]> https://gitweb.dealii.org/ - dealii-svn.git/commitdiff
Should not have deleted this file.
authorwolf <wolf@0785d39b-7218-0410-832d-ea1e28bc413d>
Mon, 2 Dec 2002 17:32:38 +0000 (17:32 +0000)
committerwolf <wolf@0785d39b-7218-0410-832d-ea1e28bc413d>
Mon, 2 Dec 2002 17:32:38 +0000 (17:32 +0000)
git-svn-id: https://svn.dealii.org/trunk@6794 0785d39b-7218-0410-832d-ea1e28bc413d

deal.II/lac/include/lac/sparse_matrix.h [new file with mode: 0644]

diff --git a/deal.II/lac/include/lac/sparse_matrix.h b/deal.II/lac/include/lac/sparse_matrix.h
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+//----------------------------  sparse_matrix.h  ---------------------------
+//    $Id$
+//    Version: $Name$
+//
+//    Copyright (C) 1998, 1999, 2000, 2001, 2002 by the deal.II authors
+//
+//    This file is subject to QPL and may not be  distributed
+//    without copyright and license information. Please refer
+//    to the file deal.II/doc/license.html for the  text  and
+//    further information on this license.
+//
+//----------------------------  sparse_matrix.h  ---------------------------
+#ifndef __deal2__sparse_matrix_h
+#define __deal2__sparse_matrix_h
+
+
+#include <base/config.h>
+#include <base/exceptions.h>
+#include <base/subscriptor.h>
+#include <base/smartpointer.h>
+#include <lac/sparsity_pattern.h>
+
+template<typename number> class Vector;
+template<typename number> class FullMatrix;
+
+/**
+ * Sparse matrix.
+ *
+ *
+ * @sect2{On template instantiations}
+ *
+ * Member functions of this class are either implemented in this file
+ * or in a file of the same name with suffix ``.templates.h''. For the
+ * most common combinations of the template parameters, instantiations
+ * of this class are provided in a file with suffix ``.cc'' in the
+ * ``source'' directory. If you need an instantiation that is not
+ * listed there, you have to include this file along with the
+ * corresponding ``.templates.h'' file and instantiate the respective
+ * class yourself.
+ *
+ * @author Original version by Roland Becker, Guido Kanschat, Franz-Theo Suttmeier; lots of enhancements, reorganisation and documentation by Wolfgang Bangerth 1998
+ */
+template <typename number>
+class SparseMatrix : public Subscriptor
+{
+  public:
+                                    /**
+                                     * Accessor class for iterators
+                                     */
+    class Accessor
+    {
+      public:
+                                        /**
+                                         * Constructor. Since we use
+                                         * accessors only for read
+                                         * access, a const matrix
+                                         * pointer is sufficient.
+                                         */
+       Accessor (const SparseMatrix<number>*,
+                 unsigned int row,
+                 unsigned short index);
+
+                                        /**
+                                         * Row number of the element
+                                         * represented by this
+                                         * object.
+                                         */
+       unsigned int row() const;
+
+                                        /**
+                                         * Index in row of the element
+                                         * represented by this
+                                         * object.
+                                         */
+       unsigned short index() const;
+
+                                        /**
+                                         * Column number of the
+                                         * element represented by
+                                         * this object.
+                                         */
+       unsigned int column() const;
+
+                                        /**
+                                         * Value of this matrix entry.
+                                         */
+       number value() const;
+       
+       protected:
+                                        /**
+                                         * The matrix accessed.
+                                         */
+       const SparseMatrix<number>* matrix;
+
+                                        /**
+                                         * Current row number.
+                                         */
+       unsigned int a_row;
+
+                                        /**
+                                         * Current index in row.
+                                         */
+       unsigned short a_index;
+      };
+
+                                    /**
+                                     * STL conforming iterator.
+                                     */
+    class const_iterator : private Accessor
+      {
+       public:
+                                          /**
+                                           * Constructor.
