QuadraticForm

class odl.solvers.functional.default_functionals.QuadraticForm(*args, **kwargs)

Bases: odl.solvers.functional.functional.Functional

Functional for a general quadratic form x^T A x + b^T x + c.

Attributes

adjoint

Adjoint of this operator (abstract).

constant

Constant offset of the functional.

convex_conj

The convex conjugate functional of the quadratic form.

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.

operator

Operator for the quadratic part of the functional.

proximal

Proximal factory of the functional.

range

Set in which the result of an evaluation of this operator lies.

vector

Vector for the linear part of the functional.

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, operator=None, vector=None, constant=0)

Initialize a new instance.

All parameters are optional, but at least one of op and vector have to be provided in order to infer the space.

The computed value is:

x.inner(operator(x)) + vector.inner(x) + constant

Parameters

operatorOperator, optional

Operator for the quadratic part of the functional. None means that this part is ignored.

vectorLinearSpaceElement, optional

Vector for the linear part of the functional. None means that this part is ignored.

constantOperator, optional

Constant offset of the functional.