Spectra::SymEigsSolver< OpType > Class Template Reference

#include <Spectra/SymEigsSolver.h>

Inheritance diagram for Spectra::SymEigsSolver< OpType >:

Public Member Functions
	SymEigsSolver (OpType &op, Index nev, Index ncv)
Public Member Functions inherited from Spectra::SymEigsBase< DenseSymMatProd< 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::LargestAlge)
CompInfo	info () const
Index	num_iterations () const
Index	num_operations () const
Vector	eigenvalues () const
virtual Matrix	eigenvectors (Index nvec) const
virtual Matrix	eigenvectors () const

Detailed Description

template<typename OpType = DenseSymMatProd<double>>
class Spectra::SymEigsSolver< OpType >

This class implements the eigen solver for real symmetric matrices, i.e., to solve \(Ax=\lambda x\) where \(A\) is symmetric.

Spectra is designed to calculate a specified number ( \(k\)) of eigenvalues of a large square matrix ( \(A\)). Usually \(k\) is much less than the size of the matrix ( \(n\)), so that only a few eigenvalues and eigenvectors are computed.

Rather than providing the whole \(A\) matrix, the algorithm only requires the matrix-vector multiplication operation of \(A\). Therefore, users of this solver need to supply a class that computes the result of \(Av\) for any given vector \(v\). The name of this class should be given to the template parameter OpType, and instance of this class passed to the constructor of SymEigsSolver.

If the matrix \(A\) is already stored as a matrix object in Eigen, for example Eigen::MatrixXd, then there is an easy way to construct such a matrix operation class, by using the built-in wrapper class DenseSymMatProd that wraps an existing matrix object in Eigen. This is also the default template parameter for SymEigsSolver. For sparse matrices, the wrapper class SparseSymMatProd can be used similarly.

If the users need to define their own matrix-vector multiplication operation class, it should define a public type Scalar to indicate the element type, and implement all the public member functions as in DenseSymMatProd.

Template Parameters

OpType

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

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

#include <Eigen/Core>
#include <Spectra/SymEigsSolver.h>
// <Spectra/MatOp/DenseSymMatProd.h> is implicitly included
#include <iostream>
 
using namespace Spectra;
 
int main()
{
    // We are going to calculate the eigenvalues of M
    Eigen::MatrixXd A = Eigen::MatrixXd::Random(10, 10);
    Eigen::MatrixXd M = A + A.transpose();
 
    // Construct matrix operation object using the wrapper class DenseSymMatProd
    DenseSymMatProd<double> op(M);
 
    // Construct eigen solver object, requesting the largest three eigenvalues
    SymEigsSolver<DenseSymMatProd<double>> eigs(op, 3, 6);
 
    // Initialize and compute
    eigs.init();
    int nconv = eigs.compute(SortRule::LargestAlge);
 
    // Retrieve results
    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/SymEigsSolver.h>
#include <iostream>
 
using namespace Spectra;
 
// M = diag(1, 2, ..., 10)
class MyDiagonalTen
{
public:
    using Scalar = 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(double *x_in, double *y_out) const
    {
        for (int i = 0; i < rows(); i++)
        {
            y_out[i] = x_in[i] * (i + 1);
        }
    }
};
 
int main()
{
    MyDiagonalTen op;
    SymEigsSolver<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 134 of file SymEigsSolver.h.

Constructor & Destructor Documentation

SymEigsSolver()

template<typename OpType = DenseSymMatProd<double>>

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

Definition at line 157 of file SymEigsSolver.h.

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

• Spectra/SymEigsSolver.h