Get_L_inv_y: The multiplication of the inverse of L with y

In FastGaSP: Fast and Exact Computation of Gaussian Stochastic Process

The multiplication of the inverse of L with y

Description

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.

Usage

Get_L_inv_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 output.

Value

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.

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.

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 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.

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