matrix.polynomial

Given $c_0,c_1,\dots,c_n$ coefficients of the polynomial and $\bold{A}$
 an $n$ by $n$ matrix. This function computes the matrix polynomial
 $$\bold{B} = \sum\limits_{k=0}^n c_k\bold{A}^k,$$
 using Horner's scheme, where $\bold{A}^0 = \bold{I}$ is the $n$ by $n$ identity matrix.

array

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.

Felipe Osorio

fastmatrix

Fast Computation of some Matrices Useful in Statistics

Alonso Ogueda

matrix.polynomial function

<dl> <dt>a</dt>
<dd>a numeric square matrix of order $n$ by $n$ for which the polinomial
 is to be computed.</dd> <dt>coef</dt>
<dd>numeric vector containing the coefficients of the polinomial in order of
 increasing power.</dd> <dt>power</dt>
<dd>a numeric exponent (which is forced to be an integer). If provided, <code>coef</code>
 is a vector of all ones. If the exponent is zero, the identity matrix is returned.</dd></dl>

Arguments

Evaluates a real general matrix polynomial — matrix.polynomial

<dl>

 <dt>a</dt>
<dd>a numeric square matrix of order $n$ by $n$ for which the polinomial
 is to be computed.</dd>

 <dt>coef</dt>
<dd>numeric vector containing the coefficients of the polinomial in order of
 increasing power.</dd>

 <dt>power</dt>
<dd>a numeric exponent (which is forced to be an integer). If provided, <code>coef</code>
 is a vector of all ones. If the exponent is zero, the identity matrix is returned.</dd>

</dl>

matrix.polynomial: Evaluates a real general matrix polynomial

Description

Usage

Value

Arguments

Examples