Matlab - Speeding up Nested For-Loops - performance

Question

I'm working on a function with three nested for loops that is way too slow for its intended use. The bottleneck is clearly the looping part - almost 100 % of the execution time is spent in the innermost loop.
The function takes a 2d matrix called rM as input and returns a 3d matrix called ec:
rows = size(rM, 1);
cols = size(rM, 2);
%preallocate.
ec = zeros(rows+1, cols, numRiskLevels);
ec(1, :, :) = 100;
for risk = minRisk:stepRisk:maxRisk;
for c = 1:cols,
for r = 2:rows+1,
ec(r, c, risk) = ec(r-1, c, risk) * (1 + risk * rM(r-1, c));
end
end
end
Any help on speeding up the for loops would be appreciated...

Answer 1

The problem is, that the inner loop is slowest, while it is also near-impossible to vectorize. As every iteration directly depends on the previous one.
The outer two are possible:
clc;
rM = rand(50);
rows = size(rM, 1);
cols = size(rM, 2);
minRisk = 1;
stepRisk = 1;
maxRisk = 100;
numRiskLevels = maxRisk/stepRisk;
%preallocate.
ec = zeros(rows+1, cols, numRiskLevels);
ec(1, :, :) = 100;
riskArray = (minRisk:stepRisk:maxRisk)';
tic
for r = 2:rows+1
tmp = riskArray * rM(r-1, :);
tmp = permute(tmp, [3 2 1]);
ec(r, :, :) = ec(r-1, :, :) .* (1 + tmp);
end
toc
%preallocate.
ec2 = zeros(rows+1, cols, numRiskLevels);
ec2(1, :, :) = 100;
tic
for risk = minRisk:stepRisk:maxRisk;
for c = 1:cols
for r = 2:rows+1
ec2(r, c, risk) = ec2(r-1, c, risk) * (1 + risk * rM(r-1, c));
end
end
end
toc
all(all(all(ec == ec2)))
But to my surprise, the vectorized code is indeed slower. (But maybe someone can improve the code, so I figured I leave it her for you.)

Answer 2

I have just tried to vectorize the outer loop, and actually noticed a significant speed increase. Of course it is hard to judge the speed of a script without knowing (the size of) the inputs but I would say this is a good starting point:
% Here you can change the input parameters
riskVec = 1:3:120;
rM = rand(50);
%preallocate and calculate non vectorized solution
ec2 = zeros(size(rM,2)+1, size(rM,1), max(riskVec));
ec2(1, :, :) = 100;
tic
for risk = riskVec
for c = 1:size(rM,2)
for r = 2:size(rM,1)+1
ec2(r, c, risk) = ec2(r-1, c, risk) * (1 + risk * rM(r-1, c));
end
end
end
t1=toc;
%preallocate and calculate vectorized solution
ec = zeros(size(rM,2)+1, size(rM,1), max(riskVec));
ec(1, :, :) = 100;
tic
for c = 1:size(rM,2)
for r = 2:size(rM,1)+1
ec(r, c, riskVec) = ec(r-1, c, riskVec) .* reshape(1 + riskVec * rM(r-1, c),[1 1 length(riskVec)]);
end
end
t2=toc;
% Check whether the vectorization is done correctly and show the timing results
if ec(:) == ec2(:)
t1
t2
end
The given output is:
t1 =
0.1288
t2 =
0.0408
So for this riskVec and rM it is about 3 times as fast as the non-vectorized solution.