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Re: Add terms surrounded by zero together in matrix
*To*: mathgroup at smc.vnet.net
*Subject*: [mg59132] Re: Add terms surrounded by zero together in matrix
*From*: Paul Abbott <paul at physics.uwa.edu.au>
*Date*: Sat, 30 Jul 2005 01:25:05 -0400 (EDT)
*Organization*: The University of Western Australia
*References*: <dcccur$3j7$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
In article <dcccur$3j7$1 at smc.vnet.net>,
"mchangun at gmail.com" <mchangun at gmail.com> wrote:
> 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.
Have a look at the literature on percolation clusters and in the
MathGroup archive.
I would have thought that you could use
<< Statistics`ClusterAnalysis`
to solve this, but I could not get it to work right. The basic idea I
had was to locate the non-zero entries in
dat = {{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}};
using Position:
pos = Position[dat, n_Integer /; n > 0]
and then apply FindClusters to these positions. For example,
cl = FindClusters[pos, DistanceFunction -> BrayCurtisDistance]
gives 3 clusters (I tried other distance metrics and several of the
myriad of options to FindClusters to try to get FindClusters to only
find "connected" clusters). From these clusters,
Extract[dat, #] & /@ cl
gets the values in each cluster, and
Total /@ %
gives the totals for each cluster. Maybe others can see how to improve
on this -- or explain why this approach cannot work.
Cheers,
Paul
--
Paul Abbott Phone: +61 8 6488 2734
School of Physics, M013 Fax: +61 8 6488 1014
The University of Western Australia (CRICOS Provider No 00126G)
AUSTRALIA http://physics.uwa.edu.au/~paul
http://InternationalMathematicaSymposium.org/IMS2005/
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