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// $Id: chunk_sparse_matrix.h 31414 2013-10-24 22:15:50Z bangerth $
//
// Copyright (C) 2008 - 2013 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef __deal2__chunk_sparse_matrix_h
#define __deal2__chunk_sparse_matrix_h
#include <deal.II/base/config.h>
#include <deal.II/base/subscriptor.h>
#include <deal.II/base/smartpointer.h>
#include <deal.II/lac/chunk_sparsity_pattern.h>
#include <deal.II/lac/identity_matrix.h>
#include <deal.II/lac/exceptions.h>
DEAL_II_NAMESPACE_OPEN
template<typename number> class Vector;
template<typename number> class FullMatrix;
/*! @addtogroup Matrix1
*@{
*/
/**
* A namespace in which we declare iterators over the elements of sparse
* matrices.
*/
namespace ChunkSparseMatrixIterators
{
// forward declaration
template <typename number, bool Constness>
class Iterator;
/**
* General template for sparse matrix accessors. The first template argument
* denotes the underlying numeric type, the second the constness of the
* matrix.
*
* The general template is not implemented, only the specializations for the
* two possible values of the second template argument. Therefore, the
* interface listed here only serves as a template provided since doxygen
* does not link the specializations.
*/
template <typename number, bool Constness>
class Accessor : public ChunkSparsityPatternIterators::Accessor
{
public:
/**
* Value of this matrix entry.
*/
number value() const;
/**
* Value of this matrix entry.
*/
number &value();
/**
* Return a reference to the matrix into which this accessor points. Note
* that in the present case, this is a constant reference.
*/
const ChunkSparseMatrix<number> &get_matrix () const;
};
/**
* Accessor class for constant matrices, used in the const_iterators. This
* class builds on the accessor classes used for sparsity patterns to loop
* over all nonzero entries, and only adds the accessor functions to gain
* access to the actual value stored at a certain location.
*/
template <typename number>
class Accessor<number,true> : public ChunkSparsityPatternIterators::Accessor
{
public:
/**
* Typedef for the type (including constness) of the matrix to be used
* here.
*/
typedef const ChunkSparseMatrix<number> MatrixType;
/**
* Constructor.
*/
Accessor (MatrixType *matrix,
const unsigned int row);
/**
* Constructor. Construct the end accessor for the given matrix.
*/
Accessor (MatrixType *matrix);
/**
* Copy constructor to get from a non-const accessor to a const accessor.
*/
Accessor (const ChunkSparseMatrixIterators::Accessor<number,false> &a);
/**
* Value of this matrix entry.
*/
number value() const;
/**
* Return a reference to the matrix into which this accessor points. Note
* that in the present case, this is a constant reference.
*/
MatrixType &get_matrix () const;
private:
/**
* Pointer to the matrix we use.
*/
MatrixType *matrix;
/**
* Make the advance function of the base class available.
*/
using ChunkSparsityPatternIterators::Accessor::advance;
/**
* Make iterator class a friend.
*/
template <typename, bool>
friend class Iterator;
};
/**
* Accessor class for non-constant matrices, used in the iterators. This
* class builds on the accessor classes used for sparsity patterns to loop
* over all nonzero entries, and only adds the accessor functions to gain
* access to the actual value stored at a certain location.
*/
template <typename number>
class Accessor<number,false> : public ChunkSparsityPatternIterators::Accessor
{
private:
/**
* Reference class. This is what the accessor class returns when you call
* the value() function. The reference acts just as if it were a reference
* to the actual value of a matrix entry, i.e. you can read and write it,
* you can add and multiply to it, etc, but since the matrix does not give
* away the address of this matrix entry, we have to go through functions
* to do all this.
*
* The constructor takes a pointer to an accessor object that describes
* which element of the matrix it points to. This creates an ambiguity
* when one writes code like iterator->value()=0 (instead of
* iterator->value()=0.0), since the right hand side is an integer that
* can both be converted to a <tt>number</tt> (i.e., most commonly a
* double) or to another object of type <tt>Reference</tt>. The compiler
* then complains about not knowing which conversion to take.
*
* For some reason, adding another overload operator=(int) doesn't seem to
* cure the problem. We avoid it, however, by adding a second, dummy
* argument to the Reference constructor, that is unused, but makes sure
* there is no second matching conversion sequence using a one-argument
* right hand side.
*/
class Reference
{
public:
/**
* Constructor. For the second argument, see the general class
* documentation.
*/
Reference (const Accessor *accessor,
const bool dummy);
/**
* Conversion operator to the data type of the matrix.
*/
operator number () const;
/**
* Set the element of the matrix we presently point to to @p n.
*/
const Reference &operator = (const number n) const;
/**
* Add @p n to the element of the matrix we presently point to.
*/
const Reference &operator += (const number n) const;
/**
* Subtract @p n from the element of the matrix we presently point to.
*/
const Reference &operator -= (const number n) const;
/**
* Multiply the element of the matrix we presently point to by @p n.
*/
const Reference &operator *= (const number n) const;
/**
* Divide the element of the matrix we presently point to by @p n.
*/
const Reference &operator /= (const number n) const;
private:
/**
* Pointer to the accessor that denotes which element we presently point
* to.
*/
const Accessor *accessor;
};
public:
/**
* Typedef for the type (including constness) of the matrix to be used
* here.
*/
typedef ChunkSparseMatrix<number> MatrixType;
/**
* Constructor.
*/
Accessor (MatrixType *matrix,
const unsigned int row);
/**
* Constructor. Construct the end accessor for the given matrix.
