# Matlab integration of numerical data

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Sib RV on 8 Apr 2021 at 9:40
Commented: Sib RV on 8 Apr 2021 at 18:24
I have numerical data for function f, calculated for a vector x (not a defined function of x). Can I create a functional form out of this so that I can use something like f(y) in further calculations and integrals ?
x = 0:1:10; F is calculated for eac x. Example : Want to integrate f(x+c) between some limits, (not 0,10) and for any constant c.

Star Strider on 8 Apr 2021 at 12:00
The cumtrapz funciton will likely do what you want, although I am not certain what result you want.

John D'Errico on 8 Apr 2021 at 12:23
Edited: John D'Errico on 8 Apr 2021 at 12:26
In order for it to be truly general, you will need to interpolate the "function". For example, we might do this:
x = 0:10;
y = sin(x); % some function
Now, we wish to integrate y, but only based on the values we have generated. Remember that integrating beyond the linits of our data will be bad idea, because then we are forced to extrapolate the function. And THAT is a bad idea, unless our extrapolant is one chosen carefully. A spline will be a terribly poor tool to extrapolate.
f = spline(x,y);
fint = fnint(f); % this lives in the curve fitting toolbox.
Now, assume we wish the integral of y, between x and x + c. In this example, I'll use x=0.1223, and c=4.75.
fintxc = @(x,c) fnval(fint,x+c) - fnval(fint,x);
fintxc(0.1223,4.75)
ans = 0.8435
How well did we do? Remember, this can be no more than an approximation. We can use integral on the original function to do the work, although I could be more intelligent, since I know the integral of the sine function. I'll take the lazy way here.
integral(@sin,0.1223,0.1223 + 4.75)
ans = 0.8333
Which given the coarseness of the original sample, is not at all bad.
Sib RV on 8 Apr 2021 at 18:24
Thank you.