[WIP] dimension reduction playground

[odunbar]

Purpose

To-do

Content

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• I have read and checked the items on the review checklist.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 88.95%. Comparing base (b84a7f9) to head (1126784).
Report is 1 commits behind head on main.

Additional details and impacted files

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  Coverage   88.95%   88.95%           
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  Misses        150      150           

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[ArneBouillon]

After the refactor:

• We now have both a linear-exponential and a Lorenz test case
• We can compare the reduced posteriors using either EKS or MCMC
• The settings have been centralised in the file settings.jl
• Data and figure files are in their own folders, to keep everything clean
• I changed the .jl files to start with step1, step2, and step3, to hopefully make the code easier to approach

[ArneBouillon]

I currently changed the projection from/to the reduced spaces to purely using U_r/U_r'/V_r/V_r'.

I believe this is equivalent to what we did before, except for setting the coefficients of the "small" eigenvectors to zero instead of setting them to the corresponding (small) eigenvalues. I'm not sure which makes more sense.

We can change it back if you think the old way was better!