Reference documentation for deal.II version Git c3b52c4 20170823 10:06:38 0600

#include <deal.II/lac/constraint_matrix.h>
Classes  
struct  ConstraintLine 
Public Types  
enum  MergeConflictBehavior { no_conflicts_allowed, left_object_wins, right_object_wins } 
typedef types::global_dof_index  size_type 
typedef std::vector< ConstraintLine >::const_iterator  const_iterator 
typedef boost::iterator_range< const_iterator >  LineRange 
Public Member Functions  
ConstraintMatrix (const IndexSet &local_constraints=IndexSet())  
ConstraintMatrix (const ConstraintMatrix &constraint_matrix)  
ConstraintMatrix (ConstraintMatrix &&constraint_matrix)=default  
ConstraintMatrix &  operator= (const ConstraintMatrix &)=delete 
ConstraintMatrix &  operator= (ConstraintMatrix &&constraint_matrix)=default 
void  copy_from (const ConstraintMatrix &other) 
void  reinit (const IndexSet &local_constraints=IndexSet()) 
bool  can_store_line (const size_type line_index) const 
const IndexSet &  get_local_lines () const 
void  add_selected_constraints (const ConstraintMatrix &constraints_in, const IndexSet &filter) 
const LineRange  get_lines () const 
Adding constraints  
void  add_line (const size_type line) 
void  add_lines (const std::vector< bool > &lines) 
void  add_lines (const std::set< size_type > &lines) 
void  add_lines (const IndexSet &lines) 
void  add_entry (const size_type line, const size_type column, const double value) 
void  add_entries (const size_type line, const std::vector< std::pair< size_type, double > > &col_val_pairs) 
void  set_inhomogeneity (const size_type line, const double value) 
void  close () 
void  merge (const ConstraintMatrix &other_constraints, const MergeConflictBehavior merge_conflict_behavior=no_conflicts_allowed, const bool allow_different_local_lines=false) 
void  shift (const size_type offset) 
void  clear () 
Querying constraints  
size_type  n_constraints () const 
bool  is_constrained (const size_type index) const 
bool  is_identity_constrained (const size_type index) const 
bool  are_identity_constrained (const size_type index1, const size_type index2) const 
size_type  max_constraint_indirections () const 
bool  is_inhomogeneously_constrained (const size_type index) const 
bool  has_inhomogeneities () const 
const std::vector< std::pair< size_type, double > > *  get_constraint_entries (const size_type line) const 
double  get_inhomogeneity (const size_type line) const 
void  print (std::ostream &out) const 
void  write_dot (std::ostream &) const 
std::size_t  memory_consumption () const 
void  resolve_indices (std::vector< types::global_dof_index > &indices) const 
Eliminating constraints from linear systems after their creation  
void  condense (SparsityPattern &sparsity) const 
void  condense (BlockSparsityPattern &sparsity) const 
void  condense (DynamicSparsityPattern &sparsity) const 
void  condense (BlockDynamicSparsityPattern &sparsity) const 
template<typename number >  
void  condense (SparseMatrix< number > &matrix) const 
template<typename number >  
void  condense (BlockSparseMatrix< number > &matrix) const 
template<class VectorType >  
void  condense (VectorType &vec) const 
template<class VectorType >  
void  condense (const VectorType &vec_ghosted, VectorType &output) const 
template<typename number , class VectorType >  
void  condense (SparseMatrix< number > &matrix, VectorType &vector) const 
template<typename number , class BlockVectorType >  
void  condense (BlockSparseMatrix< number > &matrix, BlockVectorType &vector) const 
template<class VectorType >  
void  set_zero (VectorType &vec) const 
Eliminating constraints from linear systems during their creation  
template<class InVector , class OutVector >  
void  distribute_local_to_global (const InVector &local_vector, const std::vector< size_type > &local_dof_indices, OutVector &global_vector) const 
template<typename VectorType , typename LocalType >  
void  distribute_local_to_global (const Vector< LocalType > &local_vector, const std::vector< size_type > &local_dof_indices, VectorType &global_vector, const FullMatrix< LocalType > &local_matrix) const 
template<typename VectorType , typename LocalType >  
void  distribute_local_to_global (const Vector< LocalType > &local_vector, const std::vector< size_type > &local_dof_indices_row, const std::vector< size_type > &local_dof_indices_col, VectorType &global_vector, const FullMatrix< LocalType > &local_matrix, bool diagonal=false) const 
template<class VectorType >  
void  distribute_local_to_global (const size_type index, const double value, VectorType &global_vector) const 
template<typename ForwardIteratorVec , typename ForwardIteratorInd , class VectorType >  
void  distribute_local_to_global (ForwardIteratorVec local_vector_begin, ForwardIteratorVec local_vector_end, ForwardIteratorInd local_indices_begin, VectorType &global_vector) const 
template<typename MatrixType >  
void  distribute_local_to_global (const FullMatrix< typename MatrixType::value_type > &local_matrix, const std::vector< size_type > &local_dof_indices, MatrixType &global_matrix) const 
template<typename MatrixType >  
void  distribute_local_to_global (const FullMatrix< typename MatrixType::value_type > &local_matrix, const std::vector< size_type > &row_indices, const std::vector< size_type > &col_indices, MatrixType &global_matrix) const 
template<typename MatrixType >  
void  distribute_local_to_global (const FullMatrix< typename MatrixType::value_type > &local_matrix, const std::vector< size_type > &row_indices, const ConstraintMatrix &column_constraint_matrix, const std::vector< size_type > &column_indices, MatrixType &global_matrix) const 
template<typename MatrixType , typename VectorType >  
void  distribute_local_to_global (const FullMatrix< typename MatrixType::value_type > &local_matrix, const Vector< typename VectorType::value_type > &local_vector, const std::vector< size_type > &local_dof_indices, MatrixType &global_matrix, VectorType &global_vector, bool use_inhomogeneities_for_rhs=false) const 
template<typename SparsityPatternType >  
void  add_entries_local_to_global (const std::vector< size_type > &local_dof_indices, SparsityPatternType &sparsity_pattern, const bool keep_constrained_entries=true, const Table< 2, bool > &dof_mask=default_empty_table) const 
template<typename SparsityPatternType >  
void  add_entries_local_to_global (const std::vector< size_type > &row_indices, const std::vector< size_type > &col_indices, SparsityPatternType &sparsity_pattern, const bool keep_constrained_entries=true, const Table< 2, bool > &dof_mask=default_empty_table) const 
template<typename ForwardIteratorVec , typename ForwardIteratorInd , class VectorType >  
void  get_dof_values (const VectorType &global_vector, ForwardIteratorInd local_indices_begin, ForwardIteratorVec local_vector_begin, ForwardIteratorVec local_vector_end) const 
Dealing with constraints after solving a linear system  
template<class VectorType >  
void  distribute (VectorType &vec) const 
Public Member Functions inherited from Subscriptor  
Subscriptor ()  
