Fast Computation of some Matrices Useful in Statistics
Array multiplication
Force a matrix to be symmetric
Computation of Bezier curve
Bracket product
Lin's concordance correlation coefficient
Solve linear systems using the conjugate gradients method
Rank 1 update to Cholesky factorization
Form a symmetric circulant matrix
Compact information to construct the commutation matrix
Matrix multiplication envolving the commutation matrix
Commutation matrix
AR(1) correlation structure
Compound symmetry correlation structure
Mean Square Successive Difference (MSSD) estimator of the covariance m...
Weighted covariance matrices
Matrix crossproduct envolving the duplication matrix
Compact information to construct the duplication matrix
Matrix multiplication envolving the duplication matrix
Duplication matrix
Equilibration of a rectangular or symmetric matrix
Frank matrix
Geometric mean
Hadamard product of two matrices
Form a symmetric Hankel matrix
Test for variance homogeneity of correlated variables
Helmert matrix
Check if a matrix is lower or upper triangular
Solve linear systems using the Jacobi method
Jarque-Bera test for univariate normality
Kronecker product on matrices
Computes a Krylov matrix
Mardia's multivariate skewness and kurtosis coefficients
The LDL decomposition
Reconstruct the L, U, or X matrices from an LU object
The LU factorization of a square matrix
Inverse from LU factorization
Mahalanobis distance
Compute the inner product between two rectangular matrices
Compute the norm of a rectangular matrix
Evaluates a real general matrix polynomial
Matrix square root
The modified Cholesky factorization
Mediancenter
Computes the p-norm of a vector
Central moments
Fit a linear model
Fitter functions for linear models
Fit linear regression model
Power method to approximate dominant eigenvalue and eigenvector
Generation of deviates uniformly distributed in a unitary ball
Ridge regression
Multivariate normal random deviates
Generation of deviates uniformly located on a spherical surface
Scaled condition number
Solve linear systems using the Gauss-Seidel method
Sherman-Morrison formula
Gauss-Jordan sweep operator for symmetric matrices
Compact information to construct the symmetrizer matrix
Matrix multiplication envolving the symmetrizer matrix
Symmetrizer matrix
Vectorization of a matrix
Vectorization the lower triangular part of a square matrix
Wilson-Hilferty transformation for chi-squared variates
Whitening transformation
Wilson-Hilferty transformation
Small set of functions to fast computation of some matrices and operations useful in statistics and econometrics. Currently, there are functions for efficient computation of duplication, commutation and symmetrizer matrices with minimal storage requirements. Some commonly used matrix decompositions (LU and LDL), basic matrix operations (for instance, Hadamard, Kronecker products and the Sherman-Morrison formula) and iterative solvers for linear systems are also available. In addition, the package includes a number of common statistical procedures such as the sweep operator, weighted mean and covariance matrix using an online algorithm, linear regression (using Cholesky, QR, SVD, sweep operator and conjugate gradients methods), ridge regression (with optimal selection of the ridge parameter considering several procedures), omnibus tests for univariate normality, functions to compute the multivariate skewness, kurtosis, the Mahalanobis distance (checking the positive defineteness), and the Wilson-Hilferty transformation of gamma variables. Furthermore, the package provides interfaces to C code callable by another C code from other R packages.