# Some norm functions with the weights for MM algorithms
#
# Copyright 2020 Robin Scheibler
#
# Permission is hereby granted, free of charge, to any person obtaining a copy of
# this software and associated documentation files (the "Software"), to deal in
# the Software without restriction, including without limitation the rights to
# use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
# of the Software, and to permit persons to whom the Software is furnished to do
# so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in all
# copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.
import numpy as np

eps = 1e-15


def lp_norm(E, p=1):
    assert p > 0 and p < 2
    weights = p / np.maximum(eps, 2.0 * np.abs(E) ** (2 - p))
    return weights


def lpq_norm(E, p=1, q=2, axis=1):
    assert p > 0 and q >= p and q <= 2.0

    rn = np.sum(np.abs(E) ** q, axis=axis, keepdims=True) ** (1 - p / q)
    qfn = np.abs(E) ** (2 - q)
    weights = p / np.maximum(eps, 2.0 * rn * qfn)
    return weights
