How do I make modulo and logical indexing work faster? - matlab

Question

Consider the following command:
c(c>A | c<1) = mod(c(c>A | c<1),A);
where c is a column vector, and A is a scalar.
In short: Is there any way to make this work faster?
Explanation:
c(i) represents a column number in an A-by-A matrix. However, it may have values greater than A or smaller than 1, and this command should fix it in a sort of 'PAC-MAN' way. If c(i) is greater than A then when you reach A start counting back from 1, if you reach A again start again from 1, and so forth, until you count to the value of c(i). This should work in the same way for c(i)<1, so the counting will be reversed.
Examples:
If A = 10 and c(i) = 17, then c(i) after this command
should be 7.
If A = 10 and c(i) = -8, then c(i) after this command
should be 2.
If A = 10 and c(i) = 213, then c(i) after this command
should be 3.
The motivation: This command is a part of a simulation model I have, and currently it is the slowest part in it. This specific row is called millions(!) of times in each realization of the model, and there are a lot, so any improvement will be helpful. BTW, the typical size of c is about 10K-by-1.
p.s.: if you have a better suggestion for the title, I'll be happy to change it, I couldn't find a good one.

Answer 1

You don't need to actually do any logical indexing here because any values excluded by c > A | c < 1 will not be touched by mod and it will likely be faster to just pass everything to mod rather than doing comparisons and indexing to determine which values to pass to mod.
c = [17 -8 213, 7];
c = mod(c, A);
% 7 2 3 7
In general though, for other functions in which you need logical indexing on the input and output of a function, you'll want to store the logical array in a temporary variable rather than computing it twice:
touse = c < 1 | c > A;
c(touse) = mod(c(touse), A);
Here is a quick little benchmark showing the relative performance of each method:
function timemod()
sizes = round(linspace(100, 100000, 10));
[times1, times2, times3] = deal(zeros(numel(sizes), 1));
A = 10;
for k = 1:numel(sizes)
data = round(rand(sizes(k), 1) * A * 100);
times1(k) = timeit(#()indexing(data, A));
data = round(rand(sizes(k), 1) * A * 100);
times2(k) = timeit(#()indexing_temp(data, A));
data = round(rand(sizes(k), 1) * A * 100);
times3(k) = timeit(#()mod(data, A));
end
figure
plot(sizes, 1000 * cat(2, times1, times2, times3))
legend({'Indexing', 'Indexing w/ temp', 'No Indexing'})
xlabel('Number of Elements')
ylabel('Execution Time (ms)')
fprintf('Indexing: %0.2f ms\n', mean(times1 * 1000))
fprintf('Indexing with temp: %0.2f ms\n', mean(times2 * 1000))
fprintf('No Indexing or temp: %0.2f ms\n', mean(times3 * 1000))
end
function data = indexing(data, A)
data(data > A | data < 1) = mod(data(data > A | data < 1), A);
end
function data = indexing_temp(data, A)
inds = data > A | data < 1;
data(inds) = mod(data(inds), A);
end