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

Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001) Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard University of Tennessee, Knoxville, Tennessee http://www.netlib.org/blas/blast-forum/blas-report.pdf

5
Arguments

1:     order Nag_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 3.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2:     uplo Nag_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:     n IntegerInput
On entry: n, the order of the matrix A.
Constraint: n0.
4:     alpha doubleInput
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 n-element vector x.
If incx>0, xi must be stored in x[i-1×incx], for i=1,2,,n.
If incx<0, xi must be stored in x[n-i×incx], for i=1,2,,n.
Intermediate elements of x are not referenced. If n=0, x is not referenced and may be NULL.
6:     incx IntegerInput
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
7:     beta doubleInput
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:     fail NagError *Input/Output
The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6
Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
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.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

7
Accuracy

The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001)).

8
Parallelism and Performance

nag_zhpr (f16sqc) is not threaded in any implementation.

9
Further Comments

None.

10
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 .  

10.1
Program Text

Program Text (f16sqce.c)

10.2
Program Data

Program Data (f16sqce.d)

10.3
Program Results

Program Results (f16sqce.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017