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Reference documentation for deal.II version 9.3.3
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Reference documentation for deal.II version 9.3.3
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#include <deal.II/lac/sparse_matrix.h>
Classes | |
| struct | Traits |
Public Types | |
| using | size_type = types::global_dof_index |
| using | value_type = number |
| using | real_type = typename numbers::NumberTraits< number >::real_type |
| using | const_iterator = SparseMatrixIterators::Iterator< number, true > |
| using | iterator = SparseMatrixIterators::Iterator< number, false > |
Public Member Functions | |
Constructors and initialization | |
| SparseMatrix () | |
| SparseMatrix (const SparseMatrix &) | |
| SparseMatrix (SparseMatrix< number > &&m) noexcept | |
| SparseMatrix (const SparsityPattern &sparsity) | |
| SparseMatrix (const SparsityPattern &sparsity, const IdentityMatrix &id) | |
| virtual | ~SparseMatrix () override |
| SparseMatrix< number > & | operator= (const SparseMatrix< number > &) |
| SparseMatrix< number > & | operator= (SparseMatrix< number > &&m) noexcept |
| SparseMatrix< number > & | operator= (const IdentityMatrix &id) |
| SparseMatrix & | operator= (const double d) |
| virtual void | reinit (const SparsityPattern &sparsity) |
| virtual void | clear () |
Information on the matrix | |
| bool | empty () const |
| size_type | m () const |
| size_type | n () const |
| size_type | get_row_length (const size_type row) const |
| std::size_t | n_nonzero_elements () const |
| std::size_t | n_actually_nonzero_elements (const double threshold=0.) const |
| const SparsityPattern & | get_sparsity_pattern () const |
| std::size_t | memory_consumption () const |
| void | compress (::VectorOperation::values) |
Modifying entries | |
| void | set (const size_type i, const size_type j, const number value) |
| template<typename number2 > | |
| void | set (const std::vector< size_type > &indices, const FullMatrix< number2 > &full_matrix, const bool elide_zero_values=false) |
| template<typename number2 > | |
| void | set (const std::vector< size_type > &row_indices, const std::vector< size_type > &col_indices, const FullMatrix< number2 > &full_matrix, const bool elide_zero_values=false) |
| template<typename number2 > | |
| void | set (const size_type row, const std::vector< size_type > &col_indices, const std::vector< number2 > &values, const bool elide_zero_values=false) |
| template<typename number2 > | |
| void | set (const size_type row, const size_type n_cols, const size_type *col_indices, const number2 *values, const bool elide_zero_values=false) |
| void | add (const size_type i, const size_type j, const number value) |
| template<typename number2 > | |
| void | add (const std::vector< size_type > &indices, const FullMatrix< number2 > &full_matrix, const bool elide_zero_values=true) |
| template<typename number2 > | |
| void | add (const std::vector< size_type > &row_indices, const std::vector< size_type > &col_indices, const FullMatrix< number2 > &full_matrix, const bool elide_zero_values=true) |
| template<typename number2 > | |
| void | add (const size_type row, const std::vector< size_type > &col_indices, const std::vector< number2 > &values, const bool elide_zero_values=true) |
| template<typename number2 > | |
| void | add (const size_type row, const size_type n_cols, const size_type *col_indices, const number2 *values, const bool elide_zero_values=true, const bool col_indices_are_sorted=false) |
| SparseMatrix & | operator*= (const number factor) |
| SparseMatrix & | operator/= (const number factor) |
| void | symmetrize () |
| template<typename somenumber > | |
| SparseMatrix< number > & | copy_from (const SparseMatrix< somenumber > &source) |
| template<typename ForwardIterator > | |
| void | copy_from (const ForwardIterator begin, const ForwardIterator end) |
| template<typename somenumber > | |
| void | copy_from (const FullMatrix< somenumber > &matrix) |
| SparseMatrix< number > & | copy_from (const TrilinosWrappers::SparseMatrix &matrix) |
| template<typename somenumber > | |
| void | add (const number factor, const SparseMatrix< somenumber > &matrix) |
Entry Access | |
| const number & | operator() (const size_type i, const size_type j) const |
| number & | operator() (const size_type i, const size_type j) |
| number | el (const size_type i, const size_type j) const |
| number | diag_element (const size_type i) const |
| number & | diag_element (const size_type i) |
Multiplications | |
| template<class OutVector , class InVector > | |
| void | vmult (OutVector &dst, const InVector &src) const |
| template<class OutVector , class InVector > | |
