SUBROUTINE CGEMM3MF(TRA,TRB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)

*     .. Scalar Arguments ..

      COMPLEX ALPHA,BETA

      INTEGER K,LDA,LDB,LDC,M,N

      CHARACTER TRA,TRB

*     ..

*     .. Array Arguments ..

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

*     ..

*

*  Purpose

*  =======

*

*  CGEMM  performs one of the matrix-matrix operations

*

*     C := alpha*op( A )*op( B ) + beta*C,

*

*  where  op( X ) is one of

*

*     op( X ) = X   or   op( X ) = X'   or   op( X ) = conjg( X' ),

*

*  alpha and beta are scalars, and A, B and C are matrices, with op( A )

*  an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.

*

*  Arguments

*  ==========

*

*  TRA - CHARACTER*1.

*           On entry, TRA specifies the form of op( A ) to be used in

*           the matrix multiplication as follows:

*

*              TRA = 'N' or 'n',  op( A ) = A.

*

*              TRA = 'T' or 't',  op( A ) = A'.

*

*              TRA = 'C' or 'c',  op( A ) = conjg( A' ).

*

*           Unchanged on exit.

*

*  TRB - CHARACTER*1.

*           On entry, TRB specifies the form of op( B ) to be used in

*           the matrix multiplication as follows:

*

*              TRB = 'N' or 'n',  op( B ) = B.

*

*              TRB = 'T' or 't',  op( B ) = B'.

*

*              TRB = 'C' or 'c',  op( B ) = conjg( B' ).

*

*           Unchanged on exit.

*

*  M      - INTEGER.

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

*           op( A )  and 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

*           op( B ) and the number of columns of the matrix C. N must be

*           at least zero.

*           Unchanged on exit.

*

*  K      - INTEGER.

*           On entry,  K  specifies  the number of columns of the matrix

*           op( A ) and the number of rows of the matrix op( B ). K 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

*           k  when  TRA = 'N' or 'n',  and is  m  otherwise.

*           Before entry with  TRA = 'N' or 'n',  the leading  m by k

*           part of the array  A  must contain the matrix  A,  otherwise

*           the leading  k by m  part of the array  A  must contain  the

*           matrix A.

*           Unchanged on exit.

*

*  LDA    - INTEGER.

*           On entry, LDA specifies the first dimension of A as declared

*           in the calling (sub) program. When  TRA = 'N' or 'n' then

*           LDA must be at least  max( 1, m ), otherwise  LDA must be at

*           least  max( 1, k ).

*           Unchanged on exit.

*

*  B      - COMPLEX          array of DIMENSION ( LDB, kb ), where kb is

*           n  when  TRB = 'N' or 'n',  and is  k  otherwise.

*           Before entry with  TRB = 'N' or 'n',  the leading  k by n

*           part of the array  B  must contain the matrix  B,  otherwise

*           the leading  n by k  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. When  TRB = 'N' or 'n' then

*           LDB must be at least  max( 1, k ), otherwise  LDB must be at

*           least  max( 1, n ).

*           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  matrix

*           ( alpha*op( A )*op( B ) + beta*C ).

*

*  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

*     ..

*     .. Local Scalars ..

      COMPLEX TEMP

      INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB

      LOGICAL CONJA,CONJB,NOTA,NOTB

*     ..

*     .. Parameters ..

      COMPLEX ONE

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

      COMPLEX ZERO

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

*     ..

*

*     Set  NOTA  and  NOTB  as  true if  A  and  B  respectively are not

*     conjugated or transposed, set  CONJA and CONJB  as true if  A  and

*     B  respectively are to be  transposed but  not conjugated  and set

*     NROWA, NCOLA and  NROWB  as the number of rows and  columns  of  A

*     and the number of rows of  B  respectively.

*

      NOTA = LSAME(TRA,'N')

      NOTB = LSAME(TRB,'N')

      CONJA = LSAME(TRA,'C')

      CONJB = LSAME(TRB,'C')

      IF (NOTA) THEN

          NROWA = M

          NCOLA = K

      ELSE

          NROWA = K

          NCOLA = M

      END IF

      IF (NOTB) THEN

          NROWB = K

      ELSE

          NROWB = N

      END IF

*

*     Test the input parameters.

*

      INFO = 0

      IF ((.NOT.NOTA) .AND. (.NOT.CONJA) .AND.

     +    (.NOT.LSAME(TRA,'T'))) THEN

          INFO = 1

      ELSE IF ((.NOT.NOTB) .AND. (.NOT.CONJB) .AND.

     +         (.NOT.LSAME(TRB,'T'))) THEN

          INFO = 2

      ELSE IF (M.LT.0) THEN

          INFO = 3

      ELSE IF (N.LT.0) THEN

          INFO = 4

      ELSE IF (K.LT.0) THEN

          INFO = 5

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

          INFO = 8

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

          INFO = 10

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

          INFO = 13

      END IF

      IF (INFO.NE.0) THEN

          CALL XERBLA('CGEMM ',INFO)

          RETURN

      END IF

*

*     Quick return if possible.

