NAG Library Routine Document

F06CAF

+− Contents

1 Purpose

9 Example

F06CAF generates a complex Givens plane rotation having real cosine.

SUBROUTINE F06CAF (

A, B, C, S)

REAL (KIND=nag_wp)	C
COMPLEX (KIND=nag_wp)	A, B, S

F06CAF generates a complex Givens plane rotation with parameters

c

(real

\geq 0

) and

s

(complex), such that, given complex

a

and

b

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

a

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 F06CCF.

|b| < ε |a|

, where

ε

is the machine precision, the routine sets

c = 1

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 expression

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

flmax

is the real value given by

1 / (X02AMF)

None.

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 – REAL (KIND=nag_wp)Output: On exit: the value $c$ , the cosine of the rotation.
4: S – COMPLEX (KIND=nag_wp)Output: On exit: the value $s$ , the sine of the rotation.