NAG Library Routine Document

f06cbf (zrotgs)

1
Purpose

f06cbf generates a complex Givens plane rotation having real sine.

2
Specification

Fortran Interface
Subroutine f06cbf ( a, b, c, s)
Real (Kind=nag_wp), Intent (Out):: s
Complex (Kind=nag_wp), Intent (Inout):: a, b
Complex (Kind=nag_wp), Intent (Out):: c
C Header Interface
#include <nagmk26.h>
void  f06cbf_ (Complex *a, Complex *b, Complex *c, double *s)

3
Description

f06cbf generates a complex Givens plane rotation with parameters c (complex) and s (real), such that, given complex a and b:
c- s -s c a b = d 0 ,  
If 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.
If b<εa and Ima=0, where ε is the machine precision, the routine sets c=1 and s=t.
If b<εa and Ima0, the routine sets
c=signReaa 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 × sign Reb /a , flmax × signImb / a ;  
flmax is the real value given by 1/x02amf.

4
References

None.

5
Arguments

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.

6
Error Indicators and Warnings

None.

7
Accuracy

Not applicable.

8
Parallelism and Performance

f06cbf is not threaded in any implementation.

9
Further Comments

None.

10
Example

None.