Pytorch之Tensor学习
Tensors是与数组和矩阵类似的数据结构，比如它与numpy 的ndarray类似，但tensors可以在GPU上运行。实际上，tensors和numpy数组经常共用内存，消除了拷贝数据的需要。Tensors被优化的可以自动求微分。
import torch
import numpy as np
初始化Tensor
- 直接从数据
data=[[1,2],[3,4]]
x_data=torch.tensor(data)
x_data
tensor([[1, 2],
[3, 4]])
- 从numpy数组
np_array=np.array(data)
x_np=torch.tensor(np_array)
x_np
tensor([[1, 2],
[3, 4]], dtype=torch.int32)
x_np=torch.from_numpy(np_array)
x_np
tensor([[1, 2],
[3, 4]], dtype=torch.int32)
- 从另一个tensor
新tensor与参数tensor相比，保留了其特性（shape,datatype)等，除非显式的替换：
x_ones=torch.ones_like(x_data);x_ones
tensor([[1, 1],
[1, 1]])
x_rand=torch.rand_like(x_data,dtype=torch.float);x_rand
tensor([[0.1462, 0.1567],
[0.6331, 0.8472]])
- 随机或者恒定值
shape是tensor维度的元组
shape=(2,3)
rand_tensor=torch.rand(shape)
ones_tensor=torch.ones(shape)
zeros_tensor=torch.zeros(shape)
print(rand_tensor)
print(ones_tensor)
print(zeros_tensor)
tensor([[0.4811, 0.5744, 0.8909],
[0.6602, 0.9882, 0.1145]])
tensor([[1., 1., 1.],
[1., 1., 1.]])
tensor([[0., 0., 0.],
[0., 0., 0.]])
Tensor的属性
Tensor属性为shape,datatype,被储存在的设备，device
tensor=torch.rand(3,4)
tensor.shape
torch.Size([3, 4])
tensor.dtype
torch.float32
tensor.device
device(type='cpu')
Tensor运算
超过100个tensor运算，包括算术，线性代数，矩阵操作（转置，索引，切片），采样等。每个运算都可以在GPU上进行（常常比在CPU上更快）
默认地，tensors在CPU上被创建。我们需要显式的通过.to方法来将它移动到GPU上。在设备间拷贝大型tensor对于时间和开销都是高昂的。
if torch.cuda.is_available():
tensor=tensor.to('cuda')
类似numpy的索引和切片：
tensor=torch.ones((4,4));tensor
tensor([[1., 1., 1., 1.],
[1., 1., 1., 1.],
[1., 1., 1., 1.],
[1., 1., 1., 1.]])
tensor[0]
tensor([1., 1., 1., 1.])
tensor[:,0]
tensor([1., 1., 1., 1.])
tensor[...,-1]=100;tensor
tensor([[ 1., 1., 1., 100.],
[ 1., 1., 1., 100.],
[ 1., 1., 1., 100.],
[ 1., 1., 1., 100.]])
tensor[:,1]=10;tensor
tensor([[ 1., 10., 1., 100.],
[ 1., 10., 1., 100.],
[ 1., 10., 1., 100.],
[ 1., 10., 1., 100.]])
除了常用的索引选择数据，PyTorch还提供了一些高级的选择函数：
help(torch.index_select)
Help on built-in function index_select:
index_select(...)
index_select(input, dim, index, *, out=None) -> Tensor
Returns a new tensor which indexes the :attr:`input` tensor along dimension
:attr:`dim` using the entries in :attr:`index` which is a `LongTensor`.
The returned tensor has the same number of dimensions as the original tensor
(:attr:`input`). The :attr:`dim` th dimension has the same size as the length
of :attr:`index`; other dimensions have the same size as in the original tensor.
.. note:: The returned tensor does **not** use the same storage as the original
tensor. If :attr:`out` has a different shape than expected, we
silently change it to the correct shape, reallocating the underlying
storage if necessary.
Args:
input (Tensor): the input tensor.
dim (int): the dimension in which we index
index (IntTensor or LongTensor): the 1-D tensor containing the indices to index
Keyword args:
out (Tensor, optional): the output tensor.
Example::
>>> x = torch.randn(3, 4)
>>> x
tensor([[ 0.1427, 0.0231, -0.5414, -1.0009],
[-0.4664, 0.2647, -0.1228, -1.1068],
[-1.1734, -0.6571, 0.7230, -0.6004]])
>>> indices = torch.tensor([0, 2])
>>> torch.index_select(x, 0, indices)
tensor([[ 0.1427, 0.0231, -0.5414, -1.0009],
[-1.1734, -0.6571, 0.7230, -0.6004]])
>>> torch.index_select(x, 1, indices)
tensor([[ 0.1427, -0.5414],
[-0.4664, -0.1228],
[-1.1734, 0.7230]])
help(torch.masked_select)
Help on built-in function masked_select:
masked_select(...)
masked_select(input, mask, *, out=None) -> Tensor
Returns a new 1-D tensor which indexes the :attr:`input` tensor according to
the boolean mask :attr:`mask` which is a `BoolTensor`.
