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Reference documentation for deal.II version 9.6.0
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#include <deal.II/lac/precondition_block.h>
Classes | |
class | AdditionalData |
Public Types | |
using | size_type = types::global_dof_index |
Public Member Functions | |
PreconditionBlock (bool store_diagonals=false) | |
~PreconditionBlock () override=default | |
void | initialize (const MatrixType &A, const AdditionalData parameters) |
void | clear () |
bool | empty () const |
value_type | el (size_type i, size_type j) const |
void | invert_diagblocks () |
template<typename number2 > | |
void | forward_step (Vector< number2 > &dst, const Vector< number2 > &prev, const Vector< number2 > &src, const bool transpose_diagonal) const |
template<typename number2 > | |
void | backward_step (Vector< number2 > &dst, const Vector< number2 > &prev, const Vector< number2 > &src, const bool transpose_diagonal) const |
size_type | block_size () const |
std::size_t | memory_consumption () const |
template<class Archive > | |
void | serialize (Archive &ar, const unsigned int version) |
Subscriptor functionality | |
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class. | |
void | subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const |
void | unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const |
unsigned int | n_subscriptions () const |
template<typename StreamType > | |
void | list_subscribers (StreamType &stream) const |
void | list_subscribers () const |
Static Public Member Functions | |
static ::ExceptionBase & | ExcWrongBlockSize (int arg1, int arg2) |
static ::ExceptionBase & | ExcInverseMatricesAlreadyExist () |
static ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
Protected Types | |
enum | Inversion |
Protected Member Functions | |
void | initialize (const MatrixType &A, const std::vector< size_type > &permutation, const std::vector< size_type > &inverse_permutation, const AdditionalData parameters) |
void | set_permutation (const std::vector< size_type > &permutation, const std::vector< size_type > &inverse_permutation) |
void | invert_permuted_diagblocks () |
void | reinit (unsigned int nblocks, size_type blocksize, bool compress, Inversion method=gauss_jordan) |
void | inverses_computed (bool are_they) |
bool | same_diagonal () const |
bool | store_diagonals () const |
bool | inverses_ready () const |
unsigned int | size () const |
void | inverse_vmult (size_type i, Vector< number2 > &dst, const Vector< number2 > &src) const |
void | inverse_Tvmult (size_type i, Vector< number2 > &dst, const Vector< number2 > &src) const |
FullMatrix< typename MatrixType::value_type > & | inverse (size_type i) |
const FullMatrix< typename MatrixType::value_type > & | inverse (size_type i) const |
Householder< typename MatrixType::value_type > & | inverse_householder (size_type i) |
const Householder< typename MatrixType::value_type > & | inverse_householder (size_type i) const |
LAPACKFullMatrix< typename MatrixType::value_type > & | inverse_svd (size_type i) |
const LAPACKFullMatrix< typename MatrixType::value_type > & | inverse_svd (size_type i) const |
FullMatrix< typename MatrixType::value_type > & | diagonal (size_type i) |
const FullMatrix< typename MatrixType::value_type > & | diagonal (size_type i) const |
void | log_statistics () const |
Static Protected Member Functions | |
static ::ExceptionBase & | ExcDiagonalsNotStored () |
static ::ExceptionBase & | ExcInverseNotAvailable () |
Protected Attributes | |
size_type | blocksize |
SmartPointer< const MatrixType, PreconditionBlock< MatrixType, inverse_type > > | A |
double | relaxation |
std::vector< size_type > | permutation |
std::vector< size_type > | inverse_permutation |
Inversion | inversion |
Private Types | |
using | number = typename MatrixType::value_type |
using | value_type = inverse_type |
using | map_value_type = decltype(counter_map)::value_type |
using | map_iterator = decltype(counter_map)::iterator |
Private Member Functions | |
void | check_no_subscribers () const noexcept |
Private Attributes | |
std::atomic< unsigned int > | counter |
std::map< std::string, unsigned int > | counter_map |
std::vector< std::atomic< bool > * > | validity_pointers |
const std::type_info * | object_info |
unsigned int | n_diagonal_blocks |
std::vector< FullMatrix< typename MatrixType::value_type > > | var_inverse_full |
std::vector< Householder< typename MatrixType::value_type > > | var_inverse_householder |
std::vector< LAPACKFullMatrix< typename MatrixType::value_type > > | var_inverse_svd |
std::vector< FullMatrix< typename MatrixType::value_type > > | var_diagonal |
bool | var_store_diagonals |
bool | var_same_diagonal |
bool | var_inverses_ready |
Static Private Attributes | |
static std::mutex | mutex |
Base class for actual block preconditioners. This class assumes the MatrixType
consisting of invertible blocks of blocksize
on the diagonal and provides the inversion of the diagonal blocks of the matrix. It is not necessary for this class that the matrix be block diagonal; rather, it applies to matrices of arbitrary structure with the minimal property of having invertible blocks on the diagonal. Still the matrix must have access to single matrix entries. Therefore, BlockMatrixArray and similar classes are not a possible matrix class template arguments.
