DOFMatrix.h

// ============================================================================
// ==                                                                        ==
// == AMDiS - Adaptive multidimensional simulations                          ==
// ==                                                                        ==
// ============================================================================
// ==                                                                        ==
// ==  crystal growth group                                                  ==
// ==                                                                        ==
// ==  Stiftung caesar                                                       ==
// ==  Ludwig-Erhard-Allee 2                                                 ==
// ==  53175 Bonn                                                            ==
// ==  germany                                                               ==
// ==                                                                        ==
// ============================================================================
// ==                                                                        ==
// ==  http://www.caesar.de/cg/AMDiS                                         ==
// ==                                                                        ==
// ============================================================================

/** \file DOFMatrix.h */

#ifndef AMDIS_DOFMATRIX_H
#define AMDIS_DOFMATRIX_H

// ============================================================================
// ===== includes =============================================================
// ============================================================================

#include <vector>
#include <set>
#include <memory>
#include <list>
#include "Global.h"
#include "Flag.h"
#include "RCNeighbourList.h"
#include "DOFAdmin.h"
#include "DOFIterator.h"
#include "DOFIndexed.h"
#include "MemoryManager.h"
#include "Boundary.h"
#include "Serializable.h"

namespace AMDiS {

  // ============================================================================
  // ===== forward declarations =================================================
  // ============================================================================

  class Mesh;
  class FiniteElemSpace;
  class ElInfo;
  class BasisFunction;
  class FillInfo;
  class Operator;
  class ElementMatrix;
  class BoundaryManager;

  template<typename T> class DOFVector;

  // ===========================================================================
  // ===== struct MatEntry =====================================================
  // ===========================================================================

  /** \brief
   * Represents one entry of a DOFMatrix
   */
  struct MatEntry
  {
    /** \brief
     * column index of entry (if >= 0; else unused)
     */
    DegreeOfFreedom col;

    /** \brief
     * matrix entry
     */
    double entry;
  };


  /** \brief
   * Is used to search for all entries of a matrix which column index is 
   * smaller than a given value.
   */
  class MatEntryValueLess : public std::unary_function<MatEntry, bool> {
  private:
    const double value_;
  public:
    MatEntryValueLess(const double& value) 
      : value_(value) 
    {}

    bool operator()(const MatEntry& m) {
      return (fabs(m.entry) < value_);
    }      
  };


  /** \brief
   * Is used to search for all entries of a matrix which value is smaller 
   * than a given value.
   */
  class MatEntryColLess : public std::unary_function<MatEntry, bool> {
  private:
    const int col_;
  public:
    MatEntryColLess(const int& col) 
      : col_(col) 
    {}

    bool operator()(const MatEntry& m) {
      return (fabs(m.col) < col_);
    }      
  };


  /** \brief
   * This function is required if two MatEntries are compared by their col
   * entry (for example when sorting a vector of MatEntries).
   */
  struct CmpMatEntryCol : public std::binary_function<MatEntry, MatEntry, bool> {
    bool operator()(const MatEntry& m1, const MatEntry m2) const {
      return m1.col < m2.col;
    }
  };
  

  /** \brief
   * This function compares two matrix entries by their values. It returns true,
   * if the value of m2 is greater than the value of m1.
   */
  struct CmpMatEntryValue : public std::binary_function<MatEntry, MatEntry, bool> {
    bool operator()(const MatEntry& m1, const MatEntry m2) const {
      return m1.entry < m2.entry;
    }
  };


  /** \brief
   * This function compares two matrix entries by their values. It returns true,
   * if the value of m2 is greater than the value of m1.
   */
  struct CmpMatEntryAbsValueLess : public std::binary_function<MatEntry, MatEntry, bool> {
    bool operator()(const MatEntry& m1, const MatEntry m2) const {
      return fabs(m1.entry) < fabs(m2.entry);
    }
  };
  
  /** \brief
   * This function compares two matrix entries by their values. It returns true,
   * if the value of m1 is greater than the value of m2.
   */
  struct CmpMatEntryAbsValueGreater : public std::binary_function<MatEntry, MatEntry, bool> {
    bool operator()(const MatEntry& m1, const MatEntry m2) const {
      return fabs(m1.entry) > fabs(m2.entry);
    }
  };