The shapes of the :attr:`mask` tensor and the :attr:`input` tensor don't need
to match, but they must be :ref:`broadcastable <broadcasting-semantics>`.
.. note:: The returned tensor does **not** use the same storage
as the original tensor
Args:
input (Tensor): the input tensor.
mask (BoolTensor): the tensor containing the binary mask to index with
Keyword args:
out (Tensor, optional): the output tensor.
Example::
>>> x = torch.randn(3, 4)
>>> x
tensor([[ 0.3552, -2.3825, -0.8297, 0.3477],
[-1.2035, 1.2252, 0.5002, 0.6248],
[ 0.1307, -2.0608, 0.1244, 2.0139]])
>>> mask = x.ge(0.5)
>>> mask
tensor([[False, False, False, False],
[False, True, True, True],
[False, False, False, True]])
>>> torch.masked_select(x, mask)
tensor([ 1.2252, 0.5002, 0.6248, 2.0139])
help(torch.gather)
Help on built-in function gather:
gather(...)
gather(input, dim, index, *, sparse_grad=False, out=None) -> Tensor
Gathers values along an axis specified by `dim`.
For a 3-D tensor the output is specified by::
out[i][j][k] = input[index[i][j][k]][j][k] # if dim == 0
out[i][j][k] = input[i][index[i][j][k]][k] # if dim == 1
out[i][j][k] = input[i][j][index[i][j][k]] # if dim == 2
:attr:`input` and :attr:`index` must have the same number of dimensions.
It is also required that ``index.size(d) <= input.size(d)`` for all
dimensions ``d != dim``. :attr:`out` will have the same shape as :attr:`index`.
Note that ``input`` and ``index`` do not broadcast against each other.
Args:
input (Tensor): the source tensor
dim (int): the axis along which to index
index (LongTensor): the indices of elements to gather
Keyword arguments:
sparse_grad (bool, optional): If ``True``, gradient w.r.t. :attr:`input` will be a sparse tensor.
out (Tensor, optional): the destination tensor
Example::
>>> t = torch.tensor([[1, 2], [3, 4]])
>>> torch.gather(t, 1, torch.tensor([[0, 0], [1, 0]]))
tensor([[ 1, 1],
[ 4, 3]])
可以用torch.cat来合并tensor，沿着某个方向，另外还有torch.stack，这稍微与torch.cat有些不一样。
t1=torch.cat([tensor,tensor,tensor],dim=1);t1
tensor([[ 1., 10., 1., 100., 1., 10., 1., 100., 1., 10., 1., 100.],
[ 1., 10., 1., 100., 1., 10., 1., 100., 1., 10., 1., 100.],
[ 1., 10., 1., 100., 1., 10., 1., 100., 1., 10., 1., 100.],
[ 1., 10., 1., 100., 1., 10., 1., 100., 1., 10., 1., 100.]])
torch.cat([tensor,tensor,tensor],dim=0)
tensor([[ 1., 10., 1., 100.],
[ 1., 10., 1., 100.],
[ 1., 10., 1., 100.],
[ 1., 10., 1., 100.],
[ 1., 10., 1., 100.],
[ 1., 10., 1., 100.],
[ 1., 10., 1., 100.],
[ 1., 10., 1., 100.],
[ 1., 10., 1., 100.],
[ 1., 10., 1., 100.],
[ 1., 10., 1., 100.],
[ 1., 10., 1., 100.]])
cat和stack的区别在于前者会再增加现有维度的值，可以理解为续接，后者会增加一个维度，可以理解为叠加。
a=torch.arange(0,12).reshape(3,4)
a
tensor([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
torch.cat([a,a]).shape
torch.Size([6, 4])
torch.stack([a,a]).shape
torch.Size([2, 3, 4])
torch.cat([a,a])
tensor([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
torch.stack([a,a])
tensor([[[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]],
[[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]]])
- 算术运算
tensor=torch.arange(0,9).reshape(3,3);tensor
tensor([[0, 1, 2],
[3, 4, 5],
[6, 7, 8]])
以下计算了tensor之间的矩阵乘法，y1,y2的值相同
y1=tensor@tensor.T
y1
tensor([[ 5, 14, 23],
[ 14, 50, 86],
[ 23, 86, 149]])
y2=tensor.matmul(tensor.T)
y2
tensor([[ 5, 14, 23],
[ 14, 50, 86],
[ 23, 86, 149]])
y3=torch.empty(3,3)
torch.add(tensor,tensor.T,out=y3)
print(y3)
tensor([[ 0., 4., 8.],
[ 4., 8., 12.],
[ 8., 12., 16.]])
