Re: Comparing Corresponding Columns of Two Matrices

*To*: mathgroup at smc.vnet.net*Subject*: [mg97586] Re: [mg97496] Comparing Corresponding Columns of Two Matrices*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Mon, 16 Mar 2009 04:24:21 -0500 (EST)*References*: <200903141039.FAA12977@smc.vnet.net>*Reply-to*: drmajorbob at bigfoot.com

But somebody gave a solution using Clip that's probably much faster. Bobby On Sun, 15 Mar 2009 17:22:07 -0500, Gregory Lypny <gregory.lypny at videotron.ca> wrote: > Dr. Bob, > > This is cool, a cornucopia of mapping and @'s, a tutorial to keep me > busy for some time. > > Thanks, > > Gregory > > On Sat, Mar 14, 2009, at 4:46 PM, DrMajorBob wrote: > >> If I understand the problem correctly, then... in order of increasing >> speed or simplicity (I think): >> >> x = RandomInteger[{0, 3}, {10, 4}] >> y = RandomInteger[{0, 3}, {10, 4}] >> >> {{3, 3, 0, 3}, {3, 1, 2, 3}, {1, 2, 1, 1}, {0, 1, 3, 1}, {1, 2, 1, >> 2}, {0, 2, 3, 2}, {0, 1, 0, 3}, {0, 3, 1, 1}, {0, 0, 1, 1}, {0, 0, >> 3, 2}} >> >> {{0, 0, 3, 3}, {2, 1, 1, 1}, {1, 3, 2, 2}, {3, 1, 1, 3}, {0, 0, 2, >> 0}, {2, 1, 0, 2}, {2, 3, 3, 2}, {0, 0, 2, 1}, {3, 1, 2, 2}, {3, 3, >> 1, 1}} >> >> Map[Boole, Thread /@ Thread[Transpose@x > Transpose@y], {2}] >> >> {{1, 1, 0, 0, 1, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 1, 1, 0, 1, 0, 0}, {0, >> 1, 0, 1, 0, 1, 0, 0, 0, 1}, {0, 1, 0, 0, 1, 0, 1, 0, 0, 1}} >> >> or >> >> Map[Boole, Positive /@ (Transpose@x - Transpose@y), {2}] >> >> {{1, 1, 0, 0, 1, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 1, 1, 0, 1, 0, 0}, {0, >> 1, 0, 1, 0, 1, 0, 0, 0, 1}, {0, 1, 0, 0, 1, 0, 1, 0, 0, 1}} >> >> or >> >> f[a_] = Boole@Positive@a; >> SetAttributes[f, Listable] >> f /@ (Transpose@x - Transpose@y) >> >> {{1, 1, 0, 0, 1, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 1, 1, 0, 1, 0, 0}, {0, >> 1, 0, 1, 0, 1, 0, 0, 0, 1}, {0, 1, 0, 0, 1, 0, 1, 0, 0, 1}} >> >> or >> >> f[a_] = Boole@Positive@a; >> SetAttributes[f, Listable] >> f /@ Transpose[x - y] >> >> {{1, 1, 0, 0, 1, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 1, 1, 0, 1, 0, 0}, {0, >> 1, 0, 1, 0, 1, 0, 0, 0, 1}, {0, 1, 0, 0, 1, 0, 1, 0, 0, 1}} >> >> or >> >> Clear[f] >> f[a_, b_] := Boole@Positive[a - b]; >> SetAttributes[f, Listable] >> f[Transpose@x, Transpose@y] >> >> {{1, 1, 0, 0, 1, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 1, 1, 0, 1, 0, 0}, {0, >> 1, 0, 1, 0, 1, 0, 0, 0, 1}, {0, 1, 0, 0, 1, 0, 1, 0, 0, 1}} >> >> or >> >> Clear[f] >> f[a_, b_] := Boole@Positive[a - b]; >> SetAttributes[f, Listable] >> Transpose@f[x, y] >> >> {{1, 1, 0, 0, 1, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 1, 1, 0, 1, 0, 0}, {0, >> 1, 0, 1, 0, 1, 0, 0, 0, 1}, {0, 1, 0, 0, 1, 0, 1, 0, 0, 1}} >> >> Bobby >> >> On Sat, 14 Mar 2009 05:39:39 -0500, Gregory Lypny >> <gregory.lypny at videotron.ca> wrote: >> >>> Hello everyone, >>> >>> I'm trying to develop a modest skill in mapping functions and I've >>> been working on this problem. >>> >>> Suppose I have two 100 x 4 matrices, X and Y, and I want to see >>> whether each value in a column of X is bigger than each value in the >>> corresponding column of Y. In other words, compare column 1 of X with >>> column 1 of Y, column 2 of X with column 2 of Y, and so on. >>> >>> It's easy to generate a 100 x 4 table of Booleans using Table as >>> >>> Table[Boole[X[[i , j]] > Y[[i, j]]], {i, 100}, {j, 4}] >>> >>> But what about without Table? I am able to do it for the comparison >>> of any one column as >>> >>> Boole[#[[1]] > #[[2]]] & /@ Transpose[{X[[All, ]], Y[[All, 1]]}] >>> >>> but I'm not sure how to extend this to other columns. Any tip would >>> be much appreciated. >>> >>> Regards, >>> >>> Gregory >>> >> >> >> >> --DrMajorBob at bigfoot.com > -- DrMajorBob at bigfoot.com

**References**:**Comparing Corresponding Columns of Two Matrices***From:*Gregory Lypny <gregory.lypny@videotron.ca>