Re: [eigen] MathFunctions.h patch

[grey_earl@xxxxxx]

At least from my experience, there is a widely used choice for the complex 
square root function.
This is defined by having a branch cut on the negative real axis and then 
using leaf 0, i.e. for
z = abs{z} exp(I phi) with -Pi < phi <= Pi we have
sqrt(z) = sqrt(abs(z)) exp(I phi/2) and sqrt(abs(z)) >= 0
or alternatively by the condition Re(sqrt(z)) >= 0
The exact position of the branch cut (i.e., whether to include Pi or -Pi) is 
debatable, the above is what I would expect when 0 doesn't have a sign; if 
there is -0 then no ambiguities can arise. AFAIK, the C++98  and the C99 
standard defines it in exactly this way, too, as well as the GNU libc, gsl and 
the GiNaC library.

I have a use case where I do analytic approximations to a numerically 
calculated space-time in numerical relativity and the branch cut is chosen in 
exactly this way, but this is not Eigen-ified yet.

Regards, Markus

Am Donnerstag, 7. Januar 2010 schrieb Benoit Jacob:
> It is on purpose that we excluded sqrt for complex numbers:
>  - there is no canonical choice between the 2 determinations of the square
>  root. - no important use case was known to us.
> 
> Do you have a use case?
> 
> Benoit
> 
> 2010/1/7 Trevor Irons <trevorirons@xxxxxxxxx>:
> > Any problem adding the following patch, or something similiar, to
> > MathFunctions.h to support std::complex<>.sqrt() ?
> >
> > 218d217
> > < inline std::complex<float> ei_sqrt(std::complex<float>x)  { return
> > std::sqrt(x); }
> > 256d254
> > < inline std::complex<double> ei_sqrt(std::complex<double>x)  { return
> > std::sqrt(x); }
> >
> >
> > -trevor
>