univariate_function

univariate_function(
    type,
    parameters,
    x,
    inverse=False,
    is_inverse=False,
    confidence_level=None,
)

Evaluate a univariate function.

Mirrors the Numerics LinearFunction (Y = alpha + beta*X + epsilon) and PowerFunction (Y = alpha * (X - xi)**beta * epsilon), both over optional normally distributed noise (epsilon ~ Normal(0, sigma)) via confidence_level. is_inverse (PowerFunction’s own IsInverse switch) selects which of the forward power law or its algebraic inverse Function()/inverse=True evaluates – an independent axis from inverse itself, which picks Function() vs. InverseFunction() on whichever of the two is_inverse selects.

Parameters

Name	Type	Description	Default
type	('linear', 'power')	Matched case-insensitively.	"linear"
parameters	array_like	[alpha, beta, sigma] for "linear"; [alpha, beta, xi, sigma] for "power". sigma is still required (e.g. 0) when confidence_level is None – it only enters the calculation on the non-deterministic path.	required
x	array_like	The values to evaluate the function at, or (when inverse=True) the values to evaluate the inverse function at.	required
inverse	bool	If True, evaluates the inverse function (InverseFunction()) instead of the forward function (Function()).	False
is_inverse	bool	"power"-only: PowerFunction’s own IsInverse property. An error for type="linear".	False
confidence_level	float	If given, evaluates the non-deterministic path at this quantile level; if None (default), evaluates deterministically.	None

Returns

Name	Type	Description
	numpy.ndarray

Examples

>>> from corehydropy import univariate_function
>>> univariate_function("linear", [0, 1, 0], [1, 2, 3])
array([1., 2., 3.])
>>> univariate_function("power", [5, 2, 0, 3], 6)
array([180.])
>>> univariate_function("power", [5, 2, 0, 3], 6, confidence_level=0.75)
array([1361.614084])