lanczos.hpp File Reference

Lanczos eigensolver for symmetric operators. More...

#include "core/matrix.hpp"
#include "core/policy.hpp"
#include "core/vector.hpp"
#include "kernel/subspace.hpp"
#include "linalg/eigen/jacobi_eig.hpp"
#include "linalg/sparse/sparse.hpp"
#include "core/concepts.hpp"
#include <algorithm>
#include <cmath>
#include <stdexcept>

Go to the source code of this file.

Classes
struct	num::LanczosResult

Namespaces
namespace	num
namespace	num::detail

Functions
template<class Op > requires LinearOperator<Op, Vector, Vector>
LanczosResult	num::detail::lanczos_operator_impl (const Op &A, idx k, real tol, idx max_steps, Backend backend)
template<class Op > requires SymmetricLinearOperator<Op, Vector, Vector>
LanczosResult	num::lanczos (const Op &A, idx k, real tol=1e-10, idx max_steps=0, Backend backend=Backend::seq)
	Operator Lanczos for a declared symmetric \(y=A x\) adapter.
LanczosResult	num::lanczos (const Matrix &A, idx k, real tol=1e-10, idx max_steps=0, Backend backend=Backend::seq)
LanczosResult	num::lanczos (const SparseMatrix &A, idx k, real tol=1e-10, idx max_steps=0, Backend backend=Backend::seq)

Detailed Description

Lanczos eigensolver for symmetric operators.

Builds an orthonormal basis \(Q_m\) such that \(Q_m^T A Q_m = T_m\), with \(T_m\) tridiagonal.

Todo:

Add thick-restart Lanczos and selective reorthogonalization controls.

Definition in file lanczos.hpp.