pd_check: Check Hessian matrix is positive definite by attempting a...

In optimx: Expanded Replacement and Extension of the 'optim' Function

Check Hessian matrix is positive definite by attempting a Cholesky decomposition.

Description

We desire that Hessian matrices of objective functions for optimization are symmetric and positive definite. Symmetry is easy to check, but we caution that evaluation or approximation of a Hessian often gives a slightly asymmetric, and we commonly average the elements that are supposed to be equal, thereby symmetrizing the proposed Hessian.

The Cholesky decomposition will fail for a symmetric matrix which is NOT positive definite.

Usage

   pd_check(A, pivot=TRUE, tol=1.e-07) 

Arguments

A	A symmetric matrix
pivot	Use pivoting in the Cholesky decomposition attempt
tol	A tolerance for zero

Value

The function returns a logical TRUE if the decomposition can be carried out, FALSE otherwise.

Examples

  n <- 10
  A <- pracma::moler(n)
  system.time(print(pd_check(A))) # returns FALSE
  system.time(print(eigen(A)$value))
  n <- 100
  A <- pracma::moler(n)
  system.time(print(pd_check(A))) # returns FALSE
  system.time(print(eigen(A)$value))

optimx documentation built on April 11, 2025, 5:43 p.m.