Reference documentation for deal.II version Git ca6ed5c 2017-11-20 14:53:00 +0100
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SparseMatrix< number > Class Template Reference

#include <deal.II/lac/sparse_matrix.h>

Inheritance diagram for SparseMatrix< number >:
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Classes

struct  Traits
 

Public Types

typedef types::global_dof_index size_type
 
typedef number value_type
 
typedef numbers::NumberTraits< number >::real_type real_type
 
typedef SparseMatrixIterators::Iterator< number, true > const_iterator
 
typedef SparseMatrixIterators::Iterator< number, false > iterator
 

Public Member Functions

Constructors and initialization
 SparseMatrix ()
 
 SparseMatrix (const SparseMatrix &)
 
 SparseMatrix (SparseMatrix< number > &&m)
 
 SparseMatrix (const SparsityPattern &sparsity)
 
 SparseMatrix (const SparsityPattern &sparsity, const IdentityMatrix &id)
 
virtual ~SparseMatrix ()
 
SparseMatrix< number > & operator= (const SparseMatrix< number > &)
 
SparseMatrix< number > & operator= (SparseMatrix< number > &&m)
 
SparseMatrix< number > & operator= (const IdentityMatrix &id)
 
SparseMatrixoperator= (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 SparsityPatternget_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)
 
SparseMatrixoperator*= (const number factor)
 
SparseMatrixoperator/= (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
number operator() (const size_type i, const size_type j) const
 
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)
 
Input/Output
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 block_write (std::ostream &out) const
 
void block_read (std::istream &in)
 
- Public Member Functions inherited from Subscriptor
 Subscriptor ()
 
 Subscriptor (const Subscriptor &)
 
 Subscriptor (Subscriptor &&)
 
virtual ~Subscriptor ()
 
Subscriptoroperator= (const Subscriptor &)
 
Subscriptoroperator= (Subscriptor &&)
 
void subscribe (const char *identifier=nullptr) const
 
void unsubscribe (const char *identifier=nullptr) const
 
unsigned int n_subscriptions () const
 
void list_subscribers () const
 
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
 

Static Public Member Functions

static::ExceptionBase & ExcInvalidIndex (int arg1, int arg2)
 
static::ExceptionBase & ExcDifferentSparsityPatterns ()
 
static::ExceptionBase & ExcIteratorRange (int arg1, int arg2)
 
static::ExceptionBase & ExcSourceEqualsDestination ()
 
- Static Public Member Functions inherited from Subscriptor
static::ExceptionBase & ExcInUse (int arg1, char *arg2, std::string &arg3)
 
static::ExceptionBase & ExcNoSubscriber (char *arg1, char *arg2)
 

Protected Member Functions

void prepare_add ()
 
void prepare_set ()
 

Private Attributes

SmartPointer< const SparsityPattern, SparseMatrix< number > > cols
 
std::unique_ptr< number[]> val
 
std::size_t max_len
 

Friends

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
 

Detailed Description

template<typename number>
class SparseMatrix< number >

Sparse matrix. This class implements the functionality to store matrix entry values in the locations denoted by a SparsityPattern. See Sparsity patterns 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.

Note
Instantiations for this template are provided for <float> and <double>; others can be generated in application programs (see the section on Template instantiations in the manual).
Author
Essentially everyone who has ever worked on deal.II
Date
1994-2013

Definition at line 44 of file constraint_matrix.h.

Member Typedef Documentation

template<typename number>
typedef types::global_dof_index SparseMatrix< number >::size_type

Declare type for container size.

Definition at line 465 of file sparse_matrix.h.

template<typename number>
typedef number SparseMatrix< number >::value_type

Type of the matrix entries. This typedef is analogous to value_type in the standard library containers.

Definition at line 471 of file sparse_matrix.h.

template<typename number>
typedef numbers::NumberTraits<number>::real_type SparseMatrix< 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 typedef is used to represent the return type of norms.

