Matlab - Vectorizing nested loops when the inner loop depends on the outer ones

Question

I'm working on a function which takes an n-by-1 array (called "ts") as input and creates a n-by-n matrix (called "V"), where each element of V is either 0 or 1.

Now imagine "ts" as a plot: If one can connect an arbitrary point (e.g. ts(5)) with another arbitrary point (e.g. ts(47)) using a straight line without intersecting the time series, then the matrix elements V(5,47) and V(47,5) should be 1. If the two points can't be connected without intersecting the time series then the corresponding elements in the matrix should be 0. This is supposed to be done for all possible pairs of points in "ts".

Here's the function: It works, but it's very inefficient (especially because of the three nested loops). Is there a way to vectorize this code?

function V = someFunction(ts)
len = length(ts);
V = zeros(len, len);
for a = 1:len,
   for b = 1:len,
       intersection = [];
       for c = min(a,b)+1 : max(a,b)-1,
           t_a = a;
           y_a = ts(a);
           t_b = b;
           y_b = ts(b);
           t_c = c;
           y_c = ts(c);

           if (y_c < y_b + (y_a - y_b) * ((t_b - t_c) / (t_b - t_a))),
               intersection = [intersection; 0];
           else
               intersection = [intersection; 1];
           end
       end
       if all(intersection==0),
           V(a,b) = 1;
       end
   end
end
end

You're growing intersection, yuo should preallocate it.

Oleg
– Oleg

2013-05-30 08:47:13 +00:00
Commented May 30, 2013 at 8:47 — Oleg
– Oleg, Commented May 30, 2013 at 8:47
@OlegKomarov - it can be removed altogether.

Shai
– Shai

2013-05-30 09:23:48 +00:00
Commented May 30, 2013 at 9:23 — Shai
– Shai, Commented May 30, 2013 at 9:23

Community · Accepted Answer · 2017-05-23 12:05:24Z

3

several things:

no need to create array intersection the moment you hit the else clause you know V(a,b) is zero.
Since V is symmetric, you can compute only .5*n*(n-1) entries instead of n^2 (same O(n^2), but still far less).
Another observation made by Oleg is: "you do not need to perform any check if the segment is 3 points long, in which case there cannot be any intersection by construction"

New code

V = ones(len,len); % default for all
for a = 1:(len-3),
   for b = (a+3):len,
      for c = min(a,b)+1 : max(a,b)-1,
          t_a = a;
          y_a = ts(a);
          t_b = b;
          y_b = ts(b);
          t_c = c;
          y_c = ts(c);

          if (y_c < y_b + (y_a - y_b) * ((t_b - t_c) / (t_b - t_a))),
              % do nothing
          else
              V(a,b) = 0; % intersect
              V(b,a) = 0;
              break; % stop the inner loop the moment an intersection was found
          end
      end
   end
end

edited May 23, 2017 at 12:05

CommunityBot

11 silver badge

answered May 30, 2013 at 9:23

Shai

115k39 gold badges259 silver badges398 bronze badges

Sign up to request clarification or add additional context in comments.

3 Comments

Eitan T Over a year ago

@Shai, well the original code always produces a symmetric matrix, while yours does not. Try running both with the input ts = [-1 5 20 -1].

Oleg Over a year ago

You can also include my remark (from my deleted answer) that segments of three points cannot intersect by construction, thus having a = 1:len-3 and b = a+3:len.

Shai Over a year ago

@OlegKomarov - I incorporated your remark to the code. Thanks.

Collectives™ on Stack Overflow

Matlab - Vectorizing nested loops when the inner loop depends on the outer ones

1 Answer 1

3 Comments

Your Answer

Hot Network Questions

Collectives™ on Stack Overflow

1 Answer 1

3 Comments

Your Answer

Sign up or log in

Post as a guest

Related