Base class to solve an eigenvalue problem. More...
#include <EigenvalueSolver.hxx>
Public Types | |
| enum | { REGULAR_MODE, SHIFTED_MODE, IMAG_SHIFTED_MODE, INVERT_MODE, BUCKLING_MODE, CAYLEY_MODE } |
| several available modes to find eigenvalues (Arpack) More... | |
| enum | { SMALL_EIGENVALUES, LARGE_EIGENVALUES, CENTERED_EIGENVALUES } |
| parts of the spectrum (near from 0, at infinity or around a given value) More... | |
| enum | { SORTED_REAL, SORTED_IMAG, SORTED_MODULUS } |
| different sorting strategies | |
| enum | { SOLVER_LOBPCG, SOLVER_BKS, SOLVER_BD } |
| different solvers (Anasazi) More... | |
| enum | { ORTHO_DGKS, ORTHO_SVQB } |
| orthogonalization managers (Anasazi) | |
| enum | { REGULAR_MODE, SHIFTED_MODE, IMAG_SHIFTED_MODE, INVERT_MODE, BUCKLING_MODE, CAYLEY_MODE } |
| several available modes to find eigenvalues (Arpack) More... | |
| enum | { REAL_PART, IMAG_PART, COMPLEX_PART } |
| real part, imaginary part or complex solution | |
| typedef MatMass::value_type | MassValue |
| type for number stored in mass matrix | |
Public Member Functions | |
| EigenProblem_Base () | |
| default constructor | |
| void | Init (int n) |
| initialisation of the size of the eigenvalue problem | |
| void | InitMatrix (MatStiff &) |
| initialization of a standard eigenvalue problem More... | |
| void | InitMatrix (MatStiff &, MatMass &) |
| initialization of a generalized eigenvalue problem More... | |
| int | GetComputationalMode () const |
| returns the spectral transformation used for evaluation of eigenvalues | |
| void | SetComputationalMode (int mode) |
| sets the spectral transformation used for evaluation of eigenvalues | |
| int | GetNbAskedEigenvalues () const |
| returns the number of eigenvalues asked by the user | |
| void | SetNbAskedEigenvalues (int n) |
| sets the number of eigenvalues to compute | |
| int | GetNbAdditionalEigenvalues () const |
| returns the additional number of eigenvalues | |
| void | SetNbAdditionalEigenvalues (int n) |
| sets the number of additional eigenvalues | |
| int | GetNbBlocks () const |
| returns the number of blocks used in blocked solvers | |
| void | SetNbBlocks (int) |
| returns the number of blocks used in blocked solvers | |
| int | GetNbMaximumRestarts () const |
| returns the restart parameter used in blocked solvers | |
| void | SetNbMaximumRestarts (int) |
| sets the restart parameter used in blocked solvers | |
| int | GetOrthoManager () const |
| returns orthogonalization manager set in Anasazi | |
| int | GetEigensolverType () const |
| returns the solver used in Anasazi | |
| void | SetEigensolverType (int type) |
| sets the solver used in Anasazi | |
| int | GetTypeSpectrum () const |
| returns the spectrum desired (large, small eigenvalues, etc) | |
| int | GetTypeSorting () const |
| returns how eigenvalues are sorted (real, imaginary part or modulus) | |
| T | GetShiftValue () const |
| returns the shift value used More... | |
| T | GetImagShiftValue () const |
| returns the imaginary part of shift value used More... | |
| void | SetShiftValue (const T &) |
| Sets the real part of shift value. | |
| void | SetImagShiftValue (const T &) |
| Sets the imaginary part of shift value. | |
| void | SetTypeSpectrum (int type, const T &val, int type_sort=SORTED_MODULUS) |
| sets which eigenvalues are searched More... | |
