LightweightStats.jl

A lightweight Julia package providing basic statistical functions with minimal dependencies. LightweightStats.jl serves as a lower-dependency alternative to Statistics.jl, implementing the same algorithms but without pulling in additional dependencies.

Installation

using Pkg
Pkg.add("LightweightStats")

Quick Start

using LightweightStats

# Basic statistics
x = [1, 2, 3, 4, 5]
mean(x)      # 3.0
median(x)    # 3
std(x)       # ~1.58
var(x)       # 2.5

# Correlation and covariance
y = [2, 4, 6, 8, 10]
cor(x, y)    # 1.0
cov(x, y)    # 5.0

# Quantiles
quantile(x, 0.25)  # 2.0
quantile(x, [0.25, 0.5, 0.75])  # [2.0, 3.0, 4.0]

Features

• Zero dependencies: Only requires Julia standard library
• Essential functions: mean, median, std, var, cov, cor, quantile, middle
• Complex number support: Full support for complex-valued statistics
• Dimension-aware: Most functions support operations along specific dimensions
• Type stable: Maintains appropriate type stability
• Compatible API: Matches Statistics.jl function signatures

Why LightweightStats.jl?

This package is ideal when you need:

• Basic statistical operations without heavyweight dependencies
• Minimal package load time
• Reduced dependency tree for deployment
• Core statistical functions in resource-constrained environments

Why Does Statistics.jl Have a LinearAlgebra Dependency?

Statistics.jl requires LinearAlgebra.jl for specific mathematical operations in covariance and correlation computations. Here's exactly where and why:

Complex Number Support

Statistics.jl uses conj() from LinearAlgebra to handle complex conjugates in covariance calculations:

• Line 501-502: _conj() wrapper function that returns conj(x) for complex arrays
• Line 592: Documentation explains the formula uses complex conjugate: (x_i - mean(x)) * conj(y_i - mean(y))

Matrix Operations

LinearAlgebra provides optimized matrix operations used in multivariate statistics:

• Line 520: unscaled_covzm uses x'x (adjoint multiplication) for covariance matrices
• Line 525: adjoint() for matrix-vector products
• Line 528: transpose() for real matrix operations
• Line 532: Mixed operations combining transpose() and adjoint()
• Line 626: Hermitian symmetry enforcement with adjoint()

Import Statement

• Line 10: using LinearAlgebra, SparseArrays imports the required functions

How LightweightStats.jl Handles These Operations Without LinearAlgebra

LightweightStats.jl avoids the LinearAlgebra dependency by implementing its own minimal versions of required functions:

1. Custom Complex Conjugate Implementation

• Internal _conj() function: LightweightStats.jl implements its own conjugate function:

  _conj(x::Real) = x
  _conj(x::Complex) = Complex(real(x), -imag(x))
  _conj(x::AbstractArray{<:Real}) = x
  _conj(x::AbstractArray{<:Complex}) = _conj.(x)

• This provides full complex number support without requiring LinearAlgebra

2. Explicit Loops Instead of Matrix Operations

• Manual iteration: Instead of using optimized matrix products like x'x, LightweightStats.jl uses explicit loops:

  for i in 1:p
      for j in i:p
          s = sum((X[k, i] - means[i]) * _conj(X[k, j] - means[j]) for k in 1:n)
          C[i, j] = corrected ? s / (n - 1) : s / n
          if i != j
              C[j, i] = _conj(C[i, j])
          end
      end
  end

• This avoids needing adjoint() and transpose() but may be slower for large matrices

3. Direct Implementation vs Library Reuse

• Statistics.jl leverages LinearAlgebra's optimized implementations
• LightweightStats.jl reimplements just the minimal required functionality

Trade-offs

• Pros: Zero dependencies, faster load time, simpler deployment, full complex number support
• Cons: Potentially slower for large matrices, less optimized for special matrix types, duplicates some stdlib functionality

By implementing its own _conj() function, LightweightStats.jl achieves complete feature parity with Statistics.jl for basic statistical operations while maintaining zero dependencies.

Documentation

For detailed documentation, see https://SciML.github.io/LightweightStats.jl/stable/

Contributing

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

Citation

If you use LightweightStats.jl in your research, please cite:

@software{LightweightStats.jl,
  author = {Rackauckas, Chris and contributors},
  title = {LightweightStats.jl: Lightweight Statistical Functions for Julia},
  url = {https://github.com/SciML/LightweightStats.jl},
  year = {2024}
}

License

MIT License