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# torch.matmul¶

torch.matmul(input, other, *, out=None)

Matrix product of two tensors.

The behavior depends on the dimensionality of the tensors as follows:

• If both tensors are 1-dimensional, the dot product (scalar) is returned.

• If both arguments are 2-dimensional, the matrix-matrix product is returned.

• 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.

• If the first argument is 2-dimensional and the second argument is 1-dimensional, the matrix-vector product is returned.

• If both arguments are at least 1-dimensional and at least one argument is N-dimensional (where N > 2), then a batched matrix multiply is returned. If the first argument is 1-dimensional, a 1 is prepended to its dimension for the purpose of the batched matrix multiply and removed after. If the second argument is 1-dimensional, a 1 is appended to its dimension for the purpose of the batched matrix multiple and removed after. The non-matrix (i.e. batch) dimensions are broadcasted (and thus must be broadcastable). For example, if input is a $(j \times 1 \times n \times n)$ tensor and other is a $(k \times n \times n)$ tensor, out will be a $(j \times k \times n \times n)$ tensor.

Note that the broadcasting logic only looks at the batch dimensions when determining if the inputs are broadcastable, and not the matrix dimensions. For example, if input is a $(j \times 1 \times n \times m)$ tensor and other is a $(k \times m \times p)$ tensor, these inputs are valid for broadcasting even though the final two dimensions (i.e. the matrix dimensions) are different. out will be a $(j \times k \times n \times p)$ tensor.

This operation has support for arguments with sparse layouts. In particular the matrix-matrix (both arguments 2-dimensional) supports sparse arguments with the same restrictions as torch.mm()

Warning

Sparse support is a beta feature and some layout(s)/dtype/device combinations may not be supported, or may not have autograd support. If you notice missing functionality please open a feature request.

This operator supports TensorFloat32.

On certain ROCm devices, when using float16 inputs this module will use different precision for backward.

Note

The 1-dimensional dot product version of this function does not support an out parameter.

Parameters
• input (Tensor) – the first tensor to be multiplied

• other (Tensor) – the second tensor to be multiplied

Keyword Arguments

out (Tensor, optional) – the output tensor.

Example:

>>> # vector x vector
>>> tensor1 = torch.randn(3)
>>> tensor2 = torch.randn(3)
>>> torch.matmul(tensor1, tensor2).size()
torch.Size([])
>>> # matrix x vector
>>> tensor1 = torch.randn(3, 4)
>>> tensor2 = torch.randn(4)
>>> torch.matmul(tensor1, tensor2).size()
torch.Size([3])
>>> # batched matrix x broadcasted vector
>>> tensor1 = torch.randn(10, 3, 4)
>>> tensor2 = torch.randn(4)
>>> torch.matmul(tensor1, tensor2).size()
torch.Size([10, 3])
>>> # batched matrix x batched matrix
>>> tensor1 = torch.randn(10, 3, 4)
>>> tensor2 = torch.randn(10, 4, 5)
>>> torch.matmul(tensor1, tensor2).size()
torch.Size([10, 3, 5])
>>> # batched matrix x broadcasted matrix
>>> tensor1 = torch.randn(10, 3, 4)
>>> tensor2 = torch.randn(4, 5)
>>> torch.matmul(tensor1, tensor2).size()
torch.Size([10, 3, 5])


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