+                                           */ 
+       const_iterator(const SparseMatrix<number>*,
+                      unsigned int row,
+                      unsigned short index);
+         
+                                          /**
+                                           * Prefix increment.
+                                           */
+       const_iterator& operator++ ();
+
+                                          /**
+                                           * Postfix increment.
+                                           */
+       const_iterator& operator++ (int);
+
+                                          /**
+                                           * Dereferencing operator.
+                                           */
+       const Accessor& operator* () const;
+
+                                          /**
+                                           * Dereferencing operator.
+                                           */
+       const Accessor* operator-> () const;
+
+                                          /**
+                                           * Comparison. True, if
+                                           * both iterators point to
+                                           * the same matrix
+                                           * position.
+                                           */
+       bool operator == (const const_iterator&) const;
+                                          /**
+                                           * Inverse of @p{==}.
+                                           */
+       bool operator != (const 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.
+                                           */
+       bool operator < (const const_iterator&) const;
+      };
+    
+                                    /**
+                                     * Type of matrix entries. In analogy to
+                                     * the STL container classes.
+                                     */
+    typedef number value_type;
+    
+                                    /**
+                                     * 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
+                                     * @p{reinit(SparsityPattern)}.
+                                     */
+    SparseMatrix ();
+
+                                    /**
+                                     * 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
+                                     * @p{SparsityPattern}, see there for the
+                                     * details.
+                                     *
+                                     * If you really want to copy a whole
+                                     * matrix, you can do so by using the
+                                     * @p{copy_from} function.
+                                     */
+    SparseMatrix (const SparseMatrix &);
+
+                                    /**
+                                     * 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 @p{reinit}
+                                     * 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 @p{reinit} is not
+                                     * called with a new sparsity
+                                     * structure.
+                                     *
+                                     * 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 SparseMatrix (const SparsityPattern &sparsity);
+    
+                                    /**
+                                     * Destructor. Free all memory, but do not
+                                     * release the memory of the sparsity
+                                     * structure.
+                                     */
+    virtual ~SparseMatrix ();
+
+                                    /** 
+                                     * Pseudo operator only copying
+                                     * empty objects.
+                                     */
+    SparseMatrix<number>& operator = (const SparseMatrix<number> &);
+
+                                    /**
+                                     * Reinitialize the object but
+                                     * keep to the sparsity pattern
+                                     * previously used.  This may be
+                                     * necessary if you @p{reinit}'d
+                                     * the sparsity structure and
+                                     * want to update the size of the
+                                     * matrix.
+                                     *
+                                     * Note that memory is only
+                                     * reallocated if the new size
+                                     * exceeds the old size. If that
+                                     * is not the case, the allocated
+                                     * memory is not reduced. However,
+                                     * if the sparsity structure is
+                                     * empty (i.e. the dimensions are
+                                     * zero), then all memory is
+                                     * freed.
+                                     *
+                                     * If the sparsity pattern has
+                                     * not changed, then the effect
+                                     * of this function is simply to
+                                     * reset all matrix entries to
+                                     * zero.
+                                     */
+    virtual void reinit ();
+
+                                    /**
+                                     * 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 @p{reinit} is not called
+                                     * with a new sparsity structure.
+                                     *
+                                     * The elements of the matrix are
+                                     * set to zero by this function.
+                                     */
+    virtual void reinit (const SparsityPattern &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 ();
+    
+                                    /**
+                                     * Return whether the object is
+                                     * empty. It is empty if either
+                                     * both dimensions are zero or no
+                                     * @p{SparsityPattern} is
+                                     * associated.
+                                     */
+    bool empty () const;
+
+                                    /**
+                                     * Return the dimension of the
+                                     * image space.  To remember: the
+                                     * matrix is of dimension
+                                     * $m \times n$.
+                                     */
+    unsigned int m () const;
+    
+                                    /**
+                                     * Return the dimension of the
+                                     * range space.  To remember: the
+                                     * matrix is of dimension
+                                     * $m \times n$.
+                                     */
+    unsigned int 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.