Subscriptor (const Subscriptor &)  
Subscriptor (Subscriptor &&)  
virtual  ~Subscriptor () 
Subscriptor &  operator= (const Subscriptor &) 
Subscriptor &  operator= (Subscriptor &&) 
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 &  ExcMatrixIsClosed () 
static::ExceptionBase &  ExcMatrixNotClosed () 
static::ExceptionBase &  ExcLineInexistant (size_type arg1) 
static::ExceptionBase &  ExcEntryAlreadyExists (size_type arg1, size_type arg2, double arg3, double arg4) 
static::ExceptionBase &  ExcDoFConstrainedToConstrainedDoF (int arg1, int arg2) 
static::ExceptionBase &  ExcDoFIsConstrainedFromBothObjects (size_type arg1) 
static::ExceptionBase &  ExcDoFIsConstrainedToConstrainedDoF (size_type arg1) 
static::ExceptionBase &  ExcRowNotStoredHere (size_type arg1) 
static::ExceptionBase &  ExcColumnNotStoredHere (size_type arg1, size_type arg2) 
static::ExceptionBase &  ExcIncorrectConstraint (int arg1, int arg2) 
Static Public Member Functions inherited from Subscriptor  
static::ExceptionBase &  ExcInUse (int arg1, char *arg2, std::string &arg3) 
static::ExceptionBase &  ExcNoSubscriber (char *arg1, char *arg2) 
Private Member Functions  
size_type  calculate_line_index (const size_type line) const 
template<typename MatrixType , typename VectorType >  
void  distribute_local_to_global (const FullMatrix< typename MatrixType::value_type > &local_matrix, const Vector< typename VectorType::value_type > &local_vector, const std::vector< size_type > &local_dof_indices, MatrixType &global_matrix, VectorType &global_vector, bool use_inhomogeneities_for_rhs, std::integral_constant< bool, false >) const 
template<typename MatrixType , typename VectorType >  
void  distribute_local_to_global (const FullMatrix< typename MatrixType::value_type > &local_matrix, const Vector< typename VectorType::value_type > &local_vector, const std::vector< size_type > &local_dof_indices, MatrixType &global_matrix, VectorType &global_vector, bool use_inhomogeneities_for_rhs, std::integral_constant< bool, true >) const 
template<typename SparsityPatternType >  
void  add_entries_local_to_global (const std::vector< size_type > &local_dof_indices, SparsityPatternType &sparsity_pattern, const bool keep_constrained_entries, const Table< 2, bool > &dof_mask, std::integral_constant< bool, false >) const 
template<typename SparsityPatternType >  
void  add_entries_local_to_global (const std::vector< size_type > &local_dof_indices, SparsityPatternType &sparsity_pattern, const bool keep_constrained_entries, const Table< 2, bool > &dof_mask, std::integral_constant< bool, true >) const 
void  make_sorted_row_list (const std::vector< size_type > &local_dof_indices, internals::GlobalRowsFromLocal &global_rows) const 
void  make_sorted_row_list (const std::vector< size_type > &local_dof_indices, std::vector< size_type > &active_dofs) const 
template<typename LocalType >  
LocalType  resolve_vector_entry (const size_type i, const internals::GlobalRowsFromLocal &global_rows, const Vector< LocalType > &local_vector, const std::vector< size_type > &local_dof_indices, const FullMatrix< LocalType > &local_matrix) const 
Static Private Member Functions  
static bool  check_zero_weight (const std::pair< size_type, double > &p) 
Private Attributes  
std::vector< ConstraintLine >  lines 
std::vector< size_type >  lines_cache 
IndexSet  local_lines 
bool  sorted 
Static Private Attributes  
static const Table< 2, bool >  default_empty_table = Table<2,bool>() 
This class implements dealing with linear (possibly inhomogeneous) constraints on degrees of freedom. The concept and origin of such constraints is extensively described in the Constraints on degrees of freedom module. The class is meant to deal with a limited number of constraints relative to the total number of degrees of freedom, for example a few per cent up to maybe 30 per cent; and with a linear combination of M other degrees of freedom where M is also relatively small (no larger than at most around the average number of entries per row of a linear system). It is not meant to describe full rank linear systems.
The algorithms used in the implementation of this class are described in some detail in the hp paper. There is also a significant amount of documentation on how to use this class in the Constraints on degrees of freedom module.
Each "line" in objects of this class corresponds to one constrained degree of freedom, with the number of the line being i, entered by using add_line() or add_lines(). The entries in this line are pairs of the form (j,a_{ij}), which are added by add_entry() or add_entries(). The organization is essentially a SparsityPattern, but with only a few lines containing nonzero elements, and therefore no data wasted on the others. For each line, which has been added by the mechanism above, an elimination of the constrained degree of freedom of the form
\[ x_i = \sum_j a_{ij} x_j + b_i \]
is performed, where b_{i} is optional and set by set_inhomogeneity(). Thus, if a constraint is formulated for instance as a zero mean value of several degrees of freedom, one of the degrees has to be chosen to be eliminated.
Note that the constraints are linear in the x_{i}, and that there might be a constant (nonhomogeneous) term in the constraint. This is exactly the form we need for hanging node constraints, where we need to constrain one degree of freedom in terms of others. There are other conditions of this form possible, for example for implementing mean value conditions as is done in the step11 tutorial program. The name of the class stems from the fact that these constraints can be represented in matrix form as X x = b, and this object then describes the matrix X (and the vector b; originally, the ConstraintMatrix class was only meant to handle homogenous constraints where b=0, thus the name). The most frequent way to create/fill objects of this type is using the DoFTools::make_hanging_node_constraints() function. The use of these objects is first explained in step6.
Objects of the present type are organized in lines (rows), but only those lines are stored where constraints are present. New constraints are added by adding new lines using the add_line() function, and then populating it using the add_entry() function to a given line, or add_entries() to add more than one entry at a time. The right hand side element, if nonzero, can be set using the set_inhomogeneity() function. After all constraints have been added, you need to call close(), which compresses the storage format and sorts the entries.
Definition at line 137 of file constraint_matrix.h.
Declare the type for container size.
Definition at line 143 of file constraint_matrix.h.
typedef std::vector<ConstraintLine>::const_iterator ConstraintMatrix::const_iterator 
Typedef for the iterator type that is used in the LineRange container.
Definition at line 1186 of file constraint_matrix.h.
typedef boost::iterator_range<const_iterator> ConstraintMatrix::LineRange 
Typedef for the return type used by get_lines().
Definition at line 1192 of file constraint_matrix.h.

