%POLYFIT_NOISE:  Matlab script file to fit and plot a quadratic polynomial
%                to data from a quadratic with noise added.
% 
% Usage:    >> polyfit_noise
% 
% inputs:   none
% 
% outputs:  a plot containing the original data, the noisy data,
%           the true curve, and the curve fitted to the noisy data.

% file: ~/matlab/courses/NumerComput/polyfit_noise.m
% 
% sample M-file for Intro Numer Comput I class
% 
% C.G. (11-01)

% 
% generate true and noisy points, and plot them
% 

x = linspace( -1, 1, 10 ) ;           % 10 equally spaced points in [-1,1]

y = x.^2 ;                            % 'y' values at those points

clf ;  hold on ;  box on              % prepare current figure window

plot( x, y, 'bo' )                    % plot true data points as blue circles

lev = .2 ;                            % noise level

yn = y + lev * (2*rand(size(y))-1) ;  % add uniform noise from [ -lev, lev ]

plot( x, yn, 'rd' )                   % plot noisy data points as red diamonds

% 
% fit noisy data and plot fitted curve along with true curve
% 

p = polyfit( x, yn, 2 ) ;             % coefficients of fitted polynomial

xx = linspace( -1, 1, 100 ) ;         % 'x' points for plotting curves

yy = polyval( p, xx ) ;               % 'y' values of fitted quadratic

plot( xx, yy, 'r--' )                 % plot fitted curve as red dashed

plot( xx, xx.^2, 'b-' )               % plot true curve as blue solid

axis( [ -1 1 -lev 1+lev ] )           % specify 'x', 'y' axis limits

% plot horizontal and vertical axes (black, solid) for reference/appearance

plot( [ -1 1 ], [ 0 0 ], 'k-', [ 0 0 ], [ -lev 1+lev ], 'k-' )

% 'x', 'y' axis labels

xlabel( 'x', 'FontSize', 12 )
ylabel( 'y', 'FontSize', 12 )

% give the noise level in the title for annotation/information

title( [ 'lev = ', num2str(lev) ], 'FontSize', 15 )