neural_network/numpy_nn/derivatives_7.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "fa52c791",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8c9f29c",
   "metadata": {},
   "source": [
    "$$ y = 2\\times x$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "998aac4e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return 2 * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "93e87f95",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array(range(10))\n",
    "y = f(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "7191f861",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]),\n",
       " array([ 0,  2,  4,  6,  8, 10, 12, 14, 16, 18]))"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x,y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "f4e24223",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y)\n",
    "plt.title(\"y= 2*x\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16d4b453",
   "metadata": {},
   "source": [
    "斜率"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8292026",
   "metadata": {},
   "source": [
    "$$\\frac{change \\space y}{change \\space x}   = \\frac{\\triangle y}{\\triangle x}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "793582cd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1 = [0, 0]#第一个点的坐标（x, y）\n",
    "p2 = [1, 2]#第二个点的坐标\n",
    "trianglex = p2[0] - p1[0]\n",
    "triangley = p2[1] - p1[1]\n",
    "slop = triangley / trianglex\n",
    "slop"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c495f0a",
   "metadata": {},
   "source": [
    "$$y = 2 \\times x^2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "9f3018cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return 2 * x ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "0c637185",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array(range(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "6c215cf2",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = f(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "32bb52e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0, 1, 2, 3, 4]), array([ 0,  2,  8, 18, 32], dtype=int32))"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "f5603cb6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"y=2*x*x\")\n",
    "plt.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2baccb1f",
   "metadata": {},
   "source": [
    "根据斜率求解该函数斜率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "767b3b31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(y[1] - y[0])/(x[1] - x[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "4741c14b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.0"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(y[2] - y[1])/(x[2] - x[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a111080",
   "metadata": {},
   "source": [
    "可以发现$y = 2\\times x^2$函数的斜率不止一个。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78cc36bd",
   "metadata": {},
   "source": [
    "那我们要怎么才能知道x对y的影响有多大呢？换句话说，x改变，y会变化多大？"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d8aa761",
   "metadata": {},
   "source": [
    "x=0,y=0处x的斜率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "3253f909",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00019999999999999998"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta = 0.0001\n",
    "x1 = x[0]#x = 0\n",
    "x2 = x1 + delta\n",
    "y1 = f(x1)\n",
    "y2 = f(x2)\n",
    "derivative = (y2 - y1) / (x2 - x1)\n",
    "derivative"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "583be9be",
   "metadata": {},
   "source": [
    "x=1,y=2处x的斜率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "6a9a975e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.0001999999987845"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta = 0.0001\n",
    "x1 = x[1]#x = 1\n",
    "x2 = x1 + delta\n",
    "y1 = f(x1)\n",
    "y2 = f(x2)\n",
    "derivative = (y2 - y1) / (x2 - x1)\n",
    "derivative"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58e0d39d",
   "metadata": {},
   "source": [
    "x=2,y=8处x的斜率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "a249b86f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.000199999998785"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta = 0.0001\n",
    "x1 = x[2]#x = 1\n",
    "x2 = x1 + delta\n",
    "y1 = f(x1)\n",
    "y2 = f(x2)\n",
    "derivative = (y2 - y1) / (x2 - x1)\n",
    "derivative"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c2106be",
   "metadata": {},
   "source": [
    "delta取值足够的小，但是只能无限趋近于0，但是不能为0，知道问什么吗？"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc1a82ae",
   "metadata": {},
   "source": [
    "下图是求解斜率，只有两个点无限靠近，斜率越准确。也就是delta值越小，斜率越准。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "027ddcef",
   "metadata": {},
   "source": [
    "<div>\n",
    "    <img src='slope.png' width=40% align=left>\n",
    "    <img src='derivative.png' width=35% align=right>\n",
    "</div>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bab774ec",
   "metadata": {},
   "source": [
    "我们将函数画得更平滑一点。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "57d54ea2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0, 5, 0.001)\n",
    "y = f(x)\n",
    "plt.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff913d8a",
   "metadata": {},
   "source": [
    "斜率可以用$y=mx+b$去表示，m就是x点处的derivative，现在b是未知数$b=y-mx$。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "2a1903b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[2000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "ed2d9529",
   "metadata": {},
   "outputs": [],
   "source": [
    "delta = 0.0001\n",
    "x1 = x[2000]\n",
    "x2 = x1 + delta\n",
    "y1 = f(x1)\n",
    "y2 = f(x2)\n",
    "derivative = (y2 - y1) /(x2 - x1)#这里等于m\n",
    "b = y2 - derivative * x2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "c1bf9eb6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def slope_line(x):\n",
    "    return derivative * x + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "5004f128",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = [x1 - 0.9, x1, x1 + 0.9]\n",
    "plt.plot(x, y)\n",
    "plt.plot(xs, [slope_line(i) for i in xs])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a2afe70",
   "metadata": {},
   "source": [
    "请在0.0处，1.0出，3.0处，4.0处画出斜率。"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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",
   "version": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}