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<h1>d2l(chapter1-3)</h1>
<div id="toc" class="toc2">
<div id="toctitle">Table of Contents</div>
<span id="back-to-index"><a href="index.html">Back to index</a></span><ul class="sectlevel1">
<li><a href="#_预备知识">1. 预备知识</a>
<ul class="sectlevel2">
<li><a href="#_数据操作">1.1. 数据操作</a></li>
<li><a href="#_数据预处理">1.2. 数据预处理</a></li>
<li><a href="#_线性代数">1.3. 线性代数</a></li>
<li><a href="#_微积分">1.4. 微积分</a></li>
<li><a href="#_自动微分">1.5. 自动微分</a></li>
</ul>
</li>
<li><a href="#_线性神经网络">2. 线性神经网络</a>
<ul class="sectlevel2">
<li><a href="#_线性回归">2.1. 线性回归</a></li>
<li><a href="#_线性回归的从零开始实现">2.2. 线性回归的从零开始实现</a></li>
<li><a href="#_线性回归的简洁实现">2.3. 线性回归的简洁实现</a></li>
<li><a href="#_图像分类数据集">2.4. 图像分类数据集</a></li>
<li><a href="#_softmax回归的从零开始实现">2.5. softmax回归的从零开始实现</a></li>
<li><a href="#_softmax回归的简洁实现">2.6. softmax回归的简洁实现</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="content">
<div class="sect1">
<h2 id="_预备知识"><a class="anchor" href="#_预备知识"></a>1. 预备知识</h2>
<div class="sectionbody">
<div class="sect2">
<h3 id="_数据操作"><a class="anchor" href="#_数据操作"></a>1.1. 数据操作</h3>
<div class="listingblock">
<div class="content">
<pre class="highlight"><code class="language-python" data-lang="python"># 查看pytorch中的所有函数名或属性名
import torch

print(dir(torch.distributions))

print('1.张量的创建')
# ones 函数创建一个具有指定形状的新张量，并将所有元素值设置为 1
t = torch.ones(4)
print('t:', t)

x = torch.arange(12)
print('x:', x)
print('x shape:', x.shape)  # 访问向量的形状

y = x.reshape(3, 4)  # 改变一个张量的形状而不改变元素数量和元素值
print('y:', y)
print('y.numel():', y.numel())  # 返回张量中元素的总个数

z = torch.zeros(2, 3, 4)  # 创建一个张量，其中所有元素都设置为0
print('z:', z)

w = torch.randn(2, 3, 4)  # 每个元素都从均值为0、标准差为1的标准高斯（正态）分布中随机采样。
print('w:', w)

q = torch.tensor([[1, 2, 3], [4, 3, 2], [7, 4, 3]])  # 通过提供包含数值的 Python 列表（或嵌套列表）来为所需张量中的每个元素赋予确定值
print('q:', q)

print('2.张量的运算')
x = torch.tensor([1.0, 2, 4, 8])
y = torch.tensor([2, 2, 2, 2])
print(x + y)
print(x - y)
print(x * y)
print(x / y)
print(x ** y)  # **运算符是求幂运算
print(torch.exp(x))

X = torch.arange(12, dtype=torch.float32).reshape(3, 4)
Y = torch.tensor([[2.0, 1, 4, 3], [1, 2, 3, 4], [4, 3, 2, 1]])
print('cat操作 dim=0', torch.cat((X, Y), dim=0))
print('cat操作 dim=1', torch.cat((X, Y), dim=1))  # 连结（concatenate） ,将它们端到端堆叠以形成更大的张量。

print('X == Y', X == Y)  # 通过 逻辑运算符 构建二元张量
print('X &lt; Y', X &lt; Y)
print('张量所有元素的和:', X.sum())  # 张量所有元素的和

print('3.广播机制')
a = torch.arange(3).reshape(3, 1)
b = torch.arange(2).reshape(1, 2)
print('a:', a)
print('b:', b)
print('a + b:', a + b)  # 神奇的广播运算

print('4.索引和切片')
X = torch.arange(12, dtype=torch.float32).reshape(3, 4)
print('X:', X)
print('X[-1]:', X[-1])  # 用 [-1] 选择最后一个元素
print('X[1:3]:', X[1:3])  # 用 [1:3] 选择第二个和第三个元素]

