Hierarchical log space startpoint sampling

[Doresic]

The numerical inner solver of the scaling+offset parameters has a multi-start option. However, the multi-start sampling was done in linear space. In this version, bounds of scaling and offset are not possible. Because of that [-1e20, 1e20] dummy bounds were introduced. But that resulted in the linear sampling having huge values, mostly in the order of 10^19. These startpoints would never converge, rendering the multi-start approach practically useless.

I've implemented sampling in log space for the numerical solver. The values can be negative, so I couldn't directly use pypesto's log sampling. So I used a symmetric logarithm function np.sign(x) * np.log10(np.abs(x) + 1) transformation which supports negative values, sampled in that space, and transformed the values back with its inverse np.sign(x) * (10 ** np.abs(x) - 1).

[codecov-commenter]

Codecov Report

Attention: 384 lines in your changes are missing coverage. Please review.

Comparison is base (160c2a8) 88.16% compared to head (27cd170) 82.44%.
Report is 472 commits behind head on develop.

Files	Patch %	Lines
pypesto/ensemble/ensemble.py	69.77%	68 Missing ⚠️
...ypesto/hierarchical/spline_approximation/solver.py	82.62%	53 Missing ⚠️
pypesto/ensemble/util.py	65.13%	38 Missing ⚠️
pypesto/hierarchical/optimal_scaling/solver.py	93.53%	26 Missing ⚠️
pypesto/history/base.py	88.57%	24 Missing ⚠️
pypesto/hierarchical/petab.py	84.56%	23 Missing ⚠️
pypesto/engine/mpi_pool.py	0.00%	22 Missing ⚠️
pypesto/hierarchical/inner_calculator_collector.py	88.51%	17 Missing ⚠️
...pesto/hierarchical/spline_approximation/problem.py	89.18%	16 Missing ⚠️
pypesto/hierarchical/problem.py	89.23%	14 Missing ⚠️
... and 15 more

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Additional details and impacted files

@@             Coverage Diff             @@
##           develop    #1242      +/-   ##
===========================================
- Coverage    88.16%   82.44%   -5.73%     
===========================================
  Files           79      148      +69     
  Lines         5257    11998    +6741     
===========================================
+ Hits          4635     9892    +5257     
- Misses         622     2106    +1484     

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[dweindl]

Sounds reasonable to me.

[dilpath]

Looks good! Fine to merge as-is.