L2NormSquared

class odl.functionals.default_functionals.L2NormSquared(*args, **kwargs)[source]

Bases: Functional

The functional corresponding to the squared L2-norm.

The squared L2-norm, ||x||_2^2, is defined as the integral/sum of x^2.

Notes

If the functional is defined on an $\mathbb{R}^n$ -like space, the $\| \cdot \|_2^2$ -functional is defined as

$\| x \|_2^2 = \sum_{i=1}^n |x_i|^2.$

If the functional is defined on an $L_2$ -like space, the $\| \cdot \|_2^2$ -functional is defined as

$\| x \|_2^2 = \int_\Omega |x(t)|^2 dt.$

The proximal factory allows using vector-valued stepsizes:

>>> space = odl.rn(3)
>>> f = odl.functionals.L2NormSquared(space)
>>> x = space.one()
>>> f.proximal([0.5, 1.5, 2.0])(x)
rn(3).element([ 0.5 ,  0.25,  0.2 ])

__init__(space)[source]

Initialize a new instance.

Parameters

spaceDiscretizedSpace or TensorSpace: Domain of the functional.