{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 7.6 RMSProp算法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import math\n",
    "import torch\n",
    "import sys\n",
    "sys.path.append(\"..\") \n",
    "import d2lzh_pytorch as d2l"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.6.1 算法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.010599, x2 0.000000\n"
     ]
    },
    {
     "data": {
      "image/png": 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YUIqe0eyY+l6PYmVtkNW1IVbWBs1RE2RVbZAVTr45FpBei7CgmJV9HFrr552b\n7VRKfRv4RyDopFuBBSscwhTkkmYivG8v3PwDEY1p4vEoVtWGWFUbmjD8BWaDY+dwmvYhc3QMp2gf\nStM9kuH59mHu25UZ02MBsxm/MRJgZW3AEZIgK2oCtMSCtMQCrHDEpSnqxysCIywwprOP41Lgs8Bj\nQAz4LvDquWyUMAcUsmbJbcd2eMcdsPnKardoyRD0WVMOgYGZsB9K5ekaSdMzmqF7JEv3aIbe0Qzd\noxnah9I8e3SYgWRuwmeVgoawvzRv0xwN0OQISlM0UHH4qY/4pRcjzAvTEY48kAZCmB7HIa118fgf\nERYUdgF+/H5jxHTd/4Ozrqt2i5YVSikaIn4aIn7OXl07Zb1coUh/IkvPaIbeeJY+5yjnMxzsS9KX\nyE7owbjUhX00Rvw0RgLmO6N+Gp3vboj4qQ+btC7soyHiJ+SzZPWYMGOmIxxPA3cDFwONwFeUUjdo\nrW+Y05YJs0OxCPf8Kez5mYlye8Et1W6RMAV+r4fVdSFW1x3fJEtrTTxboD+epT+RYyCRpT9p0oFE\njoGkKT/Ql+DpwzmGUrkxK8bGf2d92EddyIhJXUW+JuSj1jnqwiatCZryWNArvZtlzHSE4/0VQQi7\ngeuUUn80h20SZgut4b6/gue/B5d/DC77QLVbJMwCSinzAA/62Nh84vrFomYknWcgmWM4lWMwacRk\nKJVnKJljOJVnKJVjOJ3ncH+KodQww+n8lL0al7DfoiboIxr0Egt6iQWNoMQCXqIBL9GgSWNBL5GA\nOcI+i7DfSzhgEfZbhH1eQn4Ln6Wk57OIOKFwTBa5diGvqAJKIbyXPb/5NDz1Fbjsv8PrP1zt1ghV\nwuNR1EfMHMhMyORtRtL58pHKE8+adDRTYDSdZzSTJ54pEM8UGEnnaR9KEc8USGQKpYCV08HyKEI+\ni5DfIujzEPJZBH0WQa9FwOcxeZ9FwOsh4PWU8n73sDxjzn2WOfyWm1d4LQ9ej8JrKXxu3uPBshSW\nUlgehdej8HgUHmXa5HHKPcqUnaq4aa3R2myEs4uaotbYRY2tNcViOW8XNQXbSYuaQrFIwdbk7SJ2\nUZN38u6RszW5QtE5bHJ2sXSeLR022XyRjJOm8zaZvE3GKZsJS9KPY3fXKNs+/zAXrTO2phetq6e1\nPrS83mge+yL89rNwwR/CG//PlJ4agjAV7sN6RU3wpD5fsIskczbJbIFEtkAyWyCds0nmbFK5Aqmc\nTSpnHl6pXIF0rkg6b+q4D7NM3iaeKdAXN/M6mbxdehBm8vaYSADzhVImdIZSykmd8oqAGhojECZv\nBKNa77Ou2AZ8RpQDXiO6IafotxRlAAAgAElEQVT31xAx1349g3suSQfAttPP1Zd/5Gs8c2So5JG9\noibARevquWidEZKzVtUsXb+HZ75l5jXOug5u+AZ4rGq3SBDmhGJRk7ONkOQKRXJ2kXzBvIVnC+4b\nuXk7LxQ1BefcfYO3i+W3elub63bRPPTdN/9i0Tz0Nc