MATLAB: Alternative for a for loop. How to write this code without using a for loop

for loopMATLABvectorization

function approx = approxCosineFunction(x, t)
    approx=1;
    for i=1:1:t-1
        addterm = (-1)^i*(x^(2*i))/factorial(2*i);
        approx = approx + addterm;
    end
end

Best Answer

To get the correct result, you need to make that divide an element-wise divide, and then add up the resulting terms into approx. E.g.,
addterm = (-1).^(1:1:t-1).*(x.^(2.*(1:1:t-1)))./factorial(2.*(1:1:t-1));  % <-- changed / to ./
approx = approx + sum(addterm);  % <-- added the sum( )
But this will just give you the last approximation. If you wanted to return a vector containing all of the intermediate results as well, you could use cumsum instead. E.g.,
approx = approx + cumsum(addterm);
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