{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# パーセプトロンの実装"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 簡単な実装\n",
    "\n",
    "AND関数を実装しよう"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "def AND(x1, x2):\n",
    "    w1, w2, theta = 0.5, 0.5, 0.7\n",
    "    tmp = x1 * w1 + x2 * w2\n",
    "    if tmp <= theta:\n",
    "        return 0\n",
    "    elif tmp > theta:\n",
    "        return 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AND(0, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AND(1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AND(0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AND(1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 重みとバイアスの導入\n",
    "パーセプトロンの条件式を見てみよう\n",
    "$$\n",
    "     y = \n",
    "         \\begin{cases}\n",
    "             0 \\quad (w_1 x_1 + w_2 x_2 \\leqq \\theta) \\\\\n",
    "             1 \\quad (w_1 x_1 + w_2 x_2 > \\theta) \\\\\n",
    "         \\end{cases}\n",
    "$$\n",
    "\n",
    "ここで、$\\theta$ = $-b$ とすると\n",
    "\n",
    "$$\n",
    "     y = \n",
    "         \\begin{cases}\n",
    "             0 \\quad (w_1 x_1 + w_2 x_2 \\leqq - b) \\\\\n",
    "             1 \\quad (w_1 x_1 + w_2 x_2 > - b) \\\\\n",
    "         \\end{cases}\n",
    "$$\n",
    "\n",
    "式変形して\n",
    "\n",
    "$$\n",
    "     y = \n",
    "         \\begin{cases}\n",
    "             0 \\quad (b + w_1 x_1 + w_2 x_2 \\leqq 0) \\\\\n",
    "             1 \\quad (b + w_1 x_1 + w_2 x_2 > 0) \\\\\n",
    "         \\end{cases}\n",
    "$$\n",
    "\n",
    "ここで、$b$ を **バイアス** と呼び、$w_1$ $w_2$ を **重み** と呼びます"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0. , 0.5])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "x = np.array([0, 1])      # 入力\n",
    "w = np.array([0.5, 0.5])  # 重み\n",
    "b = -0.7                  # バイアス\n",
    "w * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(w * x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.19999999999999996"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(w * x) + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 重みとバイアスによる実装"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* $w_1$ や $w_2$ の重みは、入力信号の重要度をコントロールするパラメータ\n",
    "* $b$ のバイアスは、発火のしやすさのパラメータ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NAND(0, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NAND(1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NAND(0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NAND(1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "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": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OR(0, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OR(1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OR(0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OR(1, 1)"
   ]
  }
 ],
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