X[1, 2] = 9  # 写入元素。
print('X:', X)

X[0:2, :] = 12  # 写入元素。
print('X:', X)

print('5.节约内存')
before = id(Y)  # id()函数提供了内存中引用对象的确切地址
Y = Y + X
print(id(Y) == before)

before = id(X)
X += Y
print(id(X) == before)  # 使用 X[:] = X + Y 或 X += Y 来减少操作的内存开销。

before = id(X)
X[:] = X + Y
print(id(X) == before)  # 使用 X[:] = X + Y 或 X += Y 来减少操作的内存开销。

print('6.转换为其他 Python对象')
Y = torch.tensor([[2.0, 1, 4, 3], [1, 2, 3, 4], [4, 3, 2, 1]])
A = Y.numpy()
print(type(A))  # 打印A的类型
print(A)
B = torch.tensor(A)
print(type(B))  # 打印B的类型
print(B)

a = torch.tensor([3.5])
print(a, a.item(), float(a), int(a))</code></pre>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_数据预处理"><a class="anchor" href="#_数据预处理"></a>1.2. 数据预处理</h3>
<div class="listingblock">
<div class="content">
<pre class="highlight"><code class="language-python" data-lang="python">import os

import numpy as np
import pandas as pd
import torch
from numpy import nan as NaN

os.makedirs(os.path.join('..', 'data'), exist_ok=True)  # 在上级目录创建data文件夹
datafile = os.path.join('..', 'data', 'house_tiny.csv')  # 创建文件
with open(datafile, 'w') as f:  # 往文件中写数据
    f.write('NumRooms,Alley,Price\n')  # 列名
    f.write('NA,Pave,127500\n')  # 第1行的值
    f.write('2,NA,106000\n')  # 第2行的值
    f.write('4,NA,178100\n')  # 第3行的值
    f.write('NA,NA,140000\n')  # 第4行的值

data = pd.read_csv(datafile)  # 可以看到原始表格中的空值NA被识别成了NaN
print('1.原始数据:\n', data)

inputs, outputs = data.iloc[:, 0: 2], data.iloc[:, 2]
inputs = inputs.fillna(inputs.mean())  # 用均值填充NaN
print(inputs)
print(outputs)
# 利用pandas中的get_dummies函数来处理离散值或者类别值。
# [对于 inputs 中的类别值或离散值，我们将 “NaN” 视为一个类别。] 由于 “Alley”列只接受两种类型的类别值 “Pave” 和 “NaN”
inputs = pd.get_dummies(inputs, dummy_na=True)
print('2.利用pandas中的get_dummies函数处理:\n', inputs)

x, y = torch.tensor(inputs.values), torch.tensor(outputs.values)
print('3.转换为张量：')
print(x)
print(y)

# 扩展填充函数fillna的用法
df1 = pd.DataFrame([[1, 2, 3], [NaN, NaN, 2], [NaN, NaN, NaN], [8, 8, NaN]])  # 创建初始数据
print('4.函数fillna的用法：')
print(df1)
print(df1.fillna(100))  # 用常数填充 ，默认不会修改原对象
print(df1.fillna({0: 10, 1: 20, 2: 30}))  # 通过字典填充不同的常数，默认不会修改原对象
print(df1.fillna(method='ffill'))  # 用前面的值来填充
# print(df1.fillna(0, inplace=True))  # inplace= True直接修改原对象