  // ============================================================================
  // ===== class DOFMatrix ======================================================
  // ============================================================================

  /** \ingroup DOFAdministration
   * \brief
   * A DOFMatrix is a sparse matrix representation for matrices that work
   * on DOFVectors. Every row of a matrix is realized as a vector of MatEntry 
   * objects. Each entry consists of a column DOF index and the corresponding 
   * double matrix entry. Unused entries are marked with a negative column index.
   */
  class DOFMatrix : public DOFIndexed< std::vector<MatEntry> >,
                    public Serializable
  {
  public:
    MEMORY_MANAGED(DOFMatrix);

    /** \ingroup DOFAdministration
     * \brief
     * Alias for DOFIterator< std::vector<MatEntry<T> > >. So one can access an
     * iterator working on a DOFMatrix via DOFMatrix::Iterator
     */
    class Iterator : public DOFIterator< std::vector<MatEntry> > {
    public:
      Iterator(DOFIndexed< std::vector<MatEntry> > *c, 
	       DOFIteratorType type)
	: DOFIterator< std::vector<MatEntry> >(c, type)
      {}
    };
    
    /** \brief
     * A MatrixRow represents one row of the sparse matrix. It is realized by
     * a STL vector of MatEntry<T> objects
     */
    typedef std::vector<MatEntry> MatrixRow;
    
    /** \brief
     * Symbolic constant for an unused matrix entry
     */
    static const int UNUSED_ENTRY = -1;
    
    /** \brief
     * Symbolic constant for an unused entry which is not followed by any
     * used entry in this row
     */
    static const int NO_MORE_ENTRIES = -2;

  public:    
    DOFMatrix();

    /** \brief
     * Constructs a DOFMatrix with name n and the given row and 
     * column FESpaces.
     */
    DOFMatrix(const FiniteElemSpace* rowFESpace,
	      const FiniteElemSpace* colFESpace,
	      std::string n = "");

    /** \brief
     * Copy-Constructor
     */
    DOFMatrix(const DOFMatrix& rhs);


    /** \brief
     * Destructor
     */
    virtual ~DOFMatrix();
  
    /** \brief
     * operator=
     */
    DOFMatrix& operator=(const DOFMatrix& rhs);

    void copy(const DOFMatrix& rhs);

    /** \brief
     * Returns an iterator to the begin of matrix rows (\ref matrix.begin())
     */
    std::vector< std::vector<MatEntry> >::iterator begin() { 
      return matrix.begin();
    }

    /** \brief
     * Returns an iterator to the end of matrix rows (\ref matrix.end())
     */
    std::vector< std::vector<MatEntry> >::iterator end() { 
      return matrix.end(); 
    }
 
    /** \brief
     * Used by DOFAdmin to compress the DOFMatrix
     */
    virtual void compressDOFIndexed(int first, int last, 
				    std::vector<DegreeOfFreedom> &newDOF);

    /** \brief
     * Implements DOFIndexedBase::freeDOFContent()
     */ 
    virtual void freeDOFContent(int index);

    /** \brief
     * Returns whether entry matrix[a][b] is used
     */    
    inline bool entryUsed(DegreeOfFreedom a, int b) const {
      return (((matrix[a])[b]).col >= 0);
    }

    /** \brief
     * Returns true if matrix[a][b] has entry \ref NO_MORE_ENTRIES
     */
    inline bool noMoreEntries(DegreeOfFreedom a, int b) const {
      return (NO_MORE_ENTRIES == ((matrix[a])[b]).col);
    }

    /** \brief
     * Returns \ref coupleMatrix.
     */
    inline bool isCoupleMatrix() { 
      return coupleMatrix; 
    }

    /** \brief
     * Returns \ref coupleMatrix.
     */
    inline void setCoupleMatrix(bool c) { 
      coupleMatrix = c; 
    }

    /** \brief
     * Matrix-matrix multiplication.
     */
    void mm(MatrixTranspose aTranspose, DOFMatrix& a, 
	    MatrixTranspose bTranspose, DOFMatrix& b);
  
    /** \brief
     * a*x + y
     */
    void axpy(double a, const DOFMatrix& x, const DOFMatrix& y);

    /** \brief
     * Multiplication with a scalar.
     */
    void scal(double s);

