3. Vectorization

1. SIMD (Single Instruction, Multiple Data)

Processors are smart. They can add 4 numbers to 4 other numbers in ONE clock cycle. Python loops cannot do this. NumPy can.

Visual Proof

Imagine adding two lists of 1,000,000 numbers.

• Python Loop:
  1. Read x, Read y
  2. Check type(x), Check type(y)
  3. Add
  4. Repeat 1,000,000 times.
• NumPy Vectorization:
  1. "Hey CPU, add these two blocks of memory."
  2. Done.

python
# Slow
[x + 1 for x in huge_list]

# Fast (Vectorized)
huge_array + 1

2. Broadcasting

NumPy matches dimensions automagically. It stretches the smaller array to fit the larger one.

python
Matrix (3x3)  +  Vector (3)  =  Result (3x3)
[1, 2, 3]        [1]            [2, 3, 4]
[4, 5, 6]    +   [1]     ->     [5, 6, 7]
[7, 8, 9]        [1]            [8, 9, 10]