DTRMM - perform one of the matrix-matrix operations   B :=
       alpha*op( A )*B, or B := alpha*B*op( A ),


SYNOPSIS

       SUBROUTINE DTRMM ( SIDE, UPLO, TRANSA, DIAG, M, N,  ALPHA,
                        A, LDA, B, LDB )

           CHARACTER*1  SIDE, UPLO, TRANSA, DIAG

           INTEGER      M, N, LDA, LDB

           DOUBLE       PRECISION ALPHA

           DOUBLE       PRECISION A( LDA, * ), B( LDB, * )


PURPOSE

       DTRMM  performs one of the matrix-matrix operations

       where  alpha  is a scalar,  B  is an m by n matrix,  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'.


PARAMETERS

       SIDE   - CHARACTER*1.
              On  entry,   SIDE specifies whether  op( A ) multi­
              plies B from the left or right as follows:

              SIDE = 'L' or 'l'   B := alpha*op( A )*B.

              SIDE = 'R' or 'r'   B := alpha*B*op( A ).

              Unchanged on exit.

       UPLO   - CHARACTER*1.
              On entry, UPLO specifies whether the matrix A is an
              upper or lower triangular matrix as follows:

              UPLO  =  'U'  or  'u'    A  is  an upper triangular
              matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.

              Unchanged on exit.

              TRANSA  -  CHARACTER*1.  On entry, TRANSA specifies
              the form of op( A ) to be used in the matrix multi­
              plication as follows:

              TRANSA = 'N' or 'n'   op( A ) = A.


              TRANSA = 'C' or 'c'   op( A ) = A'.

              Unchanged on exit.

       DIAG   - CHARACTER*1.
              On  entry,  DIAG specifies whether or not A is unit
              triangular as follows:

              DIAG = 'U' or 'u'   A is assumed to be unit  trian­
              gular.

              DIAG  =  'N'  or  'n'   A is not assumed to be unit
              triangular.

              Unchanged on exit.

       M      - INTEGER.
              On entry, M specifies the number of rows  of  B.  M
              must be at least zero.  Unchanged on exit.

       N      - INTEGER.
              On  entry,  N specifies the number of columns of B.
              N must be at least zero.  Unchanged on exit.

       ALPHA  - DOUBLE PRECISION.
              On entry,  ALPHA specifies the scalar  alpha.  When
              alpha is zero then  A is not referenced and  B need
              not be set before entry.  Unchanged on exit.

       A      - DOUBLE PRECISION array of DIMENSION ( LDA, k ),
              where  k is m
              when  SIDE = 'L' or 'l'  and is  n   when   SIDE  =
              'R' or 'r'.  Before entry  with  UPLO = 'U' or 'u',
              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.  Before entry  with  UPLO = 'L' or 'l',
              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 = 'U' or 'u',
              the diagonal elements  of  A   are  not  referenced
              either,   but  are assumed to be  unity.  Unchanged
              on exit.

       LDA    - INTEGER.
              On entry, LDA specifies the first dimension of A as
              declared  in the calling (sub) program.  When  SIDE
              = 'L' or 'l'  then LDA  must be at least  max( 1, m
              ),   when   SIDE  =  'R' or 'r' then LDA must be at
              least max( 1, n ).  Unchanged on exit.

              Before entry,  the leading  m  by  n  part  of  the
              array   B must contain the matrix  B,  and  on exit
              is overwritten  by the transformed matrix.

       LDB    - INTEGER.
              On entry, LDB specifies the first dimension of B as
              declared  in   the   calling  (sub)  program.   LDB
              must  be  at  least max(  1,  m  ).   Unchanged  on
              exit.

              Level 3 Blas routine.

              --  Written  on  8-February-1989.   Jack  Dongarra,
              Argonne National Laboratory.  Iain Duff, AERE  Har­
              well.   Jeremy  Du Croz, Numerical Algorithms Group
              Ltd.  Sven Hammarling, Numerical  Algorithms  Group
              Ltd.


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