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MathGroup Archive 2005

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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


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