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Re: Threading over matrices

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90768] Re: Threading over matrices
  • From: "David Park" <djmpark at comcast.net>
  • Date: Wed, 23 Jul 2008 05:59:21 -0400 (EDT)
  • References: <g64487$djo$1@smc.vnet.net>

x = Table[Random[], {3}, {4}];
y = Table[Random[], {3}, {4}];
a = 0.5;

You need to get the Listable Attribute for your functions. Less is
 not Listable, so let's define our own Less that is.

SetAttributes[MyLess, Listable]
MyLess[p_, q_] := p < q
x~MyLess~y

And for the other two functions:

SetAttributes[f1, Listable]
f1[x_, y_] := If[x < y, 1/x, x - y]
x~f1~y

SetAttributes[f2, Listable]
f2[x_, y_] := Piecewise[{{1, x == a}, {x^2, x > a}}, x y^2]
x~f2~y


-- 
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/


<"Robert <"@frank-exchange-of-views.oucs.ox.ac.uk> wrote in message 
news:g64487$djo$1 at smc.vnet.net...
> How can I get evaluations to thread over matrices with
> conditional functions?
> Here's examples that show the behaviour that's really
> frustrating me.
> Create a couple of matrices:
>
> x = Table[Random[],{3},{4}];
> y = Table[Random[],{3},{4}];
> a=0.5;
>
> (These are example values I would like the following
> to apply to lists of any dimension.)
> When you add them they create a result with the same
> dimensions where each element corresponds to the
> input elements
>
> x + a y
>
> And some functions do similar
>
> Cos[x] + Sin[a y]
>
> But some don't, e.g.
>
> x > y
> x > a
>
> I would have liked those to produce a matrix of corresponding
> True and False results, and then something like:
>
> If[x > y, 1/x, x - y]
> Piecewise[{{1,x==a},{x^2,x>a}},x y^2]
>
> to produce a matrix of results corresponding to each element.
>
> They don't - I haven't managed to find out why they don't or
> more usefully how to do what I would like them to do.
>
> I have searched Help on all the likely commands (I think: Map,
> Thread, Apply, Distribute, ...) and this archive, where there
> are similar enquiries but none that match.  Perhaps I'm looking
> in the wrong place - I expect there's someone who can help.
>
> Robert
>
> 



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