Vectorizing multiple for loops in Matlab
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I am trying to code a mathematical model, and it involves computing a particular quantity over a grid of values thousands of times, with some changing model parameters. Currently, this is far too slow and I am looking for advice on vectorizing the most intensive part of my model.
The equation I am evaluating is:
I've currently got a basic implementation of it for ease of reading, but now want to vectorize the entire code segment below if possible. A minimal example of the code segment is:
% Setup grid to evaluate and results vector
T_max = 10000;
eval_points = linspace(0, T_max, 1000);
results = zeros(size(eval_points));
% Function that is used in computation
Z_func = @(x, omega) (1./(omega.*sqrt(2*pi))).*exp( -(x.^2)./(2.*omega.*omega) );
% Random data for now, known in full problem
historic_weights = rand(1,100);
historic_times = rand(1,100);
% Fixed single parameter omega
omega = 0.5;
% Time evaluation
tic()
for eval_counter = 1:size(eval_points,2)
temp_result = 0;
for historic_counter = 1:size(historic_weights,2)
for k = 0:1:T_max
temp_result = temp_result + Z_func( eval_points(eval_counter) - historic_times(historic_counter) + 1440*floor(historic_times(historic_counter)/1440) - 1440*k, omega );
end % End of looping over k
results(eval_counter) = results(eval_counter) + historic_weights(historic_counter)*temp_result;
end % End of looping over weights
end % End of looping over evaluation points
toc()
On my computer, this took just over 60 seconds to evaluate. I do not wish to use the parallel toolbox, as I am already using that elsewhere, and the shown segment of code is called on every process.
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Accepted Answer
darova
on 20 Sep 2019
I changed your code a bit
See attached script
2 Comments
Rik
on 20 Sep 2019
For those not wanting to download the script to see the solution:
clc,clear
% Setup grid to evaluate and results vector
T_max = 5;
t = linspace(0, T_max, 100);
res = zeros(size(t));
% Function that is used in computation
Z_func = @(x, omega) (1./(omega.*sqrt(2*pi))).*exp( -(x.^2)./(2.*omega.*omega) );
% Random data for now, known in full problem
hw = rand(1,10);
ht = rand(1,10);
% Fixed single parameter omega
omega = 0.5;
% Time evaluation
tic()
for i = 1:size(t,2)
for j = 1:size(hw,2)
tres = 0;
for k = 0:1:T_max
x = t(i) - ht(j) + 1440*floor(ht(j)/1440) - 1440*k;
tres = tres + Z_func( x, omega );
end % End of looping over k
res(i) = res(i) + hw(j)*tres;
end % End of looping over weights
end % End of looping over evaluation points
toc()
% VECTORIZE VERSION
tic
[T, HT, K] = ndgrid(t,ht, 0:T_max);
[~, HW] = ndgrid(t,hw);
X = T - HT + 1440*floor(HT/1440) - 1440*K;
tres = Z_func(X, omega);
tres = HW.*sum(tres,3);
res1 = sum(tres,2);
toc
res' - res1
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