Coverage for src/pymor/la/basic : 92%

# This file is part of the pyMOR project (http://www.pymor.org). 

# Copyright Holders: Rene Milk, Stephan Rave, Felix Schindler 

# License: BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause) 

from __future__ import absolute_import, division, print_function 

import numpy as np 

from pymor import defaults 

def induced_norm(product): 

    '''The induced norm of a scalar product. 

    The norm of a vector (an array of vectors) U is calculated by 

    calling :: 

        product.apply2(U, U, mu=mu, pairwise=True) 

    In addition, negative norm squares of absolute value smaller 

    than the `induced_norm_tol` |default| value are clipped to `0`. 

    If the `induced_norm_raise_negative` |default| value is `True`, 

    a :exc:`ValueError` exception is raised if there are still 

    negative norm squares afterwards. 

    Parameters 

    ---------- 

    product 

        The scalar product for which the norm is to be calculated, 

        given as a linear |Operator|. 

    Returns 

    ------- 

    norm 

        A function `norm(U, mu=None)` taking a |VectorArray| `U` 

        as input together with the |Parameter| `mu` which is 

        passed to the product. 

    ''' 

    def norm(U, mu=None): 

        norm_squared = product.apply2(U, U, mu=mu, pairwise=True) 

        if defaults.induced_norm_tol > 0: 

            norm_squared = np.where(np.logical_and(0 > norm_squared, norm_squared > - defaults.induced_norm_tol), 

                                    0, norm_squared) 

        if defaults.induced_norm_raise_negative and np.any(norm_squared < 0): 

            raise ValueError('norm is negative (square = {})'.format(norm_squared)) 

        return np.sqrt(norm_squared) 

    return norm