is.CNSD: Check for Conditional Negative Semi-Definiteness

In CEGO: Combinatorial Efficient Global Optimization

Check for Conditional Negative Semi-Definiteness

Description

This function checks whether a symmetric matrix is Conditionally Negative Semi-Definite (CNSD). Note that this function does not check whether the matrix is actually symmetric.

Usage

is.CNSD(X, method = "alg1", tol = 1e-08)

Arguments

X	a symmetric matrix
method	a string, specifiying the method to be used. "alg1" is based on algorithm 1 in Ikramov and Savel'eva (2000). "alg2" is based on theorem 3.2 in Ikramov and Savel'eva (2000). "eucl" is based on Glunt (1990).
tol	torelance value. Eigenvalues between -tol and tol are assumed to be zero. Symmetric, CNSD matrices are, e.g., euclidean distance matrices, whiche are required to produce Positive Semi-Definite correlation or kernel matrices. Such matrices are used in models like Kriging or Support Vector Machines.

Value

boolean, which is TRUE if X is CNSD

References

Ikramov, K. and Savel'eva, N. Conditionally definite matrices, Journal of Mathematical Sciences, Kluwer Academic Publishers-Plenum Publishers, 2000, 98, 1-50

Glunt, W.; Hayden, T. L.; Hong, S. and Wells, J. An alternating projection algorithm for computing the nearest Euclidean distance matrix, SIAM Journal on Matrix Analysis and Applications, SIAM, 1990, 11, 589-600

See Also

is.NSD, is.PSD

Examples

# The following permutations will produce
# a non-CNSD distance matrix with Insert distance
# and a CNSD distance matrix with Hamming distance
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.CNSD(D,"alg1")
is.CNSD(D,"alg2")
is.CNSD(D,"eucl")
D <- distanceMatrix(x,distancePermutationHamming)
is.CNSD(D,"alg1")
is.CNSD(D,"alg2")
is.CNSD(D,"eucl")

CEGO documentation built on May 29, 2024, 3:35 a.m.