AI-learning/lab/1_liner-regression-single.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 引入库\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "/Users/wolves/Downloads/project/python/pt/lab\n"
     ]
    }
   ],
   "source": [
    "# 检查os位置\n",
    "print(os.getcwd())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "  # 生成数据\n",
    "  def generate_data():\n",
    "      w = 1.35\n",
    "      b = 2.89\n",
    "      x_min = 0\n",
    "      x_max = 10\n",
    "      x = np.linspace(x_min, x_max, 100)\n",
    "      y = w * x + b\n",
    "      y += np.random.normal(scale=0.5, size=y.shape)\n",
    "      data = np.column_stack((x, y))\n",
    "      return data\n",
    "\n",
    "  # 保存数据\n",
    "  def save_data(filename, data):\n",
    "      np.savetxt(filename, data, delimiter=',')\n",
    "      print(f\"{filename} 已成功创建并写入数据。\")\n",
    "\n",
    "  # 生成并保存数据\n",
    "  data = generate_data()\n",
    "  #save_data('./1_data.txt', data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 读取数据\n",
    "#points = np.genfromtxt(\"./1_data.txt\", delimiter=',')\n",
    "\n",
    "points = data\n",
    " \n",
    "x = points[:, 0]\n",
    "y = points[:, 1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "损失函数: \n",
    "$$J(w,b) = \\frac{1}{2m} \\sum_{i=1}^{m} (y_{w,b}(x^{(i)}) - y^{(i)})^2$$\n",
    "\n",
    "梯度下降：\n",
    "\n",
    "分别对w和b求偏导数，然后更新w和b\n",
    "$$\n",
    "w = w - \\alpha\\cdot\\frac{\\partial J(w,b)}{\\partial w}\n",
    "$$\n",
    "\n",
    "$$\n",
    "b = b - \\alpha\\cdot\\frac{\\partial J(w,b)}{\\partial b}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 定义损失函数\n",
    "def compute_loss(w,b):\n",
    "    return np.sum((y-w*x-b)**2)/(2*len(x))\n",
    "\n",
    "# 等效\n",
    "def compute_loss_equivalent(w,b):\n",
    "    sum = 0\n",
    "    for i in range(len(x)):\n",
    "        sum += (y[i] - (w*x[i]+b))**2\n",
    "    return sum/(2*len(x))\n",
    "\n",
    "# 定义梯度下降\n",
    "def gradient_descent(w,b,alpha,num_iter):\n",
    "    m = len(x)\n",
    "    for _ in range(num_iter):\n",
    "        # 计算梯度\n",
    "        dw = -np.sum(x*(y-w*x-b))/m\n",
    "        db = -np.sum(y-w*x-b)/m\n",
    "        # 更新w和b\n",
    "        w = w - alpha*dw\n",
    "        b = b - alpha*db\n",
    "    return w,b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w: 1.368169058216238\n",
      "b: 2.770596744047831\n",
      "loss: 0.1375443007342851\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 3840x2880 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 主函数\n",
    "if __name__ == \"__main__\":\n",
    "    # 初始化w和b\n",
    "    w,b = 0,0\n",
    "    # 设置学习率\n",
    "    alpha = 0.01\n",
    "    # 设置迭代次数\n",
    "    num_iter = 1000\n",
    "    # 进行梯度下降\n",
    "    w,b = gradient_descent(w,b,alpha,num_iter)\n",
    "    print(\"w:\", w)\n",
    "    print(\"b:\", b)\n",
    "    # 计算损失\n",
    "    loss = compute_loss(w,b)\n",
    "    print(\"loss:\", loss)\n",
    "\n",
    "    plt.figure(dpi=600)\n",
    "    #plt.switch_backend('Agg')  # 使用 Agg 渲染器\n",
    "    # 绘制数据点\n",
    "    plt.scatter(x, y, color='blue', label='original data')\n",
    "\n",
    "    # 绘制回归直线\n",
    "    plt.plot(x, w*x + b, color='red', label='regression line')\n",
    "\n",
    "    # 添加标题和标签\n",
    "    plt.title('linear regression')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('y')\n",
    "\n",
    "    # 显示图例\n",
    "    plt.legend()\n",
    "\n",
    "    # 显示图像\n",
    "    plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "pt",
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