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 × 1 × n × n ) (j \times 1 \times n \times n) (j×1×n×n) tensor and other is a ( k × n × n ) (k \times n \times n) (k×n×n) tensor, out will be a ( j × k × n × n ) (j \times k \times n \times n) (j×k×n×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 × 1 × n × m ) (j \times 1 \times n \times m) (j×1×n×m) tensor and other is a ( k × m × p ) (k \times m \times p) (k×m×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 × k × n × p ) (j \times k \times n \times p) (j×k×n×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.
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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