Reference documentation for deal.II version Git d84be816e2 20190713 22:20:17 0400

#include <deal.II/lac/trilinos_sparse_matrix.h>
Classes  
struct  Traits 
Public Types  
using  size_type = ::types::global_dof_index 
using  iterator = SparseMatrixIterators::Iterator< false > 
using  const_iterator = SparseMatrixIterators::Iterator< true > 
using  value_type = TrilinosScalar 
Public Member Functions  
Constructors and initialization.  
SparseMatrix ()  
SparseMatrix (const size_type m, const size_type n, const unsigned int n_max_entries_per_row)  
SparseMatrix (const size_type m, const size_type n, const std::vector< unsigned int > &n_entries_per_row)  
SparseMatrix (const SparsityPattern &InputSparsityPattern)  
SparseMatrix (SparseMatrix &&other) noexcept  
SparseMatrix (const SparseMatrix &)=delete  
SparseMatrix &  operator= (const SparseMatrix &)=delete 
virtual  ~SparseMatrix () override=default 
template<typename SparsityPatternType >  
void  reinit (const SparsityPatternType &sparsity_pattern) 
void  reinit (const SparsityPattern &sparsity_pattern) 
void  reinit (const SparseMatrix &sparse_matrix) 
template<typename number >  
void  reinit (const ::SparseMatrix< number > &dealii_sparse_matrix, const double drop_tolerance=1e13, const bool copy_values=true, const ::SparsityPattern *use_this_sparsity=nullptr) 
void  reinit (const Epetra_CrsMatrix &input_matrix, const bool copy_values=true) 
Constructors and initialization using an Epetra_Map description  
SparseMatrix (const Epetra_Map ¶llel_partitioning, const size_type n_max_entries_per_row=0)  
SparseMatrix (const Epetra_Map ¶llel_partitioning, const std::vector< unsigned int > &n_entries_per_row)  
SparseMatrix (const Epetra_Map &row_parallel_partitioning, const Epetra_Map &col_parallel_partitioning, const size_type n_max_entries_per_row=0)  
SparseMatrix (const Epetra_Map &row_parallel_partitioning, const Epetra_Map &col_parallel_partitioning, const std::vector< unsigned int > &n_entries_per_row)  
template<typename SparsityPatternType >  
void  reinit (const Epetra_Map ¶llel_partitioning, const SparsityPatternType &sparsity_pattern, const bool exchange_data=false) 
template<typename SparsityPatternType >  
void  reinit (const Epetra_Map &row_parallel_partitioning, const Epetra_Map &col_parallel_partitioning, const SparsityPatternType &sparsity_pattern, const bool exchange_data=false) 
template<typename number >  
void  reinit (const Epetra_Map ¶llel_partitioning, const ::SparseMatrix< number > &dealii_sparse_matrix, const double drop_tolerance=1e13, const bool copy_values=true, const ::SparsityPattern *use_this_sparsity=nullptr) 
template<typename number >  
void  reinit (const Epetra_Map &row_parallel_partitioning, const Epetra_Map &col_parallel_partitioning, const ::SparseMatrix< number > &dealii_sparse_matrix, const double drop_tolerance=1e13, const bool copy_values=true, const ::SparsityPattern *use_this_sparsity=nullptr) 
Constructors and initialization using an IndexSet description  
SparseMatrix (const IndexSet ¶llel_partitioning, const MPI_Comm &communicator=MPI_COMM_WORLD, const unsigned int n_max_entries_per_row=0)  
SparseMatrix (const IndexSet ¶llel_partitioning, const MPI_Comm &communicator, const std::vector< unsigned int > &n_entries_per_row)  
SparseMatrix (const IndexSet &row_parallel_partitioning, const IndexSet &col_parallel_partitioning, const MPI_Comm &communicator=MPI_COMM_WORLD, const size_type n_max_entries_per_row=0)  
SparseMatrix (const IndexSet &row_parallel_partitioning, const IndexSet &col_parallel_partitioning, const MPI_Comm &communicator, const std::vector< unsigned int > &n_entries_per_row)  
template<typename SparsityPatternType >  
void  reinit (const IndexSet ¶llel_partitioning, const SparsityPatternType &sparsity_pattern, const MPI_Comm &communicator=MPI_COMM_WORLD, const bool exchange_data=false) 
template<typename SparsityPatternType >  
void  reinit (const IndexSet &row_parallel_partitioning, const IndexSet &col_parallel_partitioning, const SparsityPatternType &sparsity_pattern, const MPI_Comm &communicator=MPI_COMM_WORLD, const bool exchange_data=false) 
template<typename number >  
void  reinit (const IndexSet ¶llel_partitioning, const ::SparseMatrix< number > &dealii_sparse_matrix, const MPI_Comm &communicator=MPI_COMM_WORLD, const double drop_tolerance=1e13, const bool copy_values=true, const ::SparsityPattern *use_this_sparsity=nullptr) 
template<typename number >  
void  reinit (const IndexSet &row_parallel_partitioning, const IndexSet &col_parallel_partitioning, const ::SparseMatrix< number > &dealii_sparse_matrix, const MPI_Comm &communicator=MPI_COMM_WORLD, const double drop_tolerance=1e13, const bool copy_values=true, const ::SparsityPattern *use_this_sparsity=nullptr) 
Information on the matrix  
size_type  m () const 
size_type  n () const 
unsigned int  local_size () const 
std::pair< size_type, size_type >  local_range () const 
bool  in_local_range (const size_type index) const 
size_type  n_nonzero_elements () const 
unsigned int  row_length (const size_type row) const 
bool  is_compressed () const 
size_type  memory_consumption () const 
MPI_Comm  get_mpi_communicator () const 
Modifying entries  
SparseMatrix &  operator= (const double d) 
void  clear () 
void  compress (::VectorOperation::values operation) 
void  set (const size_type i, const size_type j, const TrilinosScalar value) 
void  set (const std::vector< size_type > &indices, const FullMatrix< TrilinosScalar > &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< TrilinosScalar > &full_matrix, const bool elide_zero_values=false) 
void  set (const size_type row, const std::vector< size_type > &col_indices, const std::vector< TrilinosScalar > &values, const bool elide_zero_values=false) 
template<typename Number >  
void  set (const size_type row, const size_type n_cols, const size_type *col_indices, const Number *values, const bool elide_zero_values=false) 
void  add (const size_type i, const size_type j, const TrilinosScalar value) 
void  add (const std::vector< size_type > &indices, const FullMatrix< TrilinosScalar > &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< TrilinosScalar > &full_matrix, const bool elide_zero_values=true) 
void  add (const size_type row, const std::vector< size_type > &col_indices, const std::vector< TrilinosScalar > &values, const bool elide_zero_values=true) 
void  add (const size_type row, const size_type n_cols, const size_type *col_indices, const TrilinosScalar *values, const bool elide_zero_values=true, const bool col_indices_are_sorted=false) 
SparseMatrix &  operator*= (const TrilinosScalar factor) 
SparseMatrix &  operator/= (const TrilinosScalar factor) 
void  copy_from (const SparseMatrix &source) 
void  add (const TrilinosScalar factor, const SparseMatrix &matrix) 
void  clear_row (const size_type row, const TrilinosScalar new_diag_value=0) 
void  clear_rows (const std::vector< size_type > &rows, const TrilinosScalar new_diag_value=0) 
void  transpose () 
Entry Access  
TrilinosScalar  operator() (const size_type i, const size_type j) const 
TrilinosScalar  el (const size_type i, const size_type j) const 
TrilinosScalar  diag_element (const size_type i) const 
Multiplications  
template<typename VectorType >  
std::enable_if< std::is_same< typename VectorType::value_type, TrilinosScalar >::value >::type  vmult (VectorType &dst, const VectorType &src) const 
template<typename VectorType >  
std::enable_if<!std::is_same< typename VectorType::value_type, TrilinosScalar >::value >::type  vmult (VectorType &dst, const VectorType &src) const 
template<typename VectorType >  
