FunctionalQuadraticPerturb

class odl.solvers.functional.functional.FunctionalQuadraticPerturb(*args, **kwargs)

Bases: odl.solvers.functional.functional.Functional

The functional representing F(.) + a * <., .> + <., u> + c.

Attributes

adjoint

Adjoint of this operator (abstract).

constant

The constant coefficient.

convex_conj

Convex conjugate functional of the functional.

domain

Set of objects on which this operator can be evaluated.

functional

Original functional.

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.

linear_term

Linear term.

proximal

Proximal factory of the quadratically perturbed functional.

quadratic_coeff

Cofficient of the quadratic term.

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, func, quadratic_coeff=0, linear_term=None, constant=0)

Initialize a new instance.

Parameters

funcFunctional

Function corresponding to f.

quadratic_coeffdomain.field element, optional

Coefficient of the quadratic term. Default: 0.

linear_termdomain element, optional

Element in domain of func, corresponding to the translation. Default: Zero element.

constantdomain.field element, optional

The constant coefficient. Default: 0.