# Wulfric - Crystal, Lattice, Atoms, K-path.
# Copyright (C) 2023-2024 Andrey Rybakov
#
# e-mail: anry@uv.es, web: adrybakov.com
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
__all__ = [
"compare_numerically",
"ABS_TOL",
"REL_TOL",
"MIN_LENGTH",
"MAX_LENGTH",
"ABS_TOL_ANGLE",
"REL_TOL_ANGLE",
"MIN_ANGLE",
]
# Length variables
ABS_TOL = 1e-8 # For the linear spatial variables
REL_TOL = 1e-4 # For the linear spatial variables
# MIN_LENGTH is a direct consequence of the REL_TOL and ABS_TOL:
# for l = MIN_LENGTH => ABS_TOL = l * REL_TOL
MIN_LENGTH = ABS_TOL / REL_TOL
# MAX_LENGTH is a direct consequence of the ABS_TOL:
# Inverse of the MAX_LENGTH in the real space has to be meaningful
# in the reciprocal space (< ABS_TOL).
MAX_LENGTH = 1 / ABS_TOL
# TODO Think how to connect angle tolerance with spatial tolerance.
ABS_TOL_ANGLE = 1e-4 # For the angular variables, in degrees.
REL_TOL_ANGLE = 1e-2 # For the angular variables.
# MIN_ANGLE is a direct consequence of the REL_TOL_ANGLE and ABS_TOL_ANGLE:
# for a = MIN_ANGLE => ABS_TOL_ANGLE = a * REL_TOL_ANGLE
MIN_ANGLE = ABS_TOL_ANGLE / REL_TOL_ANGLE # In degrees
[docs]
def compare_numerically(x, condition, y, eps=None, rtol=REL_TOL, atol=ABS_TOL):
r"""
Compare two numbers numerically.
The approach is taken from [1]_:
.. math::
\begin{matrix}
x < y & x < y - \varepsilon \\
x > y & y < x - \varepsilon \\
x \le y & \text{ not } (y < x - \varepsilon) \\
x \ge y & \text{ not } (x < y - \varepsilon) \\
x = y & \text{ not } (x < y - \varepsilon \text{ or } y < x - \varepsilon) \\
x \ne y & x < y - \varepsilon \text{ or } y < x - \varepsilon
\end{matrix}
Parameters
----------
x : float
First number.
condition : str
Condition to compare with. One of "<", ">", "<=", ">=", "==", "!=".
y : float
Second number.
eps : float, optional
Tolerance. Used for the comparison if provided. If ``None``, then computed as:
.. code-block:: python
eps = atol + rtol * abs(y)
rtol : float, default 1e-04
Relative tolerance.
atol : float, default 1e-08
Absolute tolerance.
Returns
-------
result: bool
Whether the condition is satisfied.
Raises
------
ValueError
If ``condition`` is not one of "<", ">", "<=", ">=", "==", "!=".
References
----------
.. [1] Grosse-Kunstleve, R.W., Sauter, N.K. and Adams, P.D., 2004.
Numerically stable algorithms for the computation of reduced unit cells.
Acta Crystallographica Section A: Foundations of Crystallography,
60(1), pp.1-6.
"""
if eps is None:
eps = atol + rtol * abs(y)
if condition == "<":
return x < y - eps
if condition == ">":
return y < x - eps
if condition == "<=":
return not y < x - eps
if condition == ">=":
return not x < y - eps
if condition == "==":
return not (x < y - eps or y < x - eps)
if condition == "!=":
return x < y - eps or y < x - eps
raise ValueError(f'Condition must be one of "<", ">", "<=", ">=", "==", "!=".')
