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Create sanity checks #41

@patnr

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@patnr

There should be tests that make sure that the results of the algorithms are sensible.
These don't necessarily need to be part of automated CI tests,
as mentioned in #40, but rather the examples.

I suggest to use a trivial case, for example, for DA:
5d, no dynamics, observe (directly) 1 component.

  • posterior mean/cov should nearly match theoretical.
  • test all of the methods
  • test for different configs (ensemble size, iteration numbers, with and without localisation)

For optimisation, for example: a 5d quadratic objective

  • Check optimum is found
  • Check number of iterations not excessive.

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