Module linalg 

Dense and sparse linear algebra.

Matrix is the dense row-major f64 type everything here operates on. The factorizations are chosen by what the matrix is: lu with partial pivoting for a general square solve, cholesky for symmetric positive-definite (half the work, and it fails cleanly if the matrix is not), qr by Householder reflections for least squares, svd by one-sided Jacobi for rank and pseudo-inverse, and tridiagonal for the Thomas algorithm in O(n).

eigen provides the symmetric eigenproblem and general eigenvalues. sparse provides CSR storage with conjugate gradient and a Jacobi-preconditioned variant, for the large systems that the PDE solvers in crate::fem produce.

Note that pcg_jacobi’s tolerance is relative to the norm of the right-hand side, not absolute.

Re-exports

pub use cholesky::cholesky;

pub use cholesky::cholesky_solve;

pub use eigen::eigen_symmetric;

pub use eigen::eigenvalues_general;

pub use eigen::SymEigen;

pub use lu::lu_decompose;

pub use lu::solve;

pub use lu::Lu;

pub use matrix::Matrix;

pub use qr::least_squares;

pub use qr::qr_householder;

pub use qr::Qr;

pub use sparse::conjugate_gradient;

pub use sparse::pcg_jacobi;

pub use sparse::CsrMatrix;

pub use svd::kabsch;

pub use svd::pseudoinverse;

pub use svd::rank;

pub use svd::svd;

pub use svd::Svd;

pub use tridiagonal::eigen_symmetric_tridiagonal;

pub use tridiagonal::thomas_solve;

Modules

cholesky

Cholesky factorization of symmetric positive-definite matrices.

eigen

Eigenvalue solvers.

lu

LU decomposition with partial pivoting (Doolittle form).

matrix

Dense row-major matrix of f64.

qr

QR decomposition by Householder reflections and least-squares solve.

sparse

Compressed sparse row (CSR) matrices and conjugate-gradient solvers.

svd

Singular value decomposition by one-sided Jacobi rotations.

tridiagonal

Tridiagonal linear solve (Thomas algorithm).

Structs

Mat3

Mat4

A dense 4x4 matrix with fixed-size storage.

Functions

cartesian_to_cylindrical

Returns (rho, phi, z) where rho is the radial distance in the xy-plane and phi is the azimuthal angle from +x.

cartesian_to_polar

Returns (r, theta) where theta is the angle from +x.

cartesian_to_spherical

Returns (r, theta, phi) where theta is the polar angle from +z and phi is the azimuthal angle from +x.

cylindrical_to_cartesian

Converts cylindrical coordinates (rho, phi, z) to Cartesian (x, y, z).

polar_to_cartesian

Converts 2D polar coordinates (r, theta) to Cartesian (x, y).

rotation_axis_angle

Rodrigues’ rotation formula: rotate by angle radians about axis. The axis is normalized internally.

rotation_x

Rotation matrix about the x-axis by the given angle in radians.

rotation_y

Rotation matrix about the y-axis by the given angle in radians.

rotation_z

Rotation matrix about the z-axis by the given angle in radians.

spherical_to_cartesian

Converts spherical coordinates (r, theta, phi) to Cartesian (x, y, z).