std::enable_if< std::is_same< typename VectorType::value_type, TrilinosScalar >::value >::type  Tvmult (VectorType &dst, const VectorType &src) const 
template<typename VectorType >  
std::enable_if<!std::is_same< typename VectorType::value_type, TrilinosScalar >::value >::type  Tvmult (VectorType &dst, const VectorType &src) const 
template<typename VectorType >  
void  vmult_add (VectorType &dst, const VectorType &src) const 
template<typename VectorType >  
void  Tvmult_add (VectorType &dst, const VectorType &src) const 
TrilinosScalar  matrix_norm_square (const MPI::Vector &v) const 
TrilinosScalar  matrix_scalar_product (const MPI::Vector &u, const MPI::Vector &v) const 
TrilinosScalar  residual (MPI::Vector &dst, const MPI::Vector &x, const MPI::Vector &b) 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 
Matrix norms  
TrilinosScalar  l1_norm () const 
TrilinosScalar  linfty_norm () const 
TrilinosScalar  frobenius_norm () const 
Access to underlying Trilinos data  
const Epetra_CrsMatrix &  trilinos_matrix () const 
const Epetra_CrsGraph &  trilinos_sparsity_pattern () const 
const Epetra_Map &  domain_partitioner () const 
const Epetra_Map &  range_partitioner () const 
const Epetra_Map &  row_partitioner () const 
const Epetra_Map &  col_partitioner () const 
Partitioners  
IndexSet  locally_owned_domain_indices () const 
IndexSet  locally_owned_range_indices () const 
Iterators  
const_iterator  begin () const 
iterator  begin () 
const_iterator  end () const 
iterator  end () 
const_iterator  begin (const size_type r) const 
iterator  begin (const size_type r) 
const_iterator  end (const size_type r) const 
iterator  end (const size_type r) 
Input/Output  
void  write_ascii () 
void  print (std::ostream &out, const bool write_extended_trilinos_info=false) const 
Public Member Functions inherited from Subscriptor  
Subscriptor ()  
Subscriptor (const Subscriptor &)  
Subscriptor (Subscriptor &&) noexcept  
virtual  ~Subscriptor () 
Subscriptor &  operator= (const Subscriptor &) 
Subscriptor &  operator= (Subscriptor &&) noexcept 
void  subscribe (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 
template<class Archive >  
void  serialize (Archive &ar, const unsigned int version) 
Static Public Member Functions  
static ::ExceptionBase &  ExcAccessToNonlocalRow (std::size_t arg1) 
static ::ExceptionBase &  ExcTrilinosError (int arg1) 
static ::ExceptionBase &  ExcInvalidIndex (size_type arg1, size_type arg2) 
static ::ExceptionBase &  ExcSourceEqualsDestination () 
static ::ExceptionBase &  ExcMatrixNotCompressed () 
static ::ExceptionBase &  ExcAccessToNonLocalElement (size_type arg1, size_type arg2, size_type arg3, size_type arg4) 
static ::ExceptionBase &  ExcAccessToNonPresentElement (size_type arg1, size_type arg2) 
Static Public Member Functions inherited from Subscriptor  
static ::ExceptionBase &  ExcInUse (int arg1, std::string arg2, std::string arg3) 
static ::ExceptionBase &  ExcNoSubscriber (std::string arg1, std::string arg2) 
Protected Member Functions  
void  prepare_add () 
void  prepare_set () 
Private Attributes  
std::unique_ptr< Epetra_Map >  column_space_map 
std::unique_ptr< Epetra_FECrsMatrix >  matrix 
std::unique_ptr< Epetra_CrsMatrix >  nonlocal_matrix 
std::unique_ptr< Epetra_Export >  nonlocal_matrix_exporter 
Epetra_CombineMode  last_action 
bool  compressed 
Friends  
class  BlockMatrixBase< SparseMatrix > 
This class implements a wrapper to use the Trilinos distributed sparse matrix class Epetra_FECrsMatrix. This is precisely the kind of matrix we deal with all the time  we most likely get it from some assembly process, where also entries not locally owned might need to be written and hence need to be forwarded to the owner process. This class is designed to be used in a distributed memory architecture with an MPI compiler on the bottom, but works equally well also for serial processes. The only requirement for this class to work is that Trilinos has been installed with the same compiler as is used for generating deal.II.
The interface of this class is modeled after the existing SparseMatrix class in deal.II. It has almost the same member functions, and is often exchangeable. However, since Trilinos only supports a single scalar type (double), it is not templated, and only works with doubles.
Note that Trilinos only guarantees that operations do what you expect if the functions GlobalAssemble
has been called after matrix assembly. Therefore, you need to call SparseMatrix::compress() before you actually use the matrix. This also calls FillComplete
that compresses the storage format for sparse matrices by discarding unused elements. Trilinos allows to continue with assembling the matrix after calls to these functions, though.
When writing into Trilinos matrices from several threads in shared memory, several things must be kept in mind as there is no builtin locks in this class to prevent data races. Simultaneous access to the same matrix row at the same time can lead to data races and must be explicitly avoided by the user. However, it is possible to access different rows of the matrix from several threads simultaneously under the following three conditions:
writeable_rows
, and the operation is an addition. At some point in the future, Trilinos support might be complete enough such that initializing from a TrilinosWrappers::SparsityPattern that has been filled by a function similar to DoFTools::make_sparsity_pattern always results in a matrix that allows several processes to write into the same matrix row. However, Trilinos until version at least 11.12 does not correctly support this feature. Note that all other reinit methods and constructors of TrilinosWrappers::SparsityPattern will result in a matrix that needs to allocate offprocessor entries on demand, which breaks threadsafety. Of course, using the respective reinit method for the block Trilinos sparsity pattern and block matrix also results in threadsafety.
Definition at line 516 of file trilinos_sparse_matrix.h.
Declare the type for container size.
Definition at line 522 of file trilinos_sparse_matrix.h.
Declare an alias for the iterator class.
Definition at line 553 of file trilinos_sparse_matrix.h.
Declare an alias for the const iterator class.
Definition at line 558 of file trilinos_sparse_matrix.h.
using TrilinosWrappers::SparseMatrix::value_type = TrilinosScalar 
Declare an alias in analogy to all the other container classes.
Definition at line 563 of file trilinos_sparse_matrix.h.
SparseMatrix< number >::SparseMatrix  (  ) 
Default constructor. Generates an empty (zerosize) matrix.
Definition at line 209 of file trilinos_sparse_matrix.cc.
SparseMatrix< number >::SparseMatrix  (  const size_type  m, 
const size_type  n,  
const unsigned int  n_max_entries_per_row  
) 
Generate a matrix that is completely stored locally, having m rows and n columns.
The number of columns entries per row is specified as the maximum number of entries argument.
Definition at line 281 of file trilinos_sparse_matrix.cc.
SparseMatrix< number >::SparseMatrix  (  const size_type  m, 
const size_type  n,  
const std::vector< unsigned int > &  n_entries_per_row  
) 
Generate a matrix that is completely stored locally, having m rows and n columns.
The vector n_entries_per_row
specifies the number of entries in each row.
Definition at line 312 of file trilinos_sparse_matrix.cc.
SparseMatrix< number >::SparseMatrix  (  const SparsityPattern &  InputSparsityPattern  ) 
Generate a matrix from a Trilinos sparsity pattern object.
Definition at line 401 of file trilinos_sparse_matrix.cc.

