Reference documentation for deal.II version 9.6.0

#include <deal.II/lac/sparse_direct.h>
Classes  
class  AdditionalData 
Public Types  
using  size_type = types::global_dof_index 
Public Member Functions  
SparseDirectUMFPACK ()  
~SparseDirectUMFPACK () override  
template<class Archive >  
void  serialize (Archive &ar, const unsigned int version) 
Setting up a sparse factorization  
void  initialize (const SparsityPattern &sparsity_pattern) 
template<class Matrix >  
void  factorize (const Matrix &matrix) 
template<class Matrix >  
void  initialize (const Matrix &matrix, const AdditionalData additional_data=AdditionalData()) 
Functions that represent the inverse of a matrix  
void  vmult (Vector< double > &dst, const Vector< double > &src) const 
void  vmult (BlockVector< double > &dst, const BlockVector< double > &src) const 
void  Tvmult (Vector< double > &dst, const Vector< double > &src) const 
void  Tvmult (BlockVector< double > &dst, const BlockVector< double > &src) const 
size_type  m () const 
size_type  n () const 
Functions that solve linear systems  
void  solve (Vector< double > &rhs_and_solution, const bool transpose=false) const 
void  solve (Vector< std::complex< double > > &rhs_and_solution, const bool transpose=false) const 
void  solve (BlockVector< double > &rhs_and_solution, const bool transpose=false) const 
void  solve (BlockVector< std::complex< double > > &rhs_and_solution, const bool transpose=false) const 
template<class Matrix >  
void  solve (const Matrix &matrix, Vector< double > &rhs_and_solution, const bool transpose=false) 
template<class Matrix >  
void  solve (const Matrix &matrix, Vector< std::complex< double > > &rhs_and_solution, const bool transpose=false) 
template<class Matrix >  
void  solve (const Matrix &matrix, BlockVector< double > &rhs_and_solution, const bool transpose=false) 
template<class Matrix >  
void  solve (const Matrix &matrix, BlockVector< std::complex< double > > &rhs_and_solution, const bool transpose=false) 
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 &  ExcUMFPACKError (std::string arg1, int arg2) 
static ::ExceptionBase &  ExcInUse (int arg1, std::string arg2, std::string arg3) 
static ::ExceptionBase &  ExcNoSubscriber (std::string arg1, std::string arg2) 
Private Types  
using  map_value_type = decltype(counter_map)::value_type 
using  map_iterator = decltype(counter_map)::iterator 
Private Member Functions  
void  clear () 
template<typename number >  
void  sort_arrays (const SparseMatrixEZ< number > &) 
template<typename number >  
void  sort_arrays (const SparseMatrix< number > &) 
template<typename number >  
void  sort_arrays (const BlockSparseMatrix< number > &) 
void  check_no_subscribers () const noexcept 
Private Attributes  
size_type  n_rows 
size_type  n_cols 
void *  symbolic_decomposition 
void *  numeric_decomposition 
std::vector< types::suitesparse_index >  Ap 
std::vector< types::suitesparse_index >  Ai 
std::vector< double >  Ax 
std::vector< double >  Az 
std::vector< double >  control 
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 
Static Private Attributes  
static std::mutex  mutex 
This class provides an interface to the sparse direct solver UMFPACK, which is part of the SuiteSparse library (see this link). UMFPACK is a set of routines for solving nonsymmetric sparse linear systems, Ax=b, using the Unsymmetricpattern MultiFrontal method and direct sparse LU factorization. Matrices may have symmetric or unsymmetric sparsity patterns, and may have unsymmetric entries. The use of this class is explained in the step22 and step29 tutorial programs.
This matrix class implements the usual interface of preconditioners, that is a function initialize(const SparseMatrix<double>&matrix,const AdditionalData) for initializing and the whole set of vmult() functions common to all matrices. Implemented here are only vmult() and vmult_add(), which perform multiplication with the inverse matrix. Furthermore, this class provides an older interface, consisting of the functions factorize() and solve(). Both interfaces are interchangeable.
There are instantiations of this class for SparseMatrix<double>, SparseMatrix<float>, SparseMatrixEZ<float>, SparseMatrixEZ<double>, BlockSparseMatrix<double>, and BlockSparseMatrix<float>.
This class is not instantiated for the matrix types in namespace PETScWrappers or TrilinosWrappers. However, PETScWrappers::SparseDirectMUMPS can be used for PETSc matrices, and in fact even works for parallel computations.
Definition at line 91 of file sparse_direct.h.
Declare type for container size.
Definition at line 97 of file sparse_direct.h.

