Implementation of Bornemann's method for Tracy-Widom distributions

[AustenLamacraft]

Switches out numerical evaluation of Painleve for evaluation of the finite dimensional approximation of the Fredholm determinant.

At the moment, pdf is not implemented, as I don't know anything better than numerical differentiation of the cdf -- a possible drawback relative to Painlevé.

I've used FastGaussQuadrature for quadrature. Potentially could switch to tanh-sinh as per this stack exchange answer. I don't know about the relative merits.

[dlfivefifty]

Do we still require OrdinaryDiffEq.jl or can that dependency be dropped?

[dlfivefifty]

I've used FastGaussQuadrature for quadrature. Potentially could switch to tanh-sinh as per this stack exchange answer. I don't know about the relative merits.

tanh-sinh is good for removing algebraic-like singularities, and allows for using Trapezoidal-like rules (so simpler, though that's less relevant when there are convenient quadrature-rule packages). I'd think that if you are not planning to optimise parameters to minimise number of evaluations, just use FastGaussQuadrature.jl.

[dlfivefifty]

@MikaelSlevinsky @ajt60gaibb any more informed knowledge about Gauss quadrature v tanh-sinh rules?

[MikaelSlevinsky]

Since the computation of the determinant is the most expensive part, I think either type of quadrature could be tuned for good performance (which means keeping the dimensions of the determinants low). Probably double exponential quadratures would be the simplest solution for extended precision at the moment. Cheers, Mikael On May 25, 2018, at 8:07 PM, Sheehan Olver <notifications@github.com<mailto:notifications@github.com>> wrote: @MikaelSlevinsky<https://github.com/MikaelSlevinsky> @ajt60gaibb<https://github.com/ajt60gaibb> any more informed knowledge about Gauss quadrature v tanh-sinh rules? — You are receiving this because you were mentioned. Reply to this email directly, view it on GitHub<#44 (comment)>, or mute the thread<https://github.com/notifications/unsubscribe-auth/AHzBpT6h-0dY9N1fA_i2olr4tbkAMmQxks5t2EhUgaJpZM4UMZkH>.

[dlfivefifty]

I’d be very surprised if there’s a high-performance application of TW distributions, so probably best to just do what’s easiest and not over-optimise.

[AustenLamacraft]

Just noticed the README needs updating ... still mentions Painlevé