## 概述

PyTorch 干的最厉害的一件事情就是帮我们把反向传播全部计算好了.

## 代码实现

### 手动定义求导

```import torch

# 方法一

# 方法二
x = torch.randn(3,4)
```
```b = torch.randn(3, 4, requires_grad=True)
t = x + b
y = t.sum()

print(y)
print(y.backward())

```

None
tensor([[1., 1., 1., 1.],
[1., 1., 1., 1.],
[1., 1., 1., 1.]])
True
True
True

### 计算流量

```# 计算流量
x = torch.rand(1)
y = w * x
z = y + b

print(x.is_leaf, w.is_leaf, b.is_leaf, y.is_leaf,z.is_leaf)```

False True True True
True True True False False

### 反向传播计算

```# 反向传播
z.backward(retain_graph= True)  # 如果不清空会累加起来

tensor([0.1485])
tensor([1.])

## 线性回归

### 导包

```import numpy as np
import torch
import torch.nn as nn
```

### 构造 x, y

```# 构造数据
X_values = [i for i in range(11)]
X_train = np.array(X_values, dtype=np.float32)
X_train = X_train.reshape(-1, 1)
print(X_train.shape)  # (11, 1)

y_values = [2 * i + 1 for i in X_values]
y_train = np.array(y_values, dtype=np.float32)
y_train = y_train.reshape(-1,1)
print(y_train.shape)  # (11, 1)```

(11, 1)
(11, 1)

### 构造模型

```# 构造模型
class LinerRegressionModel(nn.Module):
def __init__(self, input_dim, output_dim):
super(LinerRegressionModel, self).__init__()
self.liner = nn.Linear(input_dim, output_dim)

def forward(self, x):
out = self.liner(x)
return out

input_dim = 1
output_dim = 1

model = LinerRegressionModel(input_dim, output_dim)
print(model)```

LinerRegressionModel(
(liner): Linear(in_features=1, out_features=1, bias=True)
)

### 参数 & 损失函数

```# 超参数
enpochs = 1000
learning_rate = 0.01

# 损失函数
optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate)
criterion = nn.MSELoss()
```

### 训练模型

```# 训练模型
for epoch in range(enpochs):
# 转成tensor
inputs = torch.from_numpy(X_train)
labels = torch.from_numpy(y_train)

# 梯度每次迭代清零

# 前向传播
outputs = model(inputs)

# 计算损失
loss = criterion(outputs, labels)

# 反向传播
loss.backward()

# 更新参数
optimizer.step()
if epoch % 50 == 0:
print("epoch {}, loss {}".format(epoch, loss.item()))```

epoch 0, loss 114.47456359863281
epoch 50, loss 0.00021522105089388788
epoch 100, loss 0.00012275540211703628
epoch 150, loss 7.001651829341426e-05
epoch 200, loss 3.9934264350449666e-05
epoch 250, loss 2.2777328922529705e-05
epoch 300, loss 1.2990592040296178e-05
epoch 350, loss 7.409254521917319e-06
epoch 400, loss 4.227155841363128e-06
epoch 450, loss 2.410347860859474e-06
epoch 500, loss 1.3751249525739695e-06
epoch 550, loss 7.844975016269018e-07
epoch 600, loss 4.4756839656656666e-07
epoch 650, loss 2.5517596213830984e-07
epoch 700, loss 1.4577410922811396e-07
epoch 750, loss 8.30393886985803e-08
epoch 800, loss 4.747753479250605e-08
epoch 850, loss 2.709844615367274e-08
epoch 900, loss 1.5436164346738224e-08
epoch 950, loss 8.783858973515635e-09

## 完整代码

```import numpy as np
import torch
import torch.nn as nn

# 构造数据
X_values = [i for i in range(11)]
X_train = np.array(X_values, dtype=np.float32)
X_train = X_train.reshape(-1, 1)
print(X_train.shape)  # (11, 1)

y_values = [2 * i + 1 for i in X_values]
y_train = np.array(y_values, dtype=np.float32)
y_train = y_train.reshape(-1,1)
print(y_train.shape)  # (11, 1)

# 构造模型
class LinerRegressionModel(nn.Module):
def __init__(self, input_dim, output_dim):
super(LinerRegressionModel, self).__init__()
self.liner = nn.Linear(input_dim, output_dim)

def forward(self, x):
out = self.liner(x)
return out

input_dim = 1
output_dim = 1

model = LinerRegressionModel(input_dim, output_dim)
print(model)

# 超参数
enpochs = 1000
learning_rate = 0.01

# 损失函数
optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate)
criterion = nn.MSELoss()

# 训练模型
for epoch in range(enpochs):
# 转成tensor
inputs = torch.from_numpy(X_train)
labels = torch.from_numpy(y_train)

# 梯度每次迭代清零

# 前向传播
outputs = model(inputs)

# 计算损失
loss = criterion(outputs, labels)

# 反向传播
loss.backward()

# 更新参数
optimizer.step()
if epoch % 50 == 0:
print("epoch {}, loss {}".format(epoch, loss.item()))
```