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Re: Comparing Corresponding Columns of Two Matrices

  • To: mathgroup at smc.vnet.net
  • Subject: [mg97578] Re: [mg97496] Comparing Corresponding Columns of Two Matrices
  • From: Gregory Lypny <gregory.lypny at videotron.ca>
  • Date: Mon, 16 Mar 2009 04:22:52 -0500 (EST)
  • References: <200903141039.FAA12977@smc.vnet.net>

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



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