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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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