NumPy Universal Functions (ufuncs)

What are ufuncs?

A ufunc (universal function) is a function that performs element-wise operations on data in ndarrays. Think of them as fast, vectorized wrappers around simple functions that would otherwise take one scalar in and return one scalar out.

Examples:

• np.sqrt, np.exp, np.log
• np.sin, np.cos
• np.maximum, np.minimum

They are faster and cleaner than Python loops.

Example: sqrt

sqrt

import numpy as np
 
arr = np.array([1, 4, 9, 16])
print(np.sqrt(arr))

Unary vs binary ufuncs

diagram Unary vs binary ufuncs mermaid

  flowchart LR
  A["Unary ufunc
one array in"] --> B["np.sqrt, np.exp, np.log
-> transformed array"]
  C["Binary ufunc
two arrays in"] --> D["np.add, np.maximum
-> one combined array"]
  E["Rare: multi-output ufunc"] --> F["np.modf
-> (fractional, integer) arrays"]

Unary ufuncs transform one array; binary ufuncs combine two arrays element-wise into one result.

np.sqrt and np.exp are unary ufuncs — they take one array. Functions like np.add or np.maximum are binary — they take two arrays and return one result.

Common math ufuncs

math

import numpy as np
 
x = np.array([1.0, 2.0, 3.0])
print(np.exp(x))
print(np.log(x))
print(np.log10(x))

Trigonometric ufuncs

trig

import numpy as np
 
angles = np.array([0, np.pi/2, np.pi])
print(np.sin(angles))
print(np.cos(angles))

Comparison ufuncs

max-min

import numpy as np
 
a = np.array([1, 10, 3])
b = np.array([2, 5, 4])
 
print(np.maximum(a, b))
print(np.minimum(a, b))

A ufunc that returns two arrays

Most ufuncs return one array, but a few — like np.modf — return more than one. It splits a float array into fractional and whole-number parts:

modf

import numpy as np
 
arr = np.array([4.5, -8.1, 2.25])
remainder, whole_part = np.modf(arr)
print("remainder:", remainder)
print("whole:", whole_part)

Writing results into an existing array

Ufuncs accept an optional out argument to write results in place instead of allocating a new array — handy for saving memory on large arrays.

out

import numpy as np
 
arr = np.array([1.0, 2.0, 3.0])
result = np.zeros_like(arr)
np.add(arr, 1, out=result)
print(result)

Working with NaN values

Some ufuncs have NaN-safe variants.

nan

import numpy as np
 
arr = np.array([1.0, np.nan, 3.0])
print(np.nanmean(arr))
print(np.nansum(arr))

From the book

NumPy keeps adding new ufuncs, so McKinney recommends checking the official NumPy documentation for the full, current list rather than memorizing every one. Focus on recognizing the pattern — element-wise, vectorized, often with an out= option — and look up the specific function name when you need it.

Ufuncs + broadcasting

Ufuncs naturally work with broadcasting.

broadcast

import numpy as np
 
mat = np.array([[1, 2, 3], [4, 5, 6]])
print(np.sqrt(mat))

Next

Continue to: Stacking and Splitting Arrays to combine and break arrays along different axes.

🧪 Try It Yourself

Exercise 1 – Apply a Unary ufunc

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Exercise 2 – A Binary ufunc

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Exercise 3 – NaN-safe Aggregation

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