F06CBF : NAG Library, Mark 24

NAG Library Routine Document

F06CBF

Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

1 Purpose

F06CBF generates a complex Givens plane rotation having real sine.

2 Specification

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 expression

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

flmax

is the real value given by

1 / (X02AMF)

5 Parameters

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.

NAG Library Routine Document

F06CBF

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

9 Example

NAG Library Routine DocumentF06CBF

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

9 Example

NAG Library Routine Document

F06CBF