spline_kemeny.m

Incorporating Prior Knowledge in Cubic Spline Approximation - Application to the Identification of R

cav = ca;
cbv = cb;
ccv = cc;

n=length(knots); %number of nodes
nc=3; %number of components
A = []; b = [];
An = []; bn = [];
s = [];
lambda1 = 0;
lambda2 = 0;
w = [0 0 0];
sum1 = 0;
sum2 = 0;

%Egyenlosegi korlatok
A = zeros(3,3*2*n);
b = zeros(3,1);
%Kezdeti pont
A(1,1) = 1;
A(2,2*n+1) = 1;
A(3,4*n+1) = 1;
b(1) = ca0;
b(2) = cb0;
b(3) = cc0;

%Egyenlotlensegi korlatok (gradiensekre)
An = zeros(n*3-1+n+3*n,2*n*3);
bn = zeros(n*3-1+n+3*n,1);
%Az A es B vegig fogy
Anv = zeros(n,2*n);
for i = 1:n
  Anv(i,2*i) = 1;
end
An(1:n,1:2*n) = Anv;
An(n+1:2*n,2*n+1:4*n) = Anv;
%A C termelodik, de csak egy ideig, igy az utolso csomopontot kihagyjuk
Anv(end,:) = [];
Anv = -Anv;
An(2*n+1:3*n-1,4*n+1:6*n) = Anv;
%A gradiens osszegek elojele < 0
Anv = zeros(n,2*n);
for i = 1:n
  Anv(i,2*i) = 1;
end
An(3*n:4*n-1,1:6*n) = [Anv, Anv, Anv];
%A tomegek mindig > 0 (kulon mindegyikre)
Anv = zeros(n,2*n);
for i = 1:n
  Anv(i,2*i-1) = -1;
end
An(4*n:5*n-1,1:2*n) = Anv;
An(5*n:6*n-1,2*n+1:4*n) = Anv;
An(6*n:7*n-1,4*n+1:6*n) = Anv;

%spline
[spa1,spb1,spc1] = fspline3([tt,tt,tt],[cav,cbv,ccv],knots,s,lambda1,lambda2,w,sum1,sum2,A,b,An,bn);

%Results: t,c
cnew = zeros(length(te),3);
if ~exist('colorstr'),
  cnew(:,1) = drawspline(spa1,te);
  cnew(:,2) = drawspline(spb1,te);
  cnew(:,3) = drawspline(spc1,te);
else
  cnew(:,1) = drawspline(spa1,te,colorstr{1});
  cnew(:,2) = drawspline(spb1,te,colorstr{2});
  cnew(:,3) = drawspline(spc1,te,colorstr{3});
end