nn.MSELoss(reduction=True)

`nn.MSELoss` 是 PyTorch 中的一个损失函数，用于计算均方误差（Mean Squared Error，MSE）。它的定义如下：

$$
\text{MSE}=\frac{1}{n}\sum_{i=1}^{n}(y_i-\hat{y}_i)^2
$$

其中，$n$ 是样本数量，$y_i$ 是真实值，$\hat{y}_i$ 是预测值。`reduction` 是一个布尔值，用于指定是否将每个样本的 MSE 损失值相加，还是返回一个向量，其中每个元素是对应样本的 MSE 值。当 `reduction=True` 时，会将所有样本的 MSE 值相加，并返回一个标量；当 `reduction=False` 时，会返回一个向量，其中每个元素是对应样本的 MSE 值。

相关问题

torch.nn.functional.mse_loss 的代码

以下是 `torch.nn.functional.mse_loss` 的代码实现：

def mse_loss(input, target, size_average=None, reduce=None, reduction='mean'):
    if not (target.size() == input.size()):
        warnings.warn("Using a target size ({}) that is different to the input size ({}). "
                      "This will likely lead to incorrect results due to broadcasting. "
                      "Please ensure they have the same size.".format(target.size(), input.size()),
                      stacklevel=2)
    if size_average is not None or reduce is not None:
        reduction = _Reduction.legacy_get_string(size_average, reduce)
    if target.requires_grad:
        ret = (input - target) ** 2
        if reduction != 'none':
            ret = torch.mean(ret) if reduction == 'mean' else torch.sum(ret)
    else:
        expanded_input, expanded_target = torch.broadcast_tensors(input, target)
        ret = torch._C._nn.mse_loss(expanded_input, expanded_target, _Reduction.get_enum(reduction))
    return ret

该函数计算输入 `input` 和目标 `target` 之间的均方误差（MSE），返回值为标量张量。可选参数 `size_average` 和 `reduce` 被弃用，应使用 `reduction` 参数指定归约方式。参数说明如下：

- `input`：输入张量。
- `target`：目标张量，与输入张量形状相同。
- `size_average`：已弃用。
- `reduce`：已弃用。
- `reduction`：指定用于计算输出张量的归约方式，可选值为 `'none'`、`'mean'` 和 `'sum'`，默认为 `'mean'`。

当 `target.requires_grad=True` 时，计算 `input` 与 `target` 之间的 MSE，并根据 `reduction` 的值进行归约；否则，将 `input` 和 `target` 扩展为相同的形状，再调用 C++ 实现的 `mse_loss` 计算 MSE，并根据 `reduction` 的值进行归约。需要注意的是，如果 `target` 与 `input` 形状不同，该函数会发出警告。

import numpy import numpy as np import matplotlib.pyplot as plt import math import torch from torch import nn from torch.utils.data import DataLoader, Dataset import os os.environ['KMP_DUPLICATE_LIB_OK']='True' dataset = [] for data in np.arange(0, 3, .01): data = math.sin(data * math.pi) dataset.append(data) dataset = np.array(dataset) dataset = dataset.astype('float32') max_value = np.max(dataset) min_value = np.min(dataset) scalar = max_value - min_value print(scalar) dataset = list(map(lambda x: x / scalar, dataset)) def create_dataset(dataset, look_back=3): dataX, dataY = [], [] for i in range(len(dataset) - look_back): a = dataset[i:(i + look_back)] dataX.append(a) dataY.append(dataset[i + look_back]) return np.array(dataX), np.array(dataY) data_X, data_Y = create_dataset(dataset) train_X, train_Y = data_X[:int(0.8 * len(data_X))], data_Y[:int(0.8 * len(data_Y))] test_X, test_Y = data_Y[int(0.8 * len(data_X)):], data_Y[int(0.8 * len(data_Y)):] train_X = train_X.reshape(-1, 1, 3).astype('float32') train_Y = train_Y.reshape(-1, 1, 3).astype('float32') test_X = test_X.reshape(-1, 1, 3).astype('float32') train_X = torch.from_numpy(train_X) train_Y = torch.from_numpy(train_Y) test_X = torch.from_numpy(test_X) class RNN(nn.Module): def __init__(self, input_size, hidden_size, output_size=1, num_layer=2): super(RNN, self).__init__() self.input_size = input_size self.hidden_size = hidden_size self.output_size = output_size self.num_layer = num_layer self.rnn = nn.RNN(input_size, hidden_size, batch_first=True) self.linear = nn.Linear(hidden_size, output_size) def forward(self, x): out, h = self.rnn(x) out = self.linear(out[0]) return out net = RNN(3, 20) criterion = nn.MSELoss(reduction='mean') optimizer = torch.optim.Adam(net.parameters(), lr=1e-2) train_loss = [] test_loss = [] for e in range(1000): pred = net(train_X) loss = criterion(pred, train_Y) optimizer.zero_grad() # 反向传播 loss.backward() optimizer.step() if (e + 1) % 100 == 0: print('Epoch:{},loss:{:.10f}'.format(e + 1, loss.data.item())) train_loss.append(loss.item()) plt.plot(train_loss, label='train_loss') plt.legend() plt.show()请适当修改代码，并写出预测值和真实值的代码

