The gemm operator performs a matrix calculation of the form αAB +βC, with three matrices and two real constants you supply.

Synopsis

gemm(A_matrix, B_matrix, C_matrix [, transa: BOOLEAN] [, transb: BOOLEAN] [, alpha: DOUBLE] [, beta: DOUBLE] );

Library

The gemm operator resides in the Dense Linear Algebra library. Run the following query to load this library:

AFL% load_library('dense_linear_algebra');

Summary

Given matrices A, B, and C and the constants a and b, the gemm() operator can perform any of the following calculations:

αAB + βC
αA^TB + βC
αAB^T + βC
αA^TB^T + βC

where ^T is the transpose of a matrix.

Restrictions apply. The matrices must be compatible for matrix multiplication and addition. For example, for the calculation αAB + βC, if A has dimensions m × n, then B must have dimensions n × p and C must have dimensions m × p. That is, the number of columns of A must equal the number of rows of B. Furthermore, C has the same number of columns as A and the same number of rows as B. The result has the same dimensions as C.

There are four optional named parameters:

If transa: is set, perform the multiplication with the transpose of A (instead of A). Example syntax: transa: 1
If transb: is set, perform the multiplication with the transpose of B (instead of B). Example syntax: transb: true
If alpha: is set, multiply the matrix product by alpha before performing the addition. Example syntax: alpha: 3.1415926
If beta: is set, multiply matrix C by beta before performing the addition. Example syntax: beta: 434.998

For more information, see:

Limitations

The first attribute of all three arrays must be of type double. All other attributes are ignored.
The chunks of the input matrices must be square, and require a chunk interval between 32 and 1024.
Each dimension of each matrix requires the following characteristics:
- The starting index must be zero.
- The ending index cannot be '*'.
- Currently, the chunk overlap must be zero.

Example

To create three matrices and calculate the gemm, do the following:

Load the dense_linear_algebra library.

AFL% load_library('dense_linear_algebra');

Create matrices A, B, and C.

AFL% CREATE ARRAY A <val:double>[i=0:1; j=0:1];

AFL% store(build (A, i*2 + j + 1), A);

The output is:

[
[(1),(2)],
[(3),(4)]
]

AFL% store(build(<val:double>[i=0:1; j=0:1],iif(i=j,1,0)),B);

The output is:

[
[(1),(0)],
[(0),(1)]
]

AFL% CREATE ARRAY C <val:double>[i=0:1; j=0:1];

AFL% store(build (C, 1), C);

The output is:

[
[(1),(1)],
[(1),(1)]
]

Perform the gemm calculation.

AFL% gemm(A,B,C);

The output is:

[
[(2),(3)],
[(4),(5)]
]

Browser not supported