# HPL_dgemm man page

HPL_dgemm — C := alpha * op(A) * op(B) + beta * C.

## Synopsis

**#include "hpl.h"****void HPL_dgemm( const enum HPL_ORDER** *ORDER*, **const enum HPL_TRANS** *TRANSA*, **const enum HPL_TRANS** *TRANSB*, **const int** *M*, **const int** *N*, **const int** *K*, **const double** *ALPHA*, **const double *** *A*, **const int** *LDA*, **const double *** *B*, **const int** *LDB*, **const double** *BETA*, **double *** *C*, **const int** *LDC* **);**

## Description

**HPL_dgemm** performs one of the matrix-matrix operations

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

where op( X ) is one of

op( X ) = X or op( X ) = X^T.

Alpha and beta are scalars, and 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.

## Arguments

- ORDER (local input) const enum HPL_ORDER
- On entry, ORDER specifies the storage format of the operands as follows:

ORDER = HplRowMajor,

ORDER = HplColumnMajor. - TRANSA (local input) const enum HPL_TRANS
- On entry, TRANSA specifies the form of op(A) to be used in the matrix-matrix operation follows:

TRANSA==HplNoTrans : op( A ) = A,

TRANSA==HplTrans : op( A ) = A^T,

TRANSA==HplConjTrans : op( A ) = A^T. - TRANSB (local input) const enum HPL_TRANS
- On entry, TRANSB specifies the form of op(B) to be used in the matrix-matrix operation follows:

TRANSB==HplNoTrans : op( B ) = B,

TRANSB==HplTrans : op( B ) = B^T,

TRANSB==HplConjTrans : op( B ) = B^T. - M (local input) const int
- On entry, M specifies the number of rows of the matrix op(A) and of the matrix C. M must be at least zero.
- N (local input) const int
- On entry, N specifies the number of columns of the matrix op(B) and the number of columns of the matrix C. N must be at least zero.
- K (local input) const int
- On entry, K specifies the number of columns of the matrix op(A) and the number of rows of the matrix op(B). K must be be at least zero.
- ALPHA (local input) const double
- On entry, ALPHA specifies the scalar alpha. When ALPHA is supplied as zero then the elements of the matrices A and B need not be set on input.
- A (local input) const double *
- On entry, A is an array of dimension (LDA,ka), where ka is k when TRANSA==HplNoTrans, and is m otherwise. Before entry with TRANSA==HplNoTrans, the leading m by k part of the array A must contain the matrix A, otherwise the leading k by m part of the array A must contain the matrix A.
- LDA (local input) const int
- On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANSA==HplNoTrans then LDA must be at least max(1,m), otherwise LDA must be at least max(1,k).
- B (local input) const double *
- On entry, B is an array of dimension (LDB,kb), where kb is n when TRANSB==HplNoTrans, and is k otherwise. Before entry with TRANSB==HplNoTrans, the leading k by n part of the array B must contain the matrix B, otherwise the leading n by k part of the array B must contain the matrix B.
- LDB (local input) const int
- On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. When TRANSB==HplNoTrans then LDB must be at least max(1,k), otherwise LDB must be at least max(1,n).
- BETA (local input) const double
- On entry, BETA specifies the scalar beta. When BETA is supplied as zero then the elements of the matrix C need not be set on input.
- C (local input/output) double *
- On entry, C is an array of dimension (LDC,n). Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n matrix ( alpha*op( A )*op( B ) + beta*C ).
- LDC (local input) const int
- On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max(1,m).

## Example

*#include "hpl.h"*

int main(int argc, char *argv[])

{

double a[2*2], b[2*2], c[2*2];

a[0] = 1.0; a[1] = 2.0; a[2] = 3.0; a[3] = 3.0;

b[0] = 2.0; b[1] = 1.0; b[2] = 1.0; b[3] = 2.0;

c[0] = 4.0; c[1] = 3.0; c[2] = 2.0; c[3] = 1.0;

HPL_dgemm( HplColumnMajor, HplNoTrans, HplNoTrans,

2, 2, 2, 2.0, a, 2, b, 2, -1.0, c, 2 );

printf(" [%f,%f]\n", c[0], c[2]);

printf("c=[%f,%f]\n", c[1], c[3]);

exit(0); return(0);

}

## See Also

**HPL_dtrsm** (3).