NAME

zhpr - perform the hermitian rank 1 operation A := alpha*x*conjg( x' ) + A

SYNOPSIS

  SUBROUTINE ZHPR( UPLO, N, ALPHA, X, INCX, A)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX X(*), A(*)
  INTEGER N, INCX
  DOUBLE PRECISION ALPHA

  SUBROUTINE ZHPR_64( UPLO, N, ALPHA, X, INCX, A)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX X(*), A(*)
  INTEGER*8 N, INCX
  DOUBLE PRECISION ALPHA

F95 INTERFACE

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

  SUBROUTINE HPR_64( UPLO, [N], ALPHA, X, [INCX], A)
  CHARACTER(LEN=1) :: UPLO
  COMPLEX(8), DIMENSION(:) :: X, A
  INTEGER(8) :: N, INCX
  REAL(8) :: ALPHA

C INTERFACE

#include <sunperf.h>

void zhpr(char uplo, int n, double alpha, doublecomplex *x, int incx, doublecomplex *a);

void zhpr_64(char uplo, long n, double alpha, doublecomplex *x, long incx, doublecomplex *a);

PURPOSE

zhpr performs the hermitian rank 1 operation A := alpha*x*conjg( x' ) + A where alpha is a real scalar, x is an n element vector 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.
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.