Kernel.output_shape semantics and further RandomProcess refactoring

[marvinpfoertner]

In a Nutshell

A few months ago, I redefined the shape of the outputs of Kernel.__call__ to cov.output_shape + batch_shape.
However, this is very counterintuitive when in the context of random processes, since we would expect the outputs of the mean, var, and std functions to be batch_shape + randproc.output_shape, i.e. "the other way around".
My original change was made with multi-output GPs in mind, but even here it turns out that the batch_shape + cov.output_shape-order is easier to handle.

Detailed

• rename Kernel.{shape => output_shape}
• change output shapes of Kernel.{__call__, matrix} to batch_shape + kernel.output_shape
• adapt random processes to these changes
• fixed a bug in Matern 3/2 kernel
• refactor RandomProcess
  • add input_ndim and output_ndim as public arguments (also add these to Function and Kernel)
  • add default implementation of _sample_at_input
  • remove unnecessary overrides of push_forward in derived classes
  • add mean and cov arguments to the RandomProcess constructor and provide default implementations
  • improve the docstrings

Related Issues

None

[codecov]

Codecov Report

Merging #652 (6162957) into main (db6e7d3) will increase coverage by 0.02%.
The diff coverage is 89.06%.

@@            Coverage Diff             @@
##             main     #652      +/-   ##
==========================================
+ Coverage   89.99%   90.02%   +0.02%     
==========================================
  Files         186      186              
  Lines        7025     7025              
  Branches     1102     1105       +3     
==========================================
+ Hits         6322     6324       +2     
+ Misses        463      460       -3     
- Partials      240      241       +1     

Impacted Files	Coverage Δ
src/probnum/_function.py	95.12% <66.66%> (-2.25%)	⬇️
src/probnum/randprocs/markov/_markov_process.py	85.29% <85.71%> (+5.80%)	⬆️
src/probnum/randprocs/kernels/_kernel.py	93.67% <88.88%> (-1.00%)	⬇️
src/probnum/randprocs/_random_process.py	91.89% <90.24%> (+5.61%)	⬆️
src/probnum/randprocs/_gaussian_process.py	100.00% <100.00%> (ø)
src/probnum/randprocs/kernels/_matern.py	93.54% <100.00%> (ø)

[JonathanWenger]

Nice work! I didn't find anything that needs to be changed.