%! Computes the likelihood of a stationary state space model, given initial condition for the states (mean and variance).
%! @sp 2
%! @strong{Inputs}
%! @sp 1
%! @table @ @var
%! @item data_index
%! Matlab's cell, 1*T cell of column vectors of indices (in the vector of observed variables).
%! @item number_of_observations
%! Integer scalar, effective number of observations.
%! @item no_more_missing_observations
%! Integer scalar, date after which there is no more missing observation (it is then possible to switch to the steady state kalman filter).
%! @item Y
%! Matrix (@var{pp}*T) of doubles, data.
%! @item start
%! Integer scalar, first period.
%! @item last
%! Integer scalar, last period (@var{last}-@var{first} has to be inferior to T).
%! @item a
%! Vector (@var{mm}*1) of doubles, initial mean of the state vector.
%! @item P
%! Matrix (@var{mm}*@var{mm}) of doubles, initial covariance matrix of the state vector.
%! @item kalman_tol
%! Double scalar, tolerance parameter (rcond, inversibility of the covariance matrix of the prediction errors).
%! @item riccati_tol
%! Double scalar, tolerance parameter (iteration over the Riccati equation).
%! @item presample
%! Integer scalar, presampling if strictly positive (number of initial iterations to be discarded when evaluating the likelihood).
%! @item T
%! Matrix (@var{mm}*@var{mm}) of doubles, transition matrix of the state equation.
%! @item Q
%! Matrix (@var{rr}*@var{rr}) of doubles, covariance matrix of the structural innovations (noise in the state equation).
%! @item R
%! Matrix (@var{mm}*@var{rr}) of doubles, second matrix of the state equation relating the structural innovations to the state variables.
%! @item H
%! Matrix (@var{pp}*@var{pp}) of doubles, covariance matrix of the measurement errors (if no measurement errors set H as a zero scalar).
%! @item Z
%! Matrix (@var{pp}*@var{mm}) of doubles or vector of integers, matrix relating the states to the observed variables or vector of indices (depending on the value of @var{Zflag}).
%! @item mm
%! Integer scalar, number of state variables.
%! @item pp
%! Integer scalar, number of observed variables.
%! @item rr
%! Integer scalar, number of structural innovations.
%! @item Zflag
%! Integer scalar, equal to 0 if Z is a vector of indices targeting the obseved variables in the state vector, equal to 1 if Z is a @var{pp}*@var{mm} matrix.
%! @item diffuse_periods
%! Integer scalar, number of diffuse filter periods in the initialization step.
%! @end table
%! @sp 2
%! @strong{Outputs}
%! @sp 1
%! @table @ @var
%! @item LIK
%! Double scalar, value of (minus) the likelihood.
%! @item likk
%! Column vector of doubles, values of the density of each observation.
%! @item a
%! Vector (@var{mm}*1) of doubles, mean of the state vector at the end of the (sub)sample.
%! @item P
%! Matrix (@var{mm}*@var{mm}) of doubles, covariance of the state vector at the end of the (sub)sample.