Test positive semi-definiteness (relative tolerance)

is_psd() is TRUE when A is symmetric and every eigenvalue exceeds -rtol * max(abs(diag(A))); is_pd() is TRUE when every eigenvalue exceeds +rtol * max(abs(diag(A))). Both are shifted Cholesky probes, so large sparse matrices never need an eigendecomposition. is_spd() is a deprecated alias of is_psd() kept for internal callers (its tol is the relative tolerance).

Usage

is_psd(A, rtol = .metric_rtol_default())

is_pd(A, rtol = .metric_rtol_default())

is_spd(A, tol = .metric_rtol_default())

Arguments

A

numeric matrix or Matrix::Matrix

rtol

relative tolerance (default sqrt(.Machine$double.eps))

tol

relative tolerance (deprecated name; same as rtol)

Value

logical