311 implement zero truncated poisson algorithm

[jeremy-myers]

Closes #311

The tutorial is a minimal port of Listing 2 from (https://academic.oup.com/imaiai/article/12/3/1573/7159150#417226967).

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📚 Documentation preview 📚: https://pyttb--450.org.readthedocs.build/en/450/

[dmdunla]

@jeremy-myers Looks like this is failing regressions due to some slight numerical differences in the expected test output. Can you take a look and see if Nick's example of using np.allclose() shown here could work for the ZTP tests you provided?

[jeremy-myers]

@jeremy-myers Looks like this is failing regressions due to some slight numerical differences in the expected test output. Can you take a look and see if Nick's example of using np.allclose() shown here could work for the ZTP tests you provided?

@dmdunla This is failing on tests/gcp/test_optimizers.py::test_sgd which doesn't make sense to me - this PR doesn't touch that test. I don't have a debugger set up at the moment - can you take a look?

[dmdunla]

@dmdunla This is failing on tests/gcp/test_optimizers.py::test_sgd which doesn't make sense to me - this PR doesn't touch that test. I don't have a debugger set up at the moment - can you take a look?

Ugh! This is ugly. It may be that this failing part relied on a certain state of the RNG, as I can reproduce the result, then run just this failing test, and it will work most but not all of the times I run it:

$ pytest tests -k "test_optimizers"
=============================================================================================================== test session starts ===============================================================================================================
platform darwin -- Python 3.12.9, pytest-8.4.0, pluggy-1.6.0
rootdir: <nope>
configfile: pyproject.toml
plugins: cov-6.1.1
collected 610 items / 605 deselected / 5 selected                                                                                                                                                                                                 

tests/gcp/test_optimizers.py .....                                                                                                                                                                                                          [100%]

======================================================================================================== 5 passed, 605 deselected in 0.16s ========================================================================================================

... then again ...

(pyttb_312) s1075069:pyttb dmdunla$ pytest tests -k "test_optimizers"
=============================================================================================================== test session starts ===============================================================================================================
platform darwin -- Python 3.12.9, pytest-8.4.0, pluggy-1.6.0
rootdir: <nope>
configfile: pyproject.toml
plugins: cov-6.1.1
collected 610 items / 605 deselected / 5 selected                                                                                                                                                                                                 

tests/gcp/test_optimizers.py ..F..                                                                                                                                                                                                          [100%]

==================================================================================================================== FAILURES =====================================================================================================================
...
tests/gcp/test_optimizers.py:94: AssertionError

And you can see that the error shows up in a different location. Hence, my thought about the RNG.

I increased max_iters on all the solvers to see if the failures go away. But this should be addressed more systematically moving forward.

[dmdunla]

Looks like we were getting lucky with gcp_opt converging to a solution in just 1-2 iterations before I increased all of the max_iters=3 in all solver instantiations in tests/gcp/test_optimizers.py. With the introduction of the new gcp_opt tests, this may have been enough to change the state of the RNG propagating changes to the tests that filed, even though no direct change impacting any functions called in the failing tests.

I'll this PR now, then add an issue describing this behavior that needs to be addressed.