n",
    "f_new = torch.fft.rfft2(x_recon, s=(h, w), norm='ortho')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([  0.,   1.,   2.,   3.,   4.,   5.,   6.,   7.,   8.,   9.,  10.,  11.,\n",
       "         12.,  13.,  14.,  15.,  16.,  17., -18., -17., -16., -15., -14., -13.,\n",
       "        -12., -11., -10.,  -9.,  -8.,  -7.,  -6.,  -5.,  -4.,  -3.,  -2.,  -1.])"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = torch.fft.fftfreq(h, 1/h)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([  0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,  10.,  11.,\n",
       "         12.,  13.,  14.,  15.,  16.,  17., -18., -17., -16., -15., -14., -13.,\n",
       "        -12., -11., -10.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.])"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[:h//4+1] = 0\n",
    "a[-h//4:] = 0\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10., 11., 12., 13.,\n",
       "        14., 15., 16., 17., 18.])"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = torch.fft.rfftfreq(w, 1/w)\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0., 10., 11., 12., 13.,\n",
       "        14., 15., 16., 17., 18.])"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[:w//4+1] = 0\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams[\"figure.figsize\"] = (10, 5)\n",
    "\n",
    "plt.subplot(1, 3, 1)\n",
    "plt.imshow(np.abs(f))\n",
    "plt.title('f')\n",
    "\n",
    "plt.subplot(1, 3, 2)\n",
    "plt.imshow(np.abs(f_l))\n",
    "plt.title('f_new')\n",
    "\n",
    "plt.subplot(1, 3, 3)\n",
    "plt.imshow(np.abs(np.fft.fft2(x_recon)))\n",
    "plt.title('fft of x_recon')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show(close=None, block=None)>"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AFxhoAAAvMNAAAF5goAEAvMBAAwB4gYEGAPBCTMuJY6mtrc30rnbrO9RTUlKcrnsgsuPGjTPluru7zWu6NLBYs/fff795zS+++MKczczMNGdLS0tNuT//8z83r5mUlGTOXn755eas9Tb46KOPzGtu2rTJnJ04caIpt2fPHvOaLh5++GFzdsyYMaacy3nl0tRh/bzFw4cPm9dsamoyZ11+BlyaOqxOnTplzro0kFjvXy336S5tJr3xCA0A4AUGGgDACww0AIAXGGgAAC8w0