7DX5fPK8UBc6lCSMp5T0lklCM8CstjeoNW\nRa/G8pR7PpbTO/Kocg/JZ3nwWuZaoKJn5fau/ON6YTMZAlwMfhxzSksswLfedwl2UfNSd5ztRwbZ\ncWSIHUeG+PmL3YBR4fNb67hgXR0XtdVz4bp6mqJzG0p8Xth1F/zsz2HzVfD2r4poCEsaj0cR9Jie\nkTB/LMkex/F2jveMZthxZIjth4d45ugQuzpHyNvmd9DWEObCtjouXFfPBWvrOWNVbHGtHNn3APzn\nO6F1K/zhT8AfrnaLBEFYJMykx7HshGM8mbzNzo4Rnjk6xDNHhtlxdIi+uAkhEfR5OHdNLee11nFe\nay3nrKllQ2NkYfo7HHkMvv12aNpi4k8Fp94vIAiCMJ5lP1Q1E4I+i63rG9i6vgEwk1idIxmeOTLE\ns0eHefbYEN954ghZZ2li1PHHPndNLeeuqeWcNTVsaIpWN6hd53PwvT+A2lbT0xDREARhDln2wjEe\npRRr6kykU9eFrmAX2deb4MWOEXZ2jPBixwjfffIImbwRk5DP4sxVMc5ZU8vZq2s4e3UtW1ZECXjn\nYdy172X4ztuNWLzrpxCdxsJ+QRCEU2DZD1WdLAW7yMH+JDs7RtjZMcrOjhF2dY6QzJn10D5Lsbkl\n5giJEZMzVsWomU1v7KEj8PVtUCzA++6Dxk2zd29BEJYVMsdRpbDqxaLmyGCKXZ1GTHZ1jrC7c3RM\n8Lq2hjBnrarhzFU1nLkqxpmrak5uj0m824hGehDe83NYec4s/zSCICwnZI6jSng8quRv/dbzzDCX\n1pqe0Sx7ukbZ3TXK7k6T3r+7u7QGPBb0cubKspCcsaqGLS1RIoEp/jypQWP5mug17n0iGoIgzCMi\nHHOMUqpk5vOGM8qe3slsgb3dcfZ0jZaOH+5oJ5Urb/1vrQ+xpSXKaStibG6JsmVFjM11EP3+O2Bg\nP9x8J6y9uBo/liAIyxgRjioRCXidnez1pbJiUdM+lGZ31yj7euK83JtgX0+cR/cPkLOLBMjxNd/n\nuMzawxcb/4aR3S1s7j/C5uYom1qiNEb8yyusiiAIVUGEYwHh8SjaGsO0NYbZds7KUnnBLnKsf5TI\n3e+jpXMX3139MR7KXsKBp4+N6aHUh31sao6aoyXCJsdcaG19SFzkBEGYNaoiHEqpdwB/C5wJXDJZ\nBF6n3mEgDthAYboTN0sNr4INj34YOh+CN32OWy69lVswPZSu0Qz7exOl42Bfgof29vKD7WUfbJ+l\naGsIOy51ETY1mXRDU4QG6aUIgjBDqtXj2Am8HfjKNOq+QWvdP8ftWbhoDb/4MLzwA7jir+HSW0uX\nPJ7ynpPXnzZ2/8ZIKs+B/gQHehMc7E+W0t+81FsKsQJQG/KxoSnCxqYI653DzUenmpwXBGFZU5Un\ng9Z6D5x6bPtlwa/+Nzz9H/CqP4XX/s9pf6w27OPCtnoubKsfU16wi7QPpTnUn+Rgf5JD/QkO9Sd5\n/OAAP3m2Y0zdpmiADU1h1jVGWNdghtDWNoRpawjLfIogLGMW+iulBn6plNLAV7TWt09VUSl1K3Ar\nQFtb2zw1b4559Avwu3+CC98NV//9rHhqeC1PqWfxhnHX0jmbI4NJDvUlOTSQ5HB/ksP9KR5+uY/e\neHZM3ZDPYm1DiNb6MGvrQ6xtCNNaH6a1PsTa+jA1Ia8IiyAsUeZMOJRSDwIrJ7n0ca313dO8zau1\n1p1KqRbgAaXUXq31w5NVdETldjAbAE+q0QuJ7d+ABz4BZ78d3vov82LEFPJbnLGyhjNW1ky4ls7Z\ntA+lODpojmODaY4NpTg2mOKpQ4Ml3xOXWMDLmvpQSUxa682QmltWH/aJsAjCImXOhENrfdUs3KPT\nSXuVUncBlwCTCseS4sUfwb1/AVuugeu/siA8NUJ+iy0rYmxZEZtwTWvt2IamaR9KOWmaY4Mp2odS\nPHFwYIKwhHwWq+uCrHbmaNbUhVhVFzJltSFW1gbFY0EQFigLdqhKKRUBPFrruJO/BvhUlZs197x8\nP9z1x7DuVfCOb