Definition at line 482 of file sparse_matrix.h.

template<typename number>
typedef SparseMatrixIterators::Iterator<number,true> SparseMatrix< number >::const_iterator

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 490 of file sparse_matrix.h.

template<typename number>
typedef SparseMatrixIterators::Iterator<number,false> SparseMatrix< number >::iterator

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 500 of file sparse_matrix.h.

Constructor & Destructor Documentation

template<typename number>
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&).

template<typename number>
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.

template<typename number>
SparseMatrix< number >::SparseMatrix ( SparseMatrix< number > &&  m)

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.

template<typename number>
SparseMatrix< number >::SparseMatrix ( const SparsityPattern sparsity)
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.

template<typename number>
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.

template<typename number>
virtual SparseMatrix< number >::~SparseMatrix ( )
virtual

Destructor. Free all memory, but do not release the memory of the sparsity structure.

Member Function Documentation

template<typename number>
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.

template<typename number>
SparseMatrix<number>& SparseMatrix< number >::operator= ( SparseMatrix< number > &&  m)

Move assignment operator. This operator replaces the present matrix with m by transferring the internal data of m.

template<typename number>
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.

template<typename number>
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.

Note
If deal.II is configured with threads, this operation will run multi-threaded by splitting the work into smaller chunks (assuming there is enough work to make this worthwhile).
template<typename number>
virtual void SparseMatrix< number >::reinit ( const SparsityPattern sparsity)
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.

template<typename number>
virtual void SparseMatrix< number >::clear ( )
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 >.

template<typename 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.

template<typename number>
size_type SparseMatrix< number >::m ( ) const

Return the dimension of the codomain (or range) space. Note that the matrix is of dimension \(m \times n\).

template<typename number>
size_type SparseMatrix< number >::n ( ) const

Return the dimension of the domain space. Note that the matrix is of dimension \(m \times n\).

template<typename number>
size_type SparseMatrix< number >::get_row_length ( const size_type  row) const

Return the number of entries in a specific row.

template<typename number>
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.

template<typename number>
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).

template<typename number>
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.

template<typename number>
std::size_t SparseMatrix< number >::memory_consumption ( ) const

Determine an estimate for the memory consumption (in bytes) of this object. See MemoryConsumption.

template<typename number>
void SparseMatrix< number >::compress ( ::VectorOperation::values  )

Dummy function for compatibility with distributed, parallel matrices.

template<typename number>
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.

template<typename number>
template<typename number2 >
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.

template<typename number>
template<typename number2 >
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.

template<typename number>
template<typename number2 >
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.

template<typename number>
template<typename number2 >
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.

template<typename number>
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.

template<typename number>
template<typename number2 >
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.

template<typename number>
template<typename number2 >
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.

template<typename number>
template<typename number2 >
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.

template<typename number>
template<typename number2 >
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.

template<typename number>
SparseMatrix& SparseMatrix< number >::operator*= ( const number  factor)

Multiply the entire matrix by a fixed factor.

template<typename number>
SparseMatrix& SparseMatrix< number >::operator/= ( const number  factor)

Divide the entire matrix by a fixed factor.

template<typename number>
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().

template<typename number>
template<typename somenumber >
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.

template<typename number>
template<typename ForwardIterator >
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.

template<typename number>
template<typename somenumber >
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.

template<typename number>
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.

template<typename number>
template<typename somenumber >
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.

template<typename number>
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.

template<typename number>
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.

template<typename number>
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.

template<typename 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?

template<typename number>
template<class OutVector , class InVector >
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.

Note
If deal.II is configured with threads, this operation will run multi-threaded by splitting the work into smaller chunks (assuming there is enough work to make this worthwhile).
template<typename number>
template<class OutVector , class InVector >
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.

template<typename number>
template<class OutVector , class InVector >
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.

