Get_R_y: The multiplication of R with y

In FastGaSP: Fast and Exact Computation of Gaussian Stochastic Process

The multiplication of R with y

Description

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.

Usage

Get_R_y(GG, Q, K, output)

Arguments

GG	a list of matrices defined in the dynamic linear model.
Q	a vector defined in the dynamic linear model.
K	a matrix defined in the filtering algorithm for the dynamic linear model.
output	a vector of observations.

Value

A vector representing the product of the R matrix and the output vector, where R is the correlation matrix for a dynamic linear model.

Author(s)

Mengyang Gu [aut, cre], Xinyi Fang [aut], Yizi Lin [aut]

Maintainer: Mengyang Gu <[e-mail]>

References

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.

See Also

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.

FastGaSP documentation built on April 4, 2025, 5:16 a.m.