ZSYRK(3)        BLAS routine of NEC Numeric Library Collection        ZSYRK(3)



NAME
       ZSYRK - perform one of the symmetric rank k operations  C := alpha*A*A'
       + beta*C,   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, * )

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   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   - 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 leading  n by n
              upper triangular part of the array C must contain the upper tri-
              angular  part   of the  symmetric matrix  and the strictly lower
              triangular part of C is not referenced.  On exit, the upper tri-
              angular  part of the array  C is overwritten by the upper trian-
              gular 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   symmet-
              ric  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.

       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.



BLAS routine                    16 October 1992                       ZSYRK(3)