{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 7.4 动量法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0.0\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import sys\n",
    "sys.path.append(\"..\") \n",
    "import d2lzh_pytorch as d2l\n",
    "import torch\n",
    "\n",
    "eta = 0.4\n",
    "print(torch.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.4.1 梯度下降的问题"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.943467, x2 -0.000073\n"
     ]
    },
    {
     "data": {
      "image/png": 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r7QjKwd449+3uHBMoZFuKFXVh1jZFWdcYMaOdxihrGiOsaoiIK6og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\nNw4zM6vlB/boPHmkPc1SAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1110a18d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f_2d(x1, x2):\n",
    "    return 0.1 * x1 ** 2 + 2 * x2 ** 2\n",
    "\n",
    "def gd_2d(x1, x2, s1, s2):\n",
    "    return (x1 - eta * 0.2 * x1, x2 - eta * 4 * x2, 0, 0)\n",
    "\n",
    "d2l.show_trace_2d(f_2d, d2l.train_2d(gd_2d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.387814, x2 -1673.365109\n"
     ]
    },
    {
     "data": {
      "image/png": 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ktCpyIo2ainyymfUARwA3m9ltAO7+ILAS+DNwK/Apdy+EWckZwG3AQ8DK8FiA\nzwP/aGbrCGow3x/fsxGRlqTMJZGGLP/i7tcD19d47RLgkirttwC3VGlfTzCbTEQkPSroJ9Jsw2Ii\nIs1BBf1EFFxERKrRsFgiCi4iItWooJ+IgouISDXKXBJRcBERqUYF/UQUXEREqslkAFNwqZOCi4hI\nLZmshsXqpOAiIlJLJqeCfp0UXEREasnkNCxWJwUXEZFaLKvgUicFFxGRWlRzqZuCi4hILQoudVNw\nERGpRQX9uim4iIjUoppL3RRcRERqySi41EvBRUSklkxONZc6KbiIiNSign7dFFxERGpRQb9uCi4i\nIrWooF83BRcRkVpU0K+bgouISC0q6NdNwUVEpJZMVjWXOim4iIjUolWR66bgIiJSi2U0LFYnBRcR\nkVqUudStIcHFzN5vZg+aWdHMlsTa9zOznWZ2b/j4duy1N5nZ/Wa2zswuNzML22eZ2WozeyzczmzE\nOYlIC9JFlHVrVObyAHAKcEeV1x5390PDxydi7VcCK4BF4eOYsP1sYI27LwLWhPsiIsnpIsq6NSS4\nuPtD7v7ISI83s/nAHu7+e3d34EfASeHLJwLXhM+vibWLiCSjYbG6NWPNZX8zu8fM/tPM3hq27Qv0\nxI7pCdsA9nb3ZwDC7dzx66qItDQV9OuWG6sfbGa3A/OqvHSeu99Q423PAAvdfZOZvQn4DzM7CLAq\nx3odfVpBMLTGwoULR/t2EZlslLnUbcyCi7u/s4739AK94fO7zOxx4LUEmUpX7NAuYGP4/Dkzm+/u\nz4TDZ88P8/OvAq4CWLJkyaiDk4hMMiro162phsXMbI6ZZcPnBxAU7teHw13bzOzN4Syx04Eo+1kF\nLA+fL4+1i4gko4J+3Ro1FflkM+sBjgBuNrPbwpf+Gug2s/uAnwOfcPfN4WufBL4HrAMeB34Rtn8Z\neJeZPQa8K9wXEUlOqyLXbcyGxYbj7tcD11dpvw64rsZ71gIHV2nfBCxLu48iIloVuX5NNSwmItJU\ntCpy3RRcRERqUUG/bgouIiK1ZHLgxUb3YkJScBERqUUXUdZNwUVEpJrulXD3NdC/Ay47ONiXEWvI\nbDERkabWvRJuPBP6dwb7WzYE+wCLT21cvyYQZS4iIuXWXFgKLJH+nUG7jIiCi4hIuS09o2uXCgou\nIiLlZnSNrl0qKLiIiJRbdj7kO4e25TuDdhkRBRcRkXKLT4UTLocZCwALtidcrmL+KGi2mIhINYtP\nVTBJQJmLiIikTsFFRERSp+AiIiKpU3AREZHUKbiIiEjqzN0b3YeGMLMXgKfG4aNmAy+Ow+eMl1Y7\nH2i9c9L5NL+JfE6vcvc5uzuPyYp7AAADvklEQVRo0gaX8WJma919SaP7kZZWOx9ovXPS+TS/Vjyn\nchoWExGR1Cm4iIhI6hRcxt5Vje5AylrtfKD1zknn0/xa8ZyGUM1FRERSp8xFRERSp+AyDszsAjN7\n2szuDR/HNbpPaTCzs8zMzWx2o/uShJldZGbd4d/NL81sn0b3KSkzu9TMHg7P63oz27PRfUrCzN5v\nZg+aWdHMJuwsKzM7xsweMbN1ZnZ2o/szlhRcxs9l7n5o+Lil0Z1JyswWAO8C/tLovqTgUndf7O6H\nAjcBrXDTjtXAwe6+GHgUOKfB/UnqAeAU4I5Gd6ReZpYFrgCOBQ4EPmBmBza2V2NHwUXqdRnwOWDC\nF+3cfWtsdyqtcU6/dPeBcPcPwIS+haK7P+TujzS6HwktBda5+3p37wOuBU5scJ/GjILL+DkjHKK4\n2sxmNrozSZjZe4Cn3f2+RvclLWZ2iZltAD5Ia2QucX8D/KLRnRD2BTbE9nvCtpakm4WlxMxuB+ZV\neek84ErgIoLfiC8Cvk7wH75p7eZ8zgWOGt8eJTPc+bj7De5+HnCemZ0DnAF8YVw7WIfdnVN4zHnA\nAPD/xrNv9RjJ+UxwVqVtwmfJtSi4pMTd3zmS48zsuwTj+k2t1vmY2RuA/YH7zAyC4Za7zWypuz87\njl0clZH+/QA/BW5mAgSX3Z2TmS0HjgeW+QS45mAUf0cTVQ+wILbfBWxsUF/GnIbFxoGZzY/tnkxQ\nnJyQ3P1+d5/r7vu5+34E/2He2MyBZXfMbFFs9z3Aw43qS1rM7Bjg88B73H1Ho/sjANwJLDKz/c2s\nDTgNWNXgPo0ZZS7j46tmdihBCvwk8PHGdkfKfNnMXgcUCVbK/kSD+5OGbwHtwOoww/yDu0/Y8zKz\nk4FvAnOAm83sXnc/usHdGhV3HzCzM4DbgCxwtbs/2OBujRldoS8iIqnTsJiIiKROwUVERFKn4CIi\nIqlTcBERkdQpuIiISOoUXESajJndamYvm1nTX2wrUouCi0jzuRT4cKM7IZKEgotIg5jZYeFiph1m\nNjW8X8nB7r4G2Nbo/okkoSv0RRrE3e80s1XAxUAn8BN3n7BLA4nEKbiINNaFBGtO7QLObHBfRFKj\nYTGRxpoFTAOmAx0N7otIahRcRBrrKuCfCe638pUG90UkNRoWE2kQMzsdGHD3n4b3V/+dmb0D+CLw\nemCamfUAH3X32xrZV5HR0qrIIiKSOg2LiYhI6hRcREQkdQouIiKSOgUXERFJnYKLiIikTsFFRERS\np+AiIiKpU3AREZHU/X//DyYG8awXsAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1111691d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eta = 0.6\n",
    "d2l.show_trace_2d(f_2d, d2l.train_2d(gd_2d))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.4.2 动量法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.062843, x2 0.001202\n"
     ]
    },
    {
     "data": {
