carlo_cal_s.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\MSI-PC\\Anaconda3\\lib\\site-packages\\IPython\\core\\pylabtools.py:128: UserWarning: Creating legend with loc=\"best\" can be slow with large amounts of data.\n",
      "  fig.canvas.print_figure(bytes_io, **kw)\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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "当采样次数为: 1000000,x.^3在[0,1]估计面积值为:  0.24987168919036473\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "def f(x): \n",
    "    return x**3\n",
    "#times为采样次数\n",
    "#bound为上下边界矩阵\n",
    "def calro(times,a,b):\n",
    "    #此为最简形式，基于正态分布于区间[a,b]内随机采数\n",
    "    #后续添加基于样本，推测函数分布密度，决定该次采样是否接受，马尔卡尔蒙特卡洛方法\n",
    "    x = []\n",
    "    y = []\n",
    "    for i in range(times):\n",
    "        tp = np.random.rand()*(b-a)\n",
    "        x.append(tp)\n",
    "    x = np.sort(x)\n",
    "    y = f(x)\n",
    "    return np.array(x),np.array(y)\n",
    "import matplotlib.pyplot as plt\n",
    "SMALL_SIZE = 11\n",
    "MEDIUM_SIZE = 13\n",
    "BIGGER_SIZE = 13\n",
    "plt.rc('font', size=SMALL_SIZE)          # controls default text sizes\n",
    "plt.rc('axes', titlesize=SMALL_SIZE)     # fontsize of the axes title\n",
    "plt.rc('axes', labelsize=MEDIUM_SIZE)    # fontsize of the x and y labels\n",
    "plt.rc('xtick', labelsize=SMALL_SIZE)    # fontsize of the tick labels\n",
    "plt.rc('ytick', labelsize=SMALL_SIZE)    # fontsize of the tick labels\n",
    "plt.rc('legend', fontsize=SMALL_SIZE)    # legend fontsize\n",
    "plt.rc('figure', titlesize=BIGGER_SIZE)  # fontsize of the figure title\n",
    "plt.rcParams['font.sans-serif']=['SimHei']\n",
    "plt.rcParams['axes.unicode_minus']=False\n",
    "times = 1000000\n",
    "x_cal,y_cal = calro(times,0,1)\n",
    "def plot_compare(times,x_cal,y_cal):\n",
    "    #采样点是否合理直接决定估值精度\n",
    "    x_real = np.linspace(0,1,times)\n",
    "    y_real = f(x_real)\n",
    "    plt.figure()\n",
    "    gca = 'get_current_axis'\n",
    "    ax = plt.gca()\n",
    "    ax.spines['right'].set_color('none')\n",
    "    ax.spines['top'].set_color('none')\n",
    "    ax.xaxis.set_ticks_position('bottom')\n",
    "    ax.yaxis.set_ticks_position('left')\n",
    "    plt.plot(x_real,y_real,color='yellow',linestyle='-')\n",
    "    #print(x_cal)\n",
    "    plt.plot(x_cal,y_cal,color='blue',marker='o')\n",
    "    plt.legend(['sin(x)','采样值'])\n",
    "    plt.show()\n",
    "plot_compare(times,x_cal,y_cal)\n",
    "def cal_s(y_cal,times):\n",
    "    return sum(y_cal)/times\n",
    "print('当采样次数为: '+str(times)+',x.^3在[0,1]估计面积值为: ',cal_s(y_cal,times))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.13644\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\MSI-PC\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:23: DeprecationWarning: object of type <class 'float'> cannot be safely interpreted as an integer.\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": [
    "import math\n",
    "class point:\n",
    "    def __init__(self,x):\n",
    "        self.x = x[0,0]\n",
    "        self.y = x[0,1]\n",
    "        self.distance = np.sqrt(self.x**2+self.y**2)\n",
    "        \n",
    "    \n",
    "def calro_pi(times):\n",
    "    points = []\n",
    "    for i in range(times):\n",
    "        tp = point(np.random.rand(1,2))\n",
    "        points.append(tp)\n",
    "    count = 0\n",
    "    plot_x = []\n",
    "    plot_y = []\n",
    "    for x in points:\n",
    "        if x.distance <=1:\n",
    "            count+=1\n",
    "            plot_x.append(x.x)\n",
    "            plot_y.append(x.y)\n",
    "    print(count/times*4)\n",
    "    x = np.linspace(0,1,times/100)\n",
    "    y = np.sqrt(1-x**2)\n",
    "    plt.figure()\n",
    "    plt.plot(np.array(plot_x),np.array(plot_y),marker='o',label='cp')\n",
    "    plt.plot(x,y,label='circle')\n",
    "    plt.legend()\n",
    "    plt.grid()\n",
    "\n",
    "calro_pi(100000)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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