zher2

ZHER2(1)                         BLAS routine                         ZHER2(1)



NAME
       ZHER2 - performs 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)

           DOUBLE                                         COMPLEX ALPHA

           INTEGER                                        INCX,INCY,LDA,N

           CHARACTER                                      UPLO

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

PURPOSE
       ZHER2  performs the hermitian rank 2 operation

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


ARGUMENTS
       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.

FURTHER DETAILS
       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                     November 2008                        ZHER2(1)