inlineexplicit 
Constructor. The supplied IndexSet defines which indices might be constrained inside this ConstraintMatrix. In a calculation with a DoFHandler object based on parallel::distributed::Triangulation or parallel::shared::Triangulation, one should use the set of locally relevant dofs (see GlossLocallyRelevantDof).
The given IndexSet allows the ConstraintMatrix to save memory by just not caring about degrees of freedom that are not of importance to the current processor. Alternatively, if no such IndexSet is provided, internal data structures for all possible indices will be created, leading to memory consumption on every processor that is proportional to the overall size of the problem, not just proportional to the size of the portion of the overall problem that is handled by the current processor.
Definition at line 1481 of file constraint_matrix.h.

inlineexplicit 
Copy constructor
Definition at line 1496 of file constraint_matrix.h.

default 
Move constructor

delete 
Copy operator. Like for many other large objects, this operator is deleted to avoid its inadvertent use in places such as accidentally declaring a ConstraintMatrix
object as a function argument by value, rather than by reference.
However, you can use the copy_from() function to explicitly copy ConstraintMatrix objects.

default 
Move assignment operator
void ConstraintMatrix::copy_from  (  const ConstraintMatrix &  other  ) 
Copy the given object to the current one.
This function exists because operator=()
is explicitly disabled.
Definition at line 56 of file constraint_matrix.cc.
clear() the ConstraintMatrix object and supply an IndexSet with lines that may be constrained. This function is only relevant in the distributed case to supply a different IndexSet. Otherwise this routine is equivalent to calling clear(). See the constructor for details.
Definition at line 685 of file constraint_matrix.cc.

inline 
Determines if we can store a constraint for the given line_index
. This routine only matters in the distributed case and checks if the IndexSet allows storage of this line. Always returns true if not in the distributed case.
Definition at line 1686 of file constraint_matrix.h.

inline 
Return the index set describing locally relevant lines if any are present. Note that if no local lines were given, this represents an empty IndexSet, whereas otherwise it contains the global problem size and the local range.
Definition at line 1695 of file constraint_matrix.h.
void ConstraintMatrix::add_selected_constraints  (  const ConstraintMatrix &  constraints_in, 
const IndexSet &  filter  
) 
This function copies the content of constraints_in
with DoFs that are element of the IndexSet filter
. Elements that are not present in the IndexSet are ignored. All DoFs will be transformed to local index space of the filter, both the constrained DoFs and the other DoFs these entries are constrained to. The local index space of the filter is a contiguous numbering of all (global) DoFs that are elements in the filter.
If, for example, the filter represents the range [10,20)
, and the constraint matrix constraints_in
includes the global indices {7,13,14}
, the indices {3,4}
are added to the calling constraint matrix (since 13 and 14 are elements in the filter and element 13 is the fourth element in the index, and 14 is the fifth).
This function provides an easy way to create a ConstraintMatrix for certain vector components in a vectorvalued problem from a full ConstraintMatrix, i.e. extracting a diagonal subblock from a larger ConstraintMatrix. The block is specified by the IndexSet argument.
Definition at line 178 of file constraint_matrix.cc.

