承接上一篇：PyTorch 入门实战（一）——Tensor
目录
六、Variable转Numpy与Numpy转Variable
一、概念
1.Numpy里没有Variable这个概念，如果大家学过TensorFlow就会知道，Variable提供了自动求导的功能。
2.Variable需要放进一个计算图中，然后进行前后向传播和自动求导。
3.Variable的属性有三个：
- data：Variable里Tensor变量的数值
- grad：Variable反向传播的梯度
- grad_fn：得到Variable的操作
二、Variable的创建和使用
1.我们首先创建一个空的Variable：
import torch
#创建Variable
a = torch.autograd.Variable()
print(a)结果如下：
可以看到默认的类型为Tensor
2.那么，我们如果需要给Variable变量赋值，那么就一定是Tensor类型，例如：
b = torch.autograd.Variable(torch.Tensor([[1, 2], [3, 4],[5, 6], [7, 8]]))
print(b)代码变为：
import torch
#创建Variable
a = torch.autograd.Variable()
print(a)
b = torch.autograd.Variable(torch.Tensor([[1, 2], [3, 4],[5, 6], [7, 8]]))
print(b)结果为：
3.第一章提到了Variable的三个属性，我们依次打印它们：
import torch
#创建Variable
a = torch.autograd.Variable()
print(a)
b = torch.autograd.Variable(torch.Tensor([[1, 2], [3, 4],[5, 6], [7, 8]]))
print(b)
print(b.data)
print(b.grad)
print(b.grad_fn)结果为：
可以看到data就是Tensor的内容，剩下的两个属性为空
三、标量求导计算图
1.为了方便起见，我们可以将torch.autograd.Variable简写为Variable：
from torch.autograd import Variable2.之后，我们先声明一个变量x，这里requires_grad=True意义是否对这个变量求梯度，默认的 Fa!se：
x = Variable(torch.Tensor([2]),requires_grad = True)
print(x)代码变为：
import torch
#创建Variable
a = torch.autograd.Variable()
print(a)
b = torch.autograd.Variable(torch.Tensor([[1, 2], [3, 4],[5, 6], [7, 8]]))
print(b)
print(b.data)
print(b.grad)
print(b.grad_fn)
#建立计算图
from torch.autograd import Variable
x = Variable(torch.Tensor([2]),requires_grad = True)
print(x)结果为：
3.我们再声明两个变量w和b：
w = Variable(torch.Tensor([3]),requires_grad = True)
print(w)
b = Variable(torch.Tensor([4]),requires_grad = True)
print(b)4.我们再写两个变量y1和y2：
y1 = w * x + b
print(y1)
y2 = w * x + b * x
print(y2)5.我们来计算各个变量的梯度，首先是y1：
#计算梯度
y1.backward()
print(x.grad)
print(w.grad)
print(b.grad)代码变为：
import torch
#创建Variable
a = torch.autograd.Variable()
print(a)
b = torch.autograd.Variable(torch.Tensor([[1, 2], [3, 4],[5, 6], [7, 8]]))
print(b)
print(b.data)
print(b.grad)
print(b.grad_fn)
#建立计算图
from torch.autograd import Variable
x = Variable(torch.Tensor([2]),requires_grad = True)
print(x)
w = Variable(torch.Tensor([3]),requires_grad = True)
print(w)
b = Variable(torch.Tensor([4]),requires_grad = True)
print(b)
y1 = w * x + b
print(y1)
y2 = w * x + b * x
print(y2)
#计算梯度
y1.backward()
print(x.grad)
print(w.grad)
print(b.grad)结果为：
其中：
y1 = 3 * 2 + 4 = 10，
y2 = 3 * 2 + 4 * 2 = 14，
x的梯度是3因为是3 * x，
w的梯度是2因为w * 2，
b的梯度是1因为b * 1（* 1被省略）
6.其次是y2，注销y1部分：
y2.backward(x)
print(x.grad)
print(w.grad)
print(b.grad)代码为：
import torch
#创建Variable
a = torch.autograd.Variable()
print(a)
b = torch.autograd.Variable(torch.Tensor([[1, 2], [3, 4],[5, 6], [7, 8]]))
print(b)
print(b.data)
print(b.grad)
print(b.grad_fn)
#建立计算图
from torch.autograd import Variable
x = Variable(torch.Tensor([2]),requires_grad = True)
print(x)
w = Variable(torch.Tensor([3]),requires_grad = True)
print(w)
b = Variable(torch.Tensor([4]),requires_grad = True)
print(b)
y1 = w * x + b
print(y1)
y2 = w * x + b * x
print(y2)
#计算梯度
#y1.backward()
#print(x.grad)
#print(w.grad)
#print(b.grad)
y2.backward()
print(x.grad)
print(w.grad)
print(b.grad)结果为：
其中：
x的梯度是7因为是3 * x + 4 * x，
w的梯度是2因为w * 2，
b的梯度是2因为b * 2
7.backward的函数可以填入参数，例如我们填入变量a：
a = Variable(torch.Tensor([5]),requires_grad = True)
