{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "今天的日期是:  2023-05-11\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z))\n",
    "\n",
    "def costFunction(theta, X, y):\n",
    "    m = len(y)\n",
    "    \n",
    "    J = 0\n",
    "    grad = np.zeros(theta.shape)\n",
    "    \n",
    "    h = sigmoid(np.dot(X, theta))\n",
    "    J = (-1/m) * np.sum(y*np.log(h) + (1-y)*np.log(1-h))\n",
    "    grad = (1/m) * np.dot(X.T, (h-y))\n",
    "    \n",
    "    return J, grad\n",
    "\n",
    "def gradientDescent(X, y, theta, alpha, num_iters):\n",
    "    m = len(y)\n",
    "    J_history = np.zeros(num_iters)\n",
    "    \n",
    "    for i in range(num_iters):\n",
    "        J_history[i], grad = costFunction(theta, X, y)\n",
    "        theta = theta - alpha*grad\n",
    "        \n",
    "    return theta, J_history\n",
    "\n",
    "# 生成样本数据\n",
    "np.random.seed(0)\n",
    "X = np.random.randn(100, 2)\n",
    "ones = np.ones((100, 1))\n",
    "X = np.hstack((ones, X))\n",
    "y = np.random.randint(0, 2, size=(100,1))\n",
    "\n",
    "# 初始化theta\n",
    "initial_theta = np.zeros((X.shape[1], 1))\n",
    "\n",
    "# 梯度下降\n",
    "alpha = 0.1\n",
    "num_iters = 1000\n",
    "theta, J_history = gradientDescent(X, y, initial_theta, alpha, num_iters)\n",
    "\n",
    "# 绘制决策边界\n",
    "x1 = np.arange(-3, 3, 0.1)\n",
    "x2 = -(theta[0]+theta[1]*x1)/theta[2]\n",
    "plt.plot(x1, x2, label='Decision Boundary')\n",
    "plt.scatter(X[:, 1], X[:, 2], c=y.flatten())\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'numpy'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[39mimport\u001b[39;00m \u001b[39mnumpy\u001b[39;00m \u001b[39mas\u001b[39;00m \u001b[39mnp\u001b[39;00m\n\u001b[1;32m      2\u001b[0m \u001b[39mimport\u001b[39;00m \u001b[39mmatplotlib\u001b[39;00m\u001b[39m.\u001b[39;00m\u001b[39mpyplot\u001b[39;00m \u001b[39mas\u001b[39;00m \u001b[39mplt\u001b[39;00m\n\u001b[1;32m      5\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39msigmoid\u001b[39m(z):\n",
      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'numpy'"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z))\n",
    "\n",
    "def costFunction(theta, X, y):\n",
    "    m = len(y)\n",
    "    J = 0\n",
    "    grad = np.zeros(theta.shape)\n",
    "    \n",
    "    h = sigmoid(np.dot(X, theta))\n",
    "    J = (-1/m) * np.sum(y*np.log(h) + (1-y)*np.log(1-h))\n",
    "    grad = (1/m) * np.dot(X.T, (h-y))\n",
    "    \n",
    "    return J, grad\n",
    "\n",
    "def gradientDescent(X, y, theta, alpha, num_iters):\n",
    "    m = len(y)\n",
    "    J_history = np.zeros(num_iters)\n",
    "    \n",
    "    for i in range(num_iters):\n",
    "        J_history[i], grad = costFunction(theta, X, y)\n",
    "        theta = theta - alpha*grad\n",
    "        \n",
    "    return theta, J_history\n",
    "\n",
    "# 生成样本数据\n",
    "np.random.seed(0)\n",
    "X = np.random.randn(100, 2)\n",
    "ones = np.ones((100, 1))\n",
    "X = np.hstack((ones, X))\n",
    "y = np.random.randint(0, 2, size=(100,1))\n",
    "\n",
    "# 初始化theta\n",
    "initial_theta = np.zeros((X.shape[1], 1))\n",
    "\n",
    "# 梯度下降\n",
    "alpha = 0.1\n",
    "num_iters = 1000\n",
    "theta, J_history = gradientDescent(X, y, initial_theta, alpha, num_iters)\n",
    "\n",
    "# 绘制决策边界\n",
    "x1 = np.arange(-3, 3, 0.1)\n",
    "x2 = -(theta[0]+theta[1]*x1)/theta[2]\n",
    "plt.plot(x1, x2, label='Decision Boundary')\n",
    "plt.scatter(X[:, 1], X[:, 2], c=y.flatten())\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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