correctionDefinite: Correcting Definiteness of a Matrix

Description

Correcting a (possibly indefinite) symmetric matrix with chosen approach so that it will have desired definiteness type: positive or negative semi-definite (PSD, NSD).

Usage

correctionDefinite(mat, type = "PSD", method = "flip", tol = 1e-08)

Value

list with

mat: corrected matrix
isIndefinite: boolean, whether original matrix was indefinite
lambda: the eigenvalues of the original matrix
lambdanew: the eigenvalues of the corrected matrix
U: the matrix of eigenvectors
a: the transformation vector

Arguments

mat: symmetric matrix
type: string that specifies type of correction: "PSD","NSD" to enforce PSD or NSD matrices respectively.
method: string that specifies method for correction: spectrum clip "clip", spectrum flip "flip", nearest definite matrix "near", spectrum square"square", spectrum diffusion "diffusion".
tol: torelance value. Eigenvalues between -tol and tol are assumed to be zero.

References

Martin Zaefferer and Thomas Bartz-Beielstein. (2016). Efficient Global Optimization with Indefinite Kernels. Parallel Problem Solving from Nature-PPSN XIV. Accepted, in press. Springer.

Examples

Run this code

x <- list(c(2,1,4,3),c(2,4,3,1),c(4,2,1,3),c(4,3,2,1),c(1,4,3,2))
D <- distanceMatrix(x,distancePermutationInsert)
is.NSD(D) #matrix should not be CNSD
D <- correctionDefinite(D,type="NSD")$mat
is.NSD(D) #matrix should now be CNSD
# different example: PSD kernel
D <- distanceMatrix(x,distancePermutationInsert)
K <- exp(-0.01*D)
is.PSD(K)
K <- correctionDefinite(K,type="PSD")$mat
is.PSD(K)