NumPy - Logarithmic Universal Function (ufunc)

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Logarithmic Universal Function (ufunc)

A logarithmic universal function (ufunc) in NumPy is a function that applies the logarithm operation to each element in an array. This means it computes the logarithm of every individual value in the array, either using the natural logarithm (base e) or a different base such as base-2 logarithm or base-10 logarithm.

NumPy provides several logarithmic ufuncs, such as numpy.log(), numpy.log2(), numpy.log10().

NumPy Natural Logarithm

The numpy.log() function is used to compute the natural logarithm (base-e) of each element in an array. This function is commonly used in mathematical computations involving exponential growth or decay.

Example

In the following example, we use the numpy.log() function to calculate the natural logarithm of each element in an array −

import numpy as np

# Define an array
a = np.array([1, 2, 3, 4, 5])

# Compute natural logarithm
result = np.log(a)

print(result)

Following is the output obtained −

[0.         0.69314718 1.09861229 1.38629436 1.60943791]

NumPy Base-10 Logarithm

The numpy.log10() function is used to compute the base-10 logarithm of each element in an array. This function is useful in scientific fields such as chemistry and physics, where logarithmic scales are often used.

Example

In the following example, we use the numpy.log10() function to calculate the base-10 logarithm of each element in an array −

import numpy as np

# Define an array
a = np.array([1, 10, 100, 1000, 10000])

# Compute base-10 logarithm
result = np.log10(a)

print(result)

This will produce the following result −

[0. 1. 2. 3. 4.]

NumPy Base-2 Logarithm

The numpy.log2() function is used to compute the base-2 logarithm of each element in an array. This function is often used in computer science and information theory.

Example

In the following example, we use the numpy.log2() function to calculate the base-2 logarithm of each element in an array −

import numpy as np

# Define an array
a = np.array([1, 2, 4, 8, 16])

# Compute base-2 logarithm
result = np.log2(a)

print(result)

Following is the output of the above code −

[0. 1. 2. 3. 4.]

NumPy Logarithm with Any Base

While NumPy provides specific functions for base-e, base-10, and base-2 logarithms, you can compute logarithms with any base by using the numpy.log() function in combination with the change of base formula.

Example

In the following example, we calculate the base-3 logarithm of each element in an array using the change of base formula −

import numpy as np

# Define an array
a = np.array([1, 3, 9, 27, 81])

# Compute base-3 logarithm
result = np.log(a) / np.log(3)

print(result)

The result produced is as follows −

[0. 1. 2. 3. 4.]

NumPy Logarithm of 1 plus Input

The numpy.log1p() function is used to compute the natural logarithm of 1 plus the input array elements. This function provides more accurate results for small input values compared to directly using numpy.log(1 + x) function.

Example

In the following example, we use the numpy.log1p() function to calculate the natural logarithm of 1 plus each element in an array −

import numpy as np

# Define an array
a = np.array([0.1, 0.2, 0.3, 0.4, 0.5])

# Compute natural logarithm of 1 plus the input array elements
result = np.log1p(a)

print(result)

Following is the output obtained −

[0.09531018 0.18232156 0.26236426 0.33647224 0.40546511]