| void | Tvmult (OutVector &dst, const InVector &src) const |
| template<class OutVector , class InVector > | |
| void | vmult_add (OutVector &dst, const InVector &src) const |
| template<class OutVector , class InVector > | |
| void | Tvmult_add (OutVector &dst, const InVector &src) const |
| template<typename somenumber > | |
| somenumber | matrix_norm_square (const Vector< somenumber > &v) const |
| template<typename somenumber > | |
| somenumber | matrix_scalar_product (const Vector< somenumber > &u, const Vector< somenumber > &v) const |
| template<typename somenumber > | |
| somenumber | residual (Vector< somenumber > &dst, const Vector< somenumber > &x, const Vector< somenumber > &b) const |
| template<typename numberB , typename numberC > | |
| void | mmult (SparseMatrix< numberC > &C, const SparseMatrix< numberB > &B, const Vector< number > &V=Vector< number >(), const bool rebuild_sparsity_pattern=true) const |
| template<typename numberB , typename numberC > | |
| void | Tmmult (SparseMatrix< numberC > &C, const SparseMatrix< numberB > &B, const Vector< number > &V=Vector< number >(), const bool rebuild_sparsity_pattern=true) const |
Matrix norms | |
| real_type | l1_norm () const |
| real_type | linfty_norm () const |
| real_type | frobenius_norm () const |
Preconditioning methods | |
| template<typename somenumber > | |
| void | precondition_Jacobi (Vector< somenumber > &dst, const Vector< somenumber > &src, const number omega=1.) const |
| template<typename somenumber > | |
| void | precondition_SSOR (Vector< somenumber > &dst, const Vector< somenumber > &src, const number omega=1., const std::vector< std::size_t > &pos_right_of_diagonal=std::vector< std::size_t >()) const |
| template<typename somenumber > | |
| void | precondition_SOR (Vector< somenumber > &dst, const Vector< somenumber > &src, const number om=1.) const |
| template<typename somenumber > | |
| void | precondition_TSOR (Vector< somenumber > &dst, const Vector< somenumber > &src, const number om=1.) const |
| template<typename somenumber > | |
| void | SSOR (Vector< somenumber > &v, const number omega=1.) const |
| template<typename somenumber > | |
| void | SOR (Vector< somenumber > &v, const number om=1.) const |
| template<typename somenumber > | |
| void | TSOR (Vector< somenumber > &v, const number om=1.) const |
| template<typename somenumber > | |
| void | PSOR (Vector< somenumber > &v, const std::vector< size_type > &permutation, const std::vector< size_type > &inverse_permutation, const number om=1.) const |
| template<typename somenumber > | |
| void | TPSOR (Vector< somenumber > &v, const std::vector< size_type > &permutation, const std::vector< size_type > &inverse_permutation, const number om=1.) const |
| template<typename somenumber > | |
| void | Jacobi_step (Vector< somenumber > &v, const Vector< somenumber > &b, const number om=1.) const |
| template<typename somenumber > | |
| void | SOR_step (Vector< somenumber > &v, const Vector< somenumber > &b, const number om=1.) const |
| template<typename somenumber > | |
| void | TSOR_step (Vector< somenumber > &v, const Vector< somenumber > &b, const number om=1.) const |
| template<typename somenumber > | |
| void | SSOR_step (Vector< somenumber > &v, const Vector< somenumber > &b, const number om=1.) 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) |
Related Functions | |
(Note that these are not member functions.) | |
| template<typename Number > | |
| void | sum (const SparseMatrix< Number > &local, const MPI_Comm &mpi_communicator, SparseMatrix< Number > &global) |
Input/Output | |
| SmartPointer< const SparsityPattern, SparseMatrix< number > > | cols |
| std::unique_ptr< number[]> | val |
| std::size_t | max_len |
| template<typename somenumber > | |
| class | SparseMatrix |
| template<typename somenumber > | |
| class | SparseLUDecomposition |
| template<typename > | |
| class | SparseILU |
| template<typename > | |
| class | BlockMatrixBase |
| template<typename , bool > | |
| class | SparseMatrixIterators::Iterator |
| template<typename , bool > | |
| class | SparseMatrixIterators::Accessor |
| template<typename Number > | |
| void | Utilities::MPI::sum (const SparseMatrix< Number > &, const MPI_Comm &, SparseMatrix< Number > &) |
| template<class StreamType > | |
| void | print (StreamType &out, const bool across=false, const bool diagonal_first=true) const |
| void | print_formatted (std::ostream &out, const unsigned int precision=3, const bool scientific=true, const unsigned int width=0, const char *zero_string=" ", const double denominator=1.) const |
| void | print_pattern (std::ostream &out, const double threshold=0.) const |
| void | print_as_numpy_arrays (std::ostream &out, const unsigned int precision=9) const |
