HPL_dtrsm man page

HPL_dtrsm — B := A^{-1} * B  or  B := B * A^{-1}.

Synopsis

#include "hpl.h"
 void HPL_dtrsm( const enum HPL_ORDER ORDER, const enum HPL_SIDE SIDE, const enum HPL_UPLO UPLO, const enum HPL_TRANS TRANS, const enum HPL_DIAG DIAG, const int M, const int N, const double ALPHA, const double * A, const int LDA, double * B, const int LDB );

Description

HPL_dtrsm solves one of the matrix equations

  op( A ) * X = alpha * B,   or  X * op( A ) = alpha * B,
 where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op(A) is one of

  op( A ) = A   or   op( A ) = A^T.
 The matrix X is overwritten on B.
 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.                                  

SIDE    (local input)           const enum HPL_SIDE

On entry, SIDE  specifies  whether  op(A) appears on the left or right of X as follows:
  SIDE==HplLeft    op( A ) * X = alpha * B,
  SIDE==HplRight   X * op( A ) = alpha * B.

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, TRANSA  specifies the form of  op(A)  to be used in the matrix-matrix operation follows:                        
  TRANSA==HplNoTrans    : op( A ) = A,                    
  TRANSA==HplTrans      : op( A ) = A^T,                  
  TRANSA==HplConjTrans  : op( A ) = A^T.                  

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.

M       (local input)           const int

On entry,  M  specifies  the number of rows of the  matrix B. M must be at least zero.

N       (local input)           const int

On entry, N  specifies the number of columns of the matrix B. N must be at least zero.

ALPHA   (local input)           const double

On entry, ALPHA specifies the scalar alpha.   When  ALPHA  is supplied  as  zero then the elements of the matrix B need not be set on input.

A       (local input)           const double *

On entry,  A  points  to an array of size equal to or greater than LDA * k,  where  k is m  when  SIDE==HplLeft  and  is  n otherwise.  Before  entry  with  UPLO==HplUpper,  the leading k by k 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 k by k 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,m) when SIDE==HplLeft, and MAX(1,n) otherwise.

B       (local input/output)    double *

On entry,  B  points  to an array of size equal to or greater than LDB * n.  Before entry, the leading  m by n  part of the array B must contain the matrix  B, except when beta is zero, in which case B need not be set on entry.  On exit, the array B is overwritten by the m by n solution matrix.

LDB     (local input)           const int

On entry,  LDB  specifies  the  leading  dimension  of  B  as declared  in  the  calling  (sub) program.  LDB  must  be  at least MAX(1,m).

Example

#include "hpl.h"
 int main(int argc, char *argv[])
{
  double a[2*2], b[2*2];
  a[0] = 4.0; a[1] = 1.0; a[2] = 2.0; a[3] = 5.0;
  b[0] = 2.0; b[1] = 1.0; b[2] = 1.0; b[3] = 2.0;
  HPL_dtrsm( HplColumnMajor, HplLeft, HplUpper,
             HplNoTrans, HplNonUnit, 2, 2, 2.0,
             a, 2, b, 2 );
  printf("  [%f,%f]\n", b[0], b[2]);
  printf("b=[%f,%f]\n", b[1], b[3]);
  exit(0); return(0);
}

See Also

HPL_dgemm (3).

Info

October 26, 2012 HPL 2.1 HPL Library Functions