```      SUBROUTINE ZHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
*     .. Scalar Arguments ..
DOUBLE PRECISION ALPHA,BETA
INTEGER K,LDA,LDC,N
CHARACTER TRANS,UPLO
*     ..
*     .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),C(LDC,*)
*     ..
*
*  Purpose
*  =======
*
*  ZHERK  performs one of the hermitian rank k operations
*
*     C := alpha*A*conjg( A' ) + beta*C,
*
*  or
*
*     C := alpha*conjg( A' )*A + beta*C,
*
*  where  alpha and beta  are  real scalars,  C is an  n by n  hermitian
*  matrix and  A  is an  n by k  matrix in the  first case and a  k by n
*  matrix in the second case.
*
*  Arguments
*  ==========
*
*  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( A' ) + beta*C.
*
*              TRANS = 'C' or 'c'   C := alpha*conjg( A' )*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   matrix   A,   and  on   entry   with
*           TRANS = 'C' or 'c',  K  specifies  the number of rows of the
*           matrix A.  K must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - DOUBLE PRECISION            .
*           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.
*
*  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,DCMPLX,DCONJG,MAX
*     ..
*     .. Local Scalars ..
DOUBLE COMPLEX TEMP
DOUBLE PRECISION RTEMP
INTEGER I,INFO,J,L,NROWA
LOGICAL UPPER
*     ..
*     .. Parameters ..
DOUBLE PRECISION ONE,ZERO
PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
*     ..
*
*     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 (LDC.LT.MAX(1,N)) THEN
INFO = 10
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('ZHERK ',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.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.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( A' ) + beta*C.
*
IF (UPPER) THEN
DO 130 J = 1,N
IF (BETA.EQ.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.DCMPLX(ZERO)) THEN
TEMP = ALPHA*DCONJG(A(J,L))
DO 110 I = 1,J - 1
C(I,J) = C(I,J) + TEMP*A(I,L)
110                     CONTINUE
C(J,J) = DBLE(C(J,J)) + DBLE(TEMP*A(I,L))
END IF
120             CONTINUE
130         CONTINUE
ELSE
DO 180 J = 1,N
IF (BETA.EQ.ZERO) THEN
DO 140 I = J,N
C(I,J) = ZERO
140                 CONTINUE
ELSE IF (BETA.NE.ONE) THEN
C(J,J) = BETA*DBLE(C(J,J))
DO 150 I = J + 1,N
C(I,J) = BETA*C(I,J)
150                 CONTINUE
ELSE
C(J,J) = DBLE(C(J,J))
END IF
DO 170 L = 1,K
IF (A(J,L).NE.DCMPLX(ZERO)) THEN
TEMP = ALPHA*DCONJG(A(J,L))
C(J,J) = DBLE(C(J,J)) + DBLE(TEMP*A(J,L))
DO 160 I = J + 1,N
C(I,J) = C(I,J) + TEMP*A(I,L)
160                     CONTINUE
END IF
170             CONTINUE
180         CONTINUE
END IF
ELSE
*
*        Form  C := alpha*conjg( A' )*A + beta*C.
*
IF (UPPER) THEN
DO 220 J = 1,N
DO 200 I = 1,J - 1
TEMP = ZERO
DO 190 L = 1,K
TEMP = TEMP + DCONJG(A(L,I))*A(L,J)
190                 CONTINUE
IF (BETA.EQ.ZERO) THEN
C(I,J) = ALPHA*TEMP
ELSE
C(I,J) = ALPHA*TEMP + BETA*C(I,J)
END IF
200             CONTINUE
RTEMP = ZERO
DO 210 L = 1,K
RTEMP = RTEMP + DCONJG(A(L,J))*A(L,J)
210             CONTINUE
IF (BETA.EQ.ZERO) THEN
C(J,J) = ALPHA*RTEMP
ELSE
C(J,J) = ALPHA*RTEMP + BETA*DBLE(C(J,J))
END IF
220         CONTINUE
ELSE
DO 260 J = 1,N
RTEMP = ZERO
DO 230 L = 1,K
RTEMP = RTEMP + DCONJG(A(L,J))*A(L,J)
230             CONTINUE
IF (BETA.EQ.ZERO) THEN
C(J,J) = ALPHA*RTEMP
ELSE
C(J,J) = ALPHA*RTEMP + BETA*DBLE(C(J,J))
END IF
DO 250 I = J + 1,N
TEMP = ZERO
DO 240 L = 1,K
TEMP = TEMP + DCONJG(A(L,I))*A(L,J)
240                 CONTINUE
IF (BETA.EQ.ZERO) THEN
C(I,J) = ALPHA*TEMP
ELSE
C(I,J) = ALPHA*TEMP + BETA*C(I,J)
END IF
250             CONTINUE
260         CONTINUE
END IF
END IF
*
RETURN
*
*     End of ZHERK .
*
END

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