NumPy: Universal Functions (ufunc)

Last updated: 2026-08-26

1. What You'll Learn

• ❶ What is a ufunc — universal function
• ❷ ufunc attributes: nin, nout, ntypes, types
• ❸ ufunc methods: reduce, accumulate, outer, reduceat
• ❹ Creating custom ufuncs with np.frompyfunc

2. Key Concepts

(1) What Is a ufunc

A ufunc (universal function) is a C-level function that operates element-wise on ndarrays. All arithmetic operators call ufuncs under the hood.

import numpy as np

# Operators are ufuncs
print(np.add)        # ufunc 'add'
print(np.multiply)   # ufunc 'multiply'
print(np.sin)        # ufunc 'sin'

# ufunc attributes
print(np.add.nin)    # 2 (number of inputs)
print(np.add.nout)   # 1 (number of outputs)
print(np.add.ntypes)  # number of supported type combinations

(2) ufunc Methods

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

# reduce: apply repeatedly to reduce to single value
print(np.add.reduce(a))     # 15 (sum)
print(np.multiply.reduce(a))  # 120 (product)

# accumulate: running result
print(np.add.accumulate(a))  # [1 3 6 10 15]

# outer: apply to all pairs
print(np.multiply.outer([1, 2, 3], [10, 20, 30]))
# [[10 20 30]
#  [20 40 60]
#  [30 60 90]]

> **Output:** Run NumPy 2.x in your local Python environment to see the ndarray output. The Piston server does not have NumPy pre-installed — install it locally (`pip install numpy`) and compare. Actual values may vary by NumPy version and random seed.

▶ Example: ufunc attributes (Difficulty ⭐)

import numpy as np

print("add:", np.add)
print("multiply:", np.multiply)
print("sin:", np.sin)

print(f"np.add.nin: {np.add.nin}")
print(f"np.add.nout: {np.add.nout}")
print(f"np.add.ntypes: {np.add.ntypes}")

Output:

TEXT 📖 Display only

📋 Copy

add: ufunc 'add'
multiply: ufunc 'multiply'
sin: ufunc 'sin'
np.add.nin: 2
np.add.nout: 1
np.add.ntypes: 22

▶ Example: ufunc reduce and accumulate (Difficulty ⭐⭐)

import numpy as np

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

# reduce: apply repeatedly to get a single value
print("add.reduce:", np.add.reduce(a))
print("multiply.reduce:", np.multiply.reduce(a))

# accumulate: running result
print("add.accumulate:", np.add.accumulate(a))
print("multiply.accumulate:", np.multiply.accumulate(a))

Output:

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add.reduce: 15
multiply.reduce: 120
add.accumulate: [ 1  3  6 10 15]
multiply.accumulate: [  1   2   6  24 120]

▶ Example: ufunc outer (Difficulty ⭐⭐)

import numpy as np

# Outer product: multiply every pair
x = np.array([1, 2, 3])
y = np.array([10, 20, 30, 40])
print("outer:\n", np.multiply.outer(x, y))

# Comparison outer
a = np.array([1, 3, 5])
b = np.array([2, 4, 6])
print("greater.outer:\n", np.greater.outer(a, b))

Output:

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outer:
 [[ 10  20  30  40]
 [ 20  40  60  80]
 [ 30  60  90 120]]
greater.outer:
 [[False False False]
 [ True False False]
 [ True  True False]]

❓ FAQ

📖 Summary

• ufuncs are C-level element-wise functions: np.add, np.multiply, np.sin, etc.
• Attributes: nin, nout, ntypes, types describe the ufunc interface
• Methods: reduce (single value), accumulate (running), outer (all pairs), reduceat (segments)
• ufuncs are the engine behind NumPy's vectorization and broadcasting

📝 Exercises

1. Beginner (Difficulty ⭐): List the attributes of np.add — nin, nout, ntypes, types. Explain what each means.

2. Intermediate (Difficulty ⭐⭐): Use np.add.reduce to sum an array, np.add.accumulate to compute running sum, and np.multiply.outer to create a multiplication table.

3. Advanced (Difficulty ⭐⭐⭐): Use np.frompyfunc to create a custom ufunc that returns the larger of two numbers. Apply it to two arrays and compare with np.maximum.

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