Timeline for Updating Wagon's FindAllCrossings2D[] function
Current License: CC BY-SA 3.0
11 events
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| Aug 8, 2016 at 11:42 | comment | added | Szabolcs |
There is a small problem with how the Compile arguments are being handled here. With the setting SetSystemOptions["StrictLexicalScoping" -> True]; this function fails due to x and y being renamed in Compile[{x,y}, ...] but not in funcs.
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| Jan 27, 2012 at 15:29 | comment | added | J. M.'s missing motivation♦ | Oh yes, I linked to your page in the question where you used it on the SIAM challenge. Very nice! | |
| Jan 27, 2012 at 15:21 | comment | added | stan wagon | Not on hand. But this function is used many many times in the VisualDSolve project to find equilibrium points for two autonomous DEs and I must have found some difficult examples there. Now, it is possible as Mathematica changes internally that some of the problems disappear. Let me mention that this function was able to solve one of the "100 Digit Challenge" problems in optimizing a complicated function of 2 vbles by finding all of the critical points in the region, and there were well over 2000 of them. | |
| Jan 26, 2012 at 23:09 | comment | added | J. M.'s missing motivation♦ |
Oh. Would you happen to have a set of equations on hand where the asymmetry in ContourPlot[] is a necessity?
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| Jan 26, 2012 at 23:06 | comment | added | stan wagon | I'm afraid I cannot remember exactly why I chose 97 and 103, but the reason is related to the effect that when things are too symmetric then there can be problems at the centers of symmetry. So it is best to add in a little asymmetry. Also I note that someone commented that some new Mathematica functions do some of these sorts of things.. but only for nice functions. If one had the Zeta function involved, say, then I do not believe their new algebraic ideas would work. Of course, since typical usages might be in DEs, finding equil. pts., it might be worth adding some cases to detect niceness. | |
| Jan 26, 2012 at 5:36 | comment | added | J. M.'s missing motivation♦ |
BTW: is there anything special about the increments chosen in {x, a-(b-a)/97, b+(b-a)/103}, {y, c-(d-c)/98, d+(d-c)/102}?
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| Jan 26, 2012 at 5:16 | history | edited | Brett Champion | CC BY-SA 3.0 |
clean up formatting, remove sig, etc...
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| Jan 26, 2012 at 4:36 | vote | accept | J. M.'s missing motivation♦ | ||
| Jan 26, 2012 at 4:36 | comment | added | J. M.'s missing motivation♦ |
Hi Dr. Wagon! Thanks for posting your updated code (and for the book in general; I hope I can get a copy of your new one some day); I'll do the tests later for this! I've also found that RegionFunction can be profitably used here to restrict the search to roots within a domain.
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| Jan 26, 2012 at 4:34 | history | edited | J. M.'s missing motivation♦ | CC BY-SA 3.0 |
added 141 characters in body
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| Jan 26, 2012 at 4:27 | history | answered | stan wagon | CC BY-SA 3.0 |