单元素tensor，比如通过aggregate所有值得到一个值，那么就可以通过item()来得到Python的数值。
agg=tensor.sum();agg
tensor(36)
agg_item=agg.item();agg_item
36
在位操作，那些把结果储存在运算数的运算被称为在位操作，可以用_来标识。比如x.copy_(y)，x.t_()将会改变x。
tensor
tensor([[0, 1, 2],
[3, 4, 5],
[6, 7, 8]])
tensor.add_(5)
tensor([[ 5, 6, 7],
[ 8, 9, 10],
[11, 12, 13]])
tensor
tensor([[ 5, 6, 7],
[ 8, 9, 10],
[11, 12, 13]])
在位运算可能会省存储空间，但当计算导数的时候，会出错，因此不建议使用。
与numpy 数组的相互转换
使用numpy()和from_numpy()将tensor和numpy数组相互转换。但需要注意的是：这两个函数所产生的tensor和Numpy的数组共享相同的内存（所以它们之间的转换很快），改变其中一个就改变了另一个！
Tensor to Numpy array
t=torch.ones(5)
t
tensor([1., 1., 1., 1., 1.])
n=t.numpy();n
array([ 1., 1., 1., 1., 1.], dtype=float32)
t.add_(1)
tensor([2., 2., 2., 2., 2.])
Numpy array to Tensor
n=np.ones(5)
t=torch.from_numpy(n)
t
tensor([1., 1., 1., 1., 1.], dtype=torch.float64)
np.add(n,1,out=n)
array([ 2., 2., 2., 2., 2.])
t
tensor([2., 2., 2., 2., 2.], dtype=torch.float64)
n
array([ 2., 2., 2., 2., 2.])
此外，除了上面的方法，还有一个常用的方法就算直接使用torch.tensor()将numpy数组转换为tensor，需要注意的的是该方法总是会进行数据拷贝，返回的tensor和原来的数据不再共享内存。
a=np.arange(9).reshape(3,3)
c=torch.tensor(a)
a+=1
print(c)
print(a)
tensor([[0, 1, 2],
[3, 4, 5],
[6, 7, 8]], dtype=torch.int32)
[[1 2 3]
[4 5 6]
[7 8 9]]
View()
用view()来改变tensor的形状，该方法返回的新tensor与源tensor共享内存（其实是同一个tensor),也即更改其中的一个，另外一个也会跟着改变。具有相同功能的reshape,也不能保证返回的是其拷贝。
x=torch.randn(5,3);x
tensor([[-0.5722, -0.4844, 1.5515],
[-0.2504, 0.2010, 0.0182],
[ 0.0400, 0.0397, 2.0167],
[ 1.8868, -0.4670, 0.5968],
[ 0.9070, 0.5825, -1.0549]])
y=x.view(15);y
tensor([-0.5722, -0.4844, 1.5515, -0.2504, 0.2010, 0.0182, 0.0400, 0.0397,
2.0167, 1.8868, -0.4670, 0.5968, 0.9070, 0.5825, -1.0549])
y[0]=100
x
tensor([[ 1.0000e+02, -4.8445e-01, 1.5515e+00],
[-2.5042e-01, 2.0102e-01, 1.8231e-02],
[ 3.9969e-02, 3.9711e-02, 2.0167e+00],
[ 1.8868e+00, -4.6697e-01, 5.9683e-01],
[ 9.0702e-01, 5.8254e-01, -1.0549e+00]])
z=x.view(-1,5);z
tensor([[ 1.0000e+02, -4.8445e-01, 1.5515e+00, -2.5042e-01, 2.0102e-01],
[ 1.8231e-02, 3.9969e-02, 3.9711e-02, 2.0167e+00, 1.8868e+00],
[-4.6697e-01, 5.9683e-01, 9.0702e-01, 5.8254e-01, -1.0549e+00]])
q=x.reshape(15);q
tensor([ 1.0000e+02, -4.8445e-01, 1.5515e+00, -2.5042e-01, 2.0102e-01,
1.8231e-02, 3.9969e-02, 3.9711e-02, 2.0167e+00, 1.8868e+00,
-4.6697e-01, 5.9683e-01, 9.0702e-01, 5.8254e-01, -1.0549e+00])
q[0]=250;x
tensor([[ 2.5000e+02, -4.8445e-01, 1.5515e+00],
[-2.5042e-01, 2.0102e-01, 1.8231e-02],
[ 3.9969e-02, 3.9711e-02, 2.0167e+00],
[ 1.8868e+00, -4.6697e-01, 5.9683e-01],
[ 9.0702e-01, 5.8254e-01, -1.0549e+00]])
如果我们想要返回一个真正新的副本（即不共享内存），可以先用clone创造一个副本，再用view
x_cp=x.clone().view(15)
x-=1
print(x)
print(x_cp)
tensor([[ 2.4900e+02, -1.4844e+00, 5.5149e-01],
[-1.2504e+00, -7.9898e-01, -9.8177e-01],
[-9.6003e-01, -9.6029e-01, 1.0167e+00],
[ 8.8677e-01, -1.4670e+00, -4.0317e-01],
[-9.2979e-02, -4.1746e-01, -2.0549e+00]])
tensor([ 2.5000e+02, -4.8445e-01, 1.5515e+00, -2.5042e-01, 2.0102e-01,
1.8231e-02, 3.9969e-02, 3.9711e-02, 2.0167e+00, 1.8868e+00,
-4.6697e-01, 5.9683e-01, 9.0702e-01, 5.8254e-01, -1.0549e+00])
使用clone还有一个好处就是会记录在计算图中，即梯度回传到副本时也会传到源tensor.
