Public Member Functions | Private Types | Private Member Functions | Private Attributes | List of all members
Spectra::GenEigsComplexShiftSolver< Scalar, SelectionRule, OpType > Class Template Reference
Eigen Solvers

#include <GenEigsComplexShiftSolver.h>

Inheritance diagram for Spectra::GenEigsComplexShiftSolver< Scalar, SelectionRule, OpType >:
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Public Member Functions

 GenEigsComplexShiftSolver (OpType *op, Index nev, Index ncv, const Scalar &sigmar, const Scalar &sigmai)
 
- Public Member Functions inherited from Spectra::GenEigsBase< double, LARGEST_MAGN, DenseGenComplexShiftSolve< double >, IdentityBOp >
Index compute (Index maxit=1000, double tol=1e-10, int sort_rule=LARGEST_MAGN)
 
ComplexVector eigenvalues () const
 
ComplexMatrix eigenvectors () const
 
ComplexMatrix eigenvectors (Index nvec) const
 
int info () const
 
void init ()
 
void init (const double *init_resid)
 
Index num_iterations () const
 
Index num_operations () const
 

Private Types

typedef std::complex< Scalar > Complex
 
typedef Eigen::Matrix< Complex, Eigen::Dynamic, 1 > ComplexVector
 
typedef Eigen::Index Index
 
typedef Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > Vector
 

Private Member Functions

void sort_ritzpair (int sort_rule)
 

Private Attributes

const Scalar m_sigmai
 
const Scalar m_sigmar
 

Additional Inherited Members

- Protected Attributes inherited from Spectra::GenEigsBase< double, LARGEST_MAGN, DenseGenComplexShiftSolve< double >, IdentityBOp >
ArnoldiFac m_fac
 
const Index m_n
 
const Index m_ncv
 
const Index m_nev
 
Index m_niter
 
Index m_nmatop
 
DenseGenComplexShiftSolve< double > * m_op
 
ComplexVector m_ritz_est
 
ComplexVector m_ritz_val
 
ComplexMatrix m_ritz_vec
 

Detailed Description

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseGenComplexShiftSolve<double>>
class Spectra::GenEigsComplexShiftSolver< Scalar, SelectionRule, OpType >

This class implements the eigen solver for general real matrices with a complex shift value in the shift-and-invert mode. The background knowledge of the shift-and-invert mode can be found in the documentation of the SymEigsShiftSolver class.

Template Parameters
ScalarThe element type of the matrix. Currently supported types are float, double and long double.
SelectionRuleAn enumeration value indicating the selection rule of the shifted-and-inverted eigenvalues. The full list of enumeration values can be found in Enumerations.
OpTypeThe name of the matrix operation class. Users could either use the DenseGenComplexShiftSolve wrapper class, or define their own that implements all the public member functions as in DenseGenComplexShiftSolve.

Definition at line 40 of file GenEigsComplexShiftSolver.h.

Member Typedef Documentation

◆ Complex

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseGenComplexShiftSolve<double>>
typedef std::complex<Scalar> Spectra::GenEigsComplexShiftSolver< Scalar, SelectionRule, OpType >::Complex
private

Definition at line 44 of file GenEigsComplexShiftSolver.h.

◆ ComplexVector

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseGenComplexShiftSolve<double>>
typedef Eigen::Matrix<Complex, Eigen::Dynamic, 1> Spectra::GenEigsComplexShiftSolver< Scalar, SelectionRule, OpType >::ComplexVector
private

Definition at line 46 of file GenEigsComplexShiftSolver.h.

◆ Index

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseGenComplexShiftSolve<double>>
typedef Eigen::Index Spectra::GenEigsComplexShiftSolver< Scalar, SelectionRule, OpType >::Index
private

Definition at line 43 of file GenEigsComplexShiftSolver.h.

◆ Vector

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseGenComplexShiftSolve<double>>
typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Spectra::GenEigsComplexShiftSolver< Scalar, SelectionRule, OpType >::Vector
private

Definition at line 45 of file GenEigsComplexShiftSolver.h.

Constructor & Destructor Documentation

◆ GenEigsComplexShiftSolver()

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseGenComplexShiftSolve<double>>
Spectra::GenEigsComplexShiftSolver< Scalar, SelectionRule, OpType >::GenEigsComplexShiftSolver ( OpType *  op,
Index  nev,
Index  ncv,
const Scalar &  sigmar,
const Scalar &  sigmai 
)
inline

Constructor to create a eigen solver object using the shift-and-invert mode.

Parameters
opPointer to the matrix operation object. This class should implement the complex shift-solve operation of $A$: calculating $\mathrm{Re}\{(A-\sigma I)^{-1}v\}$ for any vector $v$. Users could either create the object from the DenseGenComplexShiftSolve wrapper class, or define their own that implements all the public member functions as in DenseGenComplexShiftSolve.
nevNumber of eigenvalues requested. This should satisfy $1\le nev \le n-2$, where $n$ is the size of matrix.
ncvParameter that controls the convergence speed of the algorithm. Typically a larger ncv means faster convergence, but it may also result in greater memory use and more matrix operations in each iteration. This parameter must satisfy $nev+2 \le ncv \le n$, and is advised to take $ncv \ge 2\cdot nev + 1$.
sigmarThe real part of the shift.
sigmaiThe imaginary part of the shift.

Definition at line 147 of file GenEigsComplexShiftSolver.h.

Member Function Documentation

◆ sort_ritzpair()

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseGenComplexShiftSolve<double>>
void Spectra::GenEigsComplexShiftSolver< Scalar, SelectionRule, OpType >::sort_ritzpair ( int  sort_rule)
inlineprivatevirtual

Reimplemented from Spectra::GenEigsBase< double, LARGEST_MAGN, DenseGenComplexShiftSolve< double >, IdentityBOp >.

Definition at line 52 of file GenEigsComplexShiftSolver.h.

Member Data Documentation

◆ m_sigmai

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseGenComplexShiftSolve<double>>
const Scalar Spectra::GenEigsComplexShiftSolver< Scalar, SelectionRule, OpType >::m_sigmai
private

Definition at line 49 of file GenEigsComplexShiftSolver.h.

◆ m_sigmar

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseGenComplexShiftSolve<double>>
const Scalar Spectra::GenEigsComplexShiftSolver< Scalar, SelectionRule, OpType >::m_sigmar
private

Definition at line 48 of file GenEigsComplexShiftSolver.h.

The documentation for this class was generated from the following file:

gtsam
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autogenerated on Sat Nov 16 2024 04:16:52