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

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where ||x||_{L_p} is the L_p-norm, which for finite values of p is defined as

\| x \|_{L_p} = \left( \int_{\Omega} |x|^p dx \right)^{1/p},

and for p = \infty it is defined as

||x||_{\infty} = \max_x (|x|).

The functional also allows noninteger and nonpositive values of the exponent p, however in this case \| x \|_{L_p} 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 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, exponent)[source]

Initialize a new instance.

Parameters
spaceDiscretizedSpace or TensorSpace

Domain of the functional.

exponentint or infinity

Specifies wich norm to use.