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