[Rd] branch cuts in atan(), asin(), acos() (PR#7871)

[ripley at stats.ox.ac.uk]

On Mon, 16 May 2005 r.hankin at noc.soton.ac.uk wrote:

> The complex versions of atain(), asin(), acos() are not documented
> except in the source
> code.

Thank you, but your patch does not address that so they would become 
undocumented (they no longer follow the comment in the source code, which 
BTW is regarded as documentation).

Could you please supply documentation to match this change, including the 
exact definition you have implemented.

Also: have you looked at atan2?

> The branch cuts that are implemented do not tally with those of
> Abramowitz and Stegun,
> figure 4.4, p79.  The current branch cuts appear to be inherited from
> sqrt() and log(),
> in a non-obvious manner.
>
>
> Also, the current behaviour of atan() leads to the following:
>
>
> R> tan(atan(2))
> [1] 2
> R> tan(atan(2+0i))
> [1] -0.5+0i
>
> (I would expect  a value close to 2 in both these)
>
> R> atan(2)
> [1] 1.107149
> R> atan(2+0i)
> [1] -0.4636476+0i
> >
>
> (I would expect these two expressions to evaluate to numbers with small
> absolute
> difference)
>
>
> > atan(1.0001+0i)
> [1] -0.7853482+0i
> > atan(0.9999+0i)
> [1] 0.7853482+0i
> >
>
> (I would expect these two expressions to evaluate to numbers with small
> absolute
> difference)
>
>
> The following patch to src/main/complex.c
> appears to implement the desired behaviour:<
>
>
> octopus:~/downloads/R-2.1.0/src/main% diff -c complex.c
> /Users/rksh/unix/rksh/complex.c
> *** complex.c   Mon Apr 18 22:30:00 2005
> --- /Users/rksh/unix/rksh/complex.c     Mon May 16 14:33:15 2005
> ***************
> *** 367,372 ****
> --- 367,376 ----
>       bet = t1 - t2;
>       r->r = asin(bet);
>       r->i = log(alpha + sqrt(alpha*alpha - 1));
> +
> +     if(y<0){
> +       r->i *= -1;
> +       }
>   }
>
>   static void z_acos(Rcomplex *r, Rcomplex *z)
> ***************
> *** 388,393 ****
> --- 392,404 ----
>       r->r = 0.5 * atan(2 * x / ( 1 - x * x - y * y));
>       r->i = 0.25 * log((x * x + (y + 1) * (y + 1)) /
>                       (x * x + (y - 1) * (y - 1)));
> +
> +     if((x*x+y*y > 1) && x>0){
> +       r->r += M_PI_2;
> +       }
> +     if((x*x+y*y > 1) && x<0){
> +       r->r -= M_PI_2;
> +       }
>   }
>
>   static void z_atan2(Rcomplex *r, Rcomplex *csn, Rcomplex *ccs)
> octopus:~/downloads/R-2.1.0/src/main%
>
>
>
>
>
>
>
>
> --
> Robin Hankin
> Uncertainty Analyst
> National Oceanography Centre, Southampton
> European Way, Southampton SO14 3ZH, UK
>  tel  023-8059-7743
>
> ______________________________________________
> R-devel at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel
>
>

-- 
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