    /** \brief
     * Adds an operator to the DOFMatrix. A factor, that is multipled
     * to the operator, and a multilier factor for the estimator may be
     * also given.
     */
    void addOperator(Operator *op, double* factor = NULL, double* estFactor = NULL);

    inline std::vector<double*>::iterator getOperatorFactorBegin() {
      return operatorFactor.begin();
    }

    inline std::vector<double*>::iterator getOperatorFactorEnd() {
      return operatorFactor.end();
    }

    inline std::vector<double*>::iterator getOperatorEstFactorBegin() {
      return operatorEstFactor.begin();
    }

    inline std::vector<double*>::iterator getOperatorEstFactorEnd() {
      return operatorEstFactor.end();
    }

    inline std::vector<Operator*>::iterator getOperatorsBegin() {
      return operators.begin();
    }

    inline std::vector<Operator*>::iterator getOperatorsEnd() {
      return operators.end();
    }

    Flag getAssembleFlag();

    /** \brief
     * Updates the matrix matrix by traversing the underlying mesh and assembling
     * the element contributions into the matrix. Information about the 
     * computation of element matrices and connection of local and global DOFs is
     * stored in minfo; the flags for the mesh traversal are stored at 
     * minfo->fill_flags which specifies the elements to be visited and 
     * information that should be present on the elements for the calculation of 
     * the element matrices and boundary information (if minfo->boundBas is not
     * NULL). On the elements, information about the row DOFs is accessed by 
     * minfo->rowBas using info->row_admin; this vector is also used for the 
     * column DOFs if minfo->nCol is less or equal zero, or minfo->col_admin or 
     * minfo->colBas is a NULL pointer; if row and column DOFs are the same, the 
     * boundary type of the DOFs is accessed by minfo->boundBas if 
     * minfo->boundBas is not a NULL pointer; then the element matrix is 
     * computed by minfo->fillElementMatrix(el info, minfo->myFill); these 
     * contributions, multiplied by minfo->factor, are eventually added to matrix
     * by a call of addElementMatrix() with all information about row and column 
     * DOFs, the element matrix, and boundary types, if available;
     * updateMatrix() only adds element contributions; this makes several calls 
     * for the assemblage of one matrix possible; before the first call, the 
     * matrix should be cleared by calling clear dof matrix().
     */
  
    void assemble(double factor, ElInfo *elInfo, const BoundaryType *bound);

    void assemble(double factor, ElInfo *elInfo, const BoundaryType *bound,
		  Operator *op);

    void assemble(double factor, 
		  ElInfo *rowElInfo, ElInfo *colElInfo,
		  ElInfo *smallElInfo, ElInfo *largeElInfo,
		  const BoundaryType *bound,
		  Operator *op = NULL);

    void assemble2(double factor, 
		   ElInfo *mainElInfo, ElInfo *auxElInfo,
		   ElInfo *smallElInfo, ElInfo *largeElInfo,
		   const BoundaryType *bound, 
		   Operator *op = NULL);

    /// Adds an element matrix to \ref matrix
    void addElementMatrix(double sign, 
			  const ElementMatrix& elMat, 
			  const BoundaryType *bound,
			  bool add = true);

    /* \brief
     * That function must be called after the matrix assembling has been finished. 
     * This makes it possible to start some cleanup or matrix data compressing 
     * procedures.
     */
    void finishAssembling();

    /// Returns \ref matrix
    std::vector< std::vector<MatEntry> >& getMatrix() { 
      return matrix; 
    }

    ///
    void setMatrix(std::vector< std::vector<MatEntry> > m) {
      matrix = m;
    }

    /// Returns \ref matrix[n]
    const std::vector<MatEntry>& getRow(int n) const { 
      return matrix[n];
    }

    /// Returns \ref matrix[n]
    std::vector<MatEntry>& getRow(int n) { 
      return matrix[n];
    }

    /** \brief
     * Returns whether restriction should be performed after coarsening
     * (false by default)
     */
    virtual bool coarseRestrict() {
      return false;
    }

    /// Returns const \ref rowFESpace
    const FiniteElemSpace* getRowFESpace() const { 
      return rowFESpace; 
    }

    /** \brief
     * Returns const \ref colFESpace
     */
    const FiniteElemSpace* getColFESpace() const { 
      return colFESpace; 
    }

