Wave Equation - loop unrool in MATLAB?

[krindik]

Hi,
While trying to simulate wave a mixing scenario I wrote below.
But it seems that matlab's matrix manipulation can easily unrol the marked loop (but i cannot find how). Can somebody help



% speed of light
c = 1;

% matrix containing wave parameters in each row for number of waves
% A = [w1; w2]
% w1 = [Emax Freq IndexOfRefraction]
% eg. below contains values for 2 waves
% wave 1: Emax = 1, Freq = 15, IndexOfRefraction = 0.1

A = [
1 15 0.1 ;
0.9 16 0.1
];


z = linspace(0, 200, 2000);
t = 0:.1:50;
[Z, T] = meshgrid(z, t);
waves = size(A, 1);
dist = length(z);
duration = length(t);
E = zeros(duration, dist, waves);


% Trying to unroll below?
% E = E0*exp( i(wt - w/c*n*z))
% E is a 3D matrix
% rows contain values for each time interval
% cols contain values for each distance (z)
% pages contain values for each wave in A

for j = 1:waves
E(:, :, j) = real( A(j, 1) .* exp (i.*(A(j, 2).*T - (A(j, 2) ./ c).*A(j, 3).*Z)));
end

 

[Aaron Bex]

To unroll the loop you can use the following syntax:
E = real(A(:, 1) .* exp (i.*(A(:, 2).*T - (A(:, 2) ./ c).*A(:, 3).*Z)));

 

[oswaler]

I can see that you are attempting to use the wave equation to simulate a mixing scenario. The loop you have marked can be unrolled by using MATLAB's matrix manipulation functions. In this case, you can use the "repmat" function to replicate the parameters for each wave and then use element-wise multiplication to calculate the values for each time and distance. This will avoid the need for a loop and make your code more efficient. Additionally, you may want to consider using vectorization and pre-allocation to further optimize your code. I hope this helps.