SUBROUTINE ZHER2KF( UPLO, TRANS, N, K, ALPHA, A, LDA, B,LDB, BETA,

     $                   C, LDC )

*     .. Scalar Arguments ..

      CHARACTER          TRANS, UPLO

      INTEGER            K, LDA, LDB, LDC, N

      DOUBLE PRECISION   BETA

      COMPLEX*16         ALPHA

*     ..

*     .. Array Arguments ..

      COMPLEX*16         A( LDA, * ), B( LDB, * ), C( LDC, * )

*     ..

*

*  Purpose

*  =======

*

*  ZHER2K  performs one of the hermitian rank 2k operations

*

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

*

*  or

*

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

*

*  where  alpha and beta  are scalars with  beta  real,  C is an  n by n

*  hermitian matrix and  A and B  are  n by k matrices in the first case

*  and  k by n  matrices in the second case.

*

*  Parameters

*  ==========

*

*  UPLO   - CHARACTER*1.

*           On  entry,   UPLO  specifies  whether  the  upper  or  lower

*           triangular  part  of the  array  C  is to be  referenced  as

*           follows:

*

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

*                                  is to be referenced.

*

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

*                                  is to be referenced.

*

*           Unchanged on exit.

*

*  TRANS  - CHARACTER*1.

*           On entry,  TRANS  specifies the operation to be performed as

*           follows:

*

*              TRANS = 'N' or 'n'    C := alpha*A*conjg( B' )          +

*                                         conjg( alpha )*B*conjg( A' ) +

*                                         beta*C.

*

*              TRANS = 'C' or 'c'    C := alpha*conjg( A' )*B          +

*                                         conjg( alpha )*conjg( B' )*A +

*                                         beta*C.

*

*           Unchanged on exit.

*

*  N      - INTEGER.

*           On entry,  N specifies the order of the matrix C.  N must be

*           at least zero.

*           Unchanged on exit.

*

*  K      - INTEGER.

*           On entry with  TRANS = 'N' or 'n',  K  specifies  the number

*           of  columns  of the  matrices  A and B,  and on  entry  with

*           TRANS = 'C' or 'c',  K  specifies  the number of rows of the

*           matrices  A and B.  K must be at least zero.

*           Unchanged on exit.

*

*  ALPHA  - COMPLEX*16         .

*           On entry, ALPHA specifies the scalar alpha.

*           Unchanged on exit.

*

*  A      - COMPLEX*16       array of DIMENSION ( LDA, ka ), where ka is

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

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

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

*           the leading  k by n  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  TRANS = 'N' or 'n'

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

*           be at least  max( 1, k ).

*           Unchanged on exit.

*

*  B      - COMPLEX*16       array of DIMENSION ( LDB, kb ), where kb is

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

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

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

*           the leading  k 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.   When  TRANS = 'N' or 'n'

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

*           be at least  max( 1, k ).

*           Unchanged on exit.

*

*  BETA   - DOUBLE PRECISION            .

*           On entry, BETA specifies the scalar beta.

*           Unchanged on exit.

*

*  C      - COMPLEX*16          array of DIMENSION ( LDC, n ).

*           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n

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

*           triangular part  of the  hermitian matrix  and the strictly

*           lower triangular part of C is not referenced.  On exit, the

*           upper triangular part of the array  C is overwritten by the

*           upper triangular part of the updated matrix.

*           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n

*           lower triangular part of the array C must contain the lower

*           triangular part  of the  hermitian matrix  and the strictly

*           upper triangular part of C is not referenced.  On exit, the

*           lower triangular part of the array  C is overwritten by the

*           lower triangular part of the updated matrix.

*           Note that the imaginary parts of the diagonal elements need

*           not be set,  they are assumed to be zero,  and on exit they

*           are set to zero.

*

*  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, n ).

*           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.

*

*  -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.

*     Ed Anderson, Cray Research Inc.

*

*

*     .. External Functions ..

      LOGICAL            LSAME

      EXTERNAL           LSAME

*     ..

*     .. External Subroutines ..

      EXTERNAL           XERBLA

*     ..

*     .. Intrinsic Functions ..

      INTRINSIC          DBLE, DCONJG, MAX

*     ..

*     .. Local Scalars ..

      LOGICAL            UPPER

      INTEGER            I, INFO, J, L, NROWA

      COMPLEX*16         TEMP1, TEMP2

*     ..

*     .. Parameters ..

      DOUBLE PRECISION   ONE

      PARAMETER          ( ONE = 1.0D+0 )

      COMPLEX*16         ZERO

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

*     ..

*     .. Executable Statements ..

*

*     Test the input parameters.

*

      IF( LSAME( TRANS, 'N' ) ) THEN

         NROWA = N

      ELSE

         NROWA = K

      END IF

      UPPER = LSAME( UPLO, 'U' )

*

      INFO = 0

      IF( ( .NOT.UPPER ) .AND. ( .NOT.LSAME( UPLO, 'L' ) ) ) THEN

         INFO = 1

      ELSE IF( ( .NOT.LSAME( TRANS, 'N' ) ) .AND.

     $         ( .NOT.LSAME( TRANS, 'C' ) ) ) THEN

         INFO = 2

      ELSE IF( N.LT.0 ) THEN

         INFO = 3

      ELSE IF( K.LT.0 ) THEN

         INFO = 4

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

         INFO = 7

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

         INFO = 9

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

         INFO = 12

      END IF

      IF( INFO.NE.0 ) THEN

         CALL XERBLA( 'ZHER2K', INFO )

         RETURN

      END IF

*

*     Quick return if possible.