The block matrix structure used by this class is given, e.g., for the DG method for the transport equation. For a downstream numbering the matrices even have got a block lower left matrix structure, i.e. the matrices are empty above the diagonal blocks.
For all matrices that are empty above and below the diagonal blocks (i.e. for all block diagonal matrices) the BlockJacobi
preconditioner is a direct solver. For all matrices that are empty only above the diagonal blocks (e.g. the matrices one gets by the DG method with downstream numbering) BlockSOR
is a direct solver.
This first implementation of the PreconditionBlock
assumes the matrix has blocks each of the same block size. Varying block sizes within the matrix must still be implemented if needed.
The first template parameter denotes the type of number representation in the sparse matrix, the second denotes the type of number representation in which the inverted diagonal block matrices are stored within this class by invert_diagblocks()
. If you don't want to use the block inversion as an exact solver, but rather as a preconditioner, you may probably want to store the inverted blocks with less accuracy than the original matrix; for example, number==double, inverse_type=float
might be a viable choice.
Definition at line 82 of file precondition_block.h.
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private |
Define number type of matrix.
Definition at line 89 of file precondition_block.h.
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private |
Value type for inverse matrices.
Definition at line 94 of file precondition_block.h.
using PreconditionBlock< MatrixType, inverse_type >::size_type = types::global_dof_index |
Declare type for container size.
Definition at line 100 of file precondition_block.h.
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privateinherited |
The data type used in counter_map.
Definition at line 229 of file subscriptor.h.
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privateinherited |
The iterator type used in counter_map.
Definition at line 234 of file subscriptor.h.
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inherited |
Choose a method for inverting the blocks, and thus the data type for the inverses.
Definition at line 70 of file precondition_block_base.h.
PreconditionBlock< MatrixType, inverse_type >::PreconditionBlock | ( | bool | store_diagonals = false | ) |
Constructor.
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overridedefault |
Destructor.
void PreconditionBlock< MatrixType, inverse_type >::initialize | ( | const MatrixType & | A, |
const AdditionalData | parameters ) |
Initialize matrix and block size. We store the matrix and the block size in the preconditioner object. In a second step, the inverses of the diagonal blocks may be computed.
Additionally, a relaxation parameter for derived classes may be provided.
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protected |
Initialize matrix and block size for permuted preconditioning. Additionally to the parameters of the other initialize() function, we hand over two index vectors with the permutation and its inverse. For the meaning of these vectors see PreconditionBlockSOR.
In a second step, the inverses of the diagonal blocks may be computed. Make sure you use invert_permuted_diagblocks() to yield consistent data.
Additionally, a relaxation parameter for derived classes may be provided.
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protected |
Set either the permutation of rows or the permutation of blocks, depending on the size of the vector.
If the size of the permutation vectors is equal to the dimension of the linear system, it is assumed that rows are permuted individually. In this case, set_permutation() must be called before initialize(), since the diagonal blocks are built from the permuted entries of the matrix.
If the size of the permutation vector is not equal to the dimension of the system, the diagonal blocks are computed from the unpermuted entries. Instead, the relaxation methods step() and Tstep() are executed applying the blocks in the order given by the permutation vector. They will throw an exception if length of this vector is not equal to the number of blocks.
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protected |
Replacement of invert_diagblocks() for permuted preconditioning.
void PreconditionBlock< MatrixType, inverse_type >::clear | ( | ) |
Deletes the inverse diagonal block matrices if existent, sets the blocksize to 0, hence leaves the class in the state that it had directly after calling the constructor.
bool PreconditionBlock< MatrixType, inverse_type >::empty | ( | ) | const |
Check whether the object is empty.
value_type PreconditionBlock< MatrixType, inverse_type >::el | ( | size_type | i, |
size_type | j ) const |
Read-only access to entries. This function is only possible if the inverse diagonal blocks are stored.
void PreconditionBlock< MatrixType, inverse_type >::invert_diagblocks | ( | ) |
Stores the inverse of the diagonal blocks in inverse
. This costs some additional memory - for DG methods about 1/3 (for double inverses) or 1/6 (for float inverses) of that used for the matrix - but it makes the preconditioning much faster.
