IndicatorBox

class odl.solvers.functional.default_functionals.IndicatorBox(*args, **kwargs)

Bases: Functional

Indicator on some box shaped domain.

Notes

The indicator with lower bound and upper bound is defined as:

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__(x[, out])	Return self(x[, out, **kwargs]).
bregman(point, subgrad)	Return the Bregman distance functional.
derivative(point)	Return the derivative operator in the given point.
norm([estimate])	Return the operator norm of this operator.
translated(shift)	Return a translation of the functional.

__init__(space, lower=None, upper=None)

Initialize an instance.

Parameters:

spaceLinearSpace

Domain of the functional.

lowerspace.field element or space element-like, optional

The lower bound. Default: None, interpreted as -infinity

upperspace.field element or space element-like, optional

The upper bound. Default: None, interpreted as +infinity

Examples

>>> space = odl.rn(3)
>>> func = IndicatorBox(space, 0, 2)
>>> func([0, 1, 2])  # all points inside
0
>>> func([0, 1, 3])  # one point outside
inf