Numpy isclose() function with examples

This post covers numpy.isclose(), the standard function for comparing floating-point values in Python.

Why not use ==?

• Floating-Point Inaccuracy: Computers cannot represent most decimal fractions exactly in binary, leading to small precision errors. A direct comparison with == will often fail when numbers are mathematically equal but have tiny representational differences.
• The Solution: numpy.isclose() circumvents this by checking if two values lie within a defined tolerance of each other, providing a much more practical and reliable comparison.

Core Uses of numpy.isclose()

• Scalar Comparison: Safely check if two individual floating-point numbers are effectively equal.
• Array Comparison: Perform an element-wise comparison between two NumPy arrays. This is crucial for verifying results in numerical computations where visual inspection is impractical and unreliable.

Let us started on learning how to use Numpy’s isclose() function. Let us load numpy and check Numpy’s version.

import numpy as np
np.<strong>version</strong>
1.24.0

Numpy isclose() function to check if numbers or arrays are equal

Understanding the numpy.isclose() Syntax

The basic syntax for the numpy.isclose() function provides fine-grained control over the comparison.

Function Signature:

numpy.isclose(a, b, rtol=1e-05, atol=1e-08, equal_nan=False)

Parameters Explained:

• a, b: The input arrays or scalars to be compared.
• rtol (relative tolerance): This is a relative tolerance that scales with the magnitude of the input b. The default 1e-05 is useful for most cases. It becomes more important than atol for large numbers.
• atol (absolute tolerance): This is a minimum, absolute tolerance. It’s a fixed value that is most useful for comparisons where one of the numbers is close to zero. The default is 1e-08.
• equal_nan: If set to True, the function will consider NaN (Not a Number) values in the same positions of the arrays as equal. By default, it is False.

The Underlying Formula

The function returns True for a pair of values a and b if their difference satisfies the following mathematical equation:

This formula effectively checks if the difference is within a margin of error that combines a fixed value (atol) and a percentage of the input value (rtol).

Numpy isclose() function: Check if two numbers are the same

Int he first example of Numpy’s isclose() fucntion, we check if two numbers are close enough. Let us say we have two numbers a and b

a = 1
b = 1.1

If we use Numpy’s isclose() to find if they are close enough, we will get False as result. This is because the relative difference between the two numbers is bigger than the default tolerance 1e-05.

np.isclose(a,b)

False

Now let us consider another two numbers as shown below

a = 1
b = 1.00001

Here we can see that the difference is equal to the relative tolerance level. Therefore, we would get True when we use np.close() function.

np.isclose(a,b)

True

We can change the tolerance level to force two numbers close when needed. In the example below we changed the relative tolerance level from default 1e-05 to 0.1. Now the two numbers

a = 1
b = 1.1

are close enough under the new tolerance level. And we will get True as result.

np.isclose(a, b, rtol=0.1)

True

Numpy isclose() function: Check if two arrays are the same

Now lets us consider two Numpy arrays and check if their elements are close to each other. We can use isclose as follows:

a = np.array([1, 2, 3])
b = np.array([1.01, 2.01, 3.01])

result = np.isclose(a, b)

When comparing arrays, Numpy’s isclose function returns an array of Boolean values, with each element indicating whether the corresponding element in a is close to the corresponding element in b.

In this case, we get boolean array containing three False as the relative difference between every element is bigger than the default tolerance value.

print(result)

[False False False]

Now let us consider the following two arrays and use Numpy’s np.close() with the default tolerance level.

a = np.array([1, 2, 3])
b = np.array([1.0000001, 2.00001, 3.01])

result = np.isclose(a, b)

print(result)

[ True  True False]

We got True for the first and second element as the difference is smaller than or equal to rtol value. And for the third element we got False is the difference is bigger than the default tolerance.

Another close relative of Numpy’s isclose() function is allclose() function. See this post to learn about how to use allcose() function.