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).

Info

October 26, 2012 HPL 2.1 HPL Library Functions