noexcept 
Move constructor. Create a new sparse matrix by stealing the internal data.
Definition at line 418 of file trilinos_sparse_matrix.cc.

delete 
Copy constructor is deleted.

overridevirtualdefault 
Destructor. Made virtual so that one can use pointers to this class.
SparseMatrix< number >::SparseMatrix  (  const Epetra_Map &  parallel_partitioning, 
const size_type  n_max_entries_per_row = 0 

) 
Constructor using an Epetra_Map to describe the parallel partitioning. The parameter n_max_entries_per_row
sets the number of nonzero entries in each row that will be allocated. Note that this number does not need to be exact, and it is even allowed that the actual matrix structure has more nonzero entries than specified in the constructor. However it is still advantageous to provide good estimates here since this will considerably increase the performance of the matrix setup. However, there is no effect in the performance of matrixvector products, since Trilinos reorganizes the matrix memory prior to use (in the compress() step).
Definition at line 221 of file trilinos_sparse_matrix.cc.
SparseMatrix< number >::SparseMatrix  (  const Epetra_Map &  parallel_partitioning, 
const std::vector< unsigned int > &  n_entries_per_row  
) 
Same as before, but now set a value of nonzeros for each matrix row. Since we know the number of elements in the matrix exactly in this case, we can already allocate the right amount of memory, which makes the creation process including the insertion of nonzero elements by the respective SparseMatrix::reinit call considerably faster.
Definition at line 235 of file trilinos_sparse_matrix.cc.
SparseMatrix< number >::SparseMatrix  (  const Epetra_Map &  row_parallel_partitioning, 
const Epetra_Map &  col_parallel_partitioning,  
const size_type  n_max_entries_per_row = 0 

) 
This constructor is similar to the one above, but it now takes two different Epetra maps for rows and columns. This interface is meant to be used for generating rectangular matrices, where one map describes the parallel partitioning of the dofs associated with the matrix rows and the other one the partitioning of dofs in the matrix columns. Note that there is no real parallelism along the columns – the processor that owns a certain row always owns all the column elements, no matter how far they might be spread out. The second Epetra_Map is only used to specify the number of columns and for internal arrangements when doing matrixvector products with vectors based on that column map.
The integer input n_max_entries_per_row
defines the number of columns entries per row that will be allocated.
Definition at line 250 of file trilinos_sparse_matrix.cc.
SparseMatrix< number >::SparseMatrix  (  const Epetra_Map &  row_parallel_partitioning, 
const Epetra_Map &  col_parallel_partitioning,  
const std::vector< unsigned int > &  n_entries_per_row  
) 
This constructor is similar to the one above, but it now takes two different Epetra maps for rows and columns. This interface is meant to be used for generating rectangular matrices, where one map specifies the parallel distribution of degrees of freedom associated with matrix rows and the second one specifies the parallel distribution the dofs associated with columns in the matrix. The second map also provides information for the internal arrangement in matrix vector products (i.e., the distribution of vector this matrix is to be multiplied with), but is not used for the distribution of the columns – rather, all column elements of a row are stored on the same processor in any case. The vector n_entries_per_row
specifies the number of entries in each row of the newly generated matrix.
Definition at line 265 of file trilinos_sparse_matrix.cc.
SparseMatrix< number >::SparseMatrix  (  const IndexSet &  parallel_partitioning, 
const MPI_Comm &  communicator = MPI_COMM_WORLD , 

const unsigned int  n_max_entries_per_row = 0 

) 
Constructor using an IndexSet and an MPI communicator to describe the parallel partitioning. The parameter n_max_entries_per_row
sets the number of nonzero entries in each row that will be allocated. Note that this number does not need to be exact, and it is even allowed that the actual matrix structure has more nonzero entries than specified in the constructor. However it is still advantageous to provide good estimates here since this will considerably increase the performance of the matrix setup. However, there is no effect in the performance of matrix vector products, since Trilinos reorganizes the matrix memory prior to use (in the compress() step).
Definition at line 334 of file trilinos_sparse_matrix.cc.
SparseMatrix< number >::SparseMatrix  (  const IndexSet &  parallel_partitioning, 
const MPI_Comm &  communicator,  
const std::vector< unsigned int > &  n_entries_per_row  
) 
Same as before, but now set the number of nonzeros in each matrix row separately. Since we know the number of elements in the matrix exactly in this case, we can already allocate the right amount of memory, which makes the creation process including the insertion of nonzero elements by the respective SparseMatrix::reinit call considerably faster.
Definition at line 349 of file trilinos_sparse_matrix.cc.
SparseMatrix< number >::SparseMatrix  (  const IndexSet &  row_parallel_partitioning, 
const IndexSet &  col_parallel_partitioning,  
const MPI_Comm &  communicator = MPI_COMM_WORLD , 

const size_type  n_max_entries_per_row = 0 

) 
This constructor is similar to the one above, but it now takes two different IndexSet partitions for row and columns. This interface is meant to be used for generating rectangular matrices, where the first index set describes the parallel partitioning of the degrees of freedom associated with the matrix rows and the second one the partitioning of the matrix columns. The second index set specifies the partitioning of the vectors this matrix is to be multiplied with, not the distribution of the elements that actually appear in the matrix.
The parameter n_max_entries_per_row
defines how much memory will be allocated for each row. This number does not need to be accurate, as the structure is reorganized in the compress() call.
Definition at line 366 of file trilinos_sparse_matrix.cc.
SparseMatrix< number >::SparseMatrix  (  const IndexSet &  row_parallel_partitioning, 
const IndexSet &  col_parallel_partitioning,  
const MPI_Comm &  communicator,  
const std::vector< unsigned int > &  n_entries_per_row  
) 
This constructor is similar to the one above, but it now takes two different Epetra maps for rows and columns. This interface is meant to be used for generating rectangular matrices, where one map specifies the parallel distribution of degrees of freedom associated with matrix rows and the second one specifies the parallel distribution the dofs associated with columns in the matrix. The second map also provides information for the internal arrangement in matrix vector products (i.e., the distribution of vector this matrix is to be multiplied with), but is not used for the distribution of the columns – rather, all column elements of a row are stored on the same processor in any case. The vector n_entries_per_row
specifies the number of entries in each row of the newly generated matrix.
Definition at line 383 of file trilinos_sparse_matrix.cc.

