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# Technical Reference: Base Operating System and Extensions , Volume 2

## CHPR or ZHPR Subroutine

### Purpose

Performs the Hermitian rank 1 operation.

### Library

BLAS Library (libblas.a)

### FORTRAN Syntax

SUBROUTINE CHPR(UPLO, N, ALPHA,
X, INCX, AP)
REAL ALPHA
INTEGER INCX, N
CHARACTER*1 UPLO
COMPLEX AP(*), X(*)

```SUBROUTINE ZHPR(UPLO, N, ALPHA,
X, INCX, AP)
DOUBLE PRECISION ALPHA
INTEGER INCX,N
CHARACTER*1 UPLO
COMPLEX*16 AP(*), X(*)
```

### Description

The CHPR or ZHPR subroutine 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.

### 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. 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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