    /** \brief
     * Returns const \ref rowFESpace
     */
    const FiniteElemSpace* getFESpace() const { 
      return rowFESpace; 
    }

    /** \brief
     * Returns number of rows (\ref matrix.size())
     */
    inline int getSize() const { 
      return matrix.size();
    }

    /** \brief
     * Returns the number of used rows (equal to number of used DOFs in
     * the row FE space).
     */
    inline int getUsedSize() const {
      return rowFESpace->getAdmin()->getUsedSize();
    }

    /** \brief
     * Returns number of cols. For that, the function iteratos over all
     * rows and searchs for the entry with the highest col number.
     */
    int getNumCols() const;

    /** \brief
     * Returns \ref name
     */
    inline const std::string& getName() const { 
      return name; 
    }

    /** \brief
     * Resizes \ref matrix to n rows
     */
    inline void resize(int n) { 
      TEST_EXIT_DBG(n >= 0)("Can't resize DOFMatrix to negative size\n"); 
      matrix.resize(n);
    }

    /** \brief
     * Returns \ref matrix[i] which is the i-th row
     */
    inline const std::vector<MatEntry>& operator[](int i) const {
      TEST_EXIT_DBG((i >= 0) && (i < (static_cast<int>(matrix.size()))))
      	("Illegal matrix index %d.\n",i); 
      return matrix[i];
    }

    /** \brief
     * Returns \ref matrix[i] which is the i-th row
     */
    inline std::vector<MatEntry>& operator[](int i) {
      TEST_EXIT_DBG((i >= 0) && (i < (static_cast<int>(matrix.size()))))
      	("Illegal vector index %d.\n", i);
      return matrix[i];
    }

    /** \brief
     * Access to \ref matrix[a][b].entry
     */
    inline double physAcc(DegreeOfFreedom a, DegreeOfFreedom b) const { 
      return matrix[a][b].entry; 
    }

    /** \brief
     * Access to \ref matrix[a][b].col
     */
    inline DegreeOfFreedom physToLogIndex(DegreeOfFreedom a,
					  DegreeOfFreedom b) const 
    {
      return matrix[a][b].col;
    }

    /** \brief
     * Returns physical column index of logical index b in row a
     */
    inline DegreeOfFreedom logToPhysIndex(DegreeOfFreedom a, DegreeOfFreedom b) const
    {      
      int size = static_cast<int>(matrix[a].size());
      for (int j = 0; j < size; j++) 
	if (b == matrix[a][j].col) 
	  return j;

      return -1;
    }

    /** \brief
     * Returns value at logical indices a,b
     */
    double logAcc(DegreeOfFreedom a, DegreeOfFreedom b) const;

    /** \brief
     * Changes col at logical indices a,b to c 
     */
    void changeColOfEntry(DegreeOfFreedom a, DegreeOfFreedom b, DegreeOfFreedom c);

    /** \brief
     * Changes col of \ref matrix[a][b] to c
     */
    inline void changePhysColOfEntry(DegreeOfFreedom a,
				     DegreeOfFreedom b,
				     DegreeOfFreedom c) 
    { 
      matrix[a][b].col = c;
    }

    /** \brief
     * Creates an entry with logical indices irow, icol if there is no entry
     * yet. Than sign * entry is added to the value at this logical indices
     */
    void addSparseDOFEntry(double sign,
			   int irow, int jcol, double entry,
			   bool add = true);

    inline double *hasSparseDOFEntry(int irow, int jcol) {
      std::vector<MatEntry>::iterator it;
      std::vector<MatEntry>::iterator end = matrix[irow].end();
      for (it = matrix[irow].begin(); it != end; ++it) {
	if (it->col == NO_MORE_ENTRIES) 
	  return NULL;
	if (it->col == jcol) 
	  return &(it->entry);
      }
      return NULL;
    }

    void addMatEntry(int row, MatEntry entry);

    void addMatEntry(int row, int DegreeOfFreedom, double value);

    void addRow(std::vector<MatEntry> row);

    void removeRowsWithDBC(std::set<int> *rows);

    /** \brief
     * Prints \ref matrix to stdout
     */
    void print() const;

    /** \brief
     * Prints a row of \ref matrix to stdout
     */
    void printRow(int i) const;

    /** \brief
     * Removes all matrix entries
     */
    void clear();

