SimpleNorm.jl

A lightweight implementation of norm functions without LinearAlgebra.jl, BLAS, or LAPACK dependencies.

Features

This package provides pure Julia implementations of common norm functions:

Vector norms

• norm(x) or norm(x, 2) - Euclidean norm (default)
• norm(x, 1) - 1-norm (sum of absolute values)
• norm(x, Inf) - Infinity norm (maximum absolute value)
• norm(x, -Inf) - Minimum absolute value
• norm(x, p) - p-norm for any p ≥ 1
• norm(x, 0) - Count of non-zero elements

Matrix norms

• norm(A, 1) - Maximum absolute column sum
• norm(A, Inf) - Maximum absolute row sum
• norm(A, "fro") or norm(A, :fro) - Frobenius norm

Note: The spectral norm (norm(A, 2)) is not implemented, as it requires singular value decomposition.

Installation

using Pkg
Pkg.add("SimpleNorm")

Usage

using SimpleNorm

# Vector norms
v = [3.0, 4.0]
norm(v)       # 5.0 (Euclidean norm)
norm(v, 1)    # 7.0 (1-norm)
norm(v, Inf)  # 4.0 (infinity norm)

# Matrix norms
A = [1 2 3; 4 5 6]
norm(A, 1)     # 9.0 (max column sum)
norm(A, Inf)   # 15.0 (max row sum)
norm(A, "fro") # 9.539392014169456 (Frobenius norm)

Why SimpleNorm.jl?

This package is useful when you need norm computations but want to avoid:

• Binary dependencies (BLAS/LAPACK)
• Heavy LinearAlgebra.jl dependency
• Deployment issues in constrained environments

All implementations are in pure Julia with careful attention to numerical stability, including overflow/underflow prevention in the 2-norm calculation.