ZHER2(3)        BLAS routine of NEC Numeric Library Collection        ZHER2(3)



NAME
       ZHER2 - perform the hermitian rank 2 operation   A := alpha*x*conjg( y'
       ) + conjg( alpha )*y*conjg( x' ) + A

SYNOPSIS
       SUBROUTINE ZHER2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA )

           COMPLEX*16   ALPHA

           INTEGER      INCX, INCY, LDA, N

           CHARACTER*1  UPLO

           COMPLEX*16   A( LDA, * ), X( * ), Y( * )

PURPOSE
       ZHER2  performs the hermitian rank 2 operation

          A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A

       where alpha is a scalar, x and y are n element vectors and A is an n by
       n hermitian matrix.


PARAMETERS
       UPLO   - CHARACTER*1.
              On  entry,  UPLO specifies whether the upper or lower triangular
              part of the array A is to be referenced as follows:

              UPLO = 'U' or 'u'   Only the upper triangular part of A is to be
              referenced.

              UPLO = 'L' or 'l'   Only the lower triangular part of A is to be
              referenced.

              Unchanged on exit.

       N      - INTEGER.
              On entry, N specifies the order of the matrix A.  N must  be  at
              least zero.  Unchanged on exit.

       ALPHA  - COMPLEX*16      .
              On  entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       X      - COMPLEX*16       array of dimension at least
              ( 1 + ( n - 1 )*abs( INCX ) ).  Before  entry,  the  incremented
              array X must contain the n element vector x.  Unchanged on exit.

       INCX   - INTEGER.
              On entry, INCX specifies the increment for the  elements  of  X.
              INCX must not be zero.  Unchanged on exit.

       Y      - COMPLEX*16       array of dimension at least
              (  1  +  ( n - 1 )*abs( INCY ) ).  Before entry, the incremented
              array Y must contain the n element vector y.  Unchanged on exit.

       INCY   - INTEGER.
              On  entry,  INCY  specifies the increment for the elements of Y.
              INCY must not be zero.  Unchanged on exit.

       A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
              Before entry with  UPLO = 'U' or 'u', the leading n by  n  upper
              triangular part of the array A must contain the upper triangular
              part of the hermitian matrix and the strictly  lower  triangular
              part  of A is not referenced. On exit, the upper triangular part
              of the array A 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 A must contain
              the  lower  triangular  part  of  the  hermitian  matrix and the
              strictly upper triangular part of A is not referenced. On  exit,
              the  lower  triangular part of the array A 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.

       LDA    - INTEGER.
              On entry, LDA specifies the first dimension of A as declared  in
              the  calling  (sub)  program.  LDA must be at least max( 1, n ).
              Unchanged on exit.

              Level 2 Blas routine.

              -- Written on 22-October-1986.  Jack Dongarra, Argonne  National
              Lab.   Jeremy Du Croz, Nag Central Office.  Sven Hammarling, Nag
              Central Office.  Richard Hanson, Sandia National Labs.



BLAS routine                    16 October 1992                       ZHER2(3)