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chpr

```
NAME
CHPR - perform the hermitian rank 1 operation   A :=
alpha*x*conjg( x' ) + A,

SYNOPSIS
SUBROUTINE CHPR ( UPLO, N, ALPHA, X, INCX, AP )

REAL        ALPHA

INTEGER     INCX, N

CHARACTER*1 UPLO

COMPLEX     AP( * ), X( * )

PURPOSE
CHPR    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.

PARAMETERS
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 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      - INTEGER.
On entry, N specifies the order of the matrix A.  N
must be at least zero.  Unchanged on exit.

ALPHA  - REAL            .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.

X      - COMPLEX          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 ele-
ments of X. INCX must not be zero.  Unchanged on

exit.

AP     - COMPLEX          array of DIMENSION at least
( ( n*( n + 1 ) )/2 ).  Before entry with  UPLO = 'U'
or 'u', the array AP must contain the upper triangu-
lar 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.  Before 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 ) respec-
tively, and so on. On exit, the array AP is overwrit-
ten by the lower triangular part of the updated
matrix.  Note that the imaginary parts of the diago-
nal elements need not be set, they are assumed to be
zero, and on exit they are set to zero.

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.
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