Note
If deal.II is configured with threads, this operation will run multi-threaded by splitting the work into smaller chunks (assuming there is enough work to make this worthwhile).
template<typename number>
template<class OutVector , class InVector >
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.

template<typename number>
template<typename somenumber >
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.

Note
If deal.II is configured with threads, this operation will run multi-threaded by splitting the work into smaller chunks (assuming there is enough work to make this worthwhile).
template<typename number>
template<typename somenumber >
somenumber SparseMatrix< number >::matrix_scalar_product ( const Vector< somenumber > &  u,
const Vector< somenumber > &  v 
) const

Compute the matrix scalar product \(\left(u,Mv\right)\).

Note
If deal.II is configured with threads, this operation will run multi-threaded by splitting the work into smaller chunks (assuming there is enough work to make this worthwhile).
template<typename number>
template<typename somenumber >
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.

Note
If deal.II is configured with threads, this operation will run multi-threaded by splitting the work into smaller chunks (assuming there is enough work to make this worthwhile).
template<typename number>
template<typename numberB , typename numberC >
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.

template<typename number>
template<typename numberB , typename numberC >
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.

Note
Rebuilding the sparsity pattern requires changing it. This means that all other matrices that are associated with this sparsity pattern will then have invalid entries.
template<typename number>
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)

template<typename number>
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)

template<typename number>
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.

template<typename number>
template<typename somenumber >
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.

template<typename number>
template<typename somenumber >
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.

template<typename number>
template<typename somenumber >
void SparseMatrix< number >::precondition_SOR ( Vector< somenumber > &  dst,
const Vector< somenumber > &  src,
const number  om = 1. 
) const

Apply SOR preconditioning matrix to src.

template<typename number>
template<typename somenumber >
void SparseMatrix< number >::precondition_TSOR ( Vector< somenumber > &  dst,
const Vector< somenumber > &  src,
const number  om = 1. 
) const

Apply transpose SOR preconditioning matrix to src.

template<typename number>
template<typename somenumber >
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.

template<typename number>
template<typename somenumber >
void SparseMatrix< number >::SOR ( Vector< somenumber > &  v,
const number  om = 1. 
) const

Perform an SOR preconditioning in-place. omega is the relaxation parameter.

template<typename number>
template<typename somenumber >
void SparseMatrix< number >::TSOR ( Vector< somenumber > &  v,
const number  om = 1. 
) const

Perform a transpose SOR preconditioning in-place. omega is the relaxation parameter.

template<typename number>
template<typename somenumber >
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.

template<typename number>
template<typename somenumber >
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.

template<typename number>
template<typename somenumber >
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.

template<typename number>
template<typename somenumber >
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.

template<typename number>
template<typename somenumber >
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.

template<typename number>
template<typename somenumber >
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.

template<typename number>
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.

template<typename number>
iterator SparseMatrix< number >::begin ( )

Like the function above, but for non-const matrices.

template<typename number>
const_iterator SparseMatrix< number >::end ( ) const

Return an iterator pointing the element past the last one of this matrix.

template<typename number>
iterator SparseMatrix< number >::end ( )

Like the function above, but for non-const matrices.

template<typename number>
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 dereferencable in that case if neither row r nor any of the following rows contain any nonzero entries.

template<typename number>
iterator SparseMatrix< number >::begin ( const size_type  r)

Like the function above, but for non-const matrices.

template<typename number>
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 dereferencable. This is in particular the case if it is the end iterator for the last row of a matrix.

template<typename number>
iterator SparseMatrix< number >::end ( const size_type  r)

Like the function above, but for non-const matrices.

template<typename number>
template<class StreamType >
void SparseMatrix< number >::print ( StreamType &  out,
const bool  across = false,
const bool  diagonal_first = true 
) const

Print the matrix to the given stream, using the format (row,column) value, i.e. one nonzero entry of the matrix per line. If across is true, print all entries on a single line, using the format row,column:value.

