NAME

SYNOPSIS

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

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

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