numra

Composable numerical methods for Rust — differential equations, optimization, sensitivity analysis, uncertainty quantification, linear algebra, and more in one workspace.

numra is the umbrella crate of the Numra workspace: twenty native-Rust crates covering ordinary, stochastic, delay, fractional, integro-, and partial differential equations, plus forward sensitivity analysis, uncertainty quantification, optimization, automatic differentiation, linear algebra, statistics, quadrature, interpolation, special functions, FFT, signal processing, and curve fitting — under one unified facade with shared Scalar and Vector abstractions and a single error model. Dense linear algebra builds on faer; the rest is native Rust with no FFI to C or Fortran.

Install

[dependencies]
numra = "0.1"

To depend on a single subsystem instead of the whole workspace, use the corresponding member crate directly (e.g. numra-ode = "0.1").

Quick start

use numra::ode::{DoPri5, OdeProblem, Solver, SolverOptions};

let problem = OdeProblem::new(
    |_t, y: &[f64], dydt: &mut [f64]| {
        dydt[0] = -y[0];
    },
    0.0,
    2.0,
    vec![1.0],
);
let opts = SolverOptions::default().rtol(1e-8);
let result = DoPri5::solve(&problem, 0.0, 2.0, &[1.0], &opts).expect("solve");

let y_end = result.y_final().expect("trajectory")[0];
assert!((y_end - (-2.0_f64).exp()).abs() < 1e-5);

Composability

Numra is designed so that subsystems compose without glue: ODE trajectories flow into interpolation, interpolation into quadrature, autodiff Jacobians into optimization, optimization into curve fitting, PDE state vectors into statistics — all sharing one NumraError type and the same Scalar/Vector traits. End-to-end workflows are verified in numra/tests/interop_workflows.rs:

Workflow	Test
ODE → cubic spline → quadrature	`workflow_ode_interp_integrate`
ODE → FFT → signal processing → peak detection	`workflow_ode_fft_signal_peaks`
Parameter estimation → sensitivity → uncertainty	`workflow_param_est_sensitivity_uncertainty`
Autodiff → optimization → curve fitting	`workflow_autodiff_optim_fit`
PDE method-of-lines → statistics	`workflow_pde_statistics`
Sampling → Monte Carlo ODE	`workflow_stats_monte_carlo_ode`

cargo test -p numra --test interop_workflows

Narrative patterns and worked examples live in the book chapter Composing solvers.

Subsystems

Subsystem	Module path	Member crate
Core (Scalar, Vector, Signal, errors, uncertainty)	`numra::{scalar, vector, signal, error, uncertainty}`	`numra-core`
ODE / DAE	`numra::ode`	`numra-ode`
SDE	`numra::sde`	`numra-sde`
DDE	`numra::dde`	`numra-dde`
FDE (fractional)	`numra::fde`	`numra-fde`
IDE (Volterra)	`numra::ide`	`numra-ide`
PDE (Method of Lines)	`numra::pde`	`numra-pde`
SPDE	`numra::spde`	`numra-spde`
Linear algebra	`numra::linalg`	`numra-linalg`
Nonlinear solvers	`numra::nonlinear`	`numra-nonlinear`
Optimization	`numra::optim`	`numra-optim`
Optimal control / parameter estimation	`numra::ocp`	`numra-ocp`
Quadrature	`numra::integrate`	`numra-integrate`
Interpolation	`numra::interp`	`numra-interp`
Special functions	`numra::special`	`numra-special`
FFT and spectral analysis	`numra::fft`	`numra-fft`
Statistics	`numra::stats`	`numra-stats`
Curve fitting	`numra::fit`	`numra-fit`
Automatic differentiation	`numra::autodiff`	`numra-autodiff`
Digital signal processing	`numra::dsp`	`numra-signal`

Examples

Fifteen runnable examples ship with the crate; four span the breadth:

cargo run --example lorenz                  # ODE + sensitivity + uncertainty
cargo run --example gbm_monte_carlo         # SDE Monte Carlo (geometric Brownian motion)
cargo run --example heat_equation           # 1D PDE via Method of Lines
cargo run --example robertson_sensitivity   # Stiff ODE + forward sensitivity

Full list: see [[example]] entries in numra/Cargo.toml or the examples gallery.

Documentation

Book: https://book.numra-rs.org/ — narrative chapters per subsystem with executable examples
Website: https://numra-rs.org/
API reference: https://docs.rs/numra
Source: https://github.com/moussaoutlook/numra-rs
Changelog: https://github.com/moussaoutlook/numra-rs/blob/main/CHANGELOG.md

License

Numra is licensed under the Numra Academic & Research License (Non-Commercial).

Academic and research use: free as in freedom.
Commercial use: requires a separate license. Contact contact@spectralautomata.com to discuss terms.

See LICENSE for the full text.

numra 0.1.4