Composite Simpson's rule for irregularly spaced data

Composite Simpson's rule for irregularly spaced data based on a parabolic polynomial fit.

From the Newton-Cotes family of numeric integration the Simpson's rule is a popular method to numerically evaluate the definite integral of a mathematical function f(x).

This implementation work with regularly and irregularly spaced data. For irregularly spaced data, matlabs polnomial fit function polyfit is used.

% Example:

% y = [0 1 2 4 5]

% I = simpsonQuad(y)

%

% y = [0 1 2 3 4]

% x = [4 6 8 10 12]

% I = simpsonQuad(x,y)

%

% y = [0 2 3 4 5]

% x = [4 6 9 10 13]

% I = simpsonQuad(x,y)