NAG Library Routine Document

F06BAF

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

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

SUBROUTINE F06BAF (

A, B, C, S)

REAL (KIND=nag_wp)

A, B, C, S

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 (DROT); to apply it to a pair of complex vectors, call F06KPF (ZDROT).

4 References

None.

5 Parameters

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.

6 Error Indicators and Warnings

None.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Not applicable.

9 Further Comments

None.

10 Example

None.

F06BAF (PDF version)

F06 Chapter Contents

F06 Chapter Introduction

NAG Library Manual

NAG Library Routine DocumentF06BAF

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

NAG Library Routine Document

F06BAF