Least squares cholesky

[Recktenwald]

Thank you for contributing to FSharp.Stats. Please take the time to tell us a bit more about your PR.

This is related to Issue https://github.com/fslaborg/FSharp.Stats/issues/162

Closes https://github.com/fslaborg/FSharp.Stats/issues/162

Please list the changes introduced in this PR

• Add the option to use Cholesky Decomposition for OLS.
• Add tests for the univariable and multivariable version.

[Recktenwald]

If I'm reading the failed checks correctly, I got 'unlucky' with the random numbers for the test vector / test matrix. It does not seem like a problem in the code itself, just that Cholesky is relatively unstable. I will hard code a testcase instead.

[Recktenwald]

Oh I just noticed that I was giving the univariable testcase the same y as the multivariable case, which has a bigger error term. I fixed that. Would it still be better style to have a hardcoded testcase, than a random one?

[codecov-commenter]

Codecov Report

Merging #164 (acbdb42) into developer (cc228f4) will increase coverage by 0.41%. The diff coverage is 77.41%.

@@              Coverage Diff              @@
##           developer     #164      +/-   ##
=============================================
+ Coverage      17.37%   17.79%   +0.41%     
=============================================
  Files            114      114              
  Lines           9281     9312      +31     
  Branches        1148     1150       +2     
=============================================
+ Hits            1613     1657      +44     
+ Misses          7390     7369      -21     
- Partials         278      286       +8     

Impacted Files	Coverage Δ
src/FSharp.Stats/Algebra/LinearAlgebra.fs	11.66% <0.00%> (-0.20%)	:arrow_down:
tests/FSharp.Stats.Tests/Main.fs	0.00% <0.00%> (ø)
src/FSharp.Stats/Fitting/LinearRegression.fs	3.33% <50.00%> (+3.33%)	:arrow_up:
tests/FSharp.Stats.Tests/Fitting.fs	96.00% <94.11%> (-4.00%)	:arrow_down:
...Sharp.Stats/Algebra/LinearAlgebraServiceManaged.fs	17.91% <100.00%> (+3.72%)	:arrow_up:
src/FSharp.Stats/Distributions/Continuous.fs	14.88% <0.00%> (+2.87%)	:arrow_up:
src/FSharp.Stats/Random.fs	25.00% <0.00%> (+6.25%)	:arrow_up:

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[bvenn]

If the test with random samples may fail, a discrete case is preferred. Otherwise a hypothetical failure in the future would lead to unnecessary confusion while the methods works perfectly fine. If a failure of this method should be impossible the test you provided seems fine.