IndicatorGroupL1UnitBall¶

class odl.solvers.functional.default_functionals.IndicatorGroupL1UnitBall(*args, **kwargs)[source]¶

Bases: odl.solvers.functional.functional.Functional

The convex conjugate to the mixed L1–Lp norm on ProductSpace.

See also

GroupL1Norm

Attributes

adjoint: Adjoint of this operator (abstract).
convex_conj: Convex conjugate functional of IndicatorLpUnitBall.
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)	Return `self(x)`.
`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, vfspace, exponent=None)[source]¶

Initialize a new instance.

Parameters

vfspaceProductSpace: Space of vector fields on which the operator acts. It has to be a product space of identical spaces, i.e. a power space.
exponentnon-zero float, optional: Exponent of the norm in each point. Values between 0 and 1 are currently not supported due to numerical instability. Infinity gives the supremum norm. Default: vfspace.exponent, usually 2.

Examples

>>> space = odl.rn(2)
>>> pspace = odl.ProductSpace(space, 2)
>>> op = IndicatorGroupL1UnitBall(pspace)
>>> op([[0.1, 0.5], [0.2, 0.3]])
0
>>> op([[3, 3], [4, 4]])
inf

Set exponent of inner (p) norm:

>>> op2 = IndicatorGroupL1UnitBall(pspace, exponent=1)