| void | block_write (std::ostream &out) const |
| void | block_read (std::istream &in) |
| static ::ExceptionBase & | ExcInvalidIndex (int arg1, int arg2) |
| static ::ExceptionBase & | ExcDifferentSparsityPatterns () |
| static ::ExceptionBase & | ExcIteratorRange (int arg1, int arg2) |
| static ::ExceptionBase & | ExcSourceEqualsDestination () |
| void | prepare_add () |
| void | prepare_set () |
Subscriptor functionality | |
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class. | |
| std::atomic< unsigned int > | counter |
| std::map< std::string, unsigned int > | counter_map |
| std::vector< std::atomic< bool > * > | validity_pointers |
| const std::type_info * | object_info |
| 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 ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
| static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
| using | map_value_type = decltype(counter_map)::value_type |
| using | map_iterator = decltype(counter_map)::iterator |
| static std::mutex | mutex |
| void | check_no_subscribers () const noexcept |
Sparse matrix. This class implements the functionality to store matrix entry values in the locations denoted by a SparsityPattern. See Sparsity for a discussion about the separation between sparsity patterns and matrices.
The elements of a SparseMatrix are stored in the same order in which the SparsityPattern class stores its entries. Within each row, elements are generally stored left-to-right in increasing column index order; the exception to this rule is that if the matrix is square (m() == n()), then the diagonal entry is stored as the first element in each row to make operations like applying a Jacobi or SSOR preconditioner faster. As a consequence, if you traverse the elements of a row of a SparseMatrix with the help of iterators into this object (using SparseMatrix::begin and SparseMatrix::end) you will find that the elements are not sorted by column index within each row whenever the matrix is square.
<float> and <double>; others can be generated in application programs (see the section on Template instantiations in the manual). Definition at line 495 of file sparse_matrix.h.
| using SparseMatrix< number >::size_type = types::global_dof_index |
Declare type for container size.
Definition at line 501 of file sparse_matrix.h.
| using SparseMatrix< number >::value_type = number |
Type of the matrix entries. This alias is analogous to value_type in the standard library containers.
Definition at line 507 of file sparse_matrix.h.
| using SparseMatrix< number >::real_type = typename numbers::NumberTraits<number>::real_type |
Declare a type that has holds real-valued numbers with the same precision as the template argument to this class. If the template argument of this class is a real data type, then real_type equals the template argument. If the template argument is a std::complex type then real_type equals the type underlying the complex numbers.
This alias is used to represent the return type of norms.
Definition at line 518 of file sparse_matrix.h.
| using SparseMatrix< number >::const_iterator = SparseMatrixIterators::Iterator<number, true> |
Typedef of an iterator class walking over all the nonzero entries of this matrix. This iterator cannot change the values of the matrix.
Definition at line 524 of file sparse_matrix.h.
| using SparseMatrix< number >::iterator = SparseMatrixIterators::Iterator<number, false> |
Typedef of an iterator class walking over all the nonzero entries of this matrix. This iterator can change the values of the matrix, but of course can't change the sparsity pattern as this is fixed once a sparse matrix is attached to it.
Definition at line 532 of file sparse_matrix.h.
| SparseMatrix< number >::SparseMatrix | ( | ) |
Constructor; initializes the matrix to be empty, without any structure, i.e. the matrix is not usable at all. This constructor is therefore only useful for matrices which are members of a class. All other matrices should be created at a point in the data flow where all necessary information is available.
You have to initialize the matrix before usage with reinit(const SparsityPattern&).
| SparseMatrix< number >::SparseMatrix | ( | const SparseMatrix< number > & | ) |
Copy constructor. This constructor is only allowed to be called if the matrix to be copied is empty. This is for the same reason as for the SparsityPattern, see there for the details.
If you really want to copy a whole matrix, you can do so by using the copy_from() function.
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noexcept |
Move constructor. Construct a new sparse matrix by transferring the internal data of the matrix m into a new object.