privateinherited 
The data type used in counter_map.
Definition at line 229 of file subscriptor.h.

privateinherited 
The iterator type used in counter_map.
Definition at line 234 of file subscriptor.h.
SparseDirectUMFPACK::SparseDirectUMFPACK  (  ) 
Constructor. See the documentation of this class for the meaning of the parameters to this function.
Definition at line 73 of file sparse_direct.cc.

override 
Destructor.
Definition at line 60 of file sparse_direct.cc.
void SparseDirectUMFPACK::initialize  (  const SparsityPattern &  sparsity_pattern  ) 
This function does nothing. It is only here to provide a interface consistent with other sparse direct solvers.
Definition at line 67 of file sparse_direct.cc.
void SparseDirectUMFPACK::factorize  (  const Matrix &  matrix  ) 
Factorize the matrix. This function may be called multiple times for different matrices, after the object of this class has been initialized for a certain sparsity pattern. You may therefore save some computing time if you want to invert several matrices with the same sparsity pattern. However, note that the bulk of the computing time is actually spent in the factorization, so this functionality may not always be of large benefit.
In contrast to the other direct solver classes, the initialization method does nothing. Therefore initialize is not automatically called by this method, when the initialization step has not been performed yet.
This function copies the contents of the matrix into its own storage; the matrix can therefore be deleted after this operation, even if subsequent solves are required.
Definition at line 252 of file sparse_direct.cc.
void SparseDirectUMFPACK::initialize  (  const Matrix &  matrix, 
const AdditionalData  additional_data = AdditionalData() ) 
Initialize memory and call SparseDirectUMFPACK::factorize.
Definition at line 788 of file sparse_direct.cc.
Preconditioner interface function. Usually, given the source vector, this method returns an approximate solution of Ax = b. As this class provides a wrapper to a direct solver, here it is actually the exact solution (exact within the range of numerical accuracy of course).
In other words, this function actually multiplies with the exact inverse of the matrix, \(A^{1}\).
Definition at line 795 of file sparse_direct.cc.
void SparseDirectUMFPACK::vmult  (  BlockVector< double > &  dst, 
const BlockVector< double > &  src ) const 
Same as before, but for block vectors.
Definition at line 804 of file sparse_direct.cc.
Same as before, but uses the transpose of the matrix, i.e. this function multiplies with \(A^{T}\).
Definition at line 813 of file sparse_direct.cc.
void SparseDirectUMFPACK::Tvmult  (  BlockVector< double > &  dst, 
const BlockVector< double > &  src ) const 
Same as before, but for block vectors
Definition at line 823 of file sparse_direct.cc.
SparseDirectUMFPACK::size_type SparseDirectUMFPACK::m  (  )  const 
Return the dimension of the codomain (or range) space. Note that the matrix is of dimension \(m \times n\).
Definition at line 831 of file sparse_direct.cc.
SparseDirectUMFPACK::size_type SparseDirectUMFPACK::n  (  )  const 
Return the dimension of the domain space. Note that the matrix is of dimension \(m \times n\).
Definition at line 838 of file sparse_direct.cc.
void SparseDirectUMFPACK::solve  (  Vector< double > &  rhs_and_solution, 
const bool  transpose = false ) const 
Solve for a certain right hand side vector. This function may be called multiple times for different right hand side vectors after the matrix has been factorized. This yields substantial savings in computing time, since the actual solution is fast, compared to the factorization of the matrix.
The solution will be returned in place of the right hand side vector.
[in,out]  rhs_and_solution  A vector that contains the right hand side \(b\) of a linear system \(Ax=b\) upon calling this function, and that contains the solution \(x\) of the linear system after calling this function. 
[in]  transpose  If set to true, this function solves the linear \(A^T x = b\) instead of \(Ax=b\). 
Definition at line 377 of file sparse_direct.cc.
void SparseDirectUMFPACK::solve  (  Vector< std::complex< double > > &  rhs_and_solution, 
const bool  transpose = false ) const 
Like the previous function, but for a complexvalued right hand side and solution vector.
If the matrix that was previously factorized had complexvalued entries, then the rhs_and_solution
vector will, upon return from this function, simply contain the solution of the linear system \(Ax=b\). If the matrix was realvalued, then this is also true, but the solution will simply be computed by applying the factorized \(A^{1}\) to both the real and imaginary parts of the right hand side vector.
Definition at line 417 of file sparse_direct.cc.
void SparseDirectUMFPACK::solve  (  BlockVector< double > &  rhs_and_solution, 
const bool  transpose = false ) const 
Same as before, but for block vectors.
Definition at line 532 of file sparse_direct.cc.
void SparseDirectUMFPACK::solve  (  BlockVector< std::complex< double > > &  rhs_and_solution, 
const bool  transpose = false ) const 
Same as before, but for complexvalued block vectors.
Definition at line 547 of file sparse_direct.cc.
void SparseDirectUMFPACK::solve  (  const Matrix &  matrix, 
Vector< double > &  rhs_and_solution,  
const bool  transpose = false ) 
Call the two functions factorize() and solve() in that order, i.e. perform the whole solution process for the given right hand side vector.
The solution will be returned in place of the right hand side vector.
Definition at line 573 of file sparse_direct.cc.
void SparseDirectUMFPACK::solve  (  const Matrix &  matrix, 
Vector< std::complex< double > > &  rhs_and_solution,  
const bool  transpose = false ) 
Same as before, but for complexvalued solution vectors.
Definition at line 585 of file sparse_direct.cc.
void SparseDirectUMFPACK::solve  (  const Matrix &  matrix, 
BlockVector< double > &  rhs_and_solution,  
const bool  transpose = false ) 
Same as before, but for block vectors.
Definition at line 609 of file sparse_direct.cc.
void SparseDirectUMFPACK::solve  (  const Matrix &  matrix, 
BlockVector< std::complex< double > > &  rhs_and_solution,  
const bool  transpose = false ) 
Same as before, but for complexvalued block vectors.
Definition at line 621 of file sparse_direct.cc.

