# HPL_dtrsm man page

HPL_dtrsm — B := A^{-1} * B or B := B * A^{-1}.

## Synopsis

**#include "hpl.h"****void HPL_dtrsm( const enum HPL_ORDER** *ORDER*, **const enum HPL_SIDE** *SIDE*, **const enum HPL_UPLO** *UPLO*, **const enum HPL_TRANS** *TRANS*, **const enum HPL_DIAG** *DIAG*, **const int** *M*, **const int** *N*, **const double** *ALPHA*, **const double *** *A*, **const int** *LDA*, **double *** *B*, **const int** *LDB* **);**

## Description

**HPL_dtrsm** solves one of the matrix equations

op( A ) * X = alpha * B, or X * op( A ) = alpha * B,

where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op(A) is one of

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

The matrix X is overwritten on B.

No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.

## Arguments

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

ORDER = HplRowMajor,

ORDER = HplColumnMajor. - SIDE (local input) const enum HPL_SIDE
- On entry, SIDE specifies whether op(A) appears on the left or right of X as follows:

SIDE==HplLeft op( A ) * X = alpha * B,

SIDE==HplRight X * op( A ) = alpha * B. - UPLO (local input) const enum HPL_UPLO
- On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced. When UPLO==HplUpper, only the upper triangular part of A is to be referenced, otherwise only the lower triangular part of A is to be referenced.
- TRANS (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. - DIAG (local input) const enum HPL_DIAG
- On entry, DIAG specifies whether A is unit triangular or not. When DIAG==HplUnit, A is assumed to be unit triangular, and otherwise, A is not assumed to be unit triangular.
- M (local input) const int
- On entry, M specifies the number of rows of the matrix B. M must be at least zero.
- N (local input) const int
- On entry, N specifies the number of columns of the matrix B. N must 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 matrix B need not be set on input.
- A (local input) const double *
- On entry, A points to an array of size equal to or greater than LDA * k, where k is m when SIDE==HplLeft and is n otherwise. Before entry with UPLO==HplUpper, the leading k by k upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. When UPLO==HplLower on entry, the leading k by k lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced.

Note that when DIAG==HplUnit, the diagonal elements of A not referenced either, but are assumed to be unity. - LDA (local input) const int
- On entry, LDA specifies the leading dimension of A as declared in the calling (sub) program. LDA must be at least MAX(1,m) when SIDE==HplLeft, and MAX(1,n) otherwise.
- B (local input/output) double *
- On entry, B points to an array of size equal to or greater than LDB * n. Before entry, the leading m by n part of the array B must contain the matrix B, except when beta is zero, in which case B need not be set on entry. On exit, the array B is overwritten by the m by n solution matrix.
- LDB (local input) const int
- On entry, LDB specifies the leading dimension of B as declared in the calling (sub) program. LDB must be at least MAX(1,m).

## Example

*#include "hpl.h"*

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

{

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

a[0] = 4.0; a[1] = 1.0; a[2] = 2.0; a[3] = 5.0;

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

HPL_dtrsm( HplColumnMajor, HplLeft, HplUpper,

HplNoTrans, HplNonUnit, 2, 2, 2.0,

a, 2, b, 2 );

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

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

exit(0); return(0);

}

## See Also

**HPL_dgemm** (3).