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# zhpr

## man page of zhpr

### zhpr: perform the hermitian rank 1 operation A := alpha*x*conjg( x' ) + A,

```NAME
ZHPR  - perform 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*1 UPLO

COMPLEX*16  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.

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  - 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
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 )
respectively, 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.

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.

ZHPR(3)
```