IndicatorSumConstraint¶

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

Bases: odl.solvers.functional.functional.Functional

Indicator functional of a unit sum constraint.

Notes

The functional $F$ is given by:

System Message: WARNING/2 (F(x) = \begin{cases} 0 & \text{if } \sum_i x_i = 1 \ +\infty & \text{else.} \end{cases} )

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Attributes

adjoint: Adjoint of this operator (abstract).
convex_conj: The convex conjugate.
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 `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, space, sum_value=1, sum_rtol=None)[source]¶

Initialize a new instance.

Parameters

spaceDiscretizedSpace or TensorSpace: Domain of the functional.
sum_valuefloat: Desired value of the sum constraint.
sum_rtolfloat, optional: Relative tolerance for sum comparison. If set to None, the default is space.size times 1e-10 when space.dtype is float64 and 1e-6 otherwise.

Examples

Example where a point does not have unit sum …

>>> space = odl.rn(3)
>>> ind_sum = IndicatorSumConstraint(space)
>>> x = space.one()
>>> ind_sum(x)
inf

… and one where it does.

>>> x /= x.ufuncs.sum()
>>> ind_sum(x)
0