Module alexandria.math.functions
Special functions
Expand source code
# SPDX-FileCopyrightText: © 2021 Antonio López Rivera <antonlopezr99@gmail.com>
# SPDX-License-Identifier: GPL-3.0-only
"""
Special functions
-----------------
"""
def macauley(x, k):
"""
Macauley step function for exponents > 0.
macauley(t - 5)**n for all n > 0
:param x: Domain.
:param k: Constant.
:type x: np.ndarray
:type k: float
:return: [np.ndarray] Macauley step function array.
"""
return x - k if x - k >= 0 else 0
def macauley0(x, k):
"""
Macauley step function for exponent = 0.
Necessary as 0**1 is defined as 1, while
macauley(a-b)**0 = 0
for all a, b such that b > a.
:param x: Domain.
:param k: Constant.
:type x: np.ndarray
:type k: float
:return: [np.ndarray] Macauley step function array.
"""
return 1 if x - k >= 0 else 0Functions
def macauley(x, k)-
Macauley step function for exponents > 0.
macauley(t - 5)**n for all n > 0:param x: Domain. :param k: Constant.
:type x: np.ndarray :type k: float
:return: [np.ndarray] Macauley step function array.
Expand source code
def macauley(x, k): """ Macauley step function for exponents > 0. macauley(t - 5)**n for all n > 0 :param x: Domain. :param k: Constant. :type x: np.ndarray :type k: float :return: [np.ndarray] Macauley step function array. """ return x - k if x - k >= 0 else 0 def macauley0(x, k)-
Macauley step function for exponent = 0. Necessary as 0**1 is defined as 1, while
macauley(a-b)**0 = 0for all a, b such that b > a.
:param x: Domain. :param k: Constant.
:type x: np.ndarray :type k: float
:return: [np.ndarray] Macauley step function array.
Expand source code
def macauley0(x, k): """ Macauley step function for exponent = 0. Necessary as 0**1 is defined as 1, while macauley(a-b)**0 = 0 for all a, b such that b > a. :param x: Domain. :param k: Constant. :type x: np.ndarray :type k: float :return: [np.ndarray] Macauley step function array. """ return 1 if x - k >= 0 else 0