Finding islands of zeros in a sequence

Question

Imagine you have a very long sequence. What is the most efficient way of finding the intervals where the sequence is all zeros (or more precisely the sequence drops to near-

Answer 1

As gnovice showed, we'll do a threshold test to make "near zero" really zero:

logcl = abs(sig(:)) >= zero_tolerance;

Then find regions where the cumulative sum isn't increasing:

cs = cumsum(logcl);
islands = cs(1+thresh:end) == cs(1:end-thresh);

Remembering gnovice's great method for filling in ranges of indexes

v = zeros(1,max(endInd)+1);   %# An array of zeroes
v(startInd) = 1;              %# Place 1 at the starts of the intervals
v(endInd+1) = v(endInd+1)-1;  %# Add -1 one index after the ends of the intervals
indices = find(cumsum(v));  %# Perform a cumulative sum and find the nonzero entries

We note that our islands vector already has ones in the startInd locations, and for our purposes endInd always comes thresh spots later (longer runs have runs of ones in islands)

endcap = zeros(thresh,1);
indices = find(cumsum([islands ; endcap] - [endcap ; islands]))

Test

sig = [1 1 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0];
logcl = abs(sig(:)) >= .1;
cs = cumsum(logcl);
islands = cs(1+thresh:end) == cs(1:end-thresh);
endcap = zeros(thresh,1);
indices = find(cumsum([islands ; endcap] - [endcap ; islands]))

indices =

     2
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    13
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    15