TrilinosWrappers::SparseMatrix Class Reference
[TrilinosWrappersBasic matrices]

Inheritance diagram for TrilinosWrappers::SparseMatrix:

Inheritance graph
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List of all members.

Classes

class  ExcAccessToNonLocalElement
class  ExcAccessToNonPresentElement
class  ExcInvalidIndex
class  ExcSourceEqualsDestination
class  ExcTrilinosError
struct  Traits

Public Types

typedef
MatrixIterators::const_iterator 
const_iterator
typedef TrilinosScalar value_type

Public Member Functions

Constructors and initalization.
 SparseMatrix ()
 SparseMatrix (const Epetra_Map &InputMap, const unsigned int n_max_entries_per_row)
 SparseMatrix (const Epetra_Map &InputMap, const std::vector< unsigned int > &n_entries_per_row)
 SparseMatrix (const Epetra_Map &InputRowMap, const Epetra_Map &InputColMap, const unsigned int n_max_entries_per_row)
 SparseMatrix (const Epetra_Map &InputRowMap, const Epetra_Map &InputColMap, const std::vector< unsigned int > &n_entries_per_row)
 SparseMatrix (const unsigned int m, const unsigned int n, const unsigned int n_max_entries_per_row)
 SparseMatrix (const unsigned int m, const unsigned int n, const std::vector< unsigned int > &n_entries_per_row)
 SparseMatrix (const SparsityPattern &InputSparsityPattern)
 SparseMatrix (const SparseMatrix &InputMatrix)
virtual ~SparseMatrix ()
template<typename SparsityType >
void reinit (const SparsityType &sparsity_pattern)
template<typename SparsityType >
void reinit (const Epetra_Map &input_map, const SparsityType &sparsity_pattern)
template<typename SparsityType >
void reinit (const Epetra_Map &input_row_map, const Epetra_Map &input_col_map, const SparsityType &sparsity_pattern)
void reinit (const SparsityPattern &sparsity_pattern)
void reinit (const SparseMatrix &sparse_matrix)
void reinit (const ::::SparseMatrix< double > &dealii_sparse_matrix, const double drop_tolerance=1e-13)
void reinit (const Epetra_Map &input_map, const ::::SparseMatrix< double > &dealii_sparse_matrix, const double drop_tolerance=1e-13)
void reinit (const Epetra_Map &input_row_map, const Epetra_Map &input_col_map, const ::::SparseMatrix< double > &dealii_sparse_matrix, const double drop_tolerance=1e-13)
void reinit (const Epetra_CrsMatrix &input_matrix)
SparseMatrixoperator= (const double d)
void clear ()
void compress ()
bool is_compressed () const
Information on the matrix
unsigned int m () const
unsigned int n () const
unsigned int local_size () const
std::pair< unsigned int,
unsigned int
local_range () const
bool in_local_range (const unsigned int index) const
unsigned int n_nonzero_elements () const
unsigned int row_length (const unsigned int row) const
bool is_symmetric (const double tol=0.0) const
bool is_hermitian () const
unsigned int memory_consumption () const
Modifying entries
void set (const unsigned int i, const unsigned int j, const TrilinosScalar value)
void set (const std::vector< unsigned int > &indices, const FullMatrix< TrilinosScalar > &full_matrix, const bool elide_zero_values=false)
void set (const std::vector< unsigned int > &row_indices, const std::vector< unsigned int > &col_indices, const FullMatrix< TrilinosScalar > &full_matrix, const bool elide_zero_values=false)
void set (const unsigned int row, const std::vector< unsigned int > &col_indices, const std::vector< TrilinosScalar > &values, const bool elide_zero_values=false)
void set (const unsigned int row, const unsigned int n_cols, const unsigned int *col_indices, const TrilinosScalar *values, const bool elide_zero_values=false)
void add (const unsigned int i, const unsigned int j, const TrilinosScalar value)
void add (const std::vector< unsigned int > &indices, const FullMatrix< TrilinosScalar > &full_matrix, const bool elide_zero_values=true)
void add (const std::vector< unsigned int > &row_indices, const std::vector< unsigned int > &col_indices, const FullMatrix< TrilinosScalar > &full_matrix, const bool elide_zero_values=true)
void add (const unsigned int row, const std::vector< unsigned int > &col_indices, const std::vector< TrilinosScalar > &values, const bool elide_zero_values=true)
void add (const unsigned int row, const unsigned int n_cols, const unsigned int *col_indices, const TrilinosScalar *values, const bool elide_zero_values=true, const bool col_indices_are_sorted=false)
SparseMatrixoperator*= (const TrilinosScalar factor)
SparseMatrixoperator/= (const TrilinosScalar factor)
SparseMatrixcopy_from (const SparseMatrix &source)
void add (const TrilinosScalar factor, const SparseMatrix &matrix)
void clear_row (const unsigned int row, const TrilinosScalar new_diag_value=0)
void clear_rows (const std::vector< unsigned int > &rows, const TrilinosScalar new_diag_value=0)
void transpose ()
Entry Access
TrilinosScalar operator() (const unsigned int i, const unsigned int j) const
TrilinosScalar el (const unsigned int i, const unsigned int j) const
TrilinosScalar diag_element (const unsigned int i) const
Matrix vector multiplications
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
TrilinosScalar matrix_norm_square (const VectorBase &v) const
TrilinosScalar matrix_scalar_product (const VectorBase &u, const VectorBase &v) const
TrilinosScalar residual (VectorBase &dst, const VectorBase &x, const VectorBase &b) 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
Iterators
const_iterator begin () const
const_iterator end () const
const_iterator begin (const unsigned int r) const
const_iterator end (const unsigned int r) const
Input/Output
void write_ascii ()
void print (std::ostream &out) const

