computation of a few eigenvalues for sparse matrices More...
#include <EigenvalueSolver.hxx>
Inheritance diagram for Seldon::SparseEigenProblem< T, MatStiff, MatMass >:
Public Types | |
| typedef MatMass::value_type | MassValue |
| enum | |
| several available modes to find eigenvalues (Arpack) More... | |
| enum | |
| parts of the spectrum (near from 0, at infinity or around a given value) More... | |
| enum | |
| different sorting strategies | |
| enum | |
| different solvers (Anasazi) More... | |
| enum | |
| orthogonalization managers (Anasazi) | |
| enum | |
| several available modes to find eigenvalues (Arpack) More... | |
| enum | |
| real part, imaginary part or complex solution | |
Public Member Functions | |
| SparseEigenProblem () | |
| default constructor | |
| void | SelectCholeskySolver (int type) |
| sets Cholesky solver to use | |
| void | FactorizeCholeskyMass () |
| computes Cholesky factorisation of M from matrix M | |
| template<class Storage , class Alloc > | |
| void | FactorizeCholeskyMass (double &, Matrix< double, Symmetric, Storage, Alloc > &M) |
| intermediary function | |
| template<class T0 , class T1 , class Prop , class Storage , class Alloc > | |
| void | FactorizeCholeskyMass (T0 &, Matrix< T1, Prop, Storage, Alloc > &M) |
| intermediary function | |
| template<class TransStatus , class T0 > | |
| void | MltCholeskyMass (const TransStatus &transA, Vector< T0 > &X) |
| computes L X or L^T x if M = L L^T | |
| template<class TransStatus , class T0 > | |
| void | SolveCholeskyMass (const TransStatus &transA, Vector< T0 > &X) |
| computes L^-1 X or L^-T x if M = L L^T | |
| template<class TransStatus > | |
| void | MltCholeskyMass (const TransStatus &transA, Vector< complex< double > > &X) |
| computes L X or L^T x if M = L L^T | |
| template<class TransStatus > | |
| void | MltCholeskyMass (const TransStatus &transA, Vector< complex< double > > &X, double &) |
| computes L X or L^T x if M = L L^T | |
| template<class TransStatus > | |
| void | MltCholeskyMass (const TransStatus &transA, Vector< complex< double > > &X, complex< double > &) |
| computes L X or L^T x if M = L L^T | |
| template<class TransStatus > | |
| void | SolveCholeskyMass (const TransStatus &transA, Vector< complex< double > > &X) |
| computes L^-1 X or L^-T x if M = L L^T | |
| template<class TransStatus > | |
| void | SolveCholeskyMass (const TransStatus &transA, Vector< complex< double > > &X, double &) |
| computes L^-1 X or L^-T x if M = L L^T | |
| template<class TransStatus > | |
| void | SolveCholeskyMass (const TransStatus &transA, Vector< complex< double > > &X, complex< double > &) |
| computes L^-1 X or L^-T x if M = L L^T | |
| void | ComputeAndFactorizeStiffnessMatrix (const T &a, const T &b) |
| computes and factorizes a M + b K where M is the mass matrix and K the stiffness matrix | |
| void | ComputeAndFactorizeStiffnessMatrix (const complex< T > &a, const complex< T > &b, bool real_p=true) |
| computes and factorizes matrix (a M + b K) for complex values of a and b | |
| template<class T0 > | |
| void | ComputeAndFactorizeComplexMatrix (const complex< T0 > &a, const complex< T0 > &b, bool real_p=true) |
| intermediary function | |
| void | ComputeAndFactorizeComplexMatrix (const complex< double > &a, const complex< double > &b, bool real_p=true) |
| computes and factorizes matrix (a M + b K) for complex values of a and b | |
| template<class T0 > | |
| void | ComputeSolution (const Vector< T0 > &X, Vector< T0 > &Y) |
| solves (a M + b K) Y = X with stored factorization | |
