IndicatorSimplex

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

Indicator functional of simplex.

Notes

The functional $F$ is given by:

$F(x) = \begin{cases} 0 & \text{if } x_i \geq 0 \forall i \text{ and } \sum_i x_i = r \\ +\infty & \text{else.} \end{cases}$

where $r$ is the diameter.

__init__(space, diameter=1, sum_rtol=None)[source]

Initialize a new instance.

Domain of the functional.

diameterpositive float, optional

Diameter of the simplex.

sum_rtolfloat, optional

Relative tolerance for sum comparison. Default:

space.dtype == 'float64': 1e-10 * space.size

Otherwise: 1e-6 * space.size

Example where a point lies outside the unit simplex …

>>> space = odl.rn(3)
>>> ind_simplex = IndicatorSimplex(space)
>>> x = space.one()
>>> ind_simplex(x)
inf

… and one where it lies inside the unit simplex.

>>> x /= odl.sum(x)
>>> ind_simplex(x)
0