Reference documentation for deal.II version GIT eef19498cf 20221005 14:45:02+00:00

#include <deal.II/lac/petsc_sparse_matrix.h>
Classes  
struct  Traits 
Public Types  
using  size_type = types::global_dof_index 
using  const_iterator = MatrixIterators::const_iterator 
using  value_type = PetscScalar 
Public Member Functions  
SparseMatrix ()  
~SparseMatrix () override  
template<typename SparsityPatternType >  
SparseMatrix (const MPI_Comm &communicator, const SparsityPatternType &sparsity_pattern, const std::vector< size_type > &local_rows_per_process, const std::vector< size_type > &local_columns_per_process, const unsigned int this_process, const bool preset_nonzero_locations=true)  
SparseMatrix &  operator= (const value_type d) 
void  copy_from (const SparseMatrix &other) 
template<typename SparsityPatternType >  
void  reinit (const MPI_Comm &communicator, const SparsityPatternType &sparsity_pattern, const std::vector< size_type > &local_rows_per_process, const std::vector< size_type > &local_columns_per_process, const unsigned int this_process, const bool preset_nonzero_locations=true) 
template<typename SparsityPatternType >  
void  reinit (const IndexSet &local_rows, const IndexSet &local_columns, const SparsityPatternType &sparsity_pattern, const MPI_Comm &communicator) 
void  reinit (const SparseMatrix &other) 
template<typename SparsityPatternType >  
void  reinit (const IndexSet &local_rows, const IndexSet &local_active_rows, const IndexSet &local_columns, const IndexSet &local_active_columns, const SparsityPatternType &sparsity_pattern, const MPI_Comm &communicator) 
virtual const MPI_Comm &  get_mpi_communicator () const override 
PetscScalar  matrix_norm_square (const Vector &v) const 
PetscScalar  matrix_scalar_product (const Vector &u, const Vector &v) const 
IndexSet  locally_owned_domain_indices () const 
IndexSet  locally_owned_range_indices () const 
void  mmult (SparseMatrix &C, const SparseMatrix &B, const MPI::Vector &V=MPI::Vector()) const 
void  Tmmult (SparseMatrix &C, const SparseMatrix &B, const MPI::Vector &V=MPI::Vector()) const 
void  clear () 
void  set (const size_type i, const size_type j, const PetscScalar value) 
void  set (const std::vector< size_type > &indices, const FullMatrix< PetscScalar > &full_matrix, const bool elide_zero_values=false) 
void  set (const std::vector< size_type > &row_indices, const std::vector< size_type > &col_indices, const FullMatrix< PetscScalar > &full_matrix, const bool elide_zero_values=false) 
void  set (const size_type row, const std::vector< size_type > &col_indices, const std::vector< PetscScalar > &values, const bool elide_zero_values=false) 
void  set (const size_type row, const size_type n_cols, const size_type *col_indices, const PetscScalar *values, const bool elide_zero_values=false) 
void  add (const size_type i, const size_type j, const PetscScalar value) 
void  add (const std::vector< size_type > &indices, const FullMatrix< PetscScalar > &full_matrix, const bool elide_zero_values=true) 
void  add (const std::vector< size_type > &row_indices, const std::vector< size_type > &col_indices, const FullMatrix< PetscScalar > &full_matrix, const bool elide_zero_values=true) 
void  add (const size_type row, const std::vector< size_type > &col_indices, const std::vector< PetscScalar > &values, const bool elide_zero_values=true) 
void  add (const size_type row, const size_type n_cols, const size_type *col_indices, const PetscScalar *values, const bool elide_zero_values=true, const bool col_indices_are_sorted=false) 
MatrixBase &  add (const PetscScalar factor, const MatrixBase &other) 
void  clear_row (const size_type row, const PetscScalar new_diag_value=0) 
void  clear_rows (const std::vector< size_type > &rows, const PetscScalar new_diag_value=0) 
void  compress (const VectorOperation::values operation) 
PetscScalar  operator() (const size_type i, const size_type j) const 
PetscScalar  el (const size_type i, const size_type j) const 
PetscScalar  diag_element (const size_type i) const 
size_type  m () const 
size_type  n () const 
size_type  local_size () const 
std::pair< size_type, size_type >  local_range () const 
bool  in_local_range (const size_type index) const 
std::uint64_t  n_nonzero_elements () const 
size_type  row_length (const size_type row) const 
PetscReal  l1_norm () const 
PetscReal  linfty_norm () const 
PetscReal  frobenius_norm () const 
PetscScalar  matrix_norm_square (const VectorBase &v) const 
PetscScalar  matrix_scalar_product (const VectorBase &u, const VectorBase &v) const 
PetscScalar  trace () const 
MatrixBase &  operator*= (const PetscScalar factor) 
MatrixBase &  operator/= (const PetscScalar factor) 
void  vmult (VectorBase &dst, const VectorBase &src) const 
void  Tvmult (VectorBase &dst, const VectorBase &src) const 
void  vmult_add (VectorBase &dst, const VectorBase &src) const 
void  Tvmult_add (VectorBase &dst, const VectorBase &src) const 
PetscScalar  residual (VectorBase &dst, const VectorBase &x, const VectorBase &b) const 
const_iterator  begin () const 
const_iterator  begin (const size_type r) const 
const_iterator  end () const 
const_iterator  end (const size_type r) const 
operator Mat () const  
Mat &  petsc_matrix () 
void  transpose () 
PetscBool  is_symmetric (const double tolerance=1.e12) 
PetscBool  is_hermitian (const double tolerance=1.e12) 
void  write_ascii (const PetscViewerFormat format=PETSC_VIEWER_DEFAULT) 
void  print (std::ostream &out, const bool alternative_output=false) 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 &  ExcLocalRowsTooLarge (int arg1, int arg2) 
static ::ExceptionBase &  ExcSourceEqualsDestination () 
static ::ExceptionBase &  ExcWrongMode (int arg1, int arg2) 
static ::ExceptionBase &  ExcInUse (int arg1, std::string arg2, std::string arg3) 