inline 
Add a new line to the matrix. If the line already exists, then the function simply returns without doing anything.
Definition at line 1508 of file constraint_matrix.h.
void ConstraintMatrix::add_lines  (  const std::vector< bool > &  lines  ) 
Call the first add_line() function for every index i
for which lines[i]
is true.
This function essentially exists to allow adding several constraints of the form x_{i}=0 all at once, where the set of indices i for which these constraints should be added are given by the argument of this function. On the other hand, just as if the single argument add_line() function were called repeatedly, the constraints can later be modified to include linear dependencies using the add_entry() function as well as inhomogeneities using set_inhomogeneity().
Definition at line 118 of file constraint_matrix.cc.
void ConstraintMatrix::add_lines  (  const std::set< size_type > &  lines  ) 
Call the first add_line() function for every index i
that appears in the argument.
This function essentially exists to allow adding several constraints of the form x_{i}=0 all at once, where the set of indices i for which these constraints should be added are given by the argument of this function. On the other hand, just as if the single argument add_line() function were called repeatedly, the constraints can later be modified to include linear dependencies using the add_entry() function as well as inhomogeneities using set_inhomogeneity().
Definition at line 108 of file constraint_matrix.cc.
void ConstraintMatrix::add_lines  (  const IndexSet &  lines  ) 
Call the first add_line() function for every index i
that appears in the argument.
This function essentially exists to allow adding several constraints of the form x_{i}=0 all at once, where the set of indices i for which these constraints should be added are given by the argument of this function. On the other hand, just as if the single argument add_line() function were called repeatedly, the constraints can later be modified to include linear dependencies using the add_entry() function as well as inhomogeneities using set_inhomogeneity().
Definition at line 128 of file constraint_matrix.cc.

inline 
Add an entry to a given line. The list of lines is searched from the back to the front, so clever programming would add a new line (which is pushed to the back) and immediately afterwards fill the entries of that line. This way, no expensive searching is needed.
If an entry with the same indices as the one this function call denotes already exists, then this function simply returns provided that the value of the entry is the same. Thus, it does no harm to enter a constraint twice.
Definition at line 1541 of file constraint_matrix.h.
void ConstraintMatrix::add_entries  (  const size_type  line, 
const std::vector< std::pair< size_type, double > > &  col_val_pairs  
) 
Add a whole series of entries, denoted by pairs of column indices and values, to a line of constraints. This function is equivalent to calling the preceding function several times, but is faster.
Definition at line 138 of file constraint_matrix.cc.

inline 
Set an inhomogeneity to the constraint line i, according to the discussion in the general class description.
Definition at line 1584 of file constraint_matrix.h.
void ConstraintMatrix::close  (  ) 
Close the filling of entries. Since the lines of a matrix of this type are usually filled in an arbitrary order and since we do not want to use associative constrainers to store the lines, we need to sort the lines and within the lines the columns before usage of the matrix. This is done through this function.
Also, zero entries are discarded, since they are not needed.
After closing, no more entries are accepted. If the object was already closed, then this function returns immediately.
This function also resolves chains of constraints. For example, degree of freedom 13 may be constrained to \(u_{13} = \frac{u_3}{2} + \frac{u_7}{2}\) while degree of freedom 7 is itself constrained as \(u_{7} = \frac{u_2}{2} + \frac{u_4}{2}\). Then, the resolution will be that \(u_{13} = \frac{u_3}{2} + \frac{u_2}{4} + \frac{u_4}{4}\). Note, however, that cycles in this graph of constraints are not allowed, i.e. for example \(u_4\) may not be constrained, directly or indirectly, to \(u_{13}\) again.
Definition at line 202 of file constraint_matrix.cc.
void ConstraintMatrix::merge  (  const ConstraintMatrix &  other_constraints, 
const MergeConflictBehavior  merge_conflict_behavior = no_conflicts_allowed , 

const bool  allow_different_local_lines = false 

) 
Merge the constraints represented by the object given as argument into the constraints represented by this object. Both objects may or may not be closed (by having their function close() called before). If this object was closed before, then it will be closed afterwards as well. Note, however, that if the other argument is closed, then merging may be significantly faster.
Using the default value of the second arguments, the constraints in each of the two objects (the old one represented by this object and the argument) may not refer to the same degree of freedom, i.e. a degree of freedom that is constrained in one object may not be constrained in the second. If this is nevertheless the case, an exception is thrown. However, this behavior can be changed by providing a different value for the second argument.
By default, merging two ConstraintMatrix objects that are initialized with different IndexSet objects is not allowed. This behavior can be altered by setting allow_different_local_lines
appropriately.
Merging a ConstraintMatrix that is initialized with an IndexSet and one that is not initialized with an IndexSet is not yet implemented.
Definition at line 491 of file constraint_matrix.cc.
void ConstraintMatrix::shift  (  const size_type  offset  ) 
Shift all entries of this matrix down offset
rows and over offset
columns. If this object is initialized with an IndexSet, local_lines are shifted as well.
This function is useful if you are building block matrices, where all blocks are built by the same DoFHandler object, i.e. the matrix size is larger than the number of degrees of freedom. Since several matrix rows and columns correspond to the same degrees of freedom, you'd generate several constraint objects, then shift them, and finally merge() them together again.
Definition at line 633 of file constraint_matrix.cc.
void ConstraintMatrix::clear  (  ) 
Clear all entries of this matrix. Reset the flag determining whether new entries are accepted or not.
This function may be called also on objects which are empty or already cleared.
Definition at line 668 of file constraint_matrix.cc.

inline 
Return number of constraints stored in this matrix.
Definition at line 1600 of file constraint_matrix.h.

