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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: [mg68545] Re: Newbie question about column sums of arrays
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Wed, 9 Aug 2006 04:19:56 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <eb9pue$t5p$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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.

Hi George,

Array does not do what you think. What you want is to use Table [1] in 
place of Array to get your array/table/matrix/list_of_list.

AA1 = Table[(-1)^Random[Integer], {4}, {4}]

--> {{-1, 1, -1, 1}, {-1, -1, -1, -1}, {1, 1, -1, -1},
  {-1, -1, -1, 1}}

TableForm[AA1]

-->  -1    1    -1    1

      -1   -1    -1   -1

       1    1    -1   -1

      -1   -1    -1    1

(* Sum by columns *)
Total[AA1]

--> {-2, 0, -4, 0}

(* Sum by rows *)
Total[Transpose[AA1]]

--> {0, -4, 0, -2}

HTH,
Jean-Marc

[1] http://documents.wolfram.com/mathematica/functions/Table


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