KullbackLeiblerConvexConj¶

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

The convex conjugate of Kullback-Leibler divergence functional.

See also

Notes

The functional $F^*$ with prior $g>=0$ is given by:

$F^*(x) = \begin{cases} \sum_{i} \left( -g_i \ln(1 - x_i) \right) & \text{if } x_i < 1 \forall i \\ +\infty & \text{else} \end{cases}$

Attributes:

adjoint: Adjoint of this operator (abstract).
convex_conj: The convex conjugate functional of the conjugate KL-functional.
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.
prior: The prior in convex conjugate Kullback-Leibler functional.
proximal: Return the proximal factory of the functional.
range: Set in which the result of an evaluation of this operator lies.

Methods

`__call__`(x[, out])	Return `self(x[, out, **kwargs])`.
`bregman`(point, subgrad)	Return the Bregman distance functional.
`derivative`(point)	Return the derivative operator in the given point.
`norm`([estimate])	Return the operator norm of this operator.
`translated`(shift)	Return a translation of the functional.

__init__(space, prior=None)[source]¶

Initialize a new instance.

Parameters:

spaceDiscretizedSpace or TensorSpace: Domain of the functional.
priorspace element-like, optional: Depending on the context, the prior, target or data distribution. It is assumed to be nonnegative. Default: if None it is take as the one-element.