LpNorm

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

Bases: odl.solvers.functional.functional.Functional

The functional corresponding to the Lp-norm.

Notes

If the functional is defined on an \mathbb{R}^n-like space, the \| \cdot \|_p-norm is defined as

\| x \|_p = \left(\sum_{i=1}^n |x_i|^p \right)^{1/p}.

If the functional is defined on an L_2-like space, the \| \cdot \|_p-norm is defined as

\| x \|_p = \left(\int_\Omega |x(t)|^p dt. \right)^{1/p}

Attributes
adjoint

Adjoint of this operator (abstract).

convex_conj

The convex conjugate functional of the Lp-norm.

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 the Lp-norm of 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, space, exponent)[source]

Initialize a new instance.

Parameters
spaceDiscretizedSpace or TensorSpace

Domain of the functional.

exponentfloat

Exponent for the norm (p).