这篇文章记录torch.matmul()的用法

这里仿照官方文档中的例子说明，此处取整数随机数，用于直观的查看效果：

• vector x vector
  两个一维向量的matmul相当于点积，得到一个标量

tensor1 = torch.randint(1, 6, (3,))
tensor2 = torch.randint(1, 6, (3,))
output = torch.matmul(tensor1, tensor2)
print("tensor1: {}".format(tensor1))
print("tensor2: {}".format(tensor2))
print("output: {}".format(output))
print("output_size: {}".format(output.size()))

tensor1: tensor([5, 1, 1])
tensor2: tensor([3, 1, 2])
output: 18
output_size: torch.Size([])

• matrix x vector
  一个二维张量和一个一维张量的乘积，是把多出的一维提出来，相当于沿那个维度分别点积

tensor1 = torch.randint(1, 6, (3, 4))
tensor2 = torch.randint(1, 6, (4,))
output = torch.matmul(tensor1, tensor2)
print("tensor1: {}".format(tensor1))
print("tensor2: {}".format(tensor2))
print("output: {}".format(output))
print("output_size: {}".format(output.size()))

tensor1: tensor([[5, 1, 5, 1],
        [4, 4, 4, 2],
        [2, 4, 4, 1]])
tensor2: tensor([1, 3, 4, 3])
output: tensor([31, 38, 33])
output_size: torch.Size([3])

• batched matrix x broadcasted vector
  一个批量矩阵也就是三维张量和一个一维广播向量的乘积，把多出的两维都提出来，沿这两维分别点积

tensor1 = torch.randint(1, 3, (2, 3, 4))
tensor2 = torch.randint(1, 3, (4,))
output = torch.matmul(tensor1, tensor2)
print("tensor1: {}".format(tensor1))
print("tensor2: {}".format(tensor2))
print("output: {}".format(output))
print("output_size: {}".format(output.size()))

tensor1: tensor([[[1, 2, 2, 2],
         [2, 2, 2, 2],
         [2, 2, 1, 2]],

        [[1, 2, 1, 1],
         [2, 1, 1, 1],
         [2, 2, 2, 2]]])
tensor2: tensor([2, 2, 1, 2])
output: tensor([[12, 14, 13],
        [ 9,  9, 14]])
output_size: torch.Size([2, 3])

• batched matrix x batched matrix
  批量矩阵三维和三维的乘积，把公共的维度提出来，然后二维矩阵分别乘积

tensor1 = torch.randint(1, 3, (2, 3, 4))
tensor2 = torch.randint(1, 3, (2, 4, 5))
output = torch.matmul(tensor1, tensor2)
print("tensor1: {}".format(tensor1))
print("tensor2: {}".format(tensor2))
print("output: {}".format(output))
print("output_size: {}".format(output.size()))

tensor1: tensor([[[2, 2, 2, 1],
         [2, 2, 2, 2],
         [2, 1, 1, 2]],

        [[1, 2, 2, 1],
         [1, 1, 1, 1],
         [2, 1, 2, 1]]])
tensor2: tensor([[[1, 1, 1, 1, 2],
         [2, 1, 1, 2, 1],
         [2, 1, 1, 2, 1],
         [1, 1, 1, 1, 1]],

        [[1, 2, 2, 2, 2],
         [2, 1, 1, 1, 1],
         [1, 2, 1, 1, 1],
         [1, 1, 1, 2, 2]]])
output: tensor([[[11,  7,  7, 11,  9],
         [12,  8,  8, 12, 10],
         [ 8,  6,  6,  8,  8]],

        [[ 8,  9,  7,  8,  8],
         [ 5,  6,  5,  6,  6],
         [ 7, 10,  8,  9,  9]]])
output_size: torch.Size([2, 3, 5])

• batched matrix x broadcasted matrix
  批量矩阵三维和广播矩阵二维，多出来的一维提出来，二维矩阵乘积

tensor1 = torch.randint(1, 3, (2, 3, 4))
tensor2 = torch.randint(1, 3, (4, 5))
output = torch.matmul(tensor1, tensor2)
print("tensor1: {}".format(tensor1))
print("tensor2: {}".format(tensor2))
print("output: {}".format(output))
print("output_size: {}".format(output.size()))

tensor1: tensor([[[2, 1, 2, 1],
         [1, 1, 2, 1],
         [1, 2, 1, 2]],

        [[1, 1, 1, 2],
         [1, 2, 2, 1],
         [1, 1, 2, 2]]])
tensor2: tensor([[2, 1, 1, 1, 1],
        [2, 1, 1, 2, 2],
        [1, 1, 1, 1, 1],
        [1, 2, 2, 1, 1]])
output: tensor([[[9, 7, 7, 7, 7],
         [7, 6, 6, 6, 6],
         [9, 8, 8, 8, 8]],

        [[7, 7, 7, 6, 6],
         [9, 7, 7, 8, 8],
         [8, 8, 8, 7, 7]]])
output_size: torch.Size([2, 3, 5])