Private Attributes

Epetra_Map row_map
Epetra_Map col_map
Epetra_CombineMode last_action
bool compressed
VectorBase temp_vector
std::vector< unsigned intcolumn_indices
std::vector< TrilinosScalar > column_values
std::auto_ptr< Epetra_FECrsMatrix > matrix


Detailed Description

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 exchangable. 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.

Author:
Martin Kronbichler, Wolfgang Bangerth, 2008, 2009

Member Typedef Documentation

Declare a typedef for the iterator class.

Declare a typedef in analogy to all the other container classes.


Constructor & Destructor Documentation

TrilinosWrappers::SparseMatrix::SparseMatrix (  ) 

Default constructor. Generates an empty (zero-size) matrix.

TrilinosWrappers::SparseMatrix::SparseMatrix ( const Epetra_Map &  InputMap,
const unsigned int  n_max_entries_per_row 
)

Constructor using an Epetra_Map and a maximum number of nonzero matrix entries. 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 should be no effect in the performance of matrix-vector products, since Trilinos wants to reorganize the matrix memory prior to use.

TrilinosWrappers::SparseMatrix::SparseMatrix ( const Epetra_Map &  InputMap,
const std::vector< unsigned int > &  n_entries_per_row 
)

Same as before, but now use the exact number of nonzeros in 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.

TrilinosWrappers::SparseMatrix::SparseMatrix ( const Epetra_Map &  InputRowMap,
const Epetra_Map &  InputColMap,
const unsigned int  n_max_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 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 arragements when doing matrix-vector products with vectors based on that column map.

The number of columns entries per row is specified as the maximum number of entries argument.

TrilinosWrappers::SparseMatrix::SparseMatrix ( const Epetra_Map &  InputRowMap,
const Epetra_Map &  InputColMap,
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.

TrilinosWrappers::SparseMatrix::SparseMatrix ( const unsigned int  m,
const unsigned int  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.

TrilinosWrappers::SparseMatrix::SparseMatrix ( const unsigned int  m,
const unsigned int  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.

TrilinosWrappers::SparseMatrix::SparseMatrix ( const SparsityPattern InputSparsityPattern  ) 

Generate a matrix from a Trilinos sparsity pattern object.

TrilinosWrappers::SparseMatrix::SparseMatrix ( const SparseMatrix InputMatrix  ) 

Copy constructor. Sets the calling matrix to be the same as the input matrix, i.e., using the same sparsity pattern and entries.

virtual TrilinosWrappers::SparseMatrix::~SparseMatrix (  )  [virtual]

Destructor. Made virtual so that one can use pointers to this class.


Member Function Documentation

template<typename SparsityType >
void TrilinosWrappers::SparseMatrix::reinit ( const SparsityType &  sparsity_pattern  )  [inline]

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 partioning 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.

template<typename SparsityType >
void TrilinosWrappers::SparseMatrix::reinit ( const Epetra_Map &  input_map,
const SparsityType &  sparsity_pattern 
) [inline]

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 user-supplied 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 locatoin of non-zero 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. In a parallel run, 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.

template<typename SparsityType >
void TrilinosWrappers::SparseMatrix::reinit ( const Epetra_Map &  input_row_map,
const Epetra_Map &  input_col_map,
const SparsityType &  sparsity_pattern 
) [inline]

This function is similar to the other initialization function above, but now also reassigns the matrix rows and columns according to two user-supplied Epetra maps. To be used for rectangular matrices.

