Re: [R] branch cuts of atan()

From: Robin Hankin <r.hankin_at_noc.soton.ac.uk>
Date: Mon 16 May 2005 - 21:17:44 EST

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@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

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Received on Mon May 16 21:20:44 2005

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