*/
Accessor (MatrixType *matrix);
/**
* Value of this matrix entry, returned as a read- and writable reference.
*/
Reference value() const;
/**
* Return a reference to the matrix into which this accessor points. Note
* that in the present case, this is a non-constant reference.
*/
MatrixType &get_matrix () const;
private:
/**
* Pointer to the matrix we use.
*/
MatrixType *matrix;
/**
* Make the advance function of the base class available.
*/
using ChunkSparsityPatternIterators::Accessor::advance;
/**
* Make iterator class a friend.
*/
template <typename, bool>
friend class Iterator;
/**
* Make the inner reference class a friend if the compiler has a bug and
* requires this.
*/
};
/**
* STL conforming iterator for constant and non-constant matrices.
*
* The first template argument denotes the underlying numeric type, the
* second the constness of the matrix.
*
* Since there is a specialization of this class for
* <tt>Constness=false</tt>, this class is for iterators to constant
* matrices.
*/
template <typename number, bool Constness>
class Iterator
{
public:
/**
* Typedef for the matrix type (including constness) we are to operate on.
*/
typedef
typename Accessor<number,Constness>::MatrixType
MatrixType;
/**
* A typedef for the type you get when you dereference an iterator
* of the current kind.
*/
typedef
const Accessor<number,Constness> &value_type;
/**
* Constructor. Create an iterator into the matrix @p matrix for the given
* row and the index within it.
*/
Iterator (MatrixType *matrix,
const unsigned int row);
/**
* Constructor. Create the end iterator for the given matrix.
*/
Iterator (MatrixType *matrix);
/**
* Conversion constructor to get from a non-const iterator to a const
* iterator.
*/
Iterator (const ChunkSparseMatrixIterators::Iterator<number,false> &i);
/**
* Prefix increment.
*/
Iterator &operator++ ();
/**
* Postfix increment.
*/
Iterator operator++ (int);
/**
* Dereferencing operator.
*/
const Accessor<number,Constness> &operator* () const;
/**
* Dereferencing operator.
*/
const Accessor<number,Constness> *operator-> () const;
/**
* Comparison. True, if both iterators point to the same matrix position.
*/
bool operator == (const Iterator &) const;
/**
* Inverse of <tt>==</tt>.
*/
bool operator != (const Iterator &) const;
/**
* Comparison operator. Result is true if either the first row number is
* smaller or if the row numbers are equal and the first index is smaller.
*
* This function is only valid if both iterators point into the same
* matrix.
*/
bool operator < (const Iterator &) const;
/**
* Comparison operator. Works in the same way as above operator, just the
* other way round.
*/
bool operator > (const Iterator &) const;
/**
* Return the distance between the current iterator and the argument.
* The distance is given by how many times one has to apply operator++
* to the current iterator to get the argument (for a positive return
* value), or operator-- (for a negative return value).
*/
int operator - (const Iterator &p) const;
/**
* Return an iterator that is @p n ahead of the current one.
*/
Iterator operator + (const unsigned int n) const;
private:
/**
* Store an object of the accessor class.
*/
Accessor<number,Constness> accessor;
};
}
/**
* Sparse matrix. This class implements the function to store values
* in the locations of a sparse matrix denoted by a
* SparsityPattern. The separation of sparsity pattern and values is
* done since one can store data elements of different type in these
* locations without the SparsityPattern having to know this, and more
* importantly one can associate more than one matrix with the same
* sparsity pattern.
*
* The use of this class is demonstrated in step-51.
*
* @note Instantiations for this template are provided for <tt>@<float@> and
* @<double@></tt>; others can be generated in application programs (see the
* section on @ref Instantiations in the manual).
*
* @author Wolfgang Bangerth, 2008
*/
template <typename number>
class ChunkSparseMatrix : public virtual Subscriptor
{
public:
/**
* Declare the type for container size.
*/
typedef types::global_dof_index size_type;
/**
* Type of matrix entries. In analogy to
* the STL container classes.
*/
typedef number value_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.
*/
typedef typename numbers::NumberTraits<number>::real_type real_type;
/**
* Typedef of an STL conforming iterator class walking over all the nonzero
* entries of this matrix. This iterator cannot change the values of the
* matrix.
*/
typedef
ChunkSparseMatrixIterators::Iterator<number,true>
const_iterator;
/**
* Typedef of an STL conforming iterator class walking over all the nonzero
* entries of this matrix. This iterator @em 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.
*/
typedef
ChunkSparseMatrixIterators::Iterator<number,false>
iterator;
/**
* A structure that describes some of the traits of this class in terms of
* its run-time behavior. Some other classes (such as the block matrix
* classes) that take one or other of the matrix classes as its template
* parameters can tune their behavior based on the variables in this class.
*/
struct Traits
{
/**
* It is safe to elide additions of zeros to individual elements of this
* matrix.
*/
static const bool zero_addition_can_be_elided = true;
};
/**
* @name Constructors and initalization.
*/
//@{
/**
* 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
* ChunkSparsityPattern&).
*/
ChunkSparseMatrix ();
/**
* 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
* ChunkSparsityPattern, see there for the details.
*
* If you really want to copy a whole matrix, you can do so by using the
* copy_from() function.
*/
ChunkSparseMatrix (const ChunkSparseMatrix &);
/**
* 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 ChunkSparsityPattern&) 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
* ChunkSparsityPattern&) 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.
*/
explicit ChunkSparseMatrix (const ChunkSparsityPattern &sparsity);
/**
* 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.
