function [] = lecture1(  )
%LECTURE1 Jolie demo pour le cours
%   Vincent Legat -septembre 2011-
%   Version 0.0.0.alpha
%   Fully equipped of all standard options and ABS
%   See legal notices vincent.legat.eu
%   Be careful : do not use with alcohol

close all
X = [1 2 3]';
U = [4 5 1]';
scalarProduct = X'*U;
exteriorProduc = X * U';
componentProduct = X.*U;
A = [X.^0 X.^1 X.^2 ];
%
% Do not do that, stupid boy !
%
a = inv(A) * U
%
% Fine but boring :-)
%
a = A \ U
%
%
%
b = polyfit(X,U,2)

plot(X,U,'r.','MarkerSize',25); hold on
x = linspace(X(1),X(end),10)';
uh = [x.^0 x.^1 x.^2 ] * a
plot(x,uh,'-b')
vh = polyval(b,x)
plot(x,vh,'-xb','MarkerSize',10)
end