HPL_dtrsm - B := A^{-1} * B or B := B * A^{-1}.
#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 );
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.
- 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).
#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);
}
HPL_dgemm (3).