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I have two date-time arrays a and b.

a for start time and b for end time (above horizontal line on the picture).

What is the way to parse them and get what is beneath horizontal line on the picture?

David Goodmanson
on 14 Nov 2017

Edited: David Goodmanson
on 14 Nov 2017

Hi Rostislav

It looks like you want the union of closed intervals. Here is some code that I think does the job. When the ends of intervals have the same value, it works because the sort function is stable and preserves ordering for ties.

% Nx2 matrix of endpoints x1, x2 of intervals

x = [8 10; 2 4; 4 5; 5 7; 9 11; 15 16; 14 17; 10 12]

% -----plot it first

nline = repmat((1:size(x,1))',1,2);

plot(x',nline','o-')

ylim([-.5*nrow 1.5*nrow])

% ----- find union of intervals

x = sort(x,2);

nrow = size(x,1);

[x ind] = sort(x(:));

n = [(1:nrow) (1:nrow)]';

n = n(ind);

c = [ones(1,nrow) -ones(1,nrow)]';

c = c(ind);

csc = cumsum(c); % =0 at upper end of new interval(s)

irit = find(csc==0);

ilef = [1; irit+1];

ilef(end) = []; % no new interval starting at the very end

% y matrix is start and end points of the new intervals, y1,y2

%

% ny matrix is the corresponding indices of the start and end points

% in terms of what row of x they occurred in.

y = [x(ilef) x(irit)]

ny = [n(ilef) n(irit)]

Ted Shultz
on 21 Aug 2020 at 17:03

This is really great code. I fixed a small type, and added comments so others can learn from it as well.

intervalsIn = [8 10; 2 4; 4 5; 5 7; 9 11; 15 16; 14 17; 10 12]

% -----plot it first

nline = repmat((1:size(intervalsIn,1))',1,2);

nrow = size(intervalsIn,1);

plot(intervalsIn',nline','o-')

ylim([-.5*nrow 1.5*nrow])

% ----- find union of intervals

intervalsIn = sort(intervalsIn,2); % make the pairs always increasing pairs

[intervalsIn, ind] = sort(intervalsIn(:)); % sorts all the input values, and keepts track of how they moved around

c = [ones(1,nrow) -ones(1,nrow)]'; % this is a matrix that keeps track of when intervals start (1) and stop (-1)

c = c(ind); % put in order of occurrence

csc = cumsum(c); %sum up starts (1) and stops (-1) , will be =0 at upper end of new interval(s)

irit = find(csc==0); % find index locations of 0 (ends of intervals)

ilef = [1; irit+1]; % start of intervals index is at the very start (1) and one after all the other ends

ilef(end) = []; % no new interval starting at the very end

% spansOut matrix is start and end points of the new intervals, y1,y2

spansOut = [intervalsIn(ilef) intervalsIn(irit)]

Hung Doan
on 19 Jul 2019

nrow is undefined in the initial plotting but other than that, works like a charm!

Ted Shultz
on 21 Aug 2020 at 17:04

Small typo in original answer, code could be be:

intervalsIn = [8 10; 2 4; 4 5; 5 7; 9 11; 15 16; 14 17; 10 12]

% -----plot it first

nline = repmat((1:size(intervalsIn,1))',1,2);

nrow = size(intervalsIn,1);

plot(intervalsIn',nline','o-')

ylim([-.5*nrow 1.5*nrow])

% ----- find union of intervals

intervalsIn = sort(intervalsIn,2); % make the pairs always increasing pairs

[intervalsIn, ind] = sort(intervalsIn(:)); % sorts all the input values, and keepts track of how they moved around

c = [ones(1,nrow) -ones(1,nrow)]'; % this is a matrix that keeps track of when intervals start (1) and stop (-1)

c = c(ind); % put in order of occurrence

csc = cumsum(c); %sum up starts (1) and stops (-1) , will be =0 at upper end of new interval(s)

irit = find(csc==0); % find index locations of 0 (ends of intervals)

ilef = [1; irit+1]; % start of intervals index is at the very start (1) and one after all the other ends

ilef(end) = []; % no new interval starting at the very end

% spansOut matrix is start and end points of the new intervals, y1,y2

spansOut = [intervalsIn(ilef) intervalsIn(irit)]

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