[mlpack] Numeric sensitivity of RangeSearch

[Li Dong]

This explanation is enough for me.

> 在 2014年3月25日，下午10:54，Ryan Curtin <gth671b at mail.gatech.edu> 写道：
> 
>> On Tue, Mar 25, 2014 at 10:34:12PM +0800, Li Dong wrote:
>> Hi Ryan,
>> 
>> Thanks for your quick fixing! It looks correct now. The tutorial is
>> the key resources for our users~ It would be better if you could give
>> some explanation for this change on the tutorial.
> 
> Ok, the updated tutorial has been deployed to the website.
> 
> A long time ago, the way trees and dual-tree algorithms worked in mlpack
> was different, and all of the pruning rules that were used for nearest
> neighbor search and range search worked in such a way that they did not
> depend on the triangle inequality.  This meant that the squared
> Euclidean distance worked as a distance measure, and could provide a bit
> of speedup because it avoided a call to sqrt().
> 
> However, more recent improvements included prunes that do depend on the
> triangle inequality, which means that an actual metric is required, and
> the squared Euclidean distance will no longer work.
> 
> I hope that's a better explanation.  Let me know if you'd like me to
> clarify further.
> 
> Thanks,
> 
> Ryan
> 
> -- 
> Ryan Curtin    | "Leave your stupid comments in your pocket!"
> ryan at ratml.org |   - Mark