numpy.allclose — NumPy v2.2 Manual (original) (raw)

numpy.allclose(a, b, rtol=1e-05, atol=1e-08, equal_nan=False)[source]#

Returns True if two arrays are element-wise equal within a tolerance.

The tolerance values are positive, typically very small numbers. The relative difference (rtol * abs(b)) and the absolute difference_atol_ are added together to compare against the absolute difference between a and b.

Warning

The default atol is not appropriate for comparing numbers with magnitudes much smaller than one (see Notes).

NaNs are treated as equal if they are in the same place and ifequal_nan=True. Infs are treated as equal if they are in the same place and of the same sign in both arrays.

Parameters:

a, barray_like

Input arrays to compare.

rtolarray_like

The relative tolerance parameter (see Notes).

atolarray_like

The absolute tolerance parameter (see Notes).

equal_nanbool

Whether to compare NaN’s as equal. If True, NaN’s in a will be considered equal to NaN’s in b in the output array.

Returns:

allclosebool

Returns True if the two arrays are equal within the given tolerance; False otherwise.

Notes

If the following equation is element-wise True, then allclose returns True.:

absolute(a - b) <= (atol + rtol * absolute(b))

The above equation is not symmetric in a and b, so thatallclose(a, b) might be different from allclose(b, a) in some rare cases.

The default value of atol is not appropriate when the reference value_b_ has magnitude smaller than one. For example, it is unlikely thata = 1e-9 and b = 2e-9 should be considered “close”, yetallclose(1e-9, 2e-9) is True with default settings. Be sure to select atol for the use case at hand, especially for defining the threshold below which a non-zero value in a will be considered “close” to a very small or zero value in b.

The comparison of a and b uses standard broadcasting, which means that a and b need not have the same shape in order forallclose(a, b) to evaluate to True. The same is true forequal but not array_equal.

allclose is not defined for non-numeric data types.bool is considered a numeric data-type for this purpose.

Examples

import numpy as np np.allclose([1e10,1e-7], [1.00001e10,1e-8]) False

np.allclose([1e10,1e-8], [1.00001e10,1e-9]) True

np.allclose([1e10,1e-8], [1.0001e10,1e-9]) False

np.allclose([1.0, np.nan], [1.0, np.nan]) False

np.allclose([1.0, np.nan], [1.0, np.nan], equal_nan=True) True