Numerics

Numerics is a free and open-source numerical computing library for .NET developed by the U.S. Army Corps of Engineers Risk Management Center (USACE-RMC). It provides methods and algorithms for probability distributions, statistical analysis, numerical methods, optimization, machine learning, and Bayesian MCMC sampling, with a focus on hydrological and risk assessment applications.

Supported Frameworks

Framework	Version
.NET	10.0
.NET Framework	4.8.1

The .NET 10 build runs on Windows and Linux. Version 2.3.0 targets net10.0 and net481; applications on .NET 8 or .NET 9 can stay on RMC.Numerics 2.2.0.

Install via NuGet:

dotnet add package RMC.Numerics --version 2.3.0

Or search for RMC.Numerics in the NuGet Package Manager.

Python

pynumerics ships the same Numerics.dll with typed Python wrappers over every Numerics area. It requires CPython 3.11 to 3.14 on Linux or Windows and the .NET 10 runtime:

pip install pynumerics

What's New in 2.3.0

• Hosking-Wallis regional frequency analysis: discordancy, heterogeneity and goodness-of-fit measures, and regional growth curves.
• Machine learning: Gaussian process regression, kriging, elastic net regression, and principal component analysis.
• Optimization: L-BFGS-B, CMA-ES, dynamically dimensioned search, Pareto fronts, dynamic programming, and knapsack solvers.
• Numerical methods: a QL eigensolver, an opt-in QUADPACK QAGS integrator, multi-source shortest paths, column statistics, and compensated sums.
• Accuracy fixes in the Student-t distribution, the incomplete beta and inverse incomplete gamma functions, the Archimedean copula densities, and the GEV, Gamma and Pearson Type III L-moments.
• The pynumerics Python package, published to PyPI with each release.

See the v2.3.0 release notes for the full list, including breaking changes and the results that move.

Documentation

User Guide and API Documentation - Comprehensive documentation with code examples and mathematical explanations.

Section	Topics
Mathematics	Adaptive one- and two-dimensional integration, differentiation, optimization, root finding, linear algebra, ODE solvers, special functions, Fourier methods
Data	Interpolation, linear regression, time series analysis
Statistics	Descriptive and weighted statistics, goodness-of-fit metrics, hypothesis tests, global sensitivity analysis
Distributions	43 univariate distributions, parameter estimation, uncertainty analysis, copulas, multivariate distributions, regional frequency analysis
Functions	Uncertain univariate function forms, composition, posterior ensembles, link functions
Machine Learning	GLM, elastic net, Gaussian process regression, kriging, decision trees, random forests, KNN, naive Bayes, k-means, GMM, PCA
Sampling	MCMC (RWMH, ARWMH, DE-MCz, DE-MCzs, HMC, NUTS, Gibbs), random generation, scrambled quasi-random sequences, convergence diagnostics
References	Consolidated bibliography

Prerequisites

• .NET 10 runtime on Windows or Linux, or .NET Framework 4.8.1 on Windows. Install the .NET SDK if you don't already have it.
  • The Microsoft .NET SDK is available on the App Portal for Corps users.

Support

USACE-RMC is committed to maintaining and supporting the library with regular updates, bug fixes, and enhancements.

The repository includes a unit testing library with over 4,000 tests that also serve as usage examples for the classes and methods in the library, and the pynumerics package adds over 5,000 Python tests.

Contributing

Contributions are welcome. Please see CONTRIBUTING.md for guidelines on bug reports, feature requests, and pull requests.

AI Disclosure

Frontier generative AI models and coding agents are used to assist with software development, documentation, testing, and verification workflows. Project maintainers remain responsible for reviewing contributions, validating scientific methods and results, and deciding what is accepted or released.

License

See LICENSE for details.