df2 = pd.DataFrame(np.random.randint(0, 10, (5, 5)))  # 随机创建一个5*5
df2.iloc[1:4, 3] = NaN
df2.iloc[2:4, 4] = NaN  # 指定的索引处插入值
print(df2)
print(df2.fillna(method='bfill', limit=2))  # 限制填充个数
print(df2.fillna(method="ffill", limit=1, axis=1))  #</code></pre>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_线性代数"><a class="anchor" href="#_线性代数"></a>1.3. 线性代数</h3>
<div class="listingblock">
<div class="content">
<pre class="highlight"><code class="language-python" data-lang="python">import torch

print('1.标量与变量')
x = torch.tensor([3.0])
y = torch.tensor([2.0])
print(x + y, x * y, x / y, x ** y)

x = torch.arange(4)
print('2.向量')
print('x:', x)
print('x[3]:', x[3])  # 通过张量的索引来访问任一元素
print('张量的形状:', x.shape)  # 张量的形状
print('张量的长度:', len(x))  # 张量的长度
z = torch.arange(24).reshape(2, 3, 4)
print('三维张量的长度:', len(z))

print('3.矩阵')
A = torch.arange(20).reshape(5, 4)
print('A:', A)
print('A.shape:', A.shape)
print('A.shape[-1]:', A.shape[-1])
print('A.T:', A.T)  # 矩阵的转置

print('4.矩阵的计算')
A = torch.arange(20, dtype=torch.float32).reshape(5, 4)
B = A.clone()  # 通过分配新内存，将A的一个副本分配给B
print('A:', A)
print('B:', B)
print('A + B:', A + B)  # 矩阵相加
print('A * B:', A * B)  # 矩阵相乘

a = 2
X = torch.arange(24).reshape(2, 3, 4)
print('X:', X)
print('a + X:', a + X)  # 矩阵的值加上标量
print('a * X:', a * X)
print((a * X).shape)

print('5.矩阵的sum运算')
print('A:', A)
print('A.shape:', A.shape)
print('A.sum():', A.sum())
print('A.sum(axis=0):', A.sum(axis=0))  # 沿0轴汇总以生成输出向量
print('A.sum(axis=1):', A.sum(axis=1))  # 沿1轴汇总以生成输出向量
print('A.sum(axis=1, keepdims=True)', A.sum(axis=1, keepdims=True))  # 计算总和保持轴数不变
print('A.sum(axis=[0, 1]):', A.sum(axis=[0, 1]))  # Same as `A.sum()`
print('A.mean():', A.mean())
print('A.sum() / A.numel():', A.sum() / A.numel())

print('6.向量-向量相乘（点积）')
x = torch.arange(4, dtype=torch.float32)
y = torch.ones(4, dtype=torch.float32)
print('x:', x)
print('y:', y)
print('向量-向量点积:', torch.dot(x, y))

print('7.矩阵-向量相乘(向量积)')
print('A:', A)  # 5*4维
print('x:', x)  # 4*1维
print('torch.mv(A, x):', torch.mv(A, x))

print('8.矩阵-矩阵相乘(向量积)')
print('A:', A)  # 5*4维
B = torch.ones(4, 3)  # 4*3维
print('B:', B)
print('torch.mm(A, B):', torch.mm(A, B))

print('9.范数')
u = torch.tensor([3.0, -4.0])
print('向量的𝐿2范数:', torch.norm(u))  # 向量的𝐿2范数
print('向量的𝐿1范数:', torch.abs(u).sum())  # 向量的𝐿1范数
v = torch.ones((4, 9))
print('v:', v)
print('矩阵的𝐿2范数:', torch.norm(v))  # 矩阵的𝐿2范数

print('10.根据索引访问矩阵')
y = torch.arange(10).reshape(5, 2)
print('y:', y)
index = torch.tensor([1, 4])
print('y[index]:', y[index])