Move construction allows an object to be returned from a function or packed into a tuple even when the class cannot be copy-constructed.
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explicit |
Constructor. Takes the given matrix sparsity structure to represent the sparsity pattern of this matrix. You can change the sparsity pattern later on by calling the reinit(const SparsityPattern&) function.
You have to make sure that the lifetime of the sparsity structure is at least as long as that of this matrix or as long as reinit(const SparsityPattern&) is not called with a new sparsity pattern.
The constructor is marked explicit so as to disallow that someone passes a sparsity pattern in place of a sparse matrix to some function, where an empty matrix would be generated then.
| SparseMatrix< number >::SparseMatrix | ( | const SparsityPattern & | sparsity, |
| const IdentityMatrix & | id | ||
| ) |
Copy constructor: initialize the matrix with the identity matrix. This constructor will throw an exception if the sizes of the sparsity pattern and the identity matrix do not coincide, or if the sparsity pattern does not provide for nonzero entries on the entire diagonal.
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overridevirtual |
Destructor. Free all memory, but do not release the memory of the sparsity structure.
| SparseMatrix< number > & SparseMatrix< number >::operator= | ( | const SparseMatrix< number > & | ) |
Copy operator. Since copying entire sparse matrices is a very expensive operation, we disallow doing so except for the special case of empty matrices of size zero. This doesn't seem particularly useful, but is exactly what one needs if one wanted to have a std::vector<SparseMatrix<double> >: in that case, one can create a vector (which needs the ability to copy objects) of empty matrices that are then later filled with something useful.
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noexcept |
Move assignment operator. This operator replaces the present matrix with m by transferring the internal data of m.
| SparseMatrix< number > & SparseMatrix< number >::operator= | ( | const IdentityMatrix & | id | ) |
Copy operator: initialize the matrix with the identity matrix. This operator will throw an exception if the sizes of the sparsity pattern and the identity matrix do not coincide, or if the sparsity pattern does not provide for nonzero entries on the entire diagonal.
| 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 keep the sparsity pattern previously used.
|
virtual |
Reinitialize the sparse matrix with the given sparsity pattern. The latter tells the matrix how many nonzero elements there need to be reserved.
Regarding memory allocation, the same applies as said above.
You have to make sure that the lifetime of the sparsity structure is at least as long as that of this matrix or as long as reinit(const SparsityPattern &) is not called with a new sparsity structure.
The elements of the matrix are set to zero by this function.
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virtual |
Release all memory and return to a state just like after having called the default constructor. It also forgets the sparsity pattern it was previously tied to.
Reimplemented in SparseLUDecomposition< number >, and SparseMIC< number >.
| bool SparseMatrix< number >::empty | ( | ) | const |
Return whether the object is empty. It is empty if either both dimensions are zero or no SparsityPattern is associated.
| size_type SparseMatrix< number >::m | ( | ) | const |
Return the dimension of the codomain (or range) space. Note that the matrix is of dimension \(m \times n\).
| size_type SparseMatrix< number >::n | ( | ) | const |
Return the dimension of the domain space. Note that the matrix is of dimension \(m \times n\).
| size_type SparseMatrix< number >::get_row_length | ( | const size_type | row | ) | const |
Return the number of entries in a specific row.
| std::size_t SparseMatrix< number >::n_nonzero_elements | ( | ) | const |
Return the number of nonzero elements of this matrix. Actually, it returns the number of entries in the sparsity pattern; if any of the entries should happen to be zero, it is counted anyway.
| std::size_t SparseMatrix< number >::n_actually_nonzero_elements | ( | const double | threshold = 0. | ) | const |
Return the number of actually nonzero elements of this matrix. It is possible to specify the parameter threshold in order to count only the elements that have absolute value greater than the threshold.
Note, that this function does (in contrary to n_nonzero_elements()) not count all entries of the sparsity pattern but only the ones that are nonzero (or whose absolute value is greater than threshold).
| const SparsityPattern & SparseMatrix< number >::get_sparsity_pattern | ( | ) | const |
Return a (constant) reference to the underlying sparsity pattern of this matrix.
