nag_zhpr2 (f16ssc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_zhpr2 (f16ssc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_zhpr2 (f16ssc) performs a Hermitian rank-2 update on a complex Hermitian matrix stored in packed form.

2  Specification

#include <nag.h>
#include <nagf16.h>
void  nag_zhpr2 (Nag_OrderType order, Nag_UploType uplo, Integer n, Complex alpha, const Complex x[], Integer incx, const Complex y[], Integer incy, double beta, Complex ap[], NagError *fail)

3  Description

nag_zhpr2 (f16ssc) performs the Hermitian rank-2 update operation
A α x yH + α- y xH + β A ,
where A is an n by n complex Hermitian matrix, stored in packed form, x and y are n-element complex vectors, while α is a complex scalar and β is a real scalar.

4  References

The BLAS Technical Forum Standard (2001)

5  Arguments

1:     orderNag_OrderTypeInput
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by order=Nag_RowMajor. See Section in the Essential Introduction for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2:     uploNag_UploTypeInput
On entry: specifies whether the upper or lower triangular part of A is stored.
The upper triangular part of A is stored.
The lower triangular part of A is stored.
Constraint: uplo=Nag_Upper or Nag_Lower.
3:     nIntegerInput
On entry: n, the order of the matrix A.
Constraint: n0.
4:     alphaComplexInput
On entry: the scalar α.
5:     x[dim]const ComplexInput
Note: the dimension, dim, of the array x must be at least max1,1+n-1incx.
On entry: the vector x.
6:     incxIntegerInput
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
7:     y[dim]const ComplexInput
Note: the dimension, dim, of the array y must be at least max1,1+n-1incy.
On entry: the vector y.
8:     incyIntegerInput
On entry: the increment in the subscripts of y between successive elements of y.
Constraint: incy0.
9:     betadoubleInput
On entry: the scalar β.
10:   ap[dim]ComplexInput/Output
Note: the dimension, dim, of the array ap must be at least max1, n × n+1 / 2 .
On entry: the n by n Hermitian matrix A, packed by rows or columns.
The storage of elements Aij depends on the order and uplo arguments as follows:
  • if order=Nag_ColMajor and uplo=Nag_Upper,
              Aij is stored in ap[j-1×j/2+i-1], for ij;
  • if order=Nag_ColMajor and uplo=Nag_Lower,
              Aij is stored in ap[2n-j×j-1/2+i-1], for ij;
  • if order=Nag_RowMajor and uplo=Nag_Upper,
              Aij is stored in ap[2n-i×i-1/2+j-1], for ij;
  • if order=Nag_RowMajor and uplo=Nag_Lower,
              Aij is stored in ap[i-1×i/2+j-1], for ij.
On exit: the updated matrix A. The imaginary parts of the diagonal elements are set to zero.
11:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

On entry, argument value had an illegal value.
On entry, incx=value.
Constraint: incx0.
On entry, incy=value.
Constraint: incy0.
On entry, n=value.
Constraint: n0.

7  Accuracy

The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of The BLAS Technical Forum Standard (2001)).

8  Further Comments


9  Example

Perform rank-2 update of complex Hermitian matrix A, stored using packed storage format, using vectors x and y:
A A - x yH - y xH ,
where A is the 4 by 4 matrix given by
A = 23.0+00.0i 10.0-17.0i 13.0+14.2i -19.0+8.0i 10.0+17.0i 1.0+00.0i 0.3+01.2i -4.7-2.1i 13.0-14.2i 0.3-01.2i 1.0+00.0i -5.9-0.1i -19.0-08.0i -4.7+02.1i -5.9+00.1i 1.0+0.0i ,
and where
x = 2.0+1.0i 2.0+3.0i 0.2-1.0i -1.0-2.0i
y = 5.0+1.0i -2.0+1.0i 7.0-1.0i -5.0-2.0i .
The vector y is stored in every second element of array y (incy=2).

9.1  Program Text

Program Text (f16ssce.c)

9.2  Program Data

Program Data (f16ssce.d)

9.3  Program Results

Program Results (f16ssce.r)

nag_zhpr2 (f16ssc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012