pandu / gauss

v0.1.0 2026-09-26 15:02 UTC

Requires

• php: ^8.2

Requires (Dev)

• phpunit/phpunit: ^11.0

MIT

• Pandu

• php
• optimization
• statistics
• mathematics
• probability
• linear-algebra
• time-series
• numerical-analysis

Published on Packagist.org on 2026-09-26 15:05 UTC

README

A precise and composable mathematical toolkit for PHP, designed to build reliable mathematical models from reusable mathematical primitives.

Gauss combines exact decimal arithmetic, algebraic structures, probability primitives, linear algebra, and statistical operations in one coherent library. The intent is not to hide mathematics behind a framework-like abstraction, but to make the mathematical operation explicit in the source code itself.

Features

• Decimal-backed numeric core using Number
• Explicit arithmetic operations such as add(), sub(), mul(), div(), and compare()
• Algebraic primitives such as polynomials and monomials
• Linear algebra with vectors, matrices, and system solving
• Probability and distribution primitives for statistical modelling
• Support for numerical and optimization workflows
• Composable building blocks suitable for custom domain models

Installation

composer require pandu/gauss

Then load the Composer autoloader:

<?php

require_once __DIR__ . '/vendor/autoload.php';

use Gauss\Number\Number;

Quick Start

<?php

require_once __DIR__ . '/vendor/autoload.php';

use Gauss\Number\Number;

$x = Number::of('10.5');
$y = Number::of('2.5');

$result = $x
    ->mul($y)
    ->add(Number::of('1'));

echo $result->value();

This demonstrates the core Gauss pattern: a precise numeric primitive, explicit mathematics, and a result that can be composed into larger expressions.

Why Gauss?

Precision

The numeric foundation is built around Number, which keeps arithmetic in a decimal-string based system instead of depending solely on native PHP float behavior. This makes it safer for precise operations that need controlled numeric representation.

Explicit mathematics

Operations are not hidden behind magic wrappers. Source code reads like mathematics:

$result = $a
    ->mul($b)
    ->sub($c)
    ->div($d);

This keeps the computational intent visible.

Composability

Gauss provides reusable building blocks that can be assembled into larger models:

Number
  ↓
Probability
  ↓
Distribution
  ↓
Vector / Matrix
  ↓
Numerical algorithm
  ↓
Mathematical model

Model building

Gauss is best understood as a toolkit for constructing mathematical models, not merely as a formula collection. You can combine values, distributions, vectors, and matrices into domain-specific workflows without needing a built-in abstraction for every possible model.

Examples

Example 1 — Basic numerical computation

<?php

require_once __DIR__ . '/vendor/autoload.php';

use Gauss\Number\Number;

$a = Number::of('12.5');
$b = Number::of('3.5');

$result = $a
    ->mul($b)
    ->sub(Number::of('2'));

echo $result->value();

Example 2 — Probability model

<?php

require_once __DIR__ . '/vendor/autoload.php';

use Gauss\Distribution\Poisson;
use Gauss\Number\Number;

$lambda = Number::of('2.5');
$poisson = Poisson::of($lambda);

$pmf = $poisson->pmf(3);
echo $pmf->value()->value();

Example 3 — Complex model

The repository includes a full end-to-end HSMM-style example in the usage documentation:

• docs/usage/examples/hsmm.md

It demonstrates how Gauss primitives can be assembled into a larger probabilistic model rather than being limited to isolated formulas.

Documentation

Getting started

• docs/usage/introduction.md
• docs/usage/installation.md
• docs/usage/composition.md

Usage by module

• docs/usage/number.md
• docs/usage/algebra.md
• docs/usage/linear.md
• docs/usage/geometry.md
• docs/usage/statistics.md
• docs/usage/probability.md
• docs/usage/distribution.md
• docs/usage/numerical.md
• docs/usage/optimization.md
• docs/usage/time-series.md
• docs/usage/discrete.md

Examples

• docs/usage/examples/basic-statistics.md
• docs/usage/examples/probability-model.md
• docs/usage/examples/hsmm.md

Technical documentation

• docs/technical/architecture.md
• docs/technical/number.md
• docs/technical/precision.md
• docs/technical/type-system.md
• docs/technical/composability.md
• docs/technical/module-dependencies.md
• docs/technical/mathematical-conventions.md
• docs/technical/numerical-methods.md
• docs/technical/validation.md
• docs/technical/design-decisions.md

Modules

Gauss organizes functionality around mathematical concerns rather than a single monolithic layer:

• Number — exact decimal arithmetic and numeric representation
• Algebra — polynomials and symbolic expression building blocks
• Linear — vectors, matrices, and solvers
• Probability — probability values and event-based semantics
• Distribution — discrete and continuous distributions
• Statistics — summary and relational statistical operations
• Numerical — techniques for approximation and optimization
• Optimization — objective-driven search and constraints
• TimeSeries — observation and time-dependent models
• Discrete — combinatorics and discrete structures

Design Philosophy

Gauss follows a small-primitives approach:

1. Use precise numeric primitives.
2. Keep operations explicit and composable.
3. Build larger mathematical structures from smaller units.
4. Treat model building as a composition problem, not a framework problem.

This is why there is no requirement for a single giant Hsmm abstraction before a user can build an HSMM-style model from Number, Probability, Distribution, Vector, and Matrix building blocks.

Requirements

• PHP 8.2+
• Composer

Testing

composer test

License

MIT