自动求导机制是pytorch中非常重要的性质，免去了手动计算导数，为构建模型节省了时间。下面介绍自动求导机制的基本用法。

#自动求导机制
import torch
from torch.autograd import Variable

# 1、简单的求导(求导对象是标量)
x = Variable(torch.Tensor([2]),requires_grad=True)
y = (x + 2) ** 2 + 3
print(y)
y.backward()
print(x.grad)

#对矩阵求导
x1 = Variable(torch.randn(10,20),requires_grad=True)
y1 = Variable(torch.randn(10,1),requires_grad=True)
W = Variable(torch.randn(20,1),requires_grad=True)

J = torch.mean(y1 - torch.matmul(x1,W)) #matmul表示做矩阵乘法
J.backward()
print(x1.grad)
print(y1.grad)
print(W.grad)

tensor([19.], grad_fn=<AddBackward0>)
tensor([8.])
tensor([[-0.1636,  0.0904,  0.0446, -0.1052, -0.2323,  0.0129, -0.1532,  0.0544,
          0.0231, -0.0993, -0.0387, -0.1762,  0.0477,  0.1552,  0.0493,  0.0144,
         -0.1581,  0.1986, -0.0226, -0.0454],
        [-0.1636,  0.0904,  0.0446, -0.1052, -0.2323,  0.0129, -0.1532,  0.0544,
          0.0231, -0.0993, -0.0387, -0.1762,  0.0477,  0.1552,  0.0493,  0.0144,
         -0.1581,  0.1986, -0.0226, -0.0454],
        [-0.1636,  0.0904,  0.0446, -0.1052, -0.2323,  0.0129, -0.1532,  0.0544,
          0.0231, -0.0993, -0.0387, -0.1762,  0.0477,  0.1552,  0.0493,  0.0144,
         -0.1581,  0.1986, -0.0226, -0.0454],
        [-0.1636,  0.0904,  0.0446, -0.1052, -0.2323,  0.0129, -0.1532,  0.0544,
          0.0231, -0.0993, -0.0387, -0.1762,  0.0477,  0.1552,  0.0493,  0.0144,
         -0.1581,  0.1986, -0.0226, -0.0454],
        [-0.1636,  0.0904,  0.0446, -0.1052, -0.2323,  0.0129, -0.1532,  0.0544,
          0.0231, -0.0993, -0.0387, -0.1762,  0.0477,  0.1552,  0.0493,  0.0144,
         -0.1581,  0.1986, -0.0226, -0.0454],
        [-0.1636,  0.0904,  0.0446, -0.1052, -0.2323,  0.0129, -0.1532,  0.0544,
          0.0231, -0.0993, -0.0387, -0.1762,  0.0477,  0.1552,  0.0493,  0.0144,
         -0.1581,  0.1986, -0.0226, -0.0454],
        [-0.1636,  0.0904,  0.0446, -0.1052, -0.2323,  0.0129, -0.1532,  0.0544,
          0.0231, -0.0993, -0.0387, -0.1762,  0.0477,  0.1552,  0.0493,  0.0144,
         -0.1581,  0.1986, -0.0226, -0.0454],
        [-0.1636,  0.0904,  0.0446, -0.1052, -0.2323,  0.0129, -0.1532,  0.0544,
          0.0231, -0.0993, -0.0387, -0.1762,  0.0477,  0.1552,  0.0493,  0.0144,
         -0.1581,  0.1986, -0.0226, -0.0454],
        [-0.1636,  0.0904,  0.0446, -0.1052, -0.2323,  0.0129, -0.1532,  0.0544,
          0.0231, -0.0993, -0.0387, -0.1762,  0.0477,  0.1552,  0.0493,  0.0144,
         -0.1581,  0.1986, -0.0226, -0.0454],
        [-0.1636,  0.0904,  0.0446, -0.1052, -0.2323,  0.0129, -0.1532,  0.0544,
          0.0231, -0.0993, -0.0387, -0.1762,  0.0477,  0.1552,  0.0493,  0.0144,
         -0.1581,  0.1986, -0.0226, -0.0454]])
tensor([[0.1000],
        [0.1000],
        [0.1000],
        [0.1000],
        [0.1000],
        [0.1000],
        [0.1000],
        [0.1000],
        [0.1000],
        [0.1000]])
tensor([[ 0.0224],
        [ 0.0187],
        [-0.2078],
        [ 0.5092],
        [ 0.0677],
        [ 0.3497],
        [-0.4575],
        [-0.5480],
        [ 0.4228],
        [-0.0869],
        [ 0.2876],
        [-0.1714],
        [ 0.0985],
        [-0.1364],
        [-0.1502],
        [-0.1372],
        [-0.0999],
        [-0.0006],
        [-0.0544],
        [-0.0678]])

#复杂情况的自动求导 多维数组自动求导机制
import torch
from torch.autograd import Variable

x = Variable(torch.FloatTensor([3]),requires_grad=True)
y = x ** 2 + x * 2 + 3
y.backward(retain_graph=True) #保留计算图
print(x.grad)
y.backward()#不保留计算图
print(x.grad) #得到的是第一次求导的值加上第二次求导的值 8 + 8

tensor([8.])
tensor([16.])

#小练习，向量对向量求导
import torch
from torch.autograd import Variable

x = Variable(torch.Tensor([2,3]),requires_grad = True)
k = Variable(torch.zeros_like(x))

k[0] = x[0]**2 + 3 * x[1]
k[1] = 2*x[0] + x[1] ** 2

print(k)

j = torch.zeros(2,2)
k.backward(torch.FloatTensor([1,0]),retain_graph = True)
j[0] = x.grad.data

x.grad.zero_()
k.backward(torch.FloatTensor([0,1]),retain_graph = True)
j[1] = x.grad.data
print(j)

tensor([13., 13.], grad_fn=<CopySlices>)
tensor([[4., 3.],
        [2., 6.]])