Crate axiolid_numeric

Shared numeric substrate: root finding, quadrature, dense linear algebra and least squares, and minimisation over f64.

These are the general numeric routines geometry algorithms build on – curve and surface fitting, fairing, projection and inversion – in one place instead of re-derived inline. The reference designs are OCCT’s math package, QUADPACK, Brent (1973) and MINPACK.

Need	Routine
a root of f between two points of opposite sign	find_root
every real root of a polynomial in an interval	Polynomial::real_roots
integral f with an error estimate	integrate
fixed Gauss rule for an integrand of known degree	GaussLegendre
square system	Lu
symmetric positive definite system	Cholesky
large sparse symmetric positive definite system	conjugate_gradient on a SparseMatrix
linear least squares, rank	Qr, least_squares
least squares with equality constraints	constrained_least_squares
nonlinear least squares, nonlinear equations	levenberg_marquardt
minimum of f on an interval	minimize_scalar

Contract

• Non-finite input is refused by name (NumericError::NonFiniteInput), as is a non-finite value from a caller’s function.
• Every answer says how far it can be trusted: a bracket that contains the root, an error estimate, a condition estimate, or an explicitly unresolved region. Which of these is a proven bound and which is an estimate is stated on each field.
• Iterative routines report a Status. One that ran out of budget still returns its best value and estimate; its converged() accessor turns that into NumericError::NotConverged for callers that only accept a met tolerance.
• Singular, rank-deficient, non-symmetric and indefinite matrices are refused, never solved into infinities.

There are no geometry types here and no dependencies: values are plain f64 slices, a small row-major Matrix and a compressed-row SparseMatrix.

Re-exports

pub use error::NumericError;

pub use error::NumericResult;

pub use error::Status;

pub use linalg::constrained_least_squares;

pub use linalg::least_squares;

pub use linalg::Cholesky;

pub use linalg::ConstrainedSolution;

pub use linalg::LeastSquaresSolution;

pub use linalg::LinearSolution;

pub use linalg::Lu;

pub use linalg::Matrix;

pub use linalg::Qr;

pub use optimize::levenberg_marquardt;

pub use optimize::minimize_scalar;

pub use optimize::LeastSquaresMinimum;

pub use optimize::LevenbergMarquardtOptions;

pub use optimize::Residuals;

pub use optimize::ScalarMinimum;

pub use optimize::Termination;

pub use poly::Polynomial;

pub use poly::PolynomialRoot;

pub use poly::RootKind;

pub use quad::integrate;

pub use quad::GaussLegendre;

pub use quad::Integral;

pub use quad::IntegrationOptions;

pub use root::find_root;

pub use root::Root;

pub use sparse::conjugate_gradient;

pub use sparse::ConjugateGradientOptions;

pub use sparse::ConjugateGradientSolution;

pub use sparse::SparseMatrix;

Modules

error

Refusals and convergence status shared by every routine.

linalg

Dense linear algebra for small and medium systems.

optimize

Minimisation: a bounded scalar minimiser and damped Gauss-Newton (Levenberg-Marquardt) for nonlinear least squares.

poly

Real polynomials in the power basis and all their real roots in an interval.

quad

Numerical integration of a scalar function over a finite interval.

root

Bracketed scalar root finding with guaranteed convergence.

sparse

Sparse matrices and the preconditioned conjugate-gradient solve.