Why Python 3?

[Steven D'Aprano]

On Sun, 20 Apr 2014 14:40:38 -0700, Roy Smith wrote:

> In article <mailman.9383.1398012417.18130.python-list at python.org>,
>  Chris Angelico <rosuav at gmail.com> wrote:
> 
>> On Mon, Apr 21, 2014 at 2:22 AM, Ian Kelly <ian.g.kelly at gmail.com>
>> wrote:
>> > When I'm writing a generic average function, I probably don't know
>> > whether it will ever be used to average complex numbers.
>> 
>> This keeps coming up in these discussions. How often do you really
>> write a function that generic? And if you do, isn't it doing something
>> so simple that it's then the caller's responsibility (not the
>> function's, and not the language's) to ensure that it gets the right
>> result?
>> 
>> ChrisA
> 
> Hmmm.  Taking the average of a set of complex numbers has a reasonable
> physical meaning.  But, once you start down that path, I'm not sure how
> far you can go before things no long make sense.  What's the standard
> deviation of a set of complex numbers?  Does that even have any meaning?

Yes it does. Stdev is a measure of scale of the distribution, and is 
always real and non-negative. For complex values, you can calculate it 
using:

    (abs(x - mean))**2

which is how numpy does it, or from the complex conjugate:

    x1 = x-mean
    x1.conj()*x1


which is how Matlab does it.

http://docs.scipy.org/doc/numpy/reference/generated/numpy.std.html
http://www.mathworks.com.au/matlabcentral/newsreader/view_thread/57323


Hence the variance is always non-negative, and the standard deviation is 
always real. See also: 

https://en.wikipedia.org/wiki/Variance#Generalizations




-- 
Steven D'Aprano
http://import-that.dreamwidth.org/