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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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