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Numerical accuracy#

For the full reference see numerical.

Import#

>>> # Exact import
>>> from radtools.numerical import compare_numerically
>>> # Recommended import
>>> from radtools import compare_numerically

Comparison#

Compares two numbers within a given tolerance.

Tolerance for the comparison is given as:

\[\varepsilon = atol + rtol \cdot y\]

By default \(atol\) and \(rtol\) are equal to crystal.REL_TOL and crystal.ABS_TOL respectively. You can pass exact values for eps.

The conditions are translated as (source [1]):

Condition

Numerical condition

\(x < y\)

\(x < y - \varepsilon\)

\(x > y\)

\(y < x - \varepsilon\)

\(x \le y\)

not \((y < x - \varepsilon)\)

\(x \ge y\)

not \((x < y - \varepsilon)\)

\(x = y\)

not \((x < y - \varepsilon\) or \(y < x - \varepsilon)\)

\(x \ne y\)

\(x < y - \varepsilon\) or \(y < x - \varepsilon\)

>>> compare_numerically(1.0, "==", 1.0 + 1e-10)
True
>>> compare_numerically(1.0, "==", 1.0 + 2e-4)
False
>>> compare_numerically(1.0, "!=", 1.0 + 2e-4, eps=1e-3)
False

References#