# zhpr2.f - Man Page

BLAS/SRC/zhpr2.f

## Synopsis

### Functions/Subroutines

subroutine zhpr2 (uplo, n, alpha, x, incx, y, incy, ap)
ZHPR2

## Function/Subroutine Documentation

### subroutine zhpr2 (character uplo, integer n, complex*16 alpha, complex*16, dimension(*) x, integer incx, complex*16, dimension(*) y, integer incy, complex*16, dimension(*) ap)

ZHPR2

Purpose:

``` ZHPR2  performs the hermitian rank 2 operation

A := alpha*x*y**H + conjg( alpha )*y*x**H + 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

```          UPLO is 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.```

N

```          N is INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.```

ALPHA

```          ALPHA is COMPLEX*16
On entry, ALPHA specifies the scalar alpha.```

X

```          X is COMPLEX*16 array, dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x.```

INCX

```          INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.```

Y

```          Y is COMPLEX*16 array, dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y.```

INCY

```          INCY is INTEGER
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.```

AP

```          AP is COMPLEX*16 array, 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.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Further Details:

```  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.```

Definition at line 144 of file zhpr2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zhpr2(3) is an alias of zhpr2.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK