IKF_CG_particle: IKF-CG algorithm for one-interaction physical model with 1D...
In FastGaSP: Fast and Exact Computation of Gaussian Stochastic Process

IKF_CG_particle

R Documentation

IKF-CG algorithm for one-interaction physical model with 1D output

Description

Implements the IKF-CG (Inverse Kalman Filter - Conjugate Gradient) algorithm for the one-interaction physical model with 1D output. This function provides an efficient computational method for large-scale particle systems.

Usage

IKF_CG_particle(param, kernel_type, delta_x_all, output, A_all_v, 
                sort_d_all_ix, num_neighbors_vec, tilde_nu,
                D, N, 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 kernel type. Must be either "matern_5_2" or "exp".
`delta_x_all`	A numeric vector of successive differences of sorted inputs.
`output`	A numeric vector representing the output values.
`A_all_v`	A numeric vector containing the non-zero entries in matrix A.
`sort_d_all_ix`	An integer vector containing sorted indices for distances.
`num_neighbors_vec`	An integer vector specifying the number of neighbors for each particle.
`tilde_nu`	A numeric value representing the stabilizing parameter.
`D`	An integer specifying the dimension of the output vector per particle.
`N`	An integer specifying the total dimension of the output vector.
`tol`	A numeric value specifying the convergence tolerance. Default is 1e-6.
`maxIte`	An integer specifying the maximum number of iterations. Default is 1000.

Value

Returns a list containing three elements:

`x`	A numeric vector containing the estimated state variables.
`resid`	A numeric vector containing the residuals at each iteration.
`ite`	An integer indicating the number of iterations performed.