NAG CL Interface
f16sqc (zhpr)

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1 Purpose

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

2 Specification

#include <nag.h>
void  f16sqc (Nag_OrderType order, Nag_UploType uplo, Integer n, double alpha, const Complex x[], Integer incx, double beta, Complex ap[], NagError *fail)
The function may be called by the names: f16sqc, nag_blast_zhpr or nag_zhpr.

3 Description

f16sqc performs the Hermitian rank-1 update operation
AαxxH+βA,  
where A is an n×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 https://www.netlib.org/blas/blast-forum/blas-report.pdf

5 Arguments

1: order Nag_OrderType Input
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 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2: uplo Nag_UploType Input
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 Integer Input
On entry: n, the order of the matrix A.
Constraint: n0.
4: alpha double Input
On entry: the scalar α.
5: x[dim] const Complex Input
Note: the dimension, dim, of the array x must be at least max(1,1+(n-1)|incx|).
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 Integer Input
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
7: beta double Input
On entry: the scalar β.
8: ap[dim] Complex Input/Output
Note: the dimension, dim, of the array ap must be at least max(1, n × (n+1) / 2 ) .
On entry: the n×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 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface 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 8 in the Introduction to the NAG Library CL Interface 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

Background information to multithreading can be found in the Multithreading documentation.
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 4×4 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)