+                                     */
+    unsigned int n_nonzero_elements () const;
+
+                                    /**
+                                     * Return the number of actually
+                                     * nonzero elements of this
+                                     * matrix.
+                                     *
+                                     * Note, that this function does
+                                     * (in contrary to the
+                                     * @p{n_nonzero_elements}) NOT
+                                     * count all entries of the
+                                     * sparsity pattern but only the
+                                     * ones that are nonzero.
+                                     */
+    unsigned int n_actually_nonzero_elements () const;
+    
+                                    /**
+                                     * Set the element @p{(i,j)} to @p{value}.
+                                     * Throws an error if the entry does
+                                     * not exist. Still, it is allowed to store
+                                     * zero values in non-existent fields.
+                                     */
+    void set (const unsigned int i, const unsigned int j,
+             const number value);
+    
+                                    /**
+                                     * Add @p{value} to the element
+                                     * @p{(i,j)}.  Throws an error if
+                                     * the entry does not
+                                     * exist. Still, it is allowed to
+                                     * store zero values in
+                                     * non-existent fields.
+                                     */
+    void add (const unsigned int i, const unsigned int j,
+             const number value);
+
+                                    /**
+                                     * 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 the
+                                     * @ref{SparsityPattern}@p{::symmetrize}
+                                     * function.
+                                     */
+    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 @p{operator =}, 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
+                                     * @p{this}.
+                                     */
+    template <typename somenumber>
+    SparseMatrix<number> &
+    copy_from (const SparseMatrix<somenumber> &source);
+
+                                    /**
+                                     * This function is complete
+                                     * analogous to the
+                                     * @ref{SparsityPattern}@p{::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 @p{std::pair<unsigned int, value},
+                                     * where @p{value}
+                                     * needs to be convertible to the
+                                     * element type of this class, as
+                                     * specified by the @p{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 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 @p{matrix} scaled by
+                                     * @p{factor} to this matrix. The
+                                     * 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 matrix
+                                     * of arbitrary type, as long as its
+                                     * data type is convertible to the
+                                     * data type of this matrix.
+                                     */
+    template <typename somenumber>
+    void add_scaled (const number factor,
+                    const SparseMatrix<somenumber> &matrix);
+    
+                                    /**
+                                     * 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 @p{el}
+                                     * function.
+                                     */
+    number operator () (const unsigned int i,
+                       const unsigned int j) const;
+
+                                    /**
+                                     * This function is mostly like
+                                     * @p{operator()} in that it
+                                     * returns the value of the
+                                     * matrix entry @p{(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.
+                                     */
+    number el (const unsigned int i,
+              const unsigned int j) const;
+
+                                    /**
+                                     * Return the main diagonal element in
+                                     * the @p{i}th row. This function throws an
+                                     * error if the matrix is not square.
+                                     *
+                                     * This function is considerably
+                                     * faster than the @p{operator()},
+                                     * since for square matrices, the
+                                     * diagonal entry is always the
+                                     * first to be stored in each row
+                                     * and access therefore does not
+                                     * involve searching for the
+                                     * right column number.
+                                     */
+    number diag_element (const unsigned int i) const;
+
+                                    /**
+                                     * Same as above, but return a
+                                     * writeable reference. You're
+                                     * sure you know what you do?
+                                     */
+    number & diag_element (const unsigned int i);
+
+                                    /**
+                                     * Access to values in internal
+                                     * mode.  Returns the value of
+                                     * the @p{index}th entry in
+                                     * @p{row}. Here, @p{index} refers to
+                                     * the internal representation of
+                                     * the matrix, not the column. Be
+                                     * sure to understand what you are
+                                     * doing here.
+                                     */
+    number raw_entry (const unsigned int row,
+                     const unsigned int index) const;
+    
+                                    /**
+                                     * This is for hackers. Get
+                                     * access to the @p{i}th element of
+                                     * this matrix. The elements are
+                                     * stored in a consecutive way,
+                                     * refer to the @p{SparsityPattern}
+                                     * class for more details.
