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NAME
     cherk - perform one of the Hermitian rank k  operations    C
     :=  alpha*A*conjg( A' ) + beta*C or C := alpha*conjg( A' )*A
     + beta*C

SYNOPSIS
     SUBROUTINE CHERK ( UPLO, TRANS, N, K, ALPHA, A,  LDA,  BETA,
               C, LDC )

     CHARACTER*1 UPLO, TRANS

     INTEGER N, K, LDA, LDC

     REAL ALPHA, BETA

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



     #include <sunperf.h>

     void cherk(char uplo, char trans, int n, int k, float alpha,
               complex  *ca,  int  lda, float sbeta, complex *cc,
               int ldc) ;

PURPOSE
     CHERK  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.


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(  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     - REAL            .
               On  entry,  ALPHA  specifies  the  scalar   alpha.
               Unchanged on exit.

     A         - COMPLEX          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
               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      - REAL            .
               On  entry,  BETA  specifies   the   scalar   beta.
               Unchanged on exit.

     C         - COMPLEX          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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