NN.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f0b88b58",
   "metadata": {},
   "outputs": [],
   "source": [
    "def step_func(x):\n",
    "    if x > 0:\n",
    "        return 1\n",
    "    else:\n",
    "        return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e063ae1d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 引数をnumpy配列に対応する\n",
    "\n",
    "def step_func(x):\n",
    "    y = x > 0\n",
    "    return y.astype(np.int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0aea143a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6be7b573",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1., -1.,  2.])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([1.0, -1.0, 2.0])\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b5d3551e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False,  True])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = x > 0\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "da1e3018",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('bool')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.dtype "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "99834848",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7a39dbe2",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_29574/1776589134.py:1: DeprecationWarning: `np.int` is a deprecated alias for the builtin `int`. To silence this warning, use `int` by itself. Doing this will not modify any behavior and is safe. When replacing `np.int`, you may wish to use e.g. `np.int64` or `np.int32` to specify the precision. If you wish to review your current use, check the release note link for additional information.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  y = y.astype(np.int)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([1, 0, 1])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = y.astype(np.int)\n",
    "y "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1781127d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "fb62e861",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int64')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7c4adcfd",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "52a54821",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a7fe93e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def step_function(x):\n",
    "    return np.array(x > 0, dtype=np.int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "a78afb22",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_29574/4153453922.py:5: DeprecationWarning: `np.int` is a deprecated alias for the builtin `int`. To silence this warning, use `int` by itself. Doing this will not modify any behavior and is safe. When replacing `np.int`, you may wish to use e.g. `np.int64` or `np.int32` to specify the precision. If you wish to review your current use, check the release note link for additional information.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  return np.array(x > 0, dtype=np.int)\n"
     ]
    },
    {
     "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": [
    "x = np.arange(-5.0, 5.0, 0.1)\n",
    "y = step_function(x)\n",
    "plt.plot(x, y)\n",
    "plt.ylim(-0.1, 1.1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5bd79d60",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "10277681",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "f7d27f5a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.26894142, 0.73105858, 0.88079708])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([-1.0, 1.0, 2.0])\n",
    "sigmoid(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "2052d6b5",
   "metadata": {},
   "outputs": [
    {
     "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": [
    "x = np.arange(-5.0, 5.0, 0.1)\n",
    "y = sigmoid(x)\n",
    "plt.plot(x, y)\n",
