# ================================== LICENSE ===================================
# Wulfric - Cell, Atoms, K-path, visualization.
# Copyright (C) 2023 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.
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# You should have received a copy of the GNU General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
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# ================================ END LICENSE =================================
__all__ = ["compare_with_tolerance"]
[docs]
def compare_with_tolerance(x, condition, y, eps=None, rtol=1e-5, atol=1e-8):
r"""
Compares two numbers with given accuracy.
The formal definition 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 :math:`10^{-5}`
Relative tolerance.
atol : float, default :math:`10^{-8}`
Absolute tolerance.
Returns
-------
result: bool
Whether the ``condition`` is satisfied within given tolerance.
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.
Examples
--------
.. doctest::
>>> import wulfric
>>> wulfric.compare_with_tolerance(1, "==", 1.0000001, eps=1e-6)
True
>>> wulfric.compare_with_tolerance(1, "==", 1.0000001, eps=1e-8)
False
"""
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'Expected one of "<", ">", "<=", ">=", "==", "!=" as condition, got "{condition}".'
)