This is a collective operation that needs to be called on all processors in order to avoid a dead lock.

void TrilinosWrappers::SparseMatrix::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.

void TrilinosWrappers::SparseMatrix::reinit ( const SparseMatrix sparse_matrix  ) 

This function copies the content in sparse_matrix to the calling matrix.

This is a collective operation that needs to be called on all processors in order to avoid a dead lock.

void TrilinosWrappers::SparseMatrix::reinit ( const ::::SparseMatrix< double > &  dealii_sparse_matrix,
const double  drop_tolerance = 1e-13 
)

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).

This is a collective operation that needs to be called on all processors in order to avoid a dead lock.

void TrilinosWrappers::SparseMatrix::reinit ( const Epetra_Map &  input_map,
const ::::SparseMatrix< double > &  dealii_sparse_matrix,
const double  drop_tolerance = 1e-13 
)

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 one.

This is a collective operation that needs to be called on all processors in order to avoid a dead lock.

void TrilinosWrappers::SparseMatrix::reinit ( const Epetra_Map &  input_row_map,
const Epetra_Map &  input_col_map,
const ::::SparseMatrix< double > &  dealii_sparse_matrix,
const double  drop_tolerance = 1e-13 
)

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.

This is a collective operation that needs to be called on all processors in order to avoid a dead lock.

void TrilinosWrappers::SparseMatrix::reinit ( const Epetra_CrsMatrix &  input_matrix  ) 

This reinit function takes as input a Trilinos Epetra_CrsMatrix and copies its content.

SparseMatrix& TrilinosWrappers::SparseMatrix::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.

void TrilinosWrappers::SparseMatrix::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.

void TrilinosWrappers::SparseMatrix::compress (  ) 

Trilinos 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. This is a collective operation, i.e., it needs to be run on all processors when used in parallel.

bool TrilinosWrappers::SparseMatrix::is_compressed (  )  const

Returns 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).

unsigned int TrilinosWrappers::SparseMatrix::m (  )  const

Return the number of rows in this matrix.

unsigned int 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().

std::pair<unsigned int, unsigned int> TrilinosWrappers::SparseMatrix::local_range (  )  const

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 unsigned int  index  )  const

Return whether index is in the local range or not, see also local_range().

unsigned int TrilinosWrappers::SparseMatrix::n_nonzero_elements (  )  const

Return the number of nonzero elements of this matrix.

unsigned int TrilinosWrappers::SparseMatrix::row_length ( const unsigned int  row  )  const

Number of entries in a specific row.

bool TrilinosWrappers::SparseMatrix::is_symmetric ( const double  tol = 0.0  )  const

Test whether a matrix is symmetric. Default tolerance is zero. TODO: Not implemented.

bool TrilinosWrappers::SparseMatrix::is_hermitian (  )  const

Test whether a matrix is Hermitian, i.e. it is the complex conjugate of its transpose. TODO: Not implemented.

unsigned int TrilinosWrappers::SparseMatrix::memory_consumption (  )  const

Determine an estimate for the memory consumption (in bytes) of this object. Currently not implemented for this class.

void TrilinosWrappers::SparseMatrix::set ( const unsigned int  i,
const unsigned int  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, then this is no longer possible and an insertion of elements at positions which have not been initialized will throw an exception. Moreover, if value is not a finite number an exception is thrown.

void TrilinosWrappers::SparseMatrix::set ( const std::vector< unsigned int > &  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 local-to-global 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. When compress() is called for the first time, then this 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.

void TrilinosWrappers::SparseMatrix::set ( const std::vector< unsigned int > &  row_indices,
const std::vector< unsigned int > &  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 local-to-global indexing on rows and columns, respectively.

void TrilinosWrappers::SparseMatrix::set ( const unsigned int  row,
const std::vector< unsigned int > &  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. When compress() is called for the first time, then this 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.

void TrilinosWrappers::SparseMatrix::set ( const unsigned int  row,
const unsigned int  n_cols,
const unsigned int col_indices,
const TrilinosScalar *  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. When compress() is called for the first time, then this 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.

void TrilinosWrappers::SparseMatrix::add ( const unsigned int  i,
const unsigned int  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 TrilinosWrappers::SparseMatrix::add ( const std::vector< unsigned int > &  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 local-to-global 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 non-zero data is added. The default value is true, i.e., zero values won't be added into the matrix.

void TrilinosWrappers::SparseMatrix::add ( const std::vector< unsigned int > &  row_indices,
const std::vector< unsigned int > &  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 local-to-global indexing on rows and columns, respectively.

void TrilinosWrappers::SparseMatrix::add ( const unsigned int  row,
const std::vector< unsigned int > &  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 non-zero data is added. The default value is true, i.e., zero values won't be added into the matrix.

void TrilinosWrappers::SparseMatrix::add ( const unsigned int  row,
const unsigned int  n_cols,
const unsigned int 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 non-zero data is added. The default value is true, i.e., zero values won't be added into the matrix.