static ::ExceptionBase &  ExcNoSubscriber (std::string arg1, std::string arg2) 
Protected Member Functions  
void  prepare_action (const VectorOperation::values new_action) 
void  assert_is_compressed () 
void  prepare_add () 
void  prepare_set () 
void  mmult (MatrixBase &C, const MatrixBase &B, const VectorBase &V) const 
void  Tmmult (MatrixBase &C, const MatrixBase &B, const VectorBase &V) const 
Protected Attributes  
Mat  matrix 
VectorOperation::values  last_action 
Private Types  
using  map_value_type = decltype(counter_map)::value_type 
using  map_iterator = decltype(counter_map)::iterator 
Private Member Functions  
template<typename SparsityPatternType >  
void  do_reinit (const SparsityPatternType &sparsity_pattern, const std::vector< size_type > &local_rows_per_process, const std::vector< size_type > &local_columns_per_process, const unsigned int this_process, const bool preset_nonzero_locations) 
template<typename SparsityPatternType >  
void  do_reinit (const IndexSet &local_rows, const IndexSet &local_columns, const SparsityPatternType &sparsity_pattern) 
template<typename SparsityPatternType >  
void  do_reinit (const IndexSet &local_rows, const IndexSet &local_active_rows, const IndexSet &local_columns, const IndexSet &local_active_columns, const SparsityPatternType &sparsity_pattern) 
void  check_no_subscribers () const noexcept 
Private Attributes  
MPI_Comm  communicator 
std::vector< PetscInt >  column_indices 
std::vector< PetscScalar >  column_values 
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 
Friends  
class  BlockMatrixBase< SparseMatrix > 
Implementation of a parallel sparse matrix class based on PETSc, with rows of the matrix distributed across an MPI network. All the functionality is actually in the base class, except for the calls to generate a parallel sparse matrix. This is possible since PETSc only works on an abstract matrix type and internally distributes to functions that do the actual work depending on the actual matrix type (much like using virtual functions). Only the functions creating a matrix of specific type differ, and are implemented in this particular class.
There are a number of comments on the communication model as well as access to individual elements in the documentation to the parallel vector class. These comments apply here as well.
PETSc partitions parallel matrices so that each MPI process "owns" a certain number of rows (i.e. only this process stores the respective entries in these rows). The number of rows each process owns has to be passed to the constructors and reinit() functions via the argument local_rows
. The individual values passed as local_rows
on all the MPI processes of course have to add up to the global number of rows of the matrix.
In addition to this, PETSc also partitions the rectangular chunk of the matrix it owns (i.e. the local_rows
times n() elements in the matrix), so that matrix vector multiplications can be performed efficiently. This columnpartitioning therefore has to match the partitioning of the vectors with which the matrix is multiplied, just as the rowpartitioning has to match the partitioning of destination vectors. This partitioning is passed to the constructors and reinit() functions through the local_columns
variable, which again has to add up to the global number of columns in the matrix. The name local_columns
may be named inappropriately since it does not reflect that only these columns are stored locally, but it reflects the fact that these are the columns for which the elements of incoming vectors are stored locally.
To make things even more complicated, PETSc needs a very good estimate of the number of elements to be stored in each row to be efficient. Otherwise it spends most of the time with allocating small chunks of memory, a process that can slow down programs to a crawl if it happens to often. As if a good estimate of the number of entries per row isn't even, it even needs to split this as follows: for each row it owns, it needs an estimate for the number of elements in this row that fall into the columns that are set apart for this process (see above), and the number of elements that are in the rest of the columns.
Since in general this information is not readily available, most of the initializing functions of this class assume that all of the number of elements you give as an argument to n_nonzero_per_row
or by row_lengths
fall into the columns "owned" by this process, and none into the other ones. This is a fair guess for most of the rows, since in a good domain partitioning, nodes only interact with nodes that are within the same subdomain. It does not hold for nodes on the interfaces of subdomain, however, and for the rows corresponding to these nodes, PETSc will have to allocate additional memory, a costly process.
The only way to avoid this is to tell PETSc where the actual entries of the matrix will be. For this, there are constructors and reinit() functions of this class that take a DynamicSparsityPattern object containing all this information. While in the general case it is sufficient if the constructors and reinit() functions know the number of local rows and columns, the functions getting a sparsity pattern also need to know the number of local rows (local_rows_per_process
) and columns (local_columns_per_process
) for all other processes, in order to compute which parts of the matrix are which. Thus, it is not sufficient to just count the number of degrees of freedom that belong to a particular process, but you have to have the numbers for all processes available at all processes.
Definition at line 368 of file petsc_sparse_matrix.h.
Declare type for container size.
Definition at line 374 of file petsc_sparse_matrix.h.