*/
ChunkSparseMatrix (const ChunkSparsityPattern &sparsity,
const IdentityMatrix &id);
/**
* Destructor. Free all memory, but do not release the memory of the
* sparsity structure.
*/
virtual ~ChunkSparseMatrix ();
/**
* 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
* <code>std::vector@<ChunkSparseMatrix@<double@> @></code>: 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.
*/
ChunkSparseMatrix<number> &operator = (const ChunkSparseMatrix<number> &);
/**
* 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.
*/
ChunkSparseMatrix<number> &
operator= (const IdentityMatrix &id);
/**
* 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 <tt>matrix=0</tt>, which sets
* all elements of the matrix to zero, but keep the sparsity pattern
* previously used.
*/
ChunkSparseMatrix &operator = (const double d);
/**
* 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
* ChunkSparsityPattern &) is not called with a new sparsity structure.
*
* The elements of the matrix are set to zero by this function.
*/
virtual void reinit (const ChunkSparsityPattern &sparsity);
/**
* 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.
*/
virtual void clear ();
//@}
/**
* @name Information on the matrix
*/
//@{
/**
* Return whether the object is empty. It is empty if either both dimensions
* are zero or no ChunkSparsityPattern is associated.
*/
bool empty () const;
/**
* Return the dimension of the image space. To remember: the matrix is of
* dimension $m \times n$.
*/
size_type m () const;
/**
* Return the dimension of the range space. To remember: the matrix is of
* dimension $m \times n$.
*/
size_type n () 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.
*/
size_type n_nonzero_elements () const;
/**
* Return the number of actually nonzero elements of this matrix.
*
* 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.
*/
size_type n_actually_nonzero_elements () const;
/**
* Return a (constant) reference to the underlying sparsity pattern of this
* matrix.
*
* Though the return value is declared <tt>const</tt>, you should be aware
* that it may change if you call any nonconstant function of objects which
* operate on it.
*/
const ChunkSparsityPattern &get_sparsity_pattern () const;
/**
* Determine an estimate for the memory consumption (in bytes) of this
* object. See MemoryConsumption.
*/
std::size_t memory_consumption () const;
//@}
/**
* @name Modifying entries
*/
//@{
/**
* Set the element (<i>i,j</i>) to <tt>value</tt>. Throws an error if the
* entry does not exist or if <tt>value</tt> is not a finite number. Still,
* it is allowed to store zero values in non-existent fields.
*/
void set (const size_type i,
const size_type j,
const number value);
/**
* Add <tt>value</tt> to the element (<i>i,j</i>). Throws an error if the
* entry does not exist or if <tt>value</tt> is not a finite number. Still,
* it is allowed to store zero values in non-existent fields.
*/
void add (const size_type i,
const size_type j,
const number value);
/**
* Add an array of values given by <tt>values</tt> in the given global
* matrix row at columns specified by col_indices in the sparse matrix.
*
* The optional parameter <tt>elide_zero_values</tt> 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 <tt>true</tt>,
* i.e., zero values won't be added into the matrix.
*/
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);
/**
* Multiply the entire matrix by a fixed factor.
*/
ChunkSparseMatrix &operator *= (const number factor);
/**
* Divide the entire matrix by a fixed factor.
*/
ChunkSparseMatrix &operator /= (const number factor);
/**
* 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 ChunkSparsityPattern::symmetrize().
*/
void symmetrize ();
/**
* Copy the given matrix to this one. The operation throws an error if the
* sparsity patterns of the two involved matrices do not point to the same
* object, since in this case the copy operation is cheaper. Since this
* operation is notheless not for free, we do not make it available through
* <tt>operator =</tt>, since this may lead to unwanted usage, e.g. in copy
* arguments to functions, which should really be arguments by reference.
*
* 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 <tt>*this</tt>.
*/
template <typename somenumber>
ChunkSparseMatrix<number> &
copy_from (const ChunkSparseMatrix<somenumber> &source);
/**
* This function is complete analogous to the
* ChunkSparsityPattern::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 <tt>std::pair<unsigned int,
* value</tt>, where <tt>value</tt> needs to be convertible to the element
* type of this class, as specified by the <tt>number</tt> 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 ForwardIterator>
void copy_from (const ForwardIterator begin,
const ForwardIterator end);
/**
* 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 somenumber>
void copy_from (const FullMatrix<somenumber> &matrix);
/**
* Add <tt>matrix</tt> scaled by <tt>factor</tt> to this matrix, i.e. the
* matrix <tt>factor*matrix</tt> is added to <tt>this</tt>. 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 somenumber>
void add (const number factor,
const ChunkSparseMatrix<somenumber> &matrix);
//@}
/**
* @name Entry Access
*/
//@{
/**
* Return the value of the entry (<i>i,j</i>). 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 operator () (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>i,j</i>). 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 el (const size_type i,
const size_type j) const;
/**
* Return the main diagonal
* element in the <i>i</i>th
* 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 diag_element (const size_type i) const;
/**
* Same as above, but return a writeable reference. You're sure you know
* what you do?
*/
number &diag_element (const size_type i);
//@}
/**
* @name Matrix vector multiplications
*/
//@{
/**
* Matrix-vector multiplication: let <i>dst = M*src</i> with <i>M</i> 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 @ref
* 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 BlockChunkSparseMatrix as well.
*
* Source and destination must not be the same vector.
*/
template <class OutVector, class InVector>
void vmult (OutVector &dst,
const InVector &src) const;
/**
* Matrix-vector multiplication: let <i>dst = M<sup>T</sup>*src</i> with
* <i>M</i> 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 @ref
* 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 BlockChunkSparseMatrix as well.
