[ruby-core:74609] Re: [Ruby trunk Feature#12222] Introducing basic statistics methods for Enumerable (and optimized implementation for Array)

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On Sun, Mar 27, 2016 at 10:10 PM, <[e-mail]> wrote:

> Issue #12222 has been updated by Kenta Murata.
>
>
> > Especially I want to provide Enumerable#mean and Enumerable#variance as
> built-in features because they should be implemented by precision
> compensated algorithms.
>
> Sorry, I don't want to make them be a built-in features. But I want to
> make them a standard library features, at least.
>
>
> ----------------------------------------
> Feature #12222: Introducing basic statistics methods for Enumerable (and
> optimized implementation for Array)
> https://bugs.ruby-lang.org/issues/12222#change-57736
>
> * Author: Kenta Murata
> * Status: Assigned
> * Priority: Normal
> * Assignee: Yukihiro Matsumoto
> ----------------------------------------
> As python has statistics library for calculating mean, variance, etc. of
> arrays and iterators from version 3.4,
> I would like to propose to introduce such features for built-in
> Enumerable, and optimized implementation for Array.
>
> Especially I want to provide Enumerable#mean and Enumerable#variance as
> built-in features because they should be implemented by precision
> compensated algorithms.
> The following example shows that we couldn't calculate the standard
> deviation for some arrays with simple variance algorithm because we get
> negative variance numbers.
>
> ```ruby
> class Array
>   # Kahan summation
>   def sum
>     s = 0.0
>     c = 0.0
>     n = self.length
>     i = 0
>     while i < n
>       y = self[i] - c
>       t = s + y
>       c = (t - s) - y
>       s = t
>       i += 1
>     end
>     s
>   end
>
>   # precision compensated algorithm
>   def variance
>     n = self.length
>     return Float::NAN if n < 2
>     m1 = 0.0
>     m2 = 0.0
>     i = 0
>     while i < n
>       x = self[i]
>       delta = x - m1
>       m1 += delta / (i + 1)
>       m2 += delta*(x - m1)
>       i += 1
>     end
>     m2 / (n - 1)
>   end
> end
>
> ary = [ 1.0000000081806004, 1.0000000009124625, 1.0000000099201818,
> 1.0000000061821668, 1.0000000042644555 ]
>
> # simple variance algorithm
> a = ary.map {|x| x ** 2 }.sum
> b = ary.sum ** 2 / ary.length
> p (a - b) / (ary.length - 1)  #=> -2.220446049250313e-16
>
> # precision compensated algorithm
> p ary.variance  #=> 1.2248208046392579e-17
> ```
>
> I think precision compensated algorithm is too complicated to let users
> implement it.
>
>
>
> --
> https://bugs.ruby-lang.org/
>
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