MATLAB: How can I store values generated from a nested loop into an arrray

loops with rational numbersnested loops storagestoring loop's resultes

if I have this code :-
function S = triangle_wave(n) 
  S = zeros(1,1001); %preallocation 
  e = [];
  for t = 0:((4*pi)/1000):(4*pi)
    for k = 0:n
      sigma = (((-1)^k)*sin((2*k+1)*t))/((2*k+1))^2;
      e(1, *???*) = sigma;   *(%what should I put here instead of (???)?)*

    end
    r = sum(e(:));
    S(1, *???*) = r;           *(%what should I put here instead of (???)?)*
  end
end
I can't depend on the loop's variable because they are kinda of rational numbers, so how should i store ?

Best Answer

function S = triangle_wave(n) 
    t = linspace(0,4*pi,1001)';
    k = 0:n;
    S = sum(bsxfun(@times,sin(bsxfun(@times,t,(2*k+1))),(-1).^k./(2*k+1).^2),2);
end
or with for..end loop
function S = triangle_wave(n) 
    S = zeros(1001,1); %preallocation 
    t = linspace(0,4*pi,1001);%0:((4*pi)/1000):(4*pi);
    k = 0:n;
    for jj = 1:1001
        S(jj) = sum(((-1).^k).*sin((2*k+1)*t(jj))./(2*k+1).^2);
    end
end
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