Calculates logs of multivariate Gaussian densities with varying mean and varying covariance matrix AND EXCLUDING the constant term of the density (the constant is calculated and added in R code). The varying conditional covariance matrix is calculated within the function from the regime covariance matrices and transition weights.
Gaussian_densities_Cpp(obs, means, covmats, alpha_mt)a numeric vector containing the multivariate Gaussian densities, excluding the constant term.
a \((T \times d)\) matrix such that the \(i\)th row contains the vector \(y_{i}=(y_{1i},...,y_{di})\) \((dx1)\). That is, the initial values are excluded but the last observations is included.
a \((T \times d)\) matrix such that the \(i\)th row contains the conditional mean of the process \(\mu_{y,i}\).
a \((d \times d \times M)\) array such that the slice [, , m]
contains the conditional covariance matrix of regime m.
a \((T \times M)\) matrix such that [t, m] contains the time t
transition weights of the \(m\)th regime.