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Showing content from https://docs.pytorch.org/docs/stable/generated/torch.addmm.html below:

torch.addmm — PyTorch 2.7 documentation

torch.addmm(input, mat1, mat2, *, beta=1, alpha=1, out=None) → Tensor¶

Performs a matrix multiplication of the matrices mat1 and mat2. The matrix input is added to the final result.

If mat1 is a ( n × m ) (n \times m) (n×m) tensor, mat2 is a ( m × p ) (m \times p) (m×p) tensor, then input must be broadcastable with a ( n × p ) (n \times p) (n×p) tensor and out will be a ( n × p ) (n \times p) (n×p) tensor.

alpha and beta are scaling factors on matrix-vector product between mat1 and mat2 and the added matrix input respectively.

out = β  input + α   ( mat1 i @ mat2 i ) \text{out} = \beta\ \text{input} + \alpha\ (\text{mat1}_i \mathbin{@} \text{mat2}_i) out=β input+α (mat1i​@mat2i​)

If beta is 0, then the content of input will be ignored, and nan and inf in it will not be propagated.

For inputs of type FloatTensor or DoubleTensor, arguments beta and alpha must be real numbers, otherwise they should be integers.

This operation has support for arguments with sparse layouts. If input is sparse the result will have the same layout and if out is provided it must have the same layout as input.

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.

Parameters

• input (Tensor) – matrix to be added

• mat1 (Tensor) – the first matrix to be matrix multiplied

• mat2 (Tensor) – the second matrix to be matrix multiplied

Keyword Arguments

• beta (Number, optional) – multiplier for input ( β \beta β)

• alpha (Number, optional) – multiplier for m a t 1 @ m a t 2 mat1 @ mat2 mat1@mat2 ( α \alpha α)

• out (Tensor, optional) – the output tensor.

Example:

>>> M = torch.randn(2, 3)
>>> mat1 = torch.randn(2, 3)
>>> mat2 = torch.randn(3, 3)
>>> torch.addmm(M, mat1, mat2)
tensor([[-4.8716,  1.4671, -1.3746],
        [ 0.7573, -3.9555, -2.8681]])

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