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MathGroup Archive 2006

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RE: Newbie question about column sums of arrays

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68552] RE: [mg68508] Newbie question about column sums of arrays
  • From: "David Park" <djmp at earthlink.net>
  • Date: Wed, 9 Aug 2006 04:20:23 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

George,

First let's get an actual array of + and - 1s. Use a pure function.

(AA1 = Array[ (-1)^Random[Integer] &, {4, 4}]) // MatrixForm

Then use Total on the Transpose.

Total@Transpose[AA1]

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/ 

From: George W. Gilchrist [mailto:gwgilc at wm.edu]
To: mathgroup at smc.vnet.net

I have spent several hours trying to find an answer to what must be  
an incredibly simple problem: how to sum the columns of an array  
containing a random mix of +1 and -1s. For example:

In[7]:=
AA1=Array[x, {4,4}]/. x:> (-1)^Random[Integer]


Out[7]=
\!\(\*FormBox[
   RowBox[{"(", "\[NoBreak]", GridBox[{
         {\(1[1, 1]\), \(1[1, 2]\), \(\((\(-1\))\)[1, 3]\), \(1[1, 4] 
\)},
         {\(1[2, 1]\), \(1[2, 2]\), \(\((\(-1\))\)[
           2, 3]\), \(\((\(-1\))\)[2, 4]\)},
         {\(1[3, 1]\), \(\((\(-1\))\)[3, 2]\), \(1[3, 3]\), \(1[3, 4] 
\)},
         {\(\((\(-1\))\)[4, 1]\), \(1[4,
           2]\), \(1[4, 3]\), \(\((\(-1\))\)[4, 4]\)}
         },
       RowSpacings->1,
       ColumnSpacings->1,
       ColumnAlignments->{Left}], "\[NoBreak]", ")"}],  
TraditionalForm]\)

In[8]:=
Total[AA1]

Out[8]=
{(-1)[4,1]+1[1,1]+1[2,1]+1[3,1],
  (-1)[3,2]+1[1,2]+1[2,2]+1[4,2],
  (-1)[1,3]+(-1)[2,3]+1[3,3]+1[4,3],
  (-1)[2,4]+(-1)[4,4]+1[1,4]+1[3,4]}


So, Total[] seems to do the right thing, but I cannot get the actual  
sums as real numbers, only this rather verbose representation. I have  
searched the manuals for just about everything I can think of with no  
luck. So, thanks for any help you can give me.


Cheers, George

..................................................................
George W. Gilchrist                        Email #1: gwgilc at wm.edu
Department of Biology, Box 8795          Email #2: kitesci at cox.net
College of William & Mary                    Phone: (757) 221-7751
Williamsburg, VA 23187-8795                    Fax: (757) 221-6483
http://gwgilc.people.wm.edu/




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