notebooks/algo3.7.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# シンクホーンアルゴリズム（アルゴリズム 3.2）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "! pip install POT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import ot\n",
    "import matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# データの生成\n",
    "np.random.seed(0)\n",
    "n, m = 8, 8\n",
    "C = np.random.rand(n, m)\n",
    "a = np.random.rand(n)\n",
    "a /= a.sum()\n",
    "b = np.random.rand(m)\n",
    "b /= b.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fc8128e1b50>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "P = ot.emd(a, b, C)\n",
    "plt.imshow(P, cmap=plt.cm.Blues)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPUAAAD4CAYAAAA0L6C7AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAAsTAAALEwEAmpwYAAAMEklEQVR4nO3d349c9XnH8ffj2TXG2AZshx+xnTqo1BJK1Bi5VMgqUiCpoEHARStBlUiNInHTRNBWQlD1Jn9AU3pRpYocCFIoqIUgRREJjRSiFqml2MZtA4bKsUi9hcTY4IJBtrH99GLH1cKuvWdnzzmzfvR+Savd2RnN93N297PfmTNnzjcyE0l1LBt3AEntstRSMZZaKsZSS8VYaqmYiS7u9NK163PDpk90cdezDJZFL+MAnO75hYLJQZ/b1t/GLYua2wX9bdt//+I1Dh06NOdgnZR6w6ZP8OQzz3Vx17OsWtHJJszpxMnTvY0FcMXFF/Q21rvHTvY21srlg97GOv5Bv7+zFT1t2+9c/1tnvc6H31IxlloqxlJLxVhqqRhLLRVjqaViLLVUjKWWirHUUjGNSh0RN0fEqxGxLyLu7zqUpNHNW+qIGAB/A9wCXAPcFRHXdB1M0miazNTXAfsyc39mngAeB27vNpakUTUp9QbgwIzLU8PvfUhE3B0ROyNi59uHD7WVT9ICNSn1XG/vmvV+tsz8VmZuy8xtl65bv/hkkkbSpNRTwKYZlzcCr3cTR9JiNSn1C8DVEfHJiFgO3Al8v9tYkkY17xkGMvNkRHwVeAYYAA9l5kudJ5M0kkanDcnMp4GnO84iqQUeUSYVY6mlYiy1VIylloqx1FIxlloqxlJLxXSyvEUmHP/gVBd3PcvbR0/0Mg7Aygv6W1kC4LI1/a3QcexEP78vgAsn+/s5Hu7x7wNg3arlvYxzruWEnKmlYiy1VIylloqx1FIxlloqxlJLxVhqqRhLLRVjqaViLLVUTJMVOh6KiIMR8bM+AklanCYz9XeAmzvOIakl85Y6M/8JeKuHLJJa0Npz6g8tu/OWy+5I49JaqT+07M5al92RxsW931IxlloqpslLWo8B/wJsiYipiPhK97EkjarJWlp39RFEUjt8+C0VY6mlYiy1VIylloqx1FIxlloqxlJLxXSy7M7efVP89m0PdHHXszz+yF/0Mg7AG28e620sgKsuu6i3sY59cLq3sY6f7G+s946f7G0sgLU9LbtzLs7UUjGWWirGUkvFWGqpGEstFWOppWIstVSMpZaKsdRSMZZaKqbJOco2RcSzEbE3Il6KiHv6CCZpNE2O/T4J/Flm7o6I1cCuiPhxZr7ccTZJI2iy7M4bmbl7+PW7wF5gQ9fBJI1mQe/SiojNwFbg+Tmuuxu4G4DJVS1EkzSKxjvKImIV8CRwb2a+89HrZy67ExMXtplR0gI0KnVETDJd6Ecz83vdRpK0GE32fgfwbWBvZn6j+0iSFqPJTL0d+BJwY0TsGX78Xse5JI2oybI7zwHRQxZJLfCIMqkYSy0VY6mlYiy1VIylloqx1FIxlloqxlJLxXSyltant2zih8/2c0TpygsGvYwDcLzH9aYAJgb9/c/9+KUrehtrWfR3LNOvX97vOwYnBv1s27l+hs7UUjGWWirGUkvFWGqpGEstFWOppWIstVSMpZaKsdRSMU1OPLgiIv4tIv59uOzO1/sIJmk0TQ4TPQ7cmJlHh6cKfi4ifpiZ/9pxNkkjaHLiwQSODi9ODj+yy1CSRtf0ZP6DiNgDHAR+nJlzLrsTETsjYufhQ4dajimpqUalzsxTmfkZYCNwXUR8ao7b/P+yO+vWr285pqSmFrT3OzOPAD8Fbu4ijKTFa7L3+2MRccnw6wuBzwGvdJxL0oia7P2+EngkIgZM/xP4+8z8QbexJI2qyd7v/2B6TWpJ5wGPKJOKsdRSMZZaKsZSS8VYaqkYSy0VY6mlYiy1VEwny+689tb7fOWxF7u461nu2Hp5L+MAfP07u3sbC+DVB+/obax9vzo6/41asmHthb2N9f7xU72NBbBqRSeVmuV0nv3dz87UUjGWWirGUkvFWGqpGEstFWOppWIstVSMpZaKsdRSMZZaKqZxqYcn9H8xIjzpoLSELWSmvgfY21UQSe1ouuzORuALwI5u40harKYz9YPAfcDps91g5lpaJ44eaSGapFE0WaHjVuBgZu461+1mrqW1fNUlbeWTtEBNZurtwG0R8RrwOHBjRHy301SSRjZvqTPzgczcmJmbgTuBn2TmFztPJmkkvk4tFbOgc69k5k+ZXspW0hLlTC0VY6mlYiy1VIylloqx1FIxlloqxlJLxXSyRsjmtSt5+A+3dnHXs0xO9Pd/6Q/+cmNvYwFMDKK3sa6+YlVvYy2L/rZrxeSgt7EABsv62bZz/QydqaViLLVUjKWWirHUUjGWWirGUkvFWGqpGEstFWOppWIstVRMo8NEh2cSfRc4BZzMzG1dhpI0uoUc+/3ZzDzUWRJJrfDht1RM01In8I8RsSsi7p7rBjOX3Tl82AldGpempd6emdcCtwB/HBE3fPQGM5fdWbdufashJTXXqNSZ+frw80HgKeC6LkNJGl2TBfIuiojVZ74Gfhf4WdfBJI2myd7vy4GnYvpMCxPA32XmjzpNJWlk85Y6M/cDv9lDFkkt8CUtqRhLLRVjqaViLLVUjKWWirHUUjGWWiqmk2V3Xj5whE//yVNd3PUsn//sll7Ggf6XcPmr26/pbaw3jhzrbazJQX9zyc8PHe1tLIDfuGx1L+OcPJVnvc6ZWirGUkvFWGqpGEstFWOppWIstVSMpZaKsdRSMZZaKsZSS8U0KnVEXBIRT0TEKxGxNyKu7zqYpNE0Pfb7r4EfZebvR8RyYGWHmSQtwryljog1wA3AHwFk5gngRLexJI2qycPvq4A3gYcj4sWI2DE8//eHzFx25/Sxd1oPKqmZJqWeAK4FvpmZW4H3gPs/eqOZy+4sW7Gm5ZiSmmpS6ilgKjOfH15+gumSS1qC5i11Zv4SOBARZ85GcBPwcqepJI2s6d7vrwGPDvd87we+3F0kSYvRqNSZuQfY1m0USW3wiDKpGEstFWOppWIstVSMpZaKsdRSMZZaKsZSS8V0spbWVVes5m/v+1wXdz3L8VOnexkHYHIQvY0FMFjW33inTp99baa2rVvVyZ/dnD718Yt7Gwtg+UQ/8+SycwzjTC0VY6mlYiy1VIylloqx1FIxlloqxlJLxVhqqRhLLRUzb6kjYktE7Jnx8U5E3NtDNkkjmPd4vcx8FfgMQEQMgP8Bnuo2lqRRLfTh903AzzPzF12EkbR4Cy31ncBjc10xc9md/3378OKTSRpJ41IPz/l9G/APc10/c9mdiy9d11Y+SQu0kJn6FmB3Zv6qqzCSFm8hpb6Lszz0lrR0NCp1RKwEPg98r9s4khar6