inherited 
Declare an alias for the iterator class.
Definition at line 290 of file petsc_matrix_base.h.

inherited 
Declare an alias in analogy to all the other container classes.
Definition at line 300 of file petsc_matrix_base.h.

privateinherited 
The data type used in counter_map.
Definition at line 230 of file subscriptor.h.

privateinherited 
The iterator type used in counter_map.
Definition at line 235 of file subscriptor.h.
SparseMatrix< number >::SparseMatrix  (  ) 
Default constructor. Create an empty matrix.
Definition at line 34 of file petsc_parallel_sparse_matrix.cc.

override 
Destructor to free the PETSc object.
Definition at line 47 of file petsc_parallel_sparse_matrix.cc.
SparseMatrix< SparsityPatternType >::SparseMatrix  (  const MPI_Comm &  communicator, 
const SparsityPatternType &  sparsity_pattern,  
const std::vector< size_type > &  local_rows_per_process,  
const std::vector< size_type > &  local_columns_per_process,  
const unsigned int  this_process,  
const bool  preset_nonzero_locations = true 

) 
Initialize using the given sparsity pattern with communication happening over the provided communicator
.
For the meaning of the local_rows_per_process
and local_columns_per_process
parameters, see the class documentation.
Note that PETSc can be very slow if you do not provide it with a good estimate of the lengths of rows. Using the present function is a very efficient way to do this, as it uses the exact number of nonzero entries for each row of the matrix by using the given sparsity pattern argument. If the preset_nonzero_locations
flag is true
, this function in addition not only sets the correct row sizes up front, but also preallocated the correct nonzero entries in the matrix.
PETsc allows to later add additional nonzero entries to a matrix, by simply writing to these elements. However, this will then lead to additional memory allocations which are very inefficient and will greatly slow down your program. It is therefore significantly more efficient to get memory allocation right from the start.
Definition at line 55 of file petsc_parallel_sparse_matrix.cc.
SparseMatrix & SparseMatrix< number >::operator=  (  const value_type  d  ) 
This operator assigns a scalar to a matrix. Since this does usually not make much sense (should we set all matrix entries to this value? Only the nonzero entries of the sparsity pattern?), this operation is only allowed if the actual value to be assigned is zero. This operator only exists to allow for the obvious notation matrix=0
, which sets all elements of the matrix to zero, but keep the sparsity pattern previously used.
Definition at line 112 of file petsc_parallel_sparse_matrix.cc.
void SparseMatrix< number >::copy_from  (  const SparseMatrix &  other  ) 
Make a copy of the PETSc matrix other
. It is assumed that both matrices have the same SparsityPattern.
Definition at line 119 of file petsc_parallel_sparse_matrix.cc.
void SparseMatrix< SparsityPatternType >::reinit  (  const MPI_Comm &  communicator, 
const SparsityPatternType &  sparsity_pattern,  
const std::vector< size_type > &  local_rows_per_process,  
const std::vector< size_type > &  local_columns_per_process,  
const unsigned int  this_process,  
const bool  preset_nonzero_locations = true 