*
* Source and destination must not be the same vector.
*/
template <class OutVector, class InVector>
void Tvmult (OutVector &dst,
const InVector &src) const;
/**
* Adding Matrix-vector multiplication. Add <i>M*src</i> on <i>dst</i> with
* <i>M</i> 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 @ref
* 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 BlockChunkSparseMatrix as well.
*
* Source and destination must not be the same vector.
*/
template <class OutVector, class InVector>
void vmult_add (OutVector &dst,
const InVector &src) const;
/**
* Adding Matrix-vector multiplication. Add <i>M<sup>T</sup>*src</i> to
* <i>dst</i> with <i>M</i> 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 @ref
* 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 BlockChunkSparseMatrix as well.
*
* Source and destination must not be the same vector.
*/
template <class OutVector, class InVector>
void Tvmult_add (OutVector &dst,
const InVector &src) 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.
*/
template <typename somenumber>
somenumber matrix_norm_square (const Vector<somenumber> &v) const;
/**
* Compute the matrix scalar product $\left(u,Mv\right)$.
*/
template <typename somenumber>
somenumber matrix_scalar_product (const Vector<somenumber> &u,
const Vector<somenumber> &v) const;
/**
* Compute the residual of an equation <i>Mx=b</i>, where the residual is
* defined to be <i>r=b-Mx</i>. Write the residual into <tt>dst</tt>. The
* <i>l<sub>2</sub></i> norm of the residual vector is returned.
*
* Source <i>x</i> and destination <i>dst</i> must not be the same vector.
*/
template <typename somenumber>
somenumber residual (Vector<somenumber> &dst,
const Vector<somenumber> &x,
const Vector<somenumber> &b) const;
//@}
/**
* @name Matrix norms
*/
//@{
/**
* Return the l1-norm of the matrix, that is $|M|_1=max_{all columns
* j}\sum_{all rows i} |M_ij|$, (max. sum of columns). This is the natural
* matrix norm that is compatible to the l1-norm for vectors, i.e.
* $|Mv|_1\leq |M|_1 |v|_1$. (cf. Haemmerlin-Hoffmann : Numerische
* Mathematik)
*/
real_type l1_norm () const;
/**
* Return the linfty-norm of the matrix, that is $|M|_infty=max_{all rows
* i}\sum_{all columns j} |M_ij|$, (max. sum of rows). This is the natural
* matrix norm that is compatible to the linfty-norm of vectors, i.e.
* $|Mv|_infty \leq |M|_infty |v|_infty$. (cf. Haemmerlin-Hoffmann :
* Numerische Mathematik)
*/
real_type linfty_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.
*/
real_type frobenius_norm () const;
//@}
/**
* @name Preconditioning methods
*/
//@{
/**
* Apply the Jacobi preconditioner, which multiplies every element of the
* <tt>src</tt> vector by the inverse of the respective diagonal element and
* multiplies the result with the relaxation factor <tt>omega</tt>.
*/
template <typename somenumber>
void precondition_Jacobi (Vector<somenumber> &dst,
const Vector<somenumber> &src,
const number omega = 1.) const;
/**
* Apply SSOR preconditioning to <tt>src</tt>.
*/
template <typename somenumber>
void precondition_SSOR (Vector<somenumber> &dst,
const Vector<somenumber> &src,
const number om = 1.) const;
/**
* Apply SOR preconditioning matrix to <tt>src</tt>.
*/
template <typename somenumber>
void precondition_SOR (Vector<somenumber> &dst,
const Vector<somenumber> &src,
const number om = 1.) const;
/**
* Apply transpose SOR preconditioning matrix to <tt>src</tt>.
*/
template <typename somenumber>
void precondition_TSOR (Vector<somenumber> &dst,
const Vector<somenumber> &src,
const number om = 1.) const;
/**
* Perform SSOR preconditioning in-place. Apply the preconditioner matrix
* without copying to a second vector. <tt>omega</tt> is the relaxation
* parameter.
*/
template <typename somenumber>
void SSOR (Vector<somenumber> &v,
const number omega = 1.) const;
/**
* Perform an SOR preconditioning in-place. <tt>omega</tt> is the
* relaxation parameter.
*/
template <typename somenumber>
void SOR (Vector<somenumber> &v,
const number om = 1.) const;
/**
* Perform a transpose SOR preconditioning in-place. <tt>omega</tt> is the
* relaxation parameter.
*/
template <typename somenumber>
void TSOR (Vector<somenumber> &v,
const number om = 1.) const;
/**
* Perform a permuted SOR preconditioning in-place.
*
* The standard SOR method is applied in the order prescribed by
* <tt>permutation</tt>, that is, first the row <tt>permutation[0]</tt>,
* then <tt>permutation[1]</tt> and so on. For efficiency reasons, the
* permutation as well as its inverse are required.
*
* <tt>omega</tt> is the relaxation parameter.
*/
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;
/**
* Perform a transposed permuted SOR preconditioning in-place.
*
* The transposed SOR method is applied in the order prescribed by
* <tt>permutation</tt>, that is, first the row <tt>permutation[m()-1]</tt>,
* then <tt>permutation[m()-2]</tt> and so on. For efficiency reasons, the
* permutation as well as its inverse are required.
*
* <tt>omega</tt> is the relaxation parameter.
*/
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;
/**
* Do one SOR step on <tt>v</tt>. Performs a direct SOR step with right
* hand side <tt>b</tt>.
