% Grafy:
% Funkce sin(x^2)
x=linspace(-3*pi,3*pi);
colordef none
plot(x,cos(x.^2))
hold on
plot(x,cos(x),'g')
% Polynomialni aproximace;
% Budeme aproximovat oblouk fce cos(x) popsany
% malo body pomoci polynomu:
x=linspace(-pi/2,pi/2,5)

x =

   -1.5708   -0.7854         0    0.7854    1.5708

format compact
y = cos(x);
plot(x,y,'o')
plot(x,y,'o')
n= length(x);
V=[ones(n,1),x,x.^2]
??? Error using ==> horzcat
All matrices on a row in the bracketed expression must have the 
 same number of rows.

x=x.'
x =
   -1.5708
   -0.7854
         0
    0.7854
    1.5708
y=y.'
y =
    0.0000
    0.7071
    1.0000
    0.7071
    0.0000
V=[ones(n,1),x,x.^2]
V =
    1.0000   -1.5708    2.4674
    1.0000   -0.7854    0.6169
    1.0000         0         0
    1.0000    0.7854    0.6169
    1.0000    1.5708    2.4674
a=V\y
a =
    0.9706
    0.0000
   -0.3954
xx=linspace(-pi/2,pi/2);
N=length(xx)
N =
   100
xx=xx.';
VV=[ones(N,1),xx,xx.^2];
yy=VV*a;
hold on
plot(xx,yy,'g')
plot(xx,cos(xx),'y')
% pridame k y nahodne chyby:
ys=y+randn(n,1)*0.1;
figure
plot(x,ys)
plot(x,ys,'o')
figure
plot(x,ys,'o')
exit
