Matrix Arithmetic in Noir

noir-matrix is a matrix arithmetic library for Noir.

Features

• Matrix addition, subtraction, and scalar multiplication
• Matrix multiplication
• Transpose operation
• Trace of square matrices (sum of diagonal elements)
• Dot product for vectors

Example Usage

use matrix::{Matrix, trace, dot_product};

// Define a 3x2 matrix (3 rows and 2 columns)
let b = Matrix::<3, 2, Field> {
    data: [[1,2],[3,4],[5,6]], // an array for each tow
};

// Scalar multiplication
let scaled = a.scalar_mult(2);

// Define a 2x2 matrix
let b = Matrix::<2, 2, Field> {
    data: [[1, 2], [3, 4]],
};

// Trace of a square matrix
let tr = trace(b); // Result: 5 (1 + 4)

// Dot product of two vectors
let u = [1, 2, 3];
let v = [4, 5, 6];
let dot = dot_product(u, v); // Result: 32

Benchmarks

Addition, subtraction, scalar multiplication have equal costs:

• 50x50 matrix: 2.516 gates
• 100x100 matrix: 10.016 gates

Dot product for two vectors of 100 entries: 100 gates. Trace of a 100x100 matrix: 50 gates.

Matrix multiplication:

• 50x30 x 30x60: 90.016 gates
• 50x50: 125.016 gates
• 100x100: 1.000.016 gates
• 100x120 x 120x110: 1.320.016 gates

Rerun benchmarks in folder benchmarks.

• Nargo 1.0.0-beta.0
• bb 0.63.0