Mean, Normalizer, Trend and Fitting

[MuellerSeb]

Closes: #94

Abstract

This PR adds:

• a new submodule containing normalizer classes.
• a callable mean (added to normalized data) for all Field classes
• a callable trend (added to again-transformed / input data) for all Field classes
• normalizer as input for all field classes
• auto fit option in Krige class (normalizer and variogram)

Purpose of Normalizer

Their purpose is to normalize (follow a normal distribution) and denormalize data.
Since Krige and SRF produce normal distributed fields, these normalizers offer the opportunity to transform fields into a desired distribution and, in case of krige, to normalize conditioning data beforehand.

Normalizer

• LogNormal
• BoxCox
• BoxCoxShift
• YeoJohnson
• Modulus
• Manly

Normalizer Fitting

In order to fit hyper-parameter of the normalization transformations, the Normalize base-class provides a fit method, that estimates parameters by maximizing the log-likelihood function for given data.

Callable trend and mean

In order to use trends and variable means from external source to play nicely together with Normalizer, we will allow callable means to be added to normalized data and trends applied to input data.

Auto Fitting for Krige

SInce we provide an automated workflow for estimating the empirical variogram with automatic binning, we plug that into the kriging class as an automated workflow. In addition the normalizer can be fitted automatically as well by minimizing the likelihood function as described above.

Affected Routines

• new method Field.post_field (replacing Krige._post_field and is similar to Field.pre_pos)
• Krige._krige_cond needs to care about normalizer and callable mean in correct order
• Field.__init__ needs trend_function, normalizer and fit_normalizer arguments
• add Krige.cond_mean holding mean values at conditioning points

TODO

• add to all Fields as keywords
• add examples
• add tests

[MuellerSeb]

@LSchueler this is finally ready for review. 😉 🎉

[LSchueler]

Wow, what a tremendous piece of work... again ;-)

Unfortunately, I won't be able to finish this review today. But in case you'd like to here some criticism already, here it goes:

I don't like the argument only_mean in Krige.__call__(). I think that should be taken care of in a separate method. I'm afraid the __call__ method could get as cluttered as SRF.__call__() was before you cleaned it up.

[MuellerSeb]

I don't like the argument only_mean in Krige.__call__(). I think that should be taken care of in a separate method. I'm afraid the __call__ method could get as cluttered as SRF.__call__() was before you cleaned it up.

I also struggled with that one, but:

1. This routine whould have the exact same signature as __call__()
2. When using a separate method, we can't use structured, unstructured or mesh with it
3. The argument could have another/a better name, though. "Officially" this procedure is called "kriging the mean". Maybe we could shorten it from only_mean to mean?

A separate routine would have more downsides IMHO.

[LSchueler]

This is soo cool! - I'm really sorry I kept you waiting for so long for this review.

Some comments in the code and apart from that I'm still not convinced by the only_mean argument in the Krige.__call__() method. The structured and unstructured methods are only syntactic sugar and maybe a method Krige.the_mean or Krige.krige_the_mean might be much clearer.
But I wouldn't try to block this PR if you disagree ;-)

[LSchueler]

Fixed some typos on this branch, don't forget to pull.

[MuellerSeb]

This is soo cool! - I'm really sorry I kept you waiting for so long for this review.

Some comments in the code and apart from that I'm still not convinced by the only_mean argument in the Krige.__call__() method. The structured and unstructured methods are only syntactic sugar and maybe a method Krige.the_mean or Krige.krige_the_mean might be much clearer.
But I wouldn't try to block this PR if you disagree ;-)

I'd like to keep it this way, since also mesh is using the call function and all future interfaces as well.

[MuellerSeb]

@LSchueler thanks for the review. I updated everything. Merging this beast now! 🎉