NAG Library Routine Document

F06BAF

+− Contents

1 Purpose

9 Example

F06BAF generates a real Givens plane rotation and the tangent of that rotation.

SUBROUTINE F06BAF (

A, B, C, S)

REAL (KIND=nag_wp)

A, B, C, S

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.

None.

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.