statespace_dense

The matrix formulation of the model (DK §4.13): the whole sample as one Gaussian vector. With \(\alpha\) the stacked states and \(Y_n\) the stacked observed elements,

\[\begin{split}E(Y_n) = \mu = d + Z a^*, \quad Var(Y_n) = \Omega = Z V^* Z' + H, \\ \log L = -\tfrac12 \big(N \log 2\pi + \log|\Omega| + (Y_n - \mu)' \Omega^{-1} (Y_n - \mu)\big), \\ E(\alpha | Y_n) = a^* + V^* Z' \Omega^{-1} (Y_n - \mu), \quad Var(\alpha | Y_n) = V^* - V^* Z' \Omega^{-1} Z V^*.\end{split}\]

The cost is \(O((nm)^3)\). It is a reference for small problems and a check on the recursive algorithms, which the tests use.

dense_loglike_smooth

subroutine dense_loglike_smooth(rep, llf, alphahat, V, info)
  type(ssm_rep_t), intent(in) :: rep
  real(dp), intent(out) :: llf
  real(dp), intent(out) :: alphahat(:, :)   ! (m, n)
  real(dp), intent(out) :: V(:, :, :)       ! (m, m, n)
  integer, intent(out) :: info

Known or approximate diffuse initialization only; info is SS_ERR_UNSUPPORTED with diffuse states.