Spindalis

A bioinformatics library for numerical modeling, optimisation, data analysis, and simulation written in Rust.

Spindalis provides a collection of numerical methods, polynomial parsing and evaluation tools, derivative computation, and optimisation algorithms for scientific computing and bioinformatics applications.

Table of Contents

• Features
• Installation
• Project Layout
• Contributing
• Stability
• License

Features

• Polynomial parsing and evaluation
• Derivative computation
• Root and Extrema finding with Bisection and Newton–Raphson methods
• Extensible modules for numerical modelling and optimisation

Installation

Add Spindalis as a dependency in your Cargo.toml:

Via Crates.io (Recommended)

To use the latest stable release, add spindalis as a dependency:

[dependencies]
spindalis = "0.X.X" # Always use the latest version available on crates.io

Or, use Cargo:

cargo add spindalis

Via Git Repository (Latest Development Build)

[dependencies]
spindalis = { git = "https://github.com/lignum-vitae/spindalis.git" }

Then run:

cargo build

Polynomials and Matrices

Polynomials

Spindalis makes handling polynomials easier through dedicated functions for parsing, evaluation, and derivation. Core functionality is implemented through structs for the three classes of polynomials: SimplePolynomials, PolynomialsExtended, and PolynomialAst. These structs are unified through their implementation of PolynomialTraits, where they have attached methods to parse, evaluate, integrate, and derivate univariate and multivariate polynomials.

Simple Polynomial can handle univariate polynomials with integer exponents and only addition and subtraction.

Polynomial Extended is an extension of Simple Polynomial that can handle multivariate polynomials. Polynomial extended can also handle fractional, decimal, and negative exponents.

Polynomial Ast is intended to handle all operations for a polynomial. This would include multivariate polynomials, functions such as sin or cos, constants such as pi, fractional exponents, negative exponents, and optimistically also polynomial expansion.

Arr2D

The Arr2D struct provides a convenient way to use a two-dimensional matrix that is a one-dimensional vector under the hood. This allows for efficient memory usage while enabling standard matrix operations.

Arr2D implements a wide range of methods and traits, including:

• Linear Algebra: dot product, inverse, transpose.
• Arithmetic: Implementations of multiplication by matrices, vectors, and scalars and division by scalars
• Manipulation: shape, size, full, reshape, map
• Conversion: from_flat, From, TryFrom
• Utility: new, max, min, is_empty

Project layout

This repository is split into three crates. The tests for spindalis_core and spindalis_macros are located in the tests folder of spindalis.

Crate	Description
spindalis	The main library crate that provides high-level access to all mathematical, polynomial, and utility implementations
spindalis_core	Fundamental data structures and core logic for polynomials, including polynomial structs, parsing, and methods for calculating derivatives and integrals
spindalis_macros	Procedural macros to enhance usability with compile time evaluation of polynomials

Within these crates, the following modules spindalis::<module name> are provided

Module	Description
utils	Utility functions such as Arr2D, Arr2DError, forward substitution, and back substitution
polynomials	Parsing and evaluating simple and extended polynomials
derivatives	Differentiating simple and extended polynomials
integrals	Integrating simple and extended polynomials
solvers	Solving equations and differential equations, including root-finding, extrema-finding, and ODE solvers
eigen	Algorithms to solve eigenvalue and eigenvector problems
decomposition	Decomposition algorithms including LU decomposition and LU decomposition with partial pivoting
regressors	Linear and non-linear regression, including least-squares, Gaussian, and polynomial regression
reduction	Linear and non-linear dimensionality reduction algorithms, including PCA

Running Examples

Working examples of the available algorithms as well as a full list of available algorithms can be found in the examples/ directory.

Run any example with the following command:

cargo run --example <example_name>

Do not include .rs when running examples.

Contributing

We welcome contributions! Please read our:

• Code of Conduct
• Contribution Guidelines

Stability

This project is in the alpha stage. APIs may change without warning until version 1.0.0.

License

This project is licensed under the MIT License - see the LICENSE file for details.