Concatenate and sort 2 Matrices containing intervals

I have 2 Matrices A and B that have to be concatenated and sorted in a way that C is the result for the given example

if true
A = [ 1 5 0.01 ; 5 10 0.02; 10 20 0.03];
B = [ 6 7 0.04 ; 9 15 0.05 ];

C = [1 5 0.01 ; 5 6 0.02; 6 7 0.04; 7 9 0.02; 9 15 0.05; 15 20 0.03];
end

A contains intervals and has to be extended by given intervals in B.

any suggestions?

[Azzi Abdelmalek]

This is not clear

Answer 1

[Guillaume]

Assuming that your intervals don't span too big of a range and that they're all on integer boundaries, you could expand both A and B into a list of integers and corresponding values, union the two together and transform the union back into intervals:

A = [ 1 5 0.01 ; 5 10 0.02; 10 20 0.03];
B = [ 6 7 0.04 ; 9 15 0.05 ];

%function to expand intervals
expandinterval= @(m) cell2mat(cellfun(@(row) [row(1):row(2)-1; repmat(row(3), 1, row(2)-row(1))], num2cell(m, 2)', 'UniformOutput', false));

expA = expandinterval(A);
expB = expandinterval(B);
%compute the union of the 1st row of the 2 sets. 
%Don't use union as it makes it difficult to track where the elements come from
%instead use unique:
merged = [expB, expA]; %put B first so that it takes precedence over the same values in A
[expC, origcol] = unique(merged(1, :));  %union of 1st row
expC(2, :) = merged(2, origcol); %and corresponding 2nd row
%now compact back into intervals:
%I assume here that expC(1, :) is continuous as in your example, so we only have to deal with discontinuities in the 2nd row.
%If not, the code will have to be more complex
assert(all(diff(expC(1, :)) == 1), 'intervals are not continuous');
edges = find(diff(expC(2, :))); %find discontinuities in second row
C = [expC(1, [0, edges] + 1); expC(1, [edges, end]) + 1; expC(2, [0, edges] + 1)].'

See also my two cody problems 2545 and 2528 which deal with something similar.