IKF_CG_particle_cell: Inverse Kalman Filter with Conjugate Gradient for Particle...
In FastGaSP: Fast and Exact Computation of Gaussian Stochastic Process

IKF_CG_particle_cell

R Documentation

Inverse Kalman Filter with Conjugate Gradient for Particle Systems

Description

Implements the IKF-CG (Inverse Kalman Filter - Conjugate Gradient) algorithm for the one-interaction physical model with 1D output, different particle numbers for different time, and non-identity diagonal noise.

Usage

IKF_CG_particle_cell(param, kernel_type, delta_x_all, output, A_all_v, 
                     sort_d_all_ix, sigma_2_vec, num_neighbors_vec, 
                     tilde_nu, D, n_t_record, tol = 1e-6, maxIte = 1000)

Arguments

`param`	A numeric vector containing model parameters. The first element is the log of beta (inverse range parameter), and the second element is the log of tau (variance ratio parameter).
`kernel_type`	A string specifying the covariance kernel type: "matern_5_2" or "exp".
`delta_x_all`	A numeric vector of successive differences of sorted inputs.
`output`	A numeric vector of observations.
`A_all_v`	A numeric vector containing the non-zero entries in matrix A.
`sort_d_all_ix`	An integer vector of indices for sorting distances.
`sigma_2_vec`	A numeric vector of variances for each time point.
`num_neighbors_vec`	An integer vector specifying number of neighbors for each observation.
`tilde_nu`	A numeric value for numerical stabilization.
`D`	An integer specifying the dimension of observations.
`n_t_record`	An integer vector containing number of particles at each time point.
`tol`	A numeric value specifying convergence tolerance (default: 1e-6).
`maxIte`	An integer specifying maximum number of iterations (default: 1000).

Value

Returns a list containing:

`x`	A numeric vector of solved coefficients.
`resid`	A numeric vector of residuals at each iteration.
`ite`	An integer indicating the number of iterations performed.