另外一个常用的函数就是item()，它可以将一个标量tensor转换为python number
x=torch.randn(1);x
tensor([-0.9871])
x.item()
-0.9870905876159668
线性代数
- 迹：torch.trace
help(torch.trace)
Help on built-in function trace:
trace(...)
trace(input) -> Tensor
Returns the sum of the elements of the diagonal of the input 2-D matrix.
Example::
>>> x = torch.arange(1., 10.).view(3, 3)
>>> x
tensor([[ 1., 2., 3.],
[ 4., 5., 6.],
[ 7., 8., 9.]])
>>> torch.trace(x)
tensor(15.)
- 对角线元素：torch.diag
help(torch.diag)
Help on built-in function diag:
diag(...)
diag(input, diagonal=0, *, out=None) -> Tensor
- If :attr:`input` is a vector (1-D tensor), then returns a 2-D square tensor
with the elements of :attr:`input` as the diagonal.
- If :attr:`input` is a matrix (2-D tensor), then returns a 1-D tensor with
the diagonal elements of :attr:`input`.
The argument :attr:`diagonal` controls which diagonal to consider:
- If :attr:`diagonal` = 0, it is the main diagonal.
- If :attr:`diagonal` > 0, it is above the main diagonal.
- If :attr:`diagonal` < 0, it is below the main diagonal.
Args:
input (Tensor): the input tensor.
diagonal (int, optional): the diagonal to consider
Keyword args:
out (Tensor, optional): the output tensor.
.. seealso::
:func:`torch.diagonal` always returns the diagonal of its input.
:func:`torch.diagflat` always constructs a tensor with diagonal elements
specified by the input.
Examples:
Get the square matrix where the input vector is the diagonal::
>>> a = torch.randn(3)
>>> a
tensor([ 0.5950,-0.0872, 2.3298])
>>> torch.diag(a)
tensor([[ 0.5950, 0.0000, 0.0000],
[ 0.0000,-0.0872, 0.0000],
[ 0.0000, 0.0000, 2.3298]])
>>> torch.diag(a, 1)
tensor([[ 0.0000, 0.5950, 0.0000, 0.0000],
[ 0.0000, 0.0000,-0.0872, 0.0000],
[ 0.0000, 0.0000, 0.0000, 2.3298],
[ 0.0000, 0.0000, 0.0000, 0.0000]])
Get the k-th diagonal of a given matrix::
>>> a = torch.randn(3, 3)
>>> a
tensor([[-0.4264, 0.0255,-0.1064],
[ 0.8795,-0.2429, 0.1374],
[ 0.1029,-0.6482,-1.6300]])
>>> torch.diag(a, 0)
tensor([-0.4264,-0.2429,-1.6300])
>>> torch.diag(a, 1)
tensor([ 0.0255, 0.1374])
- triu 上三角
help(torch.triu)
Help on built-in function triu:
triu(...)
triu(input, diagonal=0, *, out=None) -> Tensor
Returns the upper triangular part of a matrix (2-D tensor) or batch of matrices
:attr:`input`, the other elements of the result tensor :attr:`out` are set to 0.
The upper triangular part of the matrix is defined as the elements on and
above the diagonal.
