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