*/
template <typename somenumber>
void SOR_step (Vector<somenumber> &v,
const Vector<somenumber> &b,
const number om = 1.) const;
/**
* Do one adjoint SOR step on <tt>v</tt>. Performs a direct TSOR step with
* right hand side <tt>b</tt>.
*/
template <typename somenumber>
void TSOR_step (Vector<somenumber> &v,
const Vector<somenumber> &b,
const number om = 1.) const;
/**
* Do one SSOR step on <tt>v</tt>. Performs a direct SSOR step with right
* hand side <tt>b</tt> by performing TSOR after SOR.
*/
template <typename somenumber>
void SSOR_step (Vector<somenumber> &v,
const Vector<somenumber> &b,
const number om = 1.) const;
//@}
/**
* @name Iterators
*/
//@{
/**
* STL-like iterator with the first entry of the matrix. This is the version
* for constant matrices.
*
* Note that due to the layout in ChunkSparseMatrix, iterating over matrix
* entries is considerably slower than for a sparse matrix, as the iterator
* is travels row-by-row, whereas data is stored in chunks of several rows
* and columns.
*/
const_iterator begin () const;
/**
* Final iterator. This is the version for constant matrices.
*
* Note that due to the layout in ChunkSparseMatrix, iterating over matrix
* entries is considerably slower than for a sparse matrix, as the iterator
* is travels row-by-row, whereas data is stored in chunks of several rows
* and columns.
*/
const_iterator end () const;
/**
* STL-like iterator with the first entry of the matrix. This is the version
* for non-constant matrices.
*
* Note that due to the layout in ChunkSparseMatrix, iterating over matrix
* entries is considerably slower than for a sparse matrix, as the iterator
* is travels row-by-row, whereas data is stored in chunks of several rows
* and columns.
*/
iterator begin ();
/**
* Final iterator. This is the version for non-constant matrices.
*
* Note that due to the layout in ChunkSparseMatrix, iterating over matrix
* entries is considerably slower than for a sparse matrix, as the iterator
* is travels row-by-row, whereas data is stored in chunks of several rows
* and columns.
*/
iterator end ();
/**
* STL-like iterator with the first entry of row <tt>r</tt>. This is the
* version for constant matrices.
*
* Note that if the given row is empty, i.e. does not contain any nonzero
* entries, then the iterator returned by this function equals
* <tt>end(r)</tt>. Note also that the iterator may not be dereferencable in
* that case.
*
* Note that due to the layout in ChunkSparseMatrix, iterating over matrix
* entries is considerably slower than for a sparse matrix, as the iterator
* is travels row-by-row, whereas data is stored in chunks of several rows
* and columns.
*/
const_iterator begin (const unsigned int r) const;
/**
* Final iterator of row <tt>r</tt>. It points to the first element past the
* end of line @p r, or past the end of the entire sparsity pattern. This is
* the version for constant matrices.
*
* 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.
*
* Note that due to the layout in ChunkSparseMatrix, iterating over matrix
* entries is considerably slower than for a sparse matrix, as the iterator
* is travels row-by-row, whereas data is stored in chunks of several rows
* and columns.
*/
const_iterator end (const unsigned int r) const;
/**
* STL-like iterator with the first entry of row <tt>r</tt>. This is the
* version for non-constant matrices.
*
* Note that if the given row is empty, i.e. does not contain any nonzero
* entries, then the iterator returned by this function equals
* <tt>end(r)</tt>. Note also that the iterator may not be dereferencable in
* that case.
*
* Note that due to the layout in ChunkSparseMatrix, iterating over matrix
* entries is considerably slower than for a sparse matrix, as the iterator
* is travels row-by-row, whereas data is stored in chunks of several rows
* and columns.
*/
iterator begin (const unsigned int r);
/**
* Final iterator of row <tt>r</tt>. It points to the first element past the
* end of line @p r, or past the end of the entire sparsity pattern. This is
* the version for non-constant matrices.
*
* 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.
*
* Note that due to the layout in ChunkSparseMatrix, iterating over matrix
* entries is considerably slower than for a sparse matrix, as the iterator
* is travels row-by-row, whereas data is stored in chunks of several rows
* and columns.
*/
iterator end (const unsigned int r);
//@}
/**
* @name Input/Output
*/
//@{
/**
* Print the matrix to the given stream, using the format <tt>(line,col)
* value</tt>, i.e. one nonzero entry of the matrix per line.
*/
void print (std::ostream &out) 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:
* <tt>precision</tt> and <tt>scientific</tt> are used to determine the
* number format, where <tt>scientific = false</tt> means fixed point
* notation. A zero entry for <tt>width</tt> 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 <b>large</b> amounts of output if
* applied to a large matrix!
*/
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;
/**
* 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.
*/
void print_pattern(std::ostream &out,
const double threshold = 0.) 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 or 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.
*/
void block_write (std::ostream &out) const;
/**
* 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 ChunkSparsityPattern 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.
*/
void block_read (std::istream &in);
//@}
/** @addtogroup Exceptions
* @{ */
/**
* Exception
*/
DeclException2 (ExcInvalidIndex,
int, int,
<< "The entry with index <" << arg1 << ',' << arg2
<< "> does not exist.");
/**
* Exception
*/
DeclException1 (ExcInvalidIndex1,
int,
<< "The index " << arg1 << " is not in the allowed range.");
/**
* Exception
*/
DeclException0 (ExcDifferentChunkSparsityPatterns);
/**
* Exception
*/
DeclException2 (ExcIteratorRange,
int, int,
<< "The iterators denote a range of " << arg1
<< " elements, but the given number of rows was " << arg2);
/**
* Exception
*/
DeclException0 (ExcSourceEqualsDestination);
//@}
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.
