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Crate numeris

Crate numeris 

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§numeris

Pure-Rust numerical algorithms library, no-std compatible. Similar in scope to SciPy, suitable for embedded targets (no heap allocation, no FPU assumptions).

§Quick start

use numeris::{Matrix, Vector};

// Solve a linear system Ax = b
let a = Matrix::new([
    [2.0_f64, 1.0, -1.0],
    [-3.0, -1.0, 2.0],
    [-2.0, 1.0, 2.0],
]);
let b = Vector::from_array([8.0, -11.0, -3.0]);
let x = a.solve(&b).unwrap(); // x = [2, 3, -1]

§Modules

  • matrix — Fixed-size Matrix<T, M, N> with const-generic dimensions. Stack-allocated [[T; N]; M] row-major storage. Includes arithmetic, indexing, norms, block operations, and iteration. Vector<T, N> and ColumnVector<T, N> are type aliases for 1-row and 1-column matrices.

  • dynmatrix — Heap-allocated DynMatrix<T> with runtime dimensions (requires alloc feature, included with std). Vec<T> row-major storage. Implements MatrixRef / MatrixMut, so all linalg free functions work automatically. DynVector<T> newtype for single-index vector access. Includes DynLu, DynCholesky, DynQr wrapper structs.

  • linalg — LU (partial pivoting), Cholesky (A = LL^H), QR (Householder), SVD (Householder bidiagonalization + Golub-Kahan implicit-shift QR), symmetric/Hermitian eigendecomposition (Householder tridiagonalization + implicit QR with Wilkinson shift), and real Schur decomposition (Hessenberg reduction + Francis double-shift QR). Each provides solve(), inverse(), det(), eigenvalues(), etc. Free functions operate on &mut impl MatrixMut<T> for in-place use; wrapper structs offer a higher-level API. Convenience methods on both Matrix and DynMatrix.

  • ode — Fixed-step RK4 and 7 adaptive Runge-Kutta solvers (RKF45, RKTS54, RKV65, RKV87, RKV98, RKV98NoInterp, RKV98Efficient). PI step-size controller with dense output / interpolation. Requires ode feature.

  • optim — Optimization: scalar root finding (optim::brent, optim::newton_1d), BFGS quasi-Newton minimization (optim::minimize_bfgs), Gauss-Newton (optim::least_squares_gn) and Levenberg-Marquardt (optim::least_squares_lm) nonlinear least squares. Finite-difference Jacobian and gradient utilities. Requires optim feature.

  • control — Digital IIR filters: control::Biquad second-order section and control::BiquadCascade for cascaded filters. Design functions for Butterworth and Chebyshev Type I lowpass/highpass. No complex feature dependency. Requires control feature.

  • quaternion — Unit quaternion for 3D rotations. Scalar-first [w, x, y, z]. Construct from axis-angle, Euler angles, or rotation matrices. Supports Hamilton product, vector rotation, SLERP, and conversion back to matrices.

  • traits — Element trait hierarchy:

    • Scalar — all matrix elements (Copy + PartialEq + Debug + Zero + One + Num)
    • FloatScalar — real floats (Scalar + Float), used by quaternions
    • LinalgScalar — real floats and complex numbers, used by decompositions and norms
    • MatrixRef / MatrixMut — generic read/write access for algorithms

§Complex matrices

Enable the complex feature to use decompositions with Complex<f32> / Complex<f64>. Cholesky generalizes to Hermitian (A = LL^H), QR uses complex Householder reflections, and norms return real values. Zero overhead for real-only code paths.

