f06ba: FL CL CPP AD PY MB

NAG FL Interface
f06baf (drotgc)

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NAG Library Manual, Mark 29

Interfaces: FL CL CPP AD PY MB

NAG FL Interface Introduction

F06 (Blas) Chapter Contents

F06 (Blas) Chapter Introduction

f06ba: 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

f06baf generates a real Givens plane rotation and the tangent of that rotation.

2 Specification

Fortran Interface

Subroutine f06baf (

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	f06baf_ (double a, double b, double c, double s)

The routine may be called by the names f06baf or nagf_blas_drotgc.

3 Description

f06baf generates a real Givens plane rotation with parameters

c

(

\geq 0

) 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}) .

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 f06bcf.

| b | < \sqrt{ε} | a |

, where

ε

is the machine precision, the routine sets

c = 1

and

s = 0

; if

| a | < \sqrt{ε} | b |

, the routine sets

c = 0

and

s = sign b / a

Note that

t

is always set to

b / a

, unless this would overflow, in which case the value

flmax \times sign b / a

is returned, where

flmax

is the value given by

1 / (x02amf)

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 $t$ , the tangent of the rotation.
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.