{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 多層パーセプトロン"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "XORを実装するためには, AND, NAND, ORゲートを組み合わせなければならない。\n",
    "\n",
    "入力を $x_1$,  $x_2$, NANDの出力を $s_1$, ORの出力を $s_2$ とすると、$s_1$, $s_2$を入力としたANDの出力 $y$ は以下の表の通りになる:\n",
    "\n",
    "| $x_1$ | $x_2$ | $s_1$ | $s_2$ | $y$ |\n",
    "| ----- | ----- | ----- | ----- | --- |\n",
    "|  $0$  |  $0$  |  $1$  |  $0$  | $0$ |\n",
    "|  $1$  |  $0$  |  $1$  |  $1$  | $1$ |\n",
    "|  $0$  |  $1$  |  $1$  |  $1$  | $1$ |\n",
    "|  $1$  |  $1$  |  $0$  |  $1$  | $0$ |\n",
    "\n",
    "では、前に作成したNAND, ORを使用して、XORの結果を出力する関数を作成しよう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "def AND(x1, x2):\n",
    "    \"\"\"\n",
    "    AND関数\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    x1 : float\n",
    "        入力1\n",
    "    x2 : float\n",
    "        入力2\n",
    "    \"\"\"\n",
    "    x = np.array([x1, x2])\n",
    "    w = np.array([0.5, 0.5])\n",
    "    b = -0.7\n",
    "    tmp = np.sum(w * x) + b\n",
    "    if tmp <= 0:\n",
    "        return 0\n",
    "    else:\n",
    "        return 1\n",
    "\n",
    "def NAND(x1, x2):\n",
    "    \"\"\"\n",
    "    NAND関数\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    x1 : float\n",
    "        入力1\n",
    "    x2 : float\n",
    "        入力2\n",
    "    \"\"\"\n",
    "    x = np.array([x1, x2])\n",
    "    w = np.array([-0.5, -0.5])\n",
    "    b = 0.7\n",
    "    tmp = np.sum(w * x) + b\n",
    "    if tmp <= 0:\n",
    "        return 0\n",
    "    else:\n",
    "        return 1\n",
    "\n",
    "def OR(x1, x2):\n",
    "    \"\"\"\n",
    "    OR関数\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    x1 : float\n",
    "        入力1\n",
    "    x2 : float\n",
    "        入力2\n",
    "    \"\"\"\n",
    "    x = np.array([x1, x2])\n",
    "    w = np.array([0.5, 0.5])\n",
    "    b = -0.2\n",
    "    tmp = np.sum(w * x) + b\n",
    "    if tmp <= 0:\n",
    "        return 0\n",
    "    else:\n",
    "        return 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## XORゲートの実装"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def XOR(x1, x2):\n",
    "    \"\"\"\n",
    "    XOR関数\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    x1 : float\n",
    "        入力1\n",
    "    x2 : float\n",
    "        入力2\n",
    "    \"\"\"\n",
    "    s1 = NAND(x1, x2)\n",
    "    s2 = OR(x1, x2)\n",
    "    return AND(s1, s2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "XOR(0, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "XOR(1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "XOR(0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "XOR(1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "このように、複数のパーセプトロンを組み合わせたパーセプトロンのことを **多層パーセプトロン** という。  \n",
    "XORは、NAND, ORの出力とANDの出力の組み合わせなので、2層のパーセプトロンである。\n",
    "(本によっては、入力$x_1$, $x_2$も入れて3層とすることもある)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 🤔XORをグラフにすると？"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import itertools\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    xs = np.array([[0, 0],\n",
    "                   [1, 0],\n",
    "                   [0, 1],\n",
    "                   [1, 1]], dtype=np.float32)      # データ\n",
    "\n",
    "\n",
    "\n",
    "    w = np.array([0, 0], dtype=np.float32)  # 重み\n",
    "    b = 0  # バイアス\n",
    "    lr = 0.01  # 学習率\n",
    "\n",
    "    def predict(x):\n",
    "        u = np.dot(x, w) - b\n",
    "        return np.where(u > 0, 1, 0)\n",
    "\n",
    "    # グラフの描画 from https://teratail.com/questions/177319\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.set_xticks([0, 1]), ax.set_yticks([0, 1])\n",
    "    ax.set_xlim(-0.5, 1.5), ax.set_ylim(-0.5, 1.5)\n",
    "\n",
    "    # サンプルを描画する。\n",
    "    ax.scatter(xs[:, 0], xs[:, 1], s=30)\n",
    "\n",
    "    # 各点の推論結果を得る。\n",
    "    X, Y = np.meshgrid(np.linspace(*ax.get_xlim(), 100),\n",
    "                       np.linspace(*ax.get_ylim(), 100))\n",
    "    XY = np.column_stack([X.ravel(), Y.ravel()])\n",
    "    Z = np.array([XOR(x[0], x[1]) for x in XY]).reshape(X.shape)\n",
    "\n",
    "    # 等高線を描画する。\n",
    "    ax.contourf(X, Y, Z, alpha=0.4, cmap='RdBu')\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "曲線にならなかったね…"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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",
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 },
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