L2Norm

class odl.solvers.functional.default_functionals.L2Norm(*args, **kwargs)

Bases: odl.solvers.functional.default_functionals.LpNorm

The functional corresponding to the L2-norm.

The L2-norm, ||x||_2, is defined as the square-root out of the integral/sum of x^2.

Notes

If the functional is defined on an -like space, the -norm is defined as

If the functional is defined on an -like space, the -norm is defined as

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)

Initialize a new instance.

Parameters

spaceDiscretizedSpace or TensorSpace

Domain of the functional.