y2.backward(a)
print(x.grad)
print(w.grad)
print(b.grad)代码变为：
import torch
#创建Variable
a = torch.autograd.Variable()
print(a)
b = torch.autograd.Variable(torch.Tensor([[1, 2], [3, 4],[5, 6], [7, 8]]))
print(b)
print(b.data)
print(b.grad)
print(b.grad_fn)
#建立计算图
from torch.autograd import Variable
x = Variable(torch.Tensor([2]),requires_grad = True)
print(x)
w = Variable(torch.Tensor([3]),requires_grad = True)
print(w)
b = Variable(torch.Tensor([4]),requires_grad = True)
print(b)
y1 = w * x + b
print(y1)
y2 = w * x + b * x
print(y2)
#计算梯度
#y1.backward()
#print(x.grad)
#print(w.grad)
#print(b.grad)
a = Variable(torch.Tensor([5]),requires_grad = True)
y2.backward(a)
print(x.grad)
print(w.grad)
print(b.grad)结果为：
可以看到x，w，b的梯度乘以了a的值5，说明这个填入参数是梯度的系数。
四、矩阵求导计算图
1.例如：
#矩阵求导
c = torch.randn(3)
print(c)
c = Variable(c,requires_grad = True)
print(c)
y3 = c * 2
print(y3)
y3.backward(torch.FloatTensor([1, 0.1, 0.01]))
print(c.grad)代码变为：
import torch
#创建Variable
a = torch.autograd.Variable()
print(a)
b = torch.autograd.Variable(torch.Tensor([[1, 2], [3, 4],[5, 6], [7, 8]]))
print(b)
print(b.data)
print(b.grad)
print(b.grad_fn)
#建立计算图
from torch.autograd import Variable
x = Variable(torch.Tensor([2]),requires_grad = True)
print(x)
w = Variable(torch.Tensor([3]),requires_grad = True)
print(w)
b = Variable(torch.Tensor([4]),requires_grad = True)
print(b)
y1 = w * x + b
print(y1)
y2 = w * x + b * x
print(y2)
#计算梯度
#y1.backward()
#print(x.grad)
#print(w.grad)
#print(b.grad)
a = Variable(torch.Tensor([5]),requires_grad = True)
y2.backward(a)
print(x.grad)
print(w.grad)
print(b.grad)
#矩阵求导
c = torch.randn(3)
print(c)
c = Variable(c,requires_grad = True)
print(c)
y3 = c * 2
print(y3)
y3.backward(torch.FloatTensor([1, 0.1, 0.01]))
print(c.grad)结果为：
可以看到，c是一个1行3列的矩阵，因为y3 = c * 2，因此如果backward()里的参数为：
torch.FloatTensor([1, 1, 1])则就是每个分量的梯度，但是传入的是：
torch.FloatTensor([1, 0.1, 0.01])则每个分量梯度要分别乘以1,0.1和0.01
五、Variable放到GPU上执行
1.和Tensor一样的道理，代码如下：
#Variable放在GPU上
if torch.cuda.is_available():
d = c.cuda()
print(d)代码变为：
import torch
#创建Variable
a = torch.autograd.Variable()
print(a)
b = torch.autograd.Variable(torch.Tensor([[1, 2], [3, 4],[5, 6], [7, 8]]))
print(b)
print(b.data)
print(b.grad)
print(b.grad_fn)
#建立计算图
from torch.autograd import Variable
x = Variable(torch.Tensor([2]),requires_grad = True)
print(x)
w = Variable(torch.Tensor([3]),requires_grad = True)
print(w)
b = Variable(torch.Tensor([4]),requires_grad = True)
print(b)
y1 = w * x + b
print(y1)
y2 = w * x + b * x
print(y2)
#计算梯度
#y1.backward()
#print(x.grad)
#print(w.grad)
#print(b.grad)
a = Variable(torch.Tensor([5]),requires_grad = True)
y2.backward(a)
print(x.grad)
print(w.grad)
print(b.grad)
#矩阵求导
c = torch.randn(3)
print(c)
c = Variable(c,requires_grad = True)
print(c)
y3 = c * 2
print(y3)
y3.backward(torch.FloatTensor([1, 0.1, 0.01]))
print(c.grad)
#Variable放在GPU上
if torch.cuda.is_available():
d = c.cuda()
print(d)2.生成结果会慢一下，然后可以看到多了一个device=‘cuda:0’和grad_fn=<CopyBackwards>
六、Variable转Numpy与Numpy转Variable
1.值得注意的是，Variable里requires_grad 一般设置为 False，代码中为True则：
#变量转Numpy
e = Variable(torch.Tensor([4]),requires_grad = True)
f = e.numpy()
print(f)会报如下错误：
Can't call numpy() on Variable that requires grad. Use var.detach().numpy() instead.