      "image/png": 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7Xmhg3bPvse7Z9zjzsFo+dcIC3re4EmEPhAesDBAtHFlWXwUv3AKv3g2nf+Pg\n7xPthfU/hZd+DLEgHH6RSqyrWjJ2ddVoNHkZN+GQUp452DkhxD4hxCyrtTELyJsiI6VssbY7hRB/\nB44C8gqHlHIdsA7UGMcoq39Ajl9UyfGLKmnujvCr9bv5zYZG/vrmPpbUFPGJ4+fzkaPnUDwT7dQP\nRMVCWHImbLpbDVibzpG9Px6GDT+D538EkS6VcX76N9Tgu0ajmRAKNcbxMHCltX8l8NDAC4QQ5UII\nt7VfBZwITDp/7jllXv5t7aG8+LX388OLV+J3mXzr4Tc47rtPsXHzayR9NeDK0401kznmGujbC+88\nNvz3JGPw8jq45Uh44nqYczR85mm47FdaNDSaCaZQYxw3AQ8IIa4B9gCXAAgh1gDXSSk/DRwG3C6E\nSKME7iYp5aQTDhuP0+SSNXO5ZM1ctjR2c+/63SRf38Vmyvj+/73Ix4+bzzkr6vC6dPwmS89W02A3\n/FwNmA9FKgFb7oNnfqD8peafCJfcBfNPmJCqajSa/SmIcEgpO4H95mNKKTcCn7b2XwSOmOCqjQmr\n5paxam4ZqcZednqPoC0Y40v3b8bnMjnzsFo+vGo2Jy+rwu2YoSJimLD6Svjbd6BjR/5xiXQKtv1e\n5WR07YQ5q+HDt8Ki0/RiSo2mwMyoPI4JJRnHDDaz9KiP8fSpp7F+VyePbGnl8W2tPLylhRKPg7NX\n1PGhlbM4cUkVTnOGLeI/6pPw95vU1Ny1382WS6lyyp/+LrS/pZx1L/8NLFurBUOjmSRo4RgvehpB\npqF8AYYhOGFxFScsruLG81fw/I4OHtncwl+27eV3m5oo8zk5Z3kdH1w5ixMWV+KYCSJSXAuzjoT1\nP1Gv0npYcSHsegZat0DlUpX9vfwCFUOr0WgmDVo4xotB1nA4TYPTD6nh9ENqiCVTPPduB4++3sqj\nr7dy/8ZGyn1Ozl5ex7mWiEzblsjWB5TVum062NOo1mN4K+CCn8IRl4Kpfz01msmI/sscL4ax+M/t\nMDlzeS1nLq8lmkjxzLvtPJYjIqVeJ2cvr+WcFXW8b3El/uHYnEwVnrpRmR4OxOWDIz828fXRaDTD\nZho9iSYZgQYw3VCUbw3k/nicJuesqOOcFXVEEyme297B46+38udte/ntpiacpuCYBRWcuqyaUw+p\n5pDa4uxCw6nIoLkYzRNbD41GM2K0cIwXgQZle3EQ/fMep8lZy2s5a3ktsWSKjQ0Bnnm3nWfeaed7\nj7/N9x5/m5piNycvreaUZVWcuKSKqiL32P8M40lpvRXfmqdco9FMaoYUDiFECVA90OZDCLFSSrl1\nXGs21RkjO3W3w+TEJUocvnHvCy9IAAAgAElEQVTuYbT2RHju3Q6e3d7OU2/v4/evqm/uy2eVcPKy\nKk5eUs2aBeV4nJN8qu8Z16vs79wYV52LodFMCQYVDiHEpcCPgDYhhBP4lJRyg3X6LuDo8a/eFEVK\nJRzzjh/zW88q9XLpMXO59Ji5pNKSN1p6eG57B8++286dz+/i9md24nIYHLugghOXVHHy0iqWzyrB\nMCZZt5adf/HUjarbqrReiYbOxdBoJj2D5nEIITYDH7D8pI4F7gG+IaX8gxDiNSnlURNZ0ZEwlnkc\nB0W4C36wEM75LrzvcxP2saFYkld2dfH8jg6e397BO/tU9G2Zz8n7FlXyvsWVrJlfwSF1xZiTTUg0\nGk1BGUkex1BdVWaO9fkrQojTgT8JIeoZNLhZAxTMTt3vdnD6oTWcfqhyqW8LRnlxRycv7Ojgxfc6\neXzbXgCK3Q6OnFfG0fPKWT2/nCPnlVHiGaHZoEajmbEMJRxBIcRie3zDanmcBvwR0K5yQzFJcjhq\nij1ccNQcLjhqDlJKmgIRNu7uYmNDgE27A9zyt+1IqRZkL6sp5uj5ZRw1t5yj5pWxuLpo8nVvaTSa\nScFQwvFZwBBCLLfNBaWUQSHEWuCyCandVCVjpz55woSEEMyt8DG3wseFR6mZS8Fogi2NPby6RwnJ\no1tbue8VNdPJbpUcZfluHTm3jMqpNnNLo9GMC4MKh5RyC4AQYpsQ4l7gB4DH2q4B7p2QGk5FAg3g\nrwb3iOPSJ5Rij5OTllZx0lIVrZpOS3Z1hnhtTzev7Qnw2p5ufvz0DtJWx+TcCi+r6pWIrJpbxorZ\nJfhceka3RjPTGM5f/XHA94EXgWLgV6hsDM1gdO8ueDfVwWAYgsXVRSyuLuLi1apVEo4n2dbcy+bG\nAJsbu3ltTzd/2tqqrhewrLaYlfWlHFFfxvJZxRxSV0LRdFrhrtFo9mM4f+EJIAJ4US2OXVLK9LjW\naqoTaID6YwpdizHB53Jw7MIKjl1YkSlrC0bZ2tjD1qZutjT18Nc39/HAxuxK8HkVPg6tK+awWSUc\nWlfMIXXFzK/065lcGs00YTjCsQGV0HcMUIkKV7pYSnnxuNZsqpJKQncjHHFJoWsybtQUezhzuYcz\nl9cCIKWkpSfK2629vNXay1t7g7zV2suTb+3LdHN5nAbLaos5pFYJySF1ar+62D21rVM0mhnIcITj\nGitgCWAvcL4Q4hOj+VAhxCXADaiUv2Nz7j/wurXAzYAJ3CGlvGk0nzsh9DaBTE3JrqqDRQjBnDIv\nc8q8nHFYbaY8Ek+xvS3I23uDvGO9nn6nnd9uyrZOSr1ODqktZlldEUtrillaq7ZVRS4tKBrNJOWA\nwpHvoS6lHO3A+DbgI8Dtg10ghDCB24CzgCZggxDi4ckcHwtMyhlVhcLrMllZX8bK+rJ+5Z19Md7d\n18e7+4K8sy/I9n1BHt7cQm80mbmm3OdkaU0xS2qLWFJdxJKaIpbWFlFX4tGCotEUmEJFx74FHOgB\ncCywQ0q507r2N8D5wNQQjhnU4hgplUVu3lfk5n2LKzNlUkragjG2W4Kyva2P7fuCPLq1lZ5IInNd\nkdvB4mo/i6uLWFjlZ36VnwWVPuZX+in16kWMGs1EMJmnv8wBcu1Tm1AzvPIihLgWuBZg3rx541uz\noQg0gOGEktmFq8MURAhBbYmH2hJPZnowKEHp6Iuzo62PHe197NgXZGdHiJd2dvKH1/pbsJf5nMyv\n8DGv0m9tfcyrUK+6Eo9e0KjRjBHjJhxCiCeBfGEU35RSPjScW+QpG9TqREq5DlgHyqtqWJUcDwIN\nUDYPjEnuTjtFEEJQXeymurh/CwXUGMqerjANnSF2d4bY3RlmT1eYLY3dPPZ6K6l09tfAZRrUl3ut\nRZBe5pb7qC/P7pf5nLoLTKMZJuMmHFLKM0d5iyZgbs5xPdAyynuOP2Nkp645MF6XmZmhNZBEKk1L\nd4Q9XWEau+ytJSxN3XSHE/2u97tM5pR7qS/3UV+uBvrn2NsyL1VFbt1i0WgsJnNX1QZgqRBiIdCM\nsjmZ/JmigQaYrR3nC43TNJhf6Wd+pT/v+WA0QWNXhMaAEpTm7ghNgQjNgQgbG7r6DdSDarHMKvMw\nu9TLrDIPc8q8zLL27bJit0O3WjQzgoIIhxDiQuBWoBp4VAixWUp5jhBiNmra7blSyqQQ4vPAX1DT\nce+UUr5RiPoOm0g3RAK6xTEFKPY4WT7byfLZJXnP90YTtHRHaOlWYtLcHaXZOl7/Xid7e6OkB3SI\n+l0mdaUeZpV6qSv1UFPspqbYTXWxh5oSe9+tbVo0U55Czap6EHgwT3kLcG7O8WPAYxNYtdHRvVtt\ntXBMeUo8TkrqnBxal19Ykqk0bcEYrT1KVPb2RGjtibK3J0prT5Tnt3fQ0RcjOVBdUAJTXeymqsid\n2VYVuakscln7LiqtY92K0UxG9FefsURPxZ0xOEyD2WVeZpd5WT3Ikp10WhIIx2kLxmgPxjLbjj61\nbQ/G2NHWx0s7O/cbc7FxmQYVfheVRS619bsoH7j1qf0yn5NynwunOfKce41mJGjhGEsywqEX/2mU\naaRqObg5bNbQ1yZSabpCcdqDMTpDcTqCMbpCcTpCMbr64nSG4nT2xWjoDBEIJeiLJQe9V7HbQZnf\nSZlXiUmZz0W5z0mZ10mJ10mpV5WprZMSjyrzOA3dutEMCy0cY0mgAbwV4CktdE00UwynaWTWsQyH\naCJFdzhBZyhGIJQgEI7THY4TCCfoCqn97kiC7nCCxq4w3ZEEPZEEgyRFW3UQqovO66TE46DY46TY\n47Bear/InT0ucjvwW8d+t4MilwO/28ShWzzTHi0cY4meiquZIDxOk7pSNRg/XNJpSTCapMcSke5I\nnJ5Igt5Ikt5owtpX22A0STCaYF9vlN6oOg7HU8P6HLfDoMjtwOc28bsc+FwmfrcDr9PE6zLxOk08\n/fYNPE4Tj8PEbe87TdwOw3qpcrfDwOUwcJsmLmtfOy4PjZSSZFoSS6aJ57xiyRQxe5tIE0uOzPB8\nWgpHc3eE+zfsYWV9GUtriibuG1CgAWYdOTGfpdGMEMMQlPqclPoOzpolmUoTiqUIxlRXWV80STCW\nJGS9+mKpzH4oniQcS9EXU4ITjCZpD8aIJlKE4ykiiRSReCrv5IGRYBoCl2ngNIUSE9PAYRo4TIHT\nMHA6BA5DnTcNgdNUYuMwVLlpiMzLEKrcMMAQwnqpfzeB2hdCnUOAQGD37A2Ur9yfSkqQSLWVkrRU\nZWkpc15K2FNpSUpK0mn1wE9LSTKlyhNpSSqdJmEdJ1Np4im1TaYliVTaekklENbxUK3Mg2VaCkd3\nOMFXf/86oOy8l88qYWV9GUfMKWVlfSmLqovG/ptKOgXde2D5BWN7X41mkuAwDUp9xkELTz6SqTTR\nZJpoIpXzUt+AY4nst+JowvqmnOr/rXnggzKeTJNMpUlYD9ZESj1Q7YdvKJkkmVYP42Q6TSqtHtrJ\ndJp02trmPOBTafUQl+Q89FFbWx1kjkxISY6YZJ8xIkd0BMoRwRYlU4jMcUbATFVui5rDFJiGgdM6\n9jgNHG4HTks0HaY65zRVS8xpKtF0mUpM3U61dTmyrTWPw8i27JwmR31/+P9v01I4Vswu4YF/OZXX\nm3vYYgUO3b+hkbtebADA5zJZMbuEw+eUcoT1GrWY9DZDOqm7qjSaEeAwDYpMQ6dGTjGm7f/Wouoi\nFlUXcf6RcwD1zeG99j5eb+rh9WYlJve9sodfJFTfntdpsnx2CUfMKWX57BIOn13K0tqi4U9t1FNx\nNRrNDGHaCsdATEOwrLaYZbXFXGTlaSdTaXZ2hDJi8kZLDw9sbMwMArocBofWFVvxpyWZ/coi9/4f\nENCL/zQazcxgxghHPhymsZ+YpNKShs4Q25p7eKOll23NPTz1Vlu/TO2qIncmS1ul1xWzvGMnLsMB\nJXMK9eNoNBrNhDCjhSMfpiFYXF3E4pxuLoD2YIx39gZ5e2+vikHdF+RXL+8manV13excz2pHFTf8\n8jWWWtnaS2vVfTxObbGu0WimD1o4homdCZEbMpRKSxq7wryzL8iqP/cSSNWzuzPM399pz0wzNAQs\nqPRnsrTt7aJqvxYUjUYzJdHCMQpMQ7Cgys+CKj88upe6w87jifNOJZ5M09AZ4p29Kk/73X19bG8L\n8uRbbZlwIUPAvAofS2qKWFJTrDK1a4pYXFOkZ5hoNJpJjX5CjQWxIIQ7MgPjLkd27KTfZckUDR3h\nTKb2e21KUJ55t51EKjsXvK7Ew+IaPwur/CysKmJhlY8FlX7qy324HNrOQaPRFBYtHGNBZkbV0OaG\nbkf+xLpkKs3urrDK1bYEZWdHiIc3t/QLFDINwZwyLwuq/Cys9KnWTqWf+ZU+5lb4tCuqRqOZEAoV\n5HQJcANwGHCslHLjINc1AEEgBSSllGsmqo4jYpRrOBymkRmQP2dFtlxKSVcoTkNniIYOla29qyNE\nQ2eIV3cH+jmk2qIyv9LHvAqftfWzoEod6/AgjUYzVhTqabIN+Ahw+zCuPV1K2THO9Rkd47T4T4is\nLffq+RX9zkkp6QzF2Z0jKg2dYfZ0hvjT1lZ6Iv3zHaqK3BlRybys42qdp63RaEZAoRIA3wKmj/d/\noEFZqXvLJ+wjhRCZ5LiBogLQE06wu0uJSWNXmN2dIfZ0hXl5Zyd/3Nzcz/jM5TCYW+5lboWPueU+\n5lZ4mVvuo97aL/U6p8//lUajGTWTvf9CAn8VQkjgdinlukJXKC+T0E691Odkpa+MlfVl+52LJVM0\nByLs6QrTGIjQ2BVmT2eYxkCYV3cH+o2rgAoGmlPutRLvVKb27DIPs0tVWW2JRw/aazQziHETDiHE\nk0BdnlPflFI+NMzbnCilbBFC1ABPCCHellI+O8jnXQtcCzBv3ryDqvNBE2iA2uUT+5mjwO0wM15e\n+eiJqPCfpkCYxq4Izd3q1dId4bU9AQIDYk6FUF1hs0s91JUqYZlV6mFWmdrWlXioKXHjduh1KxrN\ndGDchENKeeYY3KPF2rYJIR4EjgXyCofVGlkHsGbNmnFwoB+EdBq6d8Oh507YR443pV4npXNKOXxO\n/iTDcDxJa0+Ulu4Ird1RWnqUqLT2RNnZHuLFHZ0E80SbVvpd1FlCUmttc/drS9y6W0yjmQJM2q4q\nIYQfMKSUQWv/bODGAldrf4KtkIpPuq6q8cTncmRmgQ1GMJpgb0+U1p4oe3ujmf19vVFaeqK81thN\nVyi+3/tcDoPaEje1xSpGtbrYTW2Jh5piNzUlbmqK1X6ZTwuMRlMoCjUd90LgVqAaeFQIsVlKeY4Q\nYjZwh5TyXKAWeNB6ODiAX0sp/1yI+g6JtlPPi8qodrJ0wCLIXGLJFG29sYywtAVjtPUqcdnXG+Ot\n1l6eeTfWb9qxjdMUVBe5qS7xUF2kRKW6SNnCVFnbmmI3lUUuPRVZoxljCjWr6kHgwTzlLcC51v5O\nYNUEV23kaOE4aNwOU83kqvANeV04nqStN8a+XktcgjHagzHaglHagzGaAmFe3RMgEI7njcn0uUwq\ni1xU+N1U+V1U+F1UFLmo9Lso97ky5yp8Lsr9TorcDt2a0WiGQH8VGy2BBhAGlM4tdE2mLT6XgwVV\nDuUJNgSJVJquUJz2YIz2PiUuHX0xOvvidIXidPSp1s2brb10huLEk+m893GagnKfEpgyn5Nyn4ty\nv4tya7/Mp/bLfE5r30WJxzFx2fYaTYHRwjFaAg1QWg/m2OUwaw4Op2lQW6LGRg6ElJJQPEVXX5zO\nUIxAOE5XKEEgFKcrHKerT227w3G2t/URCMXpjiQyJpX5KPY4KPM5KfU6KfO6KPU6KfE6M2W5rxKP\nkxKvg1Kv6tIbVWyxRjPBaOEYLZNwDYfmwAghKHI7KHI7mFc5dFeZTTotCcaSdIfjdIcTBHK2PZEE\n3eEEPRH1CoTjtPRE6LWOc00s81HkdlDicVBsCYoaI3JQYm2LM1v1KnKrLjW178Dvdui1NJoJQwvH\naAk0wCFrC10LzQRgGCLTYphfOfz3SSmJJFJ0hxP0RhP0hBP0RpMZUemJJAhGk/RGE/Ra+3t7ouxo\nSxKMquPkEC0dG5fDoNgSEb/bQZHbzO67HPjcJkVuBz6XA7/bVFuXidel9n0u03o5rDJTG2dq8qKF\nYzTEQxBq0y0OzZAIIawHs4PZeEf8fikl0URaiUgsSTCapC+apC+mBCgUs4+zr5C17eyLs6czTCie\nJBRLEYon804gGAyHIfA6TTwuE4/TwONQQuNxWGUOA7dTbT1OE3fO1u00cDtMXA4Dt8OwturYZarz\nLtPIHDutrdoXOE0DhyH0RIVxJJ2WJNLpA7aIBzIthaO1J8qvXt7Nwko/C6v91BZ7xsfEr3uP2mrh\n0IwjQgi8VsugZpT3skUoFE8StoQkHE8RtraRuCqLWPvRZIpIPE0kkSISTxJNpIkmU0QTKXoiCdoS\nKWLJNNGEKrP3h9FAGjYu08BhChyGwOUwcBjq2BYWR2arrjENgcMwMK190xCYQmCa1tYQGEJgGspV\nWghVbgj1b21k9sEQ6rwQIMDaZo8ZjqhJiVQbJBIpIZ2zL6UkLSEt7XOStJSk0upcKi1JSUk6LUmm\n7XPZl12WTKn9ZFqSTKVJpSWJVNo6VvuJVFrtW2Ix1JjdUExL4ejsi/HNB7dljr1Ok/mVPhZW+Zlf\n6c8EIy2s8lNd7D74bzR6Kq5mipErQgy+fnPUJFNpYkn7lSKWSBNPpa1tKnMukVTliVSaeDJNPCWJ\nJ9Mk7TL7gZdUD8B4Sp1TDz9JKucBaD8UU1bXYDKdfdim0unsw1ZK0mkV/Ww/pO0Hd0o90TNlEnVt\n5iGPepjbQjBcssJjiZItPpY4GUIgUN2hRo5gmUb2vMMSPsPICqDDtIVSXeN1mpiGwGlmBVQJqoHT\nFltr68xs1f4/fH/4P8+0FI7D55Ty8Nfez66OEDs7QuxqVxkW7+wL8uRb+/o1y3wuk/mVfhZU+jLb\neZVKWOpKDtBSyQjHwvH9gTSaKYbDNHCYBn53oWuiGS7/MIJrp6VwAJaTq5cTl1T1K0+m0rR0R9nV\nGcpkWezuDPHuviBPvdVGPJWd2+9yGCoUycqumF+hxGVepY85ZV48gQZwl0yonbpGo9EUmmkrHIPh\nMA0VYFTpQzmeZEmlJS3dym68oTPEnk613d0Z5qWdnYTjqcy1QsA9ng3MMau4+f7NVn6Fl/pyn2VB\n7tFusBqNZloy44RjKExDZCwwBrZUpJR09MXZ06WEpLErwtINnewWc3h1T4A/bW3db6CptsTNnLKs\nmMwp8zKn3Eu9tdUeShqNZiqin1zDRAhBdbEyz1s9v0KNjK3fS90xH+K5c95PMpWmtSeqsisCEZoC\nEZoCYZoCETY3dvP4ttb9pryV+ZzMLvVmRGV2mSfTxTanzKsjXTUazaREC8fB0rcPktHMjCqHaQxp\n2JdKS9qDMZq7lZjYwUgt3VH2dIZ56b3O/VxgHYagrlQl7c3KSd7LBCWVeqjwu/Q8d41GM6Fo4ThY\nRjijyrREoK7Uw+r5+a/piSRotUKRmrujtNri0hPl1T0B9vbs32pxOYyMiMwq9WaCknK3lX6XNuDT\naDRjhhaOg2Uc1nDYdhaH1pXkPZ9OSzpCMVq7o7T2qMS9vT0qGGlvT4RXdnXRFozuJy6GFe1aYwUk\n1ZS4qbYCkWrsoKQSlWOhLSY0Gs2B0MJxsAQaAAFlE2enbhjCSsDzsGpuWd5r0mlJZyjOvt5s+l67\nFYzUFlRlW5q66Qzlz66o8LuoscZyMq+i7H6NFZSkI141mplLoRIAfwicB8SB94CrpJTdea5bC9wM\nmKhkwJsmtKKDsfUBeOFmQMKtq+GM62HlpYWuFaDExX7ID5YZDiq7orMvnhOOFLXCkVSORXswxs72\nEO3BWL+1LTYu06CyyEVVkZsqe1vsptLvyqTw2efLfS5tG67RTCMK1eJ4Avi6lDIphPg+8HXgq7kX\nCCFM4DbgLKAJ2CCEeFhK+eaE1zaXrQ/AI1+AREQd9zSqY5g04jEcnKaRGXMZCiklvZFkJhipvU/F\nu3b0qWCkjj4lNm+29tLZF8/r4ioEVFhJe5V+NxVFLiuJz22VqdAkO4mv1KvzKTSayUyhomP/mnO4\nHrg4z2XHAjusCFmEEL8BzgcKKxxP3ZgVDZtERJVPIeEYLkIISn1OSn1OltQMbW6UTkt6owlLUOKZ\n9L3OvhgdIbXt7IvzZksvnX0xeqP7Z4mDGpMpsxL47DjXCivmNXebTeBTwUh66rJGMzFMhjGOq4H7\n85TPARpzjpuA4wa7iRDiWuBagHnz5o1l/frT0zSy8hmEYQjKrGjVJcOwcU2k0gRCcTpDcRXvGo7T\n1Rejyyrrsl67OkJs2t1NIBwf1M1TCCjxWHGuXielPpfa5iTwlXidmbKSnK3fZerxGo1mBIybcAgh\nngTq8pz6ppTyIeuabwJJ4Ff5bpGnbFA/SinlOmAdwJo1a8bQ1HkApfWqeypfuWZEOE2DmhIPNcOI\neoVst1kgrESmJyeFr9tO4bOS+LojCXZ3huiJqHCkodyjHYagxOukxOOwtraoWIl8Vnk2kS+bvlfi\ncVLkceiuNc2MYtyEQ0p55lDnhRBXAh8CzpAyr0FxE5A7ZakeaBm7Gh4kZ1zff4wDwOlV5ZpxJbfb\nbAH+Yb8vnZb0xZP05ES7DnwFowl6I9kUvr290Ux5NLH/5ICB+F0mRVbEa26ka5Hbocqtrd+dLffn\nbP1WOp/XqVs/mslPoWZVrUUNhp8qpQwPctkGYKkQYiHQDFwGfGyCqjg49jjGUzeq7qnS+kk1q0qz\nP4YhKPGolsTBTJ6OJ1X6nh33GoxmI117rW2flcIXjNnnk7T2RLPpfMNM3hMC/Fa0q9+Ke7UjXn1u\nBz6nioP1ukwr9jUb+ep19o999TrNTPaG16ljYDVjh8j/ZX+cP1SIHYAb6LSK1ksprxNCzEZNuz3X\nuu5c4Eeo6bh3Sin/azj3X7Nmjdy4ceM41FyjOTjSaUk4kSJkRb+GcuJdQ/EkfbFUpixk71upfKFY\n/62d1jecHPJccmNgvU4VBet1mir61WnidarYV49DnbMjYd2ZKFhra0XA2nGwudGwuVGwLofRLyhI\nt6QmN0KITVLKNcO5tlCzqpYMUt4CnJtz/Bjw2Ejv3xNJ8NqeAHPKvFRpo0DNJMAwRKaLqja/McCI\niSfTGRGxY1/D8aQV85pSW3s/niJsxbuqVzpzTSYGtjd7Lmql9kWTqREl3Q2Fy06dswQlNxLWFhiH\nKXDaqXWmgTMTCWv0S7szrUQ7Q1jHVjqew8gm5Bk5sbGqzE7Yy0bH5kbFGnZE7ICUPvX4UM+Q3CS/\nbOn+CbK5/2Z2amB2X+3ZiYJ2ZKx9XdpKKMyNkk3ZKYU50bF2vOzAKNmUdZxMWZGyaTtGNhs1m8xE\nymajZUfCZJhVNebs6Qpz4U9eBNQv66wyj+U+azvPKhda2zRQ25trpiLq276Lsvy+mmOClCqu1c4S\njyf338/EvloxsLlluecSaUkimY2EjSfTJNPp/nnYaZm5PhRP9cvOzj707GxtVZaNh5UjboVNNwxB\nv7x1Q6hJKBnBtYTZHJDV7jRG1o1ZkK6q8ebwVUfJH933Z1p6LIvz7ohlGBhlXzC63zeocp/TEpGs\n+2yuC21dqUf3D2s0U4R0zrfuzLfzdO43dytzXEqVH56TMa6me9tl2cxxyOaO29j7Mmeyp5TZ1ofI\nmRia2yIReTLHBf3zx+3Wj2Goc6aRbRmZhp1HbremyGSQj6Y7cNJ3VY03HqfJmctr855LpNLstXIz\nlBNtlJZuZRjYFAjzyq7O/RamCcskcLYlIrmCUleijmtK3HicOvFPoyk0hiEwEOg/x/FjWgrHUDgP\nkJsBEIolM6Ki3GcjypG2N8rO9hAv7ugkGNt/1XOF35WxMq8tsW3N3dSUeDKutBU+lx5z0Wg0U5oZ\nJxzDwe92sKSmmCU1xYNeE4wmMg60rT1R9ln25vt6ldhsaVQOtANxGEK5z5Zkbc1rbKtzy/rcNgnU\n3WMajWYyooXjICm2VhAPJS6xZIo2y868rTeWcaK1Lc4bu8Js2h2gK4/AgGrB5Fqa51qcV2W2yrtJ\nt2I0Gs1EoYVjHHE7zAN2i4GaVmm7zLYPsDhv61UOtLs6QrT3xYgn91/FbBqCSn/W2rzK71Jby9a8\nMsf6vMLv0i0ZjUYzKrRwTAJcDiMzVXgopJT0RpNKZCxBsV/twawj7XttfYOKDECZz0mlX1mcVxZl\n7cwrM9bmlv25XznP6thZjUaTixaOKYQQIhMvu7h6aItzKSXBWJKOoHKbta3OOy1xscu2t/Xx8q44\ngXD+REAhVKStEhPVLVZZlGttrsTF3pb7XJToPA2NZlqjhWOaIkTWn2lR9YGvT6bSBMIJy9Jc5WbY\n9uaBUDxTvrszzKt7DmxxXmpZmCub9fz7pV5lWGhbnZd6detGo5kKaOHQAOAwjcwAPAw+4G9jd5t1\nh+MEwgkCoTjdkTiBkLI4744kCFh25519cd5r76M7rAwAh6LI7cjJy3BkBKXUtjv39bc9L/FkszXc\nDkP7IWk0E4AWDs1BkdttNr9y+O9LpNL0Wlbm3ZFExupc5WkkrfJ45ppdHSF6rfJIIjXkvZ2myAhJ\nNjvDYb2c/bduywLdPm8de5xafDSaA6GFQzOhOE2DSmum10iJJ9OZvIzeaDIT0tQbtTM1srbn9nX7\neqMZG/RQfGjhATVDzTYjLM7Nz/A4KHJZxx4HRW4zm6fhyl7ns3I1/JYFup4mrZmOaOHQTBlcDkNN\nOT4I0QHlQ9Q3IEPDztUI2rkZsYSVq5G1Pw+E4zQGwvTZdujDECAbr9PEb2Vq+FxKbOz8jNwyj7N/\nhkZmP8cG3T7nsSzRXaZuHWkKgxYOzYzBNLIJgqMhN1ujLydXIxxLWdkayZzsjGyORl8sScTatvXG\nCCey7xlOyuBADIElItbT6kgAABFHSURBVCo3w5PJ1jCymRrW1mNlaXgGy9awhMhtvadftoa1b2du\nOK1yxyhN9TRTl0IlAP4QOA+IA+8BV0kpu/Nc1wAEgRSQHK5zYyyZpi+WpMitdVEz9vTL1hije6bT\nkpiVr9EvTyMnMyMct3I0cnI1VFluhoa1n1ACFUtmj6OJFPFU+qBEKh/Csux2m4aVsSEyORtO08Dp\nUDkarpx9Z062hp3HYWdrmFYuh2kInFbmRv8MjmwWh527kZu/YRpYORuWk6ztHpuTw5GbwWGKAQ61\nA5xqwcrlEKJf7obtbDvw3yKXgVPbc510c7M3BuZz5Drypq03ZfM37LwOMs6/udkc6TQk98vryL7s\nc8mcXI5UOp2xpB8JhXqyPgF8XUqZFEJ8H/g6Kko2H6dLKTtGcvN39wU5/Ft/sUJz3BnTwdoSD7XF\n6rjGOq4ucuNy6CmgmsJiGCIT8zre5MvYsLM1Ysk0MUtgBmZsZHI1UtlydZzN07DL7IyNuFUeTaRJ\nppIkUjKTwRFP5QYMWe+xtjM9V2OiGelQXKESAP+ac7geuHgs7z+33MdXPnAoe23Twd4oL+/sYl