Softmax回归

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# 通过ToTensor实例将图像数据从PIL类型变换成32位浮点数格式，
# 并除以255使得所有像素的数值均在0～1之间
trans = transforms.ToTensor()
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)

print(len(mnist_train), len(mnist_test))

60000 10000

print(type(mnist_train))
print(type(mnist_train[0]))
print(mnist_train[0])
print(mnist_train[0][0].shape)

def get_fashion_mnist_labels(labels):   # labels:mnist_train和mnist_test里面图像的类别index(数字)
    """返回Fashion-MNIST数据集的文本标签"""
    text_labels = ['t-shirt', 'trouser', 'pullover', 'dress', 'coat',
                   'sandal', 'shirt', 'sneaker', 'bag', 'ankle boot']
    return [text_labels[int(i)] for i in labels]    # 根据index返回文本标签列表('t-shirt', 'trouser'...)

def show_images(imgs, num_rows, num_cols, titles=None, scale=1.5):
    """绘制图像列表"""
    """
    imgs: tensor向量
    num_rows: 画图时的行数
    num_cols: 画图时的列数
    titles: 每张图片的标题
    scales: 因为要将num_rows*num_cols张图片画到一张图上,并且还要添加一些文字,
    因此需要对大图进行一定的缩放才能保证每张小图之间的间隙
    """
    figsize = (num_cols * scale, num_rows * scale)
    # figsize = (num_cols, num_rows)
    _, axes = d2l.plt.subplots(num_rows, num_cols, figsize=figsize)
    axes = axes.flatten()
    for i, (ax, img) in enumerate(zip(axes, imgs)):
        if torch.is_tensor(img):
            # 图片张量
            ax.imshow(img.numpy())
        else:
            # PIL图片
            ax.imshow(img)
        ax.axes.get_xaxis().set_visible(False)
        ax.axes.get_yaxis().set_visible(False)
        if titles:
            ax.set_title(titles[i])
    return axes

X, y = next(iter(data.DataLoader(mnist_train, batch_size=18)))
show_images(X.reshape(18, 28, 28), 2, 9, titles=get_fashion_mnist_labels(y))

batch_size = 256

def get_dataloader_workers():    # 写这一个是因为windows早期版本不支持多进程读取
    """使用4个进程来读取数据"""
    return 4

train_iter = data.DataLoader(mnist_train, batch_size, shuffle=True,
                             num_workers=get_dataloader_workers())

def load_data_fashion_mnist(batch_size, resize=None):
    """下载Fashion-MNIST数据集，然后将其加载到内存中"""
    trans = [transforms.ToTensor()]    # 此时的trans是一个列表
    if resize:
        trans.insert(0, transforms.Resize(resize))    # 如果提供了resize参数，则在转换链中插入Resize操作
    trans = transforms.Compose(trans)    # 将一系列的图像转换操作组合成一个转换链。
    # trans是一个由多个图像转换操作组成的列表。它按照列表中的顺序依次应用这些转换操作。
    # 这样可以将多个转换操作组合在一起，以便在加载数据时一次性应用它们。
    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()))

train_iter, test_iter = load_data_fashion_mnist(32, resize=64)
for X, y in train_iter:
    print(X.shape, X.dtype, y.shape, y.dtype)
    break

torch.Size([32, 1, 64, 64]) torch.float32 torch.Size([32]) torch.int64

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

batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)

num_inputs = 784
num_outputs = 10

W = torch.normal(0, 0.01, size=(num_inputs, num_outputs), requires_grad=True)
b = torch.zeros(num_outputs, requires_grad=True)

X = torch.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
print(X.sum(0, keepdim=True))
print(X.sum(1, keepdim=True))

tensor([[5., 7., 9.]])
tensor([[ 6.],
        [15.]])

def softmax(X):
    X_exp = torch.exp(X)    # 对torch X的每个元素都求指数
    partition = X_exp.sum(1, keepdim=True)
    return X_exp / partition  # 这里应用了广播机制

X = torch.normal(0, 1, (2, 5))
X_prob = softmax(X)
print(X_prob)
print(X_prob.sum(1))

tensor([[0.3612, 0.2049, 0.0552, 0.0798, 0.2988],
        [0.0243, 0.1031, 0.7090, 0.0167, 0.1469]])
tensor([1.0000, 1.0000])

def net(X):
    return softmax(torch.matmul(X.reshape((-1, W.shape[0])), W) + b)    # reshape之后的X的shape为(256, 784)，因为batch_size=256、W.shape[0]=784

y = torch.tensor([0, 2])
y_hat = torch.tensor([[0.1, 0.3, 0.6], [0.3, 0.2, 0.5]])
print(y_hat[[0, 1], y])    # 等同于 y_hat[[0, 1], [0, 2]]
print(y_hat[[0, 1], [0, 2]])    # 其实就是根据tensor的索引来找元素,可以同时获得多个元素 [0, 1]:行索引 [0, 2]:列索引
print(y_hat[0, 0])

def cross_entropy(y_hat, y):
    # print(y_hat[range(len(y_hat)), y])
    return -torch.log(y_hat[range(len(y_hat)), y]) # len(y_hat)=2, range(len(y_hat))获得了y_hat的长度, 方便根据索引进行查找, 与前面思路一样

print(cross_entropy(y_hat, y))

tensor([2.3026, 0.6931])

def accuracy(y_hat, y):
    """计算预测正确的数量"""
    if len(y_hat.shape) > 1 and y_hat.shape[1] > 1:     # 如果y_hat(h, w)中h>1、w>1,
        y_hat = y_hat.argmax(axis=1)    # 使用argmax获得每行中最大元素的索引
    print("y_hat.dtype: {}\ny.dtype: {}".format(y_hat.dtype, y.dtype))
    cmp = y_hat.type(y.dtype) == y      # 保险起见将y_hat的数据类型转换为与y的数据类型一致
    print(cmp)
    return float(cmp.type(y.dtype).sum())