+                                     *
+                                     * You should use this interface
+                                     * very carefully and only if you
+                                     * are absolutely sure to know
+                                     * what you do. You should also
+                                     * note that the structure of
+                                     * these arrays may change over
+                                     * time.  If you change the
+                                     * layout yourself, you should
+                                     * also rename this function to
+                                     * avoid programs relying on
+                                     * outdated information!
+                                     */
+    number global_entry (const unsigned int i) const;
+
+                                    /**
+                                     * Same as above, but with write
+                                     * access.  You certainly know
+                                     * what you do?
+                                     */
+    number & global_entry (const unsigned int i);
+
+                                    /**
+                                     * Matrix-vector multiplication:
+                                     * let $dst = M*src$ with $M$
+                                     * being this matrix.
+                                     */
+    template <typename somenumber>
+    void vmult (Vector<somenumber>       &dst,
+               const Vector<somenumber> &src) const;
+    
+                                    /**
+                                     * Matrix-vector multiplication:
+                                     * let $dst = M^T*src$ with $M$
+                                     * being this matrix. This
+                                     * function does the same as
+                                     * @p{vmult} but takes the
+                                     * transposed matrix.
+                                     */
+    template <typename somenumber>
+    void Tvmult (Vector<somenumber>       &dst,
+                const Vector<somenumber> &src) const;
+  
+                                    /**
+                                     * Adding Matrix-vector
+                                     * multiplication. Add $M*src$ on
+                                     * $dst$ with $M$ being this
+                                     * matrix.
+                                     */
+    template <typename somenumber>
+    void vmult_add (Vector<somenumber>       &dst,
+                   const Vector<somenumber> &src) const;
+    
+                                    /**
+                                     * Adding Matrix-vector
+                                     * multiplication. Add $M^T*src$
+                                     * to $dst$ with $M$ being this
+                                     * matrix. This function does the
+                                     * same as @p{vmult_add} but takes
+                                     * the transposed matrix.
+                                     */
+    template <typename somenumber>
+    void Tvmult_add (Vector<somenumber>       &dst,
+                    const Vector<somenumber> &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 square for this operation.
+                                     */
+    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;
+    
+                                    /**
+                                     * 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)
+                                     */
+    number 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)
+                                     */
+    number linfty_norm () const;
+
+                                    /**
+                                     * Compute the residual of an
+                                     * equation @p{Mx=b}, where the
+                                     * residual is defined to be
+                                     * @p{r=b-Mx} with @p{x} typically
+                                     * being an approximate of the
+                                     * true solution of the
+                                     * equation. Write the residual
+                                     * into @p{dst}. The l2 norm of
+                                     * the residual vector is
+                                     * returned.
+                                     */
+    template <typename somenumber>
+    somenumber residual (Vector<somenumber>       &dst,
+                        const Vector<somenumber> &x,
+                        const Vector<somenumber> &b) const;
+    
+                                    /**
+                                     * Apply the Jacobi
+                                     * preconditioner, which
+                                     * multiplies every element of
+                                     * the @p{src} vector by the
+                                     * inverse of the respective
+                                     * diagonal element and
+                                     * multiplies the result with the
+                                     * damping factor @p{omega}.
+                                     */
+    template <typename somenumber>
+    void precondition_Jacobi (Vector<somenumber>       &dst,
+                             const Vector<somenumber> &src,
+                             const number              omega = 1.) const;
+
+                                    /**
+                                     * Apply SSOR preconditioning to
+                                     * @p{src}.
+                                     */
+    template <typename somenumber>
+    void precondition_SSOR (Vector<somenumber>       &dst,
+                           const Vector<somenumber> &src,
+                           const number              om = 1.) const;
+
+                                    /**
+                                     * Apply SOR preconditioning matrix to @p{src}.
+                                     * The result of this method is
+                                     * $dst = (om D - L)^{-1} src$.
+                                     */
+    template <typename somenumber>
+    void precondition_SOR (Vector<somenumber>       &dst,
+                          const Vector<somenumber> &src,
+                          const number              om = 1.) const;
+    
+                                    /**
+                                     * Apply transpose SOR preconditioning matrix to @p{src}.
