verry.optimize.krawczyk

verry.optimize.krawczyk(fun, x, fprime=None)

Apply the Krawczyk test to the multivariate vector-valued function.

Parameters:

• fun (Callable) – Function to find a root of.

• x (IntervalMatrix) – Candidate set for which a root is expected to exist.

• fprime (Callable | IntervalMatrix, optional) – Derivative of fun, or an image of x under the derivative (the default is jacobian(fun)).

Returns:

• r0 (Literal[“EXISTS”, “NOTEXISTS”, “UNIQUE”, “UNKNOWN”])

• r1 (IntervalMatrix | None) – If r0 is "EXISTS" or "UNIQUE", r1 is the set containing the root; otherwise, r1 is None.

Warning

fun must be a \(C^1\)-function on x. Futhermore, fun must neither be a constant nor contain conditional branches (cf. Common pitfalls).

See also

krawczyk_scalar, verry.autodiff.jacobian