EigenM2 namespace — Eigen3-backed SVD / eigenvalues / eigenvectors / least-squares for DMat<R> over RR, CC, RRR, CCC. More...

#include "dmat.hpp"
#include "aring-RR.hpp"
#include "aring-CC.hpp"
#include "aring-RRR.hpp"
#include "aring-CCC.hpp"

Namespaces
namespace	EigenM2

Typedefs
using	LMatrixRR = DMat<M2::ARingRR>
using	LMatrixCC = DMat<M2::ARingCC>
using	LMatrixRRR = DMat<M2::ARingRRR>
using	LMatrixCCC = DMat<M2::ARingCCC>

Functions
bool	EigenM2::SVD (const LMatrixRR A, LMatrixRR Sigma, LMatrixRR U, LMatrixRR VT)
bool	EigenM2::SVD (const LMatrixCC A, LMatrixRR Sigma, LMatrixCC U, LMatrixCC VT)
bool	EigenM2::SVD_divide_conquer (const LMatrixRR A, LMatrixRR Sigma, LMatrixRR U, LMatrixRR VT)
bool	EigenM2::SVD_divide_conquer (const LMatrixCC A, LMatrixRR Sigma, LMatrixCC U, LMatrixCC VT)
bool	EigenM2::eigenvalues (const LMatrixRR A, LMatrixCC eigenvals)
bool	EigenM2::eigenvalues (const LMatrixCC A, LMatrixCC eigenvals)
bool	EigenM2::eigenvalues_hermitian (const LMatrixRR A, LMatrixRR eigenvals)
bool	EigenM2::eigenvalues_hermitian (const LMatrixCC A, LMatrixRR eigenvals)
bool	EigenM2::eigenvectors (const LMatrixRR A, LMatrixCC eigenvals, LMatrixCC *eigenvecs)
bool	EigenM2::eigenvectors (const LMatrixCC A, LMatrixCC eigenvals, LMatrixCC *eigenvecs)
bool	EigenM2::eigenvectors_hermitian (const LMatrixRR A, LMatrixRR eigenvals, LMatrixRR *eigenvecs)
bool	EigenM2::eigenvectors_hermitian (const LMatrixCC A, LMatrixRR eigenvals, LMatrixCC *eigenvecs)
bool	EigenM2::least_squares (const LMatrixRR A, const LMatrixRR B, LMatrixRR *X)
bool	EigenM2::least_squares (const LMatrixCC A, const LMatrixCC B, LMatrixCC *X)
bool	EigenM2::SVD (const LMatrixRRR A, LMatrixRRR Sigma, LMatrixRRR U, LMatrixRRR VT)
bool	EigenM2::SVD (const LMatrixCCC A, LMatrixRRR Sigma, LMatrixCCC U, LMatrixCCC VT)
bool	EigenM2::SVD_divide_conquer (const LMatrixRRR A, LMatrixRRR Sigma, LMatrixRRR U, LMatrixRRR VT)
bool	EigenM2::SVD_divide_conquer (const LMatrixCCC A, LMatrixRRR Sigma, LMatrixCCC U, LMatrixCCC VT)
bool	EigenM2::eigenvalues (const LMatrixRRR A, LMatrixCCC eigenvals)
bool	EigenM2::eigenvalues (const LMatrixCCC A, LMatrixCCC eigenvals)
bool	EigenM2::eigenvalues_hermitian (const LMatrixRRR A, LMatrixRRR eigenvals)
bool	EigenM2::eigenvalues_hermitian (const LMatrixCCC A, LMatrixRRR eigenvals)
bool	EigenM2::eigenvectors (const LMatrixRRR A, LMatrixCCC eigenvals, LMatrixCCC *eigenvecs)
bool	EigenM2::eigenvectors (const LMatrixCCC A, LMatrixCCC eigenvals, LMatrixCCC *eigenvecs)
bool	EigenM2::eigenvectors_hermitian (const LMatrixRRR A, LMatrixRRR eigenvals, LMatrixRRR *eigenvecs)
bool	EigenM2::eigenvectors_hermitian (const LMatrixCCC A, LMatrixRRR eigenvals, LMatrixCCC *eigenvecs)
bool	EigenM2::least_squares (const LMatrixRRR A, const LMatrixRRR B, LMatrixRRR *X)
bool	EigenM2::least_squares (const LMatrixCCC A, const LMatrixCCC B, LMatrixCCC *X)

Detailed Description

EigenM2 namespace — Eigen3-backed SVD / eigenvalues / eigenvectors / least-squares for DMat<R> over RR, CC, RRR, CCC.

Note: AI-generated documentation. Verify against the source before relying on it.

Declares aliases LMatrixRR, LMatrixCC, LMatrixRRR, LMatrixCCC over the four DMat<R> instantiations the engine cares about for numerical linear algebra, then a namespace EigenM2 of free-function wrappers — SVD, SVD_divide_conquer, eigenvalues, eigenvalues_hermitian, eigenvectors, eigenvectors_hermitian, least_squares — that operate on those DMat pointers. Each routine returns bool so the engine can surface convergence failures to the M2 user.

All implementations live in eigen.cpp and call into the Eigen3 template library (Eigen's JacobiSVD / BDCSVD / EigenSolver / SelfAdjointEigenSolver, plus mpreal-backed scalars from <unsupported/Eigen/MPRealSupport> for the MPFR-precision RRR / CCC cases). The RR / CC implementations are guarded by #ifdef NO_LAPACK: by default mat-linalg.hpp skips this header and routes hardware-precision SVD / eigen queries to Lapack:: directly; the RRR / CCC overloads are always built. Interval rings RRi / CCi are not yet plumbed through here.

See also: lapack.hpp; dmat.hpp; mat-linalg.hpp

Definition in file eigen.hpp.

Namespaces

Typedefs

Functions

Detailed Description