*/
SmartPointer<const ChunkSparsityPattern,ChunkSparseMatrix<number> > cols;
/**
* Array of values for all the nonzero entries. The position within the
* matrix, i.e. the row and column number for a given entry can only be
* deduced using the sparsity pattern. The same holds for the more common
* operation of finding an entry by its coordinates.
*/
number *val;
/**
* Allocated size of #val. This can be larger than the actually used part if
* the size of the matrix was reduced somewhen in the past by associating a
* sparsity pattern with a smaller size to this object, using the reinit()
* function.
*/
size_type max_len;
/**
* Return the location of entry $(i,j)$ within the val array.
*/
size_type compute_location (const size_type i,
const size_type j) const;
// make all other sparse matrices friends
template <typename somenumber> friend class ChunkSparseMatrix;
/**
* Also give access to internal details to the iterator/accessor
* classes.
*/
template <typename,bool> friend class ChunkSparseMatrixIterators::Iterator;
template <typename,bool> friend class ChunkSparseMatrixIterators::Accessor;
};
/*@}*/
#ifndef DOXYGEN
/*---------------------- Inline functions -----------------------------------*/
template <typename number>
inline
typename ChunkSparseMatrix<number>::size_type
ChunkSparseMatrix<number>::m () const
{
Assert (cols != 0, ExcNotInitialized());
return cols->rows;
}
template <typename number>
inline
typename ChunkSparseMatrix<number>::size_type
ChunkSparseMatrix<number>::n () const
{
Assert (cols != 0, ExcNotInitialized());
return cols->cols;
}
template <typename number>
inline
const ChunkSparsityPattern &
ChunkSparseMatrix<number>::get_sparsity_pattern () const
{
Assert (cols != 0, ExcNotInitialized());
return *cols;
}
template <typename number>
inline
typename ChunkSparseMatrix<number>::size_type
ChunkSparseMatrix<number>::compute_location (const size_type i,
const size_type j) const
{
const size_type chunk_size = cols->get_chunk_size();
const size_type chunk_index
= cols->sparsity_pattern(i/chunk_size, j/chunk_size);
if (chunk_index == ChunkSparsityPattern::invalid_entry)
return ChunkSparsityPattern::invalid_entry;
else
{
return (chunk_index * chunk_size * chunk_size
+
(i % chunk_size) * chunk_size
+
(j % chunk_size));
}
}
template <typename number>
inline
void ChunkSparseMatrix<number>::set (const size_type i,
const size_type j,
const number value)
{
Assert (numbers::is_finite(value), ExcNumberNotFinite());
Assert (cols != 0, ExcNotInitialized());
// it is allowed to set elements of the matrix that are not part of the
// sparsity pattern, if the value to which we set it is zero
const size_type index = compute_location(i,j);
Assert ((index != SparsityPattern::invalid_entry) ||
(value == 0.),
ExcInvalidIndex(i,j));
if (index != SparsityPattern::invalid_entry)
val[index] = value;
}
template <typename number>
inline
void ChunkSparseMatrix<number>::add (const size_type i,
const size_type j,
const number value)
{
Assert (numbers::is_finite(value), ExcNumberNotFinite());
Assert (cols != 0, ExcNotInitialized());
if (value != 0.)
{
const size_type index = compute_location(i,j);
Assert ((index != ChunkSparsityPattern::invalid_entry),
ExcInvalidIndex(i,j));
val[index] += value;
}
}
template <typename number>
template <typename number2>
inline
void ChunkSparseMatrix<number>::add (const size_type row,
const size_type n_cols,
const size_type *col_indices,
const number2 *values,
const bool /*elide_zero_values*/,
const bool /*col_indices_are_sorted*/)
{
// TODO: could be done more efficiently...
for (size_type col=0; col<n_cols; ++col)
add(row, col_indices[col], static_cast<number>(values[col]));
}
template <typename number>
inline
ChunkSparseMatrix<number> &
ChunkSparseMatrix<number>::operator *= (const number factor)
{
Assert (cols != 0, ExcNotInitialized());
Assert (val != 0, ExcNotInitialized());
const size_type chunk_size = cols->get_chunk_size();
// multiply all elements of the matrix with the given factor. this includes
// the padding elements in chunks that overlap the boundaries of the actual
// matrix -- but since multiplication with a number does not violate the
// invariant of keeping these elements at zero nothing can happen
number *val_ptr = val;
const number *const end_ptr = val +
cols->sparsity_pattern.n_nonzero_elements()
*
chunk_size * chunk_size;
while (val_ptr != end_ptr)
*val_ptr++ *= factor;
return *this;
}
template <typename number>
inline
ChunkSparseMatrix<number> &
ChunkSparseMatrix<number>::operator /= (const number factor)
{
Assert (cols != 0, ExcNotInitialized());
Assert (val != 0, ExcNotInitialized());
Assert (factor !=0, ExcDivideByZero());
const number factor_inv = 1. / factor;
const size_type chunk_size = cols->get_chunk_size();
// multiply all elements of the matrix with the given factor. this includes
// the padding elements in chunks that overlap the boundaries of the actual
// matrix -- but since multiplication with a number does not violate the
// invariant of keeping these elements at zero nothing can happen
number *val_ptr = val;
const number *const end_ptr = val +
cols->sparsity_pattern.n_nonzero_elements()
*
chunk_size * chunk_size;
while (val_ptr != end_ptr)
*val_ptr++ *= factor_inv;
