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);
}

See Also

HPL_dger, HPL_dgemv.