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Can anyone see a faster way to compute quantities for a pair or large matrices?

• To: mathgroup at smc.vnet.net
• Subject: [mg127412] Can anyone see a faster way to compute quantities for a pair or large matrices?
• From: W Craig Carter <ccarter at MIT.EDU>
• Date: Mon, 23 Jul 2012 01:03:32 -0400 (EDT)
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Hello,
I am computing the gradient on a grid, then computing the gradient'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[{#}] &, gradfield, 2];


(*examples*)
Do[psiField = MapThread[myArcTan, gradfield, 2], {100}] // Timing
Do[magfield =  MapThread[Norm[{#}] &, gradfield, 2], {100}] // Timing

W Craig Carter
Professor of Materials Science, MIT

• Follow-Ups:
  • Re: Can anyone see a faster way to compute quantities for a pair or large matrices?
    • From: Sseziwa Mukasa <mukasa@gmail.com>