bI77wM+UZbOAx5RJhVjqaViLLVUjKWWirHUUjGWWirGUkvFWGqpmMhsf7mViHgTWOjbM9cDh1oPszRU3Ta3a3x+LTM/NtcVnZR6FBGxMzO3jTtHF6pum9u1NPnwWyrGUkvFLKVSf2vcATpUddvcriVoyTynltSOpTRTS2qBpZaKWRKljoibI+LViNgXEfePO08bImJTRDwbEXsj4qWIuGfcmdoUEYOIeDEifjDuLG2KiEsi4omIeGX4u7t+3JkWauzPqYcLBPwX06dLmgJeAO7KzJfHGmyRIuJK4MrM3B0Rq4FdwB3n+3adERF/CmwD1mTmrePO05aIeAT458zcMTyD7srMPDLmWAuyFGbq64B9mbk/M08AjwO3jznTomXmG5m5e/j1u8BeYMN4U7UjIjYCXwB2jDtLmyJiDXAD8G2AzDxxvhUalkapNwAHZlyeosgf/xkRsRnYCjw/5ihteRC4Dzg95hxtuwp4E3h4+NRiR0RcNO5QC7UUSh1zfK/M62wRsQp4Erg3M98Zd57FiohbgYOZuWvcWTowAVwLfDMztwLvAefdPp6lUOopYNOMyxuB18eUpVURMcl0oR/NzCqnV94O3BYRrzH9VOnGiPjueCO1ZgqYyswzj6ieYLrk55WlUOoXgKsj4pPDHRN3At8fc6ZFi4hg+rnZ3sz8xrjztCUzH8jMjZm5menf1U8y84tjjtWKzPwlcCAitgy/dRNw3u3YbHTe7y5l5smI+CrwDDAAHsrMl8Ycqw3bgS8B/xkRe4bf+/PMfHp8kdTA14BHhxPMfuDLY86zYGN/SUtSu5bCw29JLbLUUjGWWirGUkvFWGqpGEstFWOppWL+D3O6ze03Sb68AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# シンクホーンアルゴリズム（アルゴリズム 3.2）\n",
    "\n",
    "eps = 1\n",
    "K = np.exp(- C / eps) # ギブスカーネルの計算\n",
    "v = np.ones(m)\n",
    "for k in range(100):\n",
    "    u = a / (K @ v)\n",
    "    v = b / (K.T @ u)\n",
    "P = u.reshape(n, 1) * K * v.reshape(1, m) # 主解\n",
    "plt.imshow(P, cmap=plt.cm.Blues, vmin=0) # 解の可視化\n",
    "plt.show() # シンクホーンアルゴリズムは「ぼやける」\n",
    "plt.clf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 近接点アルゴリズムによる正則化なしの最適輸送コストの計算（アルゴリズム 3.7）\n",
    "\n",
    "eps = 1\n",
    "K = np.exp(- C / eps) # ギブスカーネルの計算\n",
    "P = np.ones((n, m))\n",
    "v = np.ones(m)\n",
    "for k in range(20):\n",
    "    L = K * P\n",
    "    u = a / (L @ v)\n",
    "    v = b / (L.T @ u)\n",
    "    P = u.reshape(n, 1) * L * v.reshape(1, m) # 主解\n",
    "    plt.imshow(P, cmap=plt.cm.Blues) # 解の可視化\n",
    "    plt.show() # 近接点アルゴリズムを用いると厳密解に近づく\n",
    "    plt.clf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.8.3"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "44a2b068c0f563b0ccee5ab3b9cf7ca27efea6d57d435efed0db203d351dddef"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}