Tapkee
|
#include <arpack_wrapper.hpp>
Public Types | |
typedef LMatrixType::Scalar | Scalar |
typedef LMatrixType::Index | Index |
typedef NumTraits< Scalar >::Real | RealScalar |
typedef Eigen::internal::plain_col_type < LMatrixType, RealScalar > ::type | RealVectorType |
Public Member Functions | |
ArpackGeneralizedSelfAdjointEigenSolver () | |
ArpackGeneralizedSelfAdjointEigenSolver (const LMatrixType &A, const RMatrixType &B, Index nbrEigenvalues, std::string eigs_sigma="LM", int parameters=ComputeEigenvectors, RealScalar tol=0.0) | |
ArpackGeneralizedSelfAdjointEigenSolver (const LMatrixType &A, Index nbrEigenvalues, std::string eigs_sigma="LM", int parameters=ComputeEigenvectors, RealScalar tol=0.0) | |
ArpackGeneralizedSelfAdjointEigenSolver & | compute (const LMatrixType &A, const RMatrixType &B, Index nbrEigenvalues, std::string eigs_sigma="LM", int parameters=ComputeEigenvectors, RealScalar tol=0.0) |
ArpackGeneralizedSelfAdjointEigenSolver & | compute (const LMatrixType &A, Index nbrEigenvalues, std::string eigs_sigma="LM", int parameters=ComputeEigenvectors, RealScalar tol=0.0) |
const Matrix< Scalar, Dynamic, Dynamic > & | eigenvectors () const |
const Matrix< Scalar, Dynamic, 1 > & | eigenvalues () const |
Matrix< Scalar, Dynamic, Dynamic > | operatorSqrt () const |
Matrix< Scalar, Dynamic, Dynamic > | operatorInverseSqrt () const |
ComputationInfo | info () const |
size_t | getNbrConvergedEigenValues () const |
size_t | getNbrIterations () const |
Protected Attributes | |
Matrix< Scalar, Dynamic, Dynamic > | m_eivec |
Matrix< Scalar, Dynamic, 1 > | m_eivalues |
ComputationInfo | m_info |
bool | m_isInitialized |
bool | m_eigenvectorsOk |
size_t | m_nbrConverged |
size_t | m_nbrIterations |
Definition at line 36 of file arpack_wrapper.hpp.
typedef LMatrixType::Index Index |
Definition at line 43 of file arpack_wrapper.hpp.
typedef NumTraits<Scalar>::Real RealScalar |
Real scalar type for MatrixType
.
This is just Scalar
if Scalar is real (e.g., float
or Scalar
), and the type of the real part of Scalar
if Scalar is complex.
Definition at line 51 of file arpack_wrapper.hpp.
typedef Eigen::internal::plain_col_type<LMatrixType, RealScalar>::type RealVectorType |
Type for vector of eigenvalues as returned by eigenvalues().
This is a column vector with entries of type RealScalar. The length of the vector is the size of nbrEigenvalues
.
Definition at line 58 of file arpack_wrapper.hpp.
typedef LMatrixType::Scalar Scalar |
Scalar type for matrices of type MatrixType
.
Definition at line 42 of file arpack_wrapper.hpp.
Default constructor.
The default constructor is for cases in which the user intends to perform decompositions via compute().
Definition at line 66 of file arpack_wrapper.hpp.
ArpackGeneralizedSelfAdjointEigenSolver | ( | const LMatrixType & | A, |
const RMatrixType & | B, | ||
Index | nbrEigenvalues, | ||
std::string | eigs_sigma = "LM" , |
||
int | parameters = ComputeEigenvectors , |
||
RealScalar | tol = 0.0 |
||
) |
Constructor; computes generalized eigenvalues of given matrix with respect to another matrix.