The argument :attr:`diagonal` controls which diagonal to consider. If
:attr:`diagonal` = 0, all elements on and above the main diagonal are
retained. A positive value excludes just as many diagonals above the main
diagonal, and similarly a negative value includes just as many diagonals below
the main diagonal. The main diagonal are the set of indices
:math:`lbrace (i, i)
brace` for :math:`i in [0, min{d_{1}, d_{2}} - 1]` where
:math:`d_{1}, d_{2}` are the dimensions of the matrix.
Args:
input (Tensor): the input tensor.
diagonal (int, optional): the diagonal to consider
Keyword args:
out (Tensor, optional): the output tensor.
Example::
>>> a = torch.randn(3, 3)
>>> a
tensor([[ 0.2309, 0.5207, 2.0049],
[ 0.2072, -1.0680, 0.6602],
[ 0.3480, -0.5211, -0.4573]])
>>> torch.triu(a)
tensor([[ 0.2309, 0.5207, 2.0049],
[ 0.0000, -1.0680, 0.6602],
[ 0.0000, 0.0000, -0.4573]])
>>> torch.triu(a, diagonal=1)
tensor([[ 0.0000, 0.5207, 2.0049],
[ 0.0000, 0.0000, 0.6602],
[ 0.0000, 0.0000, 0.0000]])
>>> torch.triu(a, diagonal=-1)
tensor([[ 0.2309, 0.5207, 2.0049],
[ 0.2072, -1.0680, 0.6602],
[ 0.0000, -0.5211, -0.4573]])
>>> b = torch.randn(4, 6)
>>> b
tensor([[ 0.5876, -0.0794, -1.8373, 0.6654, 0.2604, 1.5235],
[-0.2447, 0.9556, -1.2919, 1.3378, -0.1768, -1.0857],
[ 0.4333, 0.3146, 0.6576, -1.0432, 0.9348, -0.4410],
[-0.9888, 1.0679, -1.3337, -1.6556, 0.4798, 0.2830]])
>>> torch.triu(b, diagonal=1)
tensor([[ 0.0000, -0.0794, -1.8373, 0.6654, 0.2604, 1.5235],
[ 0.0000, 0.0000, -1.2919, 1.3378, -0.1768, -1.0857],
[ 0.0000, 0.0000, 0.0000, -1.0432, 0.9348, -0.4410],
[ 0.0000, 0.0000, 0.0000, 0.0000, 0.4798, 0.2830]])
>>> torch.triu(b, diagonal=-1)
tensor([[ 0.5876, -0.0794, -1.8373, 0.6654, 0.2604, 1.5235],
[-0.2447, 0.9556, -1.2919, 1.3378, -0.1768, -1.0857],
[ 0.0000, 0.3146, 0.6576, -1.0432, 0.9348, -0.4410],
[ 0.0000, 0.0000, -1.3337, -1.6556, 0.4798, 0.2830]])
- tril 下三角
help(torch.tril)
Help on built-in function tril:
tril(...)
tril(input, diagonal=0, *, out=None) -> Tensor
Returns the lower triangular part of the matrix (2-D tensor) or batch of matrices
:attr:`input`, the other elements of the result tensor :attr:`out` are set to 0.
The lower triangular part of the matrix is defined as the elements on and
below the diagonal.
The argument :attr:`diagonal` controls which diagonal to consider. If
:attr:`diagonal` = 0, all elements on and below the main diagonal are
retained. A positive value includes just as many diagonals above the main
diagonal, and similarly a negative value excludes just as many diagonals below
the main diagonal. The main diagonal are the set of indices
:math:`lbrace (i, i)
brace` for :math:`i in [0, min{d_{1}, d_{2}} - 1]` where
:math:`d_{1}, d_{2}` are the dimensions of the matrix.
Args:
input (Tensor): the input tensor.
diagonal (int, optional): the diagonal to consider
Keyword args:
out (Tensor, optional): the output tensor.
