Re: Newbie question about column sums of arrays

*To*: mathgroup at smc.vnet.net*Subject*: [mg68569] Re: Newbie question about column sums of arrays*From*: Torsten Coym <torsten.coym at eas.iis.fraunhofer.de>*Date*: Wed, 9 Aug 2006 23:57:11 -0400 (EDT)*References*: <eb9pue$t5p$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

George, The array you provided does not contain 1 and -1, but 1[1,1], -1[1,3] and so forth, which are completely different expressions. To get a 4x4 matrix with random 1 and -1 you could instead write: AA1 = Array[(-1)^Random[Integer] & , {4, 4}] {{1, 1, -1, 1}, {1, 1, 1, 1}, {1, -1, 1, -1}, {1, -1, 1, -1}} Or: AA1 = Array[x, {4, 4}] /. _x :> (-1)^Random[Integer] which replaces everything that /has a head x/ with Random 1 or -1, while your replacement rule replaces everything that /is the object x/. Then Total[] does exactly what you want: Total[AA1] Out[892]= {4, 0, 2, 0} Torsten 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/ > >