% Test of integration using table data
% This case will use a not-a-knot spline to grow the
% number of points in the table, then send this table
% to the trapezoidal and Simpson's rule function.

clear
close all

load intdata2.dat
x = intdata2(:,1);
y = intdata2(:,2);
exact = 1.1064840;

% a = x(1)
% b = x(end)
S = spline(x,y);
xo = linspace(x(1),x(end),101)';
yo = ppval(xo,S);
h = xo(2)-xo(1);

% Trapezoidal method
% Trap rule
t = trap_fun(h,yo);
rt = (t-exact)/exact

% Simpsons rule
s = simp_fun(h,yo);
rs = (s-exact)/exact

% Spline
sp = integral(@(x)ppval(x,S),x(1),x(end));
rsp = (sp-exact)/exact