➕ NumPy ufunc Simple Arithmetic – Fast Element-wise Operations

🧲 Introduction – Why Use Arithmetic ufuncs in NumPy?

In scientific computing, arithmetic operations are among the most frequent and performance-critical tasks. NumPy’s universal functions (ufuncs) provide fast, element-wise arithmetic that is vectorized, broadcast-aware, and far more efficient than Python loops.

These ufuncs handle:

• Addition, subtraction, multiplication, division
• Exponentiation and modulo
• Absolute value and negation

🎯 By the end of this guide, you’ll:

• Perform element-wise arithmetic with ufuncs
• Use functions like add(), subtract(), multiply(), divide()
• Understand broadcasting and output control
• Avoid common errors with mixed shapes and types

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➕ Step 1: Basic Arithmetic with ufuncs

import numpy as np

a = np.array([10, 20, 30])
b = np.array([1, 2, 3])

print(np.add(a, b))        # [11 22 33]
print(np.subtract(a, b))   # [ 9 18 27]
print(np.multiply(a, b))   # [10 40 90]
print(np.divide(a, b))     # [10. 10. 10.]

🔍 Explanation:

Each function performs an element-wise operation between corresponding elements in a and b.

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🔢 Step 2: Exponentiation and Modulo

print(np.power(a, b))   # [10^1 20^2 30^3] = [10 400 27000]
print(np.mod(a, b))     # [10%1 20%2 30%3] = [0 0 0]

✅ Use np.power() for exponentiation and np.mod() for remainders.

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➗ Step 3: Floor Division and Reciprocal

print(np.floor_divide(a, b))  # [10 10 10]
print(np.reciprocal(b))       # [1. 0.5 0.333...]

📌 floor_divide() rounds down after division
📌 reciprocal() = 1/x for each element (works best for floats)

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📏 Step 4: Broadcasting with Scalars

print(np.add(a, 5))        # [15 25 35]
print(np.multiply(b, 10))  # [10 20 30]

🔍 Explanation:

• NumPy broadcasts scalar values across arrays
  ✅ Makes scalar-array operations easy and fast

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📦 Step 5: Using out= to Save Results

result = np.empty(3)
np.subtract(a, b, out=result)
print(result)  # [ 9. 18. 27.]

🔍 Explanation:

• out= writes the result directly into an existing array
  ✅ Saves memory and avoids creating new arrays

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🧠 Step 6: Arithmetic with Mismatched Shapes (Broadcasting)

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

print(np.add(x, y))

👉 Output:

[[11 21 31]
 [12 22 32]
 [13 23 33]]

🔍 Explanation:

• x is 3×1, y is 1×3 → Broadcasted to 3×3 matrix
  ✅ Powerful feature for matrix algebra and batch operations

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🧾 ufunc Function vs Operator

Operation	Operator Syntax	ufunc Syntax
Addition	a + b	np.add(a, b)
Subtraction	a - b	np.subtract(a, b)
Multiplication	a * b	np.multiply(a, b)
Division	a / b	np.divide(a, b)
Power	a ** b	np.power(a, b)
Modulo	a % b	np.mod(a, b)

✅ Both styles are valid. ufunc syntax allows extra control (like out= and where= arguments).

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📌 Summary – Recap & Next Steps

NumPy’s arithmetic ufuncs are core to all numerical computations. Whether you’re manipulating vectors, scaling arrays, or performing matrix operations, these functions give you fast, reliable, and readable code.

🔍 Key Takeaways:

• Use add(), subtract(), multiply(), divide(), mod(), power() for element-wise operations
• Supports broadcasting with scalars and arrays of different shapes
• Use out= to save results in-place
• Ufuncs are faster and safer than loops

⚙️ Real-world relevance: Used in data transformations, simulations, ML preprocessing, and scientific modeling.

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❓ FAQs – NumPy Arithmetic ufuncs

❓ Are NumPy ufuncs faster than using loops?
✅ Yes. Ufuncs are C-backed, optimized for performance.

❓ Can I use ufuncs with multi-dimensional arrays?
✅ Absolutely. Ufuncs operate element-wise, regardless of array dimension.

❓ What happens if array shapes don’t match?
✅ NumPy tries to broadcast them. If not compatible, it raises a ValueError.

❓ Do these ufuncs support out= for memory efficiency?
✅ Yes. You can pass an array to store the result using out=....

❓ Are ufuncs more flexible than operators (+, *)?
✅ Yes. ufuncs offer extra arguments like out, dtype, and where.

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