Improving Spectral #53
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…is PR are no longer necessary
derivative/differentiation.py
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| @@ -228,6 +228,8 @@ def x(self, X, t, axis=1): | |||
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| def _align_axes(X, t, axis) -> tuple[NDArray, tuple[int, ...]]: | |||
| """Reshapes the data so the derivative always happens along axis 1. Do we need this? | |||
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Do we need this function? All this reshaping is a bit confusing. Can we just take the data as is and differentiate along whichever axis the user specifies? There are ways of indexing in numpy that make this fairly easy usually. For instance I have this line.
The code could probably be both more general and simplified if we do this right, but it's a separate PR for sure.
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Happy for this, but the challenge is that all methods internally have been allowed to expect one particular axis. So it probably means changing a fair amount.
… because evidently unnecessary
| # Test some basic functions | ||
| # ========================= | ||
| # Test that basic functions are differentiated correctly | ||
| # ====================================================== | ||
| funcs_and_derivs = ( |
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This is a good library of examples, well thought out.
| # Add noise to avoid all zeros non-convergence warning for sklearn lasso | ||
| f_mod = lambda t: func(t) + 1e-9 * np.random.randn(*t.shape) # rename to avoid infinite loop | ||
| t = np.linspace(0, 2*np.pi, 100, endpoint=False) # For periodic functions, it's important the endpoint not be included | ||
| if m == "spectral": |
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I decided to treat spectral as a special case in here, because it already kind of was, and this was the easiest extension to get coverage.
| def test_fn(m, func_spec): | ||
| func, fname, deriv, f_id = func_spec | ||
| t = np.linspace(0, 2*np.pi, 100) | ||
| if m == 'trend_filtered': |
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f_mod stuff needn't be here to silence the warning. We can just filter warnings with pytest.
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Ah! Failing the interface tests. I neglected to run them because I was getting this I can see in the But if I open up Never used poetry, and not sure whether this hyperparam_opt is doing anything. Looks like I did cause a failure related to aligning axes. I'll try to address that one. |
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Rerun that workflow? 🥺 |
| @_memoize_arrays(1) # the memoization is 1 deep, as in only remembers the most recent args | ||
| def _global(self, t, x): | ||
| if self.basis == 'chebyshev': | ||
| return cheb_deriv(x, t, self.order, self.axis, self.filter) |
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It struck me just now that filtering by frequency on cosine-spaced points isn’t totally sound: high-frequency variations look lower frequency around the edges where sample density is higher.
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I've been pondering this more pavelkomarov/spectral-derivatives#14. Basically what I'm currently doing is keeping filter(k) amount of the filter(k) amount of the
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I've made a notebook to empirically compare spectral filtering in the Fourier and Chebyshev bases, and pulled in a little of Floris' PyNumDiff to compare with Savitzky-Golay filtering + Gaussian smoothing. Fourier spectral is the gold standard, but even it can be fragile. Chebyshev can work okay (not great but really not worse than savgoldiff) for 1st and 2nd derivatives in the presence of a little noise but starts to blow up at the edges of the domain beyond that.
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Hey sorry for the delay Pavel... I should be able to get to this next week when I'm back in town. |
…is is a little more subtle and bumped spectral-derivatives version number to get latest features
I'll add comments throughout this PR. It's far from acceptable, but I want to have something to point to and talk about.