Though the return value is declared const, you should be aware that it may change if you call any nonconstant function of objects which operate on it.
| std::size_t SparseMatrix< number >::memory_consumption | ( | ) | const |
Determine an estimate for the memory consumption (in bytes) of this object. See MemoryConsumption.
| void SparseMatrix< number >::compress | ( | ::VectorOperation::values | ) |
Dummy function for compatibility with distributed, parallel matrices.
| void SparseMatrix< number >::set | ( | const size_type | i, |
| const size_type | j, | ||
| const number | value | ||
| ) |
Set the element (i,j) to value. Throws an error if the entry does not exist or if value is not a finite number. Still, it is allowed to store zero values in non-existent fields.
| void SparseMatrix< number >::set | ( | const std::vector< size_type > & | indices, |
| const FullMatrix< number2 > & | full_matrix, | ||
| const bool | elide_zero_values = false |
||
| ) |
Set all elements given in a FullMatrix 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.
The optional parameter elide_zero_values can be used to specify whether zero values should be set anyway or they should be filtered away (and not change the previous content in the respective element if it exists). The default value is false, i.e., even zero values are treated.
| void SparseMatrix< number >::set | ( | const std::vector< size_type > & | row_indices, |
| const std::vector< size_type > & | col_indices, | ||
| const FullMatrix< number2 > & | 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 SparseMatrix< number >::set | ( | const size_type | row, |
| const std::vector< size_type > & | col_indices, | ||
| const std::vector< number2 > & | 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.
The optional parameter elide_zero_values can be used to specify whether zero values should be set anyway or they should be filtered away (and not change the previous content in the respective element if it exists). The default value is false, i.e., even zero values are treated.
| void SparseMatrix< number >::set | ( | const size_type | row, |
| const size_type | n_cols, | ||
| const size_type * | col_indices, | ||
| const number2 * | 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.
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 SparseMatrix< number >::add | ( | const size_type | i, |
| const size_type | j, | ||
| const number | value | ||
| ) |
Add value to the element (i,j). Throws an error if the entry does not exist or if value is not a finite number. Still, it is allowed to store zero values in non-existent fields.
| void SparseMatrix< number >::add | ( | const std::vector< size_type > & | indices, |
| const FullMatrix< number2 > & | 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.
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 SparseMatrix< number >::add | ( | const std::vector< size_type > & | row_indices, |
| const std::vector< size_type > & | col_indices, | ||
| const FullMatrix< number2 > & | 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 SparseMatrix< number >::add | ( | const size_type | row, |
| const std::vector< size_type > & | col_indices, | ||
| const std::vector< number2 > & | 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.
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 SparseMatrix< number >::add | ( | const size_type | row, |
| const size_type | n_cols, | ||
| const size_type * | col_indices, | ||
| const number2 * | 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.
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 & SparseMatrix< number >::operator*= | ( | const number | factor | ) |
Multiply the entire matrix by a fixed factor.
| SparseMatrix & SparseMatrix< number >::operator/= | ( | const number | factor | ) |
Divide the entire matrix by a fixed factor.
| void SparseMatrix< number >::symmetrize | ( | ) |
Symmetrize the matrix by forming the mean value between the existing matrix and its transpose, \(A = \frac 12(A+A^T)\).
This operation assumes that the underlying sparsity pattern represents a symmetric object. If this is not the case, then the result of this operation will not be a symmetric matrix, since it only explicitly symmetrizes by looping over the lower left triangular part for efficiency reasons; if there are entries in the upper right triangle, then these elements are missed in the symmetrization. Symmetrization of the sparsity pattern can be obtain by SparsityPattern::symmetrize().
| SparseMatrix< number > & SparseMatrix< number >::copy_from | ( | const SparseMatrix< somenumber > & | source | ) |
Copy the matrix given as argument into the current object.
Copying matrices is an expensive operation that we do not want to happen by accident through compiler generated code for operator=. (This would happen, for example, if one accidentally declared a function argument of the current type by value rather than by reference.) The functionality of copying matrices is implemented in this member function instead. All copy operations of objects of this type therefore require an explicit function call.
The source matrix may be a matrix of arbitrary type, as long as its data type is convertible to the data type of this matrix.
The function returns a reference to *this.
| void SparseMatrix< number >::copy_from | ( | const ForwardIterator | begin, |
| const ForwardIterator | end | ||
| ) |
This function is complete analogous to the SparsityPattern::copy_from() function in that it allows to initialize a whole matrix in one step. See there for more information on argument types and their meaning. You can also find a small example on how to use this function there.
The only difference to the cited function is that the objects which the inner iterator points to need to be of type std::pair<unsigned int, value, where value needs to be convertible to the element type of this class, as specified by the number template argument.
