[SciPy-Dev] Q-function

[Robert Kern]

On Wed, Feb 17, 2016 at 2:57 PM, Eran Hof <eran.hof at gmail.com> wrote:
>
> Enough people devoted plenty of their time to write papers about it:
http://ieeexplore.ieee.org/search/searchresult.jsp?queryText=.QT.Q%20function.QT.&newsearch=true
>
> so I guess, a little comment in the documentation is in place. Adding to
that, as said for Matlab immigrants, it be nice that when searching this
function in scipy they'll get something.

Absolutely, please do add this to the documentation. Documenting common
aliases is greatly appreciated.

To answer your question about why erf() but not Q, erf() is essentially the
most normalized form of this function, so it can be implemented efficiently
and numerically accurately more easily than Q directly. But once
implemented, it is a good building block to implement the other variants
like the Q function.

You may then ask, quite astutely, why we also have erfc() which is just
1-erf(). The answer is that for different values, you want to use one or
another approximation. In some regions, erfc() is implemented to call
1-erf(). In other regions, erf() is implemented to call 1-erfc()! They have
disjoint regions in which their approximation is numerically accurate. Our
underlying special function library implements both for this reason. It was
easier just to expose both in scipy.special. Otherwise, I would also not
feel particularly compelled to expose an erfc() even though it is also
commonly encountered in the literature.

--
Robert Kern
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