Filling in a Cell of Matrices in MATLAB - matlab

Question

In Matlab I am trying to create a cell of size 16 x1 where each entry of this cell is a matrix. I have the following equation
$$W_g = exp^{\frac{j{2\pi m}{N}(n+\frac{g}{G}))} \,\,\,\,\,\,\, m,n=0,1,.....(N-1)$$
for this work assume $N=4$ and the index $g$ is the index that refers to the cell element i.e g=0:1:15
W=cell(16,1);
for g=1:16
for m=1:3
for n=1:3
W{g,m,n}= exp((2*pi*j*m/4)* n+(g-1)/16));
end
end
end
How can I make this work? I have two problems with this, you see g starts from 0 and MATLAB doesnt accept index of zero and how to actually define the matrices within the cell.
Thanks

Answer 1

So if I understand you have this equation:
And you just want the following code:
W=cell(16,1);
n = 1:3;
m = 1:3;
N = 4;
for g=1:16
W{g}= exp((2*pi*j.*m/4*N).*n+(g-1)/16);
end
%or the 1 line version:
W = cellfun(#(g) exp((2*pi*j.*m/4*N).*n+(g-1)/16),num2cell([1:16]),'UniformOutput',0);
With matlab you can use the Element-wise multiplication symbol .*
For example:
%A matrix multiplication
A = [2,3]
B = [1,3]';
result = A * B %result = 11
%An element wise multiplication
A = [2,3]
B = [1,3];
result = A .* B %result = [2,9]

Answer 2

First of all, i is the complex number in matlab (sqrt(-1)) not j, and you are correct, matlab is indexed in 1, so simply start counting g at 1, until 16.
Next, create a zero matrix, and calculate all indices accordingly. Something like this should work just fine :
clc
clear all
W=cell(16,1);
for g=1:16;
temp = zeros(3,3);
for m=1:3
for n=1:3
temp (m,n) = exp((2*pi*1i*m/4)* n+g/16);
end
end
W{g} = temp;
end
if you are considering doing much larger operations, consider using linspace to create your m and n indices and using matrix operations