Re: Threading over matrices

*To*: mathgroup at smc.vnet.net*Subject*: [mg90762] Re: Threading over matrices*From*: Alberto Verga <Alberto.Verga at laposte.net>*Date*: Wed, 23 Jul 2008 05:58:15 -0400 (EDT)*References*: <g64487$djo$1@smc.vnet.net>

Hi, You may try MapThread[] For example: Create the data x = RandomReal[{0, 1}, {3, 4}] y = RandomReal[{0, 1}, {3, 4}] {{0.0617457, 0.895605, 0.766934, 0.0769308}, {0.226479, 0.0894829, 0.563185, 0.789292}, {0.0419649, 0.823764, 0.597748, 0.513526}} {{0.610528, 0.955936, 0.999041, 0.0561156}, {0.59444, 0.375375, 0.659419, 0.205936}, {0.278044, 0.874925, 0.532864, 0.799205}} Define the desired function f, f = If[#1 > #2, 1/#1, #1 - #2] & Use MapThread to apply f to each pair {x(i,j),y(i,j)} of numvers: MapThread[f, {x, y}, 2] You get the matrix: {{-0.548783, -0.0603309, -0.232108, 12.9987}, {-0.367961, -0.285892, -0.0962331, 1.26696}, {-0.236079, -0.0511604, 1.67295, -0.285678}} Alberto Verga "<\"@frank-exchange-of-views.oucs.ox.ac.uk" <"Robert> wrote: > 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