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

• To: mathgroup at smc.vnet.net
• Subject: [mg127456] Re: Can anyone see a faster way to compute quantities for a pair or
• From: Ray Koopman <koopman at sfu.ca>
• Date: Thu, 26 Jul 2012 03:34:05 -0400 (EDT)
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• References: <juim0j\$k9a\$1@smc.vnet.net> <20120724081538.B3AF16802@smc.vnet.net>

```On Jul 24, 11:34 pm, W Craig Carter <ccar... at MIT.EDU> wrote:
> 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]]}

I can only speculate about why the original code is slow,
but I can offer informed advice about how to keep my code
running fast: gradfield must be a packed array.

Also, my code for the angles can be simplified slightly,
with no change in speed:

psifield2 = ArcTan[gradfield[[1]] + UnitStep[-magfield2],
gradfield[[2]]]

```

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