实验1—从0实现logistic回归（只借助Tensor和Numpy相关的库）

import torch
from IPython import display
from matplotlib import pyplot as plt 
from torch import nn
import numpy as np
import random

# 特征数
num_inputs = 2
# set example number 
num_examples = 1000

true_w = [2.1,-3.0]
true_b = 1.3

# 生成1000*2个随机数，作为特征值
features = torch.tensor(np.random.normal(0,1,(num_examples,num_inputs)),dtype=torch.float)

# 根据w和b的值，生成特征相应的标签
labels = 1 / (1 + torch.exp(-1 * (true_w[0] * features[:, 0] + true_w[1] * features[:, 1]) + true_b ))

# 增加干扰
labels += torch.tensor(np.random.normal(0,0.01,size=labels.size()),dtype=float)

num0 = 0
num1 = 0
for i in range(num_examples):
    if labels[i] < 0.5:
        labels[i] = 0
        num0 += 1
    else:
        labels[i] = 1
        num1 += 1
# print(labels)
labels = labels.view(num_examples, 1) #把label变成1000*1的矩阵
#print(labels)

def use_svg_display():
    #用矢量图表示
    display.set_matplotlib_formats('svg')
def set_figsize(figsize=(3.5,2.5)):
    use_svg_display()
    #设置图的尺寸
    plt.rcParams['figure.figsize'] = figsize
set_figsize()
plt.scatter(features[:,1].numpy(),labels.numpy(),1)

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num_inputs = 2
def data_iter(batch_size, features, labels):
    num_examples = len(features)
    indices = list(range(num_examples)) # [0, 1, ..., 998, 999] 
    random.shuffle(indices) # 样本的读取顺序是随机的 
    for i in range(0, num_examples, batch_size):
        j = torch.LongTensor(indices[i: min(i + batch_size, num_examples)]) # 最后一次可能不足一 个batch
        yield features.index_select(0, j), labels.index_select(0, j)

w = torch.tensor(np.random.normal(0,0.01,(num_inputs,1)),dtype=torch.float32)
b = torch.zeros(1,dtype=torch.float32)
w.requires_grad_(requires_grad=True)
b.requires_grad_(requires_grad=True)

tensor([0.], requires_grad=True)

# 构建logistic函数
def logistic_regression(x,w,b):
    return 1/(1+torch.exp(-1*torch.mm(x,w)+b))

def bce_loss(y_hat,y):
    return -1 * (y * torch.log10(y_hat) + (1 - y) * torch.log10(1 - y_hat))

def sgd(params,lr,batch_size):
    for param in params:
        param.data -= lr * param.grad / batch_size

# super parameters init
lr = 0.03#学习率
num_epochs = 20#训练周期
batch_size = 10

net = logistic_regression
loss = bce_loss

# training
#进行20轮训练，每轮训练都是分批求解，20轮结果正确率求平均
for epoch in range(num_epochs):  # training repeats num_epochs times
    # in each epoch, all the samples in dataset will be used once
    
    # X is the feature and y is the label of a batch sample
    for X, y in data_iter(batch_size, features, labels):
        l = loss(net(X, w, b), y).sum()  
        # calculate the gradient of batch sample loss 
        l.backward()#计算梯度  
        # using small batch random gradient descent to iter model parameters模型求解
        sgd([w, b], lr, batch_size)  
        # reset parameter gradient梯度清零
        w.grad.data.zero_()
        b.grad.data.zero_()
        #模型偏差
    train_l = loss(net(features, w, b), labels)
    print('epoch %d, loss %f' % (epoch + 1, train_l.mean().item()))

epoch 1, loss 0.112721
epoch 2, loss 0.108413
epoch 3, loss 0.104645
epoch 4, loss 0.101311
epoch 5, loss 0.098335
epoch 6, loss 0.095655
epoch 7, loss 0.093226
epoch 8, loss 0.091011
epoch 9, loss 0.088979
epoch 10, loss 0.087107
epoch 11, loss 0.085374
epoch 12, loss 0.083763
epoch 13, loss 0.082262
epoch 14, loss 0.080858
epoch 15, loss 0.079540
epoch 16, loss 0.078300
epoch 17, loss 0.077130
epoch 18, loss 0.076024
epoch 19, loss 0.074977
epoch 20, loss 0.073984

print(true_w,'n',w)

[2.1, -3.0] 
 tensor([[ 1.9279],
        [-2.6933]], requires_grad=True)

print(true_b,'n',b)

1.3 
 tensor([1.2855], requires_grad=True)