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Re: Newbie question about column sums of arrays
*To*: mathgroup at smc.vnet.net
*Subject*: [mg68546] Re: [mg68508] Newbie question about column sums of arrays
*From*: "Adriano Pascoletti" <pascolet at dimi.uniud.it>
*Date*: Wed, 9 Aug 2006 04:20:07 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
George,
note that the entries of AA1 have the form (-1)[i,j] or 1[i,j], and Mathematica knows no rule for adding expresssions of that kind.
You wanted a constant function always returning x, which is written x&. That said,
use one of the following alternatives
AA1 = Array[x&, {4, 4}] /. x :> (-1)^Random[Integer]
AA1 = Array[(-1)^Random[Integer] &, {4, 4}]
AA1 = Table[ (-1)^Random[Integer], {4}, {4}]
and Total[AA1]
Adriano Pascoletti
George W. Gilchrist wrote ..
> 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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