# Partitioning a Vector

Recently on the MATLAB newsgroup, there was a thread asking how to split up a vector into pieces which were each monotonically increasing by the value 1. The post got several answers which I did not read first. Here's my thinking.

### Contents

#### Sample Data

Here's my sample data.

a=[2,3,4,7,9,12,13,14,15]

a =
2     3     4     7     9    12    13    14    15


#### Problem and Solution

I want to break this into 4 pieces: the runs 2:4 and 12:15, plus the scalars 7 and 9. Here's how I thought about the problem.

First I want to find the runs, which are elements that differ by 1. So I calculate the differences, making sure I include the final value in the array (which is why I append a 0 below).

ad = [diff(a) == 1 0]

ad =
1     1     0     0     0     1     1     1     0


Next, I figure out how many runs there are, by seeing how many 0 values are represented in the differences. This tells me how many arrays I will split my original array into.

numcells = sum(ad==0)
out = cell(1,numcells);

numcells =
4


Next I find the ending indices of the chunks by looking where ad is 0. Then I start to create contents for each cell in the cell array out, starting with index 1 in the original array.

indends = find(ad == 0);
ind = 1;
for k = 1:numcells
out{k} = a(ind:indends(k));
ind = indends(k)+1;
end


Here's what out looks like now.

out
out{:}

out =
[1x3 double]            [1x4 double]
ans =
2     3     4
ans =
7
ans =
9
ans =
12    13    14    15


#### File Exchange Function

On the File Exchange, you can get a more general purpose function called SplitVec on SplitVec by Bruno. It does this and a whole lot more.

#### Do You Need to Partition Data?

If you need to partition data, I'd like to understand why, and how you do so. Let me know here.

Published with MATLAB® R2012b

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