Re: "stepwise" integrating a 2D array

*To*: mathgroup at smc.vnet.net*Subject*: [mg91205] Re: "stepwise" integrating a 2D array*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Sat, 9 Aug 2008 07:46:44 -0400 (EDT)*References*: <g7h9mc$b73$1@smc.vnet.net>

Hi, try hvAccumulate[m_] := Reverse[Rest[FoldList[#1 + #2 & , 0, #]] & /@ Transpose[ Rest[FoldList[#1 + #2 & , 0, #]] & /@ Transpose[Reverse[m]]]] and hvAccumulate[{{a1, a2}, {b1, b2}}] gives {{a1 + b1, a1 + a2 + b1 + b2}, {b1, b1 + b2}} Regards Jens Claus wrote: > Hi, > I have an array, consisting of n tuples (x,y,z). > The first entry is the point at the bottom left (thinking in a > coordinate system, smallest (x,y) pair). > Now I want to do something like an "stepwise"/empirical integral over (x,y). > > Schematically, if I had a 2x2 array (only the z-values),like > > a1 a2 > b1 b2 > > I would want an array like this: > > a1+b1 b1+b2+a1+a2 > b1 b1+b2 > > In the code below, "xyzVals" is the array that I want to integrate, > containing the (x,y,z) tuples. > > I could do a bunch of for loops, but I am trying to not use do loops in > mathematica whenever possible. > Is it possible to do it without? > I tried some of the examples from > http://www.verbeia.com/mathematica/tips/HTMLLinks/Tricks_A-K_3.html > and I also thought about an array with sub-arrays, > but couldn't get it for me to work. > > Thanks for any pointers! > Claus > > > In[13]:= X = RandomReal[{0, 1}, 500]; > Y = RandomReal[{0, 1}, 500]; > BinWidth = 0.2; > DensVals = > Flatten[BinCounts[ > Transpose[{X, Y}], {0, 1, BinWidth}, {0, 1, BinWidth}]] > > Out[16]= {16, 16, 17, 26, 23, 23, 16, 18, 25, 17, 13, 26, 26, 21, 19, \ > 15, 32, 20, 21, 15, 11, 26, 16, 19, 23} > > In[17]:= xyzVals = Table[{i/(1/BinWidth) + (BinWidth/2), > j/(1/BinWidth) + (BinWidth/2), > DensVals[[(1/BinWidth) i + j + 1]]} > , {i, 0, (1/BinWidth) - 1} > , {j, 0, (1/BinWidth) - 1}] > > Out[17]= {{{0.1, 0.1, 16}, {0.1, 0.3, 16}, {0.1, 0.5, 17}, {0.1, 0.7, > 26}, {0.1, 0.9, 23}}, {{0.3, 0.1, 23}, {0.3, 0.3, 16}, {0.3, 0.5, > 18}, {0.3, 0.7, 25}, {0.3, 0.9, 17}}, {{0.5, 0.1, 13}, {0.5, 0.3, > 26}, {0.5, 0.5, 26}, {0.5, 0.7, 21}, {0.5, 0.9, 19}}, {{0.7, 0.1, > 15}, {0.7, 0.3, 32}, {0.7, 0.5, 20}, {0.7, 0.7, 21}, {0.7, 0.9, > 15}}, {{0.9, 0.1, 11}, {0.9, 0.3, 26}, {0.9, 0.5, 16}, {0.9, 0.7, > 19}, {0.9, 0.9, 23}}} >