# -*- coding: utf-8 -*-
##########################################################################
# pySAP - Copyright (C) CEA, 2017 - 2018
# Distributed under the terms of the CeCILL-B license, as published by
# the CEA-CNRS-INRIA. Refer to the LICENSE file or to
# http://www.cecill.info/licences/Licence_CeCILL-B_V1-en.html
# for details.
##########################################################################

"""
This module contains all the utils tools needed in the p_MRI reconstruction.
"""


# System import

# Package import

# Third party import
import numpy as np


[docs]def check_lipschitz_cst(f, x_shape, lipschitz_cst, max_nb_of_iter=10):
    """
    This methods check that for random entrees the lipschitz constraint are
    statisfied:

    * ||f(x)-f(y)|| < lipschitz_cst ||x-y||

    Parameters
    ----------
    f: callable
        This lipschitzien function
    x_shape: tuple
        Input data shape
    lipschitz_cst: float
        The Lischitz constant for the function f
    max_nb_of_iter: int
        The number of time the constraint must be satisfied

    Returns
    -------
    out: bool
        If is True than the lipschitz_cst given in argument seems to be an
        upper bound of the real lipschitz constant for the function f
    """
    is_lips_cst = True
    n = 0

    while is_lips_cst and n < max_nb_of_iter:
        n += 1
        x = np.random.randn(*x_shape)
        y = np.random.randn(*x_shape)
        is_lips_cst = (np.linalg.norm(f(x)-f(y)) <= (lipschitz_cst *
                                                     np.linalg.norm(x-y)))

    return is_lips_cst