It is not allowed to call this function twice (will produce an error) before a call of clear(...)
because at the second time there already exist the inverse matrices.
After this function is called, the lock on the matrix given through the use_matrix
function is released, i.e. you may overwrite of delete it. You may want to do this in case you use this matrix to precondition another matrix.
void PreconditionBlock< MatrixType, inverse_type >::forward_step | ( | Vector< number2 > & | dst, |
const Vector< number2 > & | prev, | ||
const Vector< number2 > & | src, | ||
const bool | transpose_diagonal ) const |
Perform one block relaxation step in forward numbering.
Depending on the arguments dst
and pref
, this performs an SOR step (both reference the same vector) of a Jacobi step (both different vectors). For the Jacobi step, the calling function must copy dst
to pref
after this.
void PreconditionBlock< MatrixType, inverse_type >::backward_step | ( | Vector< number2 > & | dst, |
const Vector< number2 > & | prev, | ||
const Vector< number2 > & | src, | ||
const bool | transpose_diagonal ) const |
Perform one block relaxation step in backward numbering.
Depending on the arguments dst
and pref
, this performs an SOR step (both reference the same vector) of a Jacobi step (both different vectors). For the Jacobi step, the calling function must copy dst
to pref
after this.
size_type PreconditionBlock< MatrixType, inverse_type >::block_size | ( | ) | const |
Return the size of the blocks.
std::size_t PreconditionBlock< MatrixType, inverse_type >::memory_consumption | ( | ) | const |
Determine an estimate for the memory consumption (in bytes) of this object.
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inherited |
Subscribes a user of the object by storing the pointer validity
. The subscriber may be identified by text supplied as identifier
.
Definition at line 135 of file subscriptor.cc.
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inherited |
Unsubscribes a user from the object.
identifier
and the validity
pointer must be the same as the one supplied to subscribe(). Definition at line 155 of file subscriptor.cc.
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inlineinherited |
Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.
Definition at line 300 of file subscriptor.h.
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inlineinherited |
List the subscribers to the input stream
.
Definition at line 317 of file subscriptor.h.
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inherited |
List the subscribers to deallog
.
Definition at line 203 of file subscriptor.cc.
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inlineinherited |
Read or write the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.
This function does not actually serialize any of the member variables of this class. The reason is that what this class stores is only who subscribes to this object, but who does so at the time of storing the contents of this object does not necessarily have anything to do with who subscribes to the object when it is restored. Consequently, we do not want to overwrite the subscribers at the time of restoring, and then there is no reason to write the subscribers out in the first place.
Definition at line 309 of file subscriptor.h.
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privatenoexceptinherited |
Check that there are no objects subscribing to this object. If this check passes then it is safe to destroy the current object. It this check fails then this function will either abort or print an error message to deallog (by using the AssertNothrow mechanism), but will not throw an exception.
Definition at line 52 of file subscriptor.cc.
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inlineinherited |
Resize to this number of diagonal blocks with the given block size. If compress
is true, then only one block will be stored.
Definition at line 110 of file precondition_block_base.h.
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inlineinherited |
Tell the class that inverses are computed.
Definition at line 119 of file precondition_block_base.h.
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inlineinherited |
Does the matrix use only one diagonal block?
Definition at line 125 of file precondition_block_base.h.
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inlineinherited |
Check, whether diagonal blocks (not their inverses) should be stored.
Definition at line 131 of file precondition_block_base.h.
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inlineinherited |
Return true, if inverses are ready for use.
Definition at line 137 of file precondition_block_base.h.
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inlineinherited |
The number of blocks.
Definition at line 143 of file precondition_block_base.h.
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inlineinherited |
Multiply with the inverse block at position i
.
Definition at line 150 of file precondition_block_base.h.
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inlineinherited |
Multiply with the transposed inverse block at position i
.
Definition at line 159 of file precondition_block_base.h.
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inlineinherited |
Access to the inverse diagonal blocks if Inversion is gauss_jordan.
Definition at line 167 of file precondition_block_base.h.
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inlineinherited |
Access to the inverse diagonal blocks.
Definition at line 185 of file precondition_block_base.h.
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inlineinherited |
Access to the inverse diagonal blocks if Inversion is householder.
Definition at line 173 of file precondition_block_base.h.
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inlineinherited |
Access to the inverse diagonal blocks if Inversion is householder.
