# 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.

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` and `b = 2e-9` should be considered “close”, yet `isclose(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.

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

Examples

```>>> import numpy as np
>>> 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])
```