doe_stationary_point Subroutine

public subroutine doe_stationary_point(mdl, n, z, nature, ok, eigenvalues)

Computes the stationary point of a quadratic (nway <= 2) response surface in coded variables and classifies its nature.

The model is written as

$$\hat{y}(z) = \beta_{0} + g^{T} z + \frac{1}{2} z^{T} H z$$

where the gradient $g$ and Hessian $H$ are recovered exactly from model evaluations. The stationary point solves $H z = -g$, and is classified by the eigenvalues of $H$: all negative is a maximum, all positive is a minimum, mixed signs is a saddle, and a (near) zero eigenvalue is singular (a ridge or flat direction, with no unique stationary point).

Arguments

Type	Intent	Optional	Attributes		Name
class(doe_model),	intent(in)			::	mdl	The fitted DOE model, defined in coded variables. Its nway must be 1 or 2.
integer(kind=int32),	intent(in)			::	n	The number of factors.
real(kind=real64),	intent(out),		allocatable, dimension(:)	::	z	The stationary point in coded variables. This is allocated only if ok is true.
character(len=:),	intent(out),		allocatable	::	nature	One of maximum, minimum, saddle, singular, or not quadratic.
logical,	intent(out)			::	ok	True if a unique stationary point was found.
real(kind=real64),	intent(out),	optional,	allocatable, dimension(:)	::	eigenvalues	The eigenvalues of the Hessian, in coded variables.