Spectra
Spectra::SymEigsSolver< Scalar, SelectionRule, OpType > Class Template Reference

#include <SymEigsSolver.h>

Inheritance diagram for Spectra::SymEigsSolver< Scalar, SelectionRule, OpType >:
Spectra::SymEigsShiftSolver< Scalar, SelectionRule, OpType >

Public Member Functions

 SymEigsSolver (OpType *op_, int nev_, int ncv_)
 
virtual ~SymEigsSolver ()
 
void init (const Scalar *init_resid)
 
void init ()
 
int compute (int maxit=1000, Scalar tol=1e-10, int sort_rule=LARGEST_ALGE)
 
int info () const
 
int num_iterations () const
 
int num_operations () const
 
Vector eigenvalues () const
 
Matrix eigenvectors (int nvec) const
 
Matrix eigenvectors () const
 

Detailed Description

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseSymMatProd<double>>
class Spectra::SymEigsSolver< Scalar, SelectionRule, 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 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
ScalarThe element type of the matrix. Currently supported types are float, double and long double.
SelectionRuleAn 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.
OpTypeThe name of the matrix operation class. Users could either use the wrapper classes such as DenseSymMatProd and SparseSymMatProd, or define their own that impelemnts all the public member functions as in DenseSymMatProd.

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

#include <Eigen/Core>
#include <SymEigsSolver.h> // Also includes <MatOp/DenseSymMatProd.h>
#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
// Construct eigen solver object, requesting the largest three eigenvalues
// 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 <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;
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;
}

Definition at line 156 of file SymEigsSolver.h.

Constructor & Destructor Documentation

◆ SymEigsSolver()

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseSymMatProd<double>>
Spectra::SymEigsSolver< Scalar, SelectionRule, OpType >::SymEigsSolver ( OpType *  op_,
int  nev_,
int  ncv_ 
)
inline

Constructor to create a solver object.

Parameters
op_Pointer to the matrix operation object, which should implement 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 impelements all the public member functions 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 484 of file SymEigsSolver.h.

◆ ~SymEigsSolver()

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseSymMatProd<double>>
virtual Spectra::SymEigsSolver< Scalar, SelectionRule, OpType >::~SymEigsSolver ( )
inlinevirtual

Virtual destructor

Definition at line 506 of file SymEigsSolver.h.

Member Function Documentation

◆ init() [1/2]

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseSymMatProd<double>>
void Spectra::SymEigsSolver< Scalar, SelectionRule, OpType >::init ( const Scalar *  init_resid)
inline

Initializes the solver by providing an initial residual vector.

Parameters
init_residPointer to the initial residual vector.

Spectra (and also ARPACK) uses an iterative algorithm to find eigenvalues. This function allows the user to provide the initial residual vector.

Definition at line 517 of file SymEigsSolver.h.

◆ init() [2/2]

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseSymMatProd<double>>
void Spectra::SymEigsSolver< Scalar, SelectionRule, OpType >::init ( )
inline

Initializes the solver by providing a random initial residual vector.

This overloaded function generates a random initial residual vector (with a fixed random seed) for the algorithm. Elements in the vector follow independent Uniform(-0.5, 0.5) distribution.

Definition at line 563 of file SymEigsSolver.h.

◆ compute()

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseSymMatProd<double>>
int Spectra::SymEigsSolver< Scalar, SelectionRule, OpType >::compute ( int  maxit = 1000,
Scalar  tol = 1e-10,
int  sort_rule = LARGEST_ALGE 
)
inline

Conducts the major computation procedure.

Parameters
maxitMaximum number of iterations allowed in the algorithm.
tolPrecision parameter for the calculated eigenvalues.
sort_ruleRule to sort the eigenvalues and eigenvectors. Supported values are Spectra::LARGEST_ALGE, Spectra::LARGEST_MAGN, Spectra::SMALLEST_ALGE and Spectra::SMALLEST_MAGN, for example LARGEST_ALGE indicates that largest eigenvalues come first. Note that this argument is only used to sort the final result, and the selection rule (e.g. selecting the largest or smallest eigenvalues in the full spectrum) is specified by the template parameter SelectionRule of SymEigsSolver.
Returns
Number of converged eigenvalues.

Definition at line 588 of file SymEigsSolver.h.

◆ info()

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseSymMatProd<double>>
int Spectra::SymEigsSolver< Scalar, SelectionRule, OpType >::info ( ) const
inline

Returns the status of the computation. The full list of enumeration values can be found in Enumerations.

Definition at line 617 of file SymEigsSolver.h.

◆ num_iterations()

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseSymMatProd<double>>
int Spectra::SymEigsSolver< Scalar, SelectionRule, OpType >::num_iterations ( ) const
inline

Returns the number of iterations used in the computation.

Definition at line 622 of file SymEigsSolver.h.

◆ num_operations()

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseSymMatProd<double>>
int Spectra::SymEigsSolver< Scalar, SelectionRule, OpType >::num_operations ( ) const
inline

Returns the number of matrix operations used in the computation.

Definition at line 627 of file SymEigsSolver.h.

◆ eigenvalues()

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseSymMatProd<double>>
Vector Spectra::SymEigsSolver< Scalar, SelectionRule, OpType >::eigenvalues ( ) const
inline

Returns the converged eigenvalues.

Returns
A vector containing the eigenvalues. Returned vector type will be Eigen::Vector<Scalar, ...>, depending on the template parameter Scalar defined.

Definition at line 636 of file SymEigsSolver.h.

◆ eigenvectors() [1/2]

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseSymMatProd<double>>
Matrix Spectra::SymEigsSolver< Scalar, SelectionRule, OpType >::eigenvectors ( int  nvec) const
inline

Returns the eigenvectors associated with the converged eigenvalues.

Parameters
nvecThe number of eigenvectors to return.
Returns
A matrix containing the eigenvectors. Returned matrix type will be Eigen::Matrix<Scalar, ...>, depending on the template parameter Scalar defined.

Definition at line 666 of file SymEigsSolver.h.

◆ eigenvectors() [2/2]

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseSymMatProd<double>>
Matrix Spectra::SymEigsSolver< Scalar, SelectionRule, OpType >::eigenvectors ( ) const
inline

Returns all converged eigenvectors.

Definition at line 694 of file SymEigsSolver.h.


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