A_t_times_x_particle

Performs the matrix-vector multiplication A^T*x for particle systems, where A is a sparse matrix stored only the non-zero entries

internal

Implements fast and exact computation of Gaussian stochastic process with the Matern kernel using forward filtering and backward smoothing algorithm. It includes efficient implementations of the inverse Kalman filter, with applications such as estimating particle interaction functions. These tools support models with or without noise. Additionally, the package offers algorithms for fast parameter estimation in latent factor models, where the factor loading matrix is orthogonal, and latent processes are modeled by Gaussian processes. See the references: 1) Mengyang Gu and Yanxun Xu (2020), Journal of Computational and Graphical Statistics; 2) Xinyi Fang and Mengyang Gu (2024), <doi:10.48550/arXiv.2407.10089>; 3) Mengyang Gu and Weining Shen (2020), Journal of Machine Learning Research; 4) Yizi Lin, Xubo Liu, Paul Segall and Mengyang Gu (2025), <doi:10.48550/arXiv.2501.01324>.

Mengyang Gu

FastGaSP

Fast and Exact Computation of Gaussian Stochastic Process

Xinyi Fang

Yizi Lin

A_t_times_x_particle function

<dl> <dt>output</dt>
<dd>A numeric vector containing the input vector for multiplication.</dd> 
 <dt>A_all_v</dt>
<dd>A numeric vector containing the interaction matrices in vectorized form.</dd> 
 <dt>num_neighbors_vec</dt>
<dd>An integer vector specifying the number of neighbors for each particle.</dd> 
 <dt>D_y</dt>
<dd>An integer specifying the dimension of the output vector per particle.</dd> 
 <dt>N_tilde</dt>
<dd>An integer specifying the total dimension of the output vector.</dd></dl>

Arguments

tools:::Rd_package_author("FastGaSP")
Maintainer: tools:::Rd_package_maintainer("FastGaSP")

Author

Transpose matrix-vector multiplication for particle systems — A_t_times_x_particle

<dl>

 <dt>output</dt>
<dd>A numeric vector containing the input vector for multiplication.</dd>

 
 <dt>A_all_v</dt>
<dd>A numeric vector containing the interaction matrices in vectorized form.</dd>

 
 <dt>num_neighbors_vec</dt>
<dd>An integer vector specifying the number of neighbors for each particle.</dd>

 
 <dt>D_y</dt>
<dd>An integer specifying the dimension of the output vector per particle.</dd>

 
 <dt>N_tilde</dt>
<dd>An integer specifying the total dimension of the output vector.</dd>

</dl>

A_t_times_x_particle: Transpose matrix-vector multiplication for particle systems

Description

Usage

Value

Arguments

Author

References