inline 
Return whether the degree of freedom with number index
is a constrained one.
Note that if close() was called before, then this function is significantly faster, since then the constrained degrees of freedom are sorted and we can do a binary search, while before close() was called, we have to perform a linear search through all entries.
Definition at line 1609 of file constraint_matrix.h.
bool ConstraintMatrix::is_identity_constrained  (  const size_type  index  )  const 
Return whether the dof is constrained, and whether it is constrained to only one other degree of freedom with weight one. The function therefore returns whether the degree of freedom would simply be eliminated in favor of exactly one other degree of freedom.
The function returns false
if either the degree of freedom is not constrained at all, or if it is constrained to more than one other degree of freedom, or if it is constrained to only one degree of freedom but with a weight different from one.
Definition at line 1098 of file constraint_matrix.cc.
bool ConstraintMatrix::are_identity_constrained  (  const size_type  index1, 
const size_type  index2  
)  const 
Return whether the two given degrees of freedom are linked by an equality constraint that either constrains index1 to be so that index1=index2
or constrains index2 so that index2=index1
.
Definition at line 1113 of file constraint_matrix.cc.
ConstraintMatrix::size_type ConstraintMatrix::max_constraint_indirections  (  )  const 
Return the maximum number of other dofs that one dof is constrained to. For example, in 2d a hanging node is constrained only to its two neighbors, so the returned value would be 2. However, for higher order elements and/or higher dimensions, or other types of constraints, this number is no more obvious.
The name indicates that within the system matrix, references to a constrained node are indirected to the nodes it is constrained to.
Definition at line 1145 of file constraint_matrix.cc.

inline 
Return true
in case the dof is constrained and there is a non trivial inhomogeneous values set to the dof.
Definition at line 1621 of file constraint_matrix.h.
bool ConstraintMatrix::has_inhomogeneities  (  )  const 
Return false
if all constraints in the ConstraintMatrix are homogeneous ones, and true
if there is at least one inhomogeneity.
Definition at line 1160 of file constraint_matrix.cc.

inline 
Return a pointer to the vector of entries if a line is constrained, and a zero pointer in case the dof is not constrained.
Definition at line 1640 of file constraint_matrix.h.

inline 
Return the value of the inhomogeneity stored in the constrained dof line
. Unconstrained dofs also return a zero value.
Definition at line 1656 of file constraint_matrix.h.
void ConstraintMatrix::print  (  std::ostream &  out  )  const 
Print the constraints represented by the current object to the given stream.
For each constraint of the form
\[ x_{42} = 0.5 x_2 + 0.25 x_{14} + 2.75 \]
this function will write a sequence of lines that look like this:
The last line is only shown if the inhomogeneity (here: 2.75) is nonzero.
A block of lines such as the one above is repeated for each constrained degree of freedom.
Definition at line 1171 of file constraint_matrix.cc.
void ConstraintMatrix::write_dot  (  std::ostream &  out  )  const 
Write the graph of constraints in 'dot' format. 'dot' is a program that can take a list of nodes and produce a graphical representation of the graph of constrained degrees of freedom and the degrees of freedom they are constrained to.
The output of this function can be used as input to the 'dot' program that can convert the graph into a graphical representation in postscript, png, xfig, and a number of other formats.
This function exists mostly for debugging purposes.
Definition at line 1208 of file constraint_matrix.cc.
std::size_t ConstraintMatrix::memory_consumption  (  )  const 
Determine an estimate for the memory consumption (in bytes) of this object.
Definition at line 1230 of file constraint_matrix.cc.
void ConstraintMatrix::resolve_indices  (  std::vector< types::global_dof_index > &  indices  )  const 
Add the constraint indices associated to the indices in the given vector. After a call to this function, the indices vector contains the initial elements and all the associated constrained indices. This function sorts the elements and suppresses duplicates.
Definition at line 1241 of file constraint_matrix.cc.
void ConstraintMatrix::condense  (  SparsityPattern &  sparsity  )  const 
Condense a sparsity pattern. The name of the function mimics the name of the function we use to condense linear systems, but it is a bit of a misnomer for the current context. This is because in the context of linear systems, we eliminate certain rows and columns of the linear system, i.e., we "reduce" or "condense" the linear system. On the other hand, in the current context, the functions does not remove nonzero entries from the sparsity pattern. Rather, it adds those nonzero entry locations to the sparsity pattern that will later be needed for the process of condensation of constrained degrees of freedom from a linear system.
Since this function adds new nonzero entries to the sparsity pattern, the given sparsity pattern must not be compressed. The constraint matrix (i.e., the current object) must be closed. The sparsity pattern is compressed at the end of the function.
Definition at line 699 of file constraint_matrix.cc.
void ConstraintMatrix::condense  (  BlockSparsityPattern &  sparsity  )  const 
Same function as above, but condenses square block sparsity patterns.
Definition at line 873 of file constraint_matrix.cc.
void ConstraintMatrix::condense  (  DynamicSparsityPattern &  sparsity  )  const 
Same function as above, but condenses square compressed sparsity patterns.
Definition at line 783 of file constraint_matrix.cc.
void ConstraintMatrix::condense  (  BlockDynamicSparsityPattern &  sparsity  )  const 
Same function as above, but condenses square compressed sparsity patterns.
Definition at line 985 of file constraint_matrix.cc.
void ConstraintMatrix::condense  (  SparseMatrix< number > &  matrix  )  const 
Condense a given matrix, i.e., eliminate the rows and columns of the matrix that correspond to constrained degrees of freedom.
See the general documentation of this class for more detailed information.
void ConstraintMatrix::condense  (  BlockSparseMatrix< number > &  matrix  )  const 
Same function as above, but condenses square block sparse matrices.
void ConstraintMatrix::condense  (  VectorType &  vec  )  const 
Condense the given vector inplace. The VectorType
may be a Vector<float>, Vector<double>, BlockVector<...>
, a PETSc or Trilinos vector wrapper class, or any other type having the same interface. Note that this function does not take any inhomogeneity into account and throws an exception in case there are any inhomogeneities. Use the function using both a matrix and vector for that case.
void ConstraintMatrix::condense  (  const VectorType &  vec_ghosted, 
VectorType &  output  
)  const 
The function copies and condenses values from vec_ghosted
into output
. In a serial code it is equivalent to calling condense (vec). If called in parallel, vec_ghosted
is supposed to contain ghost elements while output
should not.
void ConstraintMatrix::condense  (  SparseMatrix< number > &  matrix, 
VectorType &  vector  
)  const 
Condense a given matrix and a given vector by eliminating rows and columns of the linear system that correspond to constrained degrees of freedom. The sparsity pattern associated with the matrix needs to be condensed and compressed. This function is the appropriate choice for applying inhomogeneous constraints.
The constraint matrix object must be closed to call this function.
See the general documentation of this class for more detailed information.
void ConstraintMatrix::condense  (  BlockSparseMatrix< number > &  matrix, 
BlockVectorType &  vector  
)  const 
Same function as above, but condenses square block sparse matrices and vectors.
void ConstraintMatrix::set_zero  (  VectorType &  vec  )  const 
Set the values of all constrained DoFs in a vector to zero. The VectorType
may be a Vector<float>, Vector<double>, BlockVector<...>
, a PETSc or Trilinos vector wrapper class, or any other type having the same interface.

