IndicatorNonnegativity¶

class odl.solvers.functional.default_functionals.IndicatorNonnegativity(*args, **kwargs)[source]¶

Bases: odl.solvers.functional.default_functionals.IndicatorBox

Indicator on the set of non-negative numbers.

Notes

The nonnegativity indicator $F$ is defined as:

$F(x) = \begin{cases} 0 & \text{if } 0 \leq x \text{ everywhere}, \\ \infty & \text{else} \end{cases}$

Attributes

adjoint: Adjoint of this operator (abstract).
convex_conj: Convex conjugate functional of the functional.
domain: Set of objects on which this operator can be evaluated.
grad_lipschitz: Lipschitz constant for the gradient of the functional.
gradient: Gradient operator of the functional.
inverse: Return the operator inverse.
is_functional: True if this operator’s range is a Field.
is_linear: True if this operator is linear.
proximal: Return the proximal factory of the functional.
range: Set in which the result of an evaluation of this operator lies.

Methods

`_call`(self, x)	Apply the functional to the given point.
`bregman`(self, point, subgrad)	Return the Bregman distance functional.
`derivative`(self, point)	Return the derivative operator in the given point.
`norm`(self[, estimate])	Return the operator norm of this operator.
`translated`(self, shift)	Return a translation of the functional.

__init__(self, space)[source]¶

Initialize an instance.

Parameters

spaceLinearSpace: Domain of the functional.

Examples

>>> space = odl.rn(3)
>>> func = IndicatorNonnegativity(space)
>>> func([0, 1, 2])  # all points positive
0
>>> func([0, 1, -3])  # one point negative
inf