Module linalg

Dense linear algebra for small and medium systems.

• Lu: Gaussian elimination with partial pivoting, for square systems (OCCT math_Gauss).
• Cholesky: L L^T for symmetric positive definite systems, such as normal equations and fairing energies (OCCT math_Crout covers the symmetric case there).
• Qr: Householder QR with column pivoting, for linear least squares and rank detection (OCCT math_Householder, LAPACK xGEQP3).
• constrained_least_squares: least squares subject to linear equality constraints, by the null-space method (Golub and Van Loan, Matrix Computations, 6.2).

Every solve reports a condition estimate (Hager’s 1-norm estimator as refined by Higham, LAPACK xLACON) and a relative forward error estimate derived from it. Singular and rank-deficient systems are refused by name rather than solved into infinities.

Structs

Cholesky

A = L L^T for a symmetric positive definite matrix.

ConstrainedSolution

The solution of an equality-constrained least-squares problem.

LeastSquaresSolution

The solution of a linear least-squares problem.

LinearSolution

The solution of a square linear system.

Lu

P A = L U with partial pivoting.

Matrix

A dense row-major matrix of f64.

Qr

Householder QR with column pivoting: A P = Q R.

Functions

constrained_least_squares

Minimise ||A x - b||_2 subject to C x = d by the null-space method.

least_squares

Minimise ||A x - b||_2: a convenience for Qr::new followed by Qr::solve_least_squares. Factor once with Qr when several right-hand sides share A (one per coordinate when fitting points).