Timeline for How can I implement dynamic programming for a function with more than one argument?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Jan 19, 2012 at 6:34 | vote | accept | J. M.'s missing motivation♦ | ||
| Jan 18, 2012 at 0:42 | comment | added | Leonid Shifrin | @Mike Well, I'd keep that, but as you wish of course. | |
| Jan 18, 2012 at 0:38 | comment | added | Leonid Shifrin |
@Mike Thanks! I came up with this first about 5 years ago, when I needed it to compute functions with a huge number of terms. In those days, I wouldn't make a mistake with Simplify, but I got rusty since I quit Physics :)
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| Jan 18, 2012 at 0:26 | history | edited | Leonid Shifrin | CC BY-SA 3.0 |
Removed Simplify
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| Jan 18, 2012 at 0:25 | comment | added | Mike Bailey | @LeonidShifrin: Just for the record, the way you did this is very cool and borderline black magic. | |
| Jan 18, 2012 at 0:19 | comment | added | Leonid Shifrin |
@Mike Good point, I will edit. Simplify was taking the most time, I should have tried Expand alone. As to your first point: since in my case you compute all the previous ones in the process, you need almost no time to compute say CharlierC[101, a, x] fully symbolically then.
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| Jan 18, 2012 at 0:14 | comment | added | J. M.'s missing motivation♦ | I also deal with polynomials with more than three arguments, like the Hahn polynomials, and I expect to be varying indices and parameters a lot. So, Leonid's proposal seems to be most expedient for me. | |
| Jan 18, 2012 at 0:05 | comment | added | Mike Bailey |
@LeonidShifrin: If you want to vary a and x, you can simply evaluate it and attach it to a variable: poly = CharlierC[100, a, x] and then evaluate it for any arbitrary {a, x}. You just have to be careful to only evaluate CharlierC[n, a, x] for sybmolic a and x for my version, and always attach it to something beforehand.
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| Jan 18, 2012 at 0:04 | comment | added | Leonid Shifrin |
@Mike My code creates definitions for absolutely arbitrary a. Also, some time is spent on Expand and Simplify. It is slow the first run, but instant all the following runs. If your task is to vary a (say, plot when a is in some range), I only need to compute stuff once, and it will work for every value of a. If there is a single numerical a, then your code wins, but then arguably a is a constant rather than a true function argument, so the memoization is effectively 1D.
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| Jan 17, 2012 at 23:59 | comment | added | Mike Bailey | I timed both versions, and yours is significantly slower on my machine. 0.016 seconds (mine) vs 1.185 seconds (yours) for n = 20. Still, very cool idea you have. | |
| Jan 17, 2012 at 23:52 | history | answered | Leonid Shifrin | CC BY-SA 3.0 |