Add notebook demonstrating equivalence of equiangular samplings #278
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I've added some comments. Ideally I would say if we want to include this as a tutorial notebook there should be a bit more explanatory text about what the various checks / asserts in the notebook are showing and where the expressions for computing the samples points come from. For this to appear in the documentation I believe a corresponding link file needs to be added to docs/tutorials.
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| "# Equivalence of various equiangular samplings\n", | ||
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| "In this demo we show the equivalence between Fejer/Clenshaw-Curtis sampling and other equiangular sampling schemes, including MW, MWSS and DH." |
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| "In this demo we show the equivalence between Fejer/Clenshaw-Curtis sampling and other equiangular sampling schemes, including MW, MWSS and DH." | |
| "In this tutorial we show the equivalence between Fejer / Clenshaw-Curtis sampling and other equiangular sampling schemes, including [McEwen-Wiaux (MW)](https://doi.org/10.1109/TSP.2011.2166394), diametrically symmetric McEwen-Wiaux (MWSS) and [Driscoll-Healy (DH)](https://doi.org/10.1006/aama.1994.1008)." |
I think tutorial is better than demo for consistency with terminology we use in documentation and that it's worth expanding the sampling scheme acronyms as it may not be clear what these refer to .
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| "Note that Fejer tyle 2 sampling does not include end-points." |
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| "Note that Fejer tyle 2 sampling does not include end-points." | |
| "Note that Fejer type 2 sampling does not include end-points." |
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| "n = L - 1/2" |
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It's unclear what n represents here particularly given it appears to be set to be a non-integer value but is used as an argument to numpy.arange. I would say a descriptive variable name would be better or at least some explanatory text.
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| "thetas_mw_fejer1 = (np.arange(0, n) + 0.5) * np.pi / n" |
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It would be useful to have a reference for this formula or at least some explanation of how it arises.
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| "thetas_mwss_fejer2 = np.arange(1, n) * np.pi / n" |
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Again without context unclear where this formula comes from / what is being shown here.
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Thanks for your comments @matt-graham. Agreed this needs some further clarification. I don't think we should have this as a tutorial notebook as this point (i.e. it shouldn't be rendered in the documentation for now). We can perhaps extend it in future (once we have the additional sampling schemes supported) and then have a more fully featured tutorial notebook. Nevertheless, I'll make some clarifications shortly... |
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Thanks for the invitation to review. I have very straightforward comments.
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