Dirichlet | Dirichlet .NET Number Theory Library | Math library

It uses the fixed point iteration. The frequency histograms method is just an efficient way to calculate it. They provide an algebraically equivalent way to do the exact same computation. The update function consists of a sum over a large number of Digamma functions. This function by itself is difficult to compute, but the difference between two Digamma functions (where the arguments differ by an integer) is relatively easy to compute, and even better, it "telescopes" so that the answer to Digamma(a + n) - Digamma(a) is one operation away from the answer to Digamma(a + n + 1) - Digamma(a). If you work through the histogram of counts from 1 to the max, adding up the number of times you saw a count of n at each step, the calculation becomes extremely fast. Initially, we were worried that hyperparameter optimization would take so long that no one would do it. With this trick it's so fast it's not really significant compared to the Gibbs sampling.

Solved it.

The paths of Jupyter Notebook did not include the new updated library. After updating paths to the wanted folder by

You don't need to give the distribution a name. The string tn1 passed as first the argument to pm.TruncatedNormal.dist is interpreted as mu (as you pass a named mu also, you get the exception). Try

1. why are the values of phi and phi2 slightly different?

phi and phi2 are different because eq2 doesn't converge as rapidly as eq1. This is because eq1 is more implicit than eq2. If you change the tolerance for the residual, e.g., res > 1e-10, you'll see the two solutions are in much closer agreement.

1. how could I extract the outflow term for each cell (when a more complex grid will be used) while keeping 'ImplicitSourceTerm', which is more efficient?

You can still evaluate the flux phi2 * extCoef * phi2.faceGrad, even when you use the ImplicitSourceTerm.

In general, it's not easy to extract what each Term is doing physically (see issue #461). You can use the FIPY_DISPLAY_MATRIX environment variable to see how each Term contributes to the solution matrix, but this may or may not give you much physical intuition for what's going on.

Moving to Julia 1.5 fixed the issue.

[cobbling an answer from the discussion in the comments]

The results are similar between a Grid1D and a CylindricalGrid1D, particularly in the early steps, but they are not the same. They are quite different as the problem evolves.

FiPy doesn't like things outside the divergence, but you should be able to multiply the equation by J and put it in the coefficient of the TransientTerm, e.g.,

or

I believe you want to select the top 10 words and you are using a wrong syntax. You are only selecting the word ranked 10 which is not iterable. Change line 261 to this to select the top 10 instead of only selecting the 10th:

The issue here is that the likelihood of coming from each model involves probability density for the Gaussian and mass for the discrete, which are not commensurate. Specifically, the computation for comparing where a zero observation came from, will involve likelihoods

This is a bug in cupy which you should report on their GitHub.

They do not properly handle the case of an integer argument, despite the documentation. They require that you provide either a tuple or None. This is why you see the behavior you’re seeing. (If you provided a tuple (a, b), then the resulting shape would properly be (a, b, n).

The workaround here is to provide the shape you want as a length-1 tuple: (n,). Note that the comma is necessary.