Timeline for How to integrate functions of linearly interpolated data?
Current License: CC BY-SA 3.0
16 events
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| Dec 28, 2013 at 16:40 | history | edited | Michael E2 | CC BY-SA 3.0 |
Fixed grammar/typos
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| Dec 28, 2013 at 15:10 | comment | added | Michael E2 | @AlexeyPopkov Thanks! I added the derivation of the interpolation and integral. I added some explanation of the estimate of precision loss, too. I should have stressed that was far from an exact calculation. | |
| Dec 28, 2013 at 15:10 | history | edited | Michael E2 | CC BY-SA 3.0 |
Clarification
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| Dec 28, 2013 at 11:39 | comment | added | Alexey Popkov |
I accept your great answer. Only two things remain a bit unclear: 1) the logics behind your parametrization ((1 - t) y1 + t y2)/((1 - t) x1 + t x2) (x2 - x1) (section "The second integral"), 2) why do you think that Max @ Abs[(Rest[#] - Most[#])/Most[#]] &@ Sort@data[[All, 1]] gives an estimate of precision loss (the last paragraph in the same section)?
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| Dec 28, 2013 at 11:29 | vote | accept | Alexey Popkov | ||
| Dec 28, 2013 at 11:27 | history | edited | Alexey Popkov | CC BY-SA 3.0 |
added missing definitions
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| Dec 28, 2013 at 0:46 | comment | added | Michael E2 |
@AlexeyPopkov Thanks. I realized I omitted some of the explanation of the calculation of exactSum2 -- now included.
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| Dec 28, 2013 at 0:45 | history | edited | Michael E2 | CC BY-SA 3.0 |
Added explanation
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| Dec 27, 2013 at 18:16 | comment | added | Alexey Popkov | It is great update! I need time to investigate it deeply. | |
| Dec 27, 2013 at 1:23 | history | edited | Michael E2 | CC BY-SA 3.0 |
Added solution, clarified explanation
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| Dec 25, 2013 at 17:56 | comment | added | Michael E2 |
@AlexeyPopkov After ?*`*Subdivision*, one finds NIntegrate`InterpolationPointsSubdivision. Thence Options[NIntegrate`InterpolationPointsSubdivision] yields the default settings, too. This is good, too: ?NIntegrate`StrategiesDump`* -- lots of options and properties.
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| Dec 25, 2013 at 17:24 | comment | added | Alexey Popkov |
It is interesting that NIntegrate[int2[ww]/ww, {ww, data[[1, 1]], data[[-1, 1]]}, Method -> {"InterpolationPointsSubdivision", "MaxSubregions" -> 10^9}] gives even better performance but "MaxSubregions" -> 10^10 is forbidden.
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| Dec 25, 2013 at 17:03 | comment | added | Alexey Popkov |
It is amazing! Such a crucially needed option can be found only esoterically! Even the form Method -> {"InterpolationPointsSubdivision"} is undocumented (I cannot find it in the Documentation).
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| Dec 25, 2013 at 16:59 | comment | added | Michael E2 |
@AlexeyPopkov I put in a wrong option, e.g. Method -> {"InterpolationPointsSubdivision", "Foo" -> 1}, and Mma told the valid ones.
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| Dec 25, 2013 at 16:49 | comment | added | Alexey Popkov |
(+1). Your solution gives amazing speedup in integration of pure InterpolatingFunction and significant speedup in integration of the int2[ww]/ww. But "MaxSubregions" suboption is completely undocumented: searching on all Wolfram websites gives no results. Where did you find it?
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| Dec 25, 2013 at 16:18 | history | answered | Michael E2 | CC BY-SA 3.0 |