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


SYNOPSIS

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

           CHARACTER*1  SIDE, UPLO, TRANSA, DIAG

           INTEGER      M, N, LDA, LDB

           COMPLEX      ALPHA

           COMPLEX      A( LDA, * ), B( LDB, * )


PURPOSE

       CTRMM  performs one of the matrix-matrix operations


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 = 'T' or 't'   op( A ) = A'.

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


       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  - COMPLEX         .
              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       - COMPLEX          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.

       B      - COMPLEX          array of DIMENSION ( LDB, n ).
              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.

              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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