ZHPR(1) BLAS routine ZHPR(1)NAME
ZHPR - performs the hermitian rank 1 operation A := alpha*x*conjg( x'
) + A,
SYNOPSIS
SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP)
DOUBLE PRECISION ALPHA
INTEGER INCX,N
CHARACTER UPLO
DOUBLE COMPLEX AP(*),X(*)
PURPOSE
ZHPR performs the hermitian rank 1 operation
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 - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower triangular
part of the matrix A is supplied in the packed array AP as fol‐
lows:
UPLO = 'U' or 'u' The upper triangular part of A is supplied
in AP.
UPLO = 'L' or 'l' The lower triangular part of A is supplied
in AP.
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 - DOUBLE PRECISION.
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.
AP - COMPLEX*16 array of DIMENSION at least
( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u',
the array AP must contain the upper triangular part of the her‐
mitian matrix packed sequentially, column by column, so that AP(
1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
and a( 2, 2 ) respectively, and so on. On exit, the array AP is
overwritten by the upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the array AP must contain
the lower triangular part of the hermitian matrix packed sequen‐
tially, column by column, so that AP( 1 ) contains a( 1, 1 ),
AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respec‐
tively, and so on. On exit, the array AP 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.
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 ZHPR(1)