) 
Initialize using the given sparsity pattern with communication happening over the provided communicator
.
Note that PETSc can be very slow if you do not provide it with a good estimate of the lengths of rows. Using the present function is a very efficient way to do this, as it uses the exact number of nonzero entries for each row of the matrix by using the given sparsity pattern argument. If the preset_nonzero_locations
flag is true
, this function in addition not only sets the correct row sizes up front, but also preallocated the correct nonzero entries in the matrix.
PETsc allows to later add additional nonzero entries to a matrix, by simply writing to these elements. However, this will then lead to additional memory allocations which are very inefficient and will greatly slow down your program. It is therefore significantly more efficient to get memory allocation right from the start.
Definition at line 135 of file petsc_parallel_sparse_matrix.cc.
void SparseMatrix< SparsityPatternType >::reinit  (  const IndexSet &  local_rows, 
const IndexSet &  local_columns,  
const SparsityPatternType &  sparsity_pattern,  
const MPI_Comm &  communicator  
) 
Create a matrix where the size() of the IndexSets determine the global number of rows and columns and the entries of the IndexSet give the rows and columns for the calling processor. Note that only ascending, 1:1 IndexSets are supported.
Definition at line 161 of file petsc_parallel_sparse_matrix.cc.
void SparseMatrix< number >::reinit  (  const SparseMatrix &  other  ) 
Initialize this matrix to have the same structure as other
. This will not copy the values of the other matrix, but you can use copy_from() for this.
Definition at line 74 of file petsc_parallel_sparse_matrix.cc.
void SparseMatrix< SparsityPatternType >::reinit  (  const IndexSet &  local_rows, 
const IndexSet &  local_active_rows,  
const IndexSet &  local_columns,  
const IndexSet &  local_active_columns,  
const SparsityPatternType &  sparsity_pattern,  
const MPI_Comm &  communicator  
) 
Create a matrix where the size of the IndexSets determine the global number of rows and columns and the entries of the IndexSet give the rows and columns for the calling processor. Note that only ascending, 1:1 IndexSets are supported. The additional call to the local to global mappings is required to create the matrix of type IS (see DoFTools::extract_locally_active_dofs). This is required by the BDDC preconditioner.
Definition at line 90 of file petsc_parallel_sparse_matrix.cc.

inlineoverridevirtual 
Return a reference to the MPI communicator object in use with this matrix.
Implements PETScWrappers::MatrixBase.
Definition at line 658 of file petsc_sparse_matrix.h.
PetscScalar SparseMatrix< number >::matrix_norm_square  (  const Vector &  v  )  const 
Return the square of the norm of the vector \(v\) with respect to the norm induced by this matrix, i.e. \(\left(v^\ast,Mv\right)\). This is useful, e.g. in the finite element context, where the \(L_2\) norm of a function equals the matrix norm with respect to the mass matrix of the vector representing the nodal values of the finite element function.
Obviously, the matrix needs to be quadratic for this operation.
The implementation of this function is not as efficient as the one in the MatrixBase
class used in deal.II (i.e. the original one, not the PETSc wrapper class) since PETSc doesn't support this operation and needs a temporary vector.
Definition at line 755 of file petsc_parallel_sparse_matrix.cc.
PetscScalar SparseMatrix< number >::matrix_scalar_product  (  const Vector &  u, 
const Vector &  v  
)  const 
Compute the matrix scalar product \(\left(u^\ast,Mv\right)\).
The implementation of this function is not as efficient as the one in the MatrixBase
class used in deal.II (i.e. the original one, not the PETSc wrapper class) since PETSc doesn't support this operation and needs a temporary vector.
Definition at line 764 of file petsc_parallel_sparse_matrix.cc.
IndexSet SparseMatrix< number >::locally_owned_domain_indices  (  )  const 
Return the partitioning of the domain space of this matrix, i.e., the partitioning of the vectors this matrix has to be multiplied with.
Definition at line 773 of file petsc_parallel_sparse_matrix.cc.
IndexSet SparseMatrix< number >::locally_owned_range_indices  (  )  const 
Return the partitioning of the range space of this matrix, i.e., the partitioning of the vectors that result from matrixvector products.
Definition at line 799 of file petsc_parallel_sparse_matrix.cc.
void SparseMatrix< number >::mmult  (  SparseMatrix &  C, 
const SparseMatrix &  B,  
const MPI::Vector &  V = MPI::Vector() 

)  const 
Perform the matrixmatrix multiplication \(C = AB\), or, \(C = A \text{diag}(V) B\) given a compatible vector \(V\).
This function calls MatrixBase::mmult() to do the actual work.
Definition at line 825 of file petsc_parallel_sparse_matrix.cc.
void SparseMatrix< number >::Tmmult  (  SparseMatrix &  C, 
const SparseMatrix &  B,  
const MPI::Vector &  V = MPI::Vector() 

