L2Norm

class odl.functionals.default_functionals.L2Norm(*args, **kwargs)[source]

The functional corresponding to the L2-norm.

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

Notes

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

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

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

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

__init__(space)[source]

Initialize a new instance.