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# Suggestions for speeding up this plot?

Posted 8 years ago
 Consider the code: HairyStarfish[a_, plotpts_, thickness_, imagesize_] := ParametricPlot[{ Sum[(2/3)^k Sin[(3/2)^k t], {k, 0, a}], Sum[(-(2/3))^k Cos[(3/2)^k t], {k, 0, a}] }, {t, 0, 2^(a + 1) Pi}, MaxRecursion -> 5, Axes -> False, PlotPoints -> plotpts, PlotStyle -> {Thickness[thickness], Black}, PlotRange -> {{-2.5, 2.5}, {-2.5, 2.5}}, ImageSize -> {imagesize, Automatic}] HairyStarfish[11, 15000, 0.00004, 500]  I want to generate this plot at a = 25 for a large art print (interesting features emerge as a gets large). Computation time increases exponentially with each increment of the value a, since PlotPoints must be doubled to keep accuracy. I've been doing it piecewise so far, breaking {t, 0, 2^(a+1) Pi} up into segments, and then combining the plots later with ImageMultiply. I'm wondering if there's an efficient way to render several segments at once with parallelization and/or GPU. Or if anyone has general comments on a smarter way to render this plot. So far, I've tried: ParallelEvaluate, generating multiple plots at once on parallel kernels. But it is not any faster. Pairing different values of MaxRecursion and PlotPoints. No significant speed increase. Generating only half of the plot, then combing with it's mirror (since it is symmetric). But this only cuts time by a factor of 2. Does ParametricPlot use the graphics card as wisely as possible? My graphics card is a 980ti with 6gb of vram and 704 cores, so I figure it should be able to speed up the rendering somewhat if I utilize it properly. I just got CUDALink installed... I've been reading about it, but I'm still pretty lost on how i could apply it here, if at all. I've also considered purchasing a cluster computing package through gridMathematica, since the computation times are so high and it is parallelizable. But I want to make sure I'm attacking the problem as intelligently as possible before I go that route.
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Posted 8 years ago
 Using compilation and machine real numbers may be tricky here. You are going to calculate Sin and Cos of numbers that are of the order of 10^12. Can you trust the results?
Posted 8 years ago
 You should consider the following: what takes longer - rendering the figure or computing the points? If computing the points is a significant time waste then consider separating it from plotting function and use Compile with options potential CompilationTarget -> "C" and Parallelization -> True. If this is for a poster, perhaps you do not want to render in front end and then export. Use Export right away and better to a vector format such as SVG or PDF. Not sure if all this is useful, just a train of thoughts.
Posted 8 years ago
 Thank you. Yes, I generally Export directly to TIFF... I omitted for simplicity. Would SVG or PDF offer advantages over TIFF in this particular case? I'm new to the idea of a vector format.Unfortunately, compilation does not appear to increase the speed. Although, I'm guessing I am doing something wrong, since I have never compiled anything before. Here is a comparison: myHairyStarfish[a_, plotpts_, thickness_, imagesize_] := ParametricPlot[ Evaluate[{Sum[(2/3)^k Sin[(3/2)^k t], {k, 0, a}], Sum[(-(2/3))^k Cos[(3/2)^k t], {k, 0, a}]}] , {t, 0, 2^(a + 1) Pi}, MaxRecursion -> 5, Axes -> False, PlotPoints -> plotpts, PlotStyle -> {Thickness[thickness], Black}, PlotRange -> {{-2.5, 2.5}, {-2.5, 2.5}}, ImageSize -> {imagesize, Automatic}] myHairyStarfish[11, 15000, 0.00004, 500] takes 2.02 seconds. cf = Compile[{t}, Sum[{(2/3)^k Sin[(3/2)^k t], (-(2/3))^k Cos[(3/2)^k t]}, {k, 0, 11}], CompilationTarget -> "C", Parallelization -> True] ParametricPlot[ cf[t] , {t, 0, 2^(11 + 1) Pi}, MaxRecursion -> 5, Axes -> False, PlotPoints -> 15000, PlotStyle -> {Thickness[0.00004], Black}, PlotRange -> {{-2.5, 2.5}, {-2.5, 2.5}}, ImageSize -> {500, Automatic}] takes 2.42 seconds.But cf[t] still seems to be evaluating within ParametricPlot, so that's probably why. Is there a way to take cf[t] from cf[0] to cf[2^(a + 1) Pi] first, then plot it after?
Posted 8 years ago
 You also get it a bit faster by wrapping the inner bit into an Evaluate: myHairyStarfish[a_, plotpts_, thickness_, imagesize_] := ParametricPlot[ Evaluate[{Sum[(2/3)^k Sin[(3/2)^k t], {k, 0, a}], Sum[(-(2/3))^k Cos[(3/2)^k t], {k, 0, a}]}], {t, 0, 2^(a + 1) Pi}, MaxRecursion -> 5, Axes -> False, PlotPoints -> plotpts, PlotStyle -> {Thickness[thickness], Black}, PlotRange -> {{-2.5, 2.5}, {-2.5, 2.5}}, ImageSize -> {imagesize, Automatic}] AbsoluteTiming[myHairyStarfish[11, 15000, 0.00004, 500]] On my computer it goes from 5.75 secs to 2.94 secs.Cheers,Marco
Posted 8 years ago
 You may try ListPlot with ParallelTable, after you have estimated a reasonable increment for t that does not make you lose too much detail.
Posted 8 years ago
 Your function definition contains errors and, probably, it must be HairyStarfish[a_, plotpts_, thickness_, imagesize_] := ParametricPlot[{Sum[(2/3)^k Sin[(3/2)^k t], {k, 0, a}], Sum[(-(2/3))^k Cos[(3/2)^k t], {k, 0, a}]}, {t, 0, 2^(a + 1) Pi}, MaxRecursion -> 5, Axes -> False, PlotPoints -> plotpts, PlotStyle -> {Thickness[thickness], Black}, PlotRange -> {{-2.5, 2.5}, {-2.5, 2.5}}, ImageSize -> {imagesize, Automatic}] Am I right?
Posted 8 years ago
 No Errors. The code just displayed as text instead of code for some reason. Fixed.