inline 
This function takes a vector of local contributions (local_vector
) corresponding to the degrees of freedom indices given in local_dof_indices
and distributes them to the global vector. In most cases, these local contributions will be the result of an integration over a cell or face of a cell. However, as long as local_vector
and local_dof_indices
have the same number of elements, this function is happy with whatever it is given.
In contrast to the similar function in the DoFAccessor class, this function also takes care of constraints, i.e. if one of the elements of local_dof_indices
belongs to a constrained node, then rather than writing the corresponding element of local_vector
into global_vector
, the element is distributed to the entries in the global vector to which this particular degree of freedom is constrained.
Thus, by using this function to distribute local contributions to the global object, one saves the call to the condense function after the vectors and matrices are fully assembled. On the other hand, by consequence, the function does not only write into the entries enumerated by the local_dof_indices
array, but also (possibly) others as necessary.
Note that this function will apply all constraints as if they were homogeneous. For correctly setting inhomogeneous constraints, use the similar function with a matrix argument or the function with both matrix and vector arguments.
[in]  local_vector  Vector of local contributions. 
[in]  local_dof_indices  Local degrees of freedom indices corresponding to the vector of local contributions. 
[out]  global_vector  The global vector to which all local contributions will be added. 
Definition at line 1756 of file constraint_matrix.h.
void ConstraintMatrix::distribute_local_to_global  (  const Vector< LocalType > &  local_vector, 
const std::vector< size_type > &  local_dof_indices,  
VectorType &  global_vector,  
const FullMatrix< LocalType > &  local_matrix  
)  const 
This function takes a vector of local contributions (local_vector
) corresponding to the degrees of freedom indices given in local_dof_indices
and distributes them to the global vector. In most cases, these local contributions will be the result of an integration over a cell or face of a cell. However, as long as local_vector
and local_dof_indices
have the same number of elements, this function is happy with whatever it is given.
In contrast to the similar function in the DoFAccessor class, this function also takes care of constraints, i.e. if one of the elements of local_dof_indices
belongs to a constrained node, then rather than writing the corresponding element of local_vector
into global_vector
, the element is distributed to the entries in the global vector to which this particular degree of freedom is constrained.
Thus, by using this function to distribute local contributions to the global object, one saves the call to the condense function after the vectors and matrices are fully assembled. On the other hand, by consequence, the function does not only write into the entries enumerated by the local_dof_indices
array, but also (possibly) others as necessary. This includes writing into diagonal elements of the matrix if the corresponding degree of freedom is constrained.
The fourth argument local_matrix
is intended to be used in case one wants to apply inhomogeneous constraints on the vector only. Such a situation could be where one wants to assemble of a right hand side vector on a problem with inhomogeneous constraints, but the global matrix has been assembled previously. A typical example of this is a time stepping algorithm where the stiffness matrix is assembled once, and the right hand side updated every time step. Note that, however, the entries in the columns of the local matrix have to be exactly the same as those that have been written into the global matrix. Otherwise, this function will not be able to correctly handle inhomogeneities.
void ConstraintMatrix::distribute_local_to_global  (  const Vector< LocalType > &  local_vector, 
const std::vector< size_type > &  local_dof_indices_row,  
const std::vector< size_type > &  local_dof_indices_col,  
VectorType &  global_vector,  
const FullMatrix< LocalType > &  local_matrix,  
bool  diagonal = false 

)  const 
Same as the previous function, except that it uses two (possibly) different index sets to correctly handle inhomogeneities when the local matrix is computed from a combination of two neighboring elements, for example for an edge integral term in DG. Note that in the case that these two elements have different polynomial degree, the local matrix is rectangular.
local_dof_indices_row
is the set of row indices and local_dof_indices_col
is the set of column indices of the local matrix. diagonal=false
says whether the two index sets are equal or not.
If both index sets are equal, diagonal
must be set to true or we simply use the previous function. If both index sets are different (diagonal=false) the global_vector
is modified to handle inhomogeneities but no entries from local_vector
are added. Note that the edge integrals for inner edged for DG do not contribute any values to the right hand side.

inline 
Enter a single value into a result vector, obeying constraints.
Definition at line 1704 of file constraint_matrix.h.