+                                     * The result of this method is
+                                     * $dst = (om D - U)^{-1} src$.
+                                     */
+    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.
+                                     * @p{omega} is the relaxation
+                                     * parameter.
+                                     */
+    template <typename somenumber>
+    void SSOR (Vector<somenumber> &v,
+              const number        omega = 1.) const;
+
+                                    /**
+                                     * Perform an SOR preconditioning in-place.
+                                     * The result is $v = (\omega D - L)^{-1} v$.
+                                     * @p{omega} is the damping parameter.
+                                     */
+    template <typename somenumber>
+    void SOR (Vector<somenumber> &v,
+             const number        om = 1.) const;
+
+                                    /**
+                                     * Perform a transpose SOR preconditioning in-place.
+                                     * The result is $v = (\omega D - L)^{-1} v$.
+                                     * @p{omega} is the damping parameter.
+                                     */
+    template <typename somenumber>
+    void TSOR (Vector<somenumber> &v,
+             const number        om = 1.) const;
+
+                                    /**
+                                     * Do one SOR step on @p{v}.
+                                     * Performs a direct SOR step
+                                     * with right hand side @p{b}.
+                                     */
+    template <typename somenumber>
+    void SOR_step (Vector<somenumber> &v,
+                  const Vector<somenumber> &b,
+                  const number        om = 1.) const;
+
+                                    /**
+                                     * Do one adjoint SOR step on
+                                     * @p{v}.  Performs a direct TSOR
+                                     * step with right hand side @p{b}.
+                                     */
+    template <typename somenumber>
+    void TSOR_step (Vector<somenumber> &v,
+                   const Vector<somenumber> &b,
+                   const number        om = 1.) const;
+
+                                    /**
+                                     * Do one adjoint SSOR step on
+                                     * @p{v}.  Performs a direct SSOR
+                                     * step with right hand side @p{b}
+                                     * by performing TSOR after SOR.
+                                     */
+    template <typename somenumber>
+    void SSOR_step (Vector<somenumber> &v,
+                   const Vector<somenumber> &b,
+                   const number        om = 1.) const;
+
+                                    /**
+                                     * Return a (constant) reference
+                                     * to the underlying sparsity
+                                     * pattern of this matrix.
+                                     *
+                                     * Though the return value is
+                                     * declared @p{const}, you should
+                                     * be aware that it may change if
+                                     * you call any nonconstant
+                                     * function of objects which
+                                     * operate on it.
+                                     */
+    const SparsityPattern & get_sparsity_pattern () const;
+
+                                    /**
+                                     * STL-like iterator with the
+                                     * first entry.
+                                     */
+    const_iterator begin () const;
+
+                                    /**
+                                     * Final iterator.
+                                     */
+    const_iterator end () const;
+    
+                                    /**
+                                     * STL-like iterator with the
+                                     * first entry of row @p{r}.
+                                     */
+    const_iterator begin (unsigned int r) const;
+
+                                    /**
+                                     * Final iterator of row @p{r}.
+                                     */
+    const_iterator end (unsigned int r) const;
+    
+                                    /**
+                                     * Print the matrix to the given
+                                     * stream, using the format
+                                     * @p{(line,col) value}, 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: @p{precision} and
+                                     * @p{scientific} are used to
+                                     * determine the number format,
+                                     * where @p{scientific} = @p{false}
+                                     * means fixed point notation.  A
+                                     * zero entry for @p{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.
+                                     *
+                                     * This function
+                                     * may produce @em{large} 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;
+
+                                    /**
+                                     * 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.
+                                     */
+    void block_write (std::ostream &out) const;
+
+                                    /**
+                                     * Read data that has previously
+                                     * been written by
+                                     * @p{block_write} en block 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
+                                     * @ref{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 vector stored
+                                     * bitwise to a file, but not
+                                     * more.
+                                     */
+    void block_read (std::istream &in);
+
+                                    /**
+                                     * Determine an estimate for the
+                                     * memory consumption (in bytes)
+                                     * of this object.
