SUBROUTINE CHEMM3MF ( SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB,

     $                   BETA, C, LDC )

*     .. Scalar Arguments ..

      CHARACTER*1        SIDE, UPLO

      INTEGER            M, N, LDA, LDB, LDC

      COMPLEX            ALPHA, BETA

*     .. Array Arguments ..

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

*     ..

*

*  Purpose

*  =======

*

*  CHEMM  performs one of the matrix-matrix operations

*

*     C := alpha*A*B + beta*C,

*

*  or

*

*     C := alpha*B*A + beta*C,

*

*  where alpha and beta are scalars, A is an hermitian matrix and  B and

*  C are m by n matrices.

*

*  Parameters

*  ==========

*

*  SIDE   - CHARACTER*1.

*           On entry,  SIDE  specifies whether  the  hermitian matrix  A

*           appears on the  left or right  in the  operation as follows:

*

*              SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,

*

*              SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,

*

*           Unchanged on exit.

*

*  UPLO   - CHARACTER*1.

*           On  entry,   UPLO  specifies  whether  the  upper  or  lower

*           triangular  part  of  the  hermitian  matrix   A  is  to  be

*           referenced as follows:

*

*              UPLO = 'U' or 'u'   Only the upper triangular part of the

*                                  hermitian matrix is to be referenced.

*

*              UPLO = 'L' or 'l'   Only the lower triangular part of the

*                                  hermitian matrix is to be referenced.

*

*           Unchanged on exit.

*

*  M      - INTEGER.

*           On entry,  M  specifies the number of rows of the matrix  C.

*           M  must be at least zero.

*           Unchanged on exit.

*

*  N      - INTEGER.

*           On entry, N specifies the number of columns of the matrix C.

*           N  must be at least zero.

*           Unchanged on exit.

*

*  ALPHA  - COMPLEX         .

*           On entry, ALPHA specifies the scalar alpha.

*           Unchanged on exit.

*

*  A      - COMPLEX          array of DIMENSION ( LDA, ka ), where ka is

*           m  when  SIDE = 'L' or 'l'  and is n  otherwise.

*           Before entry  with  SIDE = 'L' or 'l',  the  m by m  part of

*           the array  A  must contain the  hermitian matrix,  such that

*           when  UPLO = 'U' or 'u', the leading m by m upper triangular

*           part of the array  A  must contain the upper triangular part

*           of the  hermitian matrix and the  strictly  lower triangular

*           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',

*           the leading  m by m  lower triangular part  of the  array  A

*           must  contain  the  lower triangular part  of the  hermitian

*           matrix and the  strictly upper triangular part of  A  is not

*           referenced.

*           Before entry  with  SIDE = 'R' or 'r',  the  n by n  part of

*           the array  A  must contain the  hermitian matrix,  such that

*           when  UPLO = 'U' or 'u', the leading n by n upper triangular

*           part of the array  A  must contain the upper triangular part

*           of the  hermitian matrix and the  strictly  lower triangular

*           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',

*           the leading  n by n  lower triangular part  of the  array  A

*           must  contain  the  lower triangular part  of the  hermitian

*           matrix and the  strictly upper triangular part of  A  is not

*           referenced.

*           Note that the imaginary parts  of the diagonal elements need

*           not be set, they are assumed to be zero.

*           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 ), otherwise  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.

*           Unchanged on exit.

*

*  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.

*

*  BETA   - COMPLEX         .

*           On entry,  BETA  specifies the scalar  beta.  When  BETA  is

*           supplied as zero then C need not be set on input.

*           Unchanged on exit.

*

*  C      - COMPLEX          array of DIMENSION ( LDC, n ).

*           Before entry, the leading  m by n  part of the array  C must

*           contain the matrix  C,  except when  beta  is zero, in which

*           case C need not be set on entry.

*           On exit, the array  C  is overwritten by the  m by n updated

*           matrix.

*

*  LDC    - INTEGER.

*           On entry, LDC specifies the first dimension of C as declared

*           in  the  calling  (sub)  program.   LDC  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.

*

*

*     .. External Functions ..

      LOGICAL            LSAME

      EXTERNAL           LSAME

*     .. External Subroutines ..

      EXTERNAL           XERBLA

*     .. Intrinsic Functions ..

      INTRINSIC          CONJG, MAX, REAL

*     .. Local Scalars ..

      LOGICAL            UPPER

      INTEGER            I, INFO, J, K, NROWA

      COMPLEX            TEMP1, TEMP2

*     .. Parameters ..

      COMPLEX            ONE

      PARAMETER        ( ONE  = ( 1.0E+0, 0.0E+0 ) )

      COMPLEX            ZERO

      PARAMETER        ( ZERO = ( 0.0E+0, 0.0E+0 ) )

*     ..

*     .. Executable Statements ..

*

*     Set NROWA as the number of rows of A.

