MATLAB: Applying algebraic eqns across multiple dimesions of matrix using indexing

4d matrixindexing

I am "time-stepping" an electromagnetic field at time instances per frequency
The EM field value at time-zero is a 3D matrix of dimensions [nvalues x 1 x nfrequencies] (see attached)
I want to create a 4D matrix where time is the 4th dimension and apply an algebraic equation across each dimension based on the value of the variables stored in arrays [frequency] and [time]
ie
size(EM_freq_time) = [nvalues x 1 x frequencies x time]
to attempt this i create a matrix of zeros
EM_freq_time = zeros(length(Ex), length(frequencies), length(t));
the equation i must apply is
EM_value(frequency,time,phase) = value*sin(2*pi.*frequencies.*t+Phase)
where frequency is a column vector size [nfreqs, 1]
time is a column vector size [nsteps, 1]
phase is a column vector size [nvalues]
how can i apply this equation using indexing?

Best Answer

Ok, you aren't too far off with your thoughts, but I'll include an example.
You should be able to cover the first and second dimension all at once, but because you want to look at specific values in the third and fourth dimensions you will need to loop them, as far as I know.
for  i = 1:size(Ex,3) % Loop through each frequency
    for j = 1:length(time) % Loop through each time value, not really sure where you're getting this from, but I'm also just setting this up as a template
        Ex_freq_time(:,:,i,j) = Ex(:,:,i)*sin(2*pi*frequencies(i).*time(j)+Phase);
    end
end
You may also need to index Phase (probably with i, because it matches the number of frequencies), but I wasn't entirely sure where you were getting it from. Sorry, I'm a very visual person, and this forum doesn't do pictures too well.
Let me know if you have any problems, or need clarification.
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