% Compare Error of Various Interpolation Schemes
% Newton, Hermite, Cubic Splines
% function [errN,errH,errS] = CompareInterp(func,funcH,xmin,xmax,N,plt)
% Inputs:
%   func = function to interpolate, returns f(x) 
%   funcH = same function to interpolate, but returns f(x) and f'(x)
%   xmin,xmax = range of interpolation set
%   N = array of number of interpolation points to try,
%       evenly spaced from xmin to xmax
%   plt = 1 to plot errors
%       = 0 not to
% Outputs:
%   errN = error of Newton Interpolation with N(i) points 
%          on 1000 numbers between xmin, xmax
%   errH = error of Hermite Interpolation with N(i) points 
%          on 1000 numbers between xmin, xmax
%   errS = error of cubic spline Interpolation with N(i) points 
%          on 1000 numbers between xmin, xmax
%
function [errN,errH,errS] = CompareInterp(func,funcH,xmin,xmax,N,plt)
for i = 1:length(N),
    n = N(i);
    x = xmin:(xmax-xmin)/(n-1):xmax;
    [c,errN(i),NewtonTable] = NewtonInterp(func,x,0);
    [c,errH(i),NewtonTable] = HermiteInterp(funcH,x,0);
    [xout,yout,errS(i)] = SplineFit(func,x,0);
end
errN = errN';
errH = errH';
errS = errS';
if (plt==1)
    figure(1)
    hold off, clf
    semilogy(N,errN,'b',N,errH,'r',N,errS,'k')
    grid
    title('Interpolation error (Newton = blue, Hermit = red, Cubic Spline = black)')
    xlabel('Number of Interpolation points')
end