summing to create a vector

I'm trying to write a function that calculates sum of ((-1)^k *sin((2k+1)t))/((2k+1)^2 ( for k=0 to n) t varies from 0 to 4*pi with 1001 values its supposed to return a vector with size n this is the code i wrote

function [summ ]= triangle_wave (n) 
for k=1:n;
 for t= linspace(0,4*pi,1001); 
summ=sum((-1)^k*sin((2*k+1)*t))/((2*k+1)^2); 
end 
end 
end

it keeps outputting the last calculate sum instead of adding each sum to the vector . what can i add to this code to achieve that ?

Answer 1

[Walter Roberson]

function [summ ]= triangle_wave (n) 
  t = linspace(0,4*pi,1001);
  summ = zeros(n+1, length(t));
  for k = 1 : n;
    summ(k+1,:) = summ(k,:) + (-1).^k .* sin((2*k+1) .* t)) ./ ((2*k+1).^2); 
  end 
  summ = summ(2:end,:);
end

[OLUBUKOLA ogunsola]

perfect, thanks a lot

[Walter Roberson]

Instead of looping over the values of t, I use t as a vector, operating on all of the elements at once. Each iteration through I create an entire vector of values, the application of the formula with one particular k to the entire set of t values. Normally I would just add all of those together over all of the k, but you wanted to have all of the intermediate results for all of the different k, so it is necessary to store all of the results along the way.

The result for k = 1 is stored in row 2, the result for k = 2 is stored in row 3, and so on, until at the end one more row than n has been produced. You then omit the first row and take the rest as your answer.

The reason you do it this way is to make the code easier because each step involves adding to what the step before produced while still keeping what was produced in the previous step. That's easy to think of, but you have the practical difficulty of handling the very first output. You could code like

   if k == 1
      summ(k,:) = (-1).^k .* sin((2*k+1) .* t)) ./ ((2*k+1).^2);
   else
      summ(k,:) = summ(k-1,:) + (-1).^k .* sin((2*k+1) .* t)) ./ ((2*k+1).^2);
   end

to avoid having to use the extra row, but you can see that you had to use special handling for the first row because for the first row there is no "previous" to add on to. The code is more compact if you do it the way I did, initialize a row with 0 to be there as the "previous" row.

Answer 2

[Azzi Abdelmalek]

n=20
t= linspace(0,4*pi,1001);
for k=1:n
  s(k)=sum((-1)^k *sin((2*k+1)*t)/((2*k+1)^2)) ;
end
s

[OLUBUKOLA ogunsola]

great! you guys are the best|

[OLUBUKOLA ogunsola]

I'm sorry there is still an error here , the inside loop is supposed to b k, while the outer loop be t, such that it produces a vector of 1001 elements as opposed to 20. I've tried to swap them in the code you provided but it keep sending 20 elements vector back to me .

the code i should have posted earlier is :

function [summ ]= triangle_wave (n) 
for t= linspace(0,4*pi,1001);
 for k=1:n;
summ=sum((-1)^k*sin((2*k+1)*t))/((2*k+1)^2); 
end 
end 
end

thanks