## Pytest approximately equal scalars and arrays

Pytest cleanly handles so many continuous integration issues that it is very worthwhile in terms of effort to setup tests and improving test coverage to incrementally upgrade from obsolete `nose` and legacy `unittest` modules. One of those many areas is in the constant need to compare equality of floating point numbers. In general computer representations of floating point numbers have finite precision, and so in general the fundamental arithmetic assumptions learned in elementary school about real numbers are broken, including associativity. A practical solution to this problem is to compare numbers (scalars or arrays) to within an absolute and relative tolerance. Widely known functions exist to compare “equality” of floating point numbers in Python and Fortran real/assert.F90 among other numerical languages.

`pytest.approx` provides a syntactically clean approach that may be more intuitive and readable for CI applications. It works with scalars and arrays of all sorts including the ubiquitous `numpy.ndarray`.

## Example

This example shows how to replace `numpy.testing.assert_allclose()` with `pytest.approx()`:

``````import numpy as np
from pytest import approx

def test_mynums():
x = np.array([2.00000000001, 1.99999999999])

assert x == approx(2.)``````

Whereas with Numpy, the last line would have been `np.testing.assert_allclose(x, 2.)`. I find the Pytest syntax and appearance to be more readable.

## NaN

NaN is an unrepresentable, undefined quantity as results from invalid computations like:

• ∞ / ∞
• 0 / 0

NaN are also useful as sentinel values to indicate a problem with a computation for example. Python sentinel values include `NaN` and `None`. In Julia, performance is approximately the same for `nan` vs. `nothing` sentinel values.

The option `pytest.approx(nan_ok=True)` allows one or more NaN’s in the test array.

## Tolerance

Absolute and relative tolerance are important considerations for CI, particularly across OS and computer types, where order of operation and numerical CPU/GPU/APU/etc. tolerances and low level math routines (BLAS, AVX, etc.) differ. Especially (perhaps obviously) for single precision arithmetic vs. double precision arithmetic, tolerances will be larger. The `pytest.approx()` default tolerances are:

• `rel=1e-6`
• `abs=1e-12`

Absolute tolerance shouldn’t be 0 to avoid unexpected effects near 0.

Depending on the parameter, `rel=1e-4` may be more appropriate for CI tests that need to work on a variety of systems.