return *this;
}
template <typename number>
inline
number ChunkSparseMatrix<number>::operator () (const size_type i,
const size_type j) const
{
Assert (cols != 0, ExcNotInitialized());
AssertThrow (compute_location(i,j) != SparsityPattern::invalid_entry,
ExcInvalidIndex(i,j));
return val[compute_location(i,j)];
}
template <typename number>
inline
number ChunkSparseMatrix<number>::el (const size_type i,
const size_type j) const
{
Assert (cols != 0, ExcNotInitialized());
const size_type index = compute_location(i,j);
if (index != ChunkSparsityPattern::invalid_entry)
return val[index];
else
return 0;
}
template <typename number>
inline
number ChunkSparseMatrix<number>::diag_element (const size_type i) const
{
Assert (cols != 0, ExcNotInitialized());
Assert (m() == n(), ExcNotQuadratic());
Assert (i<m(), ExcInvalidIndex1(i));
// Use that the first element in each row of a quadratic matrix is the main
// diagonal of the chunk sparsity pattern
const size_type chunk_size = cols->get_chunk_size();
return val[cols->sparsity_pattern.rowstart[i/chunk_size]
*
chunk_size * chunk_size
+
(i % chunk_size) * chunk_size
+
(i % chunk_size)];
}
template <typename number>
template <typename ForwardIterator>
inline
void
ChunkSparseMatrix<number>::copy_from (const ForwardIterator begin,
const ForwardIterator end)
{
Assert (static_cast<size_type >(std::distance (begin, end)) == m(),
ExcIteratorRange (std::distance (begin, end), m()));
// for use in the inner loop, we define a typedef to the type of the inner
// iterators
typedef typename std::iterator_traits<ForwardIterator>::value_type::const_iterator inner_iterator;
size_type row=0;
for (ForwardIterator i=begin; i!=end; ++i, ++row)
{
const inner_iterator end_of_row = i->end();
for (inner_iterator j=i->begin(); j!=end_of_row; ++j)
// write entries
set (row, j->first, j->second);
}
}
//---------------------------------------------------------------------------
namespace ChunkSparseMatrixIterators
{
template <typename number>
inline
Accessor<number,true>::
Accessor (const MatrixType *matrix,
const unsigned int row)
:
ChunkSparsityPatternIterators::Accessor (&matrix->get_sparsity_pattern(),
row),
matrix (matrix)
{}
template <typename number>
inline
Accessor<number,true>::
Accessor (const MatrixType *matrix)
:
ChunkSparsityPatternIterators::Accessor (&matrix->get_sparsity_pattern()),
matrix (matrix)
{}
template <typename number>
inline
Accessor<number,true>::
Accessor (const ChunkSparseMatrixIterators::Accessor<number,false> &a)
:
ChunkSparsityPatternIterators::Accessor (a),
matrix (&a.get_matrix())
{}
template <typename number>
inline
number
Accessor<number, true>::value () const
{
const unsigned int chunk_size = matrix->get_sparsity_pattern().get_chunk_size();
return matrix->val[reduced_index() * chunk_size * chunk_size
+
chunk_row * chunk_size
+
chunk_col];
}
template <typename number>
inline
typename Accessor<number, true>::MatrixType &
Accessor<number, true>::get_matrix () const
{
return *matrix;
}
template <typename number>
inline
Accessor<number, false>::Reference::Reference (
const Accessor *accessor,
const bool)
:
accessor (accessor)
{}
template <typename number>
inline
Accessor<number, false>::Reference::operator number() const
{
const unsigned int chunk_size = accessor->matrix->get_sparsity_pattern().get_chunk_size();
return accessor->matrix->val[accessor->reduced_index() * chunk_size * chunk_size
+
accessor->chunk_row * chunk_size
+
accessor->chunk_col];
}
template <typename number>
inline
const typename Accessor<number, false>::Reference &
Accessor<number, false>::Reference::operator = (const number n) const
{
const unsigned int chunk_size = accessor->matrix->get_sparsity_pattern().get_chunk_size();
accessor->matrix->val[accessor->reduced_index() * chunk_size * chunk_size
+
accessor->chunk_row * chunk_size
+
accessor->chunk_col] = n;
return *this;
}
template <typename number>
inline
const typename Accessor<number, false>::Reference &
Accessor<number, false>::Reference::operator += (const number n) const
{
const unsigned int chunk_size = accessor->matrix->get_sparsity_pattern().get_chunk_size();
accessor->matrix->val[accessor->reduced_index() * chunk_size * chunk_size
+
accessor->chunk_row * chunk_size
+
accessor->chunk_col] += n;
return *this;
}
template <typename number>
inline
const typename Accessor<number, false>::Reference &
Accessor<number, false>::Reference::operator -= (const number n) const
{
const unsigned int chunk_size = accessor->matrix->get_sparsity_pattern().get_chunk_size();
accessor->matrix->val[accessor->reduced_index() * chunk_size * chunk_size
+
accessor->chunk_row * chunk_size
+
accessor->chunk_col] -= n;
return *this;
}
template <typename number>
inline
const typename Accessor<number, false>::Reference &
Accessor<number, false>::Reference::operator *= (const number n) const
{
const unsigned int chunk_size = accessor->matrix->get_sparsity_pattern().get_chunk_size();
accessor->matrix->val[accessor->reduced_index() * chunk_size * chunk_size
+
accessor->chunk_row * chunk_size
+
accessor->chunk_col] *= n;
return *this;
}
template <typename number>
inline
const typename Accessor<number, false>::Reference &
Accessor<number, false>::Reference::operator /= (const number n) const