*

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

     +    (((ALPHA.EQ.ZERO).OR. (K.EQ.0)).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 (NOTB) THEN

          IF (NOTA) THEN

*

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

*

              DO 90 J = 1,N

                  IF (BETA.EQ.ZERO) THEN

                      DO 50 I = 1,M

                          C(I,J) = ZERO

   50                 CONTINUE

                  ELSE IF (BETA.NE.ONE) THEN

                      DO 60 I = 1,M

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

   60                 CONTINUE

                  END IF

                  DO 80 L = 1,K

                      IF (B(L,J).NE.ZERO) THEN

                          TEMP = ALPHA*B(L,J)

                          DO 70 I = 1,M

                              C(I,J) = C(I,J) + TEMP*A(I,L)

   70                     CONTINUE

                      END IF

   80             CONTINUE

   90         CONTINUE

          ELSE IF (CONJA) THEN

*

*           Form  C := alpha*conjg( A' )*B + beta*C.

*

              DO 120 J = 1,N

                  DO 110 I = 1,M

                      TEMP = ZERO

                      DO 100 L = 1,K

                          TEMP = TEMP + CONJG(A(L,I))*B(L,J)

  100                 CONTINUE

                      IF (BETA.EQ.ZERO) THEN

                          C(I,J) = ALPHA*TEMP

                      ELSE

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

                      END IF

  110             CONTINUE

  120         CONTINUE

          ELSE

*

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

*

              DO 150 J = 1,N

                  DO 140 I = 1,M

                      TEMP = ZERO

                      DO 130 L = 1,K

                          TEMP = TEMP + A(L,I)*B(L,J)

  130                 CONTINUE

                      IF (BETA.EQ.ZERO) THEN

                          C(I,J) = ALPHA*TEMP

                      ELSE

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

                      END IF

  140             CONTINUE

  150         CONTINUE

          END IF

      ELSE IF (NOTA) THEN

          IF (CONJB) THEN

*

*           Form  C := alpha*A*conjg( B' ) + beta*C.

*

              DO 200 J = 1,N

                  IF (BETA.EQ.ZERO) THEN

                      DO 160 I = 1,M

                          C(I,J) = ZERO

  160                 CONTINUE

                  ELSE IF (BETA.NE.ONE) THEN

                      DO 170 I = 1,M

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

  170                 CONTINUE

                  END IF

                  DO 190 L = 1,K

                      IF (B(J,L).NE.ZERO) THEN

                          TEMP = ALPHA*CONJG(B(J,L))

                          DO 180 I = 1,M

                              C(I,J) = C(I,J) + TEMP*A(I,L)

  180                     CONTINUE

                      END IF

  190             CONTINUE

  200         CONTINUE

          ELSE

*

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

*

              DO 250 J = 1,N

                  IF (BETA.EQ.ZERO) THEN

                      DO 210 I = 1,M

                          C(I,J) = ZERO

  210                 CONTINUE

                  ELSE IF (BETA.NE.ONE) THEN

                      DO 220 I = 1,M

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

  220                 CONTINUE

                  END IF

                  DO 240 L = 1,K

                      IF (B(J,L).NE.ZERO) THEN

                          TEMP = ALPHA*B(J,L)

                          DO 230 I = 1,M

                              C(I,J) = C(I,J) + TEMP*A(I,L)

  230                     CONTINUE

                      END IF

  240             CONTINUE

  250         CONTINUE

          END IF

      ELSE IF (CONJA) THEN

          IF (CONJB) THEN

*

*           Form  C := alpha*conjg( A' )*conjg( B' ) + beta*C.

*

              DO 280 J = 1,N

                  DO 270 I = 1,M

                      TEMP = ZERO

                      DO 260 L = 1,K

                          TEMP = TEMP + CONJG(A(L,I))*CONJG(B(J,L))

  260                 CONTINUE

                      IF (BETA.EQ.ZERO) THEN

                          C(I,J) = ALPHA*TEMP

                      ELSE

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

                      END IF

  270             CONTINUE

  280         CONTINUE

          ELSE

*

*           Form  C := alpha*conjg( A' )*B' + beta*C

*

              DO 310 J = 1,N

                  DO 300 I = 1,M

                      TEMP = ZERO

                      DO 290 L = 1,K

                          TEMP = TEMP + CONJG(A(L,I))*B(J,L)

  290                 CONTINUE

                      IF (BETA.EQ.ZERO) THEN

                          C(I,J) = ALPHA*TEMP

                      ELSE

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

                      END IF

  300             CONTINUE

  310         CONTINUE

          END IF

      ELSE

          IF (CONJB) THEN

*

*           Form  C := alpha*A'*conjg( B' ) + beta*C

*

              DO 340 J = 1,N

                  DO 330 I = 1,M

                      TEMP = ZERO

                      DO 320 L = 1,K

                          TEMP = TEMP + A(L,I)*CONJG(B(J,L))

  320                 CONTINUE

                      IF (BETA.EQ.ZERO) THEN

                          C(I,J) = ALPHA*TEMP

                      ELSE

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

                      END IF

  330             CONTINUE

  340         CONTINUE

          ELSE

*

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

*

              DO 370 J = 1,N

                  DO 360 I = 1,M

                      TEMP = ZERO

                      DO 350 L = 1,K

                          TEMP = TEMP + A(L,I)*B(J,L)

  350                 CONTINUE

                      IF (BETA.EQ.ZERO) THEN

                          C(I,J) = ALPHA*TEMP

                      ELSE

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

                      END IF

  360             CONTINUE

  370         CONTINUE

          END IF

      END IF

*

      RETURN

*

*     End of CGEMM .

*

      END