private 
Free all memory that hasn't been freed yet.
Definition at line 86 of file sparse_direct.cc.

private 
Make sure that the arrays Ai and Ap are sorted in each row. UMFPACK wants it this way. We need to have three versions of this function, one for the usual SparseMatrix, one for the SparseMatrixEZ, and one for the BlockSparseMatrix classes
Definition at line 174 of file sparse_direct.cc.

private 
Definition at line 128 of file sparse_direct.cc.

private 
Definition at line 203 of file sparse_direct.cc.

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.

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.

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.

inlineinherited 
List the subscribers to the input stream
.
Definition at line 317 of file subscriptor.h.

inherited 
List the subscribers to deallog
.
Definition at line 203 of file subscriptor.cc.

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.

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.

private 
The dimension of the range space, i.e., the number of rows of the matrix.
Definition at line 368 of file sparse_direct.h.

private 
The dimension of the domain space, i.e., the number of columns of the matrix.
Definition at line 374 of file sparse_direct.h.

private 
The UMFPACK routines allocate objects in which they store information about symbolic and numeric values of the decomposition. The actual data type of these objects is opaque, and only passed around as void pointers.
Definition at line 381 of file sparse_direct.h.

private 
Definition at line 382 of file sparse_direct.h.

private 
The arrays in which we store the data for the solver. These are documented in the descriptions of the umfpack_*_symbolic() and umfpack_*_numeric() functions, but in short:
Ap
is the array saying which row starts where in Ai
Ai
is the array that stores the column indices of nonzero entriesAx
is the array that stores the values of nonzero entries; if the matrix is complexvalued, then it stores the real partsAz
is the array that stores the imaginary parts of nonzero entries, and is used only if the matrix is complexvalued. Definition at line 419 of file sparse_direct.h.

private 
Definition at line 420 of file sparse_direct.h.

private 
Definition at line 421 of file sparse_direct.h.

private 
Definition at line 422 of file sparse_direct.h.

private 
Control and work arrays for the solver routines.
Definition at line 427 of file sparse_direct.h.

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.

mutableprivateinherited 
In this map, we count subscriptions for each different identification string supplied to subscribe().
Definition at line 224 of file subscriptor.h.

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.

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.

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.