(Too) Slow Compiled Function To Sum Waves

Question

I have some code that sums planar waves and outputs a graphical result, as per the mock up below :

waveZoomFactor = 1;
waveHorizontalScaling = 1;
waveVerticalScaling = 1;
imageSize = 100;
createWaves = 
  Compile[{{x, _Real}, {y, _Real}, {sym, _Real}, {phaseShift, _Real}},
   Table[Cos[
     waveZoomFactor(waveHorizontalScalingx Cos[2Pi(k/sym)] + 
         waveVerticalScalingy Sin[2Pi (k/sym)]) + phaseShift], {k, 
     0, sym - 1}]
   , CompilationTarget -> "C", RuntimeAttributes -> {Listable},
   Parallelization -> True, RuntimeOptions -> "Speed"];
waves[phaseShift_] := 
  ParallelTable[Total[createWaves[x, y, 5  , phaseShift]],
   {x, -imageSize , imageSize , 0.2 }, {y, -imageSize , imageSize , 0.2 }];
CreatePattern := Table[Image[waves[t]], {t, 0, 2*Pi, 1}]
CreatePattern

I can't figure out why the code is so incredibly slow, in particular for larger 'imageSize'. I am a bit rusty with Mathematica so I am wondering if I overlooked something obvious or something dumb is going on. Thanks in advance.

Wouldn't it be better to use Sum inside the createWaves function instead of returning list with Table, since you're going to sum it anyway with Total? — flinty, Dec 29 '22 at 16:39
Have you read this post?: https://mathematica.stackexchange.com/a/104031/1871 — xzczd, Dec 30 '22 at 02:27

flinty · Accepted Answer · 2022-12-29T17:57:32.760

If you've got OpenCL support, here's an OpenCL implementation which is almost instantaneous in returning fairly high resolution results:

Remove["Global`*"];
Needs["OpenCLLink`"];
Check[OpenCLQ[], "OpenCL not available!"];
cwSource = 
  "__kernel void waves(__global float * out, float sym, float phaseShift, mint xres, mint yres, float x0, float y0, float x1, float y1, float zoom, float waveXscale, float waveYscale) {
int xi = get_global_id(0);
int yi = get_global_id(1);
float xfrac = ((float)xi)/xres;
float yfrac = ((float)yi)/yres;
float x = mix(x0,x1,xfrac);
float y = mix(y0,y1,yfrac);
float result = 0.0f;
for(int k = 0; k < sym; ++k)
{
    float f = 2.0fM_PI_Fk/sym;
    result += cos(zoom(waveXscalexcos(f) + waveYscaleysin(f)) + phaseShift);
}
out[yi  xres + xi] = result;
}
";
createWavesOpenCL = OpenCLFunctionLoad[cwSource, "waves",
   {{"Float", _, "Output"}, "Float", "Float", _Integer, _Integer, 
    "Float", "Float", "Float", "Float", "Float", "Float", 
    "Float"}, {8, 8}, "ShellOutputFunction" -> Print];
waveZoomFactor = 1;
waveHorizontalScaling = 1;
waveVerticalScaling = 1;
resolution = 500;
minx = -100;
maxx = 100;
miny = -100;
maxy = 100;
output = OpenCLMemoryAllocate["Float", {resolution, resolution}];
Table[
 createWavesOpenCL[output, 5, phase, resolution, resolution, minx, 
  miny, maxx, maxy, waveZoomFactor, waveHorizontalScaling, 
  waveVerticalScaling];
 Image[OpenCLMemoryGet[output], "Float"],
 {phase, 0, 2 Pi, 1}]

This is fast enough, that I can generate about 256 300x300 image slices and stack them in a 3D image using Image3D. It takes just a few seconds on an nVidia 1080ti.

Thanks a lot. this is a great approach, I'll try to up my skills and use similar code moving forward. Now if I could only get CUDA set up... — Gagle, Dec 29 '22 at 19:48

(Too) Slow Compiled Function To Sum Waves

1 Answers1