#include <HermEigsSolver.h>

Inheritance diagram for Spectra::HermEigsSolver< OpType >:

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

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

RealVector	eigenvalues () const

virtual Matrix	eigenvectors () const

virtual Matrix	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::HermEigsBase< DenseHermMatProd< double >, IdentityBOp >
virtual void	sort_ritzpair (SortRule sort_rule)

Protected Attributes inherited from Spectra::HermEigsBase< DenseHermMatProd< double >, IdentityBOp >
LanczosFac	m_fac

const Index	m_n

const Index	m_ncv

const Index	m_nev

Index	m_niter

Index	m_nmatop

const DenseHermMatProd< double > &	m_op

std::vector< DenseHermMatProd< double > >	m_op_container

RealVector	m_ritz_val

Detailed Description

template<typename OpType = DenseHermMatProd<double>>
class Spectra::HermEigsSolver< OpType >

This class implements the eigen solver for Hermitian matrices, i.e., to solve $Ax=\lambda x$ where $A$ is Hermitian. An Hermitian matrix is a complex square matrix that is equal to its own conjugate transpose. It is known that all Hermitian matrices have real-valued eigenvalues.

Template Parameters

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

Below is an example that demonstrates the usage of this class.

#include <Eigen/Core>
#include <Spectra/HermEigsSolver.h>
// <Spectra/MatOp/DenseHermMatProd.h> is implicitly included
#include <iostream>
 
using namespace Spectra;
 
int main()
{
    // We are going to calculate the eigenvalues of M
    Eigen::MatrixXcd A = Eigen::MatrixXcd::Random(10, 10);
    Eigen::MatrixXcd M = A + A.adjoint();
 
    // Construct matrix operation object using the wrapper class DenseHermMatProd
    using OpType = DenseHermMatProd<std::complex<double>>;
    OpType op(M);
 
    // Construct eigen solver object, requesting the largest three eigenvalues
    HermEigsSolver<OpType> eigs(op, 3, 6);
 
    // Initialize and compute
    eigs.init();
    int nconv = eigs.compute(SortRule::LargestAlge);
 
    // Retrieve results
    // Eigenvalues are real-valued, and eigenvectors are complex-valued
    Eigen::VectorXd evalues;
    if (eigs.info() == CompInfo::Successful)
        evalues = eigs.eigenvalues();
 
    std::cout << "Eigenvalues found:\n" << evalues << std::endl;
 
    return 0;
}

And here is an example for user-supplied matrix operation class.

#include <Eigen/Core>
#include <Spectra/HermEigsSolver.h>
#include <iostream>
 
using namespace Spectra;
 
// M = diag(1+0i, 2+0i, ..., 10+0i)
class MyDiagonalTen
{
public:
    using Scalar = std::complex<double>;  // A typedef named "Scalar" is required
    int rows() const { return 10; }
    int cols() const { return 10; }
    // y_out = M * x_in
    void perform_op(Scalar *x_in, Scalar *y_out) const
    {
        for (int i = 0; i < rows(); i++)
        {
            y_out[i] = x_in[i] * Scalar(i + 1, 0);
        }
    }
};
 
int main()
{
    MyDiagonalTen op;
    HermEigsSolver<MyDiagonalTen> eigs(op, 3, 6);
    eigs.init();
    eigs.compute(SortRule::LargestAlge);
    if (eigs.info() == CompInfo::Successful)
    {
        Eigen::VectorXd evalues = eigs.eigenvalues();
        // Will get (10, 9, 8)
        std::cout << "Eigenvalues found:\n" << evalues << std::endl;
    }
 
    return 0;
}

Definition at line 116 of file HermEigsSolver.h.

Member Typedef Documentation

◆ Index

template<typename OpType = DenseHermMatProd<double>>

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

private

Definition at line 119 of file HermEigsSolver.h.

Constructor & Destructor Documentation

◆ HermEigsSolver()

template<typename OpType = DenseHermMatProd<double>>

Spectra::HermEigsSolver< OpType >::HermEigsSolver	(	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 DenseHermMatProd, or define their own that implements all the public members as in DenseHermMatProd.
nev	Number of eigenvalues requested. This should satisfy $1\le nev \le n-1$ , 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 $nev < ncv \le n$ , and is advised to take $ncv \ge 2\cdot nev$ .

Definition at line 139 of file HermEigsSolver.h.

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

HermEigsSolver.h

Public Member Functions

Private Types