waynewbishop/quiver

Features

• Vector Operations

Element-wise arithmetic (+, -, , /) Dot product, magnitude, normalization, distance Angle calculations and vector projections * Matrix operations (multiplication, transpose, inverse, determinant)

• Similarity and Distance

Cosine similarity (single and batch) Euclidean distance Top-K selection with labels Duplicate detection and cluster analysis

• Statistics

Central tendency (mean, median, min, max, argmin, argmax) Dispersion (variance, standard deviation, quartiles, percentiles) Cumulative operations (sum, product) Outlier detection (z-score method)

• Array Generation

Generate arrays (zeros, ones, linspace, arange, random uniform/normal) Special matrices (identity, diagonal) Reshape and flatten (1D ↔ 2D) Broadcasting (scalar, vector, custom)

• Data Preparation

Train/test split with reproducible seeded shuffling Stratified splitting preserving class proportions Feature scaling (min-max normalization, fit-then-transform) Panel (named-column data structure for aligned splitting) Boolean masking and conditional selection Class distribution, imbalance ratio, and oversampling for imbalanced data

• Data Visualization

Trend lines via linear regression predict Elbow curves for K-Means cluster selection Confusion matrix heatmap data Softmax probability bars * Downsampling, stacked series, correlation matrices

• Machine Learning Models

Gaussian Naive Bayes (classification) K-Nearest Neighbors (classification with Euclidean and cosine distance) Linear Regression with single-feature convenience predict K-Means Clustering with elbow method and multi-seed best fit Consistent fit/predict API across all models Full transparency — inspect coefficients, centroids, priors, means, variances * All models conform to Codable — train once, encode to JSON, decode on any platform

• Evaluation Metrics

Confusion matrix with accuracy, precision, recall, F1 score Per-class classification report with macro and weighted averages R², MSE, RMSE for regression All metrics available programmatically as typed values

• Activation Functions

Softmax (multi-class probability distribution) Sigmoid (binary classification threshold)

• Text and Embeddings

Tokenization for NLP workflows Word embedding lookups with vocabulary filtering

Quick Start

Vector Operations

import Quiver

let v = [3.0, 4.0]
v.magnitude          // 5.0
v.normalized         // [0.6, 0.8]

let force = [5.0, 3.0, 2.0]
let displacement = [10.0, 0.0, 0.0]
let work = force.dot(displacement)  // 50.0

let product1 = [4.2, 7.8, 3.1, 9.5]
let product2 = [3.8, 8.2, 2.9, 9.7]
product1.cosineOfAngle(with: product2)  // 0.999 (very similar)

Train a Model

import Quiver

// Training data: square footage → price
let features: [[Double]] = [[1000], [1500], [2000], [2500], [3000]]
let targets = [150000.0, 200000.0, 260000.0, 310000.0, 370000.0]

// Fit, predict, evaluate — three lines
let model = try LinearRegression.fit(features: features, targets: targets)
let predictions = model.predict(features)
let r2 = predictions.rSquared(actual: targets)  // 0.99+

// Generate a trend line for charting
let trendX = Array.linspace(start: 500.0, end: 3500.0, count: 50)
let trendY = model.predict(trendX)  // parallel arrays ready for Swift Charts

Statistics and Data Analysis

import Quiver

let sales = [45.0, 52.0, 48.0, 61.0, 55.0, 58.0, 49.0, 67.0, 72.0, 69.0]

sales.mean()    // 57.6
sales.median()  // 56.5
sales.std()     // 8.9

let smoothed = sales.rollingMean(window: 3)
let outliers = sales.outlierMask(threshold: 1.2).trueIndices

Design Philosophy

• Swift-first: Extends standard Swift arrays — no custom container types, no conversion overhead
• Transparent ML: Every model exposes its learned parameters — inspect coefficients, centroids, and class statistics
• Educational: Clear implementations that map directly to mathematical concepts
• Zero dependencies: Pure Swift, no external frameworks required

When to Use Quiver

• Education — Teach vector math, statistics, and ML concepts with readable, inspectable code
• Machine learning — Train and evaluate classification, regression, and clustering models in pure Swift with full algorithm transparency
• On-device intelligence — Privacy-first ML on iOS, watchOS, and visionOS without cloud dependencies or external runtimes
• Data visualization — Prepare chart-ready arrays (trend lines, elbow curves, heatmaps) for Swift Charts
• Server-side Swift — Run numerical computing and ML pipelines on Linux and Vapor

Cookbook

38 interactive recipes for learning vector math, statistics, and ML models in Swift. Each recipe is a single .swift file optimized for the Xcode #Playground macro — clone the repo, open in Xcode, and start experimenting.

Documentation

Full API documentation at waynewbishop.github.io/quiver, including:

• Vector operations and linear algebra primer
• Statistical function reference
• Matrix operations and transformations
• Data preparation and visualization guides
• Machine learning model guides (Naive Bayes, K-Nearest Neighbors, Linear Regression, K-Means)

Quiver is the companion numerical computing package for Swift Algorithms & Data Structures.

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

License

Quiver is available under the Apache License, Version 2.0. See the LICENSE file for more info.

Questions

Have a question? Feel free to contact me on LinkedIn.

Package Metadata

Repository: waynewbishop/quiver

Default branch: main

README: README.md