+                                     */
+    unsigned int memory_consumption () const;
+    
+                                    /**
+                                     * Exception
+                                     */
+    DeclException0 (ExcNotCompressed);
+                                    /**
+                                     * Exception
+                                     */
+    DeclException0 (ExcMatrixNotInitialized);
+                                    /**
+                                     * 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 (ExcMatrixNotSquare);
+                                    /**
+                                     * Exception
+                                     */
+    DeclException0 (ExcDifferentSparsityPatterns);
+                                    /**
+                                     * Exception
+                                     */
+    DeclException0 (ExcInvalidConstructorCall);
+                                    /**
+                                     * Exception
+                                     */
+    DeclException2 (ExcIteratorRange,
+                   int, int,
+                   << "The iterators denote a range of " << arg1
+                   << " elements, but the given number of rows was " << arg2);
+    
+  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 @p{SmartPointer}
+                                     * class.
+                                     */
+    SmartPointer<const SparsityPattern> 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
+                                     * @p{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
+                                     * @p{reinit} function.
+                                     */
+    unsigned int max_len;
+
+                                    /**
+                                     * Version of @p{vmult} which only
+                                     * performs its actions on the
+                                     * region defined by
+                                     * @p{[begin_row,end_row)}. This
+                                     * function is called by @p{vmult}
+                                     * in the case of enabled
+                                     * multithreading.
+                                     */
+    template <typename somenumber>
+    void threaded_vmult (Vector<somenumber>       &dst,
+                        const Vector<somenumber> &src,
+                        const unsigned int        begin_row,
+                        const unsigned int        end_row) const;
+
+                                    /**
+                                     * Version of
+                                     * @p{matrix_norm_square} which
+                                     * only performs its actions on
+                                     * the region defined by
+                                     * @p{[begin_row,end_row)}. This
+                                     * function is called by
+                                     * @p{matrix_norm_square} in the
+                                     * case of enabled
+                                     * multithreading.
+                                     */
+    template <typename somenumber>
+    void threaded_matrix_norm_square (const Vector<somenumber> &v,
+                                     const unsigned int        begin_row,
+                                     const unsigned int        end_row,
+                                     somenumber               *partial_sum) const;
+
+                                    /**
+                                     * Version of
+                                     * @p{matrix_scalar_product} which
+                                     * only performs its actions on
+                                     * the region defined by
+                                     * @p{[begin_row,end_row)}. This
+                                     * function is called by
+                                     * @p{matrix_scalar_product} in the
+                                     * case of enabled
+                                     * multithreading.
+                                     */
+    template <typename somenumber>
+    void threaded_matrix_scalar_product (const Vector<somenumber> &u,
+                                        const Vector<somenumber> &v,
+                                        const unsigned int        begin_row,
+                                        const unsigned int        end_row,
+                                        somenumber               *partial_sum) const;
+
+                                    /**
+                                     * Version of @p{residual} which
+                                     * only performs its actions on
+                                     * the region defined by
+                                     * @p{[begin_row,end_row)} (these
+                                     * numbers are the components of
+                                     * @p{interval}). This function is
+                                     * called by @p{residual} in the
+                                     * case of enabled
+                                     * multithreading.
