Modifying a function for the trapezoidal rule to work with a data set instead of an equation?

I have a formula for the Trapeziodal Rule but it only works with an equation. How would a modify it to work with a given data set?

Say my data set is:

z = [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ]; %This is just an example of what a data set could be

start = 0;
stop = 3;
N = 20; %steps

trapeziodal = trapezodial(z,start,stop,N);

function I = trapezodial(Fun,a,b,N)
h =(b-a)/N;
x = a:h:b;
F =Fun(x);
I = h*(F(1)+F(N+1))/2+h*sum(F(2:N));
end

[Rafael Hernandez-Walls]

z = [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ]; 
start = 0;
stop = 3;
N = 20; %steps

h=(stop-start)/(N-1);
I=h/2*(z(1)+z(N)+2*sum(z(2:N-1)))

Answer 1

[Sindar]

My suggestion is to check out the built-in trapz function. There are a few formulas there that should help.

Another note: your dataset should include the x-points as well as the y (or z, as you call it). At the least, you need to know the spacing.

Assuming your dataset is convenient, it isn't that tricky. By convenient, I mean:

• uniform spacing
• endpoints included in dataset
• no singularities (which you'd also like from the original function)