| template<class TransA , class T0 > | |
| void | ComputeSolution (const TransA &transA, const Vector< T0 > &X, Vector< T0 > &Y) |
| solves (a M + b K) Y = X or transpose system | |
| template<class TransA > | |
| void | ComputeComplexSolution (const TransA &, const Vector< double > &X, Vector< double > &Y) |
| solves (a M + b K) Y = X when a and b are complex | |
| template<class TransA > | |
| void | ComputeComplexSolution (const TransA &, const Vector< complex< double > > &X, Vector< complex< double > > &Y) |
| intermediary function | |
| void | Clear () |
| clears memory used by the object | |
| void | SelectCholeskySolver (int type) |
| void | InitMatrix (MatStiff &) |
| void | InitMatrix (MatStiff &, MatMass &) |
| void | ComputeDiagonalMass () |
| computation of diagonal of mass matrix | |
| void | FactorizeCholeskyMass () |
| template<class Storage > | |
| void | FactorizeCholeskyMass (Matrix< Treal, Symmetric, Storage > &M) |
| intermediary function | |
| template<class T0 , class Prop , class Storage > | |
| void | FactorizeCholeskyMass (Matrix< T0, Prop, Storage > &M) |
| intermediary function | |
| void | MltCholeskyMass (const SeldonTranspose &transA, Vector< Treal > &X) |
| computes L X or L^T x if M = L L^T | |
| void | MltCholeskyMass (const SeldonTranspose &transA, Vector< Tcplx > &X) |
| computes L X or L^T x if M = L L^T | |
| void | SolveCholeskyMass (const SeldonTranspose &transA, Vector< Treal > &X) |
| computes L^-1 X or L^-T x if M = L L^T | |
| void | SolveCholeskyMass (const SeldonTranspose &transA, Vector< Tcplx > &X) |
| computes L^-1 X or L^-T x if M = L L^T | |
| void | MltMass (const Vector< Treal > &X, Vector< Treal > &Y) |
| multiplication by mass matrix | |
| void | MltMass (const Vector< Tcplx > &X, Vector< Tcplx > &Y) |
| multiplication by mass matrix | |
| void | MltMass (const SeldonTranspose &, const Vector< Treal > &X, Vector< Treal > &Y) |
| multiplication by mass matrix | |
| void | MltMass (const SeldonTranspose &, const Vector< Tcplx > &X, Vector< Tcplx > &Y) |
| multiplication by mass matrix | |
| void | MltStiffness (const Vector< Treal > &X, Vector< Treal > &Y) |
| multiplication by stiffness matrix | |
| void | MltStiffness (const Vector< Tcplx > &X, Vector< Tcplx > &Y) |
| multiplication by stiffness matrix | |
| void | MltStiffness (const T &coef_mass, const T &coef_stiff, const Vector< Treal > &X, Vector< Treal > &Y) |
| multiplication by stiffness and mass matrix | |
| void | MltStiffness (const T &coef_mass, const T &coef_stiff, const Vector< Tcplx > &X, Vector< Tcplx > &Y) |
| multiplication by stiffness and mass matrix | |
| void | MltStiffness (const SeldonTranspose &, const Vector< Treal > &X, Vector< Treal > &Y) |
| multiplication by stiffness matrix | |
| void | MltStiffness (const SeldonTranspose &, const Vector< Tcplx > &X, Vector< Tcplx > &Y) |
| multiplication by stiffness matrix | |
| void | ComputeAndFactoRealMatrix (const Treal &, const Treal &a, const Treal &b, int which) |
| computes and factorizes a M + b K where M is the mass matrix and K the stiffness matrix | |
| void | ComputeAndFactoRealMatrix (const Tcplx &, const Treal &a, const Treal &b, int which) |
| computes and factorizes a M + b K where M is the mass matrix and K the stiffness matrix | |
| void | ComputeAndFactorizeStiffnessMatrix (const Treal &a, const Treal &b, int which=EigenProblem_Base< T >::COMPLEX_PART) |
| computes and factorizes a M + b K M is the mass matrix and K the stiffness matrix | |