4J3Zj7R1UApRV3YT13YzzlrJkbm1Vozmi7QPmxEpWMoTedwms4Rk9/TFac/kZ3w\nuaaon1WOiKyuDbKy1gjLypogq2pDtNQERFwEoQpUaznu9cC/Ac3AfymlntNav1EptRr4qtb6zcAK\n4C5nOMMLfE9rfV812jtvHH4E7nwXrDgH3vn9JWPEpJSiNuyjNlzL2asnD/meydt0j2ToHEnTOZyh\nyxGWrpEMRwdMryWeKUz4XEPEz8oaszN/RU3QyQdMvjbIiliQOhkWE4RZRYIcLhQ6noFv/h7UrIb3\n/gIijdVu0YIjkS3Q7YhJt3N0jZbzPaOZMQElXfyWh+ZYgKZYgJZYgKZogOZYgOao35RHnSMWIOK3\nRGSEZYkEOVxs9O6F7/w+hOuNp4aIxqREA142t8TY3DJxnsUlW7DpHc3SM5qhezRj8vEMffEsffEs\nxwZTPHt0iIFkjsnemYI+D40RIyLNUT+NkQANUT+NET9N0QANET+NbnnEj98rO/KF5YcIR7UZPATf\nug4sn4l0W7O62i1a1AS8FmsbzH6T41GwiwymcvTHc/QlsvTHs/Qnsgwkc/THs/QlsnQOZ3ixY4SB\nRI5CcfKeeSzgpSHqpyHipyHspBE/9c55XdhHfcRPfdhPfdhHbcgn4V+ERY8IRzUZ7YJvvw0KGTM8\n1bCx2i1aNngtDy2xIC2x4AnrupP7/cksA4kcg0kjMIOJnEmTOYZSObpHM+zpMv4rrtXwZNQEvdS5\nQlIhKHUhc14XMue1Trl7yEIAYaEgwlEtXE+NZD+86x5YcVa1WyRMQXly38emaTjzaq1J5WyGUjmG\nU/mSsAwlcwyl8oyk8+Y8lWc4leNQf4KRVJ54tjDp8JmL3+uhNuSjJuilJuSjJuhzUi+xoI9YqdxL\nLOglGjBlsaCXWMBHNOjF8sj8jXDqiHBUg2zczGkMHoQ//BG0XlTtFgmziFKKSMBLJOCltf7E9V3s\noiaeyTOcyjOcNgIz6qRufjSTZzRdYDRjxOfwQJJ4pkA8kx8Tg2wqQj6LaNBLNGCOSMByUnNEA17C\nfstJTT7ktwj7LcJ+LyGfVSoL+S1CPgufDL0tO0Q45pt8Gv7zndD1PNz0Xdjwumq3SFggWJ7yfpiZ\norUmWyg64mKEJJEtkMgUjLBkTVkyWzDlWZuEU6djOEMyWzBHrkAmP/Uw22R4PYqQzyLgswj5PYR8\nFkGfRdBrEfB5TN5nEfB6CPo8BLwmH3Cu+y0Pfq+HgHds6rPK13yWKfdZHryWwm+V8z7Lg9ejsDxK\nVsRh/i3kbU2hWDSpbdK8XSRnF8nbRfIFTc62yRW0KTvO0OpkLEnhONSf5G/v2cVmxz1vS0uU+sgC\n2Ehn5+GH7zH7Nd7+H3D6m6rdImGJoJQqPaBbJkaMmREFu0gyZ5PO2aRyBVI52zkKZPImn867120y\neZtMvkg6b/LpnE2mYPLxTIG+eJZsoUg2b5u0UCSTt6dccHAq+CyF12OExGspLE9ZVLyWwlImb3kU\nHifv8SgsBR5l8h43rxTKySsFCvN7NimAKkUCGi9XlT+ZGX7UaG3KtdYUx+Q1xSIUtalja41d1Git\nnbyxUCgUixQ1Ji2atGBrCkUjDoWiydtz8Hsdz5IUDruo+eH2YyQrTI6aon5jv9ri2LC2RNncEqU5\nFpift5SiDXfdBi/fB2/5ZzjvHXP/nYJwEngtD7UhM58ylxScN+BcwRyuqOQK5TfjymvmDdp9Wzb5\ngq3Juw9Qu0jeeXDm7aKTamznuvtALmpNwTapXdTY2jzA7aJ7HWznIW0e6tp5yIN2BUCXxWGqvXCV\nzxVXbEpC5FyvFCmU6XX6KkXNueaKn8dj8h6l8FmmzGd5jDA64uj1eIyAOj0xt8dmDtNb8zo9OdOj\nU/gti/M+O/2/3ZIUjs0tUZ7+uzfSOZJhX0+cfT0J9vXG2d+b4KfPdYzZgRwLetncEmVzsxGSzS3G\nQW9tQ3j2JhK1hp//T9j5I7jyk3Dxf5ud+wrCIsbrPMBOYmROqDJLUjjAqLkbPO