NAME

zhpr2 - perform the Hermitian rank 2 operation A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A

SYNOPSIS

  SUBROUTINE ZHPR2( UPLO, N, ALPHA, X, INCX, Y, INCY, A)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX ALPHA
  DOUBLE COMPLEX X(*), Y(*), A(*)
  INTEGER N, INCX, INCY

  SUBROUTINE ZHPR2_64( UPLO, N, ALPHA, X, INCX, Y, INCY, A)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX ALPHA
  DOUBLE COMPLEX X(*), Y(*), A(*)
  INTEGER*8 N, INCX, INCY

F95 INTERFACE

  SUBROUTINE HPR2( UPLO, [N], ALPHA, X, [INCX], Y, [INCY], A)
  CHARACTER(LEN=1) :: UPLO
  COMPLEX(8) :: ALPHA
  COMPLEX(8), DIMENSION(:) :: X, Y, A
  INTEGER :: N, INCX, INCY

  SUBROUTINE HPR2_64( UPLO, [N], ALPHA, X, [INCX], Y, [INCY], A)
  CHARACTER(LEN=1) :: UPLO
  COMPLEX(8) :: ALPHA
  COMPLEX(8), DIMENSION(:) :: X, Y, A
  INTEGER(8) :: N, INCX, INCY

C INTERFACE

#include <sunperf.h>

void zhpr2(char uplo, int n, doublecomplex alpha, doublecomplex *x, int incx, doublecomplex *y, int incy, doublecomplex *a);

void zhpr2_64(char uplo, long n, doublecomplex alpha, doublecomplex *x, long incx, doublecomplex *y, long incy, doublecomplex *a);

PURPOSE

zhpr2 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, supplied in packed form.

ARGUMENTS

UPLO (input)
On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array A as follows:
UPLO = 'U' or 'u' The upper triangular part of A is supplied in A.

UPLO = 'L' or 'l' The lower triangular part of A is supplied in A.

Unchanged on exit.
N (input)
On entry, N specifies the order of the matrix A. N > = 0. Unchanged on exit.
ALPHA (input)
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
X (input)
( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. Unchanged on exit.
INCX (input)
On entry, INCX specifies the increment for the elements of X. INCX < > 0. Unchanged on exit.
Y (input)
( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. Unchanged on exit.
INCY (input)
On entry, INCY specifies the increment for the elements of Y. INCY < > 0. Unchanged on exit.
A (input/output)
( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array A must contain the upper triangular part of the hermitian matrix packed sequentially, column by column, so that A( 1 ) contains a( 1, 1 ), A( 2 ) and A( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. On exit, the array A is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the array A must contain the lower triangular part of the hermitian matrix packed sequentially, column by column, so that A( 1 ) contains a( 1, 1 ), A( 2 ) and A( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. On exit, 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.