Crate numeris 

numeris

Pure-Rust numerical algorithms library — high performance with SIMD support (NEON, SSE2, AVX, AVX-512) while also supporting no-std for embedded and WASM targets. Similar in scope to SciPy.

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; M]; N] column-major storage (matches LAPACK conventions). Matrix::new() accepts row-major input and transposes internally. 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> column-major storage (col * nrows + row). from_rows() accepts row-major data (transposes internally); from_slice() accepts column-major data directly. Implements MatrixRef / MatrixMut, so all linalg free functions work automatically. DynVector<T> newtype for single-index vector access. Includes DynLu, DynCholesky, DynQr, DynSvd, DynSymmetricEigen, DynSchur 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. RODAS4 L-stable Rosenbrock method for stiff systems (user-supplied or finite-difference Jacobians). 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. control::Pid discrete-time PID controller with anti-windup. control::lead_compensator and control::lag_compensator for compensator design via bilinear transform. PID tuning via control::FopdtModel (Ziegler-Nichols, Cohen-Coon, SIMC) and control::ziegler_nichols_ultimate. No complex feature dependency. Requires control feature.

• estimate — State estimation: estimate::Ekf (Extended Kalman Filter), estimate::Ukf (Unscented Kalman Filter), estimate::SrUkf (Square-Root UKF), estimate::Ckf (Cubature Kalman Filter), estimate::rts_smooth (RTS smoother), and estimate::BatchLsq (batch least-squares). Closure-based dynamics and measurement models, Joseph-form covariance update, Merwe-scaled sigma points. EKF and BatchLsq are fully no-std; sigma-point filters and RTS require alloc. Requires estimate feature.

• interp — Interpolation: interp::LinearInterp, interp::HermiteInterp, interp::LagrangeInterp (barycentric), interp::CubicSpline (natural BCs), and interp::BilinearInterp (2D rectangular grid). Fixed-size (const N, stack-allocated, no-std) and dynamic variants (Dyn*, requires alloc). Out-of-bounds evaluations extrapolate. Requires interp feature.

• special — Special functions: special::gamma, special::lgamma, special::digamma, special::beta / special::lbeta, regularized incomplete gamma (special::gamma_inc / special::gamma_inc_upper), regularized incomplete beta (special::betainc), and error functions (special::erf / special::erfc). Generic over FloatScalar (f32/f64), fully no-std. Requires special feature.

• quad — Numerical quadrature (integration): quad::gauss_legendre (N-point Gauss-Legendre, N=1..10,15,20), quad::adaptive_simpson (automatic subdivision), quad::trapezoid and quad::simpson (composite rules). All no-alloc. Requires quad feature.

• stats — Statistical distributions with stats::ContinuousDistribution and stats::DiscreteDistribution traits. Continuous: stats::Normal, stats::Uniform, stats::Exponential, stats::Gamma, stats::Beta, stats::ChiSquared, stats::StudentT. Discrete: stats::Bernoulli, stats::Binomial, stats::Poisson. Built-in stats::Rng (xoshiro256++) with sample() / sample_array() on every distribution. Requires stats feature (implies special).

• 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

Feature	Default	Description
std	yes	Implies alloc. Hardware FPU via system libm
alloc	via std	DynMatrix / DynVector (heap-allocated, runtime-sized)
ode	yes	ODE integration (RK4, adaptive solvers)
optim	no	Optimization (root finding, BFGS, Gauss-Newton, LM)
control	no	Digital IIR filters, PID, lead/lag compensators, PID tuning
estimate	no	State estimation (EKF, UKF). Implies alloc
interp	no	Interpolation (linear, Hermite, Lagrange, cubic spline, bilinear 2D)
quad	no	Numerical quadrature (Gauss-Legendre, adaptive Simpson, composite rules)
special	no	Special functions (gamma, beta, erf, incomplete gamma/beta)
stats	no	Statistical distributions (Normal, Gamma, etc.) with sampling. Implies special
libm	baseline	Pure-Rust software float fallback
complex	no	Complex<f32> / Complex<f64> support via num-complex
all	no	All features

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, PID controller, compensator design, and tuning.

dynmatrix

estimate

State estimation: EKF, UKF, SR-UKF, CKF, RTS smoother, batch least-squares.

interp

Interpolation: linear, Hermite, barycentric Lagrange, natural cubic spline, and bilinear (2D).

linalg

matrix

ode

ODE integration — fixed-step, adaptive, and stiff solvers.

optim

Optimization: root finding, unconstrained minimization, nonlinear least squares.

quad

Numerical quadrature (integration).

quaternion

special

Special mathematical functions.

stats

Statistical distributions: continuous and discrete.

traits

Structs

Complex

A complex number in Cartesian form.