HP MLIB User's Guide Vol. 1 7th Ed.

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352 HP MLIB User’s Guide

F_CHPR2/F_ZHPR2 Hermitian rank-2 update

Name F_CHPR2/F_ZHPR2

Hermitian rank-2 update

Purpose F_xHPR2 performs the Hermitian rank-2 update

where A is an n-by-n complex Hermitian matrix stored in packed form, α is a

complex scalar, is the complex conjugate of α, x and y are complex n-vectors,

and x* and y* are the conjugate transposes of x and y, respectively. This routine

returns immediately if n is less than or equal to zero.

Refer to “SSPR2/DSPR2/CHPR2/ZHPR2” on page 259 for a description of the

equivalent HP MLIB legacy BLAS subprograms and an illustration of the

packed storage of symmetric or Hermitian matrices.

Matrix

Storage

Because either triangle of A can be obtained from the other, you only need to

provide one triangle of A, either the upper or the lower triangle. Compared to

storing the entire matrix, you save memory by supplying that triangle stored

column-by-column in packed form in a 1-dimensional array (refer to the AP

matrix).

Usage VECLIB

INTEGER*4 INCX, INCY, LDA, N, UPLO

REAL*4 BETA

COMPLEX*8 ALPHA, A( LDA, * ), X( * ), Y( * )

SUBROUTINE F_CHER2 (UPLO, N, ALPHA, X, INCX, Y, INCY, BETA, AP)

INTEGER*4 INCX, INCY, LDA, N, UPLO

REAL*8 BETA

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

SUBROUTINE F_ZHER2 (UPLO, N, ALPHA, X, INCX, Y, INCY, BETA, AP)

VECLIB8

INTEGER*8 INCX, INCY, LDA, N, UPLO