# Name

**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); }