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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: [mg127441] Re: Can anyone see a faster way to compute quantities for a pair or
• From: W Craig Carter <ccarter at MIT.EDU>
• Date: Wed, 25 Jul 2012 02:32:35 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• Delivered-to: mathgroup-newout@smc.vnet.net
• Delivered-to: mathgroup-newsend@smc.vnet.net
• References: <juim0j$k9a$1@smc.vnet.net> <20120724081538.B3AF16802@smc.vnet.net>

Thanks to Ray, Dan, Sseziwa, Andre, and David Park (offline response) 
for their suggestions which improve computation time by about a factor 
of 100.

I am very curious what is going on under the hood that makes my original 
method (pasted again below) using MapThread so inefficient  compared to 
the better solutions (i.e., using Apply and Map solutions not the 
Compile solution).  This seems a good learning--and 
teaching--opportunity.

(*original posting, the myArcTan is not the real culprit (btw, I am very 
impressed with Ray's UnitStep trick*)


(* original inefficient posted method*)
gradfield =  { RandomReal[{-1, 1}, {256, 256}], RandomReal[{-1, 1}, 
{256, 256}]};

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];



>
>   psifield2 = ArcTan@@{gradfield[[1]] + UnitStep[-magfield2],
>                        gradfield[[2]]}

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

• References:
  • Re: Can anyone see a faster way to compute quantities for a pair or
    • From: Ray Koopman <koopman@sfu.ca>