张量的合并：cat和stack操作

一.cat操作

torch.cat([tensor1, tensor2....], dim=)

将多个向量在同一维度上进行合并，并且要求在指定维度dim外，其他维度的形状应保持相同。
例如tensorA[2,3,4]和tensorB[2,1,4]可以在dim=1上合并，但不能在dim=0或dim=2上合并。
如果强行在不合适的维度上进行合并会报错：

import torchtensorA = torch.tensor([[[1, 2, 3],[4, 5, 6],],[[2, 4, 6],[3, 5, 7],]
])
tensorB = torch.tensor([[[0, 6, 3],[4, 2, 6],[2, 1, 1]],[[1, 4, 6],[3, 5, 4],[3, 2, 0]]
])
print(f"tensorA.shape:{tensorA.shape}")
print(f"tensorB.shape:{tensorB.shape}")
print("try to cat A with B in dim1:")
tensorC = torch.cat([tensorA, tensorB], dim=1)
print(f"successful! the final tensor.shape:{tensorC.shape}")
print("try to cat A with B in dim0:")
tensorC = torch.cat([tensorA, tensorB], dim=0)
print(f"successful! the final tensor.shape:{tensorC.shape}")

运行结果如下：

tensorA.shape:torch.Size([2, 2, 3])
tensorB.shape:torch.Size([2, 3, 3])
try to cat A with B in dim1:
successful! the final tensor.shape:torch.Size([2, 5, 3])
try to cat A with B in dim0:
Traceback (most recent call last):File "D:\\MachineLearning\\pytorchBase\\test.py", line 32, in <module>tensorC = torch.cat([tensorA, tensorB], dim=0)
RuntimeError: Sizes of tensors must match except in dimension 0. Expected size 2 but got size 3 for tensor number 1 in the list.

关于在不同维度上合并的结果

import torchtensorA = torch.tensor([[[1, 2, 3],[4, 5, 6]],[[2, 4, 6],[3, 5, 7]]
])
tensorB = torch.tensor([[[0, 6, 3],[4, 2, 6]],[[1, 4, 6],[3, 2, 0]]
])
print(f"tensorA.shape:{tensorA.shape}")
print(f"tensorB.shape:{tensorB.shape}")

tensorA.shape:torch.Size([2, 2, 3])
tensorB.shape:torch.Size([2, 2, 3])

print("try to cat A with B in dim0:")
tensorC = torch.cat([tensorA, tensorB], dim=0)
print(tensorC)

try to cat A with B in dim0:
tensor([[[1, 2, 3],[4, 5, 6]],[[2, 4, 6],[3, 5, 7]],[[0, 6, 3],[4, 2, 6]],[[1, 4, 6],[3, 2, 0]]])

print("try to cat A with B in dim1:")
tensorC = torch.cat([tensorA, tensorB], dim=1)
print(tensorC)

try to cat A with B in dim1:
tensor([[[1, 2, 3],[4, 5, 6],[0, 6, 3],[4, 2, 6]],[[2, 4, 6],[3, 5, 7],[1, 4, 6],[3, 2, 0]]])

这里简单的理解是，两个shape为[2,2,3]的张量在dim=0上合并后，由原来两个2x[2,3]的张量合并为了一个4x[2,3]的张量，即shape为[4,2,3]的张量；而两个shape为[2,2,3]的张量在dim=1上合并后第一个维度的数量不变，而将第二个维度进行合并，可以看作将原来2x[2,3]的张量合并为了2x[4，3]的张量，原来每个[2x3]的张量的行数扩展至了4行。

二.stack操作

torch.stack(tensors, dim=0, *, out=None) → Tensor

沿新维度连接一系列张量
所有张量的size必须一样
使用stack操作后，会在传入的dim前面插入一个新的维度，而其余原本维度的形状不变

import torchtensorA = torch.tensor([[1, 2, 3],[4, 5, 6]
])tensorB = torch.tensor([[7, 8, 9],[3, 2, 1]
])
print(f"tensorA.shape:{tensorA.shape}")
print(f"tensorB.shape:{tensorB.shape}")

tensorA.shape:torch.Size([2, 3])
tensorB.shape:torch.Size([2, 3])

在AB第0维度前插入新的维度进行合并：

print("try to stack A with B in dim0:")
tensorC = torch.stack([tensorA, tensorB], dim=0)
print(f"tensorC.shape:{tensorC.shape}")
print(tensorC)

try to stack A with B in dim0:
tensorC.shape:torch.Size([2, 2, 3])
tensor([[[1, 2, 3],[4, 5, 6]],[[7, 8, 9],[3, 2, 1]]])

在AB第1维度前插入新的维度进行合并：

print("try to stack A with B in dim1:")
tensorC = torch.stack([tensorA, tensorB], dim=1)
print(f"tensorC.shape:{tensorC.shape}")
print(tensorC)

try to stack A with B in dim1:
tensorC.shape:torch.Size([2, 2, 3])
tensor([[[1, 2, 3],[7, 8, 9]],[[4, 5, 6],[3, 2, 1]]])

在AB第2维度前插入新的维度进行合并：

print("try to stack A with B in dim2:")
tensorC = torch.stack([tensorA, tensorB], dim=2)
print(f"tensorC.shape:{tensorC.shape}")
print(tensorC)

try to stack A with B in dim2:
tensorC.shape:torch.Size([2, 3, 2])
tensor([[[1, 7],[2, 8],[3, 9]],[[4, 3],[5, 2],[6, 1]]])

注意原张量是2维的，所以合并插入的维度不能超过2，当在3维度前插入维度合并时，将会报错：

print("try to stack A with B in dim3:")
tensorC = torch.stack([tensorA, tensorB], dim=3)
print(f"tensorC.shape:{tensorC.shape}")
print(tensorC)

try to stack A with B in dim3:
Traceback (most recent call last):File "D:\\MachineLearning\\pytorchBase\\stack.py", line 27, in <module>tensorC = torch.stack([tensorA, tensorB], dim=3)
IndexError: Dimension out of range (expected to be in range of [-3, 2], but got 3)