[in] | A | Self-adjoint matrix whose eigenvalues / eigenvectors will computed. By default, the upper triangular part is used, but can be changed through the template parameter. |
[in] | B | Self-adjoint matrix for the generalized eigenvalue problem. |
[in] | nbrEigenvalues | The number of eigenvalues / eigenvectors to compute. Must be less than the size of the input matrix, or an error is returned. |
[in] | eigs_sigma | String containing either "LM", "SM", "LA", or "SA", with respective meanings to find the largest magnitude , smallest magnitude, largest algebraic, or smallest algebraic eigenvalues. Alternatively, this value can contain floating point value in string form, in which case the eigenvalues closest to this value will be found. |
[in] | parameters | Can be ComputeEigenvectors (default) or EigenvaluesOnly. |
[in] | tol | What tolerance to find the eigenvalues to. Default is 0, which means machine precision. |
This constructor calls compute(const MatrixType&, const MatrixType&, Index, string, int, RealScalar) to compute the eigenvalues of the matrix A
with respect to B
. The eigenvectors are computed if parameters
equals ComputeEigenvectors.
Definition at line 93 of file arpack_wrapper.hpp.
ArpackGeneralizedSelfAdjointEigenSolver | ( | const LMatrixType & | A, |
Index | nbrEigenvalues, | ||
std::string | eigs_sigma = "LM" , |
||
int | parameters = ComputeEigenvectors , |
||
RealScalar | tol = 0.0 |
||
) |
Constructor; computes eigenvalues of given matrix.
[in] | A | Self-adjoint matrix whose eigenvalues / eigenvectors will computed. By default, the upper triangular part is used, but can be changed through the template parameter. |
[in] | nbrEigenvalues | The number of eigenvalues / eigenvectors to compute. Must be less than the size of the input matrix, or an error is returned. |
[in] | eigs_sigma | String containing either "LM", "SM", "LA", or "SA", with respective meanings to find the largest magnitude , smallest magnitude, largest algebraic, or smallest algebraic eigenvalues. Alternatively, this value can contain floating point value in string form, in which case the eigenvalues closest to this value will be found. |
[in] | parameters | Can be ComputeEigenvectors (default) or EigenvaluesOnly. |
[in] | tol | What tolerance to find the eigenvalues to. Default is 0, which means machine precision. |
This constructor calls compute(const MatrixType&, Index, string, int, RealScalar) to compute the eigenvalues of the matrix A
. The eigenvectors are computed if parameters
equals ComputeEigenvectors.
Definition at line 123 of file arpack_wrapper.hpp.
ArpackGeneralizedSelfAdjointEigenSolver< LMatrixType, RMatrixType, MatrixOperation, BisSPD > & compute | ( | const LMatrixType & | A, |
const RMatrixType & | B, | ||
Index | nbrEigenvalues, | ||
std::string | eigs_sigma = "LM" , |
||
int | parameters = ComputeEigenvectors , |
||
RealScalar | tol = 0.0 |
||
) |
Computes generalized eigenvalues / eigenvectors of given matrix using the external ARPACK library.
[in] | A | Selfadjoint matrix whose eigendecomposition is to be computed. |
[in] | B | Selfadjoint matrix for generalized eigenvalues. |
[in] | nbrEigenvalues | The number of eigenvalues / eigenvectors to compute. Must be less than the size of the input matrix, or an error is returned. |
[in] | eigs_sigma | String containing either "LM", "SM", "LA", or "SA", with respective meanings to find the largest magnitude , smallest magnitude, largest algebraic, or smallest algebraic eigenvalues. Alternatively, this value can contain floating point value in string form, in which case the eigenvalues closest to this value will be found. |
[in] | parameters | Can be ComputeEigenvectors (default) or EigenvaluesOnly. |
[in] | tol | What tolerance to find the eigenvalues to. Default is 0, which means machine precision. |
*this
This function computes the generalized eigenvalues of A
with respect to B
using ARPACK. The eigenvalues() function can be used to retrieve them. If parameters
equals ComputeEigenvectors, then the eigenvectors are also computed and can be retrieved by calling eigenvectors().
Definition at line 312 of file arpack_wrapper.hpp.
