Get_L_y: The multiplication of L with y

In FastGaSP: Fast and Exact Computation of Gaussian Stochastic Process

The multiplication of L with y

Description

This function computes the product of the L matrix and the output vector, where L is the Cholesky decomposition of the correlation matrix R. Instead of explicitly forming the Cholesky matrix, this function uses the dynamic linear model (DLM) forward filtering algorithm for efficient computation.

Usage

Get_L_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 L matrix and the output vector, where L is the Cholesky decomposition of the correlation matrix.

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_t_inv_y for (L^T)^{-1}y computation.

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