ENH: Implemented methods 'extended' and '3/8-th' in simps function. fixes gh-4264 #4406
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scipy/integrate/quadrature.py
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| method : {'composite', 'extended', 'second'}, optional | ||
| 'composite' : Uses composite method of Simpson's rule. | ||
| 'second' : Uses Simpson's 3/8-th rule for calculating integral. | ||
| 'extended' : Uses extended Simpson's rule for calculating integral. |
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This needs to be typeset as a ReST list, with leading dashes IIRC: "- 'composite': Uses composite method ...''
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The methods need to be explained. Ideally, give exact formulas in the Notes section of the docstring.
| y = [0, 2.5, 5, 7.5, 10, 12.5, 15, 17.5, 20] | ||
| ans = simps(sample, x=y, method='extended') | ||
| assert_equal(ans, 88.6875) | ||
| assert_equal(val, 88.6875) |
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any tests for method='composite'?
scipy/integrate/quadrature.py
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| Formula used in 'extended' method:- | ||
| Integral = dx/48*[17*y[0] + 59*y[1] + 43*y[2] + 49*y[3] + 48*X + 49*y[N-4] + 43*y[N-3] | ||
| + 59*y[N-2] + 17*y[N-1]] | ||
| where X = (from i = 4 to i = N-5 ) Σ y[i] |
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@ev-br How to add summation formula here? Is this method fine?
Shouldn't I skip formula and just give the reference.
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IMO formulas of this complexity are best written in TeX notation.
.. math::
\frac{dx}{48} \left( 17 y_0 + 59 y_1 + 43 y_2 + 49 y_3 ... \right)
(Depending on how you write it, TeX can be anywhere between crystal clear and utterly unreadable).
In any case, unicode symbols are best avoided. Either use pseudo-python pseudocode, sum(y[i] for i in range(4, N-4)) or TeX: \sum_{i=4}{N-5} y_i
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@ev-br I have made all the changes. Please review it. |
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@ev-br Just reminding. I have made all the suggested changes. Please review it. |
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Coming back to it after quite a while. TBH I'm not sure if it's worth it. These integration methods are valid, but I'm just not sure if they are used often enough (outside of teaching intro to numerical methods) to warrant adding them. |
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@ev-br If it's already implemented I don't see any harm in adding the functionality to the function. If |
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@ev-br should we close it or integrate this? |
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@tupui have to admit I don't remember anything about this PR (facepalm). And I won't be able to come back to it in a near future I'm afraid. So it's your call |
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Besides equations there is no explanation of what the (I make this comment without knowledge of the advantages of this PR, nor whether it should be merged or not) |
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After looking back at Simpson and numerical integration in general, I think this might be useful to have the 3/8th Simpson rule as it becomes exact for n=3. But the current interface is not optimal. In the end we could base everything on Newton-Cotes (if I am not missing anything). Also, it could be useful to return the error which can be easily calculated. Or it could be used to specify the tolerance. |
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The roadmap for the module is actually quite old... I feel like this could be reevaluated. But I am not an expert at all in numerical integration. |
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Implemented methods 'extended' and '3/8-th' in simps function. fixes gh-4264