MATLAB: Write a function called triangle_wave

looptriangular wave

The function computes the sum Σ((−1^k)*sin((2k+1)(t))/((2k+1)^2)) for each of 1001 values of t uniformly spaced from 0 to 4π inclusive. The input argument is a scalar non-negative integer n, and the output argument is a row vector of 1001 such sums—one sum for each value of t. You can test your function by calling it with n == 20 or greater and plotting the result and you will see why the function is called “triangle_wave”.

For this question, I have written a function to solve it but my code is always rejected by the grader.

This is the plot I get whenever I plot my function;

My attempt made use of a nested for loop as shown:

Please any clue to get my code right will be highly appreciated. Thanks

Best Answer

Do you have any useful details about the "rejection of the grader"? Is this a Cody Coursework? I start to detest this, because many students struggle with the automatic rejection without useful information. I do not believe in automatic teaching.

Perhaps it matters than 4*pi is not 12.5664. Try:

m = linspace(0, 4*pi, 1001)

You have to reset sump to 0 for each time point. Move the sump = 0 inside the for t loop.

By the way: The iterative growing of arrays is a bad programming practice. Care for a proper pre-allocation is real programs:

a = zeros(1, length(m));
...
for t = 1:length(m)
  ...
  sump = 0;
  for k = 0:n
     ...
  end
  a(t) = sump;
end

Related Solutions

MATLAB: *** Write a function called triangle_wave that computes the sum (−1) sin(2 +1) (2 +1) for each of 1001 values of t uniformly spaced from 0 to 4π inclusive. The input argument is a scalar non-negative integer n, and the output argument is a row v

denominator = (2 * k + 1) .^ 2;

Use the elemtnwise .^ instead of the matrix operation ^ . The same for "(-1)^k" .

The corresponding error message is clear:

 Error using  ^ 
 Inputs must be a scalar and a square matrix.
 To compute elementwise POWER, use POWER (.^) instead.

[EDITED] The formula contains: "Sum from k=0 to n", you code contains:

k = 1:n;

Replace this by k = 0:n. It will be more efficient to move the definition before the loop and pre-allocate the output:

function S = triangle_wave(n)                                      
t = linspace(0, 4*pi, 1001);
S = zeros(size(t));   % Pre-allocation
k = 0:n;              % Not 1:n
for tIndex = 1 : length(t) 
  numerator   = ((-1) .^ k) .* sin(t(tIndex) .* (2 * k + 1));
  denominator = (2 .* k + 1) .^ 2;
  S(tIndex)   = sum(numerator ./ denominator);
end

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

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

Best Answer

Related Solutions

MATLAB: *** Write a function called triangle_wave that computes the sum (−1) sin(2 +1) (2 +1) for each of 1001 values of t uniformly spaced from 0 to 4π inclusive. The input argument is a scalar non-negative integer n, and the output argument is a row v

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

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