print('11.理解pytorch中的gather()函数')
a = torch.arange(15).view(3, 5)
print('11.1二维矩阵上gather()函数')
print('a:', a)
b = torch.zeros_like(a)
b[1][2] = 1  ##给指定索引的元素赋值
b[0][0] = 1  ##给指定索引的元素赋值
print('b:', b)
c = a.gather(0, b)  # dim=0
d = a.gather(1, b)  # dim=1
print('d:', d)
print('11.2三维矩阵上gather()函数')
a = torch.randint(0, 30, (2, 3, 5))
print('a:', a)
index = torch.LongTensor([[[0, 1, 2, 0, 2],
                           [0, 0, 0, 0, 0],
                           [1, 1, 1, 1, 1]],
                          [[1, 2, 2, 2, 2],
                           [0, 0, 0, 0, 0],
                           [2, 2, 2, 2, 2]]])
print(a.size() == index.size())
b = torch.gather(a, 1, index)
print('b:', b)
c = torch.gather(a, 2, index)
print('c:', c)
index2 = torch.LongTensor([[[0, 1, 1, 0, 1],
                            [0, 1, 1, 1, 1],
                            [1, 1, 1, 1, 1]],
                           [[1, 0, 0, 0, 0],
                            [0, 0, 0, 0, 0],
                            [1, 1, 0, 0, 0]]])
d = torch.gather(a, 0, index2)
print('d:', d)

print('12.理解pytorch中的max()和argmax()函数')
a = torch.tensor([[1, 2, 3], [3, 2, 1]])
b = a.argmax(1)
c = a.max(1)
d = a.max(1)[1]
print('a:', a)
print('a.argmax(1):', b)
print('a.max(1):', c)
print('a.max(1)[1]:', d)

print('13.item()函数')
a = torch.Tensor([1, 2, 3])
print('a[0]:', a[0])  # 直接取索引返回的是tensor数据
print('a[0].item():', a[0].item())  # 获取python number</code></pre>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_微积分"><a class="anchor" href="#_微积分"></a>1.4. 微积分</h3>
<div class="listingblock">
<div class="content">
<pre class="highlight"><code class="language-python" data-lang="python">import numpy as np
from d2l import torch as d2l
import os
os.environ["KMP_DUPLICATE_LIB_OK"]="TRUE"


def f(x):
    return 3 * x ** 2 - 4 * x


def numerical_lim(f, x, h):
    return (f(x + h) - f(x)) / h


h = 0.1
for i in range(5):
    print(f'h={h:.5f}, numerical limit={numerical_lim(f, 1, h):.5f}')
    h *= 0.1

x = np.arange(0, 3, 0.1)
d2l.plot(x, [f(x), 2 * x - 3], 'x', 'f(x)', legend=['f(x)', 'Tangent line (x=1)'])
d2l.plt.show();

x = np.arange(0.5, 3, 0.2)
d2l.plot(x, [x ** 3 - 1 / x, 4 * x - 4], 'x', 'f(x)', legend=['f(x)', 'Tangent line (x=1)'])
d2l.plt.show();</code></pre>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_自动微分"><a class="anchor" href="#_自动微分"></a>1.5. 自动微分</h3>
<div class="listingblock">
<div class="content">
<pre class="highlight"><code class="language-python" data-lang="python">import torch

print('1.自动梯度计算')
x = torch.arange(4.0, requires_grad=True)  # 1.将梯度附加到想要对其计算偏导数的变量
print('x:', x)
print('x.grad:', x.grad)
y = 2 * torch.dot(x, x)  # 2.记录目标值的计算
print('y:', y)
y.backward()  # 3.执行它的反向传播函数
print('x.grad:', x.grad)  # 4.访问得到的梯度
print('x.grad == 4*x:', x.grad == 4 * x)

