pytorch tensor 乘法运算汇总与解析 |
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元素一一相乘
该操作又称作 “哈达玛积”, 简单来说就是 tensor 元素逐个相乘。这个操作，是通过 * 也就是常规的乘号操作符定义的操作结果。torch.mul 是等价的。 import torch def element_by_element(): x = torch.tensor([1, 2, 3]) y = torch.tensor([4, 5, 6]) return x * y, torch.mul(x, y) element_by_element() (tensor([ 4, 10, 18]), tensor([ 4, 10, 18]))这个操作是可以 broad cast 的。 def element_by_element_broadcast(): x = torch.tensor([1, 2, 3]) y = 2 return x * y element_by_element_broadcast() tensor([2, 4, 6]) 向量点乘torch.matmul: If both tensors are 1-dimensional, the dot product (scalar) is returned. 如果都是1维的，返回的就是 dot product 结果 def vec_dot_product(): x = torch.tensor([1, 2, 3]) y = torch.tensor([4, 5, 6]) return torch.matmul(x, y) vec_dot_product() tensor(32) 矩阵乘法torch.matmul: If both arguments are 2-dimensional, the matrix-matrix product is returned. 如果都是2维，那么就是矩阵乘法的结果返回。与 torch.mm 是等价的，torch.mm 仅仅能处理的是矩阵乘法。 def matrix_multiple(): x = torch.tensor([ [1, 2, 3], [4, 5, 6] ]) y = torch.tensor([ [7, 8], [9, 10], [11, 12] ]) return torch.matmul(x, y), torch.mm(x, y) matrix_multiple() (tensor([[ 58, 64], [139, 154]]), tensor([[ 58, 64], [139, 154]])) vector 与 matrix 相乘torch.matmul: If the first argument is 1-dimensional and the second argument is 2-dimensional, a 1 is prepended to its dimension for the purpose of the matrix multiply. After the matrix multiply, the prepended dimension is removed. 如果第一个是 vector, 第二个是 matrix, 会在 vector 中增加一个维度。也就是 vector 变成了 与 matrix 相乘之后，变成 , 在结果中将 维 再去掉。 def vec_matrix(): x = torch.tensor([1, 2, 3]) y = torch.tensor([ [7, 8], [9, 10], [11, 12] ]) return torch.matmul(x, y) vec_matrix() tensor([58, 64]) matrix 与 vector 相乘同样的道理， vector会被扩充一个维度。 def matrix_vec(): x = torch.tensor([ [1, 2, 3], [4, 5, 6] ]) y = torch.tensor([ 7, 8, 9 ]) return torch.matmul(x, y) matrix_vec() tensor([ 50, 122]) 带有batch_size 的 broad cast乘法 def batched_matrix_broadcasted_vector(): x = torch.tensor([ [ [1, 2], [3, 4] ], [ [5, 6], [7, 8] ] ]) print(f"x shape: {x.size()} \n {x}") y = torch.tensor([1, 3]) return torch.matmul(x, y) batched_matrix_broadcasted_vector() x shape: torch.Size([2, 2, 2]) tensor([[[1, 2], [3, 4]], [[5, 6], [7, 8]]]) tensor([[ 7, 15], [23, 31]]) batched matrix x batched matrix def batched_matrix_batched_matrix(): x = torch.tensor([ [ [1, 2, 1], [3, 4, 4] ], [ [5, 6, 2], [7, 8, 0] ] ]) y = torch.tensor([ [ [1, 2], [3, 4], [5, 6] ], [ [7, 8], [9, 10], [1, 2] ] ]) print(f"x shape: {x.size()} \n y shape: {y.size()}") return torch.matmul(x, y) xy = batched_matrix_batched_matrix() print(f"xy shape: {xy.size()} \n {xy}") x shape: torch.Size([2, 2, 3]) y shape: torch.Size([2, 3, 2]) xy shape: torch.Size([2, 2, 2]) tensor([[[ 12, 16], [ 35, 46]], [[ 91, 104], [121, 136]]])上面的效果与 torch.bmm 是一样的。matmul 比 bmm 功能更加强大，但是 bmm 的语义非常明确， bmm 处理的只能是 3维的。 def batched_matrix_batched_matrix_bmm(): x = torch.tensor([ [ [1, 2, 1], [3, 4, 4] ], [ [5, 6, 2], [7, 8, 0] ] ]) y = torch.tensor([ [ [1, 2], [3, 4], [5, 6] ], [ [7, 8], [9, 10], [1, 2] ] ]) print(f"x shape: {x.size()} \n y shape: {y.size()}") return torch.bmm(x, y) xy = batched_matrix_batched_matrix() print(f"xy shape: {xy.size()} \n {xy}") x shape: torch.Size([2, 2, 3]) y shape: torch.Size([2, 3, 2]) xy shape: torch.Size([2, 2, 2]) tensor([[[ 12, 16], [ 35, 46]], [[ 91, 104], [121, 136]]]) tensordot def tesnordot(): x = torch.tensor([ [1, 2, 1], [3, 4, 4]]) y = torch.tensor([ [7, 8], [9, 10], [1, 2]]) print(f"x shape: {x.size()}, y shape: {y.size()}") return torch.tensordot(x, y, dims=([0], [1])) tesnordot() x shape: torch.Size([2, 3]), y shape: torch.Size([3, 2]) tensor([[31, 39, 7], [46, 58, 10], [39, 49, 9]])参考资料： https://www.jianshu.com/p/de4b6f67051f |
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