)  const 
Perform the matrixmatrix multiplication with the transpose of this
, i.e., \(C = A^T B\), or, \(C = A^T \text{diag}(V) B\) given a compatible vector \(V\).
This function calls MatrixBase::Tmmult() to do the actual work.
Definition at line 836 of file petsc_parallel_sparse_matrix.cc.

private 
Same as previous functions.
Definition at line 322 of file petsc_parallel_sparse_matrix.cc.

private 
Same as previous functions.
Definition at line 179 of file petsc_parallel_sparse_matrix.cc.

private 
Same as previous functions, but here we consider active dofs for matrices of IS type.
Definition at line 436 of file petsc_parallel_sparse_matrix.cc.

inherited 
Release all memory and return to a state just like after having called the default constructor.
Definition at line 92 of file petsc_matrix_base.cc.

inherited 
Set the element (i,j) to value
.
If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds a new entry to the matrix if it didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist. If value
is not a finite number an exception is thrown.

inherited 
Set all elements given in a FullMatrix<double> into the sparse matrix locations given by indices
. In other words, this function writes the elements in full_matrix
into the calling matrix, using the localtoglobal indexing specified by indices
for both the rows and the columns of the matrix. This function assumes a quadratic sparse matrix and a quadratic full_matrix, the usual situation in FE calculations.
If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds some new entries to the matrix if they didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist.
The optional parameter elide_zero_values
can be used to specify whether zero values should be inserted anyway or they should be filtered away. The default value is false
, i.e., even zero values are inserted/replaced.

inherited 
Same function as before, but now including the possibility to use rectangular full_matrices and different localtoglobal indexing on rows and columns, respectively.

inherited 
Set several elements in the specified row of the matrix with column indices as given by col_indices
to the respective value.
If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds some new entries to the matrix if they didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist.
The optional parameter elide_zero_values
can be used to specify whether zero values should be inserted anyway or they should be filtered away. The default value is false
, i.e., even zero values are inserted/replaced.

inherited 
Set several elements to values given by values
in a given row in columns given by col_indices into the sparse matrix.
If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds some new entries to the matrix if they didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist.
The optional parameter elide_zero_values
can be used to specify whether zero values should be inserted anyway or they should be filtered away. The default value is false
, i.e., even zero values are inserted/replaced.

inherited 
Add value
to the element (i,j).
If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds a new entry to the matrix if it didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist. If value
is not a finite number an exception is thrown.

inherited 
Add all elements given in a FullMatrix<double> into sparse matrix locations given by indices
. In other words, this function adds the elements in full_matrix
to the respective entries in calling matrix, using the localtoglobal indexing specified by indices
for both the rows and the columns of the matrix. This function assumes a quadratic sparse matrix and a quadratic full_matrix, the usual situation in FE calculations.
If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds some new entries to the matrix if they didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist.
The optional parameter elide_zero_values
can be used to specify whether zero values should be added anyway or these should be filtered away and only nonzero data is added. The default value is true
, i.e., zero values won't be added into the matrix.

inherited 
Same function as before, but now including the possibility to use rectangular full_matrices and different localtoglobal indexing on rows and columns, respectively.

inherited 
Set several elements in the specified row of the matrix with column indices as given by col_indices
to the respective value.
If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds some new entries to the matrix if they didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist.
The optional parameter elide_zero_values
can be used to specify whether zero values should be added anyway or these should be filtered away and only nonzero data is added. The default value is true
, i.e., zero values won't be added into the matrix.

inherited 
Add an array of values given by values
in the given global matrix row at columns specified by col_indices in the sparse matrix.
If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds some new entries to the matrix if they didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist.
The optional parameter elide_zero_values
can be used to specify whether zero values should be added anyway or these should be filtered away and only nonzero data is added. The default value is true
, i.e., zero values won't be added into the matrix.

inherited 
Add the matrix other
scaled by the factor factor
to the current matrix.
Definition at line 433 of file petsc_matrix_base.cc.

inherited 
Remove all elements from this row
by setting them to zero. The function does not modify the number of allocated nonzero entries, it only sets some entries to zero. It may drop them from the sparsity pattern, though (but retains the allocated memory in case new entries are again added later).
This operation is used in eliminating constraints (e.g. due to hanging nodes) and makes sure that we can write this modification to the matrix without having to read entries (such as the locations of nonzero elements) from it – without this operation, removing constraints on parallel matrices is a rather complicated procedure.
The second parameter can be used to set the diagonal entry of this row to a value different from zero. The default is to set it to zero.
Definition at line 127 of file petsc_matrix_base.cc.