| void | SetTypeSpectrum (int type, const complex< T > &val, int type_sort=SORTED_MODULUS) |
| sets which eigenvalues are searched More... | |
| double | GetLowerBoundInterval () const |
| returns lower bound of the interval where eigenvalues are searched | |
| double | GetUpperBoundInterval () const |
| returns upper bound of the interval where eigenvalues are searched | |
| void | SetIntervalSpectrum (double, double) |
| sets the interval where eigenvalues are searched | |
| void | SetCholeskyFactoForMass (bool chol=true) |
| indicates the use of Cholesky factorisation in order to solve a standard eigenvalue problem instead of a generalized one | |
| bool | UseCholeskyFactoForMass () const |
| returns true if Cholesky factorisation has to be used for mass matrix | |
| void | SetDiagonalMass (bool diag=true) |
| indicates that the mass matrix is diagonal | |
| bool | DiagonalMass () const |
| returns true if the mass matrix is diagonal | |
| void | SetStoppingCriterion (double eps) |
| modifies the stopping critertion | |
| double | GetStoppingCriterion () const |
| returns the stopping criterion | |
| void | SetNbMaximumIterations (int n) |
| sets the maximal number of iterations allowed for the iterative algorithm | |
| int | GetNbMaximumIterations () const |
| returns the maximal number of iterations allowed for the iterative algorithm | |
| int | GetNbMatrixVectorProducts () const |
| returns the number of matrix-vector products performed since last call to Init | |
| int | GetNbArnoldiVectors () const |
| returns the number of Arnoldi vectors to use | |
| void | SetNbArnoldiVectors (int n) |
| sets the number of Arnoldi vectors to use | |
| int | GetM () const |
| returns number of rows | |
| int | GetN () const |
| returns number of columns | |
| int | GetPrintLevel () const |
| returns level of verbosity | |
| void | SetPrintLevel (int lvl) |
| sets the level of verbosity | |
| void | IncrementProdMatVect () |
| increment of the number of matrix vector products | |
| void | PrintErrorInit () const |
| prints error of initialization and aborts program | |
| bool | IsSymmetricProblem () const |
| returns true if the matrix is symmetric | |
| bool | IsHermitianProblem () const |
| returns true if the matrix is hermitian | |
| void | FactorizeDiagonalMass () |
| computation of D^1/2 from D | |
| template<class T0 > | |
| void | MltInvSqrtDiagonalMass (Vector< T0 > &X) |
| multiplication of X by D^-1/2 | |
| template<class T0 > | |
| void | MltSqrtDiagonalMass (Vector< T0 > &X) |
| multiplication of X by D^1/2 | |
| void | ComputeDiagonalMass () |
| computation of diagonal of mass matrix | |
| void | ComputeMassForCholesky () |
| computation of mass matrix | |
| void | ComputeMassMatrix () |
| computation of mass matrix M | |
| void | MltMass (const Vector< T > &X, Vector< T > &Y) |
| matrix vector product with mass matrix Y = M X | |
| void | ComputeStiffnessMatrix () |
| computation of stiffness matrix K | |
| void | ComputeStiffnessMatrix (const T &a, const T &b) |
| computation of matrix a M + b*K | |
| void | MltStiffness (const Vector< T > &X, Vector< T > &Y) |
| matrix vector product with stifness matrix Y = K X | |
| void | MltStiffness (const T &a, const T &b, const Vector< T > &X, Vector< T > &Y) |
| matrix vector product with stifness and mass matrix Y = (a M + b K) X | |
| void | ComputeAndFactorizeStiffnessMatrix (const T &a, const T &b) |
