Trapezoidal Rule Approximation of Integral and Function Use

 function [integral,difference,ratio]=Trapezoidal(a,b,n0,index_f)

 integral = zeros(9,1);

 difference = zeros(9,1);

 ratio = zeros(9,1);

 sumend = (f(a,index_f) +f(b,index_f))/2;

 sum = 0;

 if(n0 > 2)

    h = (b-a)/n0;
    for i=2 : 2 : n0-2
        sum = sum + f(a+i*h, index_f);
    end
end

 for i=1:9
    n = n0*2^(i-1);
    h = (b-a)/n;
    for k = 1 : 2 : n-1
        sum = sum + f(a+k*h, index_f);
    end
    integral(i) = h*(sumend + sum);
end

 difference(2:9) = integral(2:9) - integral(1:8);
ratio(3:9) = difference(2:8)./difference(3:9);

 function f_value = f(x,index)

 switch index
    case 1
        f_value = x.^4;
    case 2
        f_value = x.^2;
 end

 end

 end

I am receiving the error: Error using Trapezoidal (line 7) Not enough input arguments. This is line 7: %sumend = (f(a,index_f) +f(b,index_f))/2;

Any advice would be useful. thanks!

Answer 1

[Jan]

How do you start the function? What are a and b?

The actual call to the local function f() seems to be ok.

Did you save the function before running it?

[Paul]

Hi Jan, Thanks for the response. I start the function by typing "Trapezoidal" (my function file name) in the Command Window. I also tried setting a and b from the window like this: "Trapezoidal; a = 0; b = 1;" It unfortunately gave the same error. Do I need to create script that calls the function? I'm not sure how to do this. Also, my function is saved as a .m file, would that be correct? Sorry, I'm new to MatLab programming.

Yes, I believe the file was properly saved before running the code.

Thanks for any more advice, Jan (or others)!!

EDIT: Okay, I did some research and made progress (whoo!). In the command window I entered in the "Trapezoidal()" with arguemnts, duh! Seems obvious now, but in any case, if I enter "Trapezoidal(0,1,2,1)" it approximates my function for case 1, accurately!

[Paul]

if true
  function [integral,difference,ratio]=Trapezoidal(a,b,n0,index_f)

 integral = zeros(9,1);
 difference = zeros(9,1);
ratio = zeros(9,1);

 sumend = (f(a,index_f) +f(b,index_f))./2;
 sum = 0;

 if(n0 > 2)
    h = (b-a)/n0;
    for i=2 : 2 : n0-2
        sum = sum + f(a+i*h, index_f);
    end
 end

 for i=1:9
    n = n0*2^(i-1);
    h = (b-a)/n;
    for k = 1 : 2 : n-1
        sum = sum + f(a+k*h, index_f);
    end
    integral(i) = h*(sumend + sum);
 end

 difference(2:9) = integral(2:9) - integral(1:8);
 ratio(3:9) = difference(2:8)./difference(3:9);

 function f_value = f(x,index)

 switch index
    case 1
        f_value = x.^4;
    case 2
        f_value = x.^2;
    case 3
        f_value = sqrt(1 + (cos(x)).^2);
    case 4
        sigma = 0;
        mu = 0;
        f_value = (1/(sigma*(sqrt(2*pi)))*exp((-0.5)*((x-mu)/sigma)^2));
 end

 end

 end

 end

When I run the following command in the command window: Trapezoidal(-1,1,2,4); It returns: Error in Trapezoidal>f (line 32) switch index

Output argument "f_value" (and maybe others) not assigned during call to "C:\Users\Paul\Documents\MATLAB\Trapezoidal.m>Trapezoidal/f".

Error in Trapezoidal (line 7) sumend = (f(a,index_f) +f(b,index_f))./2;

Any advice would be greatly appreciated.