Create Vector Ranges From Variables

Question

I have two vectors that hold the "start" and "end" locations (as logicals) that I wish to combine as to create a third vector, Final:

Starts = [0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0];
Ends =   [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0];

With the Final Vector looking like this:

Final =  [0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0];

Currently, I can accomplish this using a for loop as follows:

Start_Locations = find(Starts);
End_Locations = find(Ends);
Final = zeros(20,1);

for x=1:length(Start_Locations)

    Final(Start_Locations(x):End_Locations(x),1) = 1;

end

I was wondering if there's a way to accomplish the same exact thing without a for loop. For example, I could accomplish what I outlined above with the following "hard-coded" statement:

Final([4:8,11:19],1) = 1;

Specifically, is there a way to combine the Start_Locations and End_Locations vectors in a way such that I could have a single statement like:

Final(Combined_Start_and_End_Locations,1) = 1;

to accomplish what I did with the for loop above? I'm trying to learn to avoid for loops as much as I can and would really appreciate any solution that creates the Final vector as described above without resorting to a loop.

Answer 1

Problems like this can often be solved using either diff or cumsum. They are essentially discrete derivative and integration functions.

For your problem I believe that

Final = cumsum([Starts 0]-[0 Ends]);
Final = Final(1:end-1);

achieves the desired result.