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AIX Version 4.3 Base Operating System and Extensions Technical Reference, Volume 2

## CHPR2 or ZHPR2 Subroutine

### Purpose

Performs the Hermitian rank 2 operation.

### Library

BLAS Library (libblas.a)

### FORTRAN Syntax

```SUBROUTINE CHPR2 (UPLO, N, ALPHA,
X, INCX, Y, INCY, AP)
COMPLEX ALPHA
INTEGER INCX,INCY,N
CHARACTER*1 UPLO
COMPLEX AP(*), X(*), Y(*)```
```SUBROUTINE
ZHPR2
COMPLEX*16 ALPHA
INTEGER INCX,INCY,N
CHARACTER*1 UPLO
COMPLEX*16 AP(*), X(*), Y(*)```

### Description

The CHPR2 or ZHPR2 subroutine 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.

### Parameters

UPLO On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows:
 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 On entry, N specifies the order of the matrix A; N must be at least 0; unchanged on exit.
ALPHA On entry, ALPHA specifies the scalar alpha; unchanged on exit.
X A vector of dimension at least (1 + (N-1) * abs(INCX) ); on entry, the incremented array X must contain the N element vector x; unchanged on exit.
INCX On entry, INCX specifies the increment for the elements of X; INCX must not be 0; unchanged on exit.
Y A vector of dimension at least (1 + (N-1) * abs( INCY ) ); on entry, the incremented array Y must contain the N element vector y; unchanged on exit.
INCY On entry, INCY specifies the increment for the elements of Y; INCY must not be 0; unchanged on exit.
AP A vector of dimension at least ( ( N * (N+1) )/2 ); on entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the Hermitian 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. On entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the Hermitian matrix packed sequentially, column by column, so that AP(1) contains A(1,1), AP(2) and AP(3) contain A(2,1) and A(3,1) respectively, and so on. On exit, the array AP is overwritten by the lower triangular part of the updated matrix. The imaginary parts of the diagonal elements need not be set, they are assumed to be 0, and on exit they are set to 0.

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