NAG Library Manual, Mark 28.6

Interfaces: FL CL CPP AD PY MB

NAG FL Interface Introduction

F06 (Blas) Chapter Contents

F06 (Blas) Chapter Introduction

f06aa: FL CL CPP AD PY MB

NAG FL Interface
f06aaf (drotg)

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NAG Library Manual, Mark 28.6

Interfaces: FL CL CPP AD PY MB

NAG FL Interface Introduction

F06 (Blas) Chapter Contents

F06 (Blas) Chapter Introduction

f06aa: FL CL CPP AD PY MB

▸▿ Contents

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

8 Parallelism and Performance

9 Further Comments

© The Numerical Algorithms Group Ltd. 2022

1 Purpose

f06aaf generates a real Givens plane rotation.

2 Specification

Fortran Interface

Subroutine f06aaf (

a, b, c, s)

Real (Kind=nag_wp), Intent (Inout)	::	a, b
Real (Kind=nag_wp), Intent (Out)	::	c, s

C Header Interface

#include <nag.h>

void	f06aaf_ (double a, double b, double c, double s)

The routine may be called by the names f06aaf, nagf_blas_drotg or its BLAS name drotg.

3 Description

f06aaf generates a real Givens plane rotation with parameters

c

and

s

, such that, given real

a

and

b

:

(\begin{array}{rc} c & s \\ - s & c \end{array}) (\begin{matrix} a \\ b \end{matrix}) = (\begin{matrix} d \\ 0 \end{matrix}) .

The routine computes

c

,

s

and

d

as follows:

d = σ \sqrt{a^{2} + b^{2}};

c = {\begin{cases} a / d, & if ​ d \neq 0, \\ 1, & if ​ d = 0, \end{cases} s = {\begin{cases} b / d, & if ​ d \neq 0, \\ 0, & if ​ d = 0, \end{cases}

where σ = {\begin{cases} sign a, & if ​ | a | > | b |, \\ sign b, & if ​ | a | \leq | b | . \end{cases}

The routine also computes the value

z

defined as

z = {\begin{cases} s, & if ​ | s | < c ​ or ​ c = 0, \\ 1 / c, & if ​ 0 < | c | \leq s . \end{cases}

This enables

c

and

s

to be reconstructed from the single value

z

as

c = {\begin{cases} \sqrt{1 - z^{2}}, & if ​ | z | \leq 1, \\ 1 / z, & if ​ | z | > 1, \end{cases} s = {\begin{cases} z, & if ​ | z | \leq 1, \\ \sqrt{1 - c^{2}}, & if ​ | z | > 1 . \end{cases}

To apply the plane rotation to a pair of real vectors, call f06epf; to apply it to a pair of complex vectors, call f06kpf.

4 References

None.

5 Arguments

1: $a$ – Real (Kind=nag_wp) Input/Output: On entry: the value $a$ , the first element of the vector which determines the rotation.

On exit: the value $d$ .
2: $b$ – Real (Kind=nag_wp) Input/Output: On entry: the value $b$ , the second element of the vector which determines the rotation.

On exit: the value $z$ , from which $c$ and $s$ can be reconstructed.
3: $c$ – Real (Kind=nag_wp) Output: On exit: the value $c$ , the cosine of the rotation.
4: $s$ – Real (Kind=nag_wp) Output: On exit: 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.

f06aaf is not threaded in any implementation.

9 Further Comments

None.

10 Example

None.

NAG Library Manual, Mark 28.6

Interfaces: FL CL CPP AD PY MB

NAG FL Interface Introduction

F06 (Blas) Chapter Contents

F06 (Blas) Chapter Introduction

f06aa: FL CL CPP AD PY MB

© The Numerical Algorithms Group Ltd. 2022