verry.optimize.allroot_scalar#

verry.optimize.allroot_scalar(fun, domain, fprime=None, unique=False, max_iter=16)#

Find all roots of univariate scalar-valued function.

Parameters:

fun (Callable) – Function to find a root of.
domain (Interval) – Interval for which roots are searched.
fprime (Callable, optional) – Derivative of fun (the default is deriv(fun)).
unique (bool, default=False) – If unique is True, verification continues until the number of iterations reaches max_iter or the uniqueness of the root is verified, even if its existence has been established.
max_iter (int, default=16) – Maximum number of iterations.

Return type:

Warning

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

See also

verry.autodiff.deriv

Examples

>>> from verry import FloatInterval as FI
>>> from verry import function as vrf
>>> r = allroot_scalar(lambda x: x**3 - 2 * x, FI(-2, 3), unique=True)
>>> len(r.unique)
3
>>> root_max = max(r.unique, key=lambda x: x.sup)
>>> root_max.issuperset(vrf.sqrt(FI(2)))
True

verry.optimize.allroot_scalar#

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