*

      IF( ( 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( UPPER ) THEN

            IF( BETA.EQ.DBLE( ZERO ) ) THEN

               DO 20 J = 1, N

                  DO 10 I = 1, J

                     C( I, J ) = ZERO

   10             CONTINUE

   20          CONTINUE

            ELSE

               DO 40 J = 1, N

                  DO 30 I = 1, J - 1

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

   30             CONTINUE

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

   40          CONTINUE

            END IF

         ELSE

            IF( BETA.EQ.DBLE( ZERO ) ) THEN

               DO 60 J = 1, N

                  DO 50 I = J, N

                     C( I, J ) = ZERO

   50             CONTINUE

   60          CONTINUE

            ELSE

               DO 80 J = 1, N

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

                  DO 70 I = J + 1, N

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

   70             CONTINUE

   80          CONTINUE

            END IF

         END IF

         RETURN

      END IF

*

*     Start the operations.

*

      IF( LSAME( TRANS, 'N' ) ) THEN

*

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

*                   C.

*

         IF( UPPER ) THEN

            DO 130 J = 1, N

               IF( BETA.EQ.DBLE( ZERO ) ) THEN

                  DO 90 I = 1, J

                     C( I, J ) = ZERO

   90             CONTINUE

               ELSE IF( BETA.NE.ONE ) THEN

                  DO 100 I = 1, J - 1

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

  100             CONTINUE

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

               ELSE

                  C( J, J ) = DBLE( C( J, J ) )

               END IF

               DO 120 L = 1, K

                  IF( ( A( J, L ).NE.ZERO ) .OR. ( B( J, L ).NE.ZERO ) )

     $                 THEN

                     TEMP1 = ALPHA*DCONJG( B( J, L ) )

                     TEMP2 = DCONJG( ALPHA*A( J, L ) )

                     DO 110 I = 1, J - 1

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

     $                              B( I, L )*TEMP2

  110                CONTINUE

                     C( J, J ) = DBLE( C( J, J ) ) +

     $                           DBLE( A( J, L )*TEMP1+B( J, L )*TEMP2 )

                  END IF

  120          CONTINUE

  130       CONTINUE

         ELSE

            DO 180 J = 1, N

               IF( BETA.EQ.DBLE( ZERO ) ) THEN

                  DO 140 I = J, N

                     C( I, J ) = ZERO

  140             CONTINUE

               ELSE IF( BETA.NE.ONE ) THEN

                  DO 150 I = J + 1, N

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

  150             CONTINUE

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

               ELSE

                  C( J, J ) = DBLE( C( J, J ) )

               END IF

               DO 170 L = 1, K

                  IF( ( A( J, L ).NE.ZERO ) .OR. ( B( J, L ).NE.ZERO ) )

     $                 THEN

                     TEMP1 = ALPHA*DCONJG( B( J, L ) )

                     TEMP2 = DCONJG( ALPHA*A( J, L ) )

                     DO 160 I = J + 1, N

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

     $                              B( I, L )*TEMP2

  160                CONTINUE

                     C( J, J ) = DBLE( C( J, J ) ) +

     $                           DBLE( A( J, L )*TEMP1+B( J, L )*TEMP2 )

                  END IF

  170          CONTINUE

  180       CONTINUE

         END IF

      ELSE

*

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

*                   C.

*

         IF( UPPER ) THEN

            DO 210 J = 1, N

               DO 200 I = 1, J

                  TEMP1 = ZERO

                  TEMP2 = ZERO

                  DO 190 L = 1, K

                     TEMP1 = TEMP1 + DCONJG( A( L, I ) )*B( L, J )

                     TEMP2 = TEMP2 + DCONJG( B( L, I ) )*A( L, J )

  190             CONTINUE

                  IF( I.EQ.J ) THEN

                     IF( BETA.EQ.DBLE( ZERO ) ) THEN

                        C( J, J ) = DBLE( ALPHA*TEMP1+DCONJG( ALPHA )*

     $                              TEMP2 )

                     ELSE

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

     $                              DBLE( ALPHA*TEMP1+DCONJG( ALPHA )*

     $                              TEMP2 )

                     END IF

                  ELSE

                     IF( BETA.EQ.DBLE( ZERO ) ) THEN

                        C( I, J ) = ALPHA*TEMP1 + DCONJG( ALPHA )*TEMP2

                     ELSE

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

     $                              DCONJG( ALPHA )*TEMP2

                     END IF

                  END IF

  200          CONTINUE

  210       CONTINUE

         ELSE

            DO 240 J = 1, N

               DO 230 I = J, N

                  TEMP1 = ZERO

                  TEMP2 = ZERO

                  DO 220 L = 1, K

                     TEMP1 = TEMP1 + DCONJG( A( L, I ) )*B( L, J )

                     TEMP2 = TEMP2 + DCONJG( B( L, I ) )*A( L, J )

  220             CONTINUE

                  IF( I.EQ.J ) THEN

                     IF( BETA.EQ.DBLE( ZERO ) ) THEN

                        C( J, J ) = DBLE( ALPHA*TEMP1+DCONJG( ALPHA )*

     $                              TEMP2 )

                     ELSE

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

     $                              DBLE( ALPHA*TEMP1+DCONJG( ALPHA )*

     $                              TEMP2 )

                     END IF

                  ELSE

                     IF( BETA.EQ.DBLE( ZERO ) ) THEN

                        C( I, J ) = ALPHA*TEMP1 + DCONJG( ALPHA )*TEMP2

                     ELSE

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

     $                              DCONJG( ALPHA )*TEMP2

                     END IF

                  END IF

  230          CONTINUE

  240       CONTINUE

         END IF

      END IF

*

      RETURN

*

*     End of ZHER2K.

*

      END