f06ch: FL CL CPP AD

NAG FL Interface
f06chf (zrot2)

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NAG Library Manual, Mark 27.3

Interfaces: FL CL CPP AD

NAG FL Interface Introduction

F06 (Blas) Chapter Contents

F06 (Blas) Chapter Introduction

f06ch: FL CL CPP AD

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

1 Purpose

f06chf applies a complex similarity rotation having real cosine and complex sine to a

2 \times 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 \times 2

complex Hermitian matrix; that is, it performs the operation:

(\begin{matrix} x & y \\ \bar{y} & z \end{matrix}) \leftarrow (\begin{array}{rc} c & \bar{s} \\ - s & c \end{array}) (\begin{matrix} x & y \\ \bar{y} & z \end{matrix}) (\begin{array}{rc} c & - \bar{s} \\ s & c \end{array}),

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:

(\begin{matrix} z & \bar{y} \\ y & x \end{matrix}) \leftarrow (\begin{array}{rc} c & \bar{w} \\ - w & c \end{array}) (\begin{matrix} z & \bar{y} \\ y & x \end{matrix}) (\begin{array}{rc} c & - \bar{w} \\ w & c \end{array}),

where

w = - \bar{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.