F06CAF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06CAF

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.

▸▿ 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

F06CAF generates a complex Givens plane rotation having real cosine.

2  Specification

SUBROUTINE F06CAF ( A, B, C, S)
REAL (KIND=nag_wp)  C
COMPLEX (KIND=nag_wp)  A, B, S

3  Description

F06CAF generates a complex Givens plane rotation with parameters c (real ≥0) and s (complex), such that, given complex a and b:
c s- -s c a b = d 0 .  
If 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.
If b<εa, 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 × sign Reb /a , flmax × signImb / a ;  
flmax is the real value given by 1/X02AMF.

4  References

None.

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 – 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.

6  Error Indicators and Warnings

None.

7  Accuracy

Not applicable.

8  Parallelism and Performance

Not applicable.

9  Further Comments

None.

10  Example

None.
F06CAF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual
© The Numerical Algorithms Group Ltd, Oxford, UK. 2015