pytorch-day06

Auto-gradient 自动微分

pytorch 通过反向传播 backward 方法，实现梯度计算。该方法求得的梯度将存在对应自变量张量的grad属性下。
此外也可以使用 torch.autograd.grad函数来实现求梯度计算

使用backward方法求导数

• backward方法通常在一个标量张量上调用，如果非标量，则要传入一个和它同形状的gradient参数张量。
• 相当于用该gradient参数张量与调用张量作向量点乘，得到的标量结果再反向传播.

标量的反向传播

import numpy as np 
import torch 

# f(x) = a*x**2 + b*x + c的导数

x = torch.tensor(0.0,requires_grad = True) # x需要被求导
a = torch.tensor(1.0)
b = torch.tensor(-2.0)
c = torch.tensor(1.0)
y = a*torch.pow(x,2) + b*x + c 

y.backward()
dy_dx = x.grad
print(dy_dx)

非标量的反向传播

import numpy as np 
import torch 

# f(x) = a*x**2 + b*x + c

x = torch.tensor([[0.0,0.0],[1.0,2.0]],requires_grad = True) # x需要被求导
a = torch.tensor(1.0)
b = torch.tensor(-2.0)
c = torch.tensor(1.0)
y = a*torch.pow(x,2) + b*x + c 

gradient = torch.tensor([[1.0,1.0],[1.0,1.0]])

print("x:\n",x)
print("y:\n",y)
y.backward(gradient = gradient)
x_grad = x.grad
print("x_grad:\n",x_grad)

使用标量实现非标量的反向传播

import numpy as np 
import torch 

# f(x) = a*x**2 + b*x + c

x = torch.tensor([[0.0,0.0],[1.0,2.0]],requires_grad = True) # x需要被求导
a = torch.tensor(1.0)
b = torch.tensor(-2.0)
c = torch.tensor(1.0)
y = a*torch.pow(x,2) + b*x + c 

gradient = torch.tensor([[1.0,1.0],[1.0,1.0]])
z = torch.sum(y*gradient)

print("x:",x)
print("y:",y)
z.backward()
x_grad = x.grad
print("x_grad:\n",x_grad)

使用autograd.grad 方法求导数

import numpy as np 
import torch 

# f(x) = a*x**2 + b*x + c的导数

x = torch.tensor(0.0,requires_grad = True) # x需要被求导
a = torch.tensor(1.0)
b = torch.tensor(-2.0)
c = torch.tensor(1.0)
y = a*torch.pow(x,2) + b*x + c


# create_graph 设置为 True 将允许创建更高阶的导数 
dy_dx = torch.autograd.grad(y,x,create_graph=True)[0]
print(dy_dx.data)

# 求二阶导数
dy2_dx2 = torch.autograd.grad(dy_dx,x)[0] 

print(dy2_dx2.data)

import numpy as np 
import torch 

x1 = torch.tensor(1.0,requires_grad = True) # x需要被求导
x2 = torch.tensor(2.0,requires_grad = True)

y1 = x1*x2
y2 = x1+x2


# 允许同时对多个自变量求导数
(dy1_dx1,dy1_dx2) = torch.autograd.grad(outputs=y1,inputs = [x1,x2],retain_graph = True)
print(dy1_dx1,dy1_dx2)

# 如果有多个因变量，相当于把多个因变量的梯度结果求和
(dy12_dx1,dy12_dx2) = torch.autograd.grad(outputs=[y1,y2],inputs = [x1,x2])
print(dy12_dx1,dy12_dx2)

一个没有什么用的实际应用–利用自动微分和优化器求最小值

import numpy as np 
import torch 

# f(x) = a*x**2 + b*x + c的最小值

x = torch.tensor(0.0,requires_grad = True) # x需要被求导
a = torch.tensor(1.0)
b = torch.tensor(-2.0)
c = torch.tensor(1.0)

optimizer = torch.optim.SGD(params=[x],lr = 0.01)


def f(x):
    result = a*torch.pow(x,2) + b*x + c 
    return(result)

for i in range(500):
    optimizer.zero_grad()
    y = f(x)
    y.backward()
    optimizer.step()
   
    
print("y=",f(x).data,";","x=",x.data)