[R] branch cuts of atan()

[Robin Hankin]

Professor Ripley

thanks for this.  Always good to know that I'm not missing any 
documentation!

The source is clear;  formula 4.4.39 effectively has a branch cut at 
|z|=1.
A 'n' S show the standard branch cuts in their figure 4.4, which are 
different (they
were the ones I was expecting).  Mathematica and Maple both have branch 
cuts
matching ams-55.

Should the the Trig.Rd manpage   warn that the branch cuts are 
non-standard?
Simple workarounds exist to shift them to the standard place.

Is this type of concern worthy of a  bug report?


The archetype would be

  tan(atan(2))
[1] 2
 > tan(atan(2+0i))
[1] -0.5+0i
 >



best wishes

Robin





On May 16, 2005, at 10:23 am, Prof Brian Ripley wrote:

> On Mon, 16 May 2005, Robin Hankin wrote:
>
>> Hi
>>
>>> atan(1.0001+0i)
>> [1] -0.7853482+0i
>>> atan(0.9999+0i)
>> [1] 0.7853482+0i
>>>
>>
>>
>>
>> evidently atan()'s branch cuts aren't where I thought they were.
>>
>> Where do I look for documentation on this?
>
> In the sources.  Specifically for complex atan() in src/main/complex.c
>
> 	/* Complex Arctangent Function */
> 	/* Equation (4.4.39) Abramowitz and Stegun */
>
> static void z_atan(Rcomplex *r, Rcomplex *z)
> ...
>
>
> -- 
> Brian D. Ripley,                  ripley at stats.ox.ac.uk
> Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
> University of Oxford,             Tel:  +44 1865 272861 (self)
> 1 South Parks Road,                     +44 1865 272866 (PA)
> Oxford OX1 3TG, UK                Fax:  +44 1865 272595
>
>
--
Robin Hankin
Uncertainty Analyst
National Oceanography Centre, Southampton
European Way, Southampton SO14 3ZH, UK
  tel  023-8059-7743