def norm(self):
        """Verify ``LinearSpace.norm``.

        The norm is checked for the following properties:

        - linearity:

            ``||a * x|| = |a| * ||x||``

        - subadditivity:

            ``||x + y|| <= ||x|| + ||y||``

        - positive homogeneity:

            ``||a * x|| = |a| * ||x||``

        - positive definiteness:

            ``||x|| >= 0``

            ``||x|| = 0`` iff ``x = 0``

        - compatibility with the inner product (if available):

            ``||x||^2 = <x, x>``

        References
        ----------
        Wikipedia article on norm_.

        .. _norm: https://en.wikipedia.org/wiki/Norm_(mathematics)
        """
        self.log('\n== Verifying norm ==\n')

        try:
            self.space.zero().norm()
        except NotImplementedError:
            self.log('Space has no norm')
            return

        self._norm_positive()
        self._norm_subadditive()
        self._norm_homogeneity()
        self._norm_inner_compatible()
def norm ( self ) : self . log ( '\n== Verifying norm ==\n' ) try : self . space . zero ( ) . norm ( ) except NotImplementedError : self . log ( 'Space has no norm' ) return self . _norm_positive ( ) self . _norm_subadditive ( ) self . _norm_homogeneity ( ) self . _norm_inner_compatible ( )
Verify ``LinearSpace.norm``.

        The norm is checked for the following properties:

        - linearity:

            ``||a * x|| = |a| * ||x||``

        - subadditivity:

            ``||x + y|| <= ||x|| + ||y||``

        - positive homogeneity:

            ``||a * x|| = |a| * ||x||``

        - positive definiteness:

            ``||x|| >= 0``

            ``||x|| = 0`` iff ``x = 0``

        - compatibility with the inner product (if available):

            ``||x||^2 = <x, x>``

        References
        ----------
        Wikipedia article on norm_.

        .. _norm: https://en.wikipedia.org/wiki/Norm_(mathematics)