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Reference documentation for deal.II version 9.0.0
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Reference documentation for deal.II version 9.0.0
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#include <deal.II/lac/sparse_ilu.h>
Public Types | |
| typedef SparseLUDecomposition< number >::size_type | size_type |
| typedef SparseLUDecomposition< number >::AdditionalData | AdditionalData |
 Public Types inherited from SparseLUDecomposition< number > | |
| typedef SparseMatrix< number >::size_type | size_type |
Public Member Functions | |
| SparseILU ()=default | |
| template<typename somenumber > | |
| void | initialize (const SparseMatrix< somenumber > &matrix, const AdditionalData ¶meters=AdditionalData()) |
| template<typename somenumber > | |
| void | vmult (Vector< somenumber > &dst, const Vector< somenumber > &src) const |
| template<typename somenumber > | |
| void | Tvmult (Vector< somenumber > &dst, const Vector< somenumber > &src) const |
| std::size_t | memory_consumption () const |
| Public Member Functions inherited from SparseLUDecomposition< number > | |
| virtual | ~SparseLUDecomposition ()=0 |
| virtual void | clear () |
| template<typename somenumber > | |
| void | initialize (const SparseMatrix< somenumber > &matrix, const AdditionalData parameters) |
| bool | empty () const |
| size_type | m () const |
| size_type | n () const |
| template<class OutVector , class InVector > | |
| void | vmult_add (OutVector &dst, const InVector &src) const |
| template<class OutVector , class InVector > | |
| void | Tvmult_add (OutVector &dst, const InVector &src) const |
| Public Member Functions inherited from Subscriptor | |
| Subscriptor () | |
| Subscriptor (const Subscriptor &) | |
| Subscriptor (Subscriptor &&) noexcept | |
| virtual | ~Subscriptor () |
| Subscriptor & | operator= (const Subscriptor &) |
| Subscriptor & | operator= (Subscriptor &&) noexcept |
| void | subscribe (const char *identifier=nullptr) const |
| void | unsubscribe (const char *identifier=nullptr) const |
| unsigned int | n_subscriptions () const |
| void | list_subscribers () const |
| template<class Archive > | |
| void | serialize (Archive &ar, const unsigned int version) |
Static Public Member Functions | |
| static ::ExceptionBase & | ExcInvalidStrengthening (double arg1) |
| static ::ExceptionBase & | ExcZeroPivot (size_type arg1) |
| Static Public Member Functions inherited from SparseLUDecomposition< number > | |
| static ::ExceptionBase & | ExcInvalidStrengthening (double arg1) |
| Static Public Member Functions inherited from Subscriptor | |
| static ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
| static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
Additional Inherited Members | |
| Protected Types inherited from SparseMatrix< number > | |
| typedef types::global_dof_index | size_type |
| typedef number | value_type |
| typedef numbers::NumberTraits< number >::real_type | real_type |
| typedef SparseMatrixIterators::Iterator< number, true > | const_iterator |
| typedef SparseMatrixIterators::Iterator< number, false > | iterator |
| Protected Member Functions inherited from SparseLUDecomposition< number > | |
| SparseLUDecomposition () | |
| template<typename somenumber > | |
| void | copy_from (const SparseMatrix< somenumber > &matrix) |
| virtual void | strengthen_diagonal_impl () |
| virtual number | get_strengthen_diagonal (const number rowsum, const size_type row) const |
| void | prebuild_lower_bound () |
| Protected Member Functions inherited from SparseMatrix< number > | |
| void | prepare_add () |
| void | prepare_set () |
| SparseMatrix () | |
| SparseMatrix (const SparseMatrix &) | |
| SparseMatrix (SparseMatrix< number > &&m) noexcept | |
| SparseMatrix (const SparsityPattern &sparsity) | |
| SparseMatrix (const SparsityPattern &sparsity, const IdentityMatrix &id) | |
| virtual | ~SparseMatrix () |
| SparseMatrix< number > & | operator= (const SparseMatrix< number > &) |
