Implementation of NFW radial distribution about dhod HOT 13 CLOSED

ahh, ok, my bad, got it.

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Worst comes to worst, you could always use the scipy implementation to train a simple MLP surrogate.

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Ok, so for future reference, here is the scipy implementation, they have a few fixes for several special cases, but they still admit it can fail to converge from time to time:
https://github.com/scipy/scipy/blob/master/scipy/special/lambertw.pxd
For now however, I'm happy with just limiting the number of iterations to 100, I'll make a proper PR to TFP to propose a better fix.
Can now sample without problems 10^6 radii and get perfect match compared to theory:

10^6 sample time:

• numpy: 298ms
• TF (GPU accelerated): 81.9ms

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Also linked to the reference above, here is a cute python implementation:
https://github.com/CullanHowlett/NFWdist

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This almost works, only one problem, the TFP implementation of the Lambert W function sometimes gets stuck in an infinite loop. I should look at the scipy implementation to figure out what the difference is, and how to avoid that loop

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Hmm, I haven't noticed problems with this implementation, although I rewrote it myself so it's possible I wouldn't have. Do failures only happen for specific params?

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apparently not related to specific parameters, I haven't done extensive testing, but it gets stuck pretty often when sampling like10^4 samples

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and the code doesn't have a max number of iteration stopping criterion, so that doesnt seem safe ^^'

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Stopping criteria? Are we talking about the rnfw function in this module? Where do stopping criteria come into this algorithm?

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ahh no sorry, miscommunication I think. I'm saying the TensorFlow Probability implementation of the Lambert W function gets stuck from time to time. That function is implmented using an iterative solver, have a look here:

But they didn't include a max_iter or something like that, and apparently in practice it gets stuck from time to time in an infinite loop. I need to check the scipy implementation of lambertw to see how they achieve a more robust implementation.

The numpy code seems to be working great

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Ok, this has been super useful @all-contributors please add @aphearin for ideas

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@EiffL

I've put up a pull request to add @aphearin! 🎉

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This has been merged to master, it now has tests that compare the results to halotools.

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