Quadrature method using vectors

I was wondering if anyone knew of a method in MATLAB to numerically integrate a function using a quadrature method with a vector rather than a function as the input (step size/location defined by a second vector). The system of integrals I am attempting to integrate are coupled such that an explicit function cannot be passed to a quad(fun,a,b) type MATLAB function. I'd be happy to post the systems of integrals if you're interested.

Writing the code for a vector based quadrature method shouldn't be too bad but it would be nice to save the time if I didn't have to do it.

Any ideas?

Answer 1

[Andrew Newell]

One approach is the trapezoidal rule:

vecsum = dot(diff(t),x(1:end-1)+x(2:end))/2;

or, in loop form,

vecsum = 0;
for i=1:length(x)
    vecsum = vecsum + (t(i+1)-t(i))*(x(i+1)+x(i))/2;
end

(edited to correct errors)

Answer 2

[Jan]

See: trapz

[blindcurrent]

Yes, this one does the trick! Thanks!

Answer 3

[blindcurrent]

As I understand it, you have your function in the form of a vector containing the data points, and another vector (of the same length) with the corresponding time values.

Let vector x be the data and t the time values. Then you could use for example the rectangle method:

sum=0;
for i=1:1:size(x,1)-1
    sum=sum+x(i)*(t(i+1)-t(i));
end;

In the end, sum would be your integral value. Note that the time points need not be equispaced.

I thought Matlab would have something that does this, but could not find anything. Therefore I tried this piece of code. It is rather crude and there are much more sophisticated numerical quadrature methods available. Hope that someone has got a better idea!

[Andrew Newell]

The method you described will be inaccurate because the integrand is biased to the bottom of each interval.

[Jan]

Shadowing the builtin function "sum" by a variable is a bad idea.