delete 
operator= is deleted.
void SparseMatrix< SparsityPatternType >::reinit  (  const SparsityPatternType &  sparsity_pattern  ) 
This function initializes the Trilinos matrix with a deal.II sparsity pattern, i.e. it makes the Trilinos Epetra matrix know the position of nonzero entries according to the sparsity pattern. This function is meant for use in serial programs, where there is no need to specify how the matrix is going to be distributed among different processors. This function works in parallel, too, but it is recommended to manually specify the parallel partitioning of the matrix using an Epetra_Map. When run in parallel, it is currently necessary that each processor holds the sparsity_pattern structure because each processor sets its rows.
This is a collective operation that needs to be called on all processors in order to avoid a dead lock.
Definition at line 830 of file trilinos_sparse_matrix.cc.
void SparseMatrix< number >::reinit  (  const SparsityPattern &  sparsity_pattern  ) 
This function reinitializes the Trilinos sparse matrix from a (possibly distributed) Trilinos sparsity pattern.
This is a collective operation that needs to be called on all processors in order to avoid a dead lock.
If you want to write to the matrix from several threads and use MPI, you need to use this reinit method with a sparsity pattern that has been created with explicitly stating writeable rows. In all other cases, you cannot mix MPI with multithreaded writing into the matrix.
Definition at line 925 of file trilinos_sparse_matrix.cc.
void SparseMatrix< number >::reinit  (  const SparseMatrix &  sparse_matrix  ) 
This function copies the layout of sparse_matrix
to the calling matrix. The values are not copied, but you can use copy_from() for this.
This is a collective operation that needs to be called on all processors in order to avoid a dead lock.
Definition at line 949 of file trilinos_sparse_matrix.cc.
void SparseMatrix< number >::reinit  (  const ::SparseMatrix< number > &  dealii_sparse_matrix, 
const double  drop_tolerance = 1e13 , 

const bool  copy_values = true , 

const ::SparsityPattern *  use_this_sparsity = nullptr 

) 
This function initializes the Trilinos matrix using the deal.II sparse matrix and the entries stored therein. It uses a threshold to copy only elements with modulus larger than the threshold (so zeros in the deal.II matrix can be filtered away).
The optional parameter copy_values
decides whether only the sparsity structure of the input matrix should be used or the matrix entries should be copied, too.
This is a collective operation that needs to be called on all processors in order to avoid a deadlock.
Definition at line 1087 of file trilinos_sparse_matrix.cc.
void SparseMatrix< number >::reinit  (  const Epetra_CrsMatrix &  input_matrix, 
const bool  copy_values = true 

) 
This reinit function takes as input a Trilinos Epetra_CrsMatrix and copies its sparsity pattern. If so requested, even the content (values) will be copied.
Definition at line 1146 of file trilinos_sparse_matrix.cc.
void SparseMatrix< SparsityPatternType >::reinit  (  const Epetra_Map &  parallel_partitioning, 
const SparsityPatternType &  sparsity_pattern,  
const bool  exchange_data = false 

) 
This function is initializes the Trilinos Epetra matrix according to the specified sparsity_pattern, and also reassigns the matrix rows to different processes according to a usersupplied Epetra map. In programs following the style of the tutorial programs, this function (and the respective call for a rectangular matrix) are the natural way to initialize the matrix size, its distribution among the MPI processes (if run in parallel) as well as the location of nonzero elements. Trilinos stores the sparsity pattern internally, so it won't be needed any more after this call, in contrast to the deal.II own object. The optional argument exchange_data
can be used for reinitialization with a sparsity pattern that is not fully constructed. This feature is only implemented for input sparsity patterns of type DynamicSparsityPattern. If the flag is not set, each processor just sets the elements in the sparsity pattern that belong to its rows.
If the sparsity pattern given to this function is of type DynamicSparsity pattern, then a matrix will be created that allows several threads to write into different rows of the matrix at the same also with MPI, as opposed to most other reinit() methods.
This is a collective operation that needs to be called on all processors in order to avoid a dead lock.
Definition at line 855 of file trilinos_sparse_matrix.cc.

inline 
This function is similar to the other initialization function above, but now also reassigns the matrix rows and columns according to two usersupplied Epetra maps. To be used for rectangular matrices. The optional argument exchange_data
can be used for reinitialization with a sparsity pattern that is not fully constructed. This feature is only implemented for input sparsity patterns of type DynamicSparsityPattern.
This is a collective operation that needs to be called on all processors in order to avoid a dead lock.
Definition at line 902 of file trilinos_sparse_matrix.cc.
void SparseMatrix< number >::reinit  (  const Epetra_Map &  parallel_partitioning, 
const ::SparseMatrix< number > &  dealii_sparse_matrix,  
const double  drop_tolerance = 1e13 , 

const bool  copy_values = true , 

const ::SparsityPattern *  use_this_sparsity = nullptr 

) 
This function initializes the Trilinos matrix using the deal.II sparse matrix and the entries stored therein. It uses a threshold to copy only elements with modulus larger than the threshold (so zeros in the deal.II matrix can be filtered away). In contrast to the other reinit function with deal.II sparse matrix argument, this function takes a parallel partitioning specified by the user instead of internally generating it.
The optional parameter copy_values
decides whether only the sparsity structure of the input matrix should be used or the matrix entries should be copied, too.
This is a collective operation that needs to be called on all processors in order to avoid a dead lock.
Definition at line 1106 of file trilinos_sparse_matrix.cc.
void SparseMatrix< number >::reinit  (  const Epetra_Map &  row_parallel_partitioning, 
const Epetra_Map &  col_parallel_partitioning,  
const ::SparseMatrix< number > &  dealii_sparse_matrix,  
const double  drop_tolerance = 1e13 , 

const bool  copy_values = true , 

const ::SparsityPattern *  use_this_sparsity = nullptr 

) 
This function is similar to the other initialization function with deal.II sparse matrix input above, but now takes Epetra maps for both the rows and the columns of the matrix. Chosen for rectangular matrices.
The optional parameter copy_values
decides whether only the sparsity structure of the input matrix should be used or the matrix entries should be copied, too.
This is a collective operation that needs to be called on all processors in order to avoid a dead lock.
Definition at line 1126 of file trilinos_sparse_matrix.cc.
void TrilinosWrappers::SparseMatrix::reinit  (  const IndexSet &  parallel_partitioning, 
const SparsityPatternType &  sparsity_pattern,  
const MPI_Comm &  communicator = MPI_COMM_WORLD , 

