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:

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:

• Wikipedia's article on Matrix multiplication

• Wikipedia's article on GEMM

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:

1. Load the dense_linear_algebra library.

   AFL% load_library('dense_linear_algebra'); 

    

2. 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)] ]  

3. Perform the gemm calculation.

   AFL% gemm(A,B,C);  

    
   The output is:

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