Substitute unnecessary matrix inversion, use linear solve instead.

[ilopezgp]

This PR solves issue #73 . Inverting the observational covariance matrix is not necessary, a linear solve can be used instead. The linear solve is faster and more accurate, which can be important when the observational covariance matrix is large or ill-conditioned.

[codecov]

Codecov Report

Merging #74 into master will decrease coverage by 0.08%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master      #74      +/-   ##
==========================================
- Coverage   81.99%   81.90%   -0.09%     
==========================================
  Files           7        7              
  Lines         422      420       -2     
==========================================
- Hits          346      344       -2     
  Misses         76       76              

Impacted Files	Coverage Δ
src/MCMC.jl	76.59% <100.00%> (-0.49%)	⬇️

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[ilopezgp]

@odunbar I ran the test/MCMC/runtests.jl with this version of the code. It takes an average of 12.8 s to run with my computer. I ran the same test with master and it took an average of 13.5 s to run. At least for the MCMC test, this is faster. This PR always uses a linear solve with a diagonal matrix (stored as a Diagonal type), so the linear solve seems to be quick enough to not slow down the code.

[odunbar]

Yeah I expected if the type was recognized, then it would hopefully do something more efficient! Good to know. I'm happy for this to be merged

[ilopezgp]

bors r+

[bors]

Build succeeded:

• test-linux
• test-macos
• test-windows