This function computes the product of the inverse of the L matrix and the output vector, where the L matrix is the Cholesky decomposition of the correlation matrix. Instead of computing the Cholesky matrix, we compute it using the forward filtering algorithm.
Get_L_inv_y(GG,Q,K,output)A vector representing the product of the inverse of the L matrix and the output vector, where the L matrix is the Cholesky decomposition of the correlation matrix.
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 output.
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.
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 about \(Q\) vector and \(K\) matrix,
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.