echo on
d = 3; alpha = 10;
t=(0:0.1:1).';
if ~exist('x'), x = sin(2*pi*t)+0.2*randn(size(t)); end
tt=(-0.2:0.01:1.2).'; yy = sin(2*pi*tt);
% tt = t;
[p,S] = polyfit(t,x,d); [y1,E1]=polyconf(p,tt,S,0.01*alpha);

% PRIMA METODA STANDARDNI POLYNOMIALNI REGRESE
[y2,E,r,s] = polyfilt(d,length(t),x,t,tt,alpha,gcf); E2 = E(:,2); s
hold on; plot(tt,yy,'r'); hold off;
max(abs(y1-y2)), max(abs(E1-E2))
% ans =
%   1.3767e-014
% ans =
%   3.5527e-015
pause;

% NEPRIMA METODA STANDARDNI POLYNOMIALNI REGRESE
[R,E0] = polyfilt(d,length(t),[],t,tt,alpha); y2 = R*x; E0=s*E0; E2 = E0(:,2);
max(abs(y1-y2)), max(abs(E1-E2)), max(abs(E-E0))

% KONTROLNI VYPOCET SIGMA s:
y = polyfilt(d,length(t),x,t,[],alpha,figure);
hold on; plot(tt,yy,'r'); hold off;
s = norm(y-x)./sqrt(length(t)-d-1)
[yy,EE] = polyfilt(d,length(t),x,t,[],alpha);
max(abs(y-yy)), max(abs(E0(21:10:length(tt)-19,:)-EE))
ax = axis;
figure(gcf-1); axis(ax);
pause;

% POSTUPNA POLYNOMIALNI REGRESE
figure;
for k = 1:4
    subplot(2,2,k);
    polyfilt(d,length(t)-k,x,t,tt,alpha,gcf);
    axis(ax);
end

echo off