Name

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("b=[%f,%f]", b[0], b[2]);
   printf("  [%f,%f]", b[1], b[3]);
   exit(0);
   return(0);
}

See Also

HPL_dgemm