NAG FL Interface
f06chf (zrot2)

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1 Purpose

f06chf applies a complex similarity rotation having real cosine and complex sine to a 2×2 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 <nag.h>
void  f06chf_ (Complex *x, Complex *y, Complex *z, const double *c, const Complex *s)
The routine may be called by the names f06chf or nagf_blas_zrot2.

3 Description

f06chf applies a complex similarity rotation, with parameters c (real) and s (complex), to a given 2×2 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

Background information to multithreading can be found in the Multithreading documentation.
f06chf is not threaded in any implementation.

9 Further Comments

None.

10 Example

None.