Fast computation of some matrices useful in statistics

Yet another R package for matrices. It contains a small set of functions to fast computation of some matrices and operations useful in statistics.

Features

Latest release (Jan 17, 2024) of fastmatrix package have implemented the following functions:

• Array multiplication (see for instance, Appendix A of Wei, 1998).
• Bezier curve based on n+1 control points.
• C version of the Kronecker product which is slightly faster than the built in R base.
• Column-equilibration for rectangular and symmetric matrices.
• Constructors for AR(1) and compound symmetry correlation matrices.
• Constructors for Frank and Helmert matrices.
• Covariance matrix estimation using the Mean Square Successive (MSSD) method.
• Estimation of the weighted mean and covariance matrix using an online algorithm (Clarke, 1971).
• Computation of central moments up to fourth order using an online algorithm (Spicer, 1972).
• Fast computation of Hadamard product using unrolled loops.
• Gauss-Seidel, Jacobi and conjugate gradients (CG) iterative methods for solving linear systems.
• Geometric mean using a Fused-Multiply-and-Add (FMA) compensated scheme for accurate computation of floating-point product.
• Inner products and norms for matrices.
• Computation of the scaled condition number of a rectangular matrix.
• Interface to C code callable by another C code from other R packages.
• LDL decomposition for symmetric real matrices.
• Computation of the modified Cholesky factorization of a real symmetric but not necessarily positive definite matrix.
• Lp norms for vectors.
• LU factorization for square matrices.
• Mahalanobis distances, checking if the covariance is a positive definite matrix.
• Modified Cholesky factorization for symmetric but not necessarily positive definite matrices.
• Omnibus test for univariate normality (Jarque-Bera, Doornik-Hansen, Adjusted Lagrange multiplier test and robust version by Gel and Gastwirt, 2008).
• Operations envolving the commutation matrix, with minimum requirements of storage.
• Operations envolving the duplication matrix, with minimum requirements of storage.
• Operations envolving the symmetrizer matrix, with minimum requirements of storage.
• Ordinary least-squares (OLS) using several methods: conjugate gradients, Cholesky, QR decomposition, singular value decomposition, and the Sweep operator. This provides an alternative to extend the procedures available in R built-in function ‘lm’.
• Power method to compute the dominant eigenvalue and its associated eigenvector.
• Random number generation from the multivariate normal (Gaussian) distribution.
• Random number generation of uniformly distributed deviates within a unitary ball.
• Random number generation of uniformly distributed deviats located on a spherical surface.
• Rank 1 update to Cholesky factorization.
• Ridge estimation for linear regression.
• Routines to compute measures of multivariate skewness and kurtosis proposed by Mardia (1970).
• Routine for the computation of the mediancenter (or geometric median) of multivariate data.
• Routine to compute a Krylov matrix.
• Sherman-Morrison formula.
• Sweep operator for symmetric matrices.
• Test for variance homogeneity of correlated variables (Harris, 1985).
• vec and vech operators to handle rectangular and square matrices.
• Whitening transformation.
• Wilson-Hilferty transformation for Gamma random variables.

Our plan in the near future is the implementation of functions to handle:

• Some special matrices and operations arising in numerical analysis.

Reference Manual

• fastmatrix.pdf

Resources

Version 0.5-772 of fastmatrix can be found at the CRAN package repository:

• fastmatrix_0.5-772.tar.gz - Package sources
• fastmatrix_0.5-772.zip - Windows binaries (R-release)
• fastmatrix_0.5-772.tgz - MacOS binaries (R-release, arm64)
• fastmatrix_0.5-772.tgz - MacOS binaries (R-release, x86_64)

Installation instructions

To install fastmatrix (version 0.5-772) from CRAN, start R and enter:

install.packages("fastmatrix")

Or install it from its GitHub repository. First install the devtools package.

install.packages("devtools")

Then install fastmatrix using the install_github function in devtools

library(devtools)
install_github("faosorios/fastmatrix", subdir = "pkg")

Alternatively, you can download the source as a tarball (.tar.gz file). Unpack this file (thereby creating a directory named, fastmatrix) and install the package source by executing (at the console prompt)

R CMD INSTALL fastmatrix

Next, you can load the package by using the command: library(fastmatrix)

Providing Feedback

Please report any bugs/suggestions/improvements to Felipe Osorio. If you find these routines useful or not then please let me know. Also, acknowledgement of the use of the routines is appreciated.

To cite the fastmatrix package in publications use:

Osorio, F., Ogueda, A. (2024). fastmatrix: Fast computation of some matrices useful in statistics. R package version 0.5-772. URL: faosorios.github.io/fastmatrix

About the Authors

Felipe Osorio is an Assistant Professor at Department of Mathematics, Universidad Tecnica Federico Santa Maria, Chile.

• Webpage: fosorios.mat.utfsm.cl

Alonso Ogueda is a doctorate student of mathematics from the Mathematical Sciences Department, George Mason University, USA.

• Github: github.com/aoguedao