inline 
This function takes a pointer to a vector of local contributions (local_vector
) corresponding to the degrees of freedom indices given in local_dof_indices
and distributes them to the global vector. In most cases, these local contributions will be the result of an integration over a cell or face of a cell. However, as long as the entries in local_dof_indices
indicate reasonable global vector entries, this function is happy with whatever it is given.
If one of the elements of local_dof_indices
belongs to a constrained node, then rather than writing the corresponding element of local_vector
into global_vector
, the element is distributed to the entries in the global vector to which this particular degree of freedom is constrained.
Thus, by using this function to distribute local contributions to the global object, one saves the call to the condense function after the vectors and matrices are fully assembled. Note that this function completely ignores inhomogeneous constraints.
Definition at line 1727 of file constraint_matrix.h.

inline 
This function takes a matrix of local contributions (local_matrix
) corresponding to the degrees of freedom indices given in local_dof_indices
and distributes them to the global matrix. In most cases, these local contributions will be the result of an integration over a cell or face of a cell. However, as long as local_matrix
and local_dof_indices
have the same number of elements, this function is happy with whatever it is given.
In contrast to the similar function in the DoFAccessor class, this function also takes care of constraints, i.e. if one of the elements of local_dof_indices
belongs to a constrained node, then rather than writing the corresponding element of local_matrix
into global_matrix
, the element is distributed to the entries in the global matrix to which this particular degree of freedom is constrained.
With this scheme, we never write into rows or columns of constrained degrees of freedom. In order to make sure that the resulting matrix can still be inverted, we need to do something with the diagonal elements corresponding to constrained nodes. Thus, if a degree of freedom in local_dof_indices
is constrained, we distribute the corresponding entries in the matrix, but also add the absolute value of the diagonal entry of the local matrix to the corresponding entry in the global matrix. Assuming the discretized operator is positive definite, this guarantees that the diagonal entry is always nonzero, positive, and of the same order of magnitude as the other entries of the matrix. On the other hand, when solving a source problem \(Au=f\) the exact value of the diagonal element is not important, since the value of the respective degree of freedom will be overwritten by the distribute() call later on anyway.
By using this function to distribute local contributions to the global object, one saves the call to the condense function after the vectors and matrices are fully assembled.
Definition at line 1882 of file constraint_matrix.h.
void ConstraintMatrix::distribute_local_to_global  (  const FullMatrix< typename MatrixType::value_type > &  local_matrix, 
const std::vector< size_type > &  row_indices,  
const std::vector< size_type > &  col_indices,  
MatrixType &  global_matrix  
)  const 
Does almost the same as the function above but can treat general rectangular matrices. The main difference to achieve this is that the diagonal entries in constrained rows are left untouched instead of being filled with arbitrary values.
Since the diagonal entries corresponding to eliminated degrees of freedom are not set, the result may have a zero eigenvalue, if applied to a square matrix. This has to be considered when solving the resulting problems. For solving a source problem \(Au=f\), it is possible to set the diagonal entry after building the matrix by a piece of code of the form
The value of one which is used here is arbitrary, but in the context of Krylov space methods uncritical, since it corresponds to an invariant subspace. If the other matrix entries are smaller or larger by a factor close to machine accuracy, it may be advisable to adjust it.
For solving eigenvalue problems, this will only add one spurious zero eigenvalue (with a multiplicity that is possibly greater than one). Taking this into account, nothing else has to be changed.
void ConstraintMatrix::distribute_local_to_global  (  const FullMatrix< typename MatrixType::value_type > &  local_matrix, 
const std::vector< size_type > &  row_indices,  
const ConstraintMatrix &  column_constraint_matrix,  
const std::vector< size_type > &  column_indices,  
MatrixType &  global_matrix  
)  const 
Does almost the same as the function above for general rectangular matrices but uses different ConstraintMatrix objects on the row and column indices. The convention is that row indices are constrained according to the calling ConstraintMatrix *this
, whereas column indices are constrained according to the given ConstraintMatrix column_constraint_matrix
. This function allows to handle the case where rows and columns of a matrix are represented by different function spaces with their own enumeration of indices, as e.g. in mixed finite element problems with separate DoFHandler objects or for flux matrices between different levels in multigrid methods.
Like the other method with separate slots for row and column indices, this method does not add diagonal entries to eliminated degrees of freedom. See there for a more elaborate description.

inline 
This function simultaneously writes elements into matrix and vector, according to the constraints specified by the calling ConstraintMatrix. This function can correctly handle inhomogeneous constraints as well. For the parameter use_inhomogeneities_for_rhs see the documentation in Constraints on degrees of freedom module.
Definition at line 1901 of file constraint_matrix.h.

inline 
Do a similar operation as the distribute_local_to_global() function that distributes writing entries into a matrix for constrained degrees of freedom, except that here we don't write into a matrix but only allocate sparsity pattern entries.
As explained in the hp paper and in step27, first allocating a sparsity pattern and later coming back and allocating additional entries for those matrix entries that will be written to due to the elimination of constrained degrees of freedom (using ConstraintMatrix::condense() ), can be a very expensive procedure. It is cheaper to allocate these entries right away without having to do a second pass over the sparsity pattern object. This function does exactly that.
Because the function only allocates entries in a sparsity pattern, all it needs to know are the degrees of freedom that couple to each other. Unlike the previous function, no actual values are written, so the second input argument is not necessary here.
The third argument to this function, keep_constrained_entries determines whether the function shall allocate entries in the sparsity pattern at all for entries that will later be set to zero upon condensation of the matrix. These entries are necessary if the matrix is built unconstrained, and only later condensed. They are not necessary if the matrix is built using the distribute_local_to_global() function of this class which distributes entries right away when copying a local matrix into a global object. The default of this argument is true, meaning to allocate the few entries that may later be set to zero.
By default, the function adds entries for all pairs of indices given in the first argument to the sparsity pattern (unless keep_constrained_entries is false). However, sometimes one would like to only add a subset of all of these pairs. In that case, the last argument can be used which specifies a boolean mask which of the pairs of indices should be considered. If the mask is false for a pair of indices, then no entry will be added to the sparsity pattern for this pair, irrespective of whether one or both of the indices correspond to constrained degrees of freedom.
This function is not typically called from user code, but is used in the DoFTools::make_sparsity_pattern() function when passed a constraint matrix object.
Definition at line 1922 of file constraint_matrix.h.
void ConstraintMatrix::add_entries_local_to_global  (  const std::vector< size_type > &  row_indices, 
const std::vector< size_type > &  col_indices,  
SparsityPatternType &  sparsity_pattern,  
const bool  keep_constrained_entries = true , 

