Problem with integral() function

I have a problem with the usage of the MatLab build-in integral function and I cannot understand the essence of it. Below I am attaching the things that might be the cause of a given problem. I have also implemented the Trapezoidal and the Simson's rules and they work completly fine, so that is the thing that makes me even more confused as I guess there should not be a problem with the 'f' function.

cheby1 - function that generates Chebyshev polynomials of the first order

fibonacci - my own function that generates the Fibonacci sequence

MATLAB version - R2018b

main.m

n = -1;
while(n <= 0)
    n = input('Enter the n number: ');
end

fib = fibonacci(n);

fun = @(x) f(n,x,fib);

fx = f(n,x,fib);

disp('Simpson:')
    S = simpson(0,4,0.01,fun)
    
disp('Trapezoidal:')
    T = trapezoidal(0,4,0.01,fun)
    
disp('MatLab build-in')
    I = integral(fun,0,4)

chey1.m

function T = cheby1(x, N)

    if N == 1
      T(N) = x;
    else
      T(1) = x;
      T(2) = 2*x^2-1;
      for i = 3:N
        T(i) = 2*x*T(i-1)-T(i-2);
      end
    end

end

f.m - function that generates f(x) of the form

where is the Chebyshev polynomial

function S = f(n,x,fib)
    S = 0;
    
    T = cheby1(x, n);
    
    for i=1:n
        S = S + T(i) * fib(i); 
    end
end

The erros I get:

Answer 1

[Steven Lord]

Star Strider is correct. Your f function does not satisfy the requirements imposed upon integrand functions by integral. From the integral documentation page:

"For scalar-valued problems, the function y = fun(x) must accept a vector argument, x, and return a vector result, y. This generally means that fun must use array operators instead of matrix operators. For example, use .* (times) rather than * (mtimes). If you set the 'ArrayValued' option to true, then fun must accept a scalar and return an array of fixed size."

Your function cannot accept a vector argument for x. Either modify it so it can (the easiest way to do so would probably be to use a for loop to iterate over the elements of x and compute the value of the integrand for each of those elements in turn) or specify the 'ArrayValued' option in your integral call.

[Jakub Osek]

The only reason I pass X there is to have some unkown that is the variable of integration. My purpose was to make it to don't have any specific values and to be just an X. Is there any other way of doing it to achieve it as (I guess from your anserws that mine is not a good one)?

[Jakub Osek]

I have just set ArrayValued to true and it works fine now. Thanks for you help. MatLab is not my thing.

Answer 2

[Star Strider]

Your post lacks details. However, Iit seems that ‘x’ is a vector. It is not possible to assign a vector to a scalar array element.

Try this:

function T = cheby1(x, N)
    if N == 1
      T(N) = x;
    else
      T(1) = x(1);
      T(2) = 2*x(2)^2-1;
      for i = 3:N
        T(i) = 2*x(i)*T(i-1)-T(i-2);
      end
    end
end

That may not be the only error. If I guess correctly, it should prevent the error you posted.

[Jakub Osek]

I have tried your code and unfortenatly it doesn't work.

I have edited my post so there is more code with the full logic now. My purpose was to pass X as an unkown variable that is just an X, however my MatLab skills are not good enough so probably this approach is not a correct one.

The thing is that the only problem I have met is using this integral() function. My own implemented ones (Simpson and Trapozeidal) work as I want and return the correct value.