Quantile PDF reconstructions follow up work

[drewoldag]

• Write unit tests for PDF constructors that verify the calculations (i.e. make sure the numbers are matching expected)
• Create .../tests/distribution_generator_tests/ subdirectory. Break apart test_ensemble.py and move the quant_gen specific tests into their own unittest module - test_quant_gen.py. #153
• Address the "elephants foot", i.e. the bumps on the reconstructed PDFs. At least partially due to quant_pdf.pad_quantiles.
• Allow users to specify a specific starting point and value for the dual_spline_average pdf constructor.
• Make the quantile_distribution_demo notebook more beautiful.
• Change the default PDF constructor in quant_gen class to be cdf_spline_derivative and update associated unit tests.
• Characterize the computational performance and fidelity of each of the different reconstruction algorithms.

[elts6570]

We also see two issues a) with the PDF parameterization and b) the reconstruction prior to the point where the first quantile starts in our implementation here: https://github.com/LSSTDESC/bayesian-pipelines-cosmology/blob/photo-z/notebooks/photo-z/quantiles.py, when called as such: https://github.com/LSSTDESC/bayesian-pipelines-cosmology/blob/photo-z/notebooks/photo-z/qp_quantiles.ipynb.

[aimalz]

Temporary fix @elts6570 : When using the .convert_to() method, we should provide quantile values that aren't exactly 0 or 1, i.e. offset from those by a tiny number like 1e-15. The .pdf() method still gives wonky results, but they're not nearly as crazy.

A more comprehensive solution will entail:

1. Checking for 0 or 1 in the input values to .ppf() and performing the above offset if necessary.
2. Adding a check for inf values in the locs provided to quant_gen.
3. Debugging the .pdf() method to prevent constant-valued stretches even for reconstruction options other than piecewise_constant.
4. Debugging the .pdf() method to prevent negative values under piecewise_linear option.
5. Adding a check that the CDF in between initially provided locs is equal to initially provided quants.