    "plt.ylim(-0.1, 1.1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a789e2bb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "0b429709",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_29574/4153453922.py:5: DeprecationWarning: `np.int` is a deprecated alias for the builtin `int`. To silence this warning, use `int` by itself. Doing this will not modify any behavior and is safe. When replacing `np.int`, you may wish to use e.g. `np.int64` or `np.int32` to specify the precision. If you wish to review your current use, check the release note link for additional information.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  return np.array(x > 0, dtype=np.int)\n"
     ]
    },
    {
     "data": {
      "image/png": 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lpTFXJ/Jx6qGLNKGmruVSWgLTbod3/gGn3AJ9hsZal0hTFOgiTUjXtlz6VL0L/7oWdj8hbFoh0kap5SLShFTaKSHisFnfgw6dwlot1oLt6EQKRCN0kSakImdC6WT6rnk9bPTcc0DcJYlkpBG6SBNKV8zmmx0e4P2dT4S9z4y7HJFmKdBFGpOqZsenv8k6ujL3wOvUapFEUKCLNOaf/0fnD9/kmppLSHfpG3c1IllRoIs0tGQm/OP/WLX7GTwZHZz9nqIiMVOgi9RXsxke/gp034n3RocFRTtoSzlJCF3lIlLfsz+ED+fB+Q+yuaQnQHabRIu0ARp6iNR59yX416/goIth9+O3TixqcoMLkTZGv6kiAFs2wCNfDdvJffpGAGrSjay2KNKGqeUiAvDUdbB6IVw0eet2cumGqy2KtHEaoYvMfyYsvnXYpTD0k1sf3rp8rq5ykYRQoEv7tmkNPHIp9BsBx37vI0+lti6fqz8TSQa1XKR9e+Iq2LAMxt0DZV0+8lSjOxaJtGEaekj7NacibCl31Ldh4IEfezq9dU9RBbokgwJd2qf1y8JmzwP2h6P+q9FD6louGqFLUijQpf1xh8e+Hi5VPGMilJY1eti2PUX1ZyLJoB66tD8z/wxvPwEn/hjKRzR5WLq2h66rXCQpNPSQ9mXVOzD1uzD0SDjkKxkPrUnrOnRJFgW6tB/pFDz8ZbBSOO030Ewrpe6kqHrokhRZBbqZjTGzeWZWaWZXZTjuTDNzMxuVuxJFcuTFm2HRK/CZn0Hvwc0entp6lYvGPZIMzf6mmlkpcBtwEjASGG9mIxs5rgfwDeCVXBcp0mpLZsJzN4Wt5PY9O6sfSWktF0mYbIYeo4FKd1/g7tXAJGBsI8fdCPwE2JzD+kRar7oKHpoA3XcKo/MspbSWiyRMNoE+EFhU7/7i2se2MrMDgcHu/nimFzKzCWY23cymr1ixYruLFWmRqd+FlZVw2q+hS5+sfywdOaUlhmk/UUmIVjcHzawE+DlwZXPHuvtEdx/l7qPKy8tb+9YizZs7GWbcAYdfDrses10/WhNFardIomQT6EuA+meQBtU+VqcHsDfwnJktBA4FKnRiVGK3bilUXA4D9oNjv7/dP55Ou9otkijZBPo0YA8zG2ZmHYFxQEXdk+6+1t37uftQdx8KvAyc6u7T81KxSDaiKGxYUbMJzvwDdOi43S+RihTokizNBrq7p4DLgKnAXOA+d59tZjeY2an5LlCkRf51Kyx4Fsb8GPrt0aKXSEWRtp+TRMlq6r+7TwGmNHjs2iaOPab1ZYm0wuLp8MyNMHIsHHRRi1+m7qSoSFJo+CHFZfNaeOAL0GNn+Oyt0IorVFJpp0yBLgmixbmkeLjD5G/C2sXwhSegS+9WvVwqckq1MJckiEboUjxm/gnefBCOvQYGj271y4WTovoTkeTQb6sUhw/egCnfgd2OhSO+mZOXTEeRrnKRRFGgS/JtXgf3XQhdd4Azft/sKorZqknrpKgki3rokmx1uw+tXggXTYZu/XL20unItbmFJIpG6JJs//49zH4Yjv0e7HJ4Tl9aPXRJGv22SnK99wpMvRqGj4Ejrsj5y6fS6qFLsijQJZk2LIf7L4Reg+D03+Wsb15fSi0XSRgFuiRPOhUmD21aDefc1errzZsSRuj6E5Hk0ElRSZ6nroOF/wz7gg7YN29vo6n/kjQafkiyvD4JXvoVjJ4A+5+X17dKRU6ZWi6SIAp0SY4lM6Hi6zD0SDjxR3l/u5SuQ5eEUaBLMmxYDn89P+wLevadUFqW97dMReqhS7Kohy5tX81mmHQeVK2CS6bmdPJQJppYJEmjQJe2zR0evRQWTwtXtAzYr2Bvran/kjT6/6S0bc//BN58AI67DkYWdoOstLagk4RRoEvbNet+eO7HsN958MncrKC4PcLEIv2JSHLot1Xapnf+ETZ53uUI+Owtrdp5qKVSWj5XEkaBLm3Pstkw6XPQdzcYdw906BRLGWn10CVhFOjStqxdAvecDWVd4XMPQJc+sZUSJhbpT0SSQ1e5SNtRtQruPiNsWHHxFOg9ONZyUlGkEbokigJd2oYt6+Ges2DVO3D+A3ldoyVbKV3lIgmjQJf4pbaEnvn7r8G5d8Gwo+KuiChy3NFMUUkUBbrEK10TlsJ953k47bew52firgiAmigC0ExRSRQNPyQ+6RQ8eAm8NRlO+insPz7uirZKRw6gHrokigJd4pFOwcMTYM6jYeXEQybEXdFHpGoDXT10SZKsAt3MxpjZPDOrNLOrGnn+W2Y2x8xmmdnTZrZL7kuVopFOwSNfgTcfhON/AIddGndFH5NKK9AleZoNdDMrBW4DTgJGAuPNbGSDw14FRrn7vsADwP/mulApEqlqeOBieON+OO5a+OQVcVfUqFRtD71U16FLgmTz2zoaqHT3Be5eDUwCxtY/wN2fdfeq2rsvA4NyW6YUhZrNcN8FMLcitFmOvDLuippU10Mv0whdEiSbQB8ILKp3f3HtY025BPhbY0+Y2QQzm25m01esWJF9lZJ8W9bDX86Bt5+Az/y8TbZZ6qtrueikqCRJTi9bNLPzgVHA0Y097+4TgYkAo0aN8ly+t7RhG1aESUMfvBEuTWxDV7M0ZetJUV22KAmSTaAvAerPwR5U+9hHmNnxwDXA0e6+JTflSeKtXgh3nQ7rlsL4e2H4iXFXlJV03XXomlgkCZJNoE8D9jCzYYQgHwd8ZLt1MzsA+B0wxt2X57xKSabFM+DecRDVwIUVMHh03BVlrUZXuUgCNTv8cPcUcBkwFZgL3Ofus83sBjOr20Lmp0B34H4ze83MKvJWsSTD7IfhzpOhY1f4wtREhTloYpEkU1Y9dHefAkxp8Ni19b4/Psd1SVK5wz9/Bs/cCIMPgXF/KdimzrlU10PX8rmSJFrLRXJny4awofOcR2Dvs2DsbVDWOe6qWiSVrr0OXSN0SRAFuuTGyvlhxcQP58EJN8DhX49l27hc0VUukkQKdGm9ORXw6GVQUgLnPwS7fSruilpt29R/tVwkORTo0nI1m+Hv34d/T4SdD4Sz74A+Q+OuKie2Tv1Xy0USRIEuLbP8LXjoi2Gy0GGXwXHXQYeOcVeVM1un/qvlIgmiQJftE0Xwym/hqeuhU3cYPwlGnBR3VTlXo6n/kkAKdMne6oVQcTm88w8YfhKceit03zHuqvIiHamHLsmjQJfmRekwKn/mh2Al8Nlb4cDPJ/oqluaktAWdJJACXTJ7/1WY/C14fybscSKc8nPoVfyrI2uDC0kiBbo0rmpVmO05/Y4w0/PMP8DeZxb1qLw+Tf2XJFKgy0elqmHGHfDcTbB5LRzyFfjU1dC5V9yVFZSm/ksSKdAlcA87CT11PaxaAEOPhJN+AjvtFXdlsdB16JJECvT2zh0qn4Jn/yf0y8v3hPPuhz1OaDftlcaohy5JpEBvr+qC/Pn/hcX/ht5D4NRfwX7joVS/FlsvW1TLRRJEf7ntTToVVkN84WZY9ib0HASn3AL7f66oZnq2Vs3WHYs0QpfkUKC3F1WrYOaf4N+3w7rF0G8EnPabsMytgvxj0popKgmkQC9m7rB4Gsz4E7z5IKQ2wbCj4OSfwvAxYXVEadTW5XMV6JIgCvRitH4ZvPkAvHo3LJ8DZd1gv3Nh9Jdhp5FxV5cIqSiitMSwdnxiWJJHgV4sNq+Dt5+AWffB/GfA02FJ28/+IkwI6tQj7goTJRW52i2SOAr0JKtaBf95EuY8CpVPQ3pLOMn5yStg33OhfETcFSZWOu2UKdAlYRToSeIeWiiVT8HbU+G9l8Aj6LEzHHwJjDwNBh2s3ngOaIQuSaRAb+vWLoGF/wxL1s5/BtYvDY/vuBcceWVYi3zAAQrxHEtFka5Bl8RRoLclUQQr/wPvvVx7ewlWvxOe69IHhh0Nux8Hux0HvQbGW2uRS0euK1wkcRTocXEPYb10Fix9HZbMCFPvt6wLz3ftC4MPhdFfCuuq7LS3RuEFVJNWoEvyKNDzzR02roAV82DFW6EHvmxO+FoX3iUdwiJY+5wFAw+CwYdA393b9VoqcUtHTqk2t5CEUaDngjts/BDWvBu2aVu1AFbOh1XzYWUlbFq97dhOvcK14PucDQP2hQH7QfknoKxzbOXLx6Uip0z/I5KEUaA3J4pg06pwMnL9Mlj/Pqx7H9YtCScs1y6CtYuhpuqjP9dzEPTdNVx5Uj4C+g0PX3sO1Mg7AVLpSFe5SOK0r0CPIqjeAJvXwKY1YeS8aXUI7KpVULUyjLSrPgxtkg0rwvdRqsELWdgcuefOYbnZ3U+A3oOhzzDoMzSsXNixa+E/n+SMLluUJMoq0M1sDPALoBS43d1vavB8J+DPwEHASuBcd1+Y21JrrV4Y+tHVG8OouLoKajaGr9UboXo9bNkQgnvL+trburD7zpb14brtppR1g259oWu/MJIesH8I7u47hVuPAdCjf/iqBa2KWjpy7VYkidNsoJtZKXAbcAKwGJhmZhXuPqfeYZcAq919dzMbB/wEODcfBde88TBlz1z/sccdg7KueMfutbdueKee0GMw3q8H3qnntlvn3ltvUefeeJcd8C59oEOWfexqoLo6p59L2pZN1WmN0CVxshmhjwYq3X0BgJlNAsYC9QN9LHB97fcPAL8yM3N3z2GtAEzafCj3b7mRTXQKN+/IRjqzmY6weXv/AKtqb+/nukwpAofuukPcJYhsl2wCfSCwqN79xcAhTR3j7ikzWwv0BT6sf5CZTQAmAAwZMqRFBe8/ciSpbv1b9LMi22P0MAW6JEtBT4q6+0RgIsCoUaNaNHrfZ1Av9hnUvnagFxHJRjZnfZYAg+vdH1T7WKPHmFkHoBfh5KiIiBRINoE+DdjDzIaZWUdgHFDR4JgK4MLa788CnslH/1xERJrWbMultid+GTCVcNniH919tpndAEx39wrgD8BdZlYJrCKEvoiIFFBWPXR3nwJMafDYtfW+3wycndvSRERke2jmhIhIkVCgi4gUCQW6iEiRUKCLiBQJBbqISJFQoIuIFAkFuohIkVCgi4gUCQW6iEiRUKCLiBQJBbqISJFQoIuIFAmLa5VbM1sBvBvLm7dOPxrsxNROtMfPrc/cfiTpc+/i7uWNPRFboCeVmU1391Fx11Fo7fFz6zO3H8XyudVyEREpEgp0EZEioUDffhPjLiAm7fFz6zO3H0XxudVDFxEpEhqhi4gUCQW6iEiRUKC3gpldaWZuZv3iriXfzOynZvaWmc0ys4fNrHfcNeWTmY0xs3lmVmlmV8VdT76Z2WAze9bM5pjZbDP7Rtw1FYqZlZrZq2Y2Oe5aWkuB3kJmNhj4NPBe3LUUyN+Bvd19X+Bt4OqY68kbMysFbgNOAkYC481sZLxV5V0KuNLdRwKHApe2g89c5xvA3LiLyAUFesvdDHwHaBdnld39SXdP1d59GRgUZz15NhqodPcF7l4NTALGxlxTXrn7UnefWfv9ekLADYy3qvwzs0HAZ4Db464lFxToLWBmY4El7v563LXE5AvA3+IuIo8GAovq3V9MOwi3OmY2FDgAeCXmUgrhFsLALIq5jpzoEHcBbZWZPQX0b+Spa4DvEtotRSXTZ3b3R2uPuYbw3/N7ClmbFIaZdQceBK5w93Vx15NPZnYKsNzdZ5jZMTGXkxMK9Ca4+/GNPW5m+wDDgNfNDELrYaaZjXb3DwpYYs419ZnrmNlFwCnAcV7cExiWAIPr3R9U+1hRM7MyQpjf4+4PxV1PARwBnGpmJwOdgZ5mdre7nx9zXS2miUWtZGYLgVHunpSV2lrEzMYAPweOdvcVcdeTT2bWgXDi9zhCkE8DznP32bEWlkcWRid/Ala5+xUxl1NwtSP0b7v7KTGX0irqoUu2fgX0AP5uZq+Z2W/jLihfak/+XgZMJZwcvK+Yw7zWEcAFwLG1/76v1Y5cJUE0QhcRKRIaoYuIFAkFuohIkVCgi4gUCQW6iEiRUKCLiBQJBbqISJFQoIuIFIn/BzV2zoPON7RAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y1 = step_function(x)\n",
    "y2 = sigmoid(x)\n",
    "plt.plot(x, y1)\n",
    "plt.plot(x, y2)\n",
    "plt.ylim(-0.1, 1.1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e07ea344",
   "metadata": {},
   "source": [
    "1. <b>ステップ関数、シグモイド関数は、入力信号が重要な情報であるほど大きな値を出力し、入力信号が重要でなければ小さな値を出力する\n",
    "2. <b>どんなに入力信号の値が小さくても、またどんなに入力信号の値が大きくても、出力信号のあチアを0～１の間に押し込める\n",
    "3. <b>NNの層を深くするある利点とは、NNを非線形で表す、言い換えると、予測可能な範囲を広げることである。そのためにも、線形の活性関数を用いたところで、いくら層を深くしても線形であることは変わらないので、層を深くすることで得られる利点を享受出来なくなってしまう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e3493e19",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "555d0706",
   "metadata": {},
   "outputs": [],
   "source": [
    "def relu(x):\n",
    "    return np.maximum(0, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "8cebb10c",
   "metadata": {},
   "outputs": [
    {
     "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": [
    "x = np.arange(-5.0, 5.0, 0.1)\n",
    "y = relu(x)\n",
    "plt.plot(x, y)\n",
    "plt.ylim(-1, 6)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8267a707",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "627a720b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4a6f37d7",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "08fbd47e",
