============
Description:
============

This is the main function to obtain nonlinear, data-adaptive dynamic equations from the observed longitudinal processes. The dynamic equation is numerically estimated  via  smoothing-based procedure on the pre-smoothed trajectories and derivatives. 
dimensional data is implemented with distance-based metric Multidimensional Scaling,
mapping high-dimensional data to locations on a real interval, such that predictors that
are close in a suitable sample metric also are located close to each other on the interval. 
Established techniques from Functional Data Analysis can
be applied for further statistical analysis once an underlying stochastic process and the
corresponding random trajectory for each subject have been identified. 

Reference:  Nicolas Verzelen,  Wenwen Tao,  and Hans-Georg Müller
Inferring stochastic dynamics from functional data
Biometrika (2012) 99(3): 533-550 first published online July 9, 2012 doi:10.1093/biomet/ass015


========
Usage:
========

[mu,dyn_grid]=non_dyn(t,y,method,tout,N_f)


=======
Input:
=======
 t              :1 * N cell of observed time points. Need to be coherent for all subjects
y              :1 * N cell of observed repeated measurements for each subject, corresponding to each cell of t.
method    :a character string for the kernel to be used, default is 'gauss'; should be specified as one of the following
                 'epan' - epanechikov kernel
                 'gauss' - gaussian kernel
                 'gausvar' - variant of gaussian kernel
                 'rect' - rectangular kernel
                 'quar' - quartic kernel
tout          : m * 1 vector of the output time grid ; default is equadistance 1*100 grid between min(t{1}) and max(t{1}).               
N_f           :scalar that gives the output size of trajectory y grid; default is 200.



Details: i) Any unspecified or optional arguments can be set to "[]" for
            default values;

=======
Output:
=======


mu              :m * N_f matrix of the estimated dynamic surface on given time grid and trajectory grid (N_f equidistant grid on the support region)
dyn_grid     :m * N_f matrix of the output grid corresponding to mu.

 

 See example_non_dyn.m