Vector Math

This chapter demonstrates Trueno's vector math capabilities using the quickstart and performance_demo examples.

Quick Start

Run the quickstart example to see all core vector operations:

cargo run --example quickstart

Basic Operations

use trueno::Vector;

// Create vectors
let a = Vector::from_slice(&[1.0, 2.0, 3.0, 4.0]);
let b = Vector::from_slice(&[5.0, 6.0, 7.0, 8.0]);

// Element-wise operations
let sum = a.add(&b)?;      // [6.0, 8.0, 10.0, 12.0]
let prod = a.mul(&b)?;     // [5.0, 12.0, 21.0, 32.0]

// Reductions
let dot = a.dot(&b)?;      // 70.0
let norm = a.norm_l2()?;   // 5.477...

// Statistical operations
let mean = a.mean()?;      // 2.5
let variance = a.variance()?;

Backend Selection

Trueno automatically selects the best available backend:

use trueno::{Vector, Backend};

// Auto backend (recommended)
let v = Vector::from_slice(&data);

// Force specific backend
let scalar = Vector::from_slice_with_backend(&data, Backend::Scalar);

Performance Comparison

Run the performance demo to see SIMD speedups:

cargo run --release --example performance_demo

Expected Results

Understanding the Results

Compute-intensive operations (dot product, sum, max) show significant speedups because SIMD can process 8 f32 values simultaneously.

Memory-bound operations (add, mul) show modest speedups because performance is limited by memory bandwidth, not computation.

ML Similarity Operations

Run the similarity example:

cargo run --example ml_similarity

Cosine Similarity

use trueno::Vector;

let query = Vector::from_slice(&[0.5, 0.8, 0.2]);
let document = Vector::from_slice(&[0.6, 0.7, 0.3]);

// Compute cosine similarity
let norm_q = query.norm_l2()?;
let norm_d = document.norm_l2()?;
let dot = query.dot(&document)?;
let similarity = dot / (norm_q * norm_d);

k-NN Classification

// Compute Euclidean distances
let diff = query.sub(&sample)?;
let dist_sq = diff.dot(&diff)?;
let distance = dist_sq.sqrt();

Layer Normalization

use trueno::Vector;

let input = Vector::from_slice(&[1.0, 2.0, 3.0, 4.0, 5.0]);

// Compute mean and variance
let mean = input.mean()?;
let centered = input.sub_scalar(mean)?;
let var = centered.dot(&centered)? / input.len() as f32;
let std = (var + 1e-5).sqrt();

// Normalize
let normalized = centered.mul_scalar(1.0 / std)?;

See Also

• Performance Demo - Detailed benchmarks
• ML Similarity - ML-specific operations
• Backend Selection - How backends are chosen