inherited 
Same as clear_row(), except that it works on a number of rows at once.
The second parameter can be used to set the diagonal entries of all cleared rows to something different from zero. Note that all of these diagonal entries get the same value – if you want different values for the diagonal entries, you have to set them by hand.
Definition at line 136 of file petsc_matrix_base.cc.

inherited 
PETSc matrices store their own sparsity patterns. So, in analogy to our own SparsityPattern class, this function compresses the sparsity pattern and allows the resulting matrix to be used in all other operations where before only assembly functions were allowed. This function must therefore be called once you have assembled the matrix.
See Compressing distributed objects for more information.
Definition at line 193 of file petsc_matrix_base.cc.

inherited 
Return the value of the entry (i,j). This may be an expensive operation and you should always take care where to call this function. In contrast to the respective function in the MatrixBase
class, we don't throw an exception if the respective entry doesn't exist in the sparsity pattern of this class, since PETSc does not transmit this information.
This function is therefore exactly equivalent to the el()
function.
Return the value of the matrix entry (i,j). If this entry does not exist in the sparsity pattern, then zero is returned. While this may be convenient in some cases, note that it is simple to write algorithms that are slow compared to an optimal solution, since the sparsity of the matrix is not used.
Definition at line 165 of file petsc_matrix_base.cc.

inherited 
Return the main diagonal element in the ith row. This function throws an error if the matrix is not quadratic.
Since we do not have direct access to the underlying data structure, this function is no faster than the elementwise access using the el() function. However, we provide this function for compatibility with the SparseMatrix class.
Definition at line 181 of file petsc_matrix_base.cc.

inherited 
Return the number of rows in this matrix.
Definition at line 237 of file petsc_matrix_base.cc.

inherited 
Return the number of columns in this matrix.
Definition at line 250 of file petsc_matrix_base.cc.

inherited 
Return the local dimension of the matrix, i.e. the number of rows stored on the present MPI process. For sequential matrices, this number is the same as m(), but for parallel matrices it may be smaller.
To figure out which elements exactly are stored locally, use local_range().
Definition at line 263 of file petsc_matrix_base.cc.

inherited 
Return a pair of indices indicating which rows of this matrix are stored locally. The first number is the index of the first row stored, the second the index of the one past the last one that is stored locally. If this is a sequential matrix, then the result will be the pair (0,m()), otherwise it will be a pair (i,i+n), where n=local_size()
.
Definition at line 276 of file petsc_matrix_base.cc.
Return whether index
is in the local range or not, see also local_range().

inherited 
Return the number of nonzero elements of this matrix. Actually, it returns the number of entries in the sparsity pattern; if any of the entries should happen to be zero, it is counted anyway.
Definition at line 290 of file petsc_matrix_base.cc.

inherited 
Number of entries in a specific row.
Definition at line 304 of file petsc_matrix_base.cc.

inherited 
Return the l1norm of the matrix, that is \(M_1=max_{all columns j}\sum_{all rows i} M_ij\), (max. sum of columns). This is the natural matrix norm that is compatible to the l1norm for vectors, i.e. \(Mv_1\leq M_1 v_1\). (cf. HaemmerlinHoffmann: Numerische Mathematik)
Definition at line 340 of file petsc_matrix_base.cc.

inherited 
Return the linftynorm of the matrix, that is \(M_infty=max_{all rows i}\sum_{all columns j} M_ij\), (max. sum of rows). This is the natural matrix norm that is compatible to the linftynorm of vectors, i.e. \(Mv_infty \leq M_infty v_infty\). (cf. HaemmerlinHoffmann: Numerische Mathematik)
Definition at line 353 of file petsc_matrix_base.cc.

inherited 
Return the frobenius norm of the matrix, i.e. the square root of the sum of squares of all entries in the matrix.
Definition at line 366 of file petsc_matrix_base.cc.

inherited 
Return the square of the norm of the vector \(v\) with respect to the norm induced by this matrix, i.e. \(\left(v,Mv\right)\). This is useful, e.g. in the finite element context, where the \(L_2\) norm of a function equals the matrix norm with respect to the mass matrix of the vector representing the nodal values of the finite element function.
Obviously, the matrix needs to be quadratic for this operation.
The implementation of this function is not as efficient as the one in the MatrixBase
class used in deal.II (i.e. the original one, not the PETSc wrapper class) since PETSc doesn't support this operation and needs a temporary vector.
Note that if the current object represents a parallel distributed matrix (of type PETScWrappers::MPI::SparseMatrix), then the given vector has to be a distributed vector as well. Conversely, if the matrix is not distributed, then neither may the vector be.
Definition at line 378 of file petsc_matrix_base.cc.