| void | ComputeAndFactorizeStiffnessMatrix (const Tcplx &a, const Tcplx &b, int which=EigenProblem_Base< T >::COMPLEX_PART) |
| computes and factorizes matrix (a M + b K) for complex values of a and b | |
| void | ComputeSolution (const Vector< Treal > &X, Vector< Treal > &Y) |
| solves (a M + b K) Y = X with stored factorization | |
| void | ComputeSolution (const Vector< Tcplx > &X, Vector< Tcplx > &Y) |
| solves (a M + b K) Y = X with stored factorization | |
| void | ComputeSolution (const SeldonTranspose &transA, const Vector< Treal > &X, Vector< Treal > &Y) |
| solves (a M + b K) Y = X with stored factorization | |
| void | ComputeSolution (const SeldonTranspose &transA, const Vector< Tcplx > &X, Vector< Tcplx > &Y) |
| solves (a M + b K) Y = X or transpose system | |
| void | DistributeEigenvectors (Matrix< T, General, ColMajor > &eigen_vec) |
| changes final eigenvectors if needed | |
| void | Clear () |
| void | Init (int n) |
| initialisation of the size of the eigenvalue problem | |
| void | InitMatrix (MatStiff &, Matrix< double, Symmetric, ArrayRowSymSparse > &) |
| initialization of a generalized eigenvalue problem More... | |
| int | GetComputationalMode () const |
| returns the spectral transformation used for evaluation of eigenvalues | |
| int | GetComputationalMode () const |
| void | SetComputationalMode (int mode) |
| sets the spectral transformation used for evaluation of eigenvalues | |
| void | SetComputationalMode (int mode) |
| 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 | |
| int | GetNbAdditionalEigenvalues () const |
| void | SetNbAdditionalEigenvalues (int n) |
| sets the number of additional eigenvalues | |
| void | SetNbAdditionalEigenvalues (int n) |
| 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 | |
| void | SetCholeskyFactoForMass (bool chol=true) |
| bool | UseCholeskyFactoForMass () const |
| returns true if Cholesky factorisation has to be used for mass matrix | |
| bool | UseCholeskyFactoForMass () const |
| void | SetDiagonalMass (bool diag=true) |
| indicates that the mass matrix is diagonal | |
| void | SetDiagonalMass (bool diag=true) |
| bool | DiagonalMass () const |
| returns true if the mass matrix is diagonal | |
| bool | DiagonalMass () const |
| 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 | |
| void | PrintErrorInit () const |
| 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 | |
| virtual void | FactorizeDiagonalMass ()=0 |
| void | MltInvSqrtDiagonalMass (Vector< T0 > &X) |
| multiplication of X by D^-1/2 | |
| virtual void | MltInvSqrtDiagonalMass (Vector< Treal > &X)=0 |
| virtual void | MltInvSqrtDiagonalMass (Vector< Tcplx > &X)=0 |
| void | MltSqrtDiagonalMass (Vector< T0 > &X) |
| multiplication of X by D^1/2 | |
| virtual void | MltSqrtDiagonalMass (Vector< Treal > &X)=0 |
| virtual void | MltSqrtDiagonalMass (Vector< Tcplx > &X)=0 |
| void | ComputeMassForCholesky () |
| computation of mass matrix | |
| virtual void | ComputeMassForCholesky () |
| void | ComputeMassMatrix () |
| computation of mass matrix M | |
| virtual void | ComputeMassMatrix () |
| void | ComputeStiffnessMatrix () |
| computation of stiffness matrix K | |
| void | ComputeStiffnessMatrix (const T &a, const T &b) |
| computation of matrix a M + b*K | |
| virtual void | ComputeStiffnessMatrix () |
| virtual void | ComputeStiffnessMatrix (const T &a, const T &b) |
| void | MltCholeskyMass (const TransStatus &transA, Vector< T > &X) |
| computation of L X or L^T x if M = L L^T | |
| void | SolveCholeskyMass (const TransStatus &transA, Vector< T > &X) |
| computation of L^-1 X or L^-T x if M = L L^T | |