Previous content of the matrix is overwritten. Note that the entries specified by the input parameters need not necessarily cover all elements of the matrix. Elements not covered remain untouched.
| void SparseMatrix< number >::copy_from | ( | const FullMatrix< somenumber > & | matrix | ) |
Copy the nonzero entries of a full matrix into this object. Previous content is deleted.
Note that the underlying sparsity pattern must be appropriate to hold the nonzero entries of the full matrix. This can be achieved using that version of SparsityPattern::copy_from() that takes a FullMatrix as argument.
| SparseMatrix< number > & SparseMatrix< number >::copy_from | ( | const TrilinosWrappers::SparseMatrix< number > & | matrix | ) |
Copy the given Trilinos matrix to this one. The operation triggers an assertion if the sparsity patterns of the current object does not contain the location of a non-zero entry of the given argument.
This function assumes that the two matrices have the same sizes.
The function returns a reference to *this.
| void SparseMatrix< number >::add | ( | const number | factor, |
| const SparseMatrix< somenumber > & | matrix | ||
| ) |
Add matrix scaled by factor to this matrix, i.e. the matrix factor*matrix is added to this. This function throws an error if the sparsity patterns of the two involved matrices do not point to the same object, since in this case the operation is cheaper.
The source matrix may be a sparse matrix over an arbitrary underlying scalar type, as long as its data type is convertible to the data type of this matrix.
| const number & 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. In order to avoid abuse, this function throws an exception if the required element does not exist in the matrix.
In case you want a function that returns zero instead (for entries that are not in the sparsity pattern of the matrix), use the el() function.
If you are looping over all elements, consider using one of the iterator classes instead, since they are tailored better to a sparse matrix structure.
| number & SparseMatrix< number >::operator() | ( | const size_type | i, |
| const size_type | j | ||
| ) |
In contrast to the one above, this function allows modifying the object.
| number SparseMatrix< number >::el | ( | const size_type | i, |
| const size_type | j | ||
| ) | const |
This function is mostly like operator()() in that it returns the value of the matrix entry (i,j). The only difference is that if this entry does not exist in the sparsity pattern, then instead of raising an exception, 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.
If you are looping over all elements, consider using one of the iterator classes instead, since they are tailored better to a sparse matrix structure.
| number 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.
This function is considerably faster than the operator()(), since for quadratic matrices, the diagonal entry may be the first to be stored in each row and access therefore does not involve searching for the right column number.
| number & SparseMatrix< number >::diag_element | ( | const size_type | i | ) |
Same as above, but return a writeable reference. You're sure you know what you do?
| void SparseMatrix< number >::vmult | ( | OutVector & | dst, |
| const InVector & | src | ||
| ) | const |
Matrix-vector multiplication: let dst = M*src with M being this matrix.
Note that while this function can operate on all vectors that offer iterator classes, it is only really effective for objects of type Vector. For all classes for which iterating over elements, or random member access is expensive, this function is not efficient. In particular, if you want to multiply with BlockVector objects, you should consider using a BlockSparseMatrix as well.
Source and destination must not be the same vector.
| void SparseMatrix< number >::Tvmult | ( | OutVector & | dst, |
| const InVector & | 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.
Note that while this function can operate on all vectors that offer iterator classes, it is only really effective for objects of type Vector. For all classes for which iterating over elements, or random member access is expensive, this function is not efficient. In particular, if you want to multiply with BlockVector objects, you should consider using a BlockSparseMatrix as well.
Source and destination must not be the same vector.
| void SparseMatrix< number >::vmult_add | ( | OutVector & | dst, |
| const InVector & | src | ||
| ) | const |
Adding Matrix-vector multiplication. Add M*src on dst with M being this matrix.
Note that while this function can operate on all vectors that offer iterator classes, it is only really effective for objects of type Vector. For all classes for which iterating over elements, or random member access is expensive, this function is not efficient. In particular, if you want to multiply with BlockVector objects, you should consider using a BlockSparseMatrix as well.
Source and destination must not be the same vector.
| void SparseMatrix< number >::Tvmult_add | ( | OutVector & | dst, |
| const InVector & | 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.
Note that while this function can operate on all vectors that offer iterator classes, it is only really effective for objects of type Vector. For all classes for which iterating over elements, or random member access is expensive, this function is not efficient. In particular, if you want to multiply with BlockVector objects, you should consider using a BlockSparseMatrix as well.
