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