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NAME
     zher2k - perform 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

SYNOPSIS
     SUBROUTINE ZHER2K (UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB,
               BETA, C, LDC)

     CHARACTER*1 UPLO, TRANS

     INTEGER N, K, LDA, LDB, LDC

     DOUBLE PRECISION BETA

     COMPLEX*16 ALPHA

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



     #include <sunperf.h>

     void zher2k(char uplo, char trans, int n, int k,  doublecom-
               plex  *zalpha,  doublecomplex  *za, int lda, doub-
               lecomplex * b, int ldb, double  dbeta,  doublecom-
               plex *zc, int 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  speci-
               fies  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   other-
               wise.
               Before entry with  TRANS = 'N' or 'n',  the  lead-
               ing  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   other-
               wise.
               Before entry with  TRANS = 'N' or 'n',  the  lead-
               ing  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  lead-
               ing   n  by n upper triangular part of the array C
               must contain the upper  triangular  part   of  the
               hermitian  matrix  and the strictly lower triangu-
               lar part of C is not  referenced.   On  exit,  the
               upper triangular part of the array  C is overwrit-
               ten by the upper triangular part  of  the  updated
               matrix.
               Before entry  with  UPLO = 'L' or 'l',  the  lead-
               ing   n  by n lower triangular part of the array C
               must contain the lower  triangular  part   of  the
               hermitian  matrix  and the strictly upper triangu-
               lar part of C is not  referenced.   On  exit,  the
               lower triangular part of the array  C is overwrit-
               ten by the lower triangular part  of  the  updated
               matrix.
               Note that the imaginary parts of the diagonal ele-
               ments  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.

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