Source and destination must not be the same vector.
| somenumber SparseMatrix< number >::matrix_norm_square | ( | const Vector< somenumber > & | 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, and for the result to actually be a norm it also needs to be either real symmetric or complex hermitian.
The underlying template types of both this matrix and the given vector should either both be real or complex-valued, but not mixed, for this function to make sense.
| somenumber SparseMatrix< number >::matrix_scalar_product | ( | const Vector< somenumber > & | u, |
| const Vector< somenumber > & | v | ||
| ) | const |
Compute the matrix scalar product \(\left(u,Mv\right)\).
| somenumber SparseMatrix< number >::residual | ( | Vector< somenumber > & | dst, |
| const Vector< somenumber > & | x, | ||
| const Vector< somenumber > & | 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.
| void SparseMatrix< number >::mmult | ( | SparseMatrix< numberC > & | C, |
| const SparseMatrix< numberB > & | B, | ||
| const Vector< number > & | V = Vector< number >(), |
||
| const bool | rebuild_sparsity_pattern = true |
||
| ) | const |
Perform the matrix-matrix 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 the argument B have compatible sizes. By default, the output matrix C will be resized appropriately.
By default, i.e., if the optional argument rebuild_sparsity_pattern is true, the sparsity pattern of the matrix C will be changed to ensure that all entries that result from the product \(AB\) can be stored in \(C\). This is an expensive operation, and if there is a way to predict the sparsity pattern up front, you should probably build it yourself before calling this function with false as last argument. In this case, the rebuilding of the sparsity pattern is bypassed.
When setting rebuild_sparsity_pattern to true (i.e., leaving it at the default value), it is important to realize that the matrix C passed as first argument still has to be initialized with a sparsity pattern (either at the time of creation of the SparseMatrix object, or via the SparseMatrix::reinit() function). This is because we could create a sparsity pattern inside the current function, and then associate C with it, but there would be no way to transfer ownership of this sparsity pattern to anyone once the current function finishes. Consequently, the function requires that C be already associated with a sparsity pattern object, and this object is then reset to fit the product of A and B.
As a consequence of this, however, it is also important to realize that the sparsity pattern of C is modified and that this would render invalid all other SparseMatrix objects that happen to also use that sparsity pattern object.
| void SparseMatrix< number >::Tmmult | ( | SparseMatrix< numberC > & | C, |
| const SparseMatrix< numberB > & | B, | ||
| const Vector< number > & | V = Vector< number >(), |
||
| const bool | rebuild_sparsity_pattern = true |
||
| ) | const |
Perform the matrix-matrix multiplication with the transpose of this, i.e., C = AT * B, or, if an optional vector argument is given, C = AT * 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.
There is an optional flag rebuild_sparsity_pattern that can be used to bypass the creation of a new sparsity pattern and instead uses the sparsity pattern stored in C. In that case, make sure that it really fits. The default is to rebuild the sparsity pattern.
| real_type 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 \(l_1\)-norm for vectors, i.e. \(|Mv|_1\leq |M|_1 |v|_1\). (cf. Haemmerlin- Hoffmann: Numerische Mathematik)
| real_type SparseMatrix< number >::linfty_norm | ( | ) | const |
Return the \(l_\infty\)-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 \(l_\infty\)-norm of vectors, i.e. \(|Mv|_\infty \leq |M|_\infty |v|_\infty\). (cf. Haemmerlin-Hoffmann: Numerische Mathematik)
| real_type 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.
| void SparseMatrix< number >::precondition_Jacobi | ( | Vector< somenumber > & | dst, |
| const Vector< somenumber > & | src, | ||
| const number | omega = 1. |
||
| ) | const |
Apply the Jacobi preconditioner, which multiplies every element of the src vector by the inverse of the respective diagonal element and multiplies the result with the relaxation factor omega.
| void SparseMatrix< number >::precondition_SSOR | ( | Vector< somenumber > & | dst, |
| const Vector< somenumber > & | src, | ||
| const number | omega = 1., |
||
| const std::vector< std::size_t > & | pos_right_of_diagonal = std::vector< std::size_t >() |
||
| ) | const |
Apply SSOR preconditioning to src with damping omega. The optional argument pos_right_of_diagonal is supposed to provide an array where each entry specifies the position just right of the diagonal in the global array of nonzeros.