以下是适当修改后的代码以及预测值和真实值的代码：

import numpy as np 
import matplotlib.pyplot as plt 
import math 
import torch 
from torch import nn 
from torch.utils.data import DataLoader, Dataset 
import os 

os.environ['KMP_DUPLICATE_LIB_OK']='True' 

dataset = [] 
for data in np.arange(0, 3, .01): 
    data = math.sin(data * math.pi) 
    dataset.append(data) 

dataset = np.array(dataset) 
dataset = dataset.astype('float32') 

max_value = np.max(dataset) 
min_value = np.min(dataset) 

scalar = max_value - min_value 
print(scalar) 

dataset = list(map(lambda x: x / scalar, dataset)) 

def create_dataset(dataset, look_back=3): 
    dataX, dataY = [], [] 
    for i in range(len(dataset) - look_back): 
        a = dataset[i:(i + look_back)] 
        dataX.append(a) 
        dataY.append(dataset[i + look_back]) 
    return np.array(dataX), np.array(dataY) 

data_X, data_Y = create_dataset(dataset) 
train_X, train_Y = data_X[:int(0.8 * len(data_X))], data_Y[:int(0.8 * len(data_Y))] 
test_X, test_Y = data_Y[int(0.8 * len(data_X)):], data_Y[int(0.8 * len(data_Y)):] 

train_X = train_X.reshape(-1, 1, 3).astype('float32') 
train_Y = train_Y.reshape(-1, 1, 1).astype('float32') 
test_X = test_X.reshape(-1, 1, 3).astype('float32') 

train_X = torch.from_numpy(train_X) 
train_Y = torch.from_numpy(train_Y) 
test_X = torch.from_numpy(test_X) 

class RNN(nn.Module): 
    def __init__(self, input_size, hidden_size, output_size=1, num_layer=2): 
        super(RNN, self).__init__() 
        self.input_size = input_size 
        self.hidden_size = hidden_size 
        self.output_size = output_size 
        self.num_layer = num_layer 
        self.rnn = nn.RNN(input_size, hidden_size, batch_first=True) 
        self.linear = nn.Linear(hidden_size, output_size) 

    def forward(self, x): 
        out, h = self.rnn(x) 
        out = self.linear(out[:, -1, :]) 
        return out 

net = RNN(3, 20) 

criterion = nn.MSELoss(reduction='mean') 
optimizer = torch.optim.Adam(net.parameters(), lr=1e-2) 

train_loss = [] 
test_loss = [] 

for e in range(1000): 
    pred = net(train_X) 
    loss = criterion(pred, train_Y) 
    optimizer.zero_grad() 
    loss.backward() 
    optimizer.step() 
    if (e + 1) % 100 == 0: 
        print('Epoch:{},loss:{:.10f}'.format(e + 1, loss.data.item())) 
    train_loss.append(loss.item()) 

plt.plot(train_loss, label='train_loss') 
plt.legend() 
plt.show() 

# 预测值和真实值的代码
net.eval() 
pred_test = net(test_X) 
pred_test = pred_test.detach().numpy() * scalar 
test_Y = test_Y.reshape(-1, 1) * scalar 
plt.plot(pred_test, label='predict') 
plt.plot(test_Y, label='true') 
plt.legend() 
plt.show()