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+0iatan(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, [EMAIL PROTECTED] 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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