2.改为False后，可以看到Numpy类型的矩阵[4.]：
3.或者将numpy()改为detach().numpy()
#变量转Numpy
e = Variable(torch.Tensor([4]),requires_grad = True)
f = e.detach().numpy()
print(f)代码变为：
import torch
#创建Variable
a = torch.autograd.Variable()
print(a)
b = torch.autograd.Variable(torch.Tensor([[1, 2], [3, 4],[5, 6], [7, 8]]))
print(b)
print(b.data)
print(b.grad)
print(b.grad_fn)
#建立计算图
from torch.autograd import Variable
x = Variable(torch.Tensor([2]),requires_grad = True)
print(x)
w = Variable(torch.Tensor([3]),requires_grad = True)
print(w)
b = Variable(torch.Tensor([4]),requires_grad = True)
print(b)
y1 = w * x + b
print(y1)
y2 = w * x + b * x
print(y2)
#计算梯度
#y1.backward()
#print(x.grad)
#print(w.grad)
#print(b.grad)
a = Variable(torch.Tensor([5]),requires_grad = True)
y2.backward(a)
print(x.grad)
print(w.grad)
print(b.grad)
#矩阵求导
c = torch.randn(3)
print(c)
c = Variable(c,requires_grad = True)
print(c)
y3 = c * 2
print(y3)
y3.backward(torch.FloatTensor([1, 0.1, 0.01]))
print(c.grad)
#Variable放在GPU上
if torch.cuda.is_available():
d = c.cuda()
print(d)
#变量转Numpy
e = Variable(torch.Tensor([4]),requires_grad = True)
f = e.detach().numpy()
print(f)结果为：
4.Numpy转Variable先是转为Tensor再转为Variable：
#转换为Tensor
g = torch.from_numpy(f)
print(g)
#转换为Variable
g = Variable(g,requires_grad = True)
print(g)代码变为：
import torch
#创建Variable
a = torch.autograd.Variable()
print(a)
b = torch.autograd.Variable(torch.Tensor([[1, 2], [3, 4],[5, 6], [7, 8]]))
print(b)
print(b.data)
print(b.grad)
print(b.grad_fn)
#建立计算图
from torch.autograd import Variable
x = Variable(torch.Tensor([2]),requires_grad = True)
print(x)
w = Variable(torch.Tensor([3]),requires_grad = True)
print(w)
b = Variable(torch.Tensor([4]),requires_grad = True)
print(b)
y1 = w * x + b
print(y1)
y2 = w * x + b * x
print(y2)
#计算梯度
#y1.backward()
#print(x.grad)
#print(w.grad)
#print(b.grad)
a = Variable(torch.Tensor([5]),requires_grad = True)
y2.backward(a)
print(x.grad)
print(w.grad)
print(b.grad)
#矩阵求导
c = torch.randn(3)
print(c)
c = Variable(c,requires_grad = True)
print(c)
y3 = c * 2
print(y3)
y3.backward(torch.FloatTensor([1, 0.1, 0.01]))
print(c.grad)
#Variable放在GPU上
if torch.cuda.is_available():
d = c.cuda()
print(d)
#变量转Numpy
e = Variable(torch.Tensor([4]),requires_grad = True)
f = e.detach().numpy()
print(f)
#转换为Tensor
g = torch.from_numpy(f)
print(g)
#转换为Variable
g = Variable(g,requires_grad = True)
print(g)结果为：
七、Variable总结
1.Variable和Tensor本质上没有区别，不过Variable会被放入一个计算图中，然后进行前向传播，反向传播，自动求导。
2.Variable有三个属性，可以通过构造函数结构求取梯度得到grad值和grad_fn值
3.Variable，Tensor和Numpy互相转化很方便，类型也比较兼容