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Re: Combine matrices of equal height

  • To: mathgroup at smc.vnet.net
  • Subject: [mg111061] Re: Combine matrices of equal height
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Sun, 18 Jul 2010 01:07:10 -0400 (EDT)

First, unless I've missed something, it's not so easy find out how to do 
this by searching the documentation.

Second, I always hesitate to deem a method "the best way" to do 
something. But Join with a third argument designating joining at "level" 
2 does the trick nicely.

This is documented twice on page ref/Join, first in the Scope section 
and then again in the Applications section.  Example, like those:

   m1 = {{a,b,c},{d,e,f},{g,h,i}};
   m2 = {{x,y}, {u,v}, {z,w}};
   wider = Join[m1, m2, 2]

Thus there is no need to resort to the "trick" of using Transpose.

Third, the difficulty here is, to my mind, a limitation of Mathematica's 
inherent lack of any true array structure but rather just the 
one-dimensional structure of lists. Higher-order arrays need to be built 
more or less explicitly from lists.  And that means the seemingly 
artificial way of treating questions such as yours, by means of a 
"level" specification.

In a language that has a full-fledged development of arrays of any order 
(e.g., APL and, especially, J), such things as you ask are often easier, 
and more general, to handle.

On 7/17/2010 8:16 AM, Sam Takoy wrote:
> Hi,
>
> Given two matrices of equal height, what's the best way to combine them.
> Here's what I did
>
> TF[m_] := Flatten[Transpose[m]]
> Combine[m1_, m2_] :=
>    Partition[Join[m1 // TF, m2 // TF], Length[m1]] // T
>
>
> Surely there's a better way of doing it.
>
> Thanks!
>

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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