『練習』HW 6-1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 284,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'y-axis')"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def L(x):\n",
    "    return x*(x-1)*(x-2)*(x-3)*(x-4)\n",
    "def dL(x):\n",
    "    return 5*x**4-40*x**3+105*x**2-100*x+24\n",
    "def gd(x):\n",
    "    return x-(5*x**4-40*x**3+105*x**2-100*x+24)*0.001\n",
    "x=np.arange(-2,5,0.01)\n",
    "\n",
    "plt.plot(x,L(x))\n",
    "plt.ylim(-20,20)\n",
    "plt.grid()\n",
    "plt.xlabel(\"x-axis\")\n",
    "plt.ylabel(\"y-axis\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "x減掉lossfunction 的斜率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ipywidgets import interact"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(x,lr,epoch):\n",
    "    x_gd=[]\n",
    "    y_gd=[]      ##建立空列表來收集結果\n",
    "    \n",
    "    x_gd.append(x)\n",
    "    y_gd.append(L(x))  ##收集第一次的結果\n",
    "    \n",
    "    for i in range(epoch):\n",
    "        x=x-lr*dL(x)\n",
    "        x_gd.append(x)   ##收集每次迭代的結果\n",
    "        y_gd.append(L(x))\n",
    "        \n",
    "    return x_gd,y_gd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw(x0,lr,epoch):\n",
    "    x=np.arange(-2,5,0.01)\n",
    "    \n",
    "    plt.ylim(-5,5)\n",
    "    plt.xlim(-1,5)\n",
    "    plt.grid()\n",
    "    plt.xlabel(\"$x$\")\n",
    "    plt.ylabel(\"$y$\")\n",
    "    \n",
    "    \n",
    "    x_gd, y_gd=gradient_descent(x0,lr,epoch)    ##  x被用過改x0\n",
    "    \n",
    "    plt.plot(x,L(x))\n",
    "    plt.scatter(x_gd,y_gd,c=\"r\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 293,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([1,\n",
       "  1.06,\n",
       "  1.113502552,\n",
       "  1.1605040208396156,\n",
       "  1.201383170974082,\n",
       "  1.2367127667184605,\n",
       "  1.2671323076367287,\n",
       "  1.293273010934261,\n",
       "  1.3157193002251943,\n",
       "  1.3349928731952676,\n",
       "  1.3515494782928292],\n",
       " [0,\n",
       "  -0.3409840224000003,\n",
       "  -0.610100994172955,\n",
       "  -0.8167540324618264,\n",
       "  -0.9725798570556817,\n",
       "  -1.088748620377317,\n",
       "  -1.174783851157419,\n",
       "  -1.2382903794029987,\n",
       "  -1.2851122654457854,\n",
       "  -1.319639437953746,\n",
       "  -1.3451261979295857])"
      ]
     },
     "execution_count": 293,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw(1,0.01,10)  #畫圖\n",
    "gradient_descent(1,0.01,10)  #看值\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 10 0\n"
     ]
    }
   ],
   "source": [
    "def optimize():    #定义最优化函数\n",
    "#建空列表收集x,y,z的值\n",
    "    z_list = []     \n",
    "    x_list = []\n",
    "   \n",
    "    for x in range(-10,10,1):\n",
    "        \n",
    "        z = x**2\n",
    "        z_list.append(z)\n",
    "        x_list.append(x)\n",
    "        \n",
    "    return z_list,x_list\n",
    "\n",
    "z_list,x_list = optimize()\n",
    "#使用python自带的min()函数，找出z_value这个列表中最小的值，最小值为0\n",
    "min_value = min(z_list)\n",
    "#通过list.index(值)找出这个值在列表list中的索引值\n",
    "index = z_list.index(min(z_list))\n",
    "#因为x,y的索引值跟z是一样的，所以这样对应的索引值也是x,y的索引值\n",
    "#因此将索引值带入得到的x,y就是使得z最小的时候的值\n",
    "x_value = x_list[index]\n",
    "\n",
    "print(min_value,index,x_value)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 480x320 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum occurs at x = 1.0764494592496179\n",
      "Minimum = 9930.319069600047\n"
     ]
    }
   ],
   "source": [
    "def gradient_descent(x, lr, epoch):\n",
    "    x_gd = []\n",
    "    y_gd = []\n",
    "    \n",
    "    x_gd.append(x)\n",
    "    y_gd.append(f(x))\n",
    "\n",
    "    # begin the loops to update x and y\n",
    "    for i in range(epoch):\n",
    "        x -= lr*fp(x)\n",
    "        x_gd.append(x)\n",
    "        y_gd.append(f(x))\n",
    "\n",
    "    return x_gd, y_gd\n",
    "\n",
    "def show_graph(x0, lr, epoch):\n",
    "    x = np.arange(0, 5, 0.01)\n",
    "    y = f(x)\n",
    "\n",
    "    fig=plt.figure(figsize=(6,4), dpi=80)\n",
    "    ax=fig.add_subplot(111)\n",
    "    ax.plot(x, y, lw = 0.9, color = 'k')\n",
    "    ax.set_xlim([0., 5.])\n",
    "    ax.set_ylim([-2.,10.])\n",
    "    ax.set_xlabel(r'$x$')\n",
    "    ax.set_ylabel(r'$y$')\n",
    "    ax.text(2.5, 9, '$f(x) = (x-1)(x-1.5)(x-3)(x-4)$', size=16, ha='center', va='center')\n",
    "    ax.text(0.5, 8, 'start at x = %.2f'%x0, size=16, ha='left', va='center')\n",
    "    ax.text(0.5, 7, 'learning rate = %.2f'%lr, size=16, ha='left', va='center')\n",
    "    \n",
    "    \n",
    "    x_gd, y_gd = gradient_descent(x0, lr, epoch)\n",
    "\n",
    "\n",
    "    ax.scatter(x_gd, y_gd, c = 'b')\n",
    "\n",
    "###以下畫箭頭\n",
    "    for i in range(1, epoch+1):\n",
    "        ax.annotate('', xy=(x_gd[i], y_gd[i]), xytext=(x_gd[i-1], y_gd[i-1]),\n",
    "                       arrowprops={'arrowstyle': '->', 'color': 'r', 'lw': 1},\n",
    "                       va='center', ha='center')\n",
    "        \n",
    "    plt.grid()\n",
    "    plt.show()\n",
    "    print(\"Minimum occurs at x =\",x_gd[-1])\n",
    "    print(\"Minimum =\",y_gd[-1])\n",
    "show_graph(x0=0.3, lr=0.01, epoch=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-170-2842698c2c64>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;32mwhile\u001b[0m \u001b[0mdL\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m!=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0mx\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mgd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mL\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "x=1\n",
    "while dL(x)!=0:\n",
    "    x=gd(x)\n",
    "print(x)\n",
    "print(L(x))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
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