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 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.

References

Fang, X., & Gu, M. (2024). The inverse Kalman filter. arXiv:2407.10089.

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