Example::
>>> a = torch.randn(3, 3)
>>> a
tensor([[-1.0813, -0.8619, 0.7105],
[ 0.0935, 0.1380, 2.2112],
[-0.3409, -0.9828, 0.0289]])
>>> torch.tril(a)
tensor([[-1.0813, 0.0000, 0.0000],
[ 0.0935, 0.1380, 0.0000],
[-0.3409, -0.9828, 0.0289]])
>>> b = torch.randn(4, 6)
>>> b
tensor([[ 1.2219, 0.5653, -0.2521, -0.2345, 1.2544, 0.3461],
[ 0.4785, -0.4477, 0.6049, 0.6368, 0.8775, 0.7145],
[ 1.1502, 3.2716, -1.1243, -0.5413, 0.3615, 0.6864],
[-0.0614, -0.7344, -1.3164, -0.7648, -1.4024, 0.0978]])
>>> torch.tril(b, diagonal=1)
tensor([[ 1.2219, 0.5653, 0.0000, 0.0000, 0.0000, 0.0000],
[ 0.4785, -0.4477, 0.6049, 0.0000, 0.0000, 0.0000],
[ 1.1502, 3.2716, -1.1243, -0.5413, 0.0000, 0.0000],
[-0.0614, -0.7344, -1.3164, -0.7648, -1.4024, 0.0000]])
>>> torch.tril(b, diagonal=-1)
tensor([[ 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000],
[ 0.4785, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000],
[ 1.1502, 3.2716, 0.0000, 0.0000, 0.0000, 0.0000],
[-0.0614, -0.7344, -1.3164, 0.0000, 0.0000, 0.0000]])
广播机制
x=torch.arange(1,3).view(1,2);x
tensor([[1, 2]])
y=torch.arange(1,4).view(3,1);y
tensor([[1],
[2],
[3]])
x+y
tensor([[2, 3],
[3, 4],
[4, 5]])
运算的内存开销
索引，view是不会开辟新内存，而y=x+y这样的运算是会新开内存，然后将y指向新内存。
x=torch.tensor([1,2])
y=torch.tensor([3,4])
id_before=id(y)
y=y+x
id(y)==id_before
False
如果我们想指定结果到原来y的内存，可以使用索引来进行替换操作。
x=torch.tensor([1,2])
y=torch.tensor([3,4])
id_before=id(y)
y[:]=y+x
id_before==id(y)
True
我们还可以使用运算符全名函数的out参数或者自加符号（也即add_)：
x=torch.tensor([1,2])
y=torch.tensor([3,4])
id_before=id(y)
torch.add(x,y,out=y)
id(y)==id_before
True
y+=x
id(y)==id_before
True
y.add_(x)
id(y)==id_before
True
y.requires_grad
False
自动求梯度
Pytorch提供的autograd包能根据输入和前向传播过程自动构建计算图，并执行反向传播。
如果将Tensor类的属性.require_grad设置为True，它将追踪在其上的所有操作（这样就可以利用链式法则进行梯度传播了）。完成计算后，可以调用.backward()来完成所有梯度计算。此tensor的梯度将累积到.grad属性中。
注意在y.backward()时，如果y是标量，则不需要backward()传入任何参数，否则，需要传入一个与y同形的tensor，则此时y.backward(w)的含义是：先计算L=torch.sum(y*w)，则L是个标量，然后求L对自变量x的导数。
如果不想要被继续追踪，可以调用.detach()可将其从追踪记录中分离出来，这样就可以防止将来的计算被追踪，这样梯度就传不过去了。此外，还可以用with torch.no_grad()将不想被追踪的操作代码块包裹起来，这种方法在评价模型的时候很常用，因为在评估模型时，我们并不需要计算可训练参数（requires_grad=True)的梯度。
Function是另外一个很重要的类。Tensor和Function互相结合就可以构建一个记录有整个计算过程的有向无环图（DAG）。每个tensor都有一个.grad_fn属性，该属性即创建该Tensor的Function，也就是说该tensor是不是通过某些运算得到的，若是，则grad_fn1返回一个与这些运算相关的对象，否则是None.
x=torch.ones(2,2,requires_grad=True)
print(x)
print(x.grad_fn)
print(x.grad) # 未计算则为None
print(x.dtype)
tensor([[1., 1.],
[1., 1.]], requires_grad=True)
None
None
torch.float32
y=x+2
print(y)
print(y.grad_fn)
tensor([[3., 3.],
[3., 3.]], grad_fn=<AddBackward0>)
<AddBackward0 object at 0x000001BA1B94F860>
注意x是直接创建的，所以没有grad_fn，而y是通过一个加法操作创建的，所以它有grad_fn。像x这种直接创建的称为叶子节点，叶子节点对应的grad_fn是None.
z=y*y*3
out=z.mean()
print(z,out)
tensor([[27., 27.],
[27., 27.]], grad_fn=<MulBackward0>) tensor(27., grad_fn=<MeanBackward0>)
通过.requires_grad_()来用in-place的方式改变requires_grad属性：
a=torch.randn(2,2)
a=((a*3)/(a-1))
print(a.requires_grad)
a.requires_grad_(True)
print(a.requires_grad)
b=(a*a).sum()
print(b.grad_fn)
False
True
<SumBackward0 object at 0x000001BA1B92FBA8>
梯度
因为out是一个标量，所以调用backward()时不需要指定求导变量：
out
tensor(27., grad_fn=<MeanBackward0>)
out.backward()
print(x.grad)
tensor([[4.5000, 4.5000],
[4.5000, 4.5000]])
x
tensor([[1., 1.],
[1., 1.]], requires_grad=True)
令out为o，因为：
所以：
量为向量的函数对于向量的梯度就是一个雅可比矩阵J，而torch.autograd这个包就是用来计算一些雅可比矩阵的乘积的，例如，如果v是已给标量函数的 $$ l=g( y^{
ightarrow} ) $$ 的梯度：
根据链式法则，我们有l关于 $$ x^{ ightarrow} $$ 的雅可比矩阵
注意：grad 在反向传播过程中是累加的，这意味着每一次运行反向传播，梯度都会累加之前的梯度，所以一般在反向传播之前需要把梯度清零。
out2=x.sum();out2
tensor(4., grad_fn=<SumBackward0>)
out2.backward()
print(x.grad)
tensor([[5.5000, 5.5000],
[5.5000, 5.5000]])
out3=x.sum()
x.grad.data.zero_()
out3.backward()
print(x.grad)
tensor([[1., 1.],
[1., 1.]])