9v\nNO8vZKXfZQlJ1nSwtsRNtWU+WGNNU3U7tE+zZuojhLCiX01KPKPrthtP7ICmZFqJU27Ohp1wNzB3\nIzXgG3fm27n1jd3+lm6n52W/9WfP57YIIPvNX0oy58g53++JIsnEAuY+i/drtQxoudjn7cwNMaAF\nZFotq9ykwtwMDju0yQ5wss/ZrS+75aZSEg0MIxvwZCckipuG/38zGfpyrgbuH+ScBP4qhJDA7VLK\ndcO5YZnPyXWnLt6vPJ2WdIXj7OuNWi9l3bEvGKXNOn6zpZeOvhj5vvCU+ZxZN9vigWaD2nRQoxlL\nDEPgMgQudI/AZGPchEMI8SRQl+fUN6WUD1nXfBNIAr8a5DYnSilbhBA1wBNCiLellM8O8nnXAtcC\nzJs3L+/NDENkZuWsmF06aN1TaUlnKJZxtrUFpr0vapVZpoPBGPFUftPBCtt0sEg53CpPKLdlOpgt\nq/C7dEtGo9FMKQoWHSuEuBK4DjhDShkexvU3AH1Syv8+0LVr1qyRGzduHH0lD0Cu6WBHMEa7tbXN\nBjv6YrT3xekIxugMxQYdlCz2ODIiU+FXhoP2fmWRMh/MeEVpd1uNRjMOTProWCHEWtRg+KmDiYYQ\nwg8YUsqgtX82cOMEVvOAjNR0MBxPZcwGO/qUH1RnX4xOyxOqIxijoSOb0THY+GCJx0FlkZtynzPj\nalueIywVfmU2WOl3U+53UuR26GmTGo1mzCjUGMePATeq+wlgvZTyOiHEbOAOKeW5QC3woHXeAfxa\nSvnnAtV31Agh8FsriudX+g94fSot6YkkMsJiGw529cXpCmXLmgJhtjYp08FEKr/SOE1Bmc9FhWUy\nmOtqWz6grMwqK9UOtxqNZhAKNatqySDlLcC51v5OYNVE1msyYY+TVPhdLB3G9bmmg10hZZPeFUrQ\nFYplTAgDYWVCuL2tL2NOOJTDbYnHqdxsLSFRrrY5poM5BoS5L5/L1C0cjWYaMxlmVWnGgP6mgwdu\n0UA2s0OJiuVqG04ogQkn6LG3liHh7s5Qxh9qqGn2DkNkRKXE46DEEhllQJh1tC3xOPqV2QaEWng0\nmsmNFo4ZTG5mx0gcbtNpJTi2g61yt82aDdri0mOZEfZGEjR3R+iNqP18M9FyMQ2RdbV17+9wW5Tr\nbGuZEdpGhMVup2VC6NALOzWacUILh2bEGEa2dTP3IN4fTaQyRoO9OeJiu9gGc4wIg1F1vrk7SjAa\nzJgTDsciweUwLKdakyK3M+No63fnON3mllkGhMrl1oHfMiD0u5TrrZ7NptEotHBoJhzbmK/mwHlR\neZFSEk2klchYrra2oPTFkvRZFuq90YRys42lMk63nX1x9nSGM0aEI3G6dZkGXpeJ32Xiy3G59bsc\nGUdb2/HW5zLxuhx4LdfbjPttjgNu7jkdQqWZSmjh0Ew5hMj6OtWM8l62023YEpGM0208SV8sRSSu\nhMc+Dsdt11tVHomn2NsbJWI54drnR+q1JAR4HFlBcTsNZanez+1Wlec63XosZ9uMy60j63Bru9na\n57L7/V1vdVyvZqRo4dDMaHKdbseSeDKdcbcd6HhrO9raYpPrdquuy7rZRpPqukAoYbnfpolZ22gy\nNegU7JFgCHJs1JXgOE2RsVC3bdSV662wnG8t0TGEcsY1suVOQ+CwnG+dlsOtwzQsx9scB1zLKdc0\nc91vjf5uuNY5I8djKddfKbPN7GM54trOt9O/FZfrs9XPqytNXi+vVI7nV9Ypd2SOydNSON5uDXLe\nrc+rDO0iN1XFLmurjquL1X6xXhinGSfsb/Sl3vE1EUylZUZIlLttynK4TRNP5Zarc7YLbq67be5+\nLMcB9/+3d26xclV1GP++mTlzri0FKgYpQR7wQpAQrTyrKKAxGDQmEiPeCPBAeDIq1iuFRCSGBzVG\nTBpNFH0zElGhmhgfDAnFAEIA0xi5VCuX03N65syZ+9+Htdbee6ZzemZ3Lnv28P2S6ey9Zp3T/+qk\n882+rN9KWnCbbad8b3Us8brbDhLCZju23k4LQQqY1KY7MaCTEAbdulOpx+1JCWF4LRAkhYDrsxNB\npQ4k9OoJpXq3at39RFKhbhaU617aaHaKlHHSzGRwrCyUcO5KGf87WcPTx9a3lRaWSwUXKCvlyGG1\nd1fZ+6Riz9TelXmctTgncaGYOooF+usqWVcSYxav9xDCpNnpRN9wWx1DywdP+LYb+oe+nZ51JPp9\nW+414bb9GhbBhBt/wHoTLrotuWY9VlzEH9K9H+huXK4tNPT7vDazvl9GGf3RG0iJ/a41QNAVaMGa\nWygkAjBh0i0WGAVh9xFZbNYNR26RQTexvkmxAFx1z+Dv8UwGx76zF/Gzz18Z7bc7hhNV74/aaODV\nSg2vbTS8S8opQP6zXsNTx9axutnoe8dOmJB37nI5EhWeuxyevVMqsb2suQjiDQq9xrtUdDdCiNlj\nJoOjl2LCitvX15ug0zGsbTUjSeFrXlLolB91vLrhnl94cROrlca2d+WUS4VITtj1WAo+qVj14VQg\nZc07EELkgjdEcKShkFB9vO3NO98vWmu2naTQB83rFaf8CG6p1yt1rFabeHG1itVKAxv11ra/a2W+\nFLmiwnMImNDW65iSwFAIMWkUHEOyMFfEBXsWccGexYH6N1odrFVdqAR3lHtuYLVH+fHC61WcqDaw\nUds+bIoFRg6pPUtl7Fmcw1lLc9izGIImdkglnVO7JTEUQpwhCo4JUy4VcN5ut+b5oLTaHax5rUeQ\nE56oNrBebWJtK3ilXNvxkzU8d3wD61tNVE5zdAMAu+adRyoZLkl5YfBMnZVwTbntkhafEuINjIIj\nB5SKhfgaTQqa7Q7WqrE/an2r4cPnVKfU2lYTR1+pRO311ulvqZwvFWJRoQ+V4JOKpYXOI5UUGIY+\nK/MlHfEIkVMUHDPMXLHg5rLsShc4gPdJ9YgKT9bioAk+qZNb7nmt2sBLq9WobZB7+ZfLxVhWGESF\nCW9UEBcuzzuZ4XLknYr7LM+XsDRX1K3SQkwQBYfoS+STSnFKLUlSZBhcUr0Cw0rdtblnt398vYbN\ness5qOqtgSc3LUVCwlhMuDxfjGSFS2G/HO8vzW/vmVoqy64rxHZkFhwkDwL4GIAOgFcAfM4v5NTb\n77MAvu537zKzn0+uSnGmDCsyBNxkqq1mGxUfKpv1dkJO2Iq2K3XnmIp8Uj50Xq3UUV2tolpvY9M7\npAax6gZKBXbJCBcTwbIw1y0pjOSFiW3X7j1T5WLkoupyT5UKOloSuYOWxXx1ACR3m9lJv307gEvN\n7NaePucAOAJgP9xEzccBvMfMTpzud+/fv9+OHDkynsJFbjEz1FudLhmhC5xYULjVaGOz4eSGoX2r\n0Ua1GbcF71StGb8+jDeqXCpgIUgLvdRwvnTqc1Je2LWdEBcmZYaxf6q7PXJPBSdVUWZeAZB83Mz2\nD9I3syOOEBqeZfSfwX8NgMNmtgoAJA8DuBbAr8ZfoZg1SEYfzucsj97R0Wx3EqLCNmrNTiQw3Gq2\nUfMBU2sGiaF7vd50fqlIbOgFhvWm80OtbjrPVK3pvFGh/043MKQhBMhcCJak0DCSGjrRYFJqWPJ9\nkrLDIDgseWlhybfNFWPNRanYIzPskRuGR8HPQo9UGUFk2CM6DP6p0E6v43Dt7Ous6tZ6TJcQsctT\nhViR0kkqUrxipe21KmaIVCxm/QWHSUVLq92tb0lDptc4SN4N4EYA6wDe36fLBQBeSuy/7NtOy9FX\nKiOpT4g0hA/ZXQvjFRsGwhGUC5M4VJL7QWIY5IdOUGhotNrR600vJmx6eaFr956pTrwdhIZbW+3Y\nQdXuoNlJbLedh6qVcEzliaTUkHDBAkaaqVPkhr1Z887zd+PZ/57saovEhv67ceS/OkVwaKddknma\nGGtwkPwT+ks+DpjZb83sAIADJO8AcBuAb/X+ij4/2/efluTNAG72uxWSz59h2WnYC+C1Cfw9k0Lj\nmX5mbUwzNZ5n8z2eiwbtmNk1jq4iyIsAPGRml/W03wDgfWZ2i9//CYC/mNlUnKoieWTQc4J5QOOZ\nfmZtTBpPPsnsfkOSlyR2rwPwXJ9uDwO4muTZJM8GcLVvE0IIkRFZXuP4Lsm3w92O+wKAWwGA5H4A\nt5rZTWa26m/bfcz/zJ3hQrkQQohsyPKuqk9s034EwE2J/UMADk2qrpTcn3UBI0bjmX5mbUwaTw6Z\nimscQggh8oOcCkIIIVKh4BgCkt8meYzkE/7xkaxrGhUkv0TSSO7NupZhIHmQ5FP+/XmE5FuyrmkY\nSN5L8jk/pt+Q3JN1TcNC8pMknyHZ8dc4cwnJa0k+