nag_zhpr (f16sqc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_zhpr (f16sqc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_zhpr (f16sqc) performs a Hermitian rank-1 update on a complex Hermitian matrix stored in packed form.

2  Specification

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

3  Description

nag_zhpr (f16sqc) performs the Hermitian rank-1 update operation
AαxxH+βA,
where A is an n by n complex Hermitian matrix, stored in packed form, x is an n-element complex vector, while α and β are real scalars.

4  References

The BLAS Technical Forum Standard (2001) http://www.netlib.org/blas/blast-forum

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 3.2.1.3 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.
uplo=Nag_Upper
The upper triangular part of A is stored.
uplo=Nag_Lower
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:     alphadoubleInput
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:     betadoubleInput
On entry: the scalar β.
8:     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.
9:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, incx=value.
Constraint: incx0.
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

None.

9  Example

Perform rank-1 update of complex Hermitian matrix A, stored in packed storage format, using vector x:
A A-xxH ,
where A is the 4 by 4 Hermitian matrix given by
A = 4.0+0.0i 7.0-4.0i -0.60+2.2i -4.0+3.0i 7.0+4.0i 14.0+0.0i 0.30+1.2i -4.7-2.1i -0.6-2.2i 0.3-1.2i 2.04+0.0i -5.9-0.1i -4.0-3.0i -4.7+2.1i -5.90+0.1i 6.0+0.0i ,
and
x = 2.0+1.0i 2.0+3.0i 0.2-1.0i -1.0-2.0i .

9.1  Program Text

Program Text (f16sqce.c)

9.2  Program Data

Program Data (f16sqce.d)

9.3  Program Results

Program Results (f16sqce.r)


nag_zhpr (f16sqc) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG C Library Manual

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