ferreus_rbf_rs

Fast global radial basis function (RBF) interpolation in Rust, with Python bindings.

Overview

Radial basis function (RBF) interpolation is a flexible, mesh‑free approach for approximating scattered data, but direct solvers require O(N²) memory and O(N³) work, which becomes impractical beyond modest problem sizes.

This workspace provides a scalable alternative by combining:

• Domain decomposition preconditioning for the global RBF system, and
• A black box fast multipole method (BBFMM) evaluator for fast matrix–vector products,

reducing the overall complexity to roughly O(N log N) and enabling global interpolation on millions of points in up to three dimensions.

Crates and packages

• ferreus_rbf – Fast, memory‑efficient global RBF interpolation in 1D, 2D and 3D, using domain decomposition and FGMRES with an FMM‑based evaluator.
• ferreus_bbfmm – Parallel black box fast multipole method (BBFMM) implementation for smooth kernels in 1D, 2D and 3D, supporting adaptive trees and multiple RHS.
• ferreus_rbf_utils – Shared kernels, tree utilities and helper functions used by ferreus_rbf, ferreus_bbfmm and the Python bindings.
• py_ferreus_rbf – Python bindings for ferreus_rbf, providing a high‑level API for fast global RBF interpolation from Python.
• py_ferreus_bbfmm – Python bindings for ferreus_bbfmm, exposing fast kernel matrix–vector products and related FMM functionality to Python.

For more detailed API documentation and examples, see the individual crate and package READMEs, the Rustdoc pages, and the docs/ and examples/ directories in each sub‑project.

Documentation

• Rust:
  • ferreus_rbf - https://docs.rs/ferreus_rbf/latest/ferreus_rbf/
  • ferreus_bbfmm - https://docs.rs/ferreus_bbfmm/latest/ferreus_bbfmm/
• Python:
  • ferreus_rbf - https://graphic-goose.github.io/ferreus_rbf_rs/ferreus_rbf/
  • ferreus_bbfmm - https://graphic-goose.github.io/ferreus_rbf_rs/ferreus_bbfmm/

Installation

Rust

Add the desired crate to your Cargo.toml, for example:

[dependencies]
ferreus_rbf = "0.1"

or

[dependencies]
ferreus_bbfmm = "0.1"

Refer to crates.io for the latest published versions.

Python

For the Python bindings, install from PyPI:

pip install ferreus_rbf
pip install ferreus_bbfmm

Then, in Python:

import ferreus_rbf
import ferreus_bbfmm

See the docs/ and examples/ folders in py_ferreus_rbf and py_ferreus_bbfmm for more detailed usage.

Attribution and licensing

This project was developed while the author was working at Maptek and has been approved for open‑source distribution under the terms of the MIT license.

Unless otherwise stated, the following copyright applies:

Copyright (c) 2025 Maptek Pty Ltd.
All rights reserved.

This copyright applies to all files in this repository, whether or not an individual file contains an explicit notice.

The code is released under the MIT License – see LICENSE for details.