T/Ioya9mXc84UXAMz31mdoV//D7rYkYByQsB\nfAjAi1nXMgLuNbPLzewKAL8D8M2sCxqSwwAuM7PLAfwTwB0Z1zMKngbwcQB/zbqQM4VkEcCPAHwY\nwKUAbiB5abZVjQ8Fh+jHfQC+jG0mW+aJAdU2ucHMHjGzsELXowD2ZVnPKDCzZ81sEhN2x8mVAI6a\n2b/MrAHg13AS15lEwTE8t/nTBof8XJNcQ/I6AMfM7MmsaxkVJO8m+RKATyP/RxxJvgDgD1kXIQCc\noR4pr2g9jh04nTYFwI8BHIT7FnsQwPfh/jNPNTuM6WtwEy1zwwjUNlPFTuPxfQ4AaAH45SRrO1MG\nGVPOGViPNAsoOHbAzD44SD+SP4U7hz71bDcmku8CcDGAJ70pdB+Av5O80syOT7DEVAz6HgF4AMBD\nmPLg2Gk8fo2ajwK4ynJyP32K9yivvAzgwsT+PgCnrC80K+hU1RCQPD+xez3cRb7cYmb/MLPzzOyt\nZvZWuP8M757m0NiJAdU2uYHktQC+AuA6M6tmXY+IeAzAJSQvJlkG8CkAD2Zc09jQEcdwfI/kFXCH\npP8GcEu25Yg+9FXb5JgfApgHcNgfFT7auwBa3iB5PYAfAHgTgIdIPmFm12RcVirMrEXyNjiXXhHA\nITN7JuOyxoZmjgshhEiFTlUJIYRIhYJDCCFEKhQcQgghUqHgEEIIkQoFhxBCiFQoOISYICT/SHKN\nZC4miwrRDwWHEJPlXgCfyboIIYZBwSHEGCD5Xi+/XCC57NebuMzM/gxgI+v6hBgGzRwXYgyY2WMk\nHwRwF4BFAL8ws1wraYQIKDiEGB93wjmMagBuz7gWIUaGTlUJMT7OAbACYBeAhYxrEWJkKDiEGB/3\nA/gG3JoZ92RcixAjQ6eqhBgDJG8E0DKzB/x61H8j+QEA3wHwDgArJF8G8EUzezjLWoVIi+y4Qggh\nUqFTVUIIIVKh4BBCCJEKBYcQQohUKDiEEEKkQsEhhBAiFQoOIYQQqVBwCCGESIWCQwghRCr+D4Qk\nlQtFcwP7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11dec3c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def momentum_2d(x1, x2, v1, v2):\n",
    "    v1 = gamma * v1 + eta * 0.2 * x1\n",
    "    v2 = gamma * v2 + eta * 4 * x2\n",
    "    return x1 - v1, x2 - v2, v1, v2\n",
    "\n",
    "eta, gamma = 0.4, 0.5\n",
    "d2l.show_trace_2d(f_2d, d2l.train_2d(momentum_2d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 0.007188, x2 0.002553\n"
     ]
    },
    {
     "data": {
      "image/png": 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TMAuWG+cApXUujEsLw6ZNm/S2bcMWPY3I0Z5Bvnf3bm7edhClFP9wxjI+dPZq\n5leFctMYreHrK41//oXfzs17us1tHzYFTf+yt3R8mRIxs7zy0OPGtbJhk9stKk76WuF7m8z/n3f8\nfvLj/oNd8MNXGweyD9xf2susZyFKqSe01uP+45hRPQQni2rK+NJFJ3H3x8/mLRsX84uHX+Ksr93D\np27dwY5DPUxbCHuPmH8kpb7CyMnqzaaq98iTbrdkYmhtiq9eegDe/H0Rg7GoWgDnXGcq0p+9bXKv\n1Rpu+wj0HTHzBiIGM5YZKwg2S+vK+folJ7P1Y6/hTScv5ndPHOLC7z3AG77zAL94eD894fjU3rhU\nMxDGYtXZoDylM2z06I/gyZ/DWR+HDZeOf/9s52XvMyFOf7sWopNYePHYjfDcn6DpcyK6M5wZLwg2\nK+ZVcMOlJ/PYdU184c0n4vHA9bft5PQvb+Gjv3mKB3d3kEpNotfQYnkYlaplxUiU18GSTaUhCLu3\nGgO3498I5xRJUlix4/XBG75pvunf97WJvebIUyYw5rgLii+zWcg5JTJQnDtqyvxc+fIVXPnyFTQf\n7uH/th3kD08f4banj7CktoxLNzVw8SkNLJs7zsRka7MJJBnNSbNUaWyCe79iJmor5rrdmpFpfwH+\n7z1mIvyiH8mKosmw9HRj4fHID2Dj202Ox2hEeuD/3g0V8+EtPyjeegMhZ8zqf0nrl9TwuTev59FP\nbeY7V5zCqvoKvr31RV59wz2c/5/38407n2f7oe6Rew4tzaWVoTxRGpsAbayMi5FwJ9z0NhN/ecVN\nhfXdnyk0fQ4ClSYXYLS5NK3hj9eYXIVLfmp6j8KMZ9b1EEYi5PfyppMX86aTF3O4e5C/7jjKXc+2\n8v17dvPdu3ezoDpI0wkLaDphAS9fPZeQjkLnHuOsONNYvNG4Oe7eAidd4nZrsknGzTfWnkPwrj8Z\nq2dh8lTMg6bPGIuPHbeMPP+y7b/h2T+Y3IBlZxS6hYJLiCAMYUltGe87axXvO2sVXQMx7nm+jbue\nbeXWpw7zq0cPUOb38o6lHVynU3TXrGWEiI3SxuM1xmi7txo3y2IajvnbtbDvPhPeLg+p6XHqu+DJ\nX8Cd18Fxr8uuOD66Hf72KWh8Lbzio+61USg4IghjMKciwMWnNnDxqQ1EE0ke2dvJ1l2teHfcB8CF\n/9dN3UMP8Orj6jlj5VxOWz6HssAMKFJrbILmW0z4z6KT3W6N4fGfwOM/Nl7/+Qhvn214vGaC+cfn\nwj1fMUlrANE+0wsrr4OLflhcXwiEvCOCMEGCPi+vOa6e1xxXj/bFST5dydvOeiV3P9/BD+7dw3fv\n3o3fqzi5oZYzVtVxuiUQrmbUGaauAAAgAElEQVQ1TJXV55rt7i3FIQh774O//CusOc+Mfwu5Ycmp\nsOk98Oh/wc7fmzhYfxnEw/Duv5ihJWFWUYJPK/dRrTvxLlzPRzav5SOb19IfTbBtfyeP7O3kkb3H\n+OF9e/n+PXvwehTrF1dzxqq5nL6ijk0r5lBbHnC7+eNTtcBMmO++26zxd5Nje+Dmd8K8NfDWn8wM\nm5Biwl4Y0d9qtvGwsULvHcUpVJjRiCBMFq2hdWfWhGtl0MfZa+dz9tr5AAxEEzx5oItH93by2L5O\nfvbgfm68fy8Axy+s4mUr6njZyjpOX1HHwpocWWnkmsYmeOi7JofWraW1g91w0+WmWO6K38y8Jb7F\nwN9HMLxLxU1mgHj+zDpEECZL9wGI9oyZgVAR9HHWmnrOWlMPQCSe5JmD3Ty2r5PH9nfy+ycP8ctH\nXgJgflWQDQ01nLSk1mwbaphXWQQxlo1N8MC3YN/9cMIbC//5yYTx3O/cC++8bWY4yhYjo2UDSGbA\nrEQEYbJMIQMh5Pdyxqq5nLHKFHolkil2He3j8f2d7Djcw47DPWx9ri29JHxRTYj1S2pYv7iGkxqq\nWb+kJnemfBOl4XQIVJl5BDcE4a7rYc9WYxy44lWF//zZQk2DFTE5wnlh1iGCMFlamgEFC9ZN+S18\nXg8nWb0Bm/5ogp2WODRb2y27WtMiMb8qyImLqzlxcQ0nLjYi0TCnDJWv6lFfAFa9xiw/1bqwVapP\n/gIe+T6c8SE47d2F+9zZyObr4fZrID6YOSeZAbMWEYTJ0roD6lZBoCKnb1sZ9GX1IsDMRTx7tJcd\nh3rYeaSXnUd6uP/FDpJW5XRVyMe6RUYk1i6sZM2CKtbMr6Qq5M9Noxo3G1Ozjheh/rjcvOd47H8Q\n/vQxs9LpdV8szGfOZux5gq2fN8NENQ1GDGT+YFYigjBZWppNKlcBqAj6zAT0ioxtQCSe5PmWPpqP\nGJF49kgvv37sJSLxTJb0wuoQaxZUsrq+kjULKmmsr6RxfiVzJzs3sXqz2e7eUhhB6NoPN18Jc1YY\nm+VSyWQodTZcJgIgACIIkyPaD137YKN7hVEhv5eTl9Zy8tJMjXQypTnUFeaF1n5ebOtjd1s/u9v6\nuXnbQcKxZPq+OeV+VlvisLq+ktXzK1hdX0nDnHK8nhGGhOYsh3nHGUF4+T/m9xeL9MKvL4dUEt7+\nWyibcTXgglD0iCBMhrZnzXaMFUZu4PUols+tYPncCl67bkH6fCqlOdob4cVWIxJ72gfY09bPnc+2\n0jmQmUgMeD2smFfO6vpKVtVXsHKe2a6eV0lNYxNs+6kZYx6aT5srUkn4/fuh4wV4x+9g7ur8fI4g\nCGMigjAZ0hkIxSUIo+HxKJbUlrGktixdI2HTORBjb3s/e9sH2NPez572fp5v6ePOZ1vTcxQAbyir\n5fs6wg9+/nP6G85mWV05y+rKWVpXzqKaED5vDqwNtn4OXvgbvP4/YPU5038/QRCmhCuCoJS6FPgs\ncAJwutZ6YkHJbtPabEzAZsCSvLqKAHUVdWxakW1rHE+mONgZZm/7APs6BjjQtoBY838wr+UBvrl3\nGQmHWHg9ioXVIZbWldEwp5ylc8ppmFNGw5wylswpY2H1BATj6ZtM+Pumq+D09+fjVxUEYYK41UNo\nBi4GfuTS50+NlmbTO5jBQSF+r4dV9ZWsqrdzBlbB4Flc1vM8F197Pkd7IhzsDHOwK8yhrkEOdprt\n319sp7U3mvVeXo9iUU0o3UtZMmfItn87wduvgZWvhgsmmOAlCELecEUQtNa7gPytoc8HqZSxrDjl\nHW63pPA0NsEd1+LrPcjSuuUsrRs5TS4ST3K0J8KhrjCHuwY51DVo9rsHeWTvMVp6I9gdjMV0cFvw\n00RUHf/a/Y9U//oZFtWUsbg2xMIa07tYUB1kQXWIkF/8iwShEBT9HIJS6mrgaoBly1wMROnaB/GB\noptQLgiWILBnK2x676i3hfxeVs6rYOW8kWs04skULT0RjrZ3cNyfL6FsIMkvV/8Hwehc9nUM8MCL\nHQw4VkXZVId8zLcEYn5ViPlVQeqrgsyvDlFfGWR+tTmuCvpK60uGIBQZeRMEpdQWYOEIl67TWt82\n0ffRWt8I3AiwadOmUfL+CkDasmIWCsK8NVCzzFQtjyEI4+H3elhaG2LpnddC34vw9v/jY2uasu7p\njcQ52h2hrS9Ca2+U1t4Ibb0R2vrM/uP7O2nrjRJLpoa9f8jvYV6lEYf6yiDzqoLmuDLAPMfxvMoA\nlSIegjCMvAmC1rpp/LtKiNadxnVzrFDymYpSpmp5xy2QiBlbi6ly75dN9fN5X4E1w/+KVIf8VC/0\ns3Zh1ahvobWmdzBBW1+E9r4obX1R2voidPTHaO+L0tEf5UBnmCde6qIzHBsxNjjoM+IxtzLA3IoA\ndRVGKMxke8A6H0wflwe8IiDCjKfoh4yKhpZmmLsmf2vxi53GJnjif+DQY1M3m9txC9x/A5xyJZz5\noSk3RSlFTbmfmnI/axaMLhxgjAQ7wzE6+mJ09EfTP8f6Y3T0xzg2EKWjP8ZzLX0cG4gRSwzveQAE\nfB7mVgSYUx5gToWf2rIANeV+asv81JT5qS0322rr2P6RnohQSri17PQi4LtAPfBnpdTTWuvz3GjL\nhGndAQ0vc7sV7rHy1eDxmarlqQjCoSfgD/8Iy15hohsL9JD0eT3WvMP4brFaawZiSY71Rzk2EKOz\nP0ZnOEbnQIyugRjHrG1XOEZLTy89g3G6w/GspbhD8SioLvNTHbIFw2d6QSE/VSEf1WVmWxWyt770\ntaqQEZSAT2IshcLg1iqjW4Fb3fjsKRHpMTkIp73H7Za4R6galp5hBKHps5N7be8R+M3bTRLb2345\nvSGnPKKUojLoozLoY/nciZkXaq0Jx5J0hWP0DMbpGYzTa23NfsJsI5nzbb1ReiNx+iKJLGuR0Qj4\nPFQFfVSGTNsqrDZm9r3pc+UBHxVBLxUBH+XWtiLoNecDPsoCXhEYYVRkyGgitO4029k4oeykcbNx\nxexrNQ/3iRALw01XQKwfrrxrxuX0KqWosB7MDXMm//p4MkV/JEFfJJEWiT7HdiCWpDcSpz+SoD9q\n7uuPJmjtjbA3mqA/mmQgmmAwPr6w2Pg8irKAl/KAEYqQ3+yX+b2U2VtrP+T3EvJ7KPNn9kN+L0Gf\nh6DfS8jnJej3EPB6CPk9BLyZ44DPg9/rwe9VMmxWIpSUILT3Rflb81FWzqtk+dzywq1Pb7FWGM3G\nJadOGpuMIOy5GzZeMf79WsNt/whHn4ErbppWhsRMxe/1MKciwJyK6fWakinNQCxBOJqkP5pgIGp6\nH+FYgoFYksFYgoGoOTbnkwzGkoTj5tpg3Fzr6I8SiZvrkXiSSCI16rzKZAj4nCKh8HvNsc/a93k9\n+D0qc+xR+Bxbv0fhta57PQqfx4NHmWOPUng94FUKj0dlth6FR4FHKevH2LkopVCY80qZYT2Fwvov\nfd1mqJbZixQ0poeorQONRmtzPqW1qbmxtimtSabM9aTW5npKk0xZxymd2aY0iaxtKnOc1MSTKZIp\nTTylSSRTJJKaWDJFIpVKX4+ntyk2Lp24UWRJCUJLb4QP/u+TgPlDWlxTZpmxVbBibgUr6ytYObeC\nhjllufHYsWndAWV1ULUod+9Ziiw4CSrmm2GjiQjCfV+HnbdC0+dg7QX5b98sxutR6bmJXJNMaaIJ\nIyDRRMoIRTxFJGFEI2qJRmabJJYwD6NYIkUsqc02YR5a5rx5iMUSSfMQczzc+hOJrAdfIqXTD7vk\nsAdmipT1UE2OMZdT7HgUloApfGnx82Qd+7321mMJY0ZEq/y+tJD6bfH1evD7FKvmVfLfE2xHSQnC\niYur+flHXsXejn72dQykf2598jB90UT6Pp9HsbSunBVzy1lhiYXZlrOkdgpi0dJsegezvdvr8Zhh\noxfuMA6lnjF6aDv/YJaYnnwFvPKjhWujkHO8HkV5wMxPFDv2N+2Rvo2ntPlGb2/tb/JaZ7ZA1jJl\n6/v/sNBAuw9hn1Mq07NQyvRWcPROFIzYa7GP8z2kdtUE7yv+P2EHHqWGRU+C+cM9NhBjf8cAezsG\n2N8xwP5jA+zvCPPovs6siTufR9Ewp8yyizZmbEvnGPfOpXPKqS4bskwwlYS2XdMqyJpRNDbBMzfB\nkaeh4bSR7znyNNz6QZPL/Mb/FCEVCobHo/CgELeTqVFSgjAaSimrAjU4zL1Ta017X5R9HQO81Bnm\npWMD7D9mtk8e6KIvksi6vyroo6Eu49p5YqCNSxKDHAqtoiocHy4Ys41V5wDKDBuNJAh9LWZFUflc\nuPxX4B9/uacgCMXBjBCEsVBKMb86xPzqUFZesU1POG45d2bcOw92DXLgWJgHd3dwTuJBLgnA1XdE\nefZvd1IV9LHEtnhOO3eWs7g2xJI5ZcyrCOIZKX1splAxF5acagTh7E9mX4tH4Df/AINd8N47oHL+\nyO8hCEJRMuMFYTxMxWsN65fUDLumtSZyx8PoR3189G1v5GBf0nLwNC6ej+7tzJq7ALOaYnFNiMW1\nZSy2bZ9ry1hUG0q7eZbCWOyYNDaZiuNwJ5RbPTKt4Y//BIe3wWW/LFjutCAIuaPEn0z5RSlF2bFd\nUL+W8zYuH/Ge3kicw12D5qfb/Byxfh54sYPWvsgwL53qkI+FNSEWVIdYWB1K79vHC2qCzK0Ijpxz\nXAys3gz3fQ323gvrLzbnHvgW7LgZzv00rHuTq80TBGFqiCCMR2szLH/lqJerQ36qF/k5YVH1iNdj\niRStvREjEj2DHO2J0NoT4WhPhJbeCC+09tHeF2XoijmvR1FfGUxnAsyvDrKgymznV4fS+3XlgcIP\nUS05zSTH7dlqBOG5P5v6hPVvhbM+Udi2CIKQM0QQxiLcCb2Hp1WQFvB5zAqmUUJlwBiwdfTHaO01\nItHWm7F+bumNsP/YAI/t76Q7HB/2Wp/HTKjPrw5aOQGOvABHbsC8ygBBX46WXnh9UNcIT/8anvqV\nOVe7DN78fVlRJAgljAjCWBQoA8Hn9bCwxgwdnTzGfZF4MmP3bGUEtPVFaOuN0toX5VDXIE8d6B7V\n8rk65KPezghwbOdWBJibZQU9Tl7A9puhdTtoRwVrfyvsuh02XDat/xeCILiHCMJYpC0rTnK3HRYh\nv3fc3gYYf5zOgRhtvVHa+41gdPRHrawAkxmw80gvHX3RYZPiNgGvJysboM6yfp5bEeA9j19PZXJI\nbyURMcNGIgiCULKIIIxFa7Oxaiix5ZN+ryc9SQ3DV085icSTaavnjoEonVZGQNr+2bJ9PtAZprM/\nRl80wYeDR2GEzkOq5xDn3HCPyQwo9xuPHmu/tnzIvpUpUBaQCiJBKBZEEMaitXnGG9qF/N700tiJ\nEEuk0N9ugL5Dw671+udzckMtXeEY7f1RXmjtpyscG9PiOejzUFueHThjh83UlgfSgTO1Q4Jnqsv8\nxbsKSxBKFBGE0UgmoO05OOMDbrekqAj4PPDaz8Dt10B8MHPBX0bthV/kOxtOGfaaSDxJz2CcrnCM\nroE43eEY3Va4THc4RnfYXOsejHOgM8z2QyY3YDxL56pgJmBmeOCMM3TGT1XQnKt0BM9UBn0iKoLg\nQARhNI69CMlo0cwfFBX2PMHWz0PPIahpgM3Xjzp/