Definition at line 191 of file precondition_block_base.h.
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inlineinherited |
Access to the inverse diagonal blocks if Inversion is householder.
Definition at line 179 of file precondition_block_base.h.
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inlineinherited |
Access to the inverse diagonal blocks if Inversion is householder.
Definition at line 197 of file precondition_block_base.h.
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inlineinherited |
Access to the diagonal blocks.
Definition at line 203 of file precondition_block_base.h.
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inlineinherited |
Access to the diagonal blocks.
Definition at line 209 of file precondition_block_base.h.
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inlineinherited |
Print some statistics about the inverses to deallog
. Output depends on Inversion. It is richest for svd, where we obtain statistics on extremal singular values and condition numbers.
Definition at line 217 of file precondition_block_base.h.
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staticinherited |
You are trying to access a diagonal block (not its inverse), but you decided not to store the diagonal blocks.
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staticinherited |
You are accessing a diagonal block, assuming that it has a certain type. But, the method used for inverting the diagonal blocks does not use this type
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protected |
Size of the blocks. Each diagonal block is assumed to be of the same size.
Definition at line 338 of file precondition_block.h.
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protected |
Pointer to the matrix. Make sure that the matrix exists as long as this class needs it, i.e. until calling invert_diagblocks
, or (if the inverse matrices should not be stored) until the last call of the preconditoining vmult
function of the derived classes.
Definition at line 346 of file precondition_block.h.
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protected |
Relaxation parameter to be used by derived classes.
Definition at line 350 of file precondition_block.h.
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protected |
The permutation vector
Definition at line 355 of file precondition_block.h.
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protected |
The inverse permutation vector
Definition at line 360 of file precondition_block.h.
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mutableprivateinherited |
Store the number of objects which subscribed to this object. Initially, this number is zero, and upon destruction it shall be zero again (i.e. all objects which subscribed should have unsubscribed again).
The creator (and owner) of an object is counted in the map below if HE manages to supply identification.
We use the mutable
keyword in order to allow subscription to constant objects also.
This counter may be read from and written to concurrently in multithreaded code: hence we use the std::atomic
class template.
Definition at line 218 of file subscriptor.h.
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mutableprivateinherited |
In this map, we count subscriptions for each different identification string supplied to subscribe().
Definition at line 224 of file subscriptor.h.
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mutableprivateinherited |
In this vector, we store pointers to the validity bool in the SmartPointer objects that subscribe to this class.
Definition at line 240 of file subscriptor.h.
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mutableprivateinherited |
Pointer to the typeinfo object of this object, from which we can later deduce the class name. Since this information on the derived class is neither available in the destructor, nor in the constructor, we obtain it in between and store it here.
Definition at line 248 of file subscriptor.h.
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staticprivateinherited |
A mutex used to ensure data consistency when accessing the mutable
members of this class. This lock is used in the subscribe() and unsubscribe() functions, as well as in list_subscribers()
.
Definition at line 271 of file subscriptor.h.
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protectedinherited |
The method used for inverting blocks.
Definition at line 243 of file precondition_block_base.h.
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privateinherited |
The number of (inverse) diagonal blocks, if only one is stored.
Definition at line 249 of file precondition_block_base.h.
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privateinherited |
Storage of the inverse matrices of the diagonal blocks matrices as FullMatrix<number>
matrices, if Inversion gauss_jordan is used. Using number=float
saves memory in comparison with number=double
, but may introduce numerical instability.
Definition at line 257 of file precondition_block_base.h.
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privateinherited |
Storage of the inverse matrices of the diagonal blocks matrices as Householder
matrices if Inversion householder is used. Using number=float
saves memory in comparison with number=double
, but may introduce numerical instability.
Definition at line 265 of file precondition_block_base.h.
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privateinherited |
Storage of the inverse matrices of the diagonal blocks matrices as LAPACKFullMatrix
matrices if Inversion svd is used. Using number=float
saves memory in comparison with number=double
, but may introduce numerical instability.
Definition at line 273 of file precondition_block_base.h.
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privateinherited |
Storage of the original diagonal blocks.
Used by the blocked SSOR method.
Definition at line 280 of file precondition_block_base.h.
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privateinherited |
This is true, if the field var_diagonal is to be used.
Definition at line 286 of file precondition_block_base.h.
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privateinherited |
This is true, if only one inverse is stored.
Definition at line 291 of file precondition_block_base.h.
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privateinherited |
The inverse matrices are usable. Set by the parent class via inverses_computed().
Definition at line 297 of file precondition_block_base.h.