# numpy.allclose() in Python

`numpy.allclose() `function is used to find if two arrays are element-wise equal within a tolerance. The tolerance values are positive, typically very small numbers. The relative difference (rtol * abs(arr2)) and the absolute difference atol are added together to compare against the absolute difference between arr1 and arr2. If either array contains one or more NaNs, False is returned. Infs are treated as equal if they are in the same place and of the same sign in both arrays.

If the following equation is element-wise True, then allclose returns True.
`absolute(arr1 - arr2) <= (atol + rtol * absolute(arr2))`
As, The above equation is not symmetric in arr1 and arr2, So, allclose(arr1, arr2) might be different from allclose(arr2, arr1) in some rare cases.

Syntax : numpy.allclose(arr1, arr2, rtol, atol, equal_nan=False)

Parameters :
arr1 : [array_like] Input 1st array.
arr2 : [array_like] Input 2nd array.
rtol : [float] The relative tolerance parameter.
atol : [float] The absolute tolerance parameter.
equal_nan : [bool] Whether to compare NaN’s as equal. If True, NaN’s in arr1 will be considered equal to NaN’s in arr2 in the output array.

Return : [ bool] Returns True if the two arrays are equal within the given tolerance, otherwise it returns False.

Code #1 :

 `# Python program explaining ` `# allclose() function ` ` `  `import` `numpy as geek ` ` `  `# input arrays ` `in_arr1 ``=` `geek.array([``5e5``, ``1e``-``7``, ``4.000004e6``]) ` `print` `(``"1st Input array : "``, in_arr1)  ` ` `  `in_arr2 ``=` `geek.array([``5.00001e5``, ``1e``-``7``, ``4e6``]) ` `print` `(``"2nd Input array : "``, in_arr2)  ` ` `  `# setting the absolute and relative tolerance ` `rtol ``=` `1e``-``05` `atol ``=` `1e``-``08` ` `  `res ``=` `geek.allclose(in_arr1, in_arr2, rtol, atol) ` `print` `(``"Are the two arrays are equal within the tolerance: \t"``, res) `

Output:

```1st Input array :  [  5.00000000e+05   1.00000000e-07   4.00000400e+06]
2nd Input array :  [  5.00001000e+05   1.00000000e-07   4.00000000e+06]
Are the two arrays are equal within the tolerance:      True
```

Code #2 :

 `# Python program explaining ` `# allclose() function ` `  `  `import` `numpy as geek ` ` `  `# input arrays ` `in_arr1 ``=` `geek.array([``5e5``, ``1e``-``7``, ``4.000004e6``]) ` `print` `(``"1st Input array : "``, in_arr1)  ` ` `  `in_arr2 ``=` `geek.array([``5.00001e5``, ``1e``-``7``, ``4e6``]) ` `print` `(``"2nd Input array : "``, in_arr2)  ` ` `  `# setting the absolute and relative tolerance ` `rtol ``=` `1e``-``06` `atol ``=` `1e``-``09` ` `  `res ``=` `geek.allclose(in_arr1, in_arr2, rtol, atol) ` `print` `(``"Are the two arrays are equal within the tolerance: \t"``, res) `

Output:

```1st Input array :  [5000000.0, 1e-07, 40000004.0]
2nd Input array :  [5000001.0, 1e-07, 40000000.0]
Are the two arrays are equal within the tolerance:      True
```

Code #3 :

 `# Python program explaining ` `# allclose() function ` `  `  `import` `numpy as geek ` ` `  `# input arrays ` `in_arr1 ``=` `geek.array([``5e5``, ``1e``-``7``, geek.nan]) ` `print` `(``"1st Input array : "``, in_arr1)  ` ` `  `in_arr2 ``=` `geek.array([``5e5``, ``1e``-``7``, geek.nan]) ` `print` `(``"2nd Input array : "``, in_arr2)  ` ` `  `# setting the absolute and relative tolerance ` `rtol ``=` `1e``-``06` `atol ``=` `1e``-``09` ` `  `res ``=` `geek.allclose(in_arr1, in_arr2, rtol, atol) ` `print` `(``"Are the two arrays are equal within the tolerance: \t"``, res) `

Output:

```1st Input array :  [500000.0, 1e-07, nan]
2nd Input array :  [500000.0, 1e-07, nan]
Are the two arrays are equal within the tolerance:      False
```

Code #4 :

 `# Python program explaining ` `# allclose() function ` `  `  `import` `numpy as geek ` ` `  `# input arrays ` `in_arr1 ``=` `geek.array([``5e5``, ``1e``-``7``, geek.nan]) ` `print` `(``"1st Input array : "``, in_arr1)  ` ` `  `in_arr2 ``=` `geek.array([``5e5``, ``1e``-``7``, geek.nan]) ` `print` `(``"2nd Input array : "``, in_arr2)  ` ` `  `# setting the absolute and relative tolerance ` `rtol ``=` `1e``-``06` `atol ``=` `1e``-``09` ` `  `res ``=` `geek.allclose(in_arr1, in_arr2, rtol, atol,  ` `                                ``equal_nan ``=` `True``) ` ` `  `print` `(``"Are the two arrays are equal within the tolerance: \t"``, res) `

Output:

```1st Input array :  [500000.0, 1e-07, nan]
2nd Input array :  [500000.0, 1e-07, nan]
Are the two arrays are equal within the tolerance:      True
```

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