How to divide large data in small intervals?
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Anderson
el 22 de Abr. de 2016
Comentada: Guillaume
el 22 de Abr. de 2016
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?
2 comentarios
Image Analyst
el 22 de Abr. de 2016
Editada: Image Analyst
el 22 de Abr. de 2016
Is this your homework?
Respuesta aceptada
Guillaume
el 22 de Abr. de 2016
Editada: Guillaume
el 22 de Abr. de 2016
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)]
2 comentarios
Guillaume
el 22 de Abr. de 2016
If you're not using up to date matlab, please mention it in your question.
Any histogram function will do, the second return value of histc will work. Since histc behaves differently for the last edge, the code becomes:
binlow = floor(min(M(:, 2)));
binhigh = ceil(max(M(:, 2))) + 1; %always add an extra bin
[~, binidx] = histc(M(:, 2), binlow:binhigh);
%accumarray code as before
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the cyclist
el 22 de Abr. de 2016
Editada: the cyclist
el 22 de Abr. de 2016
M = [1 1; 2 1; 1 10; 3 10];
[~,~,idx] = unique(M(:,2));
S = accumarray(idx,M(:,1),[]);
M_out = [M(:,1)./S(idx),M(:,2)]
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