| SparseMatrix< number > & | operator= (SparseMatrix< number > &&m) noexcept |
| SparseMatrix< number > & | operator= (const IdentityMatrix &id) |
| SparseMatrix & | operator= (const double d) |
| virtual void | reinit (const SparsityPattern &sparsity) |
| bool | empty () const |
| size_type | m () const |
| size_type | n () const |
| size_type | get_row_length (const size_type row) const |
| std::size_t | n_nonzero_elements () const |
| std::size_t | n_actually_nonzero_elements (const double threshold=0.) const |
| const SparsityPattern & | get_sparsity_pattern () const |
| std::size_t | memory_consumption () const |
| void | compress (::VectorOperation::values) |
| void | set (const size_type i, const size_type j, const number value) |
| template<typename number2 > | |
| void | set (const std::vector< size_type > &indices, const FullMatrix< number2 > &full_matrix, const bool elide_zero_values=false) |
| template<typename number2 > | |
| void | set (const std::vector< size_type > &row_indices, const std::vector< size_type > &col_indices, const FullMatrix< number2 > &full_matrix, const bool elide_zero_values=false) |
| template<typename number2 > | |
| void | set (const size_type row, const std::vector< size_type > &col_indices, const std::vector< number2 > &values, const bool elide_zero_values=false) |
| template<typename number2 > | |
| void | set (const size_type row, const size_type n_cols, const size_type *col_indices, const number2 *values, const bool elide_zero_values=false) |
| void | add (const size_type i, const size_type j, const number value) |
| template<typename number2 > | |
| void | add (const std::vector< size_type > &indices, const FullMatrix< number2 > &full_matrix, const bool elide_zero_values=true) |
| template<typename number2 > | |
| void | add (const std::vector< size_type > &row_indices, const std::vector< size_type > &col_indices, const FullMatrix< number2 > &full_matrix, const bool elide_zero_values=true) |
| template<typename number2 > | |
| void | add (const size_type row, const std::vector< size_type > &col_indices, const std::vector< number2 > &values, const bool elide_zero_values=true) |
| template<typename number2 > | |
| void | add (const size_type row, const size_type n_cols, const size_type *col_indices, const number2 *values, const bool elide_zero_values=true, const bool col_indices_are_sorted=false) |
| SparseMatrix & | operator*= (const number factor) |
| SparseMatrix & | operator/= (const number factor) |
| void | symmetrize () |
| template<typename somenumber > | |
| SparseMatrix< number > & | copy_from (const SparseMatrix< somenumber > &source) |
| template<typename ForwardIterator > | |
| void | copy_from (const ForwardIterator begin, const ForwardIterator end) |
| template<typename somenumber > | |
| void | copy_from (const FullMatrix< somenumber > &matrix) |
| SparseMatrix< number > & | copy_from (const TrilinosWrappers::SparseMatrix &matrix) |
| template<typename somenumber > | |
| void | add (const number factor, const SparseMatrix< somenumber > &matrix) |
| const number & | operator() (const size_type i, const size_type j) const |
| number & | operator() (const size_type i, const size_type j) |
| number | el (const size_type i, const size_type j) const |
| number | diag_element (const size_type i) const |
| number & | diag_element (const size_type i) |
| template<class OutVector , class InVector > | |
| void | vmult (OutVector &dst, const InVector &src) const |
| template<class OutVector , class InVector > | |
| void | Tvmult (OutVector &dst, const InVector &src) const |
| template<class OutVector , class InVector > | |
| void | vmult_add (OutVector &dst, const InVector &src) const |
| template<class OutVector , class InVector > | |
| void | Tvmult_add (OutVector &dst, const InVector &src) const |
| template<typename somenumber > | |
| somenumber | matrix_norm_square (const Vector< somenumber > &v) const |
| template<typename somenumber > | |
