diff --git a/lab/1_liner-regression-single.ipynb b/lab/1_liner-regression-single.ipynb index a0815a2..3920b99 100644 --- a/lab/1_liner-regression-single.ipynb +++ b/lab/1_liner-regression-single.ipynb @@ -36,26 +36,26 @@ "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", + "# 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", + "# 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)" + "# 生成并保存数据\n", + "data = generate_data()\n", + "#save_data('./1_data.txt', data)" ] }, { @@ -100,7 +100,7 @@ "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", + " return np.sum((y-w*x-b)**2)/2*len(x)\n", "\n", "# 等效\n", "def compute_loss_equivalent(w,b):\n", diff --git a/lab/2_liner-regression-multiply.ipynb b/lab/2_liner-regression-multiply.ipynb new file mode 100644 index 0000000..c68d964 --- /dev/null +++ b/lab/2_liner-regression-multiply.ipynb @@ -0,0 +1,206 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# 引入库\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import os\n", + "from sklearn.preprocessing import StandardScaler" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "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": "markdown", + "metadata": {}, + "source": [ + "生成数据方式\n", + "$$y = 1.35x + 0.75x^2 + 2.1\\sqrt{x} + 2.89$$" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# 生成数据\n", + "def generate_data():\n", + " w = np.array([1.35, 0.75, 2.1]) # 权重\n", + " b = 2.89 # 偏置\n", + " x_min = 1\n", + " x_max = 8\n", + " x = np.linspace(x_min, x_max, 10) # 均匀分布\n", + " X = np.array([x, x**2, np.sqrt(x)]) # 特征矩阵3x10\n", + " y = np.dot(w, X) + b # 1x10 一维向量不区分行向量和列向量\n", + " y += np.random.normal(scale=0.5, size=y.shape)\n", + " data = np.column_stack((X.T, y)) # 10x4\n", + " scaler = StandardScaler()\n", + " data = scaler.fit_transform(data)\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": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# 读取数据\n", + "#points = np.genfromtxt(\"./1_data.txt\", delimiter=',')\n", + "\n", + "points = data\n", + "\n", + "m = len(points[:,0])\n", + "x = points[:, :3] # 10x3\n", + "y = points[:,3] # 1x10" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "原函数：\n", + "$$\n", + "\\vec{w} = {\\begin{bmatrix} w_1 & w_2 & w_3 & \\cdots & w_n \\end{bmatrix}}^T\n", + "$$\n", + "\n", + "$$\n", + "\\vec{x} = \\begin{bmatrix} x_1 & x_2 & x_3 & \\cdots & x_n \\end{bmatrix}\n", + "$$\n", + "\n", + "$$\n", + "f_{\\vec{w} \\cdot,b}(\\vec{x}) = \\vec{w} \\cdot \\vec{x} + b\n", + "$$\n", + "\n", + "损失函数: \n", + "\n", + "$$\n", + "\\text{MSE} = \\frac{1}{2m} \\sum_{i=1}^{m} \\left( y^{(i)} - \\hat{y}^{(i)} \\right)^2\n", + "$$\n", + "\n", + "梯度下降：\n", + "\n", + "分别对每个w和b求偏导数，然后更新w和b\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# 定义损失函数\n", + "def compute_loss(w, b):\n", + " return np.sum((y - (np.dot(w, x.T) + b)) ** 2) / (2 * m) # w 1x3 x.T 3x10 y 1x10 y-np.dot(w, x.T) 1x10 sum=number\n", + "\n", + "# 定义梯度下降\n", + "def gradient_descent(w, b, alpha, num_iter):\n", + " for _ in range(num_iter):\n", + " error = y - np.dot(w, x.T) - b # 1x10\n", + " # 计算梯度\n", + " dw = -np.dot(x.T , error) / m # dw 1x3 \n", + " db = -np.sum(error) / m # db 1x1\n", + " # 更新w和b\n", + " w -= alpha * dw\n", + " b -= alpha * db\n", + " return w, b" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "w: [0.30933908 0.51500581 0.17832512]\n", + "b: -3.2582270215186813e-16\n", + "loss: 0.0027531700168465624\n" + ] + } + ], + "source": [ + "# 主函数\n", + "if __name__ == \"__main__\":\n", + " # 初始化w和b\n", + " w = np.zeros(x.shape[1])\n", + " 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)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 编码中遇到的错误\n", + "\n", + "梯度下降算法中，把x.T和error相乘了，正确应使用矩阵乘法。" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "pt", + "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": "3.10.14" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}