标准方程法.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy import genfromtxt\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": [
    "#载入数据\n",
    "data = genfromtxt(\"data.csv\",delimiter = ',')\n",
    "x_data = data[:,0,np.newaxis]\n",
    "y_data = data[:,1,np.newaxis]\n",
    "plt.scatter(x_data,y_data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(18, 1)\n",
      "(18, 1)\n",
      "(18, 2)\n"
     ]
    }
   ],
   "source": [
    "print(np.mat(x_data).shape)\n",
    "print(np.mat(y_data).shape)\n",
    "#给样本加偏置项\n",
    "X_data = np.concatenate((np.ones((18,1)),x_data),axis=1)\n",
    "print(X_data.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#标准方程法求解回归参数\n",
    "def weights(xArr,yArr):\n",
    "    xMat = np.mat(xArr)\n",
    "    yMat = np.mat(yArr)\n",
    "    xTx = xMat.T *xMat\n",
    "    #计算矩阵的值，说明该矩阵是否为逆矩阵\n",
    "    if np.linalg.det(xTx) ==0.0:\n",
    "        print(\"This matrix cannot do inverse\")\n",
    "        return\n",
    "    #xTx.I 为xTx的逆矩阵\n",
    "    ws = xTx.I * xMat.T * yMat\n",
    "    return ws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[4.77925623e+02]\n",
      " [1.15177402e-01]]\n"
     ]
    }
   ],
   "source": [
    "ws = weights(X_data,y_data)\n",
    "print(ws)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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": [
    "#画图\n",
    "y_test = ws[0] + x_data * ws[1]\n",
    "plt.plot(x_data,y_data,'b.')\n",
    "plt.plot(x_data,y_test,'r.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}