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Testing for near equality with “allclose”

When the computer calculates a floating point value, there will often be some degree of error in the calculation, because the computer floating point format cannot represent every floating point number exactly. See:

• floating point;
• floating point error.

When we check the results of a floating point calculation, we often want to avoid checking if the returned value is exactly equal to a desired value. Rather, we want to check whether the returned value is close enough, given the usual floating point error. A common idiom in NumPy is to use the np.allclose function, which checks whether two values or two arrays are equal, within a small amount of error:

>>> import numpy as np

>>> np.pi == 3.1415926
False
>>> # pi to 7 decimal places not exactly equal to pi
>>> np.allclose(np.pi, 3.1415926)
True
>>> # pi to 7 dp is "close" to pi
>>> np.allclose([np.pi, 2 * np.pi], [3.1415926, 6.2831852])
True

See the docstring for np.allclose for details of what “close” means.