# mx.nd.linalg.gemm¶

## Description¶

Performs general matrix multiplication and accumulation. Input are tensors A, B, C, each of dimension n >= 2 and having the same shape on the leading n-2 dimensions.

If n=2, the BLAS3 function gemm is performed:

out = alpha * op(A) * op(B) + beta * C

Here, alpha and beta are scalar parameters, and op() is either the identity or matrix transposition (depending on transpose_a, transpose_b).

If n>2, gemm is performed separately for a batch of matrices. The column indices of the matrices are given by the last dimensions of the tensors, the row indices by the axis specified with the axis parameter. By default, the trailing two dimensions will be used for matrix encoding.

For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes calls. For example let A, B, C be 5 dimensional tensors. Then gemm(A, B, C, axis=1) is equivalent to

A1 = swapaxes(A, dim1=1, dim2=3)

B1 = swapaxes(B, dim1=1, dim2=3) C = swapaxes(C, dim1=1, dim2=3) C = gemm(A1, B1, C) C = swapaxis(C, dim1=1, dim2=3)

Note

The operator supports float32 and float64 data types only.

Example:

// Single matrix multiply-add
A = [[1.0, 1.0], [1.0, 1.0]]
B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]]
C = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
gemm(A, B, C, transpose_b=True, alpha=2.0, beta=10.0)
= [[14.0, 14.0, 14.0], [14.0, 14.0, 14.0]]

A = [[[1.0, 1.0]], [[0.1, 0.1]]]
B = [[[1.0, 1.0]], [[0.1, 0.1]]]
C = [[[10.0]], [[0.01]]]
gemm(A, B, C, transpose_b=True, alpha=2.0 , beta=10.0)
= [[[104.0]], [[0.14]]]


## Arguments¶

Argument

Description

A

NDArray-or-Symbol.

Tensor of input matrices

B

NDArray-or-Symbol.

Tensor of input matrices

C

NDArray-or-Symbol.

Tensor of input matrices

transpose.a

boolean, optional, default=0.

Multiply with transposed of first input (A).

transpose.b

boolean, optional, default=0.

Multiply with transposed of second input (B).

alpha

double, optional, default=1.

Scalar factor multiplied with A*B.

beta

double, optional, default=1.

Scalar factor multiplied with C.

axis

int, optional, default=’-2’.

Axis corresponding to the matrix rows.

## Value¶

out The result mx.ndarray