## 计算另一个函数
x.grad.zero_()
y = x.sum()
print('y:', y)
y.backward()
print('x.grad:', x.grad)

# 非标量变量的反向传播
x.grad.zero_()
print('x:', x)
y = x * x
y.sum().backward()
print('x.grad:', x.grad)


def f(a):
    b = a * 2
    print(b.norm())
    while b.norm() &lt; 1000:  # 求L2范数：元素平方和的平方根
        b = b * 2
    if b.sum() &gt; 0:
        c = b
    else:
        c = 100 * b
    return c


print('2.Python控制流的梯度计算')
a = torch.tensor(2.0)  # 初始化变量
a.requires_grad_(True)  # 1.将梯度赋给想要对其求偏导数的变量
print('a:', a)
d = f(a)  # 2.记录目标函数
print('d:', d)
d.backward()  # 3.执行目标函数的反向传播函数
print('a.grad:', a.grad)  # 4.获取梯度</code></pre>
</div>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_线性神经网络"><a class="anchor" href="#_线性神经网络"></a>2. 线性神经网络</h2>
<div class="sectionbody">
<div class="sect2">
<h3 id="_线性回归"><a class="anchor" href="#_线性回归"></a>2.1. 线性回归</h3>
<div class="listingblock">
<div class="content">
<pre class="highlight"><code class="language-python" data-lang="python">import math
import os

import numpy as np
import torch
from d2l import torch as d2l

os.environ["KMP_DUPLICATE_LIB_OK"] = "TRUE"

n = 10000
a = torch.ones(n)
b = torch.ones(n)
c = torch.zeros(n)
timer = d2l.Timer()
for i in range(n):
    c[i] = a[i] + b[i]
print(c)
print("{0:.5f} sec".format(timer.stop()))

timer.start()
d = a + b
print(d)
print("{0:.5f} sec".format(timer.stop()))


def normal(x, mu, sigma):
    p = 1 / math.sqrt(2 * math.pi * sigma ** 2)
    return p * np.exp((- 0.5 / sigma ** 2) * (x - mu) ** 2)


## 可视化正态分布
x = np.arange(-7, 7, 0.01)
params = [(0, 1), (0, 2), (3, 1)]
d2l.plot(x, [normal(x, mu, sigma) for mu, sigma in params], xlabel='x', ylabel='p(x)', figsize=(4.5, 2.5),
         legend=[f'mean {mu}, std {sigma}' for mu, sigma in params])
d2l.plt.show()</code></pre>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_线性回归的从零开始实现"><a class="anchor" href="#_线性回归的从零开始实现"></a>2.2. 线性回归的从零开始实现</h3>
<div class="listingblock">
<div class="content">
<pre class="highlight"><code class="language-python" data-lang="python">import random

import torch

## with torch.no_grad() 则主要是用于停止autograd模块的工作，
## 以起到加速和节省显存的作用，具体行为就是停止gradient计算，从而节省了GPU算力和显存，但是并不会影响dropout和batchnorm层的行为。

## mm只能进行矩阵乘法,也就是输入的两个tensor维度只能是( n × m ) (n\times m)(n×m)和( m × p ) (m\times p)(m×p)
## bmm是两个三维张量相乘, 两个输入tensor维度是( b × n × m )和( b × m × p ), 第一维b代表batch size，输出为( b × n × p )
## matmul可以进行张量乘法, 输入可以是高维.

## python知识补充：
## Python3 range() 函数返回的是一个可迭代对象（类型是对象），而不是列表类型， 所以打印的时候不会打印列表。
## Python3 list() 函数是对象迭代器，可以把range()返回的可迭代对象转为一个列表，返回的变量类型为列表。
## Python3 range(start, stop[, step])
## Python3 shuffle() 方法将序列的所有元素随机排序。shuffle()是不能直接访问的，需要导入 random 模块。举例：random.shuffle (list)
## Python3 yield是python中的生成器


## 人造数据集
def create_data(w, b, nums_example):
    X = torch.normal(0, 1, (nums_example, len(w)))
    y = torch.matmul(X, w) + b
    print("y_shape:", y.shape)
    y += torch.normal(0, 0.01, y.shape)  # 加入噪声
    return X, y.reshape(-1, 1)  # y从行向量转为列向量


true_w = torch.tensor([2, -3.4])
true_b = 4.2
features, labels = create_data(true_w, true_b, 1000)


