coinor-libcoinutils-dev 2.9.10-1ubuntu2 / usr / include / coin / CoinPackedMatrix.hpp

/* $Id: CoinPackedMatrix.hpp 1560 2012-11-24 00:29:01Z lou $ */
// Copyright (C) 2000, International Business Machines
// Corporation and others.  All Rights Reserved.
// This code is licensed under the terms of the Eclipse Public License (EPL).

#ifndef CoinPackedMatrix_H
#define CoinPackedMatrix_H

#include "CoinError.hpp"
#include "CoinTypes.hpp"
#ifndef CLP_NO_VECTOR
#include "CoinPackedVectorBase.hpp"
#include "CoinShallowPackedVector.hpp"
#else
class CoinRelFltEq;
#endif

/** Sparse Matrix Base Class

  This class is intended to represent sparse matrices using row-major
  or column-major ordering. The representation is very efficient for
  adding, deleting, or retrieving major-dimension vectors. Adding
  a minor-dimension vector is less efficient, but can be helped by
  providing "extra" space as described in the next paragraph. Deleting
  a minor-dimension vector requires inspecting all coefficients in the
  matrix. Retrieving a minor-dimension vector would incur the same cost
  and is not supported (except in the sense that you can write a loop to
  retrieve all coefficients one at a time). Consider physically transposing
  the matrix, or keeping a second copy with the other major-vector ordering.

  The sparse represention can be completely compact or it can have "extra"
  space available at the end of each major vector.  Incorporating extra
  space into the sparse matrix representation can improve performance in
  cases where new data needs to be inserted into the packed matrix against
  the major-vector orientation (e.g, inserting a row into a matrix stored
  in column-major order).

  For example if the matrix:
  @verbatim
     3  1  0   -2   -1  0  0   -1                 
     0  2  1.1  0    0  0  0    0                       
     0  0  1    0    0  1  0    0         
     0  0  0    2.8  0  0 -1.2  0   
   5.6  0  0    0    1  0  0    1.9

  was stored by rows (with no extra space) in 
  CoinPackedMatrix r then: 
    r.getElements() returns a vector containing: 
      3 1 -2 -1 -1 2 1.1 1 1 2.8 -1.2 5.6 1 1.9 
    r.getIndices() returns a vector containing: 
      0 1  3  4  7 1 2   2 5 3    6   0   4 7 
    r.getVectorStarts() returns a vector containing: 
      0 5 7 9 11 14 
    r.getNumElements() returns 14. 
    r.getMajorDim() returns 5. 
    r.getVectorSize(0) returns 5. 
    r.getVectorSize(1) returns 2. 
    r.getVectorSize(2) returns 2. 
    r.getVectorSize(3) returns 2. 
    r.getVectorSize(4) returns 3. 
 
  If stored by columns (with no extra space) then: 
    c.getElements() returns a vector containing: 
      3 5.6 1 2 1.1 1 -2 2.8 -1 1 1 -1.2 -1 1.9 
    c.getIndices() returns a vector containing: 
      0  4  0 1 1   2  0 3    0 4 2  3    0 4 
    c.getVectorStarts() returns a vector containing: 
      0 2 4 6 8 10 11 12 14 
    c.getNumElements() returns 14. 
    c.getMajorDim() returns 8. 
  @endverbatim

  Compiling this class with CLP_NO_VECTOR defined will excise all methods
  which use CoinPackedVectorBase, CoinPackedVector, or CoinShallowPackedVector
  as parameters or return types.

  Compiling this class with COIN_FAST_CODE defined removes index range checks.
*/
class CoinPackedMatrix  {
   friend void CoinPackedMatrixUnitTest();

public:


  //---------------------------------------------------------------------------
  /**@name Query members */
  //@{
    /** Return the current setting of the extra gap. */
    inline double getExtraGap() const { return extraGap_; }
    /** Return the current setting of the extra major. */
    inline double getExtraMajor() const { return extraMajor_; }

    /** Reserve sufficient space for appending major-ordered vectors. 
	If create is true, empty columns are created (for column generation) */
    void reserve(const int newMaxMajorDim, const CoinBigIndex newMaxSize,
		 bool create=false);
    /** Clear the data, but do not free any arrays */
    void clear();

    /** Whether the packed matrix is column major ordered or not. */
    inline bool isColOrdered() const { return colOrdered_; }

    /** Whether the packed matrix has gaps or not. */
    inline bool hasGaps() const { return (size_<start_[majorDim_]) ; } 

    /** Number of entries in the packed matrix. */
    inline CoinBigIndex getNumElements() const { return size_; }

    /** Number of columns. */
    inline int getNumCols() const
    { return colOrdered_ ? majorDim_ : minorDim_; }

    /** Number of rows. */
