M. Nagahara and C. F. Martin,
L1 Control Theoretic Smoothing Splines,
submitted to IEEE Signal Processing Letters.
Note that to execute the codes, you need
Control System Toolbox
We have made sure that the code run with no errors on MATLAB version R2012b.
On older versions of MATLAB, the code might have unexpected errors.
[theta,x,G,H] = L1cts_coef(P,Ds,lambda,W,p)
[theta,x,G,H] = L1cts_coef(P,Ds,lambda,W,p,initial_state,G,H,q)
dynamical system (SS or TF object).
Ds = [T,Y]
T is a column vector of sampling
Y is a column vector of observed data.
regularization parameter (>0)
wight matrix for empirical risk.
norm index for empirical risk (p = 1 or 2)
if this value is not 0, then the initial state of P becomes also a design variable. default = 0;
Gramian matrix for computation. default = ;
Initial state matrix for computation. default = ;
if q = 2 then this function computes
min lambda*||theta||_2^2 + ||W(G*theta-y)||
that is, the L2 optimal control theoretic spline. default = 1;
the optimal coefficient vector
the optimal initial state
Initial state matrix