+                                     */
+    template <typename somenumber>
+    void threaded_residual (Vector<somenumber>       &dst,
+                           const Vector<somenumber> &u,
+                           const Vector<somenumber> &b,
+                           const std::pair<unsigned int,unsigned int> interval,
+                           somenumber               *partial_norm) const;
+
+                                    // make all other sparse matrices
+                                    // friends
+    template <typename somenumber> friend class SparseMatrix;
+};
+
+
+/*---------------------- Inline functions -----------------------------------*/
+
+
+
+template <typename number>
+inline
+unsigned int SparseMatrix<number>::m () const
+{
+  Assert (cols != 0, ExcMatrixNotInitialized());
+  return cols->rows;
+};
+
+
+template <typename number>
+inline
+unsigned int SparseMatrix<number>::n () const
+{
+  Assert (cols != 0, ExcMatrixNotInitialized());
+  return cols->cols;
+};
+
+
+template <typename number>
+inline
+void SparseMatrix<number>::set (const unsigned int i,
+                               const unsigned int j,
+                               const number value)
+{
+  Assert (cols != 0, ExcMatrixNotInitialized());
+                                  // 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 unsigned int index = cols->operator()(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 SparseMatrix<number>::add (const unsigned int i,
+                               const unsigned int j,
+                               const number value)
+{
+  Assert (cols != 0, ExcMatrixNotInitialized());
+
+  const unsigned int index = cols->operator()(i,j);
+  Assert ((index != SparsityPattern::invalid_entry) ||
+         (value == 0.),
+         ExcInvalidIndex(i,j));
+
+  if (value != 0.)
+    val[index] += value;
+};
+
+
+
+template <typename number>
+inline
+number SparseMatrix<number>::operator () (const unsigned int i,
+                                         const unsigned int j) const
+{
+  Assert (cols != 0, ExcMatrixNotInitialized());
+  Assert (cols->operator()(i,j) != SparsityPattern::invalid_entry,
+         ExcInvalidIndex(i,j));
+  return val[cols->operator()(i,j)];
+};
+
+
+
+template <typename number>
+inline
+number SparseMatrix<number>::el (const unsigned int i,
+                                const unsigned int j) const
+{
+  Assert (cols != 0, ExcMatrixNotInitialized());
+  const unsigned int index = cols->operator()(i,j);
+
+  if (index != SparsityPattern::invalid_entry)
+    return val[index];
+  else
+    return 0;
+};
+
+
+
+template <typename number>
+inline
+number SparseMatrix<number>::diag_element (const unsigned int i) const
+{
+  Assert (cols != 0, ExcMatrixNotInitialized());
+  Assert (m() == n(), ExcMatrixNotSquare());
+  Assert (i<m(), ExcInvalidIndex1(i));
+  
+                                  // Use that the first element in each
+                                  // row of a square matrix is the main
+                                  // diagonal
+  return val[cols->rowstart[i]];
+};
+
+
+
+template <typename number>
+inline
+number & SparseMatrix<number>::diag_element (const unsigned int i)
+{
+  Assert (cols != 0, ExcMatrixNotInitialized());
+  Assert (m() == n(), ExcMatrixNotSquare());
+  Assert (i<m(), ExcInvalidIndex1(i));
+  
+                                  // Use that the first element in each
+                                  // row of a square matrix is the main
+                                  // diagonal
+  return val[cols->rowstart[i]];
+};
+
+
+
+template <typename number>
+inline
+number
+SparseMatrix<number>::raw_entry (const unsigned int row,
+                                const unsigned int index) const
+{
+  Assert(row<cols->rows, ExcIndexRange(row,0,cols->rows));
+  Assert(index<cols->row_length(row),
+        ExcIndexRange(index,0,cols->row_length(row)));
+
+  return val[cols->rowstart[row]+index];
+};
+
+
+
+template <typename number>
+inline
+number SparseMatrix<number>::global_entry (const unsigned int j) const
+{
+  Assert (cols != 0, ExcMatrixNotInitialized());
+  Assert (j < cols->n_nonzero_elements(),
+         ExcIndexRange (j, 0, cols->n_nonzero_elements()));
+  