inherited 
Compute the matrix scalar product \(\left(u,Mv\right)\).
The implementation of this function is not as efficient as the one in the MatrixBase
class used in deal.II (i.e. the original one, not the PETSc wrapper class) since PETSc doesn't support this operation and needs a temporary vector.
Note that if the current object represents a parallel distributed matrix (of type PETScWrappers::MPI::SparseMatrix), then both vectors have to be distributed vectors as well. Conversely, if the matrix is not distributed, then neither of the vectors may be.
Definition at line 387 of file petsc_matrix_base.cc.

inherited 
Return the trace of the matrix, i.e. the sum of all diagonal entries in the matrix.
Definition at line 397 of file petsc_matrix_base.cc.

inherited 
Multiply the entire matrix by a fixed factor.
Definition at line 410 of file petsc_matrix_base.cc.

inherited 
Divide the entire matrix by a fixed factor.
Definition at line 421 of file petsc_matrix_base.cc.

inherited 
Matrixvector multiplication: let dst = M*src with M being this matrix.
Source and destination must not be the same vector.
Note that if the current object represents a parallel distributed matrix (of type PETScWrappers::MPI::SparseMatrix), then both vectors have to be distributed vectors as well. Conversely, if the matrix is not distributed, then neither of the vectors may be.
Definition at line 444 of file petsc_matrix_base.cc.

inherited 
Matrixvector multiplication: let dst = M^{T}*src with M being this matrix. This function does the same as vmult() but takes the transposed matrix.
Source and destination must not be the same vector.
Note that if the current object represents a parallel distributed matrix (of type PETScWrappers::MPI::SparseMatrix), then both vectors have to be distributed vectors as well. Conversely, if the matrix is not distributed, then neither of the vectors may be.
Definition at line 455 of file petsc_matrix_base.cc.

inherited 
Adding Matrixvector multiplication. Add M*src on dst with M being this matrix.
Source and destination must not be the same vector.
Note that if the current object represents a parallel distributed matrix (of type PETScWrappers::MPI::SparseMatrix), then both vectors have to be distributed vectors as well. Conversely, if the matrix is not distributed, then neither of the vectors may be.
Definition at line 466 of file petsc_matrix_base.cc.

inherited 
Adding Matrixvector multiplication. Add M^{T}*src to dst with M being this matrix. This function does the same as vmult_add() but takes the transposed matrix.
Source and destination must not be the same vector.
Note that if the current object represents a parallel distributed matrix (of type PETScWrappers::MPI::SparseMatrix), then both vectors have to be distributed vectors as well. Conversely, if the matrix is not distributed, then neither of the vectors may be.
Definition at line 477 of file petsc_matrix_base.cc.

inherited 
Compute the residual of an equation Mx=b, where the residual is defined to be r=bMx. Write the residual into dst
. The l_{2} norm of the residual vector is returned.
Source x and destination dst must not be the same vector.
Note that if the current object represents a parallel distributed matrix (of type PETScWrappers::MPI::SparseMatrix), then all vectors have to be distributed vectors as well. Conversely, if the matrix is not distributed, then neither of the vectors may be.
Definition at line 577 of file petsc_matrix_base.cc.

inherited 
Iterator starting at the first entry. This can only be called on a processor owning the entire matrix. In all other cases refer to the version of begin() taking a row number as an argument.

inherited 
Iterator starting at the first entry of row r
.
Note that if the given row is empty, i.e. does not contain any nonzero entries, then the iterator returned by this function equals end(r)
. Note also that the iterator may not be dereferenceable in that case.

inherited 
Final iterator. This can only be called on a processor owning the entire matrix. In all other cases refer to the version of end() taking a row number as an argument.

inherited 
Final iterator of row r
. It points to the first element past the end of line r
, or past the end of the entire sparsity pattern.
Note that the end iterator is not necessarily dereferenceable. This is in particular the case if it is the end iterator for the last row of a matrix.

inherited 
Conversion operator to gain access to the underlying PETSc type. If you do this, you cut this class off some information it may need, so this conversion operator should only be used if you know what you do. In particular, it should only be used for readonly operations into the matrix.
Definition at line 593 of file petsc_matrix_base.cc.

inherited 
Return a reference to the underlying PETSc type. It can be used to modify the underlying data, so use it only when you know what you are doing.
Definition at line 599 of file petsc_matrix_base.cc.

inherited 
Make an inplace transpose of a matrix.
Definition at line 605 of file petsc_matrix_base.cc.

inherited 
Test whether a matrix is symmetric. Default tolerance is \(1000\times32\)bit machine precision.
Definition at line 617 of file petsc_matrix_base.cc.

