minkowski distance

[s-weil]

Please reference the issue(s) this PR is related to

Closes #182

Please list the changes introduced in this PR

• Minkowski distance in DistanceMetrics.fs for vectors, arrays and sequences

Description

Implement the Minkowski distance of order p in several versions, following https://en.wikipedia.org/wiki/Minkowski_distance and #182

[Required] please make sure you checked that

• [ x] The project builds without problems on your machine

[Optional]

• [ x] Added unit tests regarding the added features

[s-weil]

Note that in a separate issue, one could try to tackle code duplications in the src and tests of distance metrics.
This however may affect performance and must be conducted carefully.

[bvenn]

Is there a reason you didnt use abs (v1.[i] - v2.[i]) to determine the absolute difference?

[s-weil]

Other functions, such as cityblockNaN used System.Math.Abs
So I wanted to keep it aligned, but I am more than happy to change it

Updated

[bvenn]

Thanks for the addition! From the Wikipedia diagram I assume p could also be 0 < p <= 1, but I did not went deeper into research. Is there a reason you constrain p to be an integer? Or did I miss something?

[s-weil]

Regarding that p could also be 0 < p < 1 and restricting it to be an integer, I may have been a bit too strict on the given signature specified in #296
Also it was specified to be an integer in https://en.wikipedia.org/wiki/Minkowski_distance

Happy to change it to a float for a more generic version. It may affect performance though.

If it becomes a float, I can also handle the case when 0 < p <1 by removing the exponent 1/p as described in Wiki.

[s-weil]

Pushed the feedback.

The order p is now a float and the case 0 < p < 1 is covered

[codecov-commenter]

Codecov Report

Merging #308 (9d38186) into developer (1e680b1) will increase coverage by 0.27%.
Report is 12 commits behind head on developer.
The diff coverage is 79.57%.

@@              Coverage Diff              @@
##           developer     #308      +/-   ##
=============================================
+ Coverage      46.73%   47.00%   +0.27%     
=============================================
  Files            148      148              
  Lines          16225    16458     +233     
  Branches        2196     2219      +23     
=============================================
+ Hits            7582     7736     +154     
- Misses          7987     8052      +65     
- Partials         656      670      +14     

Files	Coverage Δ
tests/FSharp.Stats.Tests/DistanceMetrics.fs	100.00% <100.00%> (ø)
src/FSharp.Stats/DistanceMetrics.fs	25.23% <43.52%> (-15.68%)	⬇️

... and 71 files with indirect coverage changes