MATLAB: How to divide large data in small intervals

matrix reduction; division into intervals; large scaling

How to divide a large matrix into small intervals?
For example, take the matrix [1 1; 1 2; 2 3; …;5 100; 6 100; …; 1 1.0e4; …; 5 1.0e9] with many entries.
How to efficiently divide the second column into intervals of length 1, e.g. [0,1], [1,2]…[1000,1001] and so on such that, for each interval, the elements of the first column sum to 1.
Small example: M = [1 1; 2 1; 1 10; 3 10];
The output should be:
M_out = [0.333 1; 0.6667 1; 0.25 10; 0.75 10]
Take M=[1 1; 2 1; 1 1.5; 1 10; 1 10.6; 3 10];
M_out = [0.25 1; 0.5 1; 0.25 1.5; 0.20 10; 0.20 10.6; 0.6 10]
The solution could be
for i=1:1.0e9; j=find (i <= M(:,2) & M(:,2) < i+1); M(j,1) = M(j,1)./sum(M(j,1)); end
However, is it an efficiently way to do it?

Best Answer

It's not very clear from your question that you want to bin the second column in bins of width 1, and you haven't given a criteria for the bin edges. Should the edges always be integer?
Anyway, find out which bin your second column falls into with discretize and use these bins as input to accumarray as per Star's or the cyclist's answer:
M = [1 1; 2 1; 1 1.5; 1 10; 1 10.6; 3 10];
%compute bins. Assume integer edges
binlow = floor(min(M(:, 2)));  
binhigh = ceil(max(M(:, 2)));
if binhigh == max(M(:, 2)), binhigh = binhigh + 1; end %otherwise if max is integer it'll be included in the previous bin
binidx = discretize(M(:, 2), binlow : binhigh);
%apply to accumarray
binsum = accumarray(binidx, M(:, 1));
%normalise 
M_out = [M(:, 1) ./ binsum(binidx), M(:, 2)]
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