AAAXmCgAQC8wEADAHiBgQYA8AIDDQDgBQYaAMALQ7b6qr293VQBNWrUKNN6iYmJ5ut2qbKJRCLmrLX2pr293bymS/VWQ0ODKTd+/HjzmrW1tebsp59+as5aa7oKCgrMa/7FX/yFOXvNNdeYs998840p51J99cwzz5izV155pSl3yy23mNesq6szZ19++WVzNj8/35RrbW01r+lS6WWtaLrssstivqYkZWdnm7Nnzpwx5VyOlbX6S7LXlEn22+DkyZMXzVB9BQD43mOgAQC8wEADAHiBgQYA8AIDDQDgBQYaAMALDDQAgBcYaAAALzDQAABeYKABALwwZKuvOjo6Yppzqb5yqZNyqalqaWmJaU6Sjh8/bs6ePn3alHOpvAmCwJx1qd2xVh/Nnj3bvObo0aPNWet5JUkJCQmm3EMPPWRe8+jRo+as9XwNhULmNVNTU81Za/WWJI0YYfs/9KFDh8xruhg3bpwpZ62dktxquuLi4sxZ620VDofNa1rvAyS3n4H4+PiY5VzuU3rjERoAwAsMNACAFxhoAAAvMNAAAF5goAEAvMBAAwB4gYEGAPACAw0A4AUGGgDAC0O2KaSzs9P0Tnnru/QzMjLM1+3SktDU1GTOWqWkpJizLvsViURMOZdGiQkTJpiz1dXV5uxvfvMbU27KlCnmNb/44gtzNicnx5y97LLLTDlr84MkvfTSS+bsLbfcYso1Njaa16ytrTVnXdpyJk6caMq53FYuzT7W+wuXphCX89pl3fHjx5tyLvcXLu0fLo1FmZmZppzlvtV6P9UXHqEBALzgPNC2b9+u+fPnKy8vT6FQSG+99VaP7y9evFihUKjH5eabb47V9gIA0Cfngdba2qpp06Zp7dq1583cddddOnbsWPTy3nvvXdJGAgBwMc7PoZWUlKikpOSCmXA47PQcBAAAl2pAnkOrqKhQVlaWJk+erEceeUT19fXnzUYiETU3N/e4AADgKuYDraSkRK+++qq2bdum559/Xrt27dKcOXPO+8qV8vJyZWRkRC/5+fmx3iQAwPdAzF+2v2jRouifi4qKNH36dBUUFOjdd9/VwoULz8mvWLFCy5cvj/69ubmZoQYAcDbg70PLzc1VQUGBDh482Of3w+Gw0yeuAgDQlwF/H1pDQ4Nqa2uVm5s70FcFAPgec36EdurUKX355ZfRv1dXV2vfvn3KzMxUZmamysrKdN999yk3N1c1NTV66qmnNHbsWN17770x3XAAAL7LeaDt3r1bd9xxR/TvZ5//Ki0t1bp161RVVaVXXnlFjY2Nys3N1R133KHXXntNaWlpTtcTFxenuLi4i+astTsu15+UlGTOulRfWSulXJ5DzMrKMmePHTtmyiUmJprXHDNmjDl7+vRpc/brr7825eLj481rulTq7N6925w9cuSIKXf55Zeb1/zd735nzl5//fWm3NSpU81rJicnm7NVVVXmbFdXlynnUmdlPVckaezYsaacy2+UXGq6XH4GrFmX+7aEhARz9tSpU+astdLLct/qcnv25jzQZs+erSAIzvv9Dz74oN8bAwBAf9HlCADwAgMNAOAFBhoAwAsMNACAFxhoAAAvMNAAAF5goAEAvMBAAwB4gYEGAPDCgLft91diYqKphd9akeNSpeNS/ZSammrOdnd3m3IuH3JqrdOS7PU0F/pA1t5GjrSfQqNHjzZnrbfB8ePHzWv+8Ic/NGfXrFljzlprqhYsWGBe8wc/+IE5az1fXeqcRo0aZc5+8skn5uxll11myrmc1y6VZtafQZef65ycHHP2m2++MWc7OztNOevPtSSnTzZxuV2tNV2WOkPrfveFR2gAAC8w0AAAXmCgAQC8wEADAHiBgQYA8AIDDQDgBQYaAMALDDQAgBcYaAAALwzZppCRI0eaWigSEhJM67m8+9wla71+SWpqajLlDh06ZF7T8s77s6yNAl1dXeY1XaSlpZmzycnJptxXX31lXjM+Pt6cnTt3rjlrvV0PHz5sXrO0tNSc/ed//mdTrqamxrzm7bffbs6OHz/enLU2Srisecstt5iz1mYZa6OI5HZ/4dLU0dHRYcq5tCC5NPu4NCZZby/LPln3uy88QgMAeIGBBgDwAgMNAOAFBhoAwAsMNACAFxhoAAAvMNAAAF5goAEAvMBAAwB4gYEGAPDCkK2+OnPmjEaMuPi8tVa5hEIhp+u2CoLAnLVWybhUNLlUX7msa+VSEWStPZLsx9Wlnufbb781Z8eOHWvOZmRkmHJHjhwxr7ljxw5zNj093ZTLyckxr+myrVlZWeas9RzYvHmzeU2X83r69OmmnEtNmEtVncv5mpqaasq5/Ay61Eq53LdYs5ZavUup3uMRGgDACww0AIAXGGgAAC8w0AAAXmCgAQC8wEADAHiBgQYA8AIDDQDgBQYaAMALDDQAgBeGbPVVd3e3qQLFWnvjUuMSiUTMWRfWiqSUlJQBuX5rpYxLlU5bW5s5297ebs5aK4LGjBljXtOleuvYsWPmbFNTkynncl651HTdcccdppy1IkuSPv/8c3M2OTnZnD148KAp51IR5VKV9MEHH5hy06ZNM68ZDofNWUudn+u6LvV7A1E/J0kJCQmmnEutYH/wCA0A4AWngVZeXq4bb7xRaWlpysrK0j333HPO/+SCIFBZWZny8vKUlJSk2bNn68CBAzHdaAAAenMaaJWVlXrssce0c+dObd26VZ2dnSouLlZra2s089xzz2n16tVau3atdu3apZycHM2bN08tLS0x33gAAM5yeg6t90c6rF+/XllZWdqzZ49uv/12BUGgF154QStXrtTChQslSRs2bFB2drY2btyon/zkJ7HbcgAAvuOSnkM7+2R4ZmamJKm6ulp1dXUqLi6OZsLhsGbNmnXez3eKRCJqbm7ucQEAwFW/B1oQBFq+fLluvfVWFRUVSZLq6uokSdnZ2T2y2dnZ0e/1Vl5eroyMjOglPz+/v5sEAPge6/dAW7p0qfbv369f/epX53yv96dDB0Fw3k+MXrFihZqamqKX2tra/m4SAOB7rF/vQ3v88cf1zjvvaPv27ZowYUL062c/4r2urk65ubnRr9fX15/zqO2scDjs9D4OAAD64vQILQgCLV26VG+88Ya2bdumwsLCHt8vLCxUTk6Otm7dGv1aR0eHKisrNXPmzNhsMQAAfXB6hPbYY49p48aNevvtt5WWlhZ9XiwjI0NJSUkKhUJatmyZVq1apUmTJmnSpElatWqVkpOT9eCDDw7IDgAAIDkOtHXr1kmSZs+e3ePr69ev1+LFiyVJTz75pNrb27VkyRKdPHlSN910k7Zs2aK0tDS3DRs50lxrZeFSueJST+OStVYfudRJudT+WCutXKp0XFjrcSR77Y5LnZbLeyFdjoH1PP3ur+Ev5ruvFL4Y6zn4m9/8xrymtc5LkubOnWvOfvzxx6bcX/3VX5nXtFbKSdKSJUtMuXnz5pnXdKlfa2xsNGddfratXO5TXe4HBrrSysppoFl2MBQKqaysTGVlZf3dJgAAnNHlCADwAgMNAOAFBhoAwAsMNACAFxhoAAAvMNAAAF5goAEAvMBAAwB4oV/lxH8II0aMMDUgdHR0xPy6XRotrO0bkr0lwOUz4VzezW/dL5f9T05ONmddWgpOnz5typ04ccK8posrrrjCnLV+5NF3P9n9Yr799ltzdtSoUabcJ598Yl7TpdHiv//7v83Zv/mbvzHl9u3bZ16ztLTUnL333ntNucTERPOaLsfq1KlT5qy1KSQ1NdW8prWBR7I3G7mw3LfExcX1e30eoQEAvMBAAwB4gYEGAPACAw0A4AUGGgDACww0AIAXGGgAAC8w0AAAXmCgAQC8wEADAHhhyFZfWSutrNVPSUlJ5usOhULmrLWiSZLC4bApV1hYaF7TpU7KWqXjUqflor293Zxta2sz5TIyMsxr5uTkmLPjxo0zZw8fPmzKbdu2zbxmTU2NOXvLLbeYcnfffbd5TZf9f/vtt81Z63H97LPPzGuuWbPGnP3FL35hyq1atcq8Zl1dnTl79OhRczY3N9eUs96vSFJLS4s561IraK3fslRvWe+n+sIjNACAFxhoAAAvMNAAAF5goAEAvMBAAwB4gYEGAPACAw0A4AUGGgDACww0AIAXGGgAAC8M++ora/WTS0WUS51VZ2enOWutExo/frx5zTNnzpizDQ0NppzLPkUiEXO2tbXVnLVWlV1xxRXmNU+ePGnObty40Zy1ni9z5841r/nAAw+Ys9ZzoL6+3rzmvn37zNl33nnHnL311ltNuYcffti8pkv11BtvvGHKZWVlmdc8duyYOZuQkGDOWmvdBuq+rbu725y17pelVs+lerA3HqEBALzAQAMAeIGBBgDwAgMNAOAFBhoAwAsMNACAFxhoAAAvMNAAAF5goAEAvDBkm0Li4uIUFxd30dzIkbZdcGm/sLyb/SyXd+mfOnXKlNu/f795zRMnTpiz1tvApSXB2mYgSWlpaeas1VdffWXOWptSJCklJcWcnTZtmil34403mtd0OV/37t1ryrncVuFw2Jx1aWsZPXq0KefSKuOyrffff78p59LoMWrUKHPWpQXDet/i0v4xYoT9MYz1vlWSurq6YpZzaT/qjUdoAAAvOA208vJy3XjjjUpLS1NWVpbuueceff755z0yixcvVigU6nG5+eabY7rRAAD05jTQKisr9dhjj2nnzp3aunWrOjs7VVxcfM6vB+666y4dO3YsennvvfdiutEAAPTm9Bza5s2be/x9/fr1ysrK0p49e3T77bdHvx4Oh5WTkxObLQQAwOCSnkNramqSJGVmZvb4ekVFhbKysjR58mQ98sgjF/zYikgkoubm5h4XAABc9XugBUGg5cuX69Zbb1VRUVH06yUlJXr11Ve1bds2Pf/889q1a5fmzJlz3s/NKi8vV0ZGRvSSn5/f300CAHyP9ftl+0uXLtX+/fv10Ucf9fj6okWLon8uKirS9OnTVVBQoHfffVcLFy48Z50VK1Zo+fLl0b83Nzcz1AAAzvo10B5//HG988472r59uyZMmHDBbG5urgoKCnTw4ME+vx8Oh53eRwIAQF+cBloQBHr88cf15ptvqqKiQoWFhRf9Nw0NDaqtrVVubm6/NxIAgItxeg7tscce03/+539q48aNSktLU11dnerq6tTe3i7p900YP/vZz/Txxx+rpqZGFRUVmj9/vsaOHat77713QHYAAADJ8RHaunXrJEmzZ8/u8fX169dr8eLFiouLU1VVlV555RU1NjYqNzdXd9xxh1577TXn2iPrryKtNVUdHR3m63aph7HUc5118uRJU86lzspaOSPZa4fS09PNa+bl5ZmzLhU9hw4dMuVqamrMa2ZnZ5uzf/3Xf23OWs/tF1980bzm+++/b85aa7oWLFhgXvPOO+80Z5OTk83Z1157zZT77vPqF+Py25+7777blPvkk0/Ma15KVdOFtLS0mHIuVX0uT++41HSd70V//VnT5T6tN+dfOV5IUlKSPvjgg35vDAAA/UWXIwDACww0AIAXGGgAAC8w0AAAXmCgAQC8wEADAHiBgQYA8AIDDQDgBQYaAMAL/f74mIEWBIGp0qW7u9u0nktFlQvr9Uv26qVbbrnFvObFPu3gu44fP27Kvffee+Y1P/74Y3PWWv0lSddcc40p9/zzz5vX7P1RRxeyfv16c/bzzz835RITE81rrly50pydO3euKbdr1y7zmk8//bQ5e+rUKXO2r4+Q6ktZWZl5TZequOrqalOusbHRvKbLcU1KSjJnrfdZ8fHx5jVd6qxcKrVief0u29gbj9AAAF5goAEAvMBAAwB4gYEGAPACAw0A4AUGGgDACww0AIAXGGgAAC8w0AAAXhiyTSHd3d3q6uqK2XojRthnt0v7h8u72sPhsCnX1NRkXvOTTz4xZ2tqaky5JUuWmNdsb283Z7/55htztqWlxZT7+c9/bl5z8+bN5mxubq45+2d/9memnEury5dffmnOrlmzxpTr6Ogwrzlz5kxzNjk52ZxNS0sz5Y4cOWJe06WpxNrUkZ6ebl7Thct9y0C0G7mcAy5NISNH2kaJ5X7Y5b76nH/b738JAMAQwkADAHiBgQYA8AIDDQDgBQYaAMALDDQAgBcYaAAALzDQAABeYKABALzAQAMAeGHIVl/Fx8crISHhornTp0+b1jtz5oz5ulNSUsxZ6/VLUlVVlSkXHx