## 读数据集
def read_data(batch_size, features, lables):
    nums_example = len(features)
    indices = list(range(nums_example))  # 生成0-999的元组，然后将range()返回的可迭代对象转为一个列表
    random.shuffle(indices)  # 将序列的所有元素随机排序。
    for i in range(0, nums_example, batch_size):  # range(start, stop, step)
        index_tensor = torch.tensor(indices[i: min(i + batch_size, nums_example)])
        yield features[index_tensor], lables[index_tensor]  # 通过索引访问向量


batch_size = 10
for X, y in read_data(batch_size, features, labels):
    print("X:", X, "\ny", y)
    break;

##初始化参数
w = torch.normal(0, 0.01, size=(2, 1), requires_grad=True)
b = torch.zeros(1, requires_grad=True)


# 定义模型
def net(X, w, b):
    return torch.matmul(X, w) + b


# 定义损失函数
def loss(y_hat, y):
    # print("y_hat_shape:",y_hat.shape,"\ny_shape:",y.shape)
    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2  # 这里为什么要加 y_hat_shape: torch.Size([10, 1])  y_shape: torch.Size([10])


# 定义优化算法
def sgd(params, batch_size, lr):
    with torch.no_grad():  # with torch.no_grad() 则主要是用于停止autograd模块的工作，
        for param in params:
            param -= lr * param.grad / batch_size  ##  这里用param = param - lr * param.grad / batch_size会导致导数丢失， zero_()函数报错
            param.grad.zero_()  ## 导数如果丢失了，会报错‘NoneType’ object has no attribute ‘zero_’


# 训练模型
lr = 0.03
num_epochs = 3

for epoch in range(0, num_epochs):
    for X, y in read_data(batch_size, features, labels):
        f = loss(net(X, w, b), y)
        # 因为`f`形状是(`batch_size`, 1)，而不是一个标量。`f`中的所有元素被加到一起，
        # 并以此计算关于[`w`, `b`]的梯度
        f.sum().backward()
        sgd([w, b], batch_size, lr)  # 使用参数的梯度更新参数
    with torch.no_grad():
        train_l = loss(net(features, w, b), labels)
        print("w {0} \nb {1} \nloss {2:f}".format(w, b, float(train_l.mean())))

print("w误差 ", true_w - w, "\nb误差 ", true_b - b)</code></pre>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_线性回归的简洁实现"><a class="anchor" href="#_线性回归的简洁实现"></a>2.3. 线性回归的简洁实现</h3>
<div class="listingblock">
<div class="content">
<pre class="highlight"><code class="language-python" data-lang="python">import torch
from torch.utils import data
from torch import nn
from d2l import torch as d2l

'''生成数据集'''
true_w = torch.tensor([2, -3.4])
true_b = 4.2
features, labels = d2l.synthetic_data(true_w, true_b, 1000)

'''读取数据集'''
def load_array(data_arrays, batch_size, is_train=True):  #@save
    """构造一个PyTorch数据迭代器"""
    dataset = data.TensorDataset(*data_arrays)
    return data.DataLoader(dataset, batch_size, shuffle=is_train)

batch_size = 10
data_iter = load_array((features, labels), batch_size)

'''定义模型'''
net = nn.Sequential(nn.Linear(2, 1))
'''初始化模型参数'''
net[0].weight.data.normal_(0, 0.01)
net[0].bias.data.fill_(0)

'''定义损失函数'''
loss = nn.MSELoss()

'''定义优化算法'''
trainer = torch.optim.SGD(net.parameters(), lr=0.03)