§Cargo features

FeatureDefaultDescription
stdyesImplies alloc. Hardware FPU via system libm
allocvia stdDynMatrix / DynVector (heap-allocated, runtime-sized)
odeyesODE integration (RK4, adaptive solvers)
optimnoOptimization (root finding, BFGS, Gauss-Newton, LM)
controlnoDigital IIR filters (Butterworth, Chebyshev Type I)
libmbaselinePure-Rust software float fallback
complexnoComplex<f32> / Complex<f64> support via num-complex
allnoAll features: std + ode + optim + control + complex

Re-exports§

pub use matrix::vector::ColumnVector;
pub use matrix::vector::ColumnVector3;
pub use matrix::vector::Vector;
pub use matrix::vector::Vector3;
pub use matrix::Matrix;
pub use matrix::aliases::Matrix1;
pub use matrix::aliases::Matrix2;
pub use matrix::aliases::Matrix3;
pub use matrix::aliases::Matrix4;
pub use matrix::aliases::Matrix5;
pub use matrix::aliases::Matrix6;
pub use matrix::aliases::Matrix1x2;
pub use matrix::aliases::Matrix1x3;
pub use matrix::aliases::Matrix1x4;
pub use matrix::aliases::Matrix1x5;
pub use matrix::aliases::Matrix1x6;
pub use matrix::aliases::Matrix2x1;
pub use matrix::aliases::Matrix2x3;
pub use matrix::aliases::Matrix2x4;
pub use matrix::aliases::Matrix2x5;
pub use matrix::aliases::Matrix2x6;
pub use matrix::aliases::Matrix3x1;
pub use matrix::aliases::Matrix3x2;
pub use matrix::aliases::Matrix3x4;
pub use matrix::aliases::Matrix3x5;
pub use matrix::aliases::Matrix3x6;
pub use matrix::aliases::Matrix4x1;
pub use matrix::aliases::Matrix4x2;
pub use matrix::aliases::Matrix4x3;
pub use matrix::aliases::Matrix4x5;
pub use matrix::aliases::Matrix4x6;
pub use matrix::aliases::Matrix5x1;
pub use matrix::aliases::Matrix5x2;
pub use matrix::aliases::Matrix5x3;
pub use matrix::aliases::Matrix5x4;
pub use matrix::aliases::Matrix5x6;
pub use matrix::aliases::Matrix6x1;
pub use matrix::aliases::Matrix6x2;
pub use matrix::aliases::Matrix6x3;
pub use matrix::aliases::Matrix6x4;
pub use matrix::aliases::Matrix6x5;
pub use matrix::aliases::Vector1;
pub use matrix::aliases::Vector2;
pub use matrix::aliases::Vector4;
pub use matrix::aliases::Vector5;
pub use matrix::aliases::Vector6;
pub use matrix::aliases::ColumnVector1;
pub use matrix::aliases::ColumnVector2;
pub use matrix::aliases::ColumnVector4;
pub use matrix::aliases::ColumnVector5;
pub use matrix::aliases::ColumnVector6;
pub use dynmatrix::DynMatrix;
pub use dynmatrix::DynVector;
pub use dynmatrix::DynMatrixf32;
pub use dynmatrix::DynMatrixf64;
pub use dynmatrix::DynMatrixi32;
pub use dynmatrix::DynMatrixi64;
pub use dynmatrix::DynMatrixu32;
pub use dynmatrix::DynMatrixu64;
pub use dynmatrix::DynVectorf32;
pub use dynmatrix::DynVectorf64;
pub use dynmatrix::DynVectori32;
pub use dynmatrix::DynVectori64;
pub use dynmatrix::DynVectoru32;
pub use dynmatrix::DynVectoru64;
pub use dynmatrix::DynMatrixz32;
pub use dynmatrix::DynMatrixz64;
pub use dynmatrix::DynVectorz32;
pub use dynmatrix::DynVectorz64;
pub use quaternion::Quaternion;
pub use traits::FloatScalar;
pub use traits::LinalgScalar;
pub use traits::MatrixMut;
pub use traits::MatrixRef;
pub use traits::Scalar;

Modules§

control
Digital control: IIR filters (Butterworth, Chebyshev Type I), PID controller.
dynmatrix
linalg
matrix
ode
ODE integration — fixed-step, adaptive, and stiff solvers.
optim
Optimization: root finding, unconstrained minimization, nonlinear least squares.
quaternion
traits

Structs§

Complex
A complex number in Cartesian form.