F06SQF (ZHPR) (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06SQF (ZHPR)

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

 Contents

    1  Purpose
    7  Accuracy
    10  Example

1  Purpose

F06SQF (ZHPR) computes the rank-1 update of a complex Hermitian matrix stored in packed form.

2  Specification

SUBROUTINE F06SQF ( UPLO, N, ALPHA, X, INCX, AP)
INTEGER  N, INCX
REAL (KIND=nag_wp)  ALPHA
COMPLEX (KIND=nag_wp)  X(*), AP(*)
CHARACTER(1)  UPLO
The routine may be called by its BLAS name zhpr.

3  Description

F06SQF (ZHPR) performs the Hermitian rank-1 update operation
AαxxH + A ,  
where A is an n by n complex Hermitian matrix, stored in packed form, x is an n-element complex vector, and α is a real scalar.

4  References

None.

5  Parameters

1:     UPLO – CHARACTER(1)Input
On entry: specifies whether the upper or lower triangular part of A is stored.
UPLO='U'
The upper triangular part of A is stored.
UPLO='L'
The lower triangular part of A is stored.
Constraint: UPLO='U' or 'L'.
2:     N – INTEGERInput
On entry: n, the order of the matrix A.
Constraint: N0.
3:     ALPHA – REAL (KIND=nag_wp)Input
On entry: the scalar α.
4:     X* – COMPLEX (KIND=nag_wp) arrayInput
Note: the dimension of the array X must be at least max1, 1+N-1 ×INCX .
On entry: the n-element vector x.
If INCX>0, xi must be stored in X1+i-1×INCX, for i=1,2,,N.
If INCX<0, xi must be stored in X1-N-i×INCX, for i=1,2,,N.
Intermediate elements of X are not referenced.
5:     INCX – INTEGERInput
On entry: the increment in the subscripts of X between successive elements of x.
Constraint: INCX0.
6:     AP* – COMPLEX (KIND=nag_wp) arrayInput/Output
Note: the dimension of the array AP must be at least N× N+1/2 .
On entry: the n by n Hermitian matrix A, packed by columns.
More precisely,
  • if UPLO='U', the upper triangle of A must be stored with element Aij in APi+jj-1/2 for ij;
  • if UPLO='L', the lower triangle of A must be stored with element Aij in APi+2n-jj-1/2 for ij.
On exit: the updated matrix A. The imaginary parts of the diagonal elements are set to zero.

6  Error Indicators and Warnings

None.

7  Accuracy

Not applicable.

8  Parallelism and Performance

Not applicable.

9  Further Comments

None.

10  Example

None.

F06SQF (ZHPR) (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2015