Check if Matrix is Positive Semidefinite — is_psd_matrix • svrep

Check whether a matrix is positive semidefinite, based on checking for symmetric and negative eigenvalues.

Usage

is_psd_matrix(X, tolerance = sqrt(.Machine$double.eps))

Arguments

X: A matrix with no missing or infinite values.
tolerance: Tolerance for controlling whether a tiny computed eigenvalue will actually be considered negative. Computed negative eigenvalues will be considered negative if they are less than which are less than -abs(tolerance * max(eigen(X)$values)). A small nonzero tolerance is recommended since eigenvalues are nearly always computed with some floating-point error.

Value

A logical value. TRUE if the matrix is deemed positive semidefinite. Negative otherwise (including if X is not symmetric).

See also

The function get_nearest_psd_matrix() can be used to approximate a symmetric matrix which is not positive semidefinite, by a similar positive semidefinite matrix.

Examples

X <- matrix(
  c(2, 5, 5,
    5, 2, 5,
    5, 5, 2),
  nrow = 3, byrow = TRUE
)

is_psd_matrix(X)
#> [1] FALSE

eigen(X)$values
#> [1] 12 -3 -3