metaSEM (version 0.9.4)

is.pd: Test Positive Definiteness of a List of Square Matrices

Description

It tests the positive definiteness of a square matrix or a list of square matrices. It returns TRUE if the matrix is positive definite. It returns FALSE if the matrix is either non-positive definite or not symmetric. Variables with NA in the diagonals will be removed before testing. It returns NA when there are missing correlations even after deleting the missing variables.

Usage

is.pd(x, check.asyCov=FALSE, cor.analysis=TRUE, tol=1e-06)

Arguments

x

A square matrix or a list of square matrices

check.asyCov

If it is TRUE, it mirrors the checking in asyCov.

cor.analysis

Whether the input matrix is a correlation or a covariance matrix. It is ignored when check.asyCov=FALSE.

tol

Relative tolerance of positiveness of smallest eigenvalue compared to largest eigenvalue. The matrix is considered positive definite if the ratio of the smallest eigenvalue to the largest eigenvalue is larger than tol. See

Value

• If the input is a matrix, it returns TRUE, FALSE or NA. If the input is a list of matrices, it returns a list of TRUE, FALSE or NA.

Examples

A <- diag(1,3)
is.pd(A)
# TRUE

B <- matrix(c(1,2,2,1), ncol=2)
is.pd(B)
# FALSE

is.pd(list(A, B))
# TRUE FALSE

C <- A
C[2,1] <- C[1,2] <- NA
is.pd(C)
# NA