ArpackGeneralizedSelfAdjointEigenSolver< LMatrixType, RMatrixType, MatrixOperation, BisSPD > & compute | ( | const LMatrixType & | A, |
Index | nbrEigenvalues, | ||
std::string | eigs_sigma = "LM" , |
||
int | parameters = ComputeEigenvectors , |
||
RealScalar | tol = 0.0 |
||
) |
Computes eigenvalues / eigenvectors of given matrix using the external ARPACK library.
[in] | A | Selfadjoint matrix whose eigendecomposition is to be computed. |
[in] | nbrEigenvalues | The number of eigenvalues / eigenvectors to compute. Must be less than the size of the input matrix, or an error is returned. |
[in] | eigs_sigma | String containing either "LM", "SM", "LA", or "SA", with respective meanings to find the largest magnitude , smallest magnitude, largest algebraic, or smallest algebraic eigenvalues. Alternatively, this value can contain floating point value in string form, in which case the eigenvalues closest to this value will be found. |
[in] | parameters | Can be ComputeEigenvectors (default) or EigenvaluesOnly. |
[in] | tol | What tolerance to find the eigenvalues to. Default is 0, which means machine precision. |
*this
This function computes the eigenvalues of A
using ARPACK. The eigenvalues() function can be used to retrieve them. If parameters
equals ComputeEigenvectors, then the eigenvectors are also computed and can be retrieved by calling eigenvectors().
Definition at line 302 of file arpack_wrapper.hpp.
const Matrix<Scalar, Dynamic, 1>& eigenvalues | ( | ) | const |
Returns the eigenvalues of given matrix.
The eigenvalues are repeated according to their algebraic multiplicity, so there are as many eigenvalues as rows in the matrix. The eigenvalues are sorted in increasing order.
Definition at line 219 of file arpack_wrapper.hpp.
const Matrix<Scalar, Dynamic, Dynamic>& eigenvectors | ( | ) | const |
Returns the eigenvectors of given matrix.
Column of the returned matrix is an eigenvector corresponding to eigenvalue number
as returned by eigenvalues(). The eigenvectors are normalized to have (Euclidean) norm equal to one. If this object was used to solve the eigenproblem for the selfadjoint matrix
, then the matrix returned by this function is the matrix
in the eigendecomposition
. For the generalized eigenproblem, the matrix returned is the solution of
Definition at line 200 of file arpack_wrapper.hpp.
size_t getNbrConvergedEigenValues | ( | ) | const |
Definition at line 277 of file arpack_wrapper.hpp.
size_t getNbrIterations | ( | ) | const |
Definition at line 282 of file arpack_wrapper.hpp.
ComputationInfo info | ( | ) | const |
Reports whether previous computation was successful.
Success
if computation was succesful, NoConvergence
otherwise. Definition at line 271 of file arpack_wrapper.hpp.
Matrix<Scalar, Dynamic, Dynamic> operatorInverseSqrt | ( | ) | const |
Computes the inverse square root of the matrix.
This function uses the eigendecomposition to compute the inverse square root as
. This is cheaper than first computing the square root with operatorSqrt() and then its inverse with MatrixBase::inverse().
Definition at line 260 of file arpack_wrapper.hpp.
Matrix<Scalar, Dynamic, Dynamic> operatorSqrt | ( | ) | const |
Computes the positive-definite square root of the matrix.
The square root of a positive-definite matrix is the positive-definite matrix whose square equals
. This function uses the eigendecomposition
to compute the square root as
.
Definition at line 239 of file arpack_wrapper.hpp.
|
protected |
Definition at line 293 of file arpack_wrapper.hpp.
|
protected |
Definition at line 290 of file arpack_wrapper.hpp.
|
protected |
Definition at line 289 of file arpack_wrapper.hpp.
|
protected |
Definition at line 291 of file arpack_wrapper.hpp.
|
protected |
Definition at line 292 of file arpack_wrapper.hpp.
|
protected |
Definition at line 295 of file arpack_wrapper.hpp.
|
protected |
Definition at line 296 of file arpack_wrapper.hpp.