f06cb: FL CL CPP AD PY MB

NAG FL Interface
f06cbf (zrotgs)

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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

f06cb: FL CL CPP AD PY MB

▸▿ 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

f06cbf generates a complex Givens plane rotation having real sine.

2 Specification

Fortran Interface

Subroutine f06cbf (

a, b, c, s)

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

C Header Interface

#include <nag.h>

void	f06cbf_ (Complex a, Complex b, Complex c, double s)

The routine may be called by the names f06cbf or nagf_blas_zrotgs.

3 Description

f06cbf generates a complex Givens plane rotation with parameters

c

(complex) and

s

(real), such that, given complex

a

and

b

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

b

is real, then

d

is also real. On exit,

b

is overwritten by

t

, the tangent of the rotation;

c

and

s

can be reconstructed from the single stored value

t

, by a subsequent call to f06cdf.

| b | < ε | a |

and

Im (a) = 0

, where

ε

is the machine precision, the routine sets

c = 1

and

s = | t |

| b | < ε | a |

and

Im (a) \neq 0

, the routine sets

c = \frac{sign (Re (a)) a}{| a |} and s = | t |

Note that

t

is always set to

b / a

, unless overflow would occur, in which case the routine returns the value of the complex expression

(flmax \times sign (Re (b) / a), flmax \times sign (Im (b) / a));

flmax

is the real value given by

1 / (x02amf)

4 References

None.

5 Arguments

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

On exit: the value $t$ , the tangent of the rotation.
3: $c$ – Complex (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.