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numpy.isclose

# numpy.allclose¶

`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.

NaNs are treated as equal if they are in the same place and if `equal_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.

rtolfloat

The relative tolerance parameter (see Notes).

atolfloat

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.

New in version 1.10.0.

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 that `allclose(a, b)` might be different from `allclose(b, a)` in some rare cases.

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

Examples

```>>> 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
```