| computation of matrix a M + b K and factorisation of this matrix More... | |
| void | ComputeAndFactorizeStiffnessMatrix (const complex< T > &a, const complex< T > &b, bool real_p=true) |
| computation of matrix a M + b K and factorisation of this matrix More... | |
| template<class T0 > | |
| void | ComputeSolution (const Vector< T0 > &X, Vector< T0 > &Y) |
| solving the linear system (a M + b K) Y = X | |
| template<class TransA , class T0 > | |
| void | ComputeSolution (const TransA &transA, const Vector< T0 > &X, Vector< T0 > &Y) |
| solving the linear system (a M + b K) Y = X | |
| void | FactorizeCholeskyMass () |
| computation of Cholesky factorisation of M from matrix M | |
| template<class TransStatus > | |
| void | MltCholeskyMass (const TransStatus &transA, Vector< T > &X) |
| computation of L X or L^T x if M = L L^T | |
| template<class TransStatus > | |
| void | SolveCholeskyMass (const TransStatus &transA, Vector< T > &X) |
| computation of L^-1 X or L^-T x if M = L L^T | |
| void | Clear () |
| memory release | |
| int | GetComputationalMode () const |
| void | SetComputationalMode (int mode) |
| int | GetNbAdditionalEigenvalues () const |
| void | SetNbAdditionalEigenvalues (int n) |
| AnasaziParam & | GetAnasaziParameters () |
| returns parameters specific to Anasazi | |
| SlepcParam & | GetSlepcParameters () |
| returns parameters specific to Slepc | |
| FeastParam & | GetFeastParameters () |
| returns parameters specific to Feast | |
| void | SetCholeskyFactoForMass (bool chol=true) |
| bool | UseCholeskyFactoForMass () const |
| void | SetDiagonalMass (bool diag=true) |
| bool | DiagonalMass () const |
| void | PrintErrorInit () const |
| virtual void | ComputeDiagonalMass ()=0 |
| virtual void | FactorizeDiagonalMass ()=0 |
| virtual void | GetSqrtDiagonal (Vector< T > &)=0 |
| virtual void | MltInvSqrtDiagonalMass (Vector< Treal > &X)=0 |
| virtual void | MltSqrtDiagonalMass (Vector< Treal > &X)=0 |
| virtual void | MltInvSqrtDiagonalMass (Vector< Tcplx > &X)=0 |
| virtual void | MltSqrtDiagonalMass (Vector< Tcplx > &X)=0 |
| virtual void | ComputeMassForCholesky () |
| virtual void | ComputeMassMatrix () |
| virtual void | MltMass (const Vector< Treal > &X, Vector< Treal > &Y)=0 |
| virtual void | MltMass (const Vector< Tcplx > &X, Vector< Tcplx > &Y)=0 |
| virtual void | MltMass (const SeldonTranspose &, const Vector< Treal > &X, Vector< Treal > &Y)=0 |
| virtual void | MltMass (const SeldonTranspose &, const Vector< Tcplx > &X, Vector< Tcplx > &Y)=0 |
| virtual void | ComputeStiffnessMatrix () |
| virtual void | ComputeStiffnessMatrix (const T &a, const T &b) |
| virtual void | MltStiffness (const Vector< Treal > &X, Vector< Treal > &Y)=0 |
| virtual void | MltStiffness (const Vector< Tcplx > &X, Vector< Tcplx > &Y)=0 |
| virtual void | MltStiffness (const T &a, const T &b, const Vector< Treal > &X, Vector< Treal > &Y)=0 |
| virtual void | MltStiffness (const T &a, const T &b, const Vector< Tcplx > &X, Vector< Tcplx > &Y)=0 |
| virtual void | MltStiffness (const SeldonTranspose &, const Vector< Treal > &X, Vector< Treal > &Y)=0 |
| virtual void | MltStiffness (const SeldonTranspose &, const Vector< Tcplx > &X, Vector< Tcplx > &Y)=0 |
| virtual void | ComputeAndFactorizeStiffnessMatrix (const Treal &a, const Treal &b, int real_p=COMPLEX_PART) |
