从零实现softmax回归

import torch
from IPython import display
from d2l import torch as d2l

#获取和读取Fashion-MNIST数据集，返回训练集和验证集的数据迭代器
def load_data_fashion_mnist(batch_size, resize=None): 
    trans = [transforms.ToTensor()]
    if resize:
        trans.insert(0, transforms.Resize(resize))
    trans = transforms.Compose(trans)
    mnist_train = torchvision.datasets.FashionMNIST(root="./data", train=True, transform=trans, download=True)
    mnist_test = torchvision.datasets.FashionMNIST(root="./data", train=False, transform=trans, download=True)
    return (data.DataLoader(mnist_train, batch_size, shuffle=True,num_workers=get_dataloader_workers()),data.DataLoader(mnist_test, batch_size, shuffle=False,num_workers=get_dataloader_workers()))

#设置批量大小为256
batch_size = 256
#获得Fashion-MNIST数据集的训练集和验证集的数据迭代器
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)
# 输入特征X的个数（784 = 28 × 28）
num_inputs = 784
# 输出标签y的个数（10种类别）
num_outputs = 10
# 正态分布初始化权重矩阵W
W = torch.normal(0, 0.01, size=(num_inputs, num_outputs), requires_grad=True)
# 0初始化偏置向量b
b = torch.zeros(num_outputs, requires_grad=True)

# 定义softmax操作，将预测值规范化
def softmax(X):
    X_exp = torch.exp(X)
    partition = X_exp.sum(1, keepdim=True)
    return X_exp / partition  

# 定义softmax回归模型
def net(X):
    # 计算y' = softmax(o)
    # 其中o是未规范化预测o = wx+b
    # y'为规范化预测
    return softmax(torch.matmul(X.reshape((-1, W.shape[0])), W) + b)

# # 给定两个样本的真实标签
# y = torch.tensor([0, 2])
# # 给定两个样本在三种类别上的预测概率
# y_hat = torch.tensor([[0.1, 0.3, 0.6], [0.3, 0.2, 0.5]])
# # 取出每个样本真实标签所对应的预测概率
# y_hat[[0, 1], y]

# 交叉熵损失函数，输出为每个样本的损失
def cross_entropy(y_hat, y):
    return - torch.log(y_hat[range(len(y_hat)), y])

# 计算预测正确的样本个数
def accuracy(y_hat, y):  
    if len(y_hat.shape) > 1 and y_hat.shape[1] > 1:
        y_hat = y_hat.argmax(axis=1)
    cmp = y_hat.type(y.dtype) == y
    return float(cmp.type(y.dtype).sum())

# 一次迭代结束后，在这个测试集上进行一次测试，计算此时的准确度
def evaluate_accuracy(net, data_iter):  
    if isinstance(net, torch.nn.Module):
        net.eval()  # 将模型设置为评估模式(并没有走这里)
    metric = Accumulator(2)  # 预测正确的样本数、样本总数
    with torch.no_grad():
        for X, y in data_iter:
            metric.add(accuracy(net(X), y), y.numel())
    return metric[0] / metric[1]


class Accumulator:  
    # 构造函数的初始长度为n，初始值为0
    def __init__(self, n):
        self.data = [0.0] * n

    # 将训练损失、训练精度、训练样本数进行累加
    def add(self, *args):
        self.data = [a + float(b) for a, b in zip(self.data, args)]

    def reset(self):
        self.data = [0.0] * len(self.data)

