Timeline for How to obtain adaptive sampling as in Plot function?
Current License: CC BY-SA 3.0
20 events
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| Apr 13, 2017 at 12:55 | history | edited | CommunityBot |
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| Jun 10, 2015 at 6:09 | vote | accept | Kattern | ||
| Jun 10, 2015 at 5:26 | comment | added | Alexey Popkov | @Kattern In general the user is expected to accept the best answer from his own point of view while the community determines the ratings of the answers by voting. This model of "separation of powers" isn't perfect: for example the Accepted answer has more chances to be upvoted than others, so actually the user promotes the answer by Accepting it. | |
| Jun 10, 2015 at 1:38 | comment | added | Kattern | @AlexeyPopkov Michail's answer is better for the general question, but george2079's answer provides the answer of the question. I think it may be misleading for those who are just interesting in the answer of the question, not the general problem behind it. If this is not a problem, I am very happy to choose Michail's answer. | |
| Jun 9, 2015 at 15:03 | comment | added | Alexey Popkov | @Kattern According to the "Conclusions" section in your question Michail's answer provides the best solution for your problem. Why isn't it Accepted then? | |
| Jun 5, 2015 at 6:49 | history | edited | Kattern | CC BY-SA 3.0 |
added 830 characters in body
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| Jun 3, 2015 at 20:17 | answer | added | Michael E2 | timeline score: 24 | |
| May 11, 2015 at 7:24 | vote | accept | Kattern | ||
| Jun 10, 2015 at 6:09 | |||||
| May 9, 2015 at 14:02 | comment | added | Kattern | @Guesswhoitis. I think you are right. And this is why I am not so sure about george2079's trick mentioned in the answer which can force Mathematica to evaluate trapezoidal rule. | |
| May 9, 2015 at 13:57 | comment | added | Kattern |
@MichaelE2 Here is why I am interesting in this problem. I am using a software, which require me to input a tabular data for calculation. Then the software will use the given value and do linear interpolation for its own calculation. What I want to do is to use minimum points of input to get a good approximation of the original function. This is why I am thinking about the adaptive sampling in Plot function.
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| May 8, 2015 at 18:39 | comment | added | J. M.'s missing motivation♦ |
In fact, one neat trick for numerically evaluating an integral in Mathematica is to let Plot[] do the adaptive sampling and then use the output for the trapezoidal rule.
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| May 8, 2015 at 18:33 | comment | added | Michael E2 |
Some references: MaxBend mentioned by @Guess. What I was really poking the OP about was whether there was some sort of specific goal in mind. I could imagine something like sample[f, errornorm, tolerance], where the function errornorm measures the error of a particular sampling. But I can't imagine anything other than plotting and integration at this point.
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| May 8, 2015 at 18:17 | comment | added | J. M.'s missing motivation♦ |
To make it concrete, the key options that guide the adaptive sampling of Plot[] are PlotPoints, MaxRecursion, and (now hidden) MaxBend, which is the angle being talked about by @Michael.
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| May 8, 2015 at 16:15 | history | tweeted | twitter.com/#!/StackMma/status/596710110560419841 | ||
| May 8, 2015 at 14:44 | comment | added | Kattern | @MichaelE2 You have an excellent memory. Mathematica is such a large system, I can barely remember even a part of these details. Well done! | |
| May 8, 2015 at 14:34 | comment | added | Michael E2 | Aw, shucks. I've used it for 25 years, read the docs, attended conferences, read/participated on this site. Related: mathematica.stackexchange.com/a/59892 and its comments; mathematica.stackexchange.com/a/67642 | |
| May 8, 2015 at 14:18 | comment | added | Kattern | @MichaelE2 Why do you always know the internal implementation of those functions? | |
| May 8, 2015 at 14:13 | comment | added | Michael E2 |
The key is what goal is guiding the adapting. With Plot, it is the angle between consecutive line segments of the plot, which is entirely local. With NIntegrate and NDSolve, it is the estimated error in the result; NIntegrate has both global and local adaptive strategies.
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| May 8, 2015 at 13:52 | answer | added | george2079 | timeline score: 21 | |
| May 8, 2015 at 13:23 | history | asked | Kattern | CC BY-SA 3.0 |