If the argument diagonal_first is true, diagonal elements of quadratic matrices are printed first in their row, corresponding to the internal storage scheme. If it is false, the elements in a row are written in ascending column order.

template<typename number>
void SparseMatrix< number >::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

Print the matrix in the usual format, i.e. as a matrix and not as a list of nonzero elements. For better readability, elements not in the matrix are displayed as empty space, while matrix elements which are explicitly set to zero are displayed as such.

The parameters allow for a flexible setting of the output format: precision and scientific are used to determine the number format, where scientific = false means fixed point notation. A zero entry for width makes the function compute a width, but it may be changed to a positive value, if output is crude.

Additionally, a character for an empty value may be specified.

Finally, the whole matrix can be multiplied with a common denominator to produce more readable output, even integers.

Attention
This function may produce large amounts of output if applied to a large matrix!
template<typename number>
void SparseMatrix< number >::print_pattern ( std::ostream &  out,
const double  threshold = 0. 
) const

Print the actual pattern of the matrix. For each entry with an absolute value larger than threshold, a '*' is printed, a ':' for every value smaller and a '.' for every entry not allocated.

template<typename number>
void SparseMatrix< number >::block_write ( std::ostream &  out) const

Write the data of this object en bloc to a file. This is done in a binary mode, so the output is neither readable by humans nor (probably) by other computers using a different operating system of number format.

The purpose of this function is that you can swap out matrices and sparsity pattern if you are short of memory, want to communicate between different programs, or allow objects to be persistent across different runs of the program.

template<typename number>
void SparseMatrix< number >::block_read ( std::istream &  in)

Read data that has previously been written by block_write() from a file. This is done using the inverse operations to the above function, so it is reasonably fast because the bitstream is not interpreted except for a few numbers up front.

The object is resized on this operation, and all previous contents are lost. Note, however, that no checks are performed whether new data and the underlying SparsityPattern object fit together. It is your responsibility to make sure that the sparsity pattern and the data to be read match.

A primitive form of error checking is performed which will recognize the bluntest attempts to interpret some data as a matrix stored bitwise to a file that wasn't actually created that way, but not more.

template<typename number>
void SparseMatrix< number >::prepare_add ( )
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.

template<typename number>
void SparseMatrix< number >::prepare_set ( )
protected

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

Friends And Related Function Documentation

template<typename number>
template<typename somenumber >
friend class SparseMatrix
friend

Typedef for the sparse matrix type used.

Definition at line 1619 of file sparse_matrix.h.

template<typename number>
template<typename >
friend class BlockMatrixBase
friend

To allow it calling private prepare_add() and prepare_set().

Definition at line 1626 of file sparse_matrix.h.

template<typename number>
template<typename , bool >
friend class SparseMatrixIterators::Iterator
friend

Also give access to internal details to the iterator/accessor classes.

Definition at line 1631 of file sparse_matrix.h.

Member Data Documentation

template<typename number>
SmartPointer<const SparsityPattern,SparseMatrix<number> > SparseMatrix< number >::cols
private

Pointer to the sparsity pattern used for this matrix. In order to guarantee that it is not deleted while still in use, we subscribe to it using the SmartPointer class.

Definition at line 1599 of file sparse_matrix.h.

template<typename number>
std::unique_ptr<number[]> SparseMatrix< number >::val
private

Array of values for all the nonzero entries. The position of an entry within the matrix, i.e., the row and column number for a given value in this array can only be deduced using the sparsity pattern. The same holds for the more common operation of finding an entry by its coordinates.

Definition at line 1608 of file sparse_matrix.h.

template<typename number>
std::size_t SparseMatrix< number >::max_len
private

Allocated size of val. This can be larger than the actually used part if the size of the matrix was reduced sometime in the past by associating a sparsity pattern with a smaller size to this object, using the reinit() function.

Definition at line 1616 of file sparse_matrix.h.


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