9vXtOl9qe6utqU2717t3nNuro6c9ZyPM+yVg/97ne/M69ZXFxszl511VXmrPV4ffrpp+Y1XW5X63EtLCw0rzlt2jRz1uVn6+DBg6ZcQ0ODeU2Xn9esrCxTzlrRJcmpoq+1tdWcjUQippxLRZVLnVZnZ6c5a70NLNfvUifYG4/QAABeYKABALzAQAMAeIGBBgDwAgMNAOAFBhoAwAsMNACAFxhoAAAvMNAAAF5goAEAvDBkq68SEhJMVUnNzc2m9VwqX7Kzs81Z6/VLUktLiynnUlF0/fXXm7PW2p+KigrzmrW1teasS0XP1KlTTbn58+eb17z66qvN2aNHj5qzH3zwgSm3f/9+85ouNV1FRUWm3MiR9h/3mpoac/arr74yZ60/h+PHjzevOWKE/f/l1kqtEydOmNdMTEw0Z611VpLU0dFhyqWmpprXTE5ONmcHoqYrHA5fNEP1FQDge89poK1bt07XXXed0tPTlZ6erhkzZuj999+Pfj8IApWVlSkvL09JSUmaPXu2Dhw4EPONBgCgN6eBNmHCBD377LPavXu3du/erTlz5mjBggXRofXcc89p9erVWrt2rXbt2qWcnBzNmzfP/Ks2AAD6y2mgzZ8/X3fffbcmT56syZMn65lnnlFqaqp27typIAj0wgsvaOXKlVq4cKGKioq0YcMGtbW1aePGjeddMxKJqLm5uccFAABX/X4OraurS5s2bVJra6tmzJih6upq1dXV9XgyOxwOa9asWdqxY8d51ykvL1dGRkb0kp+f399NAgB8jzkPtKqqKqWmpiocDuvRRx/Vm2++qSlTpkQ/kLD3KwSzs7Mv+GGFK1asUFNTU/Ti8qo5AADOcn7Z/lVXXaV9+/apsbFRr7/+ukpLS1VZWRn9fu+XXAZBcMGXYYbDYdNLOQEAuBDnR2gJCQm68sorNX36dJWXl2vatGlas2aNcnJyJJ370fH19fVO7+sCAKA/Lvl9aEEQKBKJqLCwUDk5Odq6dWv0ex0dHaqsrNTMmTMv9WoAALggp185PvXUUyopKVF+fr5aWlq0adMmVVRUaPPmzQqFQlq2bJlWrVqlSZMmadKkSVq1apWSk5P14IMPDtT2AwAgyXGgHT9+XA899JCOHTumjIwMXXfdddq8ebPmzZsnSXryySfV3t6uJUuW6OTJk7rpppu0ZcsWpaWlOW9YEASmqqTOzk7Tei7P07lUr7jUw/z4xz825WbNmmVe01rlI0mjR4825f7u7/7OvKa1TkuS3n77bXN29+7dptzEiRPNa5aUlJizLufL0qVLTTmX43qhF1L19vXXX5tybW1t5jVPnjxpznZ1dZmz1lcxjxo1yrymy7Y2Njaaci41bS7VUy7rdnd3m3Iu1V8uXI6r9T7TUr/mcr3nrO8Sfumlly74/VAopLKyMpWVlfV7gwAA6A+6HAEAXmCgAQC8wEADAHiBgQYA8AIDDQDgBQYaAMALDDQAgBcYaAAAL4QCl7eu/wE0NzcrIyNDP/3pT01tDdb2A5e2Epfs4cOHzdlDhw7FfM1vvvnGnLU2D1xzzTXmNa+88kpz1qXRwHpaXn755eY1XZoyxowZY84mJSWZctZGD8mtKSQhIcGUy8jIMK9p3SdJiouLM2et2tvbBySbmJhoyrncVi7ntcu2WhszXG7/jo4Oc/b06dPmrPUctJxXkUhE//Iv/6Kmpialp6ebt0HiERoAwBMMNACAFxhoAAAvMNAAAF5goAEAvMBAAwB4gYEGAPACAw0A4AUGGgDACww0AIAXRg72BpxPd3e3qarJWtFjrX2SpMbGRnPWpSZrypQpptwf/dEfmddMSUkxZ0OhkCnnUqflcltZr1+SUlNTTTmXOqsJEyaYsy6sNVUtLS3mNV3OK+tt5VIjZK2IkqQzZ86Ys01NTabcQNRZSVJmZmbM13SpkxqI+rfOzk7zmtY6LUmKj483Z637FYlEYpI573b0+18CADCEMNAAAF5goAEAvMBAAwB4gYEGAPACAw0A4AUGGgDACww0AIAXGGgAAC8w0AAAXhiy1VdxcXGKi4sz5Sxc6mlcqnxcKoquuOIKUy43N9e8pkv1lfU2cKmzamhoMGddaqqsFT0ux/Xw4cPmbGtrqzkbDodNubFjx5rXtFa6Sfbbqrm52bzm0aNHzVmX6iVrpVRGRoZ5TZc6qfr6elPO5bayVlRJbnVS1vNq5Ej73fhA1FlJ9nPAUkHoUs/VG4/QAABeYKABALzAQAMAeIGBBgDwAgMNAOAFBhoAwAsMNACAFxhoAAAvMNAAAF4Ysk0hVtZ3qIdCIfOa1jYDya1V5Le//a0pV1FRYV7TpdHA2hIwevRo85pjxowxZ13aL6zH1aV95PTp0+asS0uCta3GpVGjpaXFnLW2pZw6dSrma0puTRXW29WlLcLlHLD+vLjsv7XRQ5ISEhLMWet5Zc25srR6uLIcf5f76nPW7/e/BABgCHEaaOvWrdN1112n9PR0paena8aMGXr//fej31+8eLFCoVCPy8033xzzjQYAoDenXzlOmDBBzz77rK688kpJ0oYNG7RgwQLt3btX1157rSTprrvu0vr166P/xuUhNgAA/eU00ObPn9/j788884zWrVunnTt3RgdaOBxWTk5O7LYQAACDfj+H1tXVpU2bNqm1tVUzZsyIfr2iokJZWVmaPHmyHnnkkYt+XEMkElFzc3OPCwAArpwHWlVVlVJTUxUOh/Xoo4/qzTff1JQpUyRJJSUlevXVV7Vt2zY9//zz2rVrl+bMmaNIJHLe9crLy5WRkRG95Ofn939vAADfW84v27/qqqu0b98+NTY26vXXX1dpaakqKys1ZcoULVq0KJorKirS9OnTVVBQoHfffVcLFy7sc70VK1Zo+fLl0b83Nzcz1AAAzpwHWkJCQvRFIdOnT9euXbu0Zs0a/fu///s52dzcXBUUFOjgwYPnXS8cDju9jwMAgL5c8vvQgiA4768UGxoaVFtbq9zc3Eu9GgAALsjpEdpTTz2lkpIS5efnq6WlRZs2bVJFRYU2b96sU6dOqaysTPfdd59yc3NVU1Ojp556SmPHjtW9995rvo4gCCTZ36l/Nh+rnOTWEuHCuk8u7SMu7RPWd+C7XL9Lo4LL7WrdL5frH6httTZlXEoDwoVYj5fL/rucAy6NEtZtcLmtBuIccNl/l211afWw3q4urSoDdd8Wy1aRs8fI5T47KnDw8MMPBwUFBUFCQkIwbty4YO7cucGWLVuCIAiCtra2oLi4OBg3blwQHx8fTJw4MSgtLQ2OHDnichVBbW1tIIkLFy5cuHyPL7W1tU6zIwiCIBQE/RmDA6e7u1tHjx5VWlpaj//5nH2xSG1trdLT0wdxC2PHx32S/NwvH/dJ8nO/fNwnyc/96mufgiBQS0uL8vLynB9RDrly4hEjRmjChAnn/f7Z2i2f+LhPkp/75eM+SX7ul4/7JPm5X733KSMjo1/rUE4MAPACAw0A4IVhM9DC4bCefvppr96z5uM+SX7ul4/7JPm5Xz7uk+TnfsV6n4bci0IAAOiPYfMIDQCAC2GgAQC8wEADAHiBgQYA8AIDDQDghWEx0F588UUVFhYqMTFRN9xwg/73f/93sDfpkpSVlSkUCvW45OTkDPZmOdm+fbvmz5+vvLw8hUIhvfXWWz2+HwSBysrKlJeXp6SkJM2ePVsHDhwYnI11cLH9Wrx48TnH7uabbx6cjTUqLy/XjTfeqLS0NGVlZemee+7R559/3iMz3I6XZZ+G47Fat26drrvuumhzxowZM/T+++9Hvz/cjpN08X2K5XEa8gPttdde07Jly7Ry5Urt3btXt912m0pKSnTkyJHB3rRLcu211+rYsWPRS1VV1WBvkpPW1lZNmzZNa9eu7fP7zz33nFavXq21a9dq165dysnJ0bx589TS0vIH3lI3F9svSbrrrrt6HLv33nvvD7iF7iorK/XYY49p586d2rp1qzo7O1VcXKzW1tZoZrgdL8s+ScPvWE2YMEHPPvusdu/erd27d2vOnDlasGBBdGgNt+MkXXyfpBgeJ+c64z+wP/7jPw4effTRHl+7+uqrg7/9278dpC26dE8//XQwbdq0wd6MmJEUvPnmm9G/d3d3Bzk5OcGzzz4b/drp06eDjIyM4Oc///kgbGH/9N6vIAiC0tLSYMGCBYOyPbFSX18fSAoqKyuDIPDjePXepyDw41gFQRCMHj06+OUvf+nFcTrr7D4FQWyP05B+hNbR0aE9e/aouLi4x9eLi4u1Y8eOQdqq2Dh48KDy8vJUWFioBx54QIcOHRrsTYqZ6upq1dXV9Thu4XBYs2bNGvbHTZIqKiqUlZWlyZMn65FHHlF9ff1gb5KTpqYmSVJmZqYkP45X7306azgfq66uLm3atEmtra2aMWOGF8ep9z6dFavjNOTa9r/rxIkT6urqUnZ2do+vZ2dnq66ubpC26tLddNNNeuWVVzR58mQdP35c/+///T/NnDlTBw4c0JgxYwZ78y7Z2WPT13E7fPjwYGxSzJSUlOhP//RPVVBQoOrqav393/+95syZoz179gyLSqIgCLR8+XLdeuutKioqkjT8j1df+yQN32NVVVWlGTNm6PTp00pNTdWbb76pKVOmRIfWcDxO59snKbbHaUgPtLN6fyJsEAQD9um/fwglJSXRP0+dOlUzZszQFVdcoQ0bNmj58uWDuGWx5dtxk6RFixZF/1xUVKTp06eroKBA7777rhYuXDiIW2azdOlS7d+/Xx999NE53xuux+t8+zRcj9VVV12lffv2qbGxUa+//rpKS0tVWVkZ/f5wPE7n26cpU6bE9DgN6V85jh07VnFxcec8Gquvrz/nfynDWUpKiqZOnaqDBw8O9qbExNlXbPp+3CQpNzdXBQUFw+LYPf7443rnnXf04Ycf9vjMweF8vM63T30ZLscqISFBV155paZPn67y8nJNmzZNa9asGdbH6Xz71JdLOU5DeqAlJCTohhtu0NatW3t8fevWrZo5c+YgbVXsRSIRffbZZ8rNzR3sTYmJwsJC5eTk9DhuHR0dqqys9Oq4SVJDQ4Nqa2uH9LELgkBLly7VG2+8oW3btqmwsLDH94fj8brYPvVlOByrvgRBoEgkMiyP0/mc3ae+XNJxislLSwbQpk2bgvj4+OCll14KPv3002DZsmVBSkpKUFNTM9ib1m9PPPFEUFFRERw6dCjYuXNn8MMf/jBIS0sbVvvU0tIS7N27N9i7d28gKVi9enWwd+/e4PDhw0EQBMGzzz4bZGRkBG+88UZQVVUV/OhHPwpyc3OD5ubmQd7yC7vQfrW0tARPPPFEsGPHjqC6ujr48MMPgxkzZgTjx48f0vv105/+NMjIyAgqKiqCY8eORS9tbW3RzHA7Xhfbp+F6rFasWBFs3749qK6uDvbv3x889dRTwYgRI4ItW7YEQTD8jlMQXHifYn2chvxAC4Ig+Ld/+7egoKAgSEhICK6//voeL80djhYtWhTk5uYG8fHxQV5eXrBw4cLgwIEDg71ZTj788MNA0jmX0tLSIAh+/1Lwp59+OsjJyQnC4XBw++23B1VVVYO70QYX2q+2traguLg4GDduXBAfHx9MnDgxKC0tDY4cOTLYm31Bfe2PpGD9+vXRzHA7Xhfbp+F6rB5++OHofd24ceOCuXPnRodZEAy/4xQEF96nWB8nPg8NAOCFIf0cGgAAVgw0AIAXGGgAAC8w0AAAXmCgAQC8wEADAHiBgQYA8AIDDQDgBQYaAMALDDQAgBcYaAAAL/x/0Nu8urvApTwAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(x_recon, cmap=\"gray\")\n",
    "plt.show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor(2.3842e-07)\n"
     ]
    }
   ],
   "source": [
    "print(torch.max(torch.abs(x - x_r)))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "score",
   "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": "3.11.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}