   "metadata": {},
   "source": [
    "# NNの実装\n",
    "## numpyの多次元配列の計算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "8612d24d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "81de9747",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([1,2,3,4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "f0a97d41",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3 4]\n"
     ]
    }
   ],
   "source": [
    "print(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "18174636",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ndim(A) # 次元数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "490dbb15",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "38ca1773",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int64')"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "1f361a5a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4,)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e754067e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "17d8f310",
   "metadata": {},
   "outputs": [],
   "source": [
    "B = np.array([[1,2], [3,4], [5,6]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "1f2b1ca0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2]\n",
      " [3 4]\n",
      " [5 6]]\n"
     ]
    }
   ],
   "source": [
    "print(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "7b1ee0bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ndim(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "2b0fa64f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int64')"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "1d0af118",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 2)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "028235ef",
   "metadata": {},
   "source": [
    "## 行列の積"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "eac806bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([[1,2], [3,4]])\n",
    "B = np.array([[5,6], [7,8]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "5887e40e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 2)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "6a0b4f06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 2)"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "a2fac367",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[19, 22],\n",
       "       [43, 50]])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 行列の積\n",
    "np.dot(A, B) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "38af97cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[23, 34],\n",
       "       [31, 46]])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(B, A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e25202cd",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "8a21407b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3)"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[1,2,3], [4,5,6]])\n",
    "A.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "8a56e592",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 2)"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = np.array([[1,2], [3,4], [5,6]])\n",
    "B.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "b3371aec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[22, 28],\n",
       "       [49, 64]])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(A, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "40ee31e5",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "32830919",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 2)"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[1,2], [3,4], [5,6]])\n",
    "A.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "5d3409be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2,)"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = np.array([1,2])\n",
