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NAME
     zsyrk - perform one of the symmetric rank k  operations    C
     := alpha*A*A' + beta*C or C := alpha*A'*A + beta*C

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

     CHARACTER*1 UPLO, TRANS

     INTEGER N, K, LDA, LDC

     COMPLEX*16 ALPHA, BETA

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



     #include <sunperf.h>

     void zsyrk(char uplo, char trans, int n, int  k,  doublecom-
               plex  *zalpha,  doublecomplex  *za, int lda, doub-
               lecomplex * beta, doublecomplex *zc, int ldc) ;

PURPOSE
     ZSYRK  performs one of the symmetric rank k operations
     C := alpha*A*A' + beta*C or C := alpha*A'*A +  beta*C  where
     alpha  and  beta   are  scalars,   C is an  n by n symmetric
     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*A' + beta*C.
               TRANS = 'T' or 't'   C := alpha*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  =  'T'  or  't',   K
               specifies   the number of rows of the matrix A.  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.

     BETA      - COMPLEX*16      .
               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
               symmetric  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
               symmetric  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.

     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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