Class SymEigsSolver

Synopsis

#include <include/Spectra/SymEigsSolver.h>

template < typename Scalar = double,
int SelectionRule = LARGEST_MAGN,
typename OpType = DenseSymMatProd<double> >
class SymEigsSolver: public SymEigsBase<Scalar, SelectionRule, OpType, IdentityBOp>


Description

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 matrix operation class, by using the built-in wrapper class DenseSymMatProd which 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 implement all the public member functions as in DenseSymMatProd.

Template Parameters

Scalar - The element type of the matrix. Currently supported types are float, double and long double.

SelectionRule - An enumeration value indicating the selection rule of the requested eigenvalues, for example LARGEST_MAGN to retrieve eigenvalues with the largest magnitude. The full list of enumeration values can be found in Enumerations.

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 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< double, LARGEST_ALGE, DenseSymMatProd<double> > eigs(&op, 3, 6);

// Initialize and compute
eigs.init();
int nconv = eigs.compute();

// Retrieve results
Eigen::VectorXd evalues;
if(eigs.info() == 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:
int rows() { return 10; }
int cols() { return 10; }
// y_out = M * x_in
void perform_op(double *x_in, double *y_out)
{
for(int i = 0; i < rows(); i++)
{
y_out[i] = x_in[i] * (i + 1);
}
}
};

int main()
{
MyDiagonalTen op;
SymEigsSolver<double, LARGEST_ALGE, MyDiagonalTen> eigs(&op, 3, 6);
eigs.init();
eigs.compute();
if(eigs.info() == SUCCESSFUL)
{
Eigen::VectorXd evalues = eigs.eigenvalues();
// Will get (10, 9, 8)
std::cout << "Eigenvalues found:\n" << evalues << std::endl;
}

return 0;
}


Inheritance

Ancestors: SymEigsBase

Methods

 SymEigsSolver Constructor to create a solver object.

Source

template < typename Scalar = double,
int SelectionRule = LARGEST_MAGN,
typename OpType = DenseSymMatProd<double> >
class SymEigsSolver: public SymEigsBase<Scalar, SelectionRule, OpType, IdentityBOp>
{
public:
///
/// Constructor to create a solver object.
///
/// \param op   Pointer to the matrix operation object, which should implement
///             the matrix-vector multiplication operation of \f$A\f$:
///             calculating \f$Av\f$ for any vector \f$v\f$. Users could either
///             create the object from the wrapper class such as DenseSymMatProd, or
///             define their own that implements all the public member functions
///             as in DenseSymMatProd.
/// \param nev  Number of eigenvalues requested. This should satisfy \f$1\le nev \le n-1\f$,
///             where \f$n\f$ is the size of matrix.
/// \param 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 \f$nev < ncv \le n\f$,
///             and is advised to take \f$ncv \ge 2\cdot nev\f$.
///
SymEigsSolver(OpType* op, int nev, int ncv) :
SymEigsBase<Scalar, SelectionRule, OpType, IdentityBOp>(op, NULL, nev, ncv)
{}

};