    "B.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "2b548347",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 1)"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = np.array([[1],[2]])\n",
    "C.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "80594aed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3,)"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D = np.dot(A, B)\n",
    "D.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "38790326",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 1)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E = np.dot(A, C)\n",
    "E.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cfaa456a",
   "metadata": {},
   "source": [
    "## NNの行列の積"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "2836016d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2,)"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.array([1,2])\n",
    "X.shape "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "42843622",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3)"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W = np.array([[1,3,5], [2,4,6]])\n",
    "W.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "191c88fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5, 11, 17])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y = np.dot(X, W)\n",
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "491cfab5",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "23792256",
   "metadata": {},
   "source": [
    "# 3層NNの実装"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "07f2db67",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.array([1.0, 0.5])\n",
    "W1 = np.array([[0.1, 0.3, 0.5],[0.2, 0.4, 0.6]])\n",
    "B1 = np.array([0.1, 0.2, 0.3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "2ca30b83",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2,)\n",
      "(2, 3)\n",
      "(3,)\n"
     ]
    }
   ],
   "source": [
    "print(X.shape)\n",
    "print(W1.shape)\n",
    "print(B1.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "86880dda",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.3, 0.7, 1.1])"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1 = np.dot(X, W1) + B1\n",
    "A1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "6b0d2ea9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.3 0.7 1.1]\n",
      "[0.57444252 0.66818777 0.75026011]\n"
     ]
    }
   ],
   "source": [
    "# 活性化関数をかませる\n",
    "Z1 = sigmoid(A1)\n",
    "print(A1)\n",
    "print(Z1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "01dc6c40",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,)\n",
      "(3, 2)\n",
      "(2,)\n"
     ]
    }
   ],
   "source": [
    "W2 = np.array([[0.1,0.4], [0.2, 0.5], [0.3, 0.6]])\n",
    "B2 = np.array([0.1, 0.2])\n",
    "print(Z1.shape)\n",
    "print(W2.shape)\n",
    "print(B2.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "e5b39167",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.51615984, 1.21402696])"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A2 = np.dot(Z1, W2) + B2\n",
    "A2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "bd3208ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.62624937, 0.7710107 ])"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z2 = sigmoid(A2)\n",
    "Z2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2789c21f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "9e04ecf0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 恒等関数\n",
    "def identity_function(x):\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "3171d77c",
   "metadata": {},
   "outputs": [],
   "source": [
    "W3 = np.array([[0.1, 0.3], [0.2, 0.4]])\n",
    "B3 = np.array([0.1, 0.2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "1aeba12b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.31682708, 0.69627909])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A3 = np.dot(Z2, W3) + B3 \n",
