| rank.condition {corpcor} | R Documentation |
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.
Note that the definition tol= max(dim(m))*max(D)*.Machine$double.eps
is exactly compatible with the conventions used in "Octave" or "Matlab".
is.positive.definite(m, tol, method=c("eigen", "chol"))
make.positive.definite(m, tol)
rank.condition(m, tol)
m |
matrix |
tol |
tolerance for singular values and for absolute eigenvalues
- only those with values larger than
tol are considered non-zero (default:
tol = max(dim(m))*max(D)*.Machine$double.eps)
|
method |
Determines the method to check for positive definiteness:
eigenvalue computation (eigen, default) or Cholesky decomposition
(chol). |
is.positive.definite returns
a logical value (TRUE or FALSE).
rank.condition returns a list object with the following components:
rank |
Rank of the matrix. |
condition |
Condition number. |
tol |
Tolerance. |
make.positive.definite returns a symmetric positive definite matrix.
Korbinian Strimmer (http://strimmerlab.org).
# load corpcor library
library("corpcor")
# 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