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       <TITLE>HPL_dtrsm HPL 2.0 Library Functions September 10, 2008</TITLE>
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       <H1>Name</H1>
       <B>HPL_dtrsm</B> B := A^{-1} * B  or  B := B * A^{-1}.
       <H1>Synopsis</H1>
       <CODE>#include "hpl.h"</CODE><BR><BR>
       <CODE>void</CODE>
       <CODE>HPL_dtrsm(</CODE>
       <CODE>const enum HPL_ORDER</CODE>
       <CODE>ORDER</CODE>,
       <CODE>const enum HPL_SIDE</CODE>
       <CODE>SIDE</CODE>,
       <CODE>const enum HPL_UPLO</CODE>
       <CODE>UPLO</CODE>,
       <CODE>const enum HPL_TRANS</CODE>
       <CODE>TRANS</CODE>,
       <CODE>const enum HPL_DIAG</CODE>
       <CODE>DIAG</CODE>,
       <CODE>const int</CODE>
       <CODE>M</CODE>,
       <CODE>const int</CODE>
       <CODE>N</CODE>,
       <CODE>const double</CODE>
       <CODE>ALPHA</CODE>,
       <CODE>const double *</CODE>
       <CODE>A</CODE>,
       <CODE>const int</CODE>
       <CODE>LDA</CODE>,
       <CODE>double *</CODE>
       <CODE>B</CODE>,
       <CODE>const int</CODE>
       <CODE>LDB</CODE>
       <CODE>);</CODE>
       <H1>Description</H1>
       <B>HPL_dtrsm</B>
       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.
       <H1>Arguments</H1>
       <PRE>
       ORDER   (local input)                 const enum HPL_ORDER
               On entry, ORDER  specifies the storage format of the operands
               as follows:
                  ORDER = HplRowMajor,
                  ORDER = HplColumnMajor.
       </PRE>
       <PRE>
       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.
       </PRE>
       <PRE>
       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.
       </PRE>
       <PRE>
       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.
       </PRE>
       <PRE>
       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.
       </PRE>
       <PRE>
       M       (local input)                 const int
               On entry,  M  specifies  the number of rows of the  matrix B.
               M must be at least zero.
       </PRE>
       <PRE>
       N       (local input)                 const int
               On entry, N  specifies the number of columns of the matrix B.
               N must be at least zero.
       </PRE>
       <PRE>
       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.
       </PRE>
       <PRE>
       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.
       </PRE>
       <PRE>
       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.
       </PRE>
       <PRE>
       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.
       </PRE>
       <PRE>
       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).
       </PRE>
       <H1>Example</H1>
       <CODE>#include "hpl.h"</CODE><BR><BR>
       <PRE>
       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);
+      }
       </PRE>
       <H1>See Also</H1>
       <A HREF="HPL_dgemm.html">HPL_dgemm</A>.
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