NumPy ufunc Logs

Logarithms as NumPy ufuncs

Logarithms show up constantly in data work: measuring information content, scaling wide-ranging data, or analyzing algorithmic growth. NumPy exposes them as ufuncs so they apply to an entire array at once, without a Python-level loop.

Natural, Base-2, and Base-10 Logs

np.log() computes the natural logarithm (base e). np.log2() computes the base-2 logarithm, common in computer science and information theory. np.log10() computes the base-10 logarithm, useful for orders of magnitude such as decibels or the Richter scale.

import numpy as np

values = np.array([1, 2, 8, 100, np.e])

print(np.log(values))     # natural log (base e)
print(np.log2(values))    # base-2 log
print(np.log10(values))   # base-10 log

Building a Custom Base Logarithm

NumPy has no built-in ufunc for an arbitrary base, but np.frompyfunc(function, nin, nout) can turn any plain Python function into a NumPy ufunc that broadcasts over arrays element-wise, complete with automatic support for arrays of any shape.

import numpy as np
import math

def log_base(x, base):
    return math.log(x, base)

# frompyfunc(function, number_of_inputs, number_of_outputs)
custom_log = np.frompyfunc(log_base, 2, 1)

values = np.array([8, 27, 625])
bases = np.array([2, 3, 5])

result = custom_log(values, bases)
print(result)
# [3.0 3.0 4.0]

• frompyfunc always returns an array with dtype=object, even when every result happens to be numeric.
• Because it calls back into Python for every element, it is much slower than native ufuncs like np.log for large arrays.
• You specify the number of inputs (nin) and outputs (nout) explicitly, so frompyfunc can wrap functions that take more than one argument, like a value and a base.
• It is best used for prototyping a custom operation before writing a faster fully-vectorized version.

import numpy as np

def log_any_base(x, base):
    # Change-of-base formula: log_b(x) = ln(x) / ln(b)
    return np.log(x) / np.log(base)

values = np.array([8, 27, 625, 1024])
print(log_any_base(values, 2))
print(log_any_base(values, 5))