RE: Fast (compiled) routine for element testing and replacement in large matrices?

*To*: mathgroup at smc.vnet.net*Subject*: [mg23958] RE: [mg23929] Fast (compiled) routine for element testing and replacement in large matrices?*From*: "David Park" <djmp at earthlink.net>*Date*: Sun, 18 Jun 2000 03:00:41 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

> -----Original Message----- > From: Gareth J. Russell [mailto:russell at cerc.columbia.edu] To: mathgroup at smc.vnet.net > Hello, > > My first post. I am moving from another software package to > Mathematica, and > I often work with very large matrices in the context of simulations, so > speed is important. Here is a problem for which I would like a > serious speed > increase. > > Given a matrix of real numbers, I want to generate a new matrix where > values from a certain range are replaced with 1, and the remainder with > zero. Matrix size is often on the order of 1000 by 1000 (they are always > square). > > I defined a function that does the comparison using If[], > and made it listable: > > d2wreal[w_,l_,u_] := If[(w>l)&&(D<=u),1,0] > SetAttributes[d2wreal,Listable] > > These are typical times: > > a = Table[Random[], {i, 1, 100}, {j, 1, 100}]; > t = Timing[b = d2wreal[a, 0.2, 0.4]][[1]] > 0.46666666666666856 Second > > a = Table[Random[], {i, 1, 1000}, {j, 1, 1000}]; > t = Timing[b = d2wreal[a, 0.2, 0.4]][[1]] > 65.55 Second > > I tried to generate some compiled alternatives myself, but I couldn't find > one that was faster. I reckon a 10x speed-up should be possible, possibly > more. My other software takes only 0.75 seconds for the 1000 by > 1000 matrix > function. > > Can anyone suggest a way to speed this up? > > Thanks, > > Gareth Gareth, I didn't quite understand your d2wreal routine so rewrote it as follows. op[l_, u_][x_] := If[l <= x <= u, 1, 0] This generates a random test matrix. a = Table[Random[], {i, 1, 1000}, {j, 1, 1000}]; This, more or less, corresponds to your method, and on my computer gives: Map[op[0.2, 0.4], a, {2}]; // Timing {17.2 Second, Null} After playing around, I came up with the following method which is about three times as fast. Unprotect[LessEqual]; SetAttributes[LessEqual, Listable]; Protect[LessEqual]; LessEqual[0.2, a, 0.4] /. {False -> 0, True -> 1}; // Timing {5.82 Second, Null} But with any luck at all, some of the speed demons in MathGroup will come up with something even better. David Park djmp at earthlink.net http://home.earthlink.net/~djmp/