.. _op_ai_onnx_Gemm:

Gemm
====

- **Domain**: ``ai.onnx``
- **Since version**: 13

General Matrix multiplication:
https://en.wikipedia.org/wiki/Basic_Linear_Algebra_Subprograms#Level_3

A' = transpose(A) if transA else A

B' = transpose(B) if transB else B

Compute Y = alpha \* A' \* B' + beta \* C, where input tensor A has shape (M, K) or (K, M),
input tensor B has shape (K, N) or (N, K), input tensor C is broadcastable to shape (M, N),
and output tensor Y has shape (M, N). A will be transposed before doing the
computation if attribute transA is non-zero, same for B and transB.

**Inputs**

- **A** (*T*): Input tensor A. The shape of A should be (M, K) if transA is 0, or (K, M) if transA is non-zero.
- **B** (*T*): Input tensor B. The shape of B should be (K, N) if transB is 0, or (N, K) if transB is non-zero.
- **C** (*T*): Optional input tensor C. If not specified, the computation is done as if C is a scalar 0. The shape of C should be unidirectional broadcastable to (M, N).

**Outputs**

- **Y** (*T*): Output tensor of shape (M, N).

**Type Constraints**

- **T**: Constrain input and output types to float/int tensors.
  Allowed types: tensor(bfloat16), tensor(double), tensor(float), tensor(float16), tensor(int32), tensor(int64), tensor(uint32), tensor(uint64).

Differences with previous version (11)
--------------------------------------

**SchemaDiff**: ``Gemm`` (domain ``'ai.onnx'``)

* old version: 11
* new version: 13
* breaking: no

**Type constraints:**

* changed 'T': added types: ['tensor(bfloat16)']

Version History
---------------

- :doc:`Version 11 <Gemm-11>`
- :doc:`Version 9 <Gemm-9>`
- :doc:`Version 7 <Gemm-7>`
- :doc:`Version 6 <Gemm-6>`
- :doc:`Version 1 <Gemm-1>`