/y01tK5VpreuNZ\n9vUk2N8bZ3+fcc779Ut9/HBHe6me3/KwoSlSYcFatmKdscHRQ38H278Or/4QvPYvZ+tHFARBqApL\nVjimQinFihoT1+g1W5rGXBtO5TjQl+BAb9KkfQn2dMW5b2c3lcOGLbEAG5qM9er6pgjrGyOsbwqz\nriFCyD9urf3v/i888i+w9X1w1d/O+c8nCIIw1yw74TgedWE/F61r4KJ1DWPKswWbowMpDvQlOdhv\nhOXwQJIHdvdMiI20sibIusYw6xrDvDn7cy7f9xmGN70Nz5WfoUZWfAiCsAQQ4ZgGAe/UXhSjmTxH\n+lMcdh3zBlIcHUwS2PNjXlf4Vx4sXsBtu95OYdeD1Id9tDk2rOsajQVrm2PJuiIWxCObswRBWASI\ncJwiNUEf57bWcm5rRbjwl34B3/8i9rpXs+aqr/PF0SJHBlIcGUxxdCDFs8eGuPeFzjHDX36vp2TB\n6gpKa71J1zaEiAXndoWLIAjCdBHhmG0OPQx3vhtWnY91y/c5MxDjzEmq5e0incNpjgy4Vqwpjgyk\nODaUYseRoQneE3VhX8nP2/h7m3xrvbFjDfvlTykIwvwgT5vZpH272RXesBH+8McQmDr8t8/ysK4x\nwrrGyKTXR1J5IyiOr7dJ07zUE+ehvb3kxu30bIz4SyLSWh8urShb7dix1obEzEgQhNlBhGO26Nlt\n4k9FmuCP7oJww4k/cxxqwz7ODY8bAnMoFjV9iewEj+/2oRR7u+I8tKd3QnTWsN9iZW3QeHu7Nqy1\nxiVvVW2IVXVBYgGviIsgCCdEhGM2GDxowqP7Qo6nxqo5/TqPp7yk+KJ1E6Poaa3pT+RoH0oZG1bX\njtVxz3u5p4/eeHZCJNaI32JFbdAIS40RmBW1jh1rTZAVNQEaowGJsCoIy5xqeY5/DrgWyAEHgPdq\nrYcnqbcN+AJgYbzIPzOvDZ0Oo53GiMnOG0+N+vXVbhFKKWONGgtwQdvkdfJ2kd54lq5hIyauqPSM\nZugayfD4gX564tkJcW8sj6IlFnCEK1ASMPe8JWZSGRoThKVLtXocDwAf1VoXlFKfBT4KfKSyglLK\nAr4EXA20A08rpe7RWu+e99aO54U74aFPwUg7eCxQFrzvPmg5o9otmzY+y1OaB5kKu6gZSGTpHi17\nept8lt54hkP9SR4/MMDouIl8MKvEmqMBWmqMz7cxTXLPgyVha4z4xRFPEBYZVREOrfUvK06fAG6Y\npNolwH6t9UEApdT3geuA6grHC3fCz/7MhEcHKBbAsmBgP6y5sKpNm20sj6KlJkhLTZDzWqeul87Z\n9Ixm6I1nS2lv3Ph998YzHOxL8sTBQUbS+QmfVQoawv6SkDRF3dRfOjce4MaKVURGEKrPQpjjeB/w\ng0nK1wDHKs7bgUvnpUXH46FPlUXDxc6a8vNurE6bqkzIb5nQK02TrxBzyRZs+uJZeuNZ+ioO97w/\nkeVgX5L+RHZS61VXZBqjfhojARqifhodj+/GCp/vhqjr9+3H7xWhEYTZZs6EQyn1ILBykksf11rf\n7dT5OFAAvjvZLSYpmzLQvFLqVuBWgLa2KQb2Z4OR9pmVCyUCXovWerOx8XhorUlkjY/DQDJHvyMq\nfYkc/Yksg066p9P4e0/Wk3GJBbzURXw0hI2w1If91IV91Dte38b725S55WG/JfMzgnAc5kw4tNZX\nHe+6UurdwFuBK/XkAe3bgbUV561A53G+73bgdoCtW7fOnZNJbSuMHJu8XJgVlFKOh7aPjdPw+M7b\nRcfTu+zvPZjMjfH6HnS8v/f3JhhOGee7qfBZitqQIyYhH7Uh4zdeF/KbfMhrPMhD5cP1AA/6rCnv\nKwhLhWqtqtqGmQx/vdY6NUW1p4EtSqkNQAdwE3DzPDVxaq78xNg5DjDLcK/8RPXatMzxWR5n8j04\n7c/kCkWG0zmGU3mGkjmG03mGU7mS37ebH0nn6RrJsLc7zkj6+IIDZlFATdCISyzoCoqXmpCPWNBL\nTdCksaCXWMDNl8siAa94eAsLnmrNcXwRCAAPOEMCT2itb1NKrcYsu32zs+Lqg8D9mOW4X9da76pS\ne8u48xjuqqraViMay3R+Y7Hi985cbMD0bkbTRlAqj3imwEg6z2gmz2i64Hh/m2vtgylGM6YsZ5/Y\n2zno8xAL+ogGvEQDXiIBi2jARzRgESmVeZ28VcpH/KZuxO8l7KQhnyXBM4VZR01le7iY2bp1q96+\nfXu1myEIE3B9uOOZvJM6+WyBRKZAIlu+lsgWSGZNmsjaJLJ5klmbRLYwIeTM8Qj5LCIBi5DfIuzz\nmtQ5Qn4vIZ+HsN9L0GcR8pnyoM9jzv0WQa+T+jwEvJbjbe7mTeqzlMwLLXKUUju01lunU3chrKqa\ndZagFgpLBPPQtWiOBU7pPrlCkVTOiEoqZ8QklbVJ5gpOuU06VyCZtUnnbZJOvVTOpOmczXAqTzpv\n8qlcgUy+OK0e0WQoBQGvEZGA1/Gzds79Xg8Bq1zmsxR+r1Xyuy77YXvwW+bc6/hju+Vey3hsu37a\nlscp8zh+247/tuvH7bUUluPbbVV4eFtj/LxNFAaPMnVVyf+77Ac+12KotS75lxe18UHXjte5639e\nLBq/dON/jsk7/uiFcR7qhWKFx7pz3Xi1l73YC3a5zD2f6d99SQrHzs4RXv2ZX5U9LxqNO9/ahhBt\nDWHZ1SwsesxD2Cw5nk0KdpF03iaTL5LJ207eiEumYMoyeZtsvki2YJfEJpu3yTrXs4UiuUKRrF0k\n61zPFYw4DaeL5AvaKTPX8naRfME8yE5WuOYSpcwST6WUkzrlqNLaz/FPEz3uRFMWCK21k85xw+eQ\nJSkcLbEAW9fXc3QwNalLXyzoNT4X9UZUXB8MN1x5wCsrY4TlidfyELM8zHDqZ9bQzltzwdbki2VB\nydvF0tt05dtz6a3aeYsu2Lr0Rl75Nl56S3fSosZ5o3cP542/6L7xm4d9UVf2CnTpYV/54NeVMqGp\nEJOynJTFx5SPESOnp6Mo94A8bu/H6RlZpXKF5aHUq/Io0wtzy3yWp9TzcntiXqdX5vbcvB5V7tF5\nPPi8HrweReiz0/87LUnhWFET5As3XVA6T2QLHBss+14cdY59vXF+9dLEEOUragKT+l601odZVReU\nVS+CMEcopZwhKgghL3ALlSUpHOOJBrycuaqGM1fVTLjmhiivFJX2oTTHBlM8dWiQu59Lj3Hq8yjj\nK95aH3a8L0y8J9cHY3VdUHosgiAsaZaFcByPyhDlF6+f6KGRt4t0DWdoHx7re9E+mJ5UWACaY4GS\nmLj+F6tqjaHSqtoQjRG/LJEUBGHRsuyF40T4LA9tjWYuZDLydpHukQztQ2k6htN0DKXpGDY+GLs7\nR3lgd8+EoTC/5WFlyUTJMVJyzlfWmDLxvRAEYaEiwnGK+CxPaWJ9MrTWDCRzdFUYKXWOpOkaNiHK\nnzk6RPdIF3l7ou/FiligZKS0oqYsLJX5kF+GxQRBmF9EOOYYpRRNURMefDIbWDDzLIOpXElMukfS\ndDuGSt0jGV7qifPwy30kc/aEz8aC3pKYtLjGSo7RUktN2QND5l0EQZgtRDgWAB5PhbgwubgAxDN5\nekYz9IxmjbFSPEPPiDnviWd44kCCvkR2Qu8FoC7sG2Oo1FxhqNTieGG0xAJExXdcEIQTIMKxiHAj\nxm5uiU1Zp1jUDKVyJTHpHXUNlYypUs9olkP9Sfri2Uk3WwV9nrKhUrRsrtQUc8/9JZGLBOSfjyAs\nR+T//CWGx6NojAZojAY4i4nLj1201oyk8yUjpd54hv54jr5E2WDp8ECSpw8PMpSa3O8i5LOMqVI0\nQJNjqOSaK1UaLdU75kshn/hcCMJSQIRjmaKUos5xyduyYuoeDJiVY4PJnBGURNYxVnJMlZI5BpI5\nukcz7O4aZSCRmzJsRMDrKTv1OYLSUMr7SkZL9WE/9RFjqiT+FoKw8BDhEE6Iz/KU9rqcCNe9zxWU\nwYRjquSYKw0kcgwmswyl8hwdTDGYzBHPTO1xEfJZZae+iEnrQr6Sa19tyClzTZecMlkMIAhzhwiH\nMKtUuvetazy+B7lLrlBkOJVjKJUvOfZV5l1jpaFUnj1do4w4Zkv2+J2XFYR8VklYakJj3fpqHXOl\n2rDPMV0qO/jVhLwypCYIJ0CEQ6g6fq/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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1158e3908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def rmsprop_2d(x1, x2, s1, s2):\n",
