class.py

import numpy as np
from helpers import *

class LinearRegression():
    def __init__(self, train_data, learning_rate=0.01,train_iter=100):
        self.weights = np.zeros((len(train_data[1])-1, 1)) # by default, the input train_data has shape: [num_samples, num_features + 1], where 1 for labels
        self.lr = learning_rate
        self.train_iter = train_iter

    def feat_normalize(self, data):
        print(f"Normalizing...\n")
        data_norm = np.array(data)

        mu = np.mean(data, 0)
        sigma = np.std(data, 0)
        
        sigma[sigma==0] = 1.0   # 避免除以0
        data_norm = (data_norm - mu)/sigma
        return data_norm

    # 将权重和偏差放到一个向量中，并相应地扩展数据矩阵
    # data: [num_samples, num_feat] -> [num_samples, num_feat+1]
    # weights: (num_weights, ) -> (num_wegits+1, )
    def extend_matrix(self, normalized_data):
        print(f"Extending Matrix...\n")
        num_samples = normalized_data.shape[0]

        x_extend = np.hstack((normalized_data, np.ones((num_samples,1))))
        # print(f"shape of x_extend is: {x_extend.shape}\n")
        self.weights = np.vstack((self.weights, np.ones((1,1))))
        # print(f"shape of self.weights is: {self.weights.shape}\n")
        print(f"Extending Done!\n")
        return x_extend

    # 平方误差和作为损失函数
    def get_loss(self,x_extend, labels):
        J = 0
        J = 0.5 * np.transpose(x_extend @ self.weights - labels) @ (x_extend @ self.weights - labels)
        print(f"current loss is: {J}\n")
        return J

    def compute_gradient(self, x_extend, labels):
        print(f"Computing Gradient...\n")
        n = len(self.weights)
        J_history = np.zeros((self.train_iter, 1))
        
        for i in range(self.train_iter):
            grad = np.transpose(x_extend) @ (x_extend @ self.weights - labels)
            self.weights = self.weights - self.lr*grad
            J_history[i] = self.get_loss(x_extend, labels)
            print(f"---\n{i}_th iterate step: \n weights are: {self.weights}\n loss is: {J_history[i]}\n ### \n ")
        
        return J_history

    # shape of data: [num_samples, num_features]
    def train(self, data):
        # pre-process data
        x = self.feat_normalize(data[:,:-1])
        x_extend = self.extend_matrix(x)
        print(f"check the weight size again: {len(self.weights)}\n")
        
        # labels = data[:,-1] 返回的是一维数组(num_samples, )，需要改成二维列向量
        labels = data[:,-1].reshape(-1,1)

        J_history = self.compute_gradient(x_extend, labels)
        plotJ(J_history, self.train_iter)

if __name__ == "__main__":
    data = np.loadtxt("data.txt", delimiter=",", dtype=np.float64)
    linear_regression = LinearRegression(data) 
    linear_regression.train(data)