Module 4: Array Operations

The true power of NumPy lies in its ability to perform high-speed computations on entire arrays without writing single for loops. This is called Vectorization.

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Lesson 8: Arithmetic Operations

Element-wise Operations

Arithmetic operators (+, -, *, /) applied to arrays perform operations element by element.

Scalar vs Array Operations

• Scalar: Adding a single number to an array applies it to every element.
• Array-Array: Adding two arrays of the same shape adds corresponding elements.

Broadcasting Rules

What if the shapes are different? NumPy uses Broadcasting to "stretch" the smaller array to match the larger one, provided they are compatible.

1. The axes must match exactly, OR
2. One of the axes must be 1.

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Lesson 9: Mathematical Functions

NumPy provides Universal Functions (ufuncs) that operate efficiently on arrays.

Common ufuncs:

• np.sqrt(arr): Square root.
• np.exp(arr): Exponential.
• np.log(arr): Natural logarithm.
• np.sin(arr), np.cos(arr): Trigonometric functions.

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Lesson 10: Aggregations

Aggregations reduce an array to a single value (or a lower-dimensional array).

Essential Aggregates:

• np.sum(), np.mean(), np.median()
• np.min(), np.max()
• np.std(), np.var() (Standard deviation and variance)

Axis-based Operations

You can perform these along specific axes:

• axis=0: Vertical (column-wise).
• axis=1: Horizontal (row-wise).

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Assignment: Statistical Analysis

Given an array of student marks: [78, 92, 45, 88, 56, 91, 74]. Challenge: Find the mean, detect if anyone scored above 90 (using np.max()), and find the index of the highest score using np.argmax().

Key Takeaways

✅ Vectorization replaces slow loops with fast, internal C-code.
✅ Broadcasting allows math between arrays of different (but compatible) sizes.
✅ Use axis parameters to aggregate data specifically by row or column.