accuracy(y_hat, y) / len(y)

y_hat.dtype: torch.int64
y.dtype: torch.int64
tensor([False,  True])
0.5

def evaluate_accuracy(net, data_iter):  #@save
    """计算在指定数据集上模型的精度"""
    if isinstance(net, torch.nn.Module):
        net.eval()  # 将模型设置为评估模式，不再计算梯度
    metric = Accumulator(2)  # 正确预测数、预测总数
    with torch.no_grad():
        for X, y in data_iter:
            metric.add(accuracy(net(X), y), y.numel())
    return metric[0] / metric[1]    # 返回分类正确样本数和总样本数的比例

class Accumulator:
    """在n个变量上累加"""
    def __init__(self, n):
        self.data = [0.0] * n   # self.data本质是一个长为n的列表

    def add(self, *args):       # *args在Python中用于表示可变数量的参数
        self.data = [a + float(b) for a, b in zip(self.data, args)]  # zip()函数用于将self.data和args中的元素分别匹配起来，返回一个迭代器对象

    def reset(self):            # 重置self.data，归零
        self.data = [0.0] * len(self.data)

    def __getitem__(self, idx):     # 通过索引访问Accumulator对象的data属性
        return self.data[idx]

# [0.0] * n 创建列表
"""[0.0] * n 用于创建一个元素为0.0、长度为n的列表"""
l = [0.0] * 5   # 创建了一个包含5个元素的列表，并将元素初始化为0.1
print(l)

[0.0, 0.0, 0.0, 0.0, 0.0]

"""当函数定义中使用*args作为参数时，它表示可以接受任意数量的位置参数，并将这些位置参数作为一个元组传递给函数体。
在函数调用时，可以传递任意数量的位置参数，它们将被打包成一个元组，然后传递给*args。"""
def my_function(*args):
    for arg in args:
        print(arg)

my_function(1, 2, 3)  # 输出：1 2 3

1
2
3

# 关于zip()函数
"""zip函数将按照索引位置一一对应地将两个列表中的元素配对在一起"""
list1 = [1.0, 2.0, 3.0]
list2 = [4, 5, 6]
for t in zip(list1, list2): # zip(list1, list2)将返回一个迭代器，依次生成(1.0, 4)，(2.0, 5)，(3.0, 6)。
    print(t)

(1.0, 4)
(2.0, 5)
(3.0, 6)

# 关于__getitem__()
"""在Python中，__getitem__()是一个特殊方法（也被称为魔术方法或双下划线方法），用于实现对象的索引访问。
当使用索引操作符[]来访问对象的元素时，Python会调用该对象的__getitem__()方法来处理索引操作。"""
class MyClass:
    def __init__(self, data):
        self.data = data

    def __getitem__(self, idx):
        return self.data[idx]

my_obj = MyClass([1, 2, 3, 4, 5])
print(my_obj[2])  # 输出：3

3

def train_epoch_ch3(net, train_iter, loss, updater):
    """训练模型一个迭代周期"""
    if isinstance(net, torch.nn.Module):
        net.train()         # 将模型设置为训练模式
    metric = Accumulator(3) # 训练损失总和、训练准确数量总和、样本数
    for X, y in train_iter:
        # 计算梯度并更新参数
        y_hat = net(X)
        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
            updater.zero_grad()
            l.mean().backward()
            updater.step()
        else:
            # 使用定制的优化器和损失函数
            l.sum().backward()
            updater(X.shape[0])
        metric.add(float(l.sum()), accuracy(y_hat, y), y.numel())
    # 返回训练损失（平均）和训练精度（正确率）
    return metric[0] / metric[2], metric[1] / metric[2]

class Animator:  #@save
    """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):
    """训练模型"""
    animator = Animator(xlabel='epoch', xlim=[1, num_epochs], ylim=[0.3, 0.9],
                        legend=['train loss', 'train acc', 'test acc'])
    for epoch in range(num_epochs):
        train_metrics = train_epoch_ch3(net, train_iter, loss, updater)
        test_acc = evaluate_accuracy(net, test_iter)
        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

lr = 0.1

def updater(batch_size):
    return d2l.sgd([W, b], lr, batch_size)

num_epochs = 10
train_ch3(net, train_iter, test_iter, cross_entropy, num_epochs, updater)

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def predict_ch3(net, test_iter, n=6):
    """预测标签"""
    for X, y in test_iter:
        break
    trues = d2l.get_fashion_mnist_labels(y)
    preds = d2l.get_fashion_mnist_labels(net(X).argmax(axis=1))
    titles = [true +'\n' + pred for true, pred in zip(trues, preds)]
    d2l.show_images(
        X[0:n].reshape((n, 28, 28)), 1, n, titles=titles[0:n])

predict_ch3(net, test_iter)

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import torch
from torch import nn
from d2l import torch as d2l

batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)

# PyTorch不会隐式地调整输入的形状。因此，
# 我们在线性层前定义了展平层（flatten），来调整网络输入的形状
net = nn.Sequential(nn.Flatten(), nn.Linear(784, 10))

def init_weights(m):
    if type(m) == nn.Linear:
        nn.init.normal_(m.weight, std=0.01) # 如果layer是Linear的话就init成一个均值0（默认）标准差0.01的随机初始化权重

net.apply(init_weights) # 将init_weights()函数apply到net上面去，net上面的每一层都会跑一下这个函数，就完成了初始化

loss = nn.CrossEntropyLoss(reduction='none')

trainer = torch.optim.SGD(net.parameters(), lr=0.1)

num_epochs = 10
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)

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