| computation of matrix a M + b K and factorisation of this matrix More... | |
| virtual void | ComputeAndFactorizeStiffnessMatrix (const Tcplx &a, const Tcplx &b, int real_p=COMPLEX_PART) |
| computation of matrix a M + b K and factorisation of this matrix More... | |
| virtual void | ComputeSolution (const Vector< Treal > &X, Vector< Treal > &Y) |
| solving the linear system (a M + b K) Y = X | |
| virtual void | ComputeSolution (const Vector< Tcplx > &X, Vector< Tcplx > &Y) |
| solving the linear system (a M + b K) Y = X | |
| virtual void | ComputeSolution (const SeldonTranspose &, const Vector< Treal > &X, Vector< Treal > &Y) |
| solving the linear system (a M + b K) Y = X | |
| virtual void | ComputeSolution (const SeldonTranspose &, const Vector< Tcplx > &X, Vector< Tcplx > &Y) |
| solving the linear system (a M + b K) Y = X | |
| virtual void | FactorizeCholeskyMass () |
| virtual void | MltCholeskyMass (const SeldonTranspose &transA, Vector< Treal > &X) |
| computation of L X or L^T x if M = L L^T | |
| virtual void | MltCholeskyMass (const SeldonTranspose &transA, Vector< Tcplx > &X) |
| computation of L X or L^T x if M = L L^T | |
| virtual void | SolveCholeskyMass (const SeldonTranspose &transA, Vector< Treal > &X) |
| computation of L^-1 X or L^-T x if M = L L^T | |
| virtual void | SolveCholeskyMass (const SeldonTranspose &transA, Vector< Tcplx > &X) |
| computation of L^-1 X or L^-T x if M = L L^T | |
| virtual void | Clear () |
Protected Types | |
| typedef ClassComplexType< T >::Tcplx | Tcplx |
| typedef ClassComplexType< T >::Treal | Treal |
Protected Attributes | |
| int | eigenvalue_computation_mode |
| mode used to find eigenvalues (regular, shifted, Cayley, etc) | |
| int | nb_eigenvalues_wanted |
| number of eigenvalues to be computed | |
| int | nb_add_eigenvalues |
| additional number of eigenvalues More... | |
| int | type_spectrum_wanted |
| which spectrum ? Near from Zero ? Near from Infinity ? or near from a value ? | |
| int | type_sort_eigenvalues |
| large eigenvalues because of their real part, imaginary part or magnitude ? | |
| bool | use_cholesky |
| if true, the generalized problem is reduced to a standard problem More... | |
| bool | diagonal_mass |
| if true, the generalized problem is reduced to a standard problem More... | |
| double | stopping_criterion |
| threshold for Arpack's iterative process | |
| int | nb_maximum_iterations |
| Maximal number of iterations. | |
| int | nb_prod |
| number of matrix-vector products | |
| int | n_ |
| size of the problem | |
| T | shift |
| shift sigma (if type_spectrum = centered_eigenvalues) | |
| T | shift_imag |
| int | nb_arnoldi_vectors |
| number of Arnoldi vectors | |
| bool | automatic_selection_arnoldi_vectors |
| if true nb_arnoldi_vectors is automatically computed | |
| int | print_level |
| print level | |
| Vector< MassValue > | sqrt_diagonal_mass |
| diagonal D^1/2 if the mass matrix is diagonal positive | |
| bool | complex_system |
| if true consider Real( (a M + bK)^-1) or Imag( (a M + b K)^-1 ) or the whole system, a and/or b being complex | |
| MatMass * | Mh |
| mass matrix | |
| MatStiff * | Kh |
| stiffness matrix | |
| int | type_solver |
| which solver ? | |
| int | ortho_manager |
| orthogonalization manager | |
| int | nb_blocks |
| number of blocks for blocked solvers | |
| int | restart_number |
| restart parameter for blocked solvers | |
