IndicatorLpUnitBall

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

The indicator function on the unit ball in given the Lp norm.

It does not implement gradient since it is not differentiable everywhere.

Notes

This functional is defined as

$f(x) = \begin{cases} 0 & \text{if } ||x||_{L_p} \leq 1, \\ +\infty & \text{else} \end{cases}$

where $||x||_{L_p}$ is the $L_p$ -norm, which for finite values of $p$ is defined as

$\| x \|_{L_p} = \left( \int_{\Omega} |x|^p dx \right)^{1/p},$

and for $p = \infty$ it is defined as

$||x||_{\infty} = \max_x (|x|).$

The functional also allows noninteger and nonpositive values of the exponent $p$ , however in this case $\| x \|_{L_p}$ is not a norm.

__init__(space, exponent)[source]

Initialize a new instance.