F06CHF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06CHF

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
    9  Example

1  Purpose

F06CHF applies a complex similarity rotation having real cosine and complex sine to a 2 by 2 complex Hermitian matrix.

2  Specification

SUBROUTINE F06CHF ( X, Y, Z, C, S)
REAL (KIND=nag_wp)  C
COMPLEX (KIND=nag_wp)  X, Y, Z, S

3  Description

F06CHF applies a complex similarity rotation, with parameters c (real) and s (complex), to a given 2 by 2 complex Hermitian matrix; that is, it performs the operation:
x y y- z c s- -s c x y y- z c -s- s c ,
where x and z are real.
The parameter X and Z which hold x and z are declared complex for convenience when using the routine to operate on submatrices of larger Hermitian matrices.
Note that:
z y- y x c w- -w c z y- y x c -w- w c ,
where w=-s-, so to use F06CHF when y is the 2,1 element of the matrix, you can make the call
CALL F06CHF(Z, Y, X, C, -CONJG(S))

4  References

None.

5  Parameters

1:     X – COMPLEX (KIND=nag_wp)Input/Output
On entry: the value x, the 1,1  element of the input matrix. The imaginary part of X need not be set; it is assumed to be zero.
On exit: the transformed value x. The imaginary part of X is set to zero.
2:     Y – COMPLEX (KIND=nag_wp)Input/Output
On entry: the value y, the 1,2  element of the input matrix.
On exit: the transformed value y.
3:     Z – COMPLEX (KIND=nag_wp)Input/Output
On entry: the value z, the 2,2  element of the input matrix. The imaginary part of Z need not be set; it is assumed to be zero.
On exit: the transformed value z. The imaginary part of Z is set to zero.
4:     C – REAL (KIND=nag_wp)Input
On entry: the value c, the cosine of the rotation.
5:     S – COMPLEX (KIND=nag_wp)Input
On entry: the value s, the sine of the rotation.

6  Error Indicators and Warnings

None.

7  Accuracy

Not applicable.

8  Further Comments

None.

9  Example

None.

F06CHF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

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