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Re: Can anyone see a faster way to compute quantities for a pair or

  • To: mathgroup at smc.vnet.net
  • Subject: [mg127425] Re: Can anyone see a faster way to compute quantities for a pair or
  • From: daniel.lichtblau0 at gmail.com
  • Date: Mon, 23 Jul 2012 19:56:52 -0400 (EDT)
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  • References: <juim0j$k9a$1@smc.vnet.net>

On Monday, July 23, 2012 12:04:19 AM UTC-5, W Craig Carter wrote:
> Hello,
> I am computing the gradient on a grid, then computing the gradient&#39;s 
> angle, and its magnitude. The computations below are the bottleneck for 
> a longer bit of code.  I would be grateful for any insights on how to 
> speed these up.
> 
> (*
> Let gradfield be the gradient that I have computed and placed in two matrices. Here I will just use random numbers as a proxy:
> *)
> 
> (*i.e., df/dx, df/dy*)
> gradfield =  { RandomReal[{-1, 1}, {256, 256}], RandomReal[{-1, 1}, {256, 256}]};
> 
> (*my gradients has many zeroes, so I need to handle these*)
> 
> SetAttributes[myArcTan, {Listable, NumericFunction}];
> myArcTan[0.0, 0.0] = 0.0;
> myArcTan[x_, y_] := ArcTan[x, y]
> 
> 
> (*the angles, this is slow*)
> psiField = MapThread[myArcTan, gradfield, 2];
> 
> (*the magnitudes, this is slower*)
> magfield =  MapThread[Norm[{#}] &amp;, gradfield, 2];
> 
> 
> (*examples*)
> Do[psiField = MapThread[myArcTan, gradfield, 2], {100}] // Timing
> Do[magfield =  MapThread[Norm[{#}] &amp;, gradfield, 2], {100}] // Timing
> 
> W Craig Carter
> Professor of Materials Science, MIT

Could use Compile to get a speed improvement. below shows one way to go about this.

In[445]:= myArcTanC2 = Compile[{{xy, _Real, 1}},
   With[{x = xy[[1]], y = xy[[2]]},
    If[x == 0. && y == 0., 0., ArcTan[x, y]]]];

In[452]:= psiFieldFinder = Compile[{{gfield, _Real, 3}},
   Map[myArcTanC2, Transpose[gfield, {3, 1, 2}], {2}], 
   CompilationOptions -> {"ExpressionOptimization" -> True, 
     "InlineCompiledFunctions" -> True},
   CompilationTarget -> "C"];

In[453]:= Do[psiField2 = psiFieldFinder[gradfield], {100}] // Timing

Out[453]= {0.85, Null}

If you intend to do this on the same array then pre-transposing, and removing that step from the compiled function, might give a further slight improvement.

For norms you might get better speed using Sqrt[arg1.arg2].

Daniel Lichtblau
Wolfram Research



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