小练习：
a=torch.tensor([1,2,3],requires_grad=True,dtype=torch.float32)
print(a.grad)
None
b=a**2;b
tensor([1., 4., 9.], grad_fn=<PowBackward0>)
b.requires_grad
True
w=torch.tensor([0.1,0.2,0.3])
b.backward(w)
print(a.grad)
tensor([0.2000, 0.8000, 1.8000])
d=b.sum();d
tensor(14., grad_fn=<SumBackward0>)
d.requires_grad
True
d.backward()
RuntimeError Traceback (most recent call last)
----> 1 d.backward()
E:softwareAnacondaenvspytorch_envlibsite-packages orch_tensor.py in backward(self, gradient, retain_graph, create_graph, inputs)
253 create_graph=create_graph,
254 inputs=inputs)
--> 255 torch.autograd.backward(self, gradient, retain_graph, create_graph, inputs=inputs)
256
257 def register_hook(self, hook):
E:softwareAnacondaenvspytorch_envlibsite-packages orchautograd_init_.py in backward(tensors, grad_tensors, retain_graph, create_graph, grad_variables, inputs)
147 Variable.execution_engine.run_backward(
148 tensors, grad_tensors, retain_graph, create_graph, inputs,
--> 149 allow_unreachable=True, accumulate_grad=True) # allow_unreachable flag
150
151
RuntimeError: Trying to backward through the graph a second time (or directly access saved variables after they have already been freed). Saved intermediate values of the graph are freed when you call .backward() or autograd.grad(). Specify retain_graph=True if you need to backward through the graph a second time or if you need to access saved variables after calling backward.
d=2*x
for i in range(11):
d.backward(retain_graph=True)
print(x.grad)
tensor(4.)
tensor(6.)
tensor(8.)
tensor(10.)
tensor(12.)
tensor(14.)
tensor(16.)
tensor(18.)
tensor(20.)
tensor(22.)
tensor(24.)
```
d=2*x
for i in range(11):
d.backward()
print(x.grad)
```
tensor(26.)
RuntimeError Traceback (most recent call last)
1 d=2*x
2 for i in range(11):
----> 3 d.backward()
4 print(x.grad)
E:softwareAnacondaenvspytorch_envlibsite-packages orch_tensor.py in backward(self, gradient, retain_graph, create_graph, inputs)
253 create_graph=create_graph,
254 inputs=inputs)
--> 255 torch.autograd.backward(self, gradient, retain_graph, create_graph, inputs=inputs)
256
257 def register_hook(self, hook):
E:softwareAnacondaenvspytorch_envlibsite-packages orchautograd_init_.py in backward(tensors, grad_tensors, retain_graph, create_graph, grad_variables, inputs)
147 Variable.execution_engine.run_backward(
148 tensors, grad_tensors, retain_graph, create_graph, inputs,
--> 149 allow_unreachable=True, accumulate_grad=True) # allow_unreachable flag
150
151
RuntimeError: Trying to backward through the graph a second time (or directly access saved variables after they have already been freed). Saved intermediate values of the graph are freed when you call .backward() or autograd.grad(). Specify retain_graph=True if you need to backward through the graph a second time or if you need to access saved variables after calling backward.
c=a.sum();c
tensor(6., grad_fn=<SumBackward0>)
c.backward()
a.grad
tensor([1.2000, 1.8000, 2.8000])
a.grad.data.zero_()
tensor([0., 0., 0.])
c=a.sum()
c.backward()
print(a.grad)
tensor([1., 1., 1.])
