%
% Written by:
% --
% John L. Weatherwax                2009-04-21
%
% email: wax@alum.mit.edu
%
% Please send comments and especially bug reports to the
% above email address.
%
%-----

% EPage 136

close all; clc; clear;

xs = -1:0.2:+1;
ys = sin(pi * xs / 2).^2;
plot( xs, ys, '-og' ); hold('on'); grid('on');

quad_coefs = polyfit( xs, ys, 2 )
ys_quad = polyval( quad_coefs, xs );
plot( xs, ys_quad, '-xb' );

quartic_coefs = polyfit( xs, ys, 4 )
ys_quartic = polyval( quartic_coefs, xs );
plot( xs, ys_quartic, '-xr' );

pp = spline( xs, ys );
ys_spline = ppval( pp, xs );
plot( xs, ys_spline, '-ok' );

legend( 'truth', 'quadradic LS fit', 'quartic LS fit', 'spline', 'location', 'best' );

%saveas( gcf, '../../WriteUp/Graphics/Chapter7/c_7_p_3_ls_plot.eps', 'epsc' );