[WIP] convergence plots for Emulator examples & a bugfix

[odunbar]

Purpose

Adds convergence plots over many repeats of Emulator experiments Closes #278

To-do

• improve the extraction of EKI diagnostics or other information from training (e.g. EKI itself?) currently get_optimizer only returns diagnostics
• neaten plots (e.g. start them at iteration 0, consistent axis labels etc)

Content

• adds repeats for the EDMF example
• adds convergence plots (normalized by the initiali iteration to error=1) for Emulator/Ishigami, Emulator/L63, and EDMF_data/
• adds a way of extracting the error of EKI
• bugfixes the scalar RF index error

Example convergence plots

From the current example library - the plots look like this:

Ishigami (14 params)

L63 (41 params) - NB log-scale

EDMF (634 params)

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

[codecov[bot]]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 88.35%. Comparing base (acf1051) to head (42ca861). Report is 17 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #279      +/-   ##
==========================================
+ Coverage   88.17%   88.35%   +0.18%     
==========================================
  Files           8        8              
  Lines        1184     1194      +10     
==========================================
+ Hits         1044     1055      +11     
+ Misses        140      139       -1     

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[odunbar]

Merging to support code availability in the submission https://arxiv.org/abs/2407.00584