    # 取出训练损失、训练精度或训练样本数
    def __getitem__(self, idx):
        return self.data[idx]


# 一次完整的迭代训练过程
def train_epoch_ch3(net, train_iter, loss, updater): 
    
    # 将模型设置为训练模式(并没有走这里)
    if isinstance(net, torch.nn.Module):
        net.train()
    # 训练损失总和、预测正确的个数总和、训练样本数总和
    metric = Accumulator(3) 
    for X, y in train_iter:# 从训练集中取出一个批量的样本以及其对应的标签
        # 计算网络模型的规范化预测结果,y_hat中存放的是一个批量（256）的预测结果，每个预测结果包括10个类别的概率
        y_hat = net(X)
        # 计算每个样本的损失,所以l中存放了一个批量（256）的样本损失
        l = loss(y_hat, y)
        if isinstance(updater, torch.optim.Optimizer):
            # 使用PyTorch内置的优化器和损失函数(并没有走这里)
            updater.zero_grad()
            l.mean().backward()
            updater.step()
        else:
            # 小梯度批量下降优化函数
            l.sum().backward()
            updater(X.shape[0])
        # 将训练损失、预测正确的个数、训练样本数进行累加
        metric.add(float(l.sum()), accuracy(y_hat, y), y.numel())
    # 返回平均训练损失、平均训练精度
    return metric[0] / metric[2], metric[1] / metric[2]

class Animator: 
    """在动画中绘制数据"""
    def __init__(self, xlabel=None, ylabel=None, legend=None, xlim=None,
                 ylim=None, xscale='linear', yscale='linear',
                 fmts=('-', 'm--', 'g-.', 'r:'), nrows=1, ncols=1,
                 figsize=(3.5, 2.5)):
        # 增量地绘制多条线
        if legend is None:
            legend = []
        d2l.use_svg_display()
        self.fig, self.axes = d2l.plt.subplots(nrows, ncols, figsize=figsize)
        if nrows * ncols == 1:
            self.axes = [self.axes, ]
        # 使用lambda函数捕获参数
        self.config_axes = lambda: d2l.set_axes(
            self.axes[0], xlabel, ylabel, xlim, ylim, xscale, yscale, legend)
        self.X, self.Y, self.fmts = None, None, fmts

    def add(self, x, y):
        # 向图表中添加多个数据点
        if not hasattr(y, "__len__"):
            y = [y]
        n = len(y)
        if not hasattr(x, "__len__"):
            x = [x] * n
        if not self.X:
            self.X = [[] for _ in range(n)]
        if not self.Y:
            self.Y = [[] for _ in range(n)]
        for i, (a, b) in enumerate(zip(x, y)):
            if a is not None and b is not None:
                self.X[i].append(a)
                self.Y[i].append(b)
        self.axes[0].cla()
        for x, y, fmt in zip(self.X, self.Y, self.fmts):
            self.axes[0].plot(x, y, fmt)
        self.config_axes()
        display.display(self.fig)
        display.clear_output(wait=True)

def train_ch3(net, train_iter, test_iter, loss, num_epochs, updater):  
    # 定义一个动画对象
    animator = Animator(xlabel='epoch', xlim=[1, num_epochs], ylim=[0.3, 0.9],legend=['train loss', 'train acc', 'test acc'])
    # 每一次迭代的过程中
    for epoch in range(num_epochs):
        # 迭代训练一次，得到（平均训练损失，平均训练精度）
        train_metrics = train_epoch_ch3(net, train_iter, loss, updater)
        # 一次迭代结束后，在测试集上进行一次测试，计算此时的准确度
        test_acc = evaluate_accuracy(net, test_iter)
        # 画图
        animator.add(epoch + 1, train_metrics + (test_acc,))
    train_loss, train_acc = train_metrics
    assert train_loss < 0.5, train_loss
    assert train_acc <= 1 and train_acc > 0.7, train_acc
    assert test_acc <= 1 and test_acc > 0.7, test_acc

# 学习率
lr = 0.1
# 定义小梯度批量下降优化函数
def updater(batch_size):
    return d2l.sgd([W, b], lr, batch_size)


num_epochs = 10 # 迭代次数
# train_iter：Fashion-MNIST数据集的训练集数据迭代器
# test_iter：Fashion-MNIST数据集的测试集数据迭代器
# cross_entropy：交叉熵损失函数
# updater：小梯度批量下降优化函数
# net：softmax函数
train_ch3(net, train_iter, test_iter, cross_entropy, num_epochs, updater)