| double | emin_interval |
| interval where eigenvalues are searched | |
| double | emax_interval |
| int | selected_part |
| AnasaziParam | anasazi_param |
| additional parameters for Anasazi | |
| SlepcParam | slepc_param |
| additional parameters for Slepc | |
| FeastParam | feast_param |
| additional parameters for Feast | |
Friends | |
| template<class EigenPb , class Vector1 , class Matrix1 , class T0 > | |
| void | ApplyScalingEigenvec (EigenPb &var, Vector1 &eigen_values, Vector1 &lambda_imag, Matrix1 &eigen_vectors, const T0 &shiftr, const T0 &shifti) |
| modification of eigenvectors to take into account scaling by mass matrix More... | |
| template<class EigenPb , class Vector1 , class Matrix1 , class T0 > | |
| void | ApplyScalingEigenvec (EigenPb &var, Vector1 &eigen_values, Vector1 &lambda_imag, Matrix1 &eigen_vectors, const complex< T0 > &shiftr, const complex< T0 > &shifti) |
| modification of eigenvectors to take into account scaling by mass matrix More... | |
| template<class T0 , class Prop , class Storage > | |
| void | ApplyScalingEigenvec (EigenProblem_Base< T0 > &var, Vector< T0 > &eigen_values, Vector< T0 > &lambda_imag, Matrix< T0, Prop, Storage > &eigen_vectors, const T0 &shiftr, const T0 &shifti) |
| modification of eigenvectors to take into account scaling by mass matrix More... | |
| template<class T0 , class Prop , class Storage > | |
| void | ApplyScalingEigenvec (EigenProblem_Base< complex< T0 > > &var, Vector< complex< T0 > > &eigen_values, Vector< complex< T0 > > &lambda_imag, Matrix< complex< T0 >, Prop, Storage > &eigen_vectors, const complex< T0 > &shiftr, const complex< T0 > &shifti) |
| modification of eigenvectors to take into account scaling by mass matrix More... | |
Base class to solve an eigenvalue problem.
Base class to solve a linear eigenvalue problem.
Resolution of a standard eigenvalue problem : K x = lambda x or a generalized eigenvalue problem K x = lambda M x M is called mass matrix, K stiffness matrix, lambda is the eigenvalue and x the eigenvector.
This class should not be instantiated directly, but rather derived classes like DenseEigenProblem, SparseEigenProblem, MatrixFreeEigenProblem.
Solution of a standard eigenvalue problem : K x = lambda x or a generalized eigenvalue problem K x = lambda M x M is called mass matrix, K stiffness matrix, lambda is the eigenvalue and x the eigenvector.
This class should not be instantiated directly, but rather derived classes like DenseEigenProblem, SparseEigenProblem, VirtualEigenProblem.
Definition at line 18 of file EigenvalueSolver.hxx.
| anonymous enum |
several available modes to find eigenvalues (Arpack)
REGULAR_MODE : Regular mode standard problem => no linear system to solve generalized problem => M^-1 K x = lambda x (inverse of M required) SHIFTED_MODE : Shifted mode standard problem => (K - sigma I)^-1 X = lambda X generalized problem => (K - sigma M)^-1 M X = lambda X BUCKLING_MODE : Buckling mode (real symmetric problem) generalized problem => (K - sigma M)^-1 K X = lambda X CAYLEY_MODE : Cayley mode (real symmetric problem) generalized problem => (K - sigma M)^-1 (K + sigma M) X = lambda X INVERT_MODE : Shifted mode on matrix M^-1 K
IMAG_SHIFTED_MODE : using Imag( (K - sigma M)^-1 M) instead of Real( (K - sigma M)^-1 M) mode 4 in Arpack (dnaupd.f)
Definition at line 441 of file VirtualEigenvalueSolver.hxx.
