NumPy Vectorization, Boolean Masks & Statistical Aggregations

NumPy powers modern numerical computing in Python. This guide covers the 2D Axis mental model , NaN-safe aggregations , Boolean masking , and statistical reductions .

1. The 2D Axis Mental Model One of the most common points of confusion in NumPy and Pandas is the axis parameter in 2D arrays:

import numpy as np

matrix = np.array([ [10, 20, 30], [40, 50, 60] ]) # Shape: (2, 3) -> 2 rows, 3 columns

Axis Setting Direction of Collapse Code Example Result None (Default) Entire array into a single scalar matrix.sum() 210 axis=0 Down columns (collapses rows; results in 1 value per column) matrix.sum(axis=0) [50, 70, 90] (length 3) axis=1 Across rows (collapses columns; results in 1 value per row) matrix.sum(axis=1) [60, 150] (length 2)

2. Handling NaN Values with NaN-Safe Aggregations In NumPy, standard aggregations propagate np.nan values. If a single element is NaN, the result is NaN:

data = np.array([10.0, 20.0, np.nan, 40.0])

print(np.mean(data)) # Output: nan (Standard aggregation fails) print(np.nanmean(data)) # Output: 23.333 (Safely ignores NaN) print(np.nansum(data)) # Output: 70.0 print(np.nanstd(data)) # Output: 12.472

3. Boolean Masking & Conditional Filtering Boolean indexing allows you to filter elements in a NumPy array without writing a loop:

scores = np.array([55, 82, 90, 45, 78, 95, 60])

# 1. Create a boolean mask passing_mask = scores >= 70 # Output: [False, True, True, False, True, True, False]

# 2. Extract matching elements passing_scores = scores[passing_mask] # Output: [82, 90, 78, 95]

# 3. Compound conditions (use & for AND, | for OR, ~ for NOT): honors = scores[(scores >= 80) & (scores <= 95)] # Output: [82, 90, 95]

# 4. Conditional replacement with np.where(condition, if_true, if_false) grade_labels = np.where(scores >= 70, "PASS", "FAIL") # Output: ['FAIL', 'PASS', 'PASS', 'FAIL', 'PASS', 'PASS', 'FAIL']

4. Statistical Operations: Percentiles & Cumulative Sums

sales = np.array([100, 150, 200, 250, 300])

# Cumulative Revenue over time: cum_sales = np.cumsum(sales) # Output: [100, 250, 450, 700, 1000]

# Percentiles / Quartiles: q25, q50, q75 = np.percentile(sales, [25, 50, 75]) print(f"25th: {q25}, Median: {q50}, 75th: {q75}")

# Finding index positions of min and max: arr = np.array([10, 45, 3, 99, 24]) max_idx = np.argmax(arr) # 3 (points to 99) min_idx = np.argmin(arr) # 2 (points to 3)