torch.arange(0,9).view(3,3)
tensor([[0, 1, 2],
[3, 4, 5],
[6, 7, 8]])
torch.arange(0,9).view(3,3).sum()
tensor(36)
- 更实际的例子
x=torch.tensor([1.0,2.0,3.0,4.0],requires_grad=True) #注意赋值时候是1.0，而不是1,2,3，否则dtype不是torch.float
x.dtype
torch.float32
y=2*x
z=y.view(2,2)
print(z)
v=torch.tensor([[1.0,0.1],[0.01,0.001]],dtype=torch.float)
z.backward(v)
print(x.grad)
tensor([[2., 4.],
[6., 8.]], grad_fn=<ViewBackward>)
tensor([2.0000, 0.2000, 0.0200, 0.0020])
- 中断梯度追踪的例子
x=torch.tensor(1.0,requires_grad=True)
y1=x**2
with torch.no_grad():
y2=x**3
y3=y1+y2
print(x.requires_grad)
print(y1,y1.requires_grad)
print(y2,y2.requires_grad)
print(y3,y3.requires_grad)
True
tensor(1., grad_fn=<PowBackward0>) True
tensor(1.) False
tensor(2., grad_fn=<AddBackward0>) True
y3.backward()
print(x.grad)
tensor(2.)
$$ y_3=y_1+y_2=x^2+x^3 $$ ，当x=1时， $$ frac {d y_3} {dx} $$ 不应该是5么？实际上，由于 y2的定义被`torch.no_grad()`包裹，所以与y2有关的梯度是不会回传的，只有y1有关的梯度才会回传。
上面提到，y2.requires_grad=False，所以不能调用y2.backward()，会报错：
y2.backward()
RuntimeError Traceback (most recent call last)
----> 1 y2.backward()
E:softwareAnacondaenvspytorch_envlibsite-packages orch_tensor.py in backward(self, gradient, retain_graph, create_graph, inputs)
253 create_graph=create_graph,
254 inputs=inputs)
--> 255 torch.autograd.backward(self, gradient, retain_graph, create_graph, inputs=inputs)
256
257 def register_hook(self, hook):
E:softwareAnacondaenvspytorch_envlibsite-packages orchautograd_init_.py in backward(tensors, grad_tensors, retain_graph, create_graph, grad_variables, inputs)
147 Variable.execution_engine.run_backward(
148 tensors, grad_tensors, retain_graph, create_graph, inputs,
--> 149 allow_unreachable=True, accumulate_grad=True) # allow_unreachable flag
150
151
RuntimeError: element 0 of tensors does not require grad and does not have a grad_fn
此外,若我们要修改tensor的数值,但又不希望被autograd记录(即不影响反向传播),那么就可以对tensor.data操作.
x=torch.ones(1,requires_grad=True)
print(x.data) # 还是一个tensor
print(x.data.requires_grad) #但已经独立于计算图之外
y=2*x
x.data*=100 #仅仅改变了值,不会记录在计算图,所以不会影响梯度传播
y.backward()
print(x)
print(x.grad)
tensor([1.])
False
tensor([100.], requires_grad=True)
tensor([2.])
注意reshape的使用
考虑 $$ y=sum_{i=1}^{n} {x_i} $$
example 1:
x=torch.tensor([[1,2,3,4,5]],dtype=torch.float,requires_grad=True)
y=x.sum()
print(y)
y.backward()
print(x.grad)
tensor(15., grad_fn=<SumBackward0>)
tensor([[1., 1., 1., 1., 1.]])
example 2:故意多一个步骤,让输入变下形状
x=torch.tensor([[1,2,3,4,5]],dtype=torch.float,requires_grad=True).reshape(-1,1);x
tensor([[1.],
[2.],
[3.],
[4.],
[5.]], grad_fn=<ViewBackward>)
y=x.sum()
y.backward()
print(x.grad)
None
E:softwareAnacondaenvspytorch_envlibsite-packagesipykernel\__main__.py:3: UserWarning: The .grad attribute of a Tensor that is not a leaf Tensor is being accessed. Its .grad attribute won't be populated during autograd.backward(). If you indeed want the gradient for a non-leaf Tensor, use .retain_grad() on the non-leaf Tensor. If you access the non-leaf Tensor by mistake, make sure you access the leaf Tensor instead. See github.com/pytorch/pytorch/pull/30531 for more information.
app.launch_new_instance()
如果初始时就使用reshape,那么被求导的变量实际是reshape之前的tensor,而非x,但被要求求导的对象没有变量名,所以不能使用.grad，正确的方法：
x=torch.tensor([[1,2,3,4,5]],dtype=torch.float,requires_grad=True)
print(x)
z=x.reshape(-1,1)
print(z)
y=z.sum()
y.backward()
x.grad
tensor([[1., 2., 3., 4., 5.]], requires_grad=True)
tensor([[1.],
[2.],
[3.],
[4.],
[5.]], grad_fn=<ViewBackward>)
tensor([[1., 1., 1., 1., 1.]])