const bool  exchange_data = false 

) 
This function is initializes the Trilinos Epetra matrix according to the specified sparsity_pattern, and also reassigns the matrix rows to different processes according to a usersupplied index set and parallel communicator. In programs following the style of the tutorial programs, this function (and the respective call for a rectangular matrix) are the natural way to initialize the matrix size, its distribution among the MPI processes (if run in parallel) as well as the location of nonzero elements. Trilinos stores the sparsity pattern internally, so it won't be needed any more after this call, in contrast to the deal.II own object. The optional argument exchange_data
can be used for reinitialization with a sparsity pattern that is not fully constructed. This feature is only implemented for input sparsity patterns of type DynamicSparsityPattern. If the flag is not set, each processor just sets the elements in the sparsity pattern that belong to its rows.
This is a collective operation that needs to be called on all processors in order to avoid a dead lock.

inline 
This function is similar to the other initialization function above, but now also reassigns the matrix rows and columns according to two usersupplied index sets. To be used for rectangular matrices. The optional argument exchange_data
can be used for reinitialization with a sparsity pattern that is not fully constructed. This feature is only implemented for input sparsity patterns of type DynamicSparsityPattern.
This is a collective operation that needs to be called on all processors in order to avoid a dead lock.
Definition at line 873 of file trilinos_sparse_matrix.cc.
void TrilinosWrappers::SparseMatrix::reinit  (  const IndexSet &  parallel_partitioning, 
const ::SparseMatrix< number > &  dealii_sparse_matrix,  
const MPI_Comm &  communicator = MPI_COMM_WORLD , 

const double  drop_tolerance = 1e13 , 

const bool  copy_values = true , 

const ::SparsityPattern *  use_this_sparsity = nullptr 

) 
This function initializes the Trilinos matrix using the deal.II sparse matrix and the entries stored therein. It uses a threshold to copy only elements with modulus larger than the threshold (so zeros in the deal.II matrix can be filtered away). In contrast to the other reinit function with deal.II sparse matrix argument, this function takes a parallel partitioning specified by the user instead of internally generating it.
The optional parameter copy_values
decides whether only the sparsity structure of the input matrix should be used or the matrix entries should be copied, too.
This is a collective operation that needs to be called on all processors in order to avoid a dead lock.

inline 
This function is similar to the other initialization function with deal.II sparse matrix input above, but now takes index sets for both the rows and the columns of the matrix. Chosen for rectangular matrices.
The optional parameter copy_values
decides whether only the sparsity structure of the input matrix should be used or the matrix entries should be copied, too.
This is a collective operation that needs to be called on all processors in order to avoid a dead lock.
Definition at line 975 of file trilinos_sparse_matrix.cc.
size_type TrilinosWrappers::SparseMatrix::m  (  )  const 
Return the number of rows in this matrix.
size_type TrilinosWrappers::SparseMatrix::n  (  )  const 
Return the number of columns in this matrix.
unsigned int TrilinosWrappers::SparseMatrix::local_size  (  )  const 
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().
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()
.
bool TrilinosWrappers::SparseMatrix::in_local_range  (  const size_type  index  )  const 
Return whether index
is in the local range or not, see also local_range().
size_type TrilinosWrappers::SparseMatrix::n_nonzero_elements  (  )  const 
Return the total number of nonzero elements of this matrix (summed over all MPI processes).
unsigned int SparseMatrix< number >::row_length  (  const size_type  row  )  const 
Number of entries in a specific row.
Definition at line 1481 of file trilinos_sparse_matrix.cc.
bool TrilinosWrappers::SparseMatrix::is_compressed  (  )  const 
Return the state of the matrix, i.e., whether compress() needs to be called after an operation requiring data exchange. A call to compress() is also needed when the method set() has been called (even when working in serial).
SparseMatrix::size_type SparseMatrix< number >::memory_consumption  (  )  const 
Determine an estimate for the memory consumption (in bytes) of this object. Note that only the memory reserved on the current processor is returned in case this is called in an MPIbased program.
Definition at line 2425 of file trilinos_sparse_matrix.cc.
MPI_Comm SparseMatrix< number >::get_mpi_communicator  (  )  const 
Return the MPI communicator object in use with this matrix.
Definition at line 2470 of file trilinos_sparse_matrix.cc.
SparseMatrix & SparseMatrix< number >::operator=  (  const double  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 keeps the sparsity pattern previously used.
Definition at line 1907 of file trilinos_sparse_matrix.cc.
void SparseMatrix< number >::clear  (  ) 
Release all memory and return to a state just like after having called the default constructor.
This is a collective operation that needs to be called on all processors in order to avoid a dead lock.
Definition at line 1240 of file trilinos_sparse_matrix.cc.
void SparseMatrix< number >::compress  (  ::VectorOperation::values  operation  ) 
This command does two things:
In both cases, this function compresses the data structures and allows the resulting matrix to be used in all other operations like matrix vector products. This is a collective operation, i.e., it needs to be run on all processors when used in parallel.
See Compressing distributed objects for more information.
Definition at line 1181 of file trilinos_sparse_matrix.cc.
void TrilinosWrappers::SparseMatrix::set  (  const size_type  i, 
const size_type  j,  
const TrilinosScalar  value  
) 
Set the element (i,j) to value
.
This function is able to insert new elements into the matrix as long as compress() has not been called, so the sparsity pattern will be extended. When compress() is called for the first time (or in case the matrix is initialized from a sparsity pattern), no new elements can be added and an insertion of elements at positions which have not been initialized will throw an exception.
For the case that the matrix is constructed without a sparsity pattern and new matrix entries are added on demand, please note the following behavior imposed by the underlying Epetra_FECrsMatrix data structure: If the same matrix entry is inserted more than once, the matrix entries will be added upon calling compress() (since Epetra does not track values to the same entry before the final compress() is called), even if VectorOperation::insert is specified as argument to compress(). In the case you cannot make sure that matrix entries are only set once, initialize the matrix with a sparsity pattern to fix the matrix structure before inserting elements.
void TrilinosWrappers::SparseMatrix::set  (  const std::vector< size_type > &  indices, 
const FullMatrix< TrilinosScalar > &  full_matrix,  
const bool  elide_zero_values = false 

