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.
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)Returns a list containing three elements:
A numeric vector containing the estimated state variables.
A numeric vector containing the residuals at each iteration.
An integer indicating the number of iterations performed.
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).
A string specifying the kernel type. Must be either "matern_5_2" or "exp".
A numeric vector of successive differences of sorted inputs.
A numeric vector representing the output values.
A numeric vector containing the non-zero entries in matrix A.
An integer vector containing sorted indices for distances.
An integer vector specifying the number of neighbors for each particle.
A numeric value representing the stabilizing parameter.
An integer specifying the dimension of the output vector per particle.
An integer specifying the total dimension of the output vector.
A numeric value specifying the convergence tolerance. Default is 1e-6.
An integer specifying the maximum number of iterations. Default is 1000.
Fang, X., & Gu, M. (2024). The inverse Kalman filter. arXiv:2407.10089.