    /** \brief
     * Test whether \ref matrix is symmetric. Exits if not.
     */
    void test();

    bool symmetric();

    inline std::vector<Operator*> getOperators() { 
      return operators; 
    }
    
    inline std::vector<double*> getOperatorFactor() { 
      return operatorFactor; 
    }

    inline std::vector<double*> getOperatorEstFactor() { 
      return operatorEstFactor; 
    }

    inline BoundaryManager* getBoundaryManager() const { 
      return boundaryManager; 
    }

    std::set<int>* getApplyDBCs() {
      return &applyDBCs;
    }

    inline void setBoundaryManager(BoundaryManager *bm) {
      boundaryManager = bm;
    }

    void createPictureFile(const char* filename, int dim);

    // ===== Serializable implementation =====
    
    void serialize(std::ostream &out) 
    {
      unsigned int matrixSize = matrix.size();
      unsigned int vecSize = 0;

      out.write(reinterpret_cast<const char*>(&matrixSize), sizeof(unsigned int));
      for(unsigned int i = 0; i < matrixSize; i++) {
	vecSize = matrix[i].size();
	out.write(reinterpret_cast<const char*>(&vecSize), sizeof(unsigned int));
	out.write(reinterpret_cast<const char*>(&(matrix[i][0])), vecSize * sizeof(MatEntry));
      }
    }

    void deserialize(std::istream &in) {
      unsigned int matrixSize, vecSize;

      in.read(reinterpret_cast<char*>(&matrixSize), sizeof(unsigned int));
      matrix.resize(matrixSize);
      for(unsigned int i = 0; i < matrixSize; i++) {
	in.read(reinterpret_cast<char*>(&vecSize), sizeof(unsigned int));
	matrix[i].resize(vecSize);
	in.read(reinterpret_cast<char*>(&(matrix[i][0])), vecSize * sizeof(MatEntry));
      }
    }

    int memsize();

  protected:
    /** \brief
     * Used by updateMatrix
     */
    //static int assembleFct(ElInfo *el_info);

  protected:
    /** \brief
     * Pointer to a FiniteElemSpace with information about corresponding row DOFs
     * and basis functions
     */
    const FiniteElemSpace *rowFESpace;

    /** \brief
     * Pointer to a FiniteElemSpace with information about corresponding 
     * column DOFs and basis functions
     */
    const FiniteElemSpace *colFESpace;

    /** \brief
     * Name of the DOFMatrix
     */
    std::string name;

    /** \brief
     * Sparse matrix stored in an STL vector of MatrixRow objects
     */
    std::vector<MatrixRow> matrix;

    /** \brief
     * Used while mesh traversal
     */
    static DOFMatrix *traversePtr;
  
    /** \brief
     * Pointers to all operators of the equation systems. Are used in the
     * assembling process.
     */
    std::vector<Operator*> operators;
    
    /** \brief
     * Defines for each operator a factor which is used to scal the element
     * matrix after the assembling process of the operator.
     */
    std::vector<double*> operatorFactor;

    /** \brief
     *
     */
    std::vector<double*> operatorEstFactor;

    /** \brief
     *
     */
    BoundaryManager *boundaryManager;

    /** \brief
     *
     */
    bool coupleMatrix;

    /** \brief
     * Temporary variable used in assemble()
     */
    ElementMatrix *elementMatrix;

    std::set<int> applyDBCs;

    friend class DOFAdmin;
    friend class DOFVector<double>;
    friend class DOFVector<unsigned char>;
    friend class DOFVector<int>;
    friend class DOFVector<WorldVector<double> >;
  };


  inline DegreeOfFreedom logToPhysIndex(DOFMatrix *m, DegreeOfFreedom a, DegreeOfFreedom b)
  {
    return m->logToPhysIndex(a, b);
  }

  double norm(std::vector<MatEntry> *row);

  double min(std::vector<MatEntry> *row);

  double max(std::vector<MatEntry> *row);

  /** \brief
   * Addes two matrices. The result matrix is overwritten.
   */
  void addDOFMatrix(DOFMatrix *result, const DOFMatrix *a, const DOFMatrix *b);

  /** \brief
   * Addes matrix a to matrix result.
   */
  void addDOFMatrix(DOFMatrix *result, const DOFMatrix *a);

}

#endif  // AMDIS_DOFMATRIX_H