Reference documentation for deal.II version 9.0.0
|
#include <deal.II/lac/sparse_mic.h>
Public Types | |
typedef types::global_dof_index | size_type |
typedef SparseLUDecomposition< number >::AdditionalData | AdditionalData |
Public Types inherited from SparseLUDecomposition< number > | |
typedef SparseMatrix< number >::size_type | size_type |
Public Member Functions | |
SparseMIC () | |
virtual | ~SparseMIC () |
virtual void | clear () |
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 |
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 & | ExcStrengthenDiagonalTooSmall () |
static ::ExceptionBase & | ExcInvalidStrengthening (double arg1) |
static ::ExceptionBase & | ExcDecompositionNotStable (int arg1, double arg2) |
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) |
Private Member Functions | |
number | get_rowsum (const size_type row) const |
Private Attributes | |
std::vector< number > | diag |
std::vector< number > | inv_diag |
std::vector< number > | inner_sums |
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) |
Implementation of the Modified Incomplete Cholesky (MIC(0)) preconditioner for symmetric matrices. This class conforms to the state and usage specification in SparseLUDecomposition.
Let a symmetric, positive-definite, sparse matrix \(A\) be in the form \(A = D - L - L^T\), where \(D\) is the diagonal part of \(A\) and \(-L\) is a strictly lower triangular matrix. The MIC(0) decomposition of the matrix \(A\) is defined by \(B = (X-L)X^{-1}(X-L^T)\), where \(X\) is a diagonal matrix defined by the condition \(\text{rowsum}(A) = \text{rowsum}(B)\).
Definition at line 47 of file sparse_mic.h.
typedef types::global_dof_index SparseMIC< number >::size_type |
Declare type for container size.
Definition at line 53 of file sparse_mic.h.
typedef SparseLUDecomposition<number>::AdditionalData SparseMIC< number >::AdditionalData |
Make the AdditionalData
type in the base class accessible to this class as well.
Definition at line 78 of file sparse_mic.h.
Constructor. Does nothing, so you have to call decompose
sometimes afterwards.
|
virtual |
Deletes all member variables. Leaves the class in the state that it had directly after calling the constructor
Reimplemented from SparseLUDecomposition< number >.
template void SparseMIC< 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 MIC decomposition.
After this function is called the preconditioner is ready to be used.
template void SparseMIC< number >::vmult< float > | ( | Vector< somenumber > & | dst, |
const Vector< somenumber > & | src | ||
) | const |
Apply the incomplete decomposition, i.e. do one forward-backward step \(dst=(LU)^{-1}src\).
Call initialize
before calling this function.
template void SparseMIC< 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 \(dst=(LU)^{-1}src\).
Call initialize
before calling this function.
|
virtual |
Determine an estimate for the memory consumption (in bytes) of this object.
Reimplemented from SparseLUDecomposition< number >.
|
private |
Compute the row-th "inner sum".
|
private |
Values of the computed diagonal.
Definition at line 158 of file sparse_mic.h.
|
private |
Inverses of the diagonal: precomputed for faster vmult.
Definition at line 163 of file sparse_mic.h.
|
private |
Values of the computed "inner sums", i.e. per-row sums of the elements laying on the right side of the diagonal.
Definition at line 169 of file sparse_mic.h.