    "    g1, g2, eps = 0.2 * x1, 4 * x2, 1e-6\n",
    "    s1 = gamma * s1 + (1 - gamma) * g1 ** 2\n",
    "    s2 = gamma * s2 + (1 - gamma) * g2 ** 2\n",
    "    x1 -= eta / math.sqrt(s1 + eps) * g1\n",
    "    x2 -= eta / math.sqrt(s2 + eps) * g2\n",
    "    return x1, x2, s1, s2\n",
    "\n",
    "def f_2d(x1, x2):\n",
    "    return 0.1 * x1 ** 2 + 2 * x2 ** 2\n",
    "\n",
    "eta, gamma = 0.4, 0.9\n",
    "d2l.show_trace_2d(f_2d, d2l.train_2d(rmsprop_2d))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.6.2 从零开始实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "features, labels = d2l.get_data_ch7()\n",
    "\n",
    "def init_rmsprop_states():\n",
    "    s_w = torch.zeros((features.shape[1], 1), dtype=torch.float32)\n",
    "    s_b = torch.zeros(1, dtype=torch.float32)\n",
    "    return (s_w, s_b)\n",
    "\n",
    "def rmsprop(params, states, hyperparams):\n",
    "    gamma, eps = hyperparams['gamma'], 1e-6\n",
    "    for p, s in zip(params, states):\n",
    "        s.data = gamma * s.data + (1 - gamma) * (p.grad.data)**2\n",
    "        p.data -= hyperparams['lr'] * p.grad.data / torch.sqrt(s + eps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss: 0.242014, 0.053250 sec per epoch\n"
     ]
    },
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    "d2l.train_ch7(rmsprop, init_rmsprop_states(), {'lr': 0.01, 'gamma': 0.9},\n",
    "              features, labels)"
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   "source": [
    "## 7.6.3 简洁实现"
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   "execution_count": 5,
   "metadata": {},
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      "loss: 0.243676, 0.043637 sec per epoch\n"
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