| AnasaziParam & | GetAnasaziParameters () |
| returns parameters specific to Anasazi | |
| SlepcParam & | GetSlepcParameters () |
| returns parameters specific to Slepc | |
| FeastParam & | GetFeastParameters () |
| returns parameters specific to Feast | |
| virtual void | GetSqrtDiagonal (Vector< T > &)=0 |
Protected Types | |
| typedef ClassComplexType< T >::Tcplx | Complexe |
| typedef ClassComplexType< T >::Tcplx | Tcplx |
| typedef ClassComplexType< T >::Treal | Treal |
Protected Member Functions | |
| int | RetrieveLocalNumbers (MatStiff &K) |
Protected Attributes | |
| SparseDirectSolver< T > | mat_lu |
| LU factorisation of sparse matrix. | |
| SparseDirectSolver< Complexe > | mat_lu_cplx |
| factorisation of complex system | |
| SparseCholeskySolver< double > | chol_facto_mass_matrix |
| Cholesky factorisation of mass matrix if required. | |
| Vector< double > | Xchol_real |
| temporary vectors for Cholesky | |
| Vector< double > | Xchol_imag |
| bool | imag_solution |
| if true, we take imaginary part of (K - sigma M)^-1 | |
| SparseDirectSolver< Treal > | mat_lu_real |
| LU factorisation of sparse matrix. | |
| SparseDirectSolver< Tcplx > | mat_lu_cplx |
| factorisation of complex system | |
| SparseCholeskySolver< Treal > | chol_facto_mass_matrix |
| Cholesky factorisation of mass matrix if required. | |
| Vector< Treal > | Xchol_real |
| temporary vectors for Cholesky | |
| Vector< Treal > | Xchol_imag |
| MatMass * | Mh |
| MatStiff * | Kh |
| bool | distributed |
| int | nloc |
| Vector< int > | local_col_numbers |
| Vector< int > * | ProcSharingRows |
| Vector< Vector< int > > * | SharingRowNumbers |
| int | nodl_scalar_ |
| int | nb_unknowns_scal_ |
| 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 | |
| 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 | |
Detailed Description
template<class T, class MatStiff, class MatMass = Matrix<double, Symmetric, ArrayRowSymSparse>>
class Seldon::SparseEigenProblem< T, MatStiff, MatMass >
computation of a few eigenvalues for sparse matrices
Definition at line 396 of file EigenvalueSolver.hxx.
Member Enumeration Documentation
◆ anonymous enum
|
inherited |
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
|
inherited |
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
|
inherited |
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
|
inherited |
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.
Member Function Documentation
◆ GetImagShiftValue()
|
inherited |
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.
◆ GetShiftValue()
|
inherited |
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.
◆ InitMatrix()
|
inherited |
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.
◆ SetTypeSpectrum() [1/2]
|
inherited |
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.
◆ SetTypeSpectrum() [2/2]
|
inherited |
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.
Member Data Documentation
◆ diagonal_mass
|
protectedinherited |
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.
◆ nb_add_eigenvalues
|
protectedinherited |
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.
◆ use_cholesky
|
protectedinherited |
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.
The documentation for this class was generated from the following files:
- computation/interfaces/eigenvalue/EigenvalueSolver.hxx
- computation/interfaces/eigenvalue/VirtualEigenvalueSolver.hxx
- computation/interfaces/eigenvalue/EigenvalueSolver.cxx
- computation/interfaces/eigenvalue/VirtualEigenvalueSolver.cxx