NumPy Arrays - The Foundation of Numerical ML

import numpy as np

# CREATING ARRAYS
arr1d = np.array([1, 2, 3, 4, 5])
arr2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])  # 3x3 matrix
print(f"1D shape: {arr1d.shape} | dtype: {arr1d.dtype}")
print(f"2D shape: {arr2d.shape}\n")

# USEFUL CONSTRUCTORS
zeros  = np.zeros((3, 4))          # 3 rows, 4 cols of 0.0
ones   = np.ones((2, 3))           # 2 rows, 3 cols of 1.0
eye    = np.eye(3)                 # 3x3 identity matrix
rng    = np.random.default_rng(42) # reproducible random generator
rand   = rng.normal(0, 1, (5, 3)) # 5x3 standard normal samples
linsp  = np.linspace(0, 1, 10)    # 10 evenly spaced values from 0 to 1

# VECTORIZED OPS -- no loops, much faster
prices = np.array([100, 200, 150, 300, 250])

# Apply discount: 15% off all prices
discounted = prices * 0.85          # element-wise multiplication
above_200  = prices[prices > 200]   # boolean indexing

print(f"Original prices:   {prices}")
print(f"Discounted 15%:    {discounted}")
print(f"Prices above 200:  {above_200}")

# SPEED COMPARISON: loop vs vectorized
large = rng.random(1_000_000)

import time
# Loop approach (slow)
t0 = time.time()
result_loop = [x ** 2 for x in large]
t_loop = time.time() - t0

# NumPy approach (fast)
t0 = time.time()
result_np = large ** 2
t_np = time.time() - t0

print(f"\nLoop: {t_loop*1000:.1f}ms | NumPy: {t_np*1000:.1f}ms | Speedup: {t_loop/t_np:.0f}x")

# BROADCASTING -- apply ops across different shapes
# Each row of X, subtract the mean of that column
X = rng.random((100, 5))   # 100 samples, 5 features
col_means = X.mean(axis=0)  # shape (5,)
X_centered = X - col_means  # broadcasting: (100,5) - (5,) -> (100,5)
print(f"\nAfter centering, column means: {X_centered.mean(axis=0).round(10)}")

# KEY ARRAY OPERATIONS FOR ML
matrix = rng.random((4, 3))
print(f"\nMatrix shape: {matrix.shape}")
print(f"Row sums:     {matrix.sum(axis=1)}")    # sum each row
print(f"Col means:    {matrix.mean(axis=0).round(3)}")  # mean of each column
print(f"Overall mean: {matrix.mean():.4f}")
print(f"Transposed:   {matrix.T.shape}")        # transpose for matrix operations