Spectra::GenEigsSolver< OpType > Class Template Reference

#include <Spectra/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 >
void	init (const Scalar *init_resid)
void	init ()
Index	compute (SortRule selection=SortRule::LargestMagn, Index maxit=1000, Scalar tol=1e-10, SortRule sorting=SortRule::LargestMagn)
CompInfo	info () const
Index	num_iterations () const
Index	num_operations () const
ComplexVector	eigenvalues () const
ComplexMatrix	eigenvectors (Index nvec) const
ComplexMatrix	eigenvectors () const

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.

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 \(A\): calculating \(Av\) for any vector \(v\). 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 \(n\) 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.

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

• Spectra/GenEigsSolver.h