{
const unsigned int chunk_size = accessor->matrix->get_sparsity_pattern().get_chunk_size();
accessor->matrix->val[accessor->reduced_index() * chunk_size * chunk_size
+
accessor->chunk_row * chunk_size
+
accessor->chunk_col] /= n;
return *this;
}
template <typename number>
inline
Accessor<number,false>::
Accessor (MatrixType *matrix,
const unsigned int row)
:
ChunkSparsityPatternIterators::Accessor (&matrix->get_sparsity_pattern(),
row),
matrix (matrix)
{}
template <typename number>
inline
Accessor<number,false>::
Accessor (MatrixType *matrix)
:
ChunkSparsityPatternIterators::Accessor (&matrix->get_sparsity_pattern()),
matrix (matrix)
{}
template <typename number>
inline
typename Accessor<number, false>::Reference
Accessor<number, false>::value() const
{
return Reference(this,true);
}
template <typename number>
inline
typename Accessor<number, false>::MatrixType &
Accessor<number, false>::get_matrix () const
{
return *matrix;
}
template <typename number, bool Constness>
inline
Iterator<number, Constness>::
Iterator (MatrixType *matrix,
const unsigned int row)
:
accessor(matrix, row)
{}
template <typename number, bool Constness>
inline
Iterator<number, Constness>::
Iterator (MatrixType *matrix)
:
accessor(matrix)
{}
template <typename number, bool Constness>
inline
Iterator<number, Constness>::
Iterator (const ChunkSparseMatrixIterators::Iterator<number,false> &i)
:
accessor(*i)
{}
template <typename number, bool Constness>
inline
Iterator<number, Constness> &
Iterator<number,Constness>::operator++ ()
{
accessor.advance ();
return *this;
}
template <typename number, bool Constness>
inline
Iterator<number,Constness>
Iterator<number,Constness>::operator++ (int)
{
const Iterator iter = *this;
accessor.advance ();
return iter;
}
template <typename number, bool Constness>
inline
const Accessor<number,Constness> &
Iterator<number,Constness>::operator* () const
{
return accessor;
}
template <typename number, bool Constness>
inline
const Accessor<number,Constness> *
Iterator<number,Constness>::operator-> () const
{
return &accessor;
}
template <typename number, bool Constness>
inline
bool
Iterator<number,Constness>::
operator == (const Iterator &other) const
{
return (accessor == other.accessor);
}
template <typename number, bool Constness>
inline
bool
Iterator<number,Constness>::
operator != (const Iterator &other) const
{
return ! (*this == other);
}
template <typename number, bool Constness>
inline
bool
Iterator<number,Constness>::
operator < (const Iterator &other) const
{
Assert (&accessor.get_matrix() == &other.accessor.get_matrix(),
ExcInternalError());
return (accessor < other.accessor);
}
template <typename number, bool Constness>
inline
bool
Iterator<number,Constness>::
operator > (const Iterator &other) const
{
return (other < *this);
}
template <typename number, bool Constness>
inline
int
Iterator<number,Constness>::
operator - (const Iterator &other) const
{
Assert (&accessor.get_matrix() == &other.accessor.get_matrix(),
ExcInternalError());
// TODO: can be optimized
int difference = 0;
if (*this < other)
{
Iterator copy = *this;
while (copy != other)
{
++copy;
--difference;
}
}
else
{
Iterator copy = other;
while (copy != *this)
{
++copy;
++difference;
}
}
return difference;
}
template <typename number, bool Constness>
inline
Iterator<number,Constness>
Iterator<number,Constness>::
operator + (const unsigned int n) const
{
Iterator x = *this;
for (unsigned int i=0; i<n; ++i)
++x;
return x;
}
}
template <typename number>
inline
typename ChunkSparseMatrix<number>::const_iterator
ChunkSparseMatrix<number>::begin () const
{
return const_iterator(this, 0);
}
template <typename number>
inline
typename ChunkSparseMatrix<number>::const_iterator
ChunkSparseMatrix<number>::end () const
{
return const_iterator(this);
}
template <typename number>
inline
typename ChunkSparseMatrix<number>::iterator
ChunkSparseMatrix<number>::begin ()
{
return iterator(this, 0);
}
template <typename number>
inline
typename ChunkSparseMatrix<number>::iterator
ChunkSparseMatrix<number>::end ()
{
return iterator(this);
}
template <typename number>
inline
typename ChunkSparseMatrix<number>::const_iterator
ChunkSparseMatrix<number>::begin (const unsigned int r) const
{
Assert (r<m(), ExcIndexRange(r,0,m()));
return const_iterator(this, r);
}
template <typename number>
inline
typename ChunkSparseMatrix<number>::const_iterator
ChunkSparseMatrix<number>::end (const unsigned int r) const
{
Assert (r<m(), ExcIndexRange(r,0,m()));
return const_iterator(this, r+1);
}
template <typename number>
inline
typename ChunkSparseMatrix<number>::iterator
ChunkSparseMatrix<number>::begin (const unsigned int r)
{
Assert (r<m(), ExcIndexRange(r,0,m()));
return iterator(this, r);
}
template <typename number>
inline
typename ChunkSparseMatrix<number>::iterator
ChunkSparseMatrix<number>::end (const unsigned int r)
{
Assert (r<m(), ExcIndexRange(r,0,m()));
return iterator(this, r+1);
}
#endif // DOXYGEN
/*---------------------------- chunk_sparse_matrix.h ---------------------------*/
DEAL_II_NAMESPACE_CLOSE
#endif
/*---------------------------- chunk_sparse_matrix.h ---------------------------*/
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