| somenumber | matrix_scalar_product (const Vector< somenumber > &u, const Vector< somenumber > &v) const |
| template<typename somenumber > | |
| somenumber | residual (Vector< somenumber > &dst, const Vector< somenumber > &x, const Vector< somenumber > &b) const |
| template<typename numberB , typename numberC > | |
| void | mmult (SparseMatrix< numberC > &C, const SparseMatrix< numberB > &B, const Vector< number > &V=Vector< number >(), const bool rebuild_sparsity_pattern=true) const |
| template<typename numberB , typename numberC > | |
| void | Tmmult (SparseMatrix< numberC > &C, const SparseMatrix< numberB > &B, const Vector< number > &V=Vector< number >(), const bool rebuild_sparsity_pattern=true) const |
| real_type | l1_norm () const |
| real_type | linfty_norm () const |
| real_type | frobenius_norm () const |
| template<typename somenumber > | |
| void | precondition_Jacobi (Vector< somenumber > &dst, const Vector< somenumber > &src, const number omega=1.) const |
| template<typename somenumber > | |
| void | precondition_SSOR (Vector< somenumber > &dst, const Vector< somenumber > &src, const number omega=1., const std::vector< std::size_t > &pos_right_of_diagonal=std::vector< std::size_t >()) const |
| template<typename somenumber > | |
| void | precondition_SOR (Vector< somenumber > &dst, const Vector< somenumber > &src, const number om=1.) const |
| template<typename somenumber > | |
| void | precondition_TSOR (Vector< somenumber > &dst, const Vector< somenumber > &src, const number om=1.) const |
| template<typename somenumber > | |
| void | SSOR (Vector< somenumber > &v, const number omega=1.) const |
| template<typename somenumber > | |
| void | SOR (Vector< somenumber > &v, const number om=1.) const |
| template<typename somenumber > | |
| void | TSOR (Vector< somenumber > &v, const number om=1.) const |
| template<typename somenumber > | |
| void | PSOR (Vector< somenumber > &v, const std::vector< size_type > &permutation, const std::vector< size_type > &inverse_permutation, const number om=1.) const |
| template<typename somenumber > | |
| void | TPSOR (Vector< somenumber > &v, const std::vector< size_type > &permutation, const std::vector< size_type > &inverse_permutation, const number om=1.) const |
| template<typename somenumber > | |
| void | Jacobi_step (Vector< somenumber > &v, const Vector< somenumber > &b, const number om=1.) const |
| template<typename somenumber > | |
| void | SOR_step (Vector< somenumber > &v, const Vector< somenumber > &b, const number om=1.) const |
| template<typename somenumber > | |
| void | TSOR_step (Vector< somenumber > &v, const Vector< somenumber > &b, const number om=1.) const |
| template<typename somenumber > | |
| void | SSOR_step (Vector< somenumber > &v, const Vector< somenumber > &b, const number om=1.) const |
| const_iterator | begin () const |
| iterator | begin () |
| const_iterator | end () const |
| iterator | end () |
| const_iterator | begin (const size_type r) const |
| iterator | begin (const size_type r) |
| const_iterator | end (const size_type r) const |
| iterator | end (const size_type r) |
| template<class StreamType > | |
| void | print (StreamType &out, const bool across=false, const bool diagonal_first=true) const |
| void | print_formatted (std::ostream &out, const unsigned int precision=3, const bool scientific=true, const unsigned int width=0, const char *zero_string=" ", const double denominator=1.) const |
| void | print_pattern (std::ostream &out, const double threshold=0.) const |
| void | block_write (std::ostream &out) const |
| void | block_read (std::istream &in) |
| Protected Member Functions inherited from Subscriptor | |
| Subscriptor () | |
| Subscriptor (const Subscriptor &) | |
| Subscriptor (Subscriptor &&) noexcept | |
| virtual | ~Subscriptor () |
| Subscriptor & | operator= (const Subscriptor &) |
| Subscriptor & | operator= (Subscriptor &&) noexcept |
| void | subscribe (const char *identifier=nullptr) const |
