Re: Add terms surrounded by zero together in matrix

*To*: mathgroup at smc.vnet.net*Subject*: [mg59150] Re: Add terms surrounded by zero together in matrix*From*: Peter Pein <petsie at dordos.net>*Date*: Sat, 30 Jul 2005 01:25:31 -0400 (EDT)*References*: <dcccur$3j7$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

mchangun at gmail.com schrieb: > Hi All, > > I think this is a rather tough problem to solve. I'm stumped and would > really appreciated it if someone can come up with a solution. > > What i want to do is this. Suppose i have the following matrix: > > 0 0 0 1 0 > 0 0 1 2 0 > 0 0 0 2 1 > 1 3 0 0 0 > 0 0 0 0 0 > 0 0 0 0 0 > 0 0 1 1 0 > 5 0 3 0 0 > 0 0 0 0 0 > 0 0 0 3 1 > > I'd like to go through it and sum the elements which are surrounded by > zeros. So for the above case, an output: > > [7 4 5 5 4] > > is required. The order in which the groups surrounded by zero is > summed does not matter. > > The elements are always integers greater than 0. > > Thanks for any help! > slow, but working: Clear[IslandSum]; IslandSum[m_] := Module[{pos = Position[m, _?Positive], r = {}, neighborQ = Max @@ Abs[#1 - #2] <= 1 & , neighbors, q, dq}, neighbors[l_, y_] := Pick[l, neighborQ[y, #1]& /@ l]; While[pos != {}, For[q = dq = {First[pos]}; pos = Rest[pos], pos != {} != dq, pos = Complement[pos, dq], dq = Flatten[neighbors[pos, #1]& /@ dq, 1]; q = Join[q, dq] ]; AppendTo[r, Union[q]]; ]; Plus @@@ Map[Extract[m, #1]& , r, {2}] ] (* your example *) mat = {{0, 0, 0, 1, 0}, {0, 0, 1, 2, 0}, {0, 0, 0, 2, 1}, {1, 3, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 1, 1, 0}, {5, 0, 3, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 3, 1}}; IslandSum[mat] --> {7, 4, 5, 5, 4} SeedRandom[19630724]; bigmat = Table[Boole[Random[] > 0.8], {100}, {50}]; First[Timing[ result = IslandSum[bigmat];]] Length[result] --> 6.359*Second 383 testmat = Table[Boole[Random[] > 0.8], {10}, {10}]; ListDensityPlot[Reverse[testmat]]; IslandSum[testmat] --> [graphic omitted] {4, 3, 1, 1, 1, 8, 3, 3, 1, 1} -- Peter Pein Berlin