) 
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.
This function is able to insert new elements into the matrix as long as compress() has not been called, so the sparsity pattern will be extended. After compress() has been called for the first time or the matrix has been initialized from a sparsity pattern, extending the sparsity pattern is no longer possible and an insertion of elements at positions which have not been initialized will throw an exception.
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.
For the case that the matrix is constructed without a sparsity pattern and new matrix entries are added on demand, please note the following behavior imposed by the underlying Epetra_FECrsMatrix data structure: If the same matrix entry is inserted more than once, the matrix entries will be added upon calling compress() (since Epetra does not track values to the same entry before the final compress() is called), even if VectorOperation::insert is specified as argument to compress(). In the case you cannot make sure that matrix entries are only set once, initialize the matrix with a sparsity pattern to fix the matrix structure before inserting elements.
void SparseMatrix< number >::set  (  const std::vector< size_type > &  row_indices, 
const std::vector< size_type > &  col_indices,  
const FullMatrix< TrilinosScalar > &  full_matrix,  
const bool  elide_zero_values = false 

) 
Same function as before, but now including the possibility to use rectangular full_matrices and different localtoglobal indexing on rows and columns, respectively.
Definition at line 1507 of file trilinos_sparse_matrix.cc.
void SparseMatrix< number >::set  (  const size_type  row, 
const std::vector< size_type > &  col_indices,  
const std::vector< TrilinosScalar > &  values,  
const bool  elide_zero_values = false 

) 
Set several elements in the specified row of the matrix with column indices as given by col_indices
to the respective value.
This function is able to insert new elements into the matrix as long as compress() has not been called, so the sparsity pattern will be extended. After compress() has been called for the first time or the matrix has been initialized from a sparsity pattern, extending the sparsity pattern is no longer possible and an insertion of elements at positions which have not been initialized will throw an exception.
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.
For the case that the matrix is constructed without a sparsity pattern and new matrix entries are added on demand, please note the following behavior imposed by the underlying Epetra_FECrsMatrix data structure: If the same matrix entry is inserted more than once, the matrix entries will be added upon calling compress() (since Epetra does not track values to the same entry before the final compress() is called), even if VectorOperation::insert is specified as argument to compress(). In the case you cannot make sure that matrix entries are only set once, initialize the matrix with a sparsity pattern to fix the matrix structure before inserting elements.
Definition at line 1528 of file trilinos_sparse_matrix.cc.
void TrilinosWrappers::SparseMatrix::set  (  const size_type  row, 
const size_type  n_cols,  
const size_type *  col_indices,  
const Number *  values,  
const bool  elide_zero_values = false 

) 
Set several elements to values given by values
in a given row in columns given by col_indices into the sparse matrix.
This function is able to insert new elements into the matrix as long as compress() has not been called, so the sparsity pattern will be extended. After compress() has been called for the first time or the matrix has been initialized from a sparsity pattern, extending the sparsity pattern is no longer possible and an insertion of elements at positions which have not been initialized will throw an exception.
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.
For the case that the matrix is constructed without a sparsity pattern and new matrix entries are added on demand, please note the following behavior imposed by the underlying Epetra_FECrsMatrix data structure: If the same matrix entry is inserted more than once, the matrix entries will be added upon calling compress() (since Epetra does not track values to the same entry before the final compress() is called), even if VectorOperation::insert is specified as argument to compress(). In the case you cannot make sure that matrix entries are only set once, initialize the matrix with a sparsity pattern to fix the matrix structure before inserting elements.
void TrilinosWrappers::SparseMatrix::add  (  const size_type  i, 
const size_type  j,  
const TrilinosScalar  value  
) 
Add value
to the element (i,j).
Just as the respective call in deal.II SparseMatrix<Number> class (but in contrast to the situation for PETSc based matrices), this function throws an exception if an entry does not exist in the sparsity pattern. Moreover, if value
is not a finite number an exception is thrown.
void SparseMatrix< number >::add  (  const std::vector< size_type > &  indices, 
const FullMatrix< TrilinosScalar > &  full_matrix,  
const bool  elide_zero_values = true 

) 
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.
Just as the respective call in deal.II SparseMatrix<Number> class (but in contrast to the situation for PETSc based matrices), this function throws an exception if an entry does not exist in the sparsity pattern.
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.
Definition at line 1681 of file trilinos_sparse_matrix.cc.
void SparseMatrix< number >::add  (  const std::vector< size_type > &  row_indices, 
const std::vector< size_type > &  col_indices,  
const FullMatrix< TrilinosScalar > &  full_matrix,  
const bool  elide_zero_values = true 

) 
Same function as before, but now including the possibility to use rectangular full_matrices and different localtoglobal indexing on rows and columns, respectively.
Definition at line 1700 of file trilinos_sparse_matrix.cc.
void SparseMatrix< number >::add  (  const size_type  row, 
const std::vector< size_type > &  col_indices,  
const std::vector< TrilinosScalar > &  values,  
const bool  elide_zero_values = true 

) 
Set several elements in the specified row of the matrix with column indices as given by col_indices
to the respective value.
Just as the respective call in deal.II SparseMatrix<Number> class (but in contrast to the situation for PETSc based matrices), this function throws an exception if an entry does not exist in the sparsity pattern.
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.
Definition at line 1721 of file trilinos_sparse_matrix.cc.
void SparseMatrix< number >::add  (  const size_type  row, 
const size_type  n_cols,  
const size_type *  col_indices,  
const TrilinosScalar *  values,  
const bool  elide_zero_values = true , 

const bool  col_indices_are_sorted = false 

) 
Add an array of values given by values
in the given global matrix row at columns specified by col_indices in the sparse matrix.
Just as the respective call in deal.II SparseMatrix<Number> class (but in contrast to the situation for PETSc based matrices), this function throws an exception if an entry does not exist in the sparsity pattern.
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.
Definition at line 1739 of file trilinos_sparse_matrix.cc.
SparseMatrix & SparseMatrix< number >::operator*=  (  const TrilinosScalar  factor  ) 
Multiply the entire matrix by a fixed factor.
Definition at line 2030 of file trilinos_sparse_matrix.cc.
SparseMatrix & SparseMatrix< number >::operator/=  (  const TrilinosScalar  factor  ) 
Divide the entire matrix by a fixed factor.
Definition at line 2042 of file trilinos_sparse_matrix.cc.
void SparseMatrix< number >::copy_from  (  const SparseMatrix &  source  ) 
Copy the given (Trilinos) matrix (sparsity pattern and entries).
Definition at line 433 of file trilinos_sparse_matrix.cc.
void SparseMatrix< number >::add  (  const TrilinosScalar  factor, 
const SparseMatrix &  matrix  
) 
Add matrix
scaled by factor
to this matrix, i.e. the matrix factor*matrix
is added to this
. If the sparsity pattern of the calling matrix does not contain all the elements in the sparsity pattern of the input matrix, this function will throw an exception.
Definition at line 1925 of file trilinos_sparse_matrix.cc.
void SparseMatrix< number >::clear_row  (  const size_type  row, 
const TrilinosScalar  new_diag_value = 0 

) 
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 the entries to zero.
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 1262 of file trilinos_sparse_matrix.cc.
void SparseMatrix< number >::clear_rows  (  const std::vector< size_type > &  rows, 
const TrilinosScalar  new_diag_value = 0 