| void | unsubscribe (const char *identifier=nullptr) const |
| unsigned int | n_subscriptions () const |
| void | list_subscribers () const |
| template<class Archive > | |
| void | serialize (Archive &ar, const unsigned int version) |
| Static Protected Member Functions inherited from SparseMatrix< number > | |
| static ::ExceptionBase & | ExcInvalidIndex (int arg1, int arg2) |
| static ::ExceptionBase & | ExcDifferentSparsityPatterns () |
| static ::ExceptionBase & | ExcIteratorRange (int arg1, int arg2) |
| static ::ExceptionBase & | ExcSourceEqualsDestination () |
| Static Protected Member Functions inherited from Subscriptor | |
| static ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
| static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
| Protected Attributes inherited from SparseLUDecomposition< number > | |
| double | strengthen_diagonal |
| std::vector< const size_type * > | prebuilt_lower_bound |
| Related Functions inherited from SparseMatrix< number > | |
| template<typename Number > | |
| void | sum (const SparseMatrix< Number > &local, const MPI_Comm &mpi_communicator, SparseMatrix< Number > &global) |
This class computes an Incomplete LU (ILU) decomposition of a sparse matrix, using either the same sparsity pattern or a different one. By incomplete we mean that unlike the exact decomposition, the incomplete one is also computed using sparse factors, and entries in the decomposition that do not fit into the given sparsity structure are discarded.
The algorithm used by this class is essentially a copy of the algorithm given in the book Y. Saad: "Iterative methods for sparse linear systems", second edition, in section 10.3.2.
Refer to SparseLUDecomposition documentation for suggested usage and state management. This class is used in the step-22 tutorial program.
<float> and <double>; others can be generated in application programs (see the section on Template instantiations in the manual).Definition at line 60 of file sparse_ilu.h.
| typedef SparseLUDecomposition<number>::size_type SparseILU< number >::size_type |
Declare type for container size.
Definition at line 66 of file sparse_ilu.h.
| typedef SparseLUDecomposition<number>::AdditionalData SparseILU< number >::AdditionalData |
Make SparseLUDecomposition::AdditionalData accessible to this class as well.
Definition at line 82 of file sparse_ilu.h.
Constructor. Does nothing.
Call the initialize function before using this object as preconditioner.
| template void SparseILU< number >::initialize< float > | ( | const SparseMatrix< somenumber > & | matrix, |
| const AdditionalData & | parameters = AdditionalData() |
||
| ) |
Perform the incomplete LU factorization of the given matrix.
This function needs to be called before an object of this class is used as preconditioner.
For more details about possible parameters, see the class documentation of SparseLUDecomposition and the documentation of the SparseLUDecomposition::AdditionalData class.
According to the parameters, this function creates a new SparsityPattern or keeps the previous sparsity or takes the sparsity given by the user to data. Then, this function performs the LU decomposition.
After this function is called the preconditioner is ready to be used.
| template void SparseILU< number >::vmult< float > | ( | Vector< somenumber > & | dst, |
| const Vector< somenumber > & | src | ||
| ) | const |
Apply the incomplete decomposition, i.e. do one forward-backward step \(dst=(LU)^{-1}src\).
The initialize() function needs to be called before.
| template void SparseILU< number >::Tvmult< float > | ( | Vector< somenumber > & | dst, |
| const Vector< somenumber > & | src | ||
| ) | const |
Apply the transpose of the incomplete decomposition, i.e. do one forward- backward step \(dst=(LU)^{-T}src\).
The initialize() function needs to be called before.
|
virtual |
Determine an estimate for the memory consumption (in bytes) of this object.
Reimplemented from SparseLUDecomposition< number >.
1.8.14