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guilgautier / DPPy

Python toolbox for sampling Determinantal Point Processes
https://dppy.readthedocs.io
MIT License
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Ratio for Laguerre ensemble in the graphical output #33

Closed adrienhardy closed 5 years ago

adrienhardy commented 5 years ago

It would be great to add the ratio N/M (or M/N) in the graphical output for the Laguerre ensemble, since the MP-law depends on this parameter

guilgautier commented 5 years ago

Hi @adrienhardy, thanks for pointing out this issue. You would expect the display of this ratio only when sampling from the full matrix model for Laguerre Ensemble ?

adrienhardy commented 5 years ago

I think if would be nice to give the parameter of the Marchenko-Pastur law, which is indeed M/N (or the other way around) for the full matrix model, but it is also related to the first parameter of your Gamma law in the tridiagonal matrix model. Basically, if the gamma density reads x^c e^{-x}, then when you rescale the parameters so that the density reads x^{Nc} e^{-Nx}, then you get the MP-law of parameter "some simple function of c", which is one when c=0. If you just rescale as x^{c} e^{-Nx} then you get in the large N limit the MP-law of parameter 1. Maybe it is easier to discuss about that verbally :-)

guilgautier commented 5 years ago

Hi @adrienhardy,

I've added completely reshaped the BetaEnsemble class see #34 to make it easier and more natural to use and to be maintained Regarding issue #33, for both the full matrix and banded matrix models I've added the associated:

Note that it is now easier to compare the speed of full and tridiagonal matrix models, since you can call with the same syntax both samplers: laguerre.sample_full_model(size_N=500, size_M=800) laguerre.sample_banded_model(size_N=500, size_M=800)

If you are ok with the change you can close the issue 🙃