) 
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 1299 of file trilinos_sparse_matrix.cc.
void SparseMatrix< number >::transpose  (  ) 
Sets an internal flag so that all operations performed by the matrix, i.e., multiplications, are done in transposed order. However, this does not reshape the matrix to transposed form directly, so care should be taken when using this flag.
Definition at line 2006 of file trilinos_sparse_matrix.cc.
TrilinosScalar SparseMatrix< number >::operator()  (  const size_type  i, 
const size_type  j  
)  const 
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. As in the deal.II sparse matrix class, we throw an exception if the respective entry doesn't exist in the sparsity pattern of this class, which is requested from Trilinos. Moreover, an exception will be thrown when the requested element is not saved on the calling process.
Definition at line 1309 of file trilinos_sparse_matrix.cc.
TrilinosScalar SparseMatrix< number >::el  (  const size_type  i, 
const size_type  j  
)  const 
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. On the other hand, if you want to be sure the entry exists, you should use operator() instead.
The lack of error checking in this function can also yield surprising results if you have a parallel matrix. In that case, just because you get a zero result from this function does not mean that either the entry does not exist in the sparsity pattern or that it does but has a value of zero. Rather, it could also be that it simply isn't stored on the current processor; in that case, it may be stored on a different processor, and possibly so with a nonzero value.
Definition at line 1388 of file trilinos_sparse_matrix.cc.
TrilinosScalar SparseMatrix< number >::diag_element  (  const size_type  i  )  const 
Return the main diagonal element in the ith row. This function throws an error if the matrix is not quadratic and it also throws an error if (i,i) is not element of the local matrix. See also the comment in trilinos_sparse_matrix.cc.
Definition at line 1460 of file trilinos_sparse_matrix.cc.
std::enable_if< !std::is_same< typename VectorType::value_type, TrilinosScalar >::value >::type SparseMatrix< VectorType >::vmult  (  VectorType &  dst, 
const VectorType &  src  
)  const 
Matrixvector multiplication: let dst = M*src with M being this matrix.
Source and destination must not be the same vector.
This function can be called with several types of vector objects, namely VectorType
can be
When using vectors of type TrilinosWrappers::MPI::Vector, the vector dst
has to be initialized with the same IndexSet that was used for the row indices of the matrix and the vector src
has to be initialized with the same IndexSet that was used for the column indices of the matrix.
This function will be called when the underlying number type for the matrix object and the one for the vector object are the same. Despite looking complicated, the return type is just void
.
In case of a serial vector, this function will only work when running on one processor, since the matrix object is inherently distributed. Otherwise, an exception will be thrown.
Definition at line 2116 of file trilinos_sparse_matrix.cc.
std::enable_if<!std::is_same<typename VectorType::value_type, TrilinosScalar>::value>::type TrilinosWrappers::SparseMatrix::vmult  (  VectorType &  dst, 
const VectorType &  src  
)  const 
Same as the function above for the case that the underlying number type for the matrix object and the one for the vector object do not coincide. This case is not implemented. Calling it will result in a runtime error. Despite looking complicated, the return type is just void
.
std::enable_if< !std::is_same< typename VectorType::value_type, TrilinosScalar >::value >::type SparseMatrix< VectorType >::Tvmult  (  VectorType &  dst, 
const VectorType &  src  
)  const 
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.
This function can be called with several types of vector objects, see the discussion about VectorType
in vmult().
This function will be called when the underlying number type for the matrix object and the one for the vector object are the same. Despite looking complicated, the return type is just void
.
Definition at line 2160 of file trilinos_sparse_matrix.cc.
std::enable_if<!std::is_same<typename VectorType::value_type, TrilinosScalar>::value>::type TrilinosWrappers::SparseMatrix::Tvmult  (  VectorType &  dst, 
const VectorType &  src  
)  const 
Same as the function above for the case that the underlying number type for the matrix object and the one for the vector object do not coincide. This case is not implemented. Calling it will result in a runtime error. Despite looking complicated, the return type is just void
.
void SparseMatrix< VectorType >::vmult_add  (  VectorType &  dst, 
const VectorType &  src  
)  const 
Adding matrixvector multiplication. Add M*src on dst with M being this matrix.
Source and destination must not be the same vector.
This function can be called with several types of vector objects, see the discussion about VectorType
in vmult().
Definition at line 2200 of file trilinos_sparse_matrix.cc.
void SparseMatrix< VectorType >::Tvmult_add  (  VectorType &  dst, 
const VectorType &  src  
)  const 
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.
This function can be called with several types of vector objects, see the discussion about VectorType
in vmult().
Definition at line 2216 of file trilinos_sparse_matrix.cc.
TrilinosScalar SparseMatrix< number >::matrix_norm_square  (  const MPI::Vector &  v  )  const 
Return the square of the norm of the vector \(v\) with respect to the norm induced by this matrix, i.e., \(\left(v,Mv\right)\). 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 SparseMatrix
class used in deal.II (i.e. the original one, not the Trilinos wrapper class) since Trilinos doesn't support this operation and needs a temporary vector.
The vector has to be initialized with the same IndexSet the matrix was initialized with.
In case of a localized Vector, this function will only work when running on one processor, since the matrix object is inherently distributed. Otherwise, an exception will be thrown.
Definition at line 2231 of file trilinos_sparse_matrix.cc.
TrilinosScalar SparseMatrix< number >::matrix_scalar_product  (  const MPI::Vector &  u, 
const MPI::Vector &  v  
)  const 
Compute the matrix scalar product \(\left(u,Mv\right)\).
The implementation of this function is not as efficient as the one in the SparseMatrix
class used in deal.II (i.e. the original one, not the Trilinos wrapper class) since Trilinos doesn't support this operation and needs a temporary vector.
The vector u
has to be initialized with the same IndexSet that was used for the row indices of the matrix and the vector v
has to be initialized with the same IndexSet that was used for the column indices of the matrix.
In case of a localized Vector, this function will only work when running on one processor, since the matrix object is inherently distributed. Otherwise, an exception will be thrown.
This function is only implemented for square matrices.
Definition at line 2245 of file trilinos_sparse_matrix.cc.
TrilinosScalar SparseMatrix< number >::residual  (  MPI::Vector &  dst, 
const MPI::Vector &  x,  
const MPI::Vector &  b  
)  const 
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.
The vectors dst
and b
have to be initialized with the same IndexSet that was used for the row indices of the matrix and the vector x
has to be initialized with the same IndexSet that was used for the column indices of the matrix.
In case of a localized Vector, this function will only work when running on one processor, since the matrix object is inherently distributed. Otherwise, an exception will be thrown.
Definition at line 2260 of file trilinos_sparse_matrix.cc.
void SparseMatrix< number >::mmult  (  SparseMatrix &  C, 
const SparseMatrix &  B,  
const MPI::Vector &  V = MPI::Vector() 