SparseMatrix& TrilinosWrappers::SparseMatrix::operator*= ( const TrilinosScalar  factor  ) 

Multiply the entire matrix by a fixed factor.

SparseMatrix& TrilinosWrappers::SparseMatrix::operator/= ( const TrilinosScalar  factor  ) 

Divide the entire matrix by a fixed factor.

SparseMatrix& TrilinosWrappers::SparseMatrix::copy_from ( const SparseMatrix source  ) 

Copy the given matrix to this one.

The function returns a reference to *this.

void TrilinosWrappers::SparseMatrix::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.

void TrilinosWrappers::SparseMatrix::clear_row ( const unsigned int  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 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). Note that this is a global operation, so this needs to be done on all MPI processes.

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 non-zero 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.

void TrilinosWrappers::SparseMatrix::clear_rows ( const std::vector< unsigned int > &  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.

void TrilinosWrappers::SparseMatrix::transpose (  ) 

Make an in-place transpose of a matrix.

TrilinosScalar TrilinosWrappers::SparseMatrix::operator() ( const unsigned int  i,
const unsigned int  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.

TrilinosScalar TrilinosWrappers::SparseMatrix::el ( const unsigned int  i,
const unsigned int  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.

TrilinosScalar TrilinosWrappers::SparseMatrix::diag_element ( const unsigned int  i  )  const

Return the main diagonal element in the ith row. This function throws an error if the matrix is not quadratic.

void TrilinosWrappers::SparseMatrix::vmult ( VectorBase dst,
const VectorBase src 
) const

Matrix-vector multiplication: let dst = M*src with M being this matrix.

Source and destination must not be the same vector.

Note that both vectors have to be distributed vectors generated using the same Map as was used for the matrix in case you work on a distributed memory architecture, using the interface in the TrilinosWrappers::VectorBase class (or one of the two derived classes Vector and MPI::Vector).

In case of a localized Vector, this function will only work when running on one processor, since the matrix object is inherently distributed. Otherwise, and exception will be thrown.

void TrilinosWrappers::SparseMatrix::Tvmult ( VectorBase dst,
const VectorBase src 
) const

Matrix-vector multiplication: let dst = MT*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 both vectors have to be distributed vectors generated using the same Map as was used for the matrix in case you work on a distributed memory architecture, using the interface in the TrilinosWrappers::VectorBase class (or one of the two derived classes Vector and MPI::Vector).

In case of a localized Vector, this function will only work when running on one processor, since the matrix object is inherently distributed. Otherwise, and exception will be thrown.

void TrilinosWrappers::SparseMatrix::vmult_add ( VectorBase dst,
const VectorBase src 
) const

Adding Matrix-vector multiplication. Add M*src on dst with M being this matrix.

Source and destination must not be the same vector.

Note that both vectors have to be distributed vectors generated using the same Map as was used for the matrix in case you work on a distributed memory architecture, using the interface in the TrilinosWrappers::VectorBase class (or one of the two derived classes Vector and MPI::Vector).

In case of a localized Vector, this function will only work when running on one processor, since the matrix object is inherently distributed. Otherwise, and exception will be thrown.

void TrilinosWrappers::SparseMatrix::Tvmult_add ( VectorBase dst,
const VectorBase src 
) const

Adding Matrix-vector multiplication. Add MT*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 both vectors have to be distributed vectors generated using the same Map as was used for the matrix in case you work on a distributed memory architecture, using the interface in the TrilinosWrappers::VectorBase class (or one of the two derived classes Vector and MPI::Vector).

In case of a localized Vector, this function will only work when running on one processor, since the matrix object is inherently distributed. Otherwise, and exception will be thrown.

TrilinosScalar TrilinosWrappers::SparseMatrix::matrix_norm_square ( const VectorBase 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.

Note that both vectors have to be distributed vectors generated using the same Map as was used for the matrix in case you work on a distributed memory architecture, using the interface in the TrilinosWrappers::VectorBase class (or one of the two derived classes Vector and MPI::Vector).