    "A3 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "f8640c22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.31682708, 0.69627909])"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y = identity_function(A3)\n",
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5632e167",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "01e5c6f4",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "5872b4fc",
   "metadata": {},
   "source": [
    "# 出力層の設計"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "7d1dc073",
   "metadata": {},
   "outputs": [],
   "source": [
    "# ソフトマックス関数の実装\n",
    "a = np.array([0.3, 2.9, 4.0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "1cedf026",
   "metadata": {},
   "outputs": [],
   "source": [
    "exp_a = np.exp(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "2372988e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.34985881 18.17414537 54.59815003]\n"
     ]
    }
   ],
   "source": [
    "print(exp_a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "05ac9dd6",
   "metadata": {},
   "outputs": [],
   "source": [
    "sum_exp_a = np.sum(exp_a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "aa7f7897",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "74.1221542101633\n"
     ]
    }
   ],
   "source": [
    "print(sum_exp_a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "709a5e03",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.01821127, 0.24519181, 0.73659691])"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = exp_a / sum_exp_a\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "d7feee12",
   "metadata": {},
   "outputs": [],
   "source": [
    "def softmax(a):\n",
    "    exp_a = np.exp(a)\n",
    "    sum_exp_a = np.sum(exp_a)\n",
    "    y = exp_a / sum_exp_a\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "105beea0",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "79cb7428",
   "metadata": {},
   "source": [
    "## ソフトマックス関数の実装上の対策"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "a9ace1a2",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_29574/832863605.py:2: RuntimeWarning: overflow encountered in exp\n",
      "  np.exp(a) / np.sum(np.exp(a))\n",
      "/tmp/ipykernel_29574/832863605.py:2: RuntimeWarning: invalid value encountered in true_divide\n",
      "  np.exp(a) / np.sum(np.exp(a))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([nan, nan, nan])"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([1010, 1000, 990])\n",
    "np.exp(a) / np.sum(np.exp(a))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00b335fd",
   "metadata": {},
   "source": [
    "- <b> 有効桁数を超えてオーバーフローを起こし、計算結果が不定値(nan: not a number)になっている"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "edff4ed5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0, -10, -20])"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.max(a)\n",
    "a - c "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "423b1fb2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9.99954600e-01, 4.53978686e-05, 2.06106005e-09])"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(a - c) / np.sum(np.exp(a - c)) \n",
    "# オーバーフロー対策、(3.11)式を参考にする。\n",
    "#ソフトマックス関数の分母分子の引数に同じ値を足しても計算結果は変わらない性質を利用"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "8a4fddef",
   "metadata": {},
   "outputs": [],
   "source": [
    "# オーバーフロー対策を施したソフトマックス関数を再定義\n",
    "\n",
    "def softmax(a):\n",
    "    c = np.max(a)\n",
    "    exp_a = np.exp(a - c)\n",
    "    sum_exp_a = np.sum(exp_a)\n",
    "    y = exp_a / sum_exp_a\n",
    "    return y "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "6443ff35",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[7.43453301e-05 6.69235334e-03 9.93233301e-01]\n",
      "0.9999999999999999\n"
     ]
    }
   ],
   "source": [
    "a = np.array([0.3, 4.8, 9.8])\n",
    "y = softmax(a)\n",
    "print(y)\n",
    "print(np.sum(y))"
   ]
  },
  {
   "cell_type": "code",
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