% Problem 2
% J. Watlington, 11/19/95

% Define the x vector
x = -10:10;
[m,num_samples] = size( x );

% Define the y vector
y = testfun( x );

%  Solve for polynomials of 5, 10, and 15 terms

p5  = pfit( x, y, 4 )
p10 = pfit( x, y, 9 )
p15 = pfit( x, y, 14 )

%  Solve for radial basis functions of 5, 10, and 15

c5  = linspace( x(1), x(num_samples), 5 );   %  pick centers (evenly dist.)
c10 = linspace( x(1), x(num_samples), 10 );
c15 = linspace( x(1), x(num_samples), 15 );

r5  = rfit( x, y, c5 )
r10 = rfit( x, y, c10 )
r15 = rfit( x, y, c15 )

%  Now calculate the error for the sample set

y_p5  = psolve( p5,  x );
y_p10 = psolve( p10, x );
y_p15 = psolve( p15, x );

y_r5  = rsolve( r5,  c5,  x );
y_r10 = rsolve( r10, c10, x );
y_r15 = rsolve( r15, c15, x );

is_error = [ x' (y_p5-y)' (y_p10-y)' (y_p15-y)' (y_r5-y)' (y_r10-y)' (y_r15-y)' ]

%  Now calculate the error for the out-of-sample set

oos = -10.5:10.5;
y_oos = testfun( oos );

oos_p5  = psolve( p5,  oos );
oos_p10 = psolve( p10, oos );
oos_p15 = psolve( p15, oos );

oos_r5  = rsolve( r5,  c5,  oos );
oos_r10 = rsolve( r10, c10, oos );
oos_r15 = rsolve( r15, c15, oos );

oos_error = [ oos' (oos_p5-y_oos)' (oos_p10-y_oos)' (oos_p15-y_oos)' (oos_r5-y_oos)' (oos_r10-y_oos)' (oos_r15-y_oos)' ]

%  And now for some matlab fun

test = -10:0.05:10;
test_p = psolve( p15, test );
test_r = rsolve( r15, c15, test );
test_y = testfun( test );
plot( test, test_p, '--', test, test_r, '.', test, test_y, '-' );