HPL_dtrsv - x := A^{-1} x.
#include "hpl.h"
void HPL_dtrsv( const enum HPL_ORDER ORDER,
const
enum HPL_UPLO UPLO,
const enum HPL_TRANS TRANS,
const enum HPL_DIAG DIAG,
const int N,
const
double * A,
const int LDA,
double * X,
const int INCX );
HPL_dtrsv solves one of the systems of equations
A * x = b, or A^T * x = b,
where b and x are n-element vectors and A is an n by n non-unit, or unit, upper
or lower triangular matrix.
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.
- 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, TRANS specifies the equations to be solved as follows:
TRANS==HplNoTrans A * x = b,
TRANS==HplTrans A^T * x = b.
- 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.
- N (local input) const int
- On entry, N specifies the order of the matrix A. N must be at least
zero.
- A (local input) const double *
- On entry, A points to an array of size equal to or greater than LDA * n.
Before entry with UPLO==HplUpper, the leading n by n 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 n by n 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,n).
- X (local input/output) double *
- On entry, X is an incremented array of dimension at least ( 1 + ( n - 1 )
* abs( INCX ) ) that contains the vector x. Before entry, the incremented
array X must contain the n element right-hand side vector b. On exit, X is
overwritten with the solution vector x.
- INCX (local input) const int
- On entry, INCX specifies the increment for the elements of X. INCX must
not be zero.
#include "hpl.h"
int main(int argc, char *argv[])
{
double a[2*2], x[2];
a[0] = 4.0; a[1] = 1.0; a[2] = 2.0; a[3] = 5.0;
x[0] = 2.0; x[1] = 1.0;
HPL_dtrsv( HplColumnMajor, HplLower, HplNoTrans,
HplNoUnit, a, 2, x, 1 );
printf("x=[%f,%f]\n", x[0], x[1]);
exit(0); return(0);
}
HPL_dger (3),
HPL_dgemv (3).