%-----------------------------------------------------
%
% Conversion of a script into a function, from the
% Matlab script that uses linear least squares to
% find hill heights from multiple observations.
%  
%  
% From ground level,
%   A is measured 1236 meters high
%   B is measured 1941 meters high
%   C is measured 2417 meters high
%  
% From A, B is 711 meters higher 
% From A, C is 1177 meters higher 
% From B, C is 475 meters higher 
%  
%
%    Created : Wed 11 Jan 2009
%    Modified: 11 Feb 2009
%
%-----------------------------------------------------

function [h, Y, I] = experiment_least_squares(A, b)

    [number_of_observations, number_of_parameters] = size(A);
    
    h = A\b;
    
    s = sprintf('Best least squares fit for data is A = %g, B = %g , C = %g', ...
                 h(1), h(2), h(3));
    disp(s);
    
    residual = b - A*h;
    % Debugging statements for horzcat error:
    % temp1 = num2str(residual)
    % temp2 = 'Residual vector is '
    display(['Residual vector is ', num2str(residual')]);
    
    plot(1:number_of_observations, residual, 'r-',...
         1:number_of_observations, residual, 'b*');
    title('Residual Vector');
    xlabel('Residual Vector Component');
    ylabel('Residual Vector Values');
    
    figure;
    plot(1:number_of_observations, abs(residual), 'r-',...
         1:number_of_observations, abs(residual), 'b*');
    title('Absolute Values of Residual Vector');
    xlabel('Residual Vector Component');
    ylabel('Residual Vector Values');
    
    [Y, I] = max(abs(residual));
    
    s = sprintf('Worst outlier is observation %s', num2str(I));
    disp(s);

return