#include <GenEigsSolver.h>

Inheritance diagram for Spectra::GenEigsSolver< OpType >:

Public Member Functions
	GenEigsSolver (OpType &op, Index nev, Index ncv)

Public Member Functions inherited from Spectra::GenEigsBase< DenseGenMatProd< double >, IdentityBOp >
Index	compute (SortRule selection=SortRule::LargestMagn, Index maxit=1000, Scalar tol=1e-10, SortRule sorting=SortRule::LargestMagn)

ComplexVector	eigenvalues () const

ComplexMatrix	eigenvectors () const

ComplexMatrix	eigenvectors (Index nvec) const

CompInfo	info () const

void	init ()

void	init (const Scalar *init_resid)

Index	num_iterations () const

Index	num_operations () const

Private Types
using	Index = Eigen::Index

Additional Inherited Members
Protected Member Functions inherited from Spectra::GenEigsBase< DenseGenMatProd< double >, IdentityBOp >
virtual void	sort_ritzpair (SortRule sort_rule)

Protected Attributes inherited from Spectra::GenEigsBase< DenseGenMatProd< double >, IdentityBOp >
ArnoldiFac	m_fac

const Index	m_n

const Index	m_ncv

const Index	m_nev

Index	m_niter

Index	m_nmatop

DenseGenMatProd< double > &	m_op

ComplexVector	m_ritz_est

ComplexVector	m_ritz_val

ComplexMatrix	m_ritz_vec

Detailed Description

template<typename OpType = DenseGenMatProd<double>>
class Spectra::GenEigsSolver< OpType >

This class implements the eigen solver for general real matrices, i.e., to solve $Ax=\lambda x$ for a possibly non-symmetric $A$ matrix.

Most of the background information documented in the SymEigsSolver class also applies to the GenEigsSolver class here, except that the eigenvalues and eigenvectors of a general matrix can now be complex-valued.

Template Parameters

OpType The name of the matrix operation class. Users could either use the wrapper classes such as DenseGenMatProd and SparseGenMatProd, or define their own that implements the type definition Scalar and all the public member functions as in DenseGenMatProd.

An example that illustrates the usage of GenEigsSolver is give below:

#include <Eigen/Core>
#include <Spectra/GenEigsSolver.h>
// <Spectra/MatOp/DenseGenMatProd.h> is implicitly included
#include <iostream>
 
using namespace Spectra;
 
int main()
{
    // We are going to calculate the eigenvalues of M
    Eigen::MatrixXd M = Eigen::MatrixXd::Random(10, 10);
 
    // Construct matrix operation object using the wrapper class
    DenseGenMatProd<double> op(M);
 
    // Construct eigen solver object, requesting the largest
    // (in magnitude, or norm) three eigenvalues
    GenEigsSolver<DenseGenMatProd<double>> eigs(op, 3, 6);
 
    // Initialize and compute
    eigs.init();
    int nconv = eigs.compute(SortRule::LargestMagn);
 
    // Retrieve results
    Eigen::VectorXcd evalues;
    if (eigs.info() == CompInfo::Successful)
        evalues = eigs.eigenvalues();
 
    std::cout << "Eigenvalues found:\n" << evalues << std::endl;
 
    return 0;
}

And also an example for sparse matrices:

#include <Eigen/Core>
#include <Eigen/SparseCore>
#include <Spectra/GenEigsSolver.h>
#include <Spectra/MatOp/SparseGenMatProd.h>
#include <iostream>
 
using namespace Spectra;
 
int main()
{
    // A band matrix with 1 on the main diagonal, 2 on the below-main subdiagonal,
    // and 3 on the above-main subdiagonal
    const int n = 10;
    Eigen::SparseMatrix<double> M(n, n);
    M.reserve(Eigen::VectorXi::Constant(n, 3));
    for (int i = 0; i < n; i++)
    {
        M.insert(i, i) = 1.0;
        if (i > 0)
            M.insert(i - 1, i) = 3.0;
        if (i < n - 1)
            M.insert(i + 1, i) = 2.0;
    }
 
    // Construct matrix operation object using the wrapper class SparseGenMatProd
    SparseGenMatProd<double> op(M);
 
    // Construct eigen solver object, requesting the largest three eigenvalues
    GenEigsSolver<SparseGenMatProd<double>> eigs(op, 3, 6);
 
    // Initialize and compute
    eigs.init();
    int nconv = eigs.compute(SortRule::LargestMagn);
 
    // Retrieve results
    Eigen::VectorXcd evalues;
    if (eigs.info() == CompInfo::Successful)
        evalues = eigs.eigenvalues();
 
    std::cout << "Eigenvalues found:\n" << evalues << std::endl;
 
    return 0;
}

Definition at line 119 of file GenEigsSolver.h.

Member Typedef Documentation

◆ Index

template<typename OpType = DenseGenMatProd<double>>

using Spectra::GenEigsSolver< OpType >::Index = Eigen::Index

private

Definition at line 122 of file GenEigsSolver.h.

Constructor & Destructor Documentation

◆ GenEigsSolver()

template<typename OpType = DenseGenMatProd<double>>

Spectra::GenEigsSolver< OpType >::GenEigsSolver	(	OpType &	op,
		Index	nev,
		Index	ncv
	)

inline

Constructor to create a solver object.

Parameters

op	The matrix operation object that implements the matrix-vector multiplication operation of : calculating for any vector . Users could either create the object from the wrapper class such as DenseGenMatProd, or define their own that implements all the public members as in DenseGenMatProd.
nev	Number of eigenvalues requested. This should satisfy $1\le nev \le n-2$ , where is the size of matrix.
ncv	Parameter 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 $ncv \ge 2\cdot nev + 1$ .

Definition at line 142 of file GenEigsSolver.h.

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

GenEigsSolver.h

Public Member Functions

Private Types