🛠️ NumPy ufunc Create Function – Define Your Own Vectorized ufuncs

🧲 Introduction – Why Create Custom ufuncs in NumPy?

While NumPy provides many built-in universal functions (ufuncs) like add, subtract, and sqrt, sometimes you need custom behavior—such as a domain-specific formula or a multi-step transformation.

Using np.frompyfunc() or np.vectorize(), you can create your own ufuncs that behave just like NumPy’s built-ins: they work on entire arrays, support broadcasting, and improve code readability.

🎯 By the end of this guide, you’ll:

• Understand how to build custom NumPy ufuncs
• Use frompyfunc() and vectorize() for vectorized function creation
• Handle multi-input and multi-output functions
• Know when to use (and not use) custom ufuncs

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🔬 Step 1: Create ufunc Using np.frompyfunc()

import numpy as np

def custom_add(x, y):
    return x + y

add_ufunc = np.frompyfunc(custom_add, 2, 1)

a = np.array([1, 2, 3])
b = np.array([4, 5, 6])
print(add_ufunc(a, b))

🔍 Explanation:

• 2 → number of input arguments
• 1 → number of outputs
• Works element-wise on a and b
  ✅ Output:

[5 7 9]

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📏 Step 2: Create ufunc with np.vectorize()

def custom_power(x):
    return x ** 3 + 2

vec_power = np.vectorize(custom_power)

arr = np.array([1, 2, 3])
print(vec_power(arr))

🔍 Explanation:

• Converts regular function to act element-wise on NumPy arrays
• Automatically infers number of inputs/outputs
  ✅ Output:

[  3 10 29]

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🔀 Step 3: Multi-Input Custom ufunc Example

def weighted_sum(x, y, w):
    return x * w + y * (1 - w)

weighted = np.vectorize(weighted_sum)

x = np.array([10, 20, 30])
y = np.array([1, 2, 3])
w = 0.75

print(weighted(x, y, w))

✅ Output:

[7.75 15.5 23.25]

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🧮 Step 4: Multi-Output Custom ufuncs

def div_mod(a, b):
    return divmod(a, b)

multi_output = np.vectorize(div_mod)

a = np.array([10, 20, 30])
b = np.array([3, 7, 5])

quotients, remainders = multi_output(a, b)
print("Quotients:", quotients)
print("Remainders:", remainders)

✅ Output:

Quotients: [3 2 6]
Remainders: [1 6 0]

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⚠️ Performance Note

Method	Pros	Cons
np.frompyfunc()	True ufunc, returns object	Slower, lacks type info
np.vectorize()	Simple, returns native dtype	Still uses Python loops under the hood

📌 Important: These methods provide convenience, not performance gains over vectorized NumPy functions. Use NumPy built-ins or numba for speed-critical tasks.

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🧠 When Should You Create Custom ufuncs?

✅ Use when:

• No built-in NumPy function fits your logic
• You want to apply element-wise operations cleanly
• You need broadcasting behavior on custom logic

❌ Avoid when:

• You need high-performance processing
• You can refactor your logic using existing NumPy functions

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📌 Summary – Recap & Next Steps

Creating ufuncs in NumPy allows you to extend vectorization to your own functions, keeping code clean, readable, and broadcast-compatible. While not a performance boost, they offer tremendous convenience for element-wise logic.

🔍 Key Takeaways:

• Use frompyfunc(func, nin, nout) for explicit ufuncs
• Use vectorize(func) for quick vectorization with native types
• Supports multi-input and multi-output operations
• Best for readability and simplicity, not speed

⚙️ Real-world relevance: Used in data preprocessing, simulation modeling, and custom math transformations in NumPy pipelines.

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❓ FAQs – NumPy Custom ufuncs

❓ What’s the difference between frompyfunc() and vectorize()?
✅ frompyfunc() returns object arrays; vectorize() preserves native data types.

❓ Are custom ufuncs faster than Python loops?
❌ No. They use Python under the hood. For speed, use NumPy built-ins or numba.

❓ Can I return multiple outputs from a ufunc?
✅ Yes, especially with np.vectorize(), which unpacks into multiple arrays.

❓ Do custom ufuncs support broadcasting?
✅ Yes, they follow NumPy’s broadcasting rules.

❓ Is vectorize() the same as JIT compilation?
❌ No. vectorize() improves syntax, not performance. Use numba for JIT.

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