const Table< 2, bool > &  dof_mask = default_empty_table 

)  const 
Similar to the other function, but for nonquadratic sparsity patterns.

inline 
This function imports values from a global vector (global_vector
) by applying the constraints to a vector of local values, expressed in iterator format. In most cases, the local values will be identified by the local dof values on a cell. However, as long as the entries in local_dof_indices
indicate reasonable global vector entries, this function is happy with whatever it is given.
If one of the elements of local_dof_indices
belongs to a constrained node, then rather than writing the corresponding element of global_vector
into local_vector
, the constraints are resolved as the respective distribute function does, i.e., the local entry is constructed from the global entries to which this particular degree of freedom is constrained.
In contrast to the similar function get_dof_values in the DoFAccessor class, this function does not need the constrained values to be correctly set (i.e., distribute to be called).
Definition at line 1772 of file constraint_matrix.h.
void ConstraintMatrix::distribute  (  VectorType &  vec  )  const 
Given a vector, set all constrained degrees of freedom to values so that the constraints are satisfied. For example, if the current object stores the constraint \(x_3=\frac 12 x_1 + \frac 12 x_2\), then this function will read the values of \(x_1\) and \(x_1\) from the given vector and set the element \(x_3\) according to this constraints. Similarly, if the current object stores the constraint \(x_{42}=208\), then this function will set the 42nd element of the given vector to 208.
vec
, then the vector must not contain ghost elements. const ConstraintMatrix::LineRange ConstraintMatrix::get_lines  (  )  const 
Return a range object containing (const) iterators to all line entries stored in the ConstraintMatrix. Such a range is useful to initialize rangebased for loops as supported by C++11.
[this>begin(), this>end())
of line entries. Definition at line 100 of file constraint_matrix.cc.

inlineprivate 
Internal function to calculate the index of line line
in the vector lines_cache using local_lines.
Definition at line 1671 of file constraint_matrix.h.

staticprivate 
Return true
if the weight of an entry (the second element of the pair) equals zero. This function is used to delete entries with zero weight.
Definition at line 67 of file constraint_matrix.cc.

private 
This function actually implements the local_to_global function for standard (nonblock) matrices.

private 
This function actually implements the local_to_global function for block matrices.

private 
This function actually implements the local_to_global function for standard (nonblock) sparsity types.

private 
This function actually implements the local_to_global function for block sparsity types.

private 
Internal helper function for distribute_local_to_global function.
Creates a list of affected global rows for distribution, including the local rows where the entries come from. The list is sorted according to the global row indices.

private 
Internal helper function for add_entries_local_to_global function.
Creates a list of affected rows for distribution without any additional information, otherwise similar to the other make_sorted_row_list() function.

private 
Internal helper function for distribute_local_to_global function.

private 
Store the lines of the matrix. Entries are usually appended in an arbitrary order and insertion into a vector is done best at the end, so the order is unspecified after all entries are inserted. Sorting of the entries takes place when calling the close()
function.
We could, instead of using a vector, use an associative array, like a map to store the lines. This, however, would mean a much more fragmented heap since it allocates many small objects, and would additionally make usage of this matrix much slower.
Definition at line 1324 of file constraint_matrix.h.

private 
A list of size_type that contains the position of the ConstraintLine of a constrained degree of freedom, or numbers::invalid_size_type if the degree of freedom is not constrained. The numbers::invalid_size_type return value returns thus whether there is a constraint line for a given degree of freedom index. Note that this class has no notion of how many degrees of freedom there really are, so if we check whether there is a constraint line for a given degree of freedom, then this vector may actually be shorter than the index of the DoF we check for.
This field exists since when adding a new constraint line we have to figure out whether it already exists. Previously, we would simply walk the unsorted list of constraint lines until we either hit the end or found it. This algorithm is O(N) if N is the number of constraints, which makes it O(N^2) when inserting all constraints. For large problems with many constraints, this could easily take 510 per cent of the total run time. With this field, we can save this time since we find any constraint in O(1) time or get to know that it a certain degree of freedom is not constrained.
To make things worse, traversing the list of existing constraints requires reads from many different places in memory. Thus, in large 3d applications, the add_line() function showed up very prominently in the overall compute time, mainly because it generated a lot of cache misses. This should also be fixed by using the O(1) algorithm to access the fields of this array.
The field is useful in a number of other contexts as well, e.g. when one needs random access to the constraints as in all the functions that apply constraints on the fly while add cell contributions into vectors and matrices.
Definition at line 1358 of file constraint_matrix.h.

private 
This IndexSet is used to limit the lines to save in the ConstraintMatrix to a subset. This is necessary, because the lines_cache vector would become too big in a distributed calculation.
Definition at line 1365 of file constraint_matrix.h.

private 
Store whether the arrays are sorted. If so, no new entries can be added.
Definition at line 1370 of file constraint_matrix.h.
Dummy table that serves as default argument for function add_entries_local_to_global()
.
Definition at line 1388 of file constraint_matrix.h.