NAG Library Routine Document

f06chf (zrot2)

 Contents

    1  Purpose
    7  Accuracy
    10  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

Fortran Interface
Subroutine f06chf ( x, y, z, c, s)
Real (Kind=nag_wp), Intent (In):: c
Complex (Kind=nag_wp), Intent (In):: s
Complex (Kind=nag_wp), Intent (Inout):: x, y, z
C Header Interface
#include nagmk26.h
void  f06chf_ (Complex *x, Complex *y, Complex *z, const double *c, const Complex *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 argument 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
Arguments

1:     x – Complex (Kind=nag_wp)Input/Output
On entry: the value x, the 1,1  element of the input matrix.
On exit: the transformed value x.
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.
On exit: the transformed value z.
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
Parallelism and Performance

f06chf is not threaded in any implementation.

9
Further Comments

None.

10
Example

None.
© The Numerical Algorithms Group Ltd, Oxford, UK. 2017