In case of a localized Vector, this function will only work when running on one processor, since the matrix object is inherently distributed. Otherwise, and exception will be thrown.

TrilinosScalar TrilinosWrappers::SparseMatrix::matrix_scalar_product ( const VectorBase u,
const VectorBase 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.

Note that both vectors have to be distributed vectors generated using the same Map as was used for the matrix in case you work on a distributed memory architecture, using the interface in the TrilinosWrappers::VectorBase class (or one of the two derived classes Vector and MPI::Vector).

In case of a localized Vector, this function will only work when running on one processor, since the matrix object is inherently distributed. Otherwise, and exception will be thrown.

TrilinosScalar TrilinosWrappers::SparseMatrix::residual ( VectorBase dst,
const VectorBase x,
const VectorBase b 
) const

Compute the residual of an equation Mx=b, where the residual is defined to be r=b-Mx. Write the residual into dst. The l2 norm of the residual vector is returned.

Source x and destination dst must not be the same vector.

Note that both vectors have to be distributed vectors generated using the same Map as was used for the matrix in case you work on a distributed memory architecture, using the interface in the TrilinosWrappers::VectorBase class (or one of the two derived classes Vector and MPI::Vector).

In case of a localized Vector, this function will only work when running on one processor, since the matrix object is inherently distributed. Otherwise, and exception will be thrown.

TrilinosScalar TrilinosWrappers::SparseMatrix::l1_norm (  )  const

Return the l1-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 l1-norm for vectors, i.e. $|Mv|_1 \leq |M|_1 |v|_1$. (cf. Haemmerlin-Hoffmann: Numerische Mathematik)

TrilinosScalar TrilinosWrappers::SparseMatrix::linfty_norm (  )  const

Return the linfty-norm 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 linfty-norm of vectors, i.e. $|Mv|_\infty \leq |M|_\infty |v|_\infty$. (cf. Haemmerlin-Hoffmann: Numerische Mathematik)

TrilinosScalar TrilinosWrappers::SparseMatrix::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.

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& TrilinosWrappers::SparseMatrix::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.

const Epetra_Map& TrilinosWrappers::SparseMatrix::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 matrix-vector products.

const Epetra_Map& TrilinosWrappers::SparseMatrix::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.

const Epetra_Map& TrilinosWrappers::SparseMatrix::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.

const_iterator TrilinosWrappers::SparseMatrix::begin (  )  const

STL-like iterator with the first entry.

const_iterator TrilinosWrappers::SparseMatrix::end (  )  const

Final iterator.

const_iterator TrilinosWrappers::SparseMatrix::begin ( const unsigned int  r  )  const

STL-like iterator with 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 dereferencable in that case.

const_iterator TrilinosWrappers::SparseMatrix::end ( const unsigned int  r  )  const

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 dereferencable. This is in particular the case if it is the end iterator for the last row of a matrix.

void TrilinosWrappers::SparseMatrix::write_ascii (  ) 

Abstract Trilinos object that helps view in ASCII other Trilinos objects. Currently this function is not implemented. TODO: Not implemented.

void TrilinosWrappers::SparseMatrix::print ( std::ostream &  out  )  const

Print the matrix to the given stream, using the format (line,col) value, i.e. one nonzero entry of the matrix per line.


Member Data Documentation

Epetra Trilinos mapping of the matrix rows that assigns parts of the matrix to the individual processes. This map is provided either via the constructor or in a reinit function.

Pointer to the user-supplied Epetra Trilinos mapping of the matrix columns that assigns parts of the matrix to the individual processes.

Epetra_CombineMode TrilinosWrappers::SparseMatrix::last_action [private]

Trilinos doesn't allow to mix additions to matrix entries and overwriting them (to make synchronisation 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.

A boolean variable to hold information on whether the vector is compressed or not.

An internal Trilinos vector that is used for accelerating vmult_add functions (do not need to allocate too many temporary vectors).

An internal array of integer values that is used to store the column indices when adding/inserting local data into the (large) sparse matrix.

std::vector<TrilinosScalar> TrilinosWrappers::SparseMatrix::column_values [private]

An internal array of double values that is used to store the column indices when adding/inserting local data into the (large) sparse matrix.

std::auto_ptr<Epetra_FECrsMatrix> TrilinosWrappers::SparseMatrix::matrix [private]

A sparse matrix object in Trilinos to be used for finite element based problems which allows for assembling into non-local elements. The actual type, a sparse matrix, is set in the constructor.


The documentation for this class was generated from the following file:

deal.II documentation generated on Sat Aug 15 16:52:54 2009 by doxygen 1.5.9