| anonymous enum |
several available modes to find eigenvalues (Arpack)
REGULAR_MODE : Regular mode standard problem => no linear system to solve generalized problem => M^-1 K x = lambda x (inverse of M required) SHIFTED_MODE : Shifted mode standard problem => (K - sigma I)^-1 X = lambda X generalized problem => (K - sigma M)^-1 M X = lambda X BUCKLING_MODE : Buckling mode (real symmetric problem) generalized problem => (K - sigma M)^-1 K X = lambda X CAYLEY_MODE : Cayley mode (real symmetric problem) generalized problem => (K - sigma M)^-1 (K + sigma M) X = lambda X INVERT_MODE : Shifted mode on matrix M^-1 K
IMAG_SHIFTED_MODE : using Imag( (K - sigma M)^-1 M) instead of Real( (K - sigma M)^-1 M) mode 4 in Arpack (dnaupd.f)
Definition at line 38 of file EigenvalueSolver.hxx.
| anonymous enum |
parts of the spectrum (near from 0, at infinity or around a given value)
SMALL_EIGENVALUES : seeking eigenvalues near 0 LARGE_EIGENVALUES : seeking largest eigenvalues CENTERED_EIGENVALUES : seeking eigenvalues near the shift sigma
Definition at line 47 of file EigenvalueSolver.hxx.
| anonymous enum |
different solvers (Anasazi)
SOLVER_LOBPCG : Locally Optimal Block Preconditioned Conjugate Gradient SOLVER_BKS : Block Krylov Schur SOLVER_BD : Block Davidson
Definition at line 58 of file EigenvalueSolver.hxx.
| void Seldon::EigenProblem_Base< T, MatStiff, MatMass >::ComputeAndFactorizeStiffnessMatrix | ( | const complex< T > & | a, |
| const complex< T > & | b, | ||
| bool | real_part = true |
||
| ) |
computation of matrix a M + b K and factorisation of this matrix
The factorisation process can be also the construction of preconditioning if an iterative solver is used to solve linear system (a M + b K) y = x
Definition at line 771 of file EigenvalueSolver.cxx.
| void Seldon::EigenProblem_Base< T, MatStiff, MatMass >::ComputeAndFactorizeStiffnessMatrix | ( | const T & | a, |
| const T & | b | ||
| ) |
computation of matrix a M + b K and factorisation of this matrix
The factorisation process can be also the construction of preconditioning if an iterative solver is used to solve linear system (a M + b K) y = x
Definition at line 758 of file EigenvalueSolver.cxx.
|
virtual |
computation of matrix a M + b K and factorisation of this matrix
The factorisation process can be also the construction of preconditioning if an iterative solver is used to solve linear system (a M + b K) y = x
Reimplemented in Seldon::DenseEigenProblem< T, Prop, Storage, Tmass, PropM, StorageM >, and Seldon::SparseEigenProblem< T, MatStiff, MatMass >.
Definition at line 941 of file VirtualEigenvalueSolver.cxx.
|
virtual |
computation of matrix a M + b K and factorisation of this matrix
The factorisation process can be also the construction of preconditioning if an iterative solver is used to solve linear system (a M + b K) y = x
Reimplemented in Seldon::DenseEigenProblem< T, Prop, Storage, Tmass, PropM, StorageM >, and Seldon::SparseEigenProblem< T, MatStiff, MatMass >.
Definition at line 927 of file VirtualEigenvalueSolver.cxx.
| T Seldon::EigenProblem_Base< T, MatStiff, MatMass >::GetImagShiftValue |
returns the imaginary part of shift value used
If type_spectrum_wanted is set to CENTERED_EIGENVALUES, we search closest eigenvalues to the shift value. Matrix (A - (shift + i shift_imag)*I)^{-1} will be used instead of A shift_imag is accessed only for real unsymmetric problems
Definition at line 288 of file EigenvalueSolver.cxx.
| T Seldon::EigenProblem_Base< T, MatStiff, MatMass >::GetShiftValue |
returns the shift value used
If type_spectrum_wanted is set to CENTERED_EIGENVALUES, we search closest eigenvalues to the shift value. Matrix (A - (shift + i shift_imag)*I)^{-1} will be used instead of A
Definition at line 274 of file EigenvalueSolver.cxx.