ELK89M0Q1sSJxJNZYTN2Qpnz2M4R6B2Mc7Qn\nwgttfVaWQGJC7pflAa8Rh1B26EyVtXUG0FQMCaUpD9ihNOZ60OeZ3bYmQskjgjAaLYVZYVSybLgs\n7xPItpDMn6SQgKkyH4wn0+LQF4mnA2bMftJshwTPDEQTdA6E0/sD0SSx5MTyALweRbnfm04qKw96\nKfeblLKKoJcyv88KpfGmA2rKAj7zmoCXkBVOY4fVhByBNSG/V3ozQt4RQRiN1h3gDcC8NW63RJgC\nSmUsmxeMXDM4YWKJFANRSzBiGaEYiJrwGfvaYCyZDqmx77PjNQ93JzPXY8kphc7YqWS2UIR8mQQz\nO8XMmWqWTjbzeQhayWZBn8cKq/Fm9tPnzHW/N3PODrLxe1VuM0aEoqSkBKF3MM5TB7pYWBOivjKY\n37+gLc1Qvxa8uQ8cEUoL83CcfqqZk0QyxWA8aX7sBLN4kohjfzCWJGIF00Ti5v6I9ZPZN+e7w7F0\neM3Qba5yYzwKKxIzk3rmd4iFz6Oyjv1DQlzse7wehd/jwet1hMF4zL1eD3g9mfvSaWgeD14r8cyZ\nI5DZt9PPMtfAkT3gGTkVTVlpaVZ8gUFl8g5grMS0THSaHnI+nbGQvq5JpXBkMDjzGkyPNmllNpjs\nhkyCWkqTDgaysx5SVkhQSuusNLWsdDVru2rexPLBocQE4aXOMBf94CHA/OWcVxkcxRMoyELL4bQ6\nNEW76tZm49kjCHnA5/VQ5fVQlYeEs6HEkybNLOqIxHQmm0UTKSu9LJWVdBZPZtLO0udSKeIJk2aW\nSJnkM3s/njSpZ3Z8YzSeIp5KppPQ4qkUqZQmntRZSWhDU9BKOfms0HgU+DwevI7wHTtRzT6vR6pS\nHYWSEoTG+ZV8512baOk1fkAtvcYT6MCxMI/t66RncLi1Q5nfywLb/6fa2Dqk/YFsb6CqYHZlbn+7\nqbyd4UtOhdmB/U2+Mlga/9ztb8vmG3ImHjOZyk4/y3yDznyL1tY3a2cKmv1N3E5J09bXdu34Zm8/\nNJ3f9K27SF8YKzENq9dhHds9FOXokdi9FWevxO7dZGU/e5znMw96r6PX5LOvT3Be6dsTSLyFEhOE\nMr+XzScsGPX6YCyZ8QOy7B3McZTWngg7DnXT2hsdcTljmd+bFoezPDu4Bvj9kTlEHztghe8E0lYP\nIYljEoS8oZQ1xOR2Q2YhM+r/eVnAa7KTxxgz01rTH02kzeNsL6A2h0dQ4NguAD7/uIfux3cMe4/K\noC8tEPNsD6DKIPXWdl5lkLqKAPMqA9SU+WUpoiAIJcGMEoSJoJSyCpb8NM6vHPmm3/8M9i3m0U9f\nyjHL+6ej3/6JZbZ9UfZ29PPY/hhdoxjK+TzK8gOyTeQCllgEM15B6W1QIjoFQXCNWScIE8KyrAj6\nvOnks/FIJFN0hmN09Nn+P0Y0jllC0jkQo6Pf8gQaiNE/iqmcz6OYUxGgrtyIRF2lY78ikL5Wm/YK\n8lPm94qICIIwbVwRBKXUDcCFQAzYA7xHa93tRluGkYhB+/Ow5nWTepnP6zGT1FUTK6KKxJN0DmTM\n4zoHohyzzOScP7uO9HJsIDbihLlNwOdJewDVlgfS+3PKbX+ggOUNlPECqi33j21xLQjCrMOtHsJd\nwLVa64RS6mvAtcAnx3lN/tl+M9z5aUjF4Ymfw/wT8laNG/JPvPcBpgdi+wEd64/RFc54AnWFY/RY\nfkBdYeMH9Mwhsz9WAZTXo7LM4mrT+77M+VDmuvO4MiQ+QIIw03BFELTWdzoOHwEucaMdWWy/Oduw\nbfCYOYai8Pj3eT1WiE2Qxkm4cUfiplK2ZzBOTzhOt+0DZHkCdQ/G6BlMWCZzMV46NkDPYJzeCXgB\nZZnLlfmpHsFkrtqar8kYzmVM52SoSxCKi2KYQ3gv8Fu3G8HWz2e7d4I5LvHQl5Dfy6KaMhbVTKwn\nYmOvxuqNJOgJx9MGcr2RhMNYLk7voPEG6o3EOdwd4blIX9ovaLz6Iq9HGQfSoMOZ1DKaSxvJBXxU\nBL0OUznbdC5zriLgI+QXYzlBmC55EwSl1BZg4QiXrtNa32bdcx2QAH41xvtcDVwNsGzZsjy01KJn\nuL//mOdnOM7VWBPNSnCitWYgZtxKbYFIO5NGEvQPM5wzx619EXa3Gx+gvkiC6AQ9fzyKtDikzeUs\nF9KygJeKgHEnrbBcSssd5nIVabM5X9pYzjagk16MMJvImyBorZvGuq6UehfwRmCzHqO2Wmt9I3Aj\nwKZNm/JX017TAD0HRz4vTBqlVNpOejrEkynC0ST9lllcxoXUMpiLOY3mMsZy4ViS/miCtr4I4Vgy\n6/xkrRHKHK6j6a3fdif1UG71UEJ+h0upZTIXHHIc8htTuqDfkzancxrPifgIbuLWKqPzMZPIr9Fa\nh91owzA2Xz9i6Aubr3evTQJ+r4eacg815bnx/NFaE0umLOfRJIOWSAxEjVlcOJYkHEswmN63zycY\njKUYjCfS53oH47T1JtP32sZz8eTUv7fY7qQhvy0SGcfSgOVaGhhyHHS4lTqv2W6lQadrqc+Yztnn\n0s6mlv+N3+vB77G8cLzGhG6i9ghC6ePWHML3gCBwl/WN6BGt9QfHe1HnQIw7drakrSTmVgapCOSo\nSz/J0BehNFFKWQ9RL7Xl+fmMRDJFJJEiHEsQjRsTuUg8lXYnjcSNi6m973Qnjdpb67ptQmeupdKu\nprYpXdRhUhdLpkYsjpwuthup0zTNZzu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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11de85ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eta = 0.6\n",
    "d2l.show_trace_2d(f_2d, d2l.train_2d(momentum_2d))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.4.3 从零开始实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "features, labels = d2l.get_data_ch7()\n",
    "\n",
    "def init_momentum_states():\n",
    "    v_w = torch.zeros((features.shape[1], 1), dtype=torch.float32)\n",
    "    v_b = torch.zeros(1, dtype=torch.float32)\n",
    "    return (v_w, v_b)\n",
    "\n",
    "def sgd_momentum(params, states, hyperparams):\n",
    "    for p, v in zip(params, states):\n",
    "        v.data = hyperparams['momentum'] * v.data + hyperparams['lr'] * p.grad.data\n",
    "        p.data -= v.data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss: 0.247369, 0.040711 sec per epoch\n"
     ]
    },
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    "              {'lr': 0.02, 'momentum': 0.5}, features, labels)"
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    "              {'lr': 0.02, 'momentum': 0.9}, features, labels)"
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    "d2l.train_ch7(sgd_momentum, init_momentum_states(),\n",
    "              {'lr': 0.004, 'momentum': 0.9}, features, labels)"
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   "source": [
    "## 7.4.4 简洁实现"
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      "loss: 0.253280, 0.060247 sec per epoch\n"
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