IndicatorGroupL1UnitBall

class odl.functionals.default_functionals.IndicatorGroupL1UnitBall(*args, **kwargs)[source]

Bases: Functional

The convex conjugate to the mixed L1–Lp norm on ProductSpace.

See Also

GroupL1Norm

__init__(vfspace, exponent=None)[source]

Initialize a new instance.

Parameters

vfspaceProductSpace: Space of vector fields on which the operator acts. It has to be a product space of identical spaces, i.e. a power space.
exponentnon-zero float, optional: Exponent of the norm in each point. Values between 0 and 1 are currently not supported due to numerical instability. Infinity gives the supremum norm. Default: vfspace.exponent, usually 2.

Examples

>>> space = odl.rn(2)
>>> pspace = odl.ProductSpace(space, 2)
>>> op = IndicatorGroupL1UnitBall(pspace)
>>> op([[0.1, 0.5], [0.2, 0.3]])
0
>>> op([[3, 3], [4, 4]])
inf

Set exponent of inner (p) norm:

>>> op2 = IndicatorGroupL1UnitBall(pspace, exponent=1)