inherited 
Test whether a matrix is Hermitian, i.e. it is the complex conjugate of its transpose. Default tolerance is \(1000\times32\)bit machine precision.
Definition at line 627 of file petsc_matrix_base.cc.

inherited 
Print the PETSc matrix object values using PETSc internal matrix viewer function MatView
. The default format prints the non zero matrix elements. For other valid view formats, consult http://www.mcs.anl.gov/petsc/petsccurrent/docs/manualpages/Mat/MatView.html
Definition at line 639 of file petsc_matrix_base.cc.

inherited 
Print the elements of a matrix to the given output stream.
[in,out]  out  The output stream to which to write. 
[in]  alternative_output  This argument is ignored. It exists for compatibility with similar functions in other matrix classes. 
Definition at line 654 of file petsc_matrix_base.cc.

inherited 
Return the number bytes consumed by this matrix on this CPU.
Definition at line 685 of file petsc_matrix_base.cc.

protectedinherited 
Ensure that the add/set mode that is required for actions following this call is compatible with the current mode. Should be called from all internal functions accessing matrix elements.

protectedinherited 
Internal function that checks that there are no pending insert/add operations. Throws an exception otherwise. Useful before calling any PETSc internal functions modifying the matrix.

protectedinherited 
For some matrix storage formats, in particular for the PETSc distributed blockmatrices, set and add operations on individual elements can not be freely mixed. Rather, one has to synchronize operations when one wants to switch from setting elements to adding to elements. BlockMatrixBase automatically synchronizes the access by calling this helper function for each block. This function ensures that the matrix is in a state that allows adding elements; if it previously already was in this state, the function does nothing.

protectedinherited 
Same as prepare_add() but prepare the matrix for setting elements if the representation of elements in this class requires such an operation.

protectedinherited 
Base function to perform the matrixmatrix multiplication \(C = AB\), or, if a vector \(V\) whose size is compatible with B is given, \(C = A \text{diag}(V) B\), where \(\text{diag}(V)\) defines a diagonal matrix with the vector entries.
This function assumes that the calling matrix \(A\) and \(B\) have compatible sizes. The size of \(C\) will be set within this function.
The content as well as the sparsity pattern of the matrix \(C\) will be reset by this function, so make sure that the sparsity pattern is not used somewhere else in your program. This is an expensive operation, so think twice before you use this function.
Definition at line 561 of file petsc_matrix_base.cc.

protectedinherited 
Base function to perform the matrixmatrix multiplication with the transpose of this
, i.e., \(C = A^T B\), or, if an optional vector \(V\) whose size is compatible with \(B\) is given, \(C = A^T \text{diag}(V) B\), where \(\text{diag}(V)\) defines a diagonal matrix with the vector entries.
This function assumes that the calling matrix \(A\) and \(B\) have compatible sizes. The size of \(C\) will be set within this function.
The content as well as the sparsity pattern of the matrix \(C\) will be changed by this function, so make sure that the sparsity pattern is not used somewhere else in your program. This is an expensive operation, so think twice before you use this function.
Definition at line 569 of file petsc_matrix_base.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 136 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 156 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 204 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 53 of file subscriptor.cc.

friend 
Definition at line 643 of file petsc_sparse_matrix.h.

private 
Copy of the communicator object to be used for this parallel vector.
Definition at line 615 of file petsc_sparse_matrix.h.

protectedinherited 
A generic matrix object in PETSc. The actual type, a sparse matrix, is set in the constructor.
Definition at line 958 of file petsc_matrix_base.h.

protectedinherited 
Store whether the last action was a write or add operation.
Definition at line 963 of file petsc_matrix_base.h.

mutableprivateinherited 
An internal array of integer values that is used to store the column indices when adding/inserting local data into the (large) sparse matrix.
This variable does not store any "state" of the matrix object. Rather, it is only used as a temporary buffer by some of the member functions of this class. As with all mutable
member variables, the use of this variable is not threadsafe unless guarded by a mutex. However, since PETSc matrix operations are not threadsafe anyway, there is no need to attempt to make things threadsafe, and so there is no mutex associated with this variable.
Definition at line 1053 of file petsc_matrix_base.h.

mutableprivateinherited 
An internal array of double values that is used to store the column indices when adding/inserting local data into the (large) sparse matrix.
The same comment as for the column_indices
variable above applies.
Definition at line 1063 of file petsc_matrix_base.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 219 of file subscriptor.h.

mutableprivateinherited 
In this map, we count subscriptions for each different identification string supplied to subscribe().
Definition at line 225 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 241 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 249 of file subscriptor.h.

staticprivateinherited 
A mutex used to ensure data consistency when printing out the list of subscribers.
Definition at line 271 of file subscriptor.h.