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README.md

ggemm

Perform the matrix-matrix operation C = α*op(A)*op(B) + β*C where op(X) is one of the op(X) = X, or op(X) = X^T.

Usage

var ggemm = require( '@stdlib/blas/base/ggemm' );

ggemm( ord, ta, tb, M, N, K, α, A, lda, B, ldb, β, C, ldc )

Performs the matrix-matrix operation C = α*op(A)*op(B) + β*C where op(X) is either op(X) = X or op(X) = X^T, α and β are scalars, A, B, and C are matrices, with op(A) an M by K matrix, op(B) a K by N matrix, and C an M by N matrix.

var A = [ 1.0, 2.0, 3.0, 4.0 ];
var B = [ 1.0, 1.0, 0.0, 1.0 ];
var C = [ 1.0, 2.0, 3.0, 4.0 ];

ggemm( 'row-major', 'no-transpose', 'no-transpose', 2, 2, 2, 1.0, A, 2, B, 2, 1.0, C, 2 );
// C => [ 2.0, 5.0, 6.0, 11.0 ]

The function has the following parameters:

  • ord: storage layout.
  • ta: specifies whether A should be transposed, conjugate-transposed, or not transposed.
  • tb: specifies whether B should be transposed, conjugate-transposed, or not transposed.
  • M: number of rows in the matrix op(A) and in the matrix C.
  • N: number of columns in the matrix op(B) and in the matrix C.
  • K: number of columns in the matrix op(A) and number of rows in the matrix op(B).
  • α: scalar constant.
  • A: first input matrix stored in linear memory.
  • lda: stride of the first dimension of A (leading dimension of A).
  • B: second input matrix stored in linear memory.
  • ldb: stride of the first dimension of B (leading dimension of B).
  • β: scalar constant.
  • C: third input matrix stored in linear memory.
  • ldc: stride of the first dimension of C (leading dimension of C).

The stride parameters determine how elements in the input arrays are accessed at runtime. For example, to perform matrix multiplication of two subarrays

var A = [ 1.0, 2.0, 0.0, 0.0, 3.0, 4.0, 0.0, 0.0 ];
var B = [ 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0 ];
var C = [ 1.0, 2.0, 3.0, 4.0 ];

ggemm( 'row-major', 'no-transpose', 'no-transpose', 2, 2, 2, 1.0, A, 4, B, 4, 1.0, C, 2 );
// C => [ 2.0, 5.0, 6.0, 11.0 ]

ggemm.ndarray( ta, tb, M, N, K, α, A, sa1, sa2, oa, B, sb1, sb2, ob, β, C, sc1, sc2, oc )

Performs the matrix-matrix operation C = α*op(A)*op(B) + β*C, using alternative indexing semantics and where op(X) is either op(X) = X or op(X) = X^T, α and β are scalars, A, B, and C are matrices, with op(A) an M by K matrix, op(B) a K by N matrix, and C an M by N matrix.

var A = [ 1.0, 2.0, 3.0, 4.0 ];
var B = [ 1.0, 1.0, 0.0, 1.0 ];
var C = [ 1.0, 2.0, 3.0, 4.0 ];

ggemm.ndarray( 'no-transpose', 'no-transpose', 2, 2, 2, 1.0, A, 2, 1, 0, B, 2, 1, 0, 1.0, C, 2, 1, 0 );
// C => [ 2.0, 5.0, 6.0, 11.0 ]

The function has the following additional parameters:

  • sa1: stride of the first dimension of A.
  • sa2: stride of the second dimension of A.
  • oa: starting index for A.
  • sb1: stride of the first dimension of B.
  • sb2: stride of the second dimension of B.
  • ob: starting index for B.
  • sc1: stride of the first dimension of C.
  • sc2: stride of the second dimension of C.
  • oc: starting index for C.

While typed array views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example,

var A = [ 0.0, 0.0, 1.0, 3.0, 2.0, 4.0 ];
var B = [ 0.0, 1.0, 0.0, 1.0, 1.0 ];
var C = [ 0.0, 0.0, 0.0, 1.0, 3.0, 2.0, 4.0 ];

ggemm.ndarray( 'no-transpose', 'no-transpose', 2, 2, 2, 1.0, A, 1, 2, 2, B, 1, 2, 1, 1.0, C, 1, 2, 3 );
// C => [ 0.0, 0.0, 0.0, 2.0, 6.0, 5.0, 11.0 ]

Notes

  • ggemm() corresponds to the BLAS level 3 function dgemm with the exception that this implementation works with any array type, not just Float64Arrays. Depending on the environment, the typed versions (dgemm, sgemm, etc.) are likely to be significantly more performant.
  • Both functions support array-like objects having getter and setter accessors for array element access (e.g., @stdlib/array/base/accessor).

Examples

var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var ggemm = require( '@stdlib/blas/base/ggemm' );

var opts = {
    'dtype': 'generic'
};

var M = 3;
var N = 4;
var K = 2;

var A = discreteUniform( M*K, 0, 10, opts ); // 3x2
var B = discreteUniform( K*N, 0, 10, opts ); // 2x4
var C = discreteUniform( M*N, 0, 10, opts ); // 3x4

ggemm( 'row-major', 'no-transpose', 'no-transpose', M, N, K, 1.0, A, K, B, N, 1.0, C, N );
console.log( C );

ggemm.ndarray( 'no-transpose', 'no-transpose', M, N, K, 1.0, A, K, 1, 0, B, N, 1, 0, 1.0, C, N, 1, 0 );
console.log( C );