zher2kf.f

      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