isposdef: Positive Definiteness

In pracma: Practical Numerical Math Functions

Positive Definiteness

Description

Test for positive definiteness.

Usage

isposdef(A, psd = FALSE, tol = 1e-10)

Arguments

A	symmetric matrix
psd	logical, shall semi-positive definiteness be tested?
tol	tolerance to check symmetry and Cholesky decomposition.

Details

Whether matrix A is positive definite will be determined by applying the Cholesky decomposition. The matrix must be symmetric.

With psd=TRUE the matrix will be tested for being semi-positive definite. If not positive definite, still a warning will be generated.

Value

Returns TRUE or FALSE.

Examples

A <- magic(5)
# isposdef(A)
## [1] FALSE
## Warning message:
## In isposdef(A) : Matrix 'A' is not symmetric.
## FALSE

A <- t(A) %*% A
isposdef(A)
## [1] TRUE

A[5, 5] <- 0
isposdef(A)
## [1] FALSE

pracma documentation built on Nov. 10, 2023, 1:14 a.m.