*

      IF( LSAME( SIDE, 'L' ) )THEN

         NROWA = M

      ELSE

         NROWA = N

      END IF

      UPPER = LSAME( UPLO, 'U' )

*

*     Test the input parameters.

*

      INFO = 0

      IF(      ( .NOT.LSAME( SIDE, 'L' ) ).AND.

     $         ( .NOT.LSAME( SIDE, 'R' ) )      )THEN

         INFO = 1

      ELSE IF( ( .NOT.UPPER              ).AND.

     $         ( .NOT.LSAME( UPLO, 'L' ) )      )THEN

         INFO = 2

      ELSE IF( M  .LT.0               )THEN

         INFO = 3

      ELSE IF( N  .LT.0               )THEN

         INFO = 4

      ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN

         INFO = 7

      ELSE IF( LDB.LT.MAX( 1, M     ) )THEN

         INFO = 9

      ELSE IF( LDC.LT.MAX( 1, M     ) )THEN

         INFO = 12

      END IF

      IF( INFO.NE.0 )THEN

         CALL XERBLA( 'CHEMM3M', INFO )

         RETURN

      END IF

*

*     Quick return if possible.

*

      IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.

     $    ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )

     $   RETURN

*

*     And when  alpha.eq.zero.

*

      IF( ALPHA.EQ.ZERO )THEN

         IF( BETA.EQ.ZERO )THEN

            DO 20, J = 1, N

               DO 10, I = 1, M

                  C( I, J ) = ZERO

   10          CONTINUE

   20       CONTINUE

         ELSE

            DO 40, J = 1, N

               DO 30, I = 1, M

                  C( I, J ) = BETA*C( I, J )

   30          CONTINUE

   40       CONTINUE

         END IF

         RETURN

      END IF

*

*     Start the operations.

*

      IF( LSAME( SIDE, 'L' ) )THEN

*

*        Form  C := alpha*A*B + beta*C.

*

         IF( UPPER )THEN

            DO 70, J = 1, N

               DO 60, I = 1, M

                  TEMP1 = ALPHA*B( I, J )

                  TEMP2 = ZERO

                  DO 50, K = 1, I - 1

                     C( K, J ) = C( K, J ) + TEMP1*A( K, I )

                     TEMP2     = TEMP2     +

     $                           B( K, J )*CONJG(  A( K, I ) )

   50             CONTINUE

                  IF( BETA.EQ.ZERO )THEN

                     C( I, J ) = TEMP1*REAL( A( I, I ) ) +

     $                           ALPHA*TEMP2

                  ELSE

                     C( I, J ) = BETA *C( I, J )         +

     $                           TEMP1*REAL( A( I, I ) ) +

     $                           ALPHA*TEMP2

                  END IF

   60          CONTINUE

   70       CONTINUE

         ELSE

            DO 100, J = 1, N

               DO 90, I = M, 1, -1

                  TEMP1 = ALPHA*B( I, J )

                  TEMP2 = ZERO

                  DO 80, K = I + 1, M

                     C( K, J ) = C( K, J ) + TEMP1*A( K, I )

                     TEMP2     = TEMP2     +

     $                           B( K, J )*CONJG(  A( K, I ) )

   80             CONTINUE

                  IF( BETA.EQ.ZERO )THEN

                     C( I, J ) = TEMP1*REAL( A( I, I ) ) +

     $                           ALPHA*TEMP2

                  ELSE

                     C( I, J ) = BETA *C( I, J )         +

     $                           TEMP1*REAL( A( I, I ) ) +

     $                           ALPHA*TEMP2

                  END IF

   90          CONTINUE

  100       CONTINUE

         END IF

      ELSE

*

*        Form  C := alpha*B*A + beta*C.

*

         DO 170, J = 1, N

            TEMP1 = ALPHA*REAL( A( J, J ) )

            IF( BETA.EQ.ZERO )THEN

               DO 110, I = 1, M

                  C( I, J ) = TEMP1*B( I, J )

  110          CONTINUE

            ELSE

               DO 120, I = 1, M

                  C( I, J ) = BETA*C( I, J ) + TEMP1*B( I, J )

  120          CONTINUE

            END IF

            DO 140, K = 1, J - 1

               IF( UPPER )THEN

                  TEMP1 = ALPHA*A( K, J )

               ELSE

                  TEMP1 = ALPHA*CONJG( A( J, K ) )

               END IF

               DO 130, I = 1, M

                  C( I, J ) = C( I, J ) + TEMP1*B( I, K )

  130          CONTINUE

  140       CONTINUE

            DO 160, K = J + 1, N

               IF( UPPER )THEN

                  TEMP1 = ALPHA*CONJG( A( J, K ) )

               ELSE

                  TEMP1 = ALPHA*A( K, J )

               END IF

               DO 150, I = 1, M

                  C( I, J ) = C( I, J ) + TEMP1*B( I, K )

  150          CONTINUE

  160       CONTINUE

  170    CONTINUE

      END IF

*

      RETURN

*

*     End of CHEMM .

*

      END