Compute the log likelihood for a statespace system described by a model template.

This is an internal helper function, used by the function factory ll_FUN. For a more detailed documentation of the log Likelihood, see ll_kf.

Usage

ll_kf_theta_cpp(
  theta,
  y,
  SYS,
  H_SYS,
  h_SYS,
  sigma_L,
  H_sigma_L,
  h_sigma_L,
  VAR,
  P1,
  tol,
  err
)

theta: \((K)\) dimensional vector of "deep" parameters.
y: \((m,N)\) matrix with the observed outputs: \((y_1,y_2,\ldots,y_N)\).
SYS: \((m+s,m+s)\) matrix, is overwritten with the system matrix \([A,B | C,D]\).
H_SYS: \((m+s)^2, K)\) matrix.
h_SYS: \(((m+s)^2)\)-dimensional vector. Note that vec(SYS) = H_SYS*theta + h_SYS.
sigma_L: \((m,m)\) matrix, is overwritten with the left square root of the noise covariance matrix.
H_sigma_L: \((m^2, K)\) matrix.
h_sigma_L: \((m^2)\)-dimensional vector. Note that vec(sigma_L) = H_sigma_L*theta + h_sigma_L.
VAR: \((m+s,m+s)\) matrix, is overwritten with the covariance matrix \([Q,S | S',R] = [B | C] sigma_L sigma_L' [B', C']\)
P1: \((s,s)\) matrix, is overwritten with the initial state covariance matrix (computed via a Lyapunov equation).
tol: (double) tolerance used by ll_kf_cpp.
err: (double) return err, if the computation of P1 fails.