CTRMM(3)        BLAS routine of NEC Numeric Library Collection        CTRMM(3)



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

PARAMETERS
       SIDE   - CHARACTER*1.
              On entry,  SIDE specifies whether  op( A ) multiplies 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 multiplication as follows:

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

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

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

              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  con-
              tain  the lower triangular matrix  and the strictly upper trian-
              gular 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.

       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 Harwell.  Jeremy Du Croz, Numerical
              Algorithms  Group  Ltd.   Sven  Hammarling, Numerical Algorithms
              Group Ltd.



BLAS routine                    16 October 1992                       CTRMM(3)