+  return val[j];
+};
+
+
+
+template <typename number>
+inline
+number & SparseMatrix<number>::global_entry (const unsigned int j)
+{
+  Assert (cols != 0, ExcMatrixNotInitialized());
+  Assert (j < cols->n_nonzero_elements(),
+         ExcIndexRange (j, 0, cols->n_nonzero_elements()));
+
+  return val[j];
+};
+
+
+
+template <typename number>
+template <typename ForwardIterator>
+void
+SparseMatrix<number>::copy_from (const ForwardIterator begin,
+                                const ForwardIterator end)
+{
+  Assert (static_cast<unsigned int>(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;
+  unsigned int 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);
+    };
+};
+
+
+//----------------------------------------------------------------------//
+
+template <typename number>
+inline
+SparseMatrix<number>::Accessor::Accessor (
+  const SparseMatrix<number>* matrix,
+  unsigned int r,
+  unsigned short i)
+               :
+               matrix(matrix),
+               a_row(r),
+               a_index(i)
+{}
+
+
+template <typename number>
+inline
+unsigned int
+SparseMatrix<number>::Accessor::row() const
+{
+  return a_row;
+}
+
+
+template <typename number>
+inline
+unsigned int
+SparseMatrix<number>::Accessor::column() const
+{
+  const SparsityPattern& pat = matrix->get_sparsity_pattern();
+  return pat.get_column_numbers()[pat.get_rowstart_indices()[a_row]+a_index];
+}
+
+
+template <typename number>
+inline
+unsigned short
+SparseMatrix<number>::Accessor::index() const
+{
+  return a_index;
+}
+
+
+
+template <typename number>
+inline
+number
+SparseMatrix<number>::Accessor::value() const
+{
+  return matrix->raw_entry(a_row, a_index);
+}
+
+
+template <typename number>
+inline
+SparseMatrix<number>::const_iterator::const_iterator(
+  const SparseMatrix<number>* matrix,
+  unsigned int r,
+  unsigned short i)
+               :
+               Accessor(matrix, r, i)
+{}
+
+
+template <typename number>
+inline
+typename SparseMatrix<number>::const_iterator&
+SparseMatrix<number>::const_iterator::operator++ ()
+{
+  Assert (a_row < matrix->m(), ExcIteratorPastEnd());
+  
+  ++a_index;
+  if (a_index >= matrix->get_sparsity_pattern().row_length(a_row))
+    {
+      a_index = 0;
+      a_row++;
+    }
+  return *this;
+}
+
+
+template <typename number>
+inline
+const typename SparseMatrix<number>::Accessor&
+SparseMatrix<number>::const_iterator::operator* () const
+{
+  return *this;
+}
+
+
+template <typename number>
+inline
+const typename SparseMatrix<number>::Accessor*
+SparseMatrix<number>::const_iterator::operator-> () const
+{
+  return this;
+}
+
+
+template <typename number>
+inline
+bool
+SparseMatrix<number>::const_iterator::operator == (
+  const const_iterator& other) const
+{
+  return (row() == other->row() && index() == other->index());
+}
+
+
+template <typename number>
+inline
+bool
+SparseMatrix<number>::const_iterator::operator != (
+  const const_iterator& other) const
+{
+  return ! (*this == other);
+}
+
+
+template <typename number>
+inline
+bool
+SparseMatrix<number>::const_iterator::operator < (
+  const const_iterator& other) const
+{
+  return (row() < other->row() ||
+         (row() == other->row() && index() < other->index()));
+}
+
+
+template <typename number>
+inline
+typename SparseMatrix<number>::const_iterator
+SparseMatrix<number>::begin () const
+{
+  return const_iterator(this, 0, 0);
+}
+
+template <typename number>
+inline
+typename SparseMatrix<number>::const_iterator
+SparseMatrix<number>::end () const
+{
+  return const_iterator(this, m(), 0);
+}
+
+template <typename number>
+inline
+typename SparseMatrix<number>::const_iterator
+SparseMatrix<number>::begin (unsigned int r) const
+{
+  Assert (r<m(), ExcIndexRange(r,0,m()));
+  return const_iterator(this, r, 0);
+}
+
+template <typename number>
+inline
+typename SparseMatrix<number>::const_iterator
+SparseMatrix<number>::end (unsigned int r) const
+{
+  Assert (r<m(), ExcIndexRange(r,0,m()));
+  return const_iterator(this, r+1, 0);
+}
+
+
+
+
+/*----------------------------   sparse_matrix.h     ---------------------------*/
+
+#endif
+/*----------------------------   sparse_matrix.h     ---------------------------*/

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