| void Seldon::EigenProblem_Base< T, MatStiff, MatMass >::InitMatrix | ( | MatStiff & | K | ) |
initialization of a standard eigenvalue problem
Stiffness matrix K is given in argument. we will search (lambda, x) such as K x = lambda x
Definition at line 93 of file EigenvalueSolver.cxx.
| void Seldon::EigenProblem_Base< T, MatStiff, MatMass >::InitMatrix | ( | MatStiff & | K, |
| MatMass & | M | ||
| ) |
initialization of a generalized eigenvalue problem
Mass matrix M and stiffness matrix K are given in argument we will search (lambda, x) such as K x = lambda M x
Definition at line 117 of file EigenvalueSolver.cxx.
| void Seldon::EigenProblem_Base< T, MatStiff, MatMass >::SetTypeSpectrum | ( | int | type, |
| const complex< T > & | val, | ||
| int | type_sort = SORTED_MODULUS |
||
| ) |
sets which eigenvalues are searched
You can ask small eigenvalues, large, or eigenvalues close to the shift.
Definition at line 332 of file EigenvalueSolver.cxx.
| void Seldon::EigenProblem_Base< T, MatStiff, MatMass >::SetTypeSpectrum | ( | int | type, |
| const T & | val, | ||
| int | type_sort = SORTED_MODULUS |
||
| ) |
sets which eigenvalues are searched
You can ask small eigenvalues, large, or eigenvalues close to the shift.
Definition at line 317 of file EigenvalueSolver.cxx.
|
friend |
modification of eigenvectors to take into account scaling by mass matrix
One may desire to use matrix D^-1/2 K D^-1/2 or L^-1 K L^-T instead of K in order to solve a standard eigenvalue problem instead of a generalized one. => eigenvectors are recovered by multiplying them by matrix D^1/2 or by L^T with this function
Definition at line 983 of file EigenvalueSolver.cxx.
|
friend |
modification of eigenvectors to take into account scaling by mass matrix
One may desire to use matrix D^-1/2 K D^-1/2 or L^-1 K L^-T instead of K in order to solve a standard eigenvalue problem instead of a generalized one. => eigenvectors are recovered by multiplying them by matrix D^1/2 or by L^T with this function
Definition at line 846 of file EigenvalueSolver.cxx.
|
friend |
modification of eigenvectors to take into account scaling by mass matrix
One may desire to use matrix D^-1/2 K D^-1/2 or L^-1 K L^-T instead of K in order to solve a standard eigenvalue problem instead of a generalized one. => eigenvectors are recovered by multiplying them by matrix D^1/2 or by L^T with this function
Definition at line 1618 of file VirtualEigenvalueSolver.cxx.
|
friend |
modification of eigenvectors to take into account scaling by mass matrix
One may desire to use matrix D^-1/2 K D^-1/2 or L^-1 K L^-T instead of K in order to solve a standard eigenvalue problem instead of a generalized one. => eigenvectors are recovered by multiplying them by matrix D^1/2 or by L^T with this function
Definition at line 1468 of file VirtualEigenvalueSolver.cxx.
|
protected |
if true, the generalized problem is reduced to a standard problem
if M is diagonal, one can seek eigenvalues of the standard problem M^-1/2 K M^-1/2 x = lambda x
Definition at line 98 of file EigenvalueSolver.hxx.
|
protected |
additional number of eigenvalues
Sometimes Arpack finds more converged eigenvalues than asked it is needed to store these eigenvalues and eigenvalues to avoid segmentation fault
Definition at line 77 of file EigenvalueSolver.hxx.
|
protected |
if true, the generalized problem is reduced to a standard problem
If matrix M is symmetric definite positive, one may compute Cholesky factorisation of M = L L^T, and find eigenvalues of the standard problem : L^-1 K L^-T x = lambda x
Definition at line 91 of file EigenvalueSolver.hxx.