#include <GenEigsSolver.h>

Inheritance diagram for GenEigsSolver< Scalar, SelectionRule, OpType >:

Public Member Functions
	GenEigsSolver (OpType *op_, int nev_, int ncv_)

void	init (Scalar *init_resid)

void	init ()

int	compute (int maxit=1000, Scalar tol=1e-10)

int	num_iterations ()

int	num_operations ()

ComplexVector	eigenvalues ()

ComplexMatrix	eigenvectors (int nvec)

ComplexMatrix	eigenvectors ()

Detailed Description

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseGenMatProd<double>>
class GenEigsSolver< Scalar, SelectionRule, OpType >

This class implements the eigen solver for general real matrices.

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

Scalar	The element type of the matrix. Currently supported types are `float` and `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 SelectionRule.h .
OpType	The name of the matrix operation class. Users could either use the DenseGenMatProd wrapper class, or define their own that impelemnts all the public member functions as in DenseGenMatProd.

An example that illustrates the usage of GenEigsSolver is give below:

#include <armadillo>
#include <GenEigsSolver.h>  // Also includes <MatOp/DenseGenMatProd.h>
int main()
{
    // We are going to calculate the eigenvalues of M
    arma::mat M = arma::randu(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< double, LARGEST_MAGN, DenseGenMatProd<double> > eigs(&op, 3, 6);
    // Initialize and compute
    eigs.init();
    int nconv = eigs.compute();
    // Retrieve results
    arma::cx_vec evalues;
    if(nconv > 0)
        evalues = eigs.eigenvalues();
    evalues.print("Eigenvalues found:");
    return 0;
}

Definition at line 83 of file GenEigsSolver.h.

Constructor & Destructor Documentation

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseGenMatProd<double>>

GenEigsSolver< Scalar, SelectionRule, OpType >::GenEigsSolver	(	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 \(Ay\) for any vector \(y\). Users could either create the object from the DenseGenMatProd wrapper class, or define their own that impelemnts all the public member functions 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 173 of file GenEigsSolver.h.

Member Function Documentation

template<typename Scalar , int SelectionRule, typename OpType >

void GenEigsSolver< Scalar, SelectionRule, OpType >::init ( Scalar * init_resid )

inline

Providing the initial residual vector for the algorithm.

Parameters

init_resid Pointer to the initial residual vector.

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

Definition at line 247 of file GenEigsSolver_Impl.h.

template<typename Scalar , int SelectionRule, typename OpType >

void GenEigsSolver< Scalar, SelectionRule, OpType >::init ( )

inline

Providing a random initial residual vector.

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

Definition at line 280 of file GenEigsSolver_Impl.h.

template<typename Scalar , int SelectionRule, typename OpType >

int GenEigsSolver< Scalar, SelectionRule, OpType >::compute	(	int	maxit = `1000`,
		Scalar	tol = `1e-10`
	)

inline

Conducting the major computation procedure.

Parameters

maxit	Maximum number of iterations allowed in the algorithm.
tol	Precision parameter for the calculated eigenvalues.

Returns: Number of converged eigenvalues.

Definition at line 291 of file GenEigsSolver_Impl.h.

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseGenMatProd<double>>

int GenEigsSolver< Scalar, SelectionRule, OpType >::num_iterations ( )

inline

Returning the number of iterations used in the computation.

Definition at line 222 of file GenEigsSolver.h.

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseGenMatProd<double>>

int GenEigsSolver< Scalar, SelectionRule, OpType >::num_operations ( )

inline

Returning the number of matrix operations used in the computation.

Definition at line 227 of file GenEigsSolver.h.

template<typename Scalar , int SelectionRule, typename OpType >

GenEigsSolver< Scalar, SelectionRule, OpType >::ComplexVector GenEigsSolver< Scalar, SelectionRule, OpType >::eigenvalues ( )

inline

Returning the converged eigenvalues.

Returns: A complex-valued vector containing the eigenvalues. Returned vector type will be arma::cx_vec or arma::cx_fvec, depending on the template parameter Scalar defined.

Definition at line 319 of file GenEigsSolver_Impl.h.

template<typename Scalar , int SelectionRule, typename OpType >

GenEigsSolver< Scalar, SelectionRule, OpType >::ComplexMatrix GenEigsSolver< Scalar, SelectionRule, OpType >::eigenvectors ( int nvec )

inline

Returning the eigenvectors associated with the converged eigenvalues.

Parameters

nvec	The number of eigenvectors to return.

Returns: A complex-valued matrix containing the eigenvectors. Returned matrix type will be arma::cx_mat or arma::cx_fmat, depending on the template parameter Scalar defined.

Definition at line 344 of file GenEigsSolver_Impl.h.

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseGenMatProd<double>>

ComplexMatrix GenEigsSolver< Scalar, SelectionRule, OpType >::eigenvectors ( )

inline

Returning all converged eigenvectors.

Definition at line 251 of file GenEigsSolver.h.

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

Public Member Functions

Detailed Description

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseGenMatProd<double>> class GenEigsSolver< Scalar, SelectionRule, OpType >

Constructor & Destructor Documentation

Member Function Documentation

template<typename Scalar = double, int SelectionRule = LARGEST_MAGN, typename OpType = DenseGenMatProd<double>>
class GenEigsSolver< Scalar, SelectionRule, OpType >