This function computes the product of the R matrix and the output vector, where R is the correlation matrix for a dynamic linear model (DLM). Instead of explicitly forming the Cholesky decomposition of R, this function computes the product as \(L (L^T y)\), where \(L\) is the Cholesky decomposition of R. This is achieved using the forward filtering algorithm for efficient computation.
Get_R_y(GG, Q, K, output)A vector representing the product of the R matrix and the output vector, where \(R\) is the correlation matrix for a dynamic linear model.
a list of matrices defined in the dynamic linear model.
a vector defined in the dynamic linear model.
a matrix defined in the filtering algorithm for the dynamic linear model.
a vector of observations.
tools:::Rd_package_author("FastGaSP")
Maintainer: tools:::Rd_package_maintainer("FastGaSP")
Hartikainen, J. and Sarkka, S. (2010). Kalman filtering and smoothing solutions to temporal Gaussian process regression models. Machine Learning for Signal Processing (MLSP), 2010 IEEE International Workshop, 379-384.
Fang, X., & Gu, M. (2024). The inverse Kalman filter. arXiv:2407.10089.
M. Gu, Y. Xu (2019), Fast nonseparable Gaussian stochastic process with application to methylation level interpolation. Journal of Computational and Graphical Statistics, In Press, arXiv:1711.11501.
Campagnoli P, Petris G, Petrone S. (2009), Dynamic linear model with R. Springer-Verlag New York.
Get_Q_K for more details on \(K\) and \(Q\) matrices,
Get_L_inv_y for \(L^{-1}y\) computation,
Get_L_t_y for \(L^T y\) computation,
Get_L_y for \(L y\) computation,
Get_L_t_inv_y for \((L^T)^{-1}y\) computation.