mat.util {GeneTS}R Documentation

Various Matrix Utilities

Description

is.positive.definite tests whether all eigenvalues of a symmetric matrix are positive.

make.positive.definite computes the nearest positive definite of a real symmetric matrix, using the algorithm of NJ Higham (1988, Linear Algebra Appl. 103:103-118).

rank.condition estimates the rank and the condition of a matrix by computing its singular values D[i] (using svd). The rank of the matrix is the number of singular values D[i] > tol) and the condition is the ratio of the largest and the smallest singular value.

is.square checks whether a matrix has squared form.

is.symmetric checks whether a matrix is symmetric.

Usage

is.positive.definite(m, tol, method=c("eigen", "chol"))
make.positive.definite(m, tol)
rank.condition(m, tol)
is.square(m)
is.symmetric(m, eps = .Machine$double.eps)

Arguments

m matrix
tol tolerance for singular values and for absolute eigenvalues - only those with values larger than tol are considered non-zero (default: tol = max(dim(m))*max(D)*.Machine$double.eps)
method Determines the method to check for positive definiteness: eigenvalue computation (eigen, default) or Cholesky decomposition (chol).
eps values smaller than < eps are considered zero

Value

For is.positive.definite, is.square, and is.symmetric a logical value (TRUE or FALSE).
For rank.condition a list object with the following components:

rank Rank of the matrix.
condition Condition number.
tol Tolerance.


For make.positive.definite a symmetric positive definite matrix.

Author(s)

Korbinian Strimmer (http://www.stat.uni-muenchen.de/~strimmer/).

See Also

svd, pseudoinverse.

Examples

# load GeneTS library
library(GeneTS)

# Hilbert matrix
hilbert <- function(n) { i <- 1:n; 1 / outer(i - 1, i, "+") }

# positive definite ?
m <- hilbert(8)
is.positive.definite(m)

# numerically ill-conditioned
m <- hilbert(15)
rank.condition(m)

# make positive definite
m2 <- make.positive.definite(m)
is.positive.definite(m2)
rank.condition(m2)
m2 - m

# square and symmetric ?
is.square(m)
is.symmetric(m)

[Package GeneTS version 2.3 Index]