Re: Comparing Corresponding Columns of Two Matrices

*To*: mathgroup at smc.vnet.net*Subject*: [mg97552] Re: [mg97496] Comparing Corresponding Columns of Two Matrices*From*: "David Park" <djmpark at comcast.net>*Date*: Sat, 14 Mar 2009 18:19:24 -0500 (EST)*References*: <17032823.1237030239609.JavaMail.root@m02>

Gregory, Here is one method. Whenever I want to perform some operation on two equal length vectors I think of the Inner command. In your problem we are going to apply this twice, once to compare the elements in two columns, and once to accumulate a list of results for all the columns. Here is a routine to compare the elements in two columns, each column given by a list, to see if all the elements in the first column are greater than the corresponding elements in the second column. greaterColumn[column1_, column2_] := Inner[#1 > #2 &, column1, column2, And] Try it out on two cases. greaterColumn[{2, 3, 4, 5}, {1, 2, 3, 4}] True greaterColumn[{2, 3, 4, 5}, {1, 6, 3, 7}] False The following will generate text xmat and ymat matrices. I make them only 8 rows long instead of 100. I also bias xmat to be greater than ymat so that we might get some True conditions. (xmat = Table[ RandomInteger[{3, 7}], {x, 1, 8}, {y, 1, 4}]) // MatrixForm (ymat = Table[ RandomInteger[{0, 5}], {x, 1, 8}, {y, 1, 4}]) // MatrixForm The following then compares the two matrices column by column. Inner[greaterColumn[#1, #2] &, f @@ Transpose[xmat], f @@ Transpose[ymat], List] There is one caveat or trick that I have used. For arrays, Inner works like Dot and this is not what we want. We want the two items to look like vectors and not arrays, so I used f@@ on the transposed matrices to change the outer List brackets to f, and now they no longer look like 2-dimensional arrays, but like 1-dimensional vectors. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: Gregory Lypny [mailto:gregory.lypny at videotron.ca] 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