Source code for pymor.tools.floatcmp

# This file is part of the pyMOR project (http://www.pymor.org).
# Copyright 2013-2020 pyMOR developers and contributors. All rights reserved.
# License: BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)

import operator
import warnings
from functools import partial

import numpy as np

from pymor.core.defaults import defaults


[docs]@defaults('rtol', 'atol') def float_cmp(x, y, rtol=1e-14, atol=1e-14): """Compare x and y component-wise for almost equality. For scalars we define almost equality as :: float_cmp(x,y) <=> |x - y| <= atol + |y|*rtol .. note:: Numpy's :meth:`~numpy.allclose` method uses the same definition but treats arrays containing infinities as close if the infinities are at the same places and all other entries are close. In our definition, arrays containing infinities can never be close which seems more appropriate in most cases. Parameters ---------- x, y |NumPy arrays| to be compared. Have to be broadcastable to the same shape. rtol The relative tolerance. atol The absolute tolerance. """ return np.abs(x - y) <= atol + np.abs(y) * rtol
[docs]def float_cmp_all(x, y, rtol=None, atol=None): """Compare x and y for almost equality. Returns `True` if all components of `x` are almost equal to the corresponding components of `y`. See :meth:`float_cmp`. """ return np.all(float_cmp(x, y, rtol, atol))
[docs]def bounded(lower, upper, x, rtol=None, atol=None): """Check if x is strictly in bounds (lower, upper) or float_compares equal to lower or upper Parameters ---------- lower Lower bound upper Upper bound x value to check rtol relative tolerance for float_cmp atol absolute tolerance for float_cmp """ return (lower < x < upper) or float_cmp(x, lower, rtol, atol) or float_cmp(x, upper, rtol, atol)
[docs]@defaults('rtol', 'atol') def compare_with_tolerance(x, y, comparison_op, rtol=1e-14, atol=1e-14): """ 'One-sided' Comparison x and y component-wise with given comparison op. For scalars we define almost equality as :: compare_with_tolerance(x,y) <=> op(x - y, atol + y*rtol) Parameters ---------- x, y |NumPy arrays| to be compared. Have to be broadcastable to the same shape. comparison_op binary operator object, see |operator| module. rtol The relative tolerance. atol The absolute tolerance. """ if comparison_op is operator.eq: warnings.warn('Use float_cmp for float equality tests') return comparison_op(x-y, atol + y * rtol)
[docs]def almost_less(x, y, rtol=None, atol=None): return compare_with_tolerance(x, y, operator.le, rtol, atol)