numpy.isclose#
- numpy.isclose(a, b, rtol=1e-05, atol=1e-08, equal_nan=False)[source]#
Returns a boolean array where 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).
- 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:
- yarray_like
Returns a boolean array of where a and b are equal within the given tolerance. If both a and b are scalars, returns a single boolean value.
See also
Notes
New in version 1.7.0.
For finite values, isclose uses the following equation to test whether two floating point values are equivalent.:
absolute(a - b) <= (atol + rtol * absolute(b))
Unlike the built-in
math.isclose
, the above equation is not symmetric in a and b – it assumes b is the reference value – so that isclose(a, b) might be different from isclose(b, a).The default value of atol is not appropriate when the reference value b has magnitude smaller than one. For example, it is unlikely that
a = 1e-9
andb = 2e-9
should be considered “close”, yetisclose(1e-9, 2e-9)
isTrue
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.isclose
is not defined for non-numeric data types.bool
is considered a numeric data-type for this purpose.Examples
>>> np.isclose([1e10,1e-7], [1.00001e10,1e-8]) array([ True, False]) >>> np.isclose([1e10,1e-8], [1.00001e10,1e-9]) array([ True, True]) >>> np.isclose([1e10,1e-8], [1.0001e10,1e-9]) array([False, True]) >>> np.isclose([1.0, np.nan], [1.0, np.nan]) array([ True, False]) >>> np.isclose([1.0, np.nan], [1.0, np.nan], equal_nan=True) array([ True, True]) >>> np.isclose([1e-8, 1e-7], [0.0, 0.0]) array([ True, False]) >>> np.isclose([1e-100, 1e-7], [0.0, 0.0], atol=0.0) array([False, False]) >>> np.isclose([1e-10, 1e-10], [1e-20, 0.0]) array([ True, True]) >>> np.isclose([1e-10, 1e-10], [1e-20, 0.999999e-10], atol=0.0) array([False, True])