| void SparseMatrix< number >::precondition_SOR | ( | Vector< somenumber > & | dst, |
| const Vector< somenumber > & | src, | ||
| const number | om = 1. |
||
| ) | const |
Apply SOR preconditioning matrix to src.
| void SparseMatrix< number >::precondition_TSOR | ( | Vector< somenumber > & | dst, |
| const Vector< somenumber > & | src, | ||
| const number | om = 1. |
||
| ) | const |
Apply transpose SOR preconditioning matrix to src.
| void SparseMatrix< number >::SSOR | ( | Vector< somenumber > & | v, |
| const number | omega = 1. |
||
| ) | const |
Perform SSOR preconditioning in-place. Apply the preconditioner matrix without copying to a second vector. omega is the relaxation parameter.
| void SparseMatrix< number >::SOR | ( | Vector< somenumber > & | v, |
| const number | om = 1. |
||
| ) | const |
Perform an SOR preconditioning in-place. omega is the relaxation parameter.
| void SparseMatrix< number >::TSOR | ( | Vector< somenumber > & | v, |
| const number | om = 1. |
||
| ) | const |
Perform a transpose SOR preconditioning in-place. omega is the relaxation parameter.
| void SparseMatrix< number >::PSOR | ( | Vector< somenumber > & | v, |
| const std::vector< size_type > & | permutation, | ||
| const std::vector< size_type > & | inverse_permutation, | ||
| const number | om = 1. |
||
| ) | const |
Perform a permuted SOR preconditioning in-place.
The standard SOR method is applied in the order prescribed by permutation, that is, first the row permutation[0], then permutation[1] and so on. For efficiency reasons, the permutation as well as its inverse are required.
omega is the relaxation parameter.
| void SparseMatrix< number >::TPSOR | ( | Vector< somenumber > & | v, |
| const std::vector< size_type > & | permutation, | ||
| const std::vector< size_type > & | inverse_permutation, | ||
| const number | om = 1. |
||
| ) | const |
Perform a transposed permuted SOR preconditioning in-place.
The transposed SOR method is applied in the order prescribed by permutation, that is, first the row permutation[m()-1], then permutation[m()-2] and so on. For efficiency reasons, the permutation as well as its inverse are required.
omega is the relaxation parameter.
| void SparseMatrix< number >::Jacobi_step | ( | Vector< somenumber > & | v, |
| const Vector< somenumber > & | b, | ||
| const number | om = 1. |
||
| ) | const |
Do one Jacobi step on v. Performs a direct Jacobi step with right hand side b. This function will need an auxiliary vector, which is acquired from GrowingVectorMemory.
| void SparseMatrix< number >::SOR_step | ( | Vector< somenumber > & | v, |
| const Vector< somenumber > & | b, | ||
| const number | om = 1. |
||
| ) | const |
Do one SOR step on v. Performs a direct SOR step with right hand side b.
| void SparseMatrix< number >::TSOR_step | ( | Vector< somenumber > & | v, |
| const Vector< somenumber > & | b, | ||
| const number | om = 1. |
||
| ) | const |
Do one adjoint SOR step on v. Performs a direct TSOR step with right hand side b.
| void SparseMatrix< number >::SSOR_step | ( | Vector< somenumber > & | v, |
| const Vector< somenumber > & | b, | ||
| const number | om = 1. |
||
| ) | const |
Do one SSOR step on v. Performs a direct SSOR step with right hand side b by performing TSOR after SOR.
| const_iterator SparseMatrix< number >::begin | ( | ) | const |
Return an iterator pointing to the first element of the matrix.
Note the discussion in the general documentation of this class about the order in which elements are accessed.
| iterator SparseMatrix< number >::begin | ( | ) |
Like the function above, but for non-const matrices.
| const_iterator SparseMatrix< number >::end | ( | ) | const |
Return an iterator pointing the element past the last one of this matrix.
| iterator SparseMatrix< number >::end | ( | ) |
Like the function above, but for non-const matrices.
| const_iterator SparseMatrix< number >::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.
| iterator SparseMatrix< number >::begin | ( | const size_type | r | ) |
Like the function above, but for non-const matrices.
| const_iterator SparseMatrix< number >::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.
| iterator SparseMatrix< number >::end | ( | const size_type | r | ) |
Like the function above, but for non-const matrices.
|
related |
Perform an MPI sum of the entries of a SparseMatrix.
local and global should have the same sparsity pattern and it should be the same for all MPI processes. 
1.9.4