# HPL_dtrsv man page

HPL_dtrsv — x := A^{-1} x.

## Synopsis

**#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* **);**

## Description

**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.

## Arguments

- 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.

## Example

*#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);

}

## See Also

**HPL_dger** (3), **HPL_dgemv** (3).