)  const 
Perform the matrixmatrix multiplication C = A * B
, or, if an optional vector argument is given, C = A * diag(V) * B
, where 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 2366 of file trilinos_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, if an optional vector argument is given, C = A^{T} * diag(V) * B
, where 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 2376 of file trilinos_sparse_matrix.cc.
TrilinosScalar SparseMatrix< number >::l1_norm  (  )  const 
Return the l_{1}norm of the matrix, that is \(M_1= \max_{\mathrm{all\ columns\ } j} \sum_{\mathrm{all\ rows\ } i} M_{ij}\), (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 2058 of file trilinos_sparse_matrix.cc.
TrilinosScalar SparseMatrix< number >::linfty_norm  (  )  const 
Return the linftynorm of the matrix, that is \(M_\infty=\max_{\mathrm{all\ rows\ } i}\sum_{\mathrm{all\ columns\ } j} M_{ij}\), (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 2067 of file trilinos_sparse_matrix.cc.
TrilinosScalar SparseMatrix< number >::frobenius_norm  (  )  const 
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 2076 of file trilinos_sparse_matrix.cc.
const Epetra_CrsMatrix& TrilinosWrappers::SparseMatrix::trilinos_matrix  (  )  const 
Return a const reference to the underlying Trilinos Epetra_CrsMatrix data.
const Epetra_CrsGraph& TrilinosWrappers::SparseMatrix::trilinos_sparsity_pattern  (  )  const 
Return a const reference to the underlying Trilinos Epetra_CrsGraph data that stores the sparsity pattern of the matrix.
const Epetra_Map & SparseMatrix< number >::domain_partitioner  (  )  const 
Return a const reference to the underlying Trilinos Epetra_Map that sets 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 2438 of file trilinos_sparse_matrix.cc.
const Epetra_Map & SparseMatrix< number >::range_partitioner  (  )  const 
Return a const reference to the underlying Trilinos Epetra_Map that sets the partitioning of the range space of this matrix, i.e., the partitioning of the vectors that are result from matrixvector products.
Definition at line 2446 of file trilinos_sparse_matrix.cc.
const Epetra_Map & SparseMatrix< number >::row_partitioner  (  )  const 
Return a const reference to the underlying Trilinos Epetra_Map that sets the partitioning of the matrix rows. Equal to the partitioning of the range.
Definition at line 2454 of file trilinos_sparse_matrix.cc.
const Epetra_Map & SparseMatrix< number >::col_partitioner  (  )  const 
Return a const reference to the underlying Trilinos Epetra_Map that sets the partitioning of the matrix columns. This is in general not equal to the partitioner Epetra_Map for the domain because of overlap in the matrix.
Definition at line 2462 of file trilinos_sparse_matrix.cc.
IndexSet TrilinosWrappers::SparseMatrix::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.
IndexSet TrilinosWrappers::SparseMatrix::locally_owned_range_indices  (  )  const 
Return the partitioning of the range space of this matrix, i.e., the partitioning of the vectors that are result from matrixvector products.
const_iterator TrilinosWrappers::SparseMatrix::begin  (  )  const 
Return an iterator pointing to the first element of the matrix.
The elements accessed by iterators within each row are ordered in the way in which Trilinos stores them, though the implementation guarantees that all elements of one row are accessed before the elements of the next row. If your algorithm relies on visiting elements within one row, you will need to consult with the Trilinos documentation on the order in which it stores data. It is, however, generally not a good and long term stable idea to rely on the order in which receive elements if you iterate over them.
When you iterate over the elements of a parallel matrix, you will only be able to access the locally owned rows. (You can access the other rows as well, but they will look empty.) In that case, you probably want to call the begin() function that takes the row as an argument to limit the range of elements to loop over.
iterator TrilinosWrappers::SparseMatrix::begin  (  ) 
Like the function above, but for nonconst matrices.
const_iterator TrilinosWrappers::SparseMatrix::end  (  )  const 
Return an iterator pointing the element past the last one of this matrix.
iterator TrilinosWrappers::SparseMatrix::end  (  ) 
Like the function above, but for nonconst matrices.
const_iterator TrilinosWrappers::SparseMatrix::begin  (  const size_type  r  )  const 
Return an iterator pointing to the first element 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)
. The returned iterator may not be dereferenceable in that case if neither row r
nor any of the following rows contain any nonzero entries.
The elements accessed by iterators within each row are ordered in the way in which Trilinos stores them, though the implementation guarantees that all elements of one row are accessed before the elements of the next row. If your algorithm relies on visiting elements within one row, you will need to consult with the Trilinos documentation on the order in which it stores data. It is, however, generally not a good and long term stable idea to rely on the order in which receive elements if you iterate over them.
Like the function above, but for nonconst matrices.
const_iterator TrilinosWrappers::SparseMatrix::end  (  const size_type  r  )  const 
Return an iterator pointing the element past the last one of row r
, or past the end of the entire sparsity pattern if none of the rows after r
contain any entries at all.
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.
Like the function above, but for nonconst matrices.
void SparseMatrix< number >::write_ascii  (  ) 
Abstract Trilinos object that helps view in ASCII other Trilinos objects. Currently this function is not implemented. TODO: Not implemented.
Definition at line 2386 of file trilinos_sparse_matrix.cc.
void SparseMatrix< number >::print  (  std::ostream &  out, 
const bool  write_extended_trilinos_info = false 

)  const 
Print the matrix to the given stream, using the format (line,col) value
, i.e. one nonzero entry of the matrix per line. The optional flag outputs the sparsity pattern in Trilinos style, where the data is sorted according to the processor number when printed to the stream, as well as a summary of the matrix like the global size.
Definition at line 2397 of file trilinos_sparse_matrix.cc.

protected 
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.

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

friend 
To allow calling protected prepare_add() and prepare_set().
Definition at line 2155 of file trilinos_sparse_matrix.h.

private 
Pointer to the usersupplied Epetra Trilinos mapping of the matrix columns that assigns parts of the matrix to the individual processes.
Definition at line 2112 of file trilinos_sparse_matrix.h.

private 
A sparse matrix object in Trilinos to be used for finite element based problems which allows for assembling into nonlocal elements. The actual type, a sparse matrix, is set in the constructor.
Definition at line 2119 of file trilinos_sparse_matrix.h.

private 
A sparse matrix object in Trilinos to be used for collecting the non local elements if the matrix was constructed from a Trilinos sparsity pattern with the respective option.
Definition at line 2126 of file trilinos_sparse_matrix.h.

private 
An export object used to communicate the nonlocal matrix.
Definition at line 2131 of file trilinos_sparse_matrix.h.

private 
Trilinos doesn't allow to mix additions to matrix entries and overwriting them (to make synchronization of parallel computations simpler). The way we do it is to, for each access operation, store whether it is an insertion or an addition. If the previous one was of different type, then we first have to flush the Trilinos buffers; otherwise, we can simply go on. Luckily, Trilinos has an object for this which does already all the parallel communications in such a case, so we simply use their model, which stores whether the last operation was an addition or an insertion.
Definition at line 2144 of file trilinos_sparse_matrix.h.

private 
A boolean variable to hold information on whether the vector is compressed or not.
Definition at line 2150 of file trilinos_sparse_matrix.h.