How to speed up a for while loop in Matlab - matlab

Question

I defined two same size vectors t and coverage in Matlab, and I need to define a third vector n_steps.
In particular I need to speed up the following loop:
t = 1:100000;
coverage = double(rand(size(t)) > 0.9);
for j=1:(length(t)-1)
n_steps(j)=0;
while coverage(j+n_steps(j)+1)==0 && j+n_steps(j)+1<length(t)
n_steps(j)=n_steps(j)+1;
end
end
t is a time vector, and coverage at each time step can be 1 or 0.
For each instant t(j) I must find the number of time steps n_steps(j) to wait before the first 1 appears in the vector coverage(j+1:length(coverage)),

Answer 1

Your code (with the example data I added to it) runs in 0.0163 s on MATLAB Online. Just adding
n_steps = zeros(1,length(t)-1);
before the loop reduces the execution time to 0.0057 seconds. Preallocation is very important!
Next, I was able to change your code a bit, such that you don't need to search through the same array over and over again:
n_steps = zeros(1,length(t)-1);
cov = [find(coverage), length(t)];
k = 1;
for j=1:(length(t)-1)
if cov(k) <= j
k = k+1;
end
n_steps(j) = cov(k) - j - 1;
end
This code runs in 0.0015 seconds. It relies on creating a smaller array, cov, that contains the indices to non-zero elements in coverage. cov(k) is the index into coverage for a non-zero element. As we move j forward, sometimes we need to move the index k forward too, such that cov(k) comes after j.
It might be possible to further vectorize the outer loop, but I doubt it will make the code much faster.
This is the script I wrote for timing and testing correctness:
t = 1:100000;
coverage = double(rand(size(t)) > 0.9);
timeit(#() method1(t, coverage))
timeit(#() method2(t, coverage))
timeit(#() method3(t, coverage))
a = method1(t, coverage);
b = method3(t, coverage);
assert(isequal(a,b))
function n_steps = method1(t, coverage)
for j=1:(length(t)-1)
n_steps(j)=0;
while coverage(j+n_steps(j)+1)==0 && j+n_steps(j)+1<length(t)
n_steps(j)=n_steps(j)+1;
end
end
end
function n_steps = method2(t, coverage)
n_steps = zeros(1,length(t)-1);
for j=1:(length(t)-1)
while coverage(j+n_steps(j)+1)==0 && j+n_steps(j)+1<length(t)
n_steps(j) = n_steps(j)+1;
end
end
end
function n_steps = method3(t, coverage)
n_steps = zeros(1,length(t)-1);
cov = [find(coverage), length(t)];
k = 1;
for j=1:(length(t)-1)
if cov(k) <= j
k = k+1;
end
n_steps(j) = cov(k) - j - 1;
end
end