'''训练'''
num_epochs = 3
for epoch in range(num_epochs):
    for X, y in data_iter:
        l = loss(net(X) ,y)
        trainer.zero_grad()
        l.backward()
        trainer.step()
    l = loss(net(features), labels)
    print(f'epoch {epoch + 1}, loss {l:f}')

w = net[0].weight.data
print('w的估计误差：', true_w - w.reshape(true_w.shape))
b = net[0].bias.data
print('b的估计误差：', true_b - b)</code></pre>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_图像分类数据集"><a class="anchor" href="#_图像分类数据集"></a>2.4. 图像分类数据集</h3>
<div class="listingblock">
<div class="content">
<pre class="highlight"><code class="language-python" data-lang="python">import torch
import torchvision
from torch.utils import data
from torchvision import transforms
from d2l import torch as d2l

d2l.use_svg_display()

'''读取数据集'''
# 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到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)

def get_fashion_mnist_labels(labels):  #@save
    """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]


'''可视化样本'''
def show_images(imgs, num_rows, num_cols, titles=None, scale=1.5):  #@save
    """绘制图像列表"""
    figsize = (num_cols * scale, num_rows * scale)
    _, 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));
d2l.plt.show()           #  <i class="conum" data-value="1"></i><b>(1)</b>

'''读取小批量'''
batch_size = 256

def get_dataloader_workers():  #@save
    """使用4个进程来读取数据"""
    return 4

'''整合所有组件'''

def load_data_fashion_mnist(batch_size, resize=None):  #@save
    """下载Fashion-MNIST数据集，然后将其加载到内存中"""
    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()))</code></pre>
</div>
</div>
<div class="olist arabic">
<ol class="arabic">
<li>
<p>jupyter notebook中不需要这一行，pycharm中需要</p>
</li>
</ol>
</div>
</div>
<div class="sect2">
<h3 id="_softmax回归的从零开始实现"><a class="anchor" href="#_softmax回归的从零开始实现"></a>2.5. softmax回归的从零开始实现</h3>
<div class="listingblock">
<div class="content">
<pre class="highlight"><code class="language-python" data-lang="python">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)

'''初始化模型参数'''
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)

'''定义softmax操作'''
def softmax(X):
    X_exp = torch.exp(X)
    partition = X_exp.sum(1, keepdim=True)
    return X_exp / partition  # 这里应用了广播机制

'''定义模型'''
def net(X):
    return softmax(torch.matmul(X.reshape((-1, W.shape[0])), W) + b)

'''定义损失函数'''
def cross_entropy(y_hat, y):
    return - torch.log(y_hat[range(len(y_hat)), y])

'''分类精度'''
def accuracy(y_hat, y):  #@save
    """计算预测正确的数量"""
    if len(y_hat.shape) &gt; 1 and y_hat.shape[1] &gt; 1:
        y_hat = y_hat.argmax(axis=1)
    cmp = y_hat.type(y.dtype) == y
    return float(cmp.type(y.dtype).sum())

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
    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]

class Accumulator:  #@save
    """在n个变量上累加"""
    def __init__(self, n):
        self.data = [0.0] * n

    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)

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

'''训练'''
def train_epoch_ch3(net, train_iter, loss, updater):  #@save
    """训练模型一个迭代周期（定义见第3章）"""
    # 将模型设置为训练模式
    if isinstance(net, torch.nn.Module):
        net.train()
    # 训练损失总和、训练准确度总和、样本数
    metric = Accumulator(3)
    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())
    # 返回训练损失和训练精度
    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):  #@save
    """训练模型（定义见第3章）"""
    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 &lt; 0.5, train_loss
    assert train_acc &lt;= 1 and train_acc &gt; 0.7, train_acc
    assert test_acc &lt;= 1 and test_acc &gt; 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)

'''预测'''
def predict_ch3(net, test_iter, n=6):  #@save
    """预测标签（定义见第3章）"""
    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)</code></pre>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_softmax回归的简洁实现"><a class="anchor" href="#_softmax回归的简洁实现"></a>2.6. softmax回归的简洁实现</h3>
<div class="listingblock">
<div class="content">
<pre class="highlight"><code class="language-python" data-lang="python">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)

net.apply(init_weights)

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

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

'''训练'''
num_epochs = 10
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)</code></pre>
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