IndicatorLpUnitBall¶
-
class
odl.solvers.functional.default_functionals.
IndicatorLpUnitBall
(*args, **kwargs)[source]¶ Bases:
odl.solvers.functional.functional.Functional
The indicator function on the unit ball in given the
Lp
norm.It does not implement
gradient
since it is not differentiable everywhere.Notes
This functional is defined as
where is the -norm, which for finite values of is defined as
and for it is defined as
The functional also allows noninteger and nonpositive values of the exponent , however in this case is not a norm.
- Attributes
adjoint
Adjoint of this operator (abstract).
convex_conj
The conjugate functional of IndicatorLpUnitBall.
domain
Set of objects on which this operator can be evaluated.
exponent
Exponent corresponding to the norm.
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 aField
.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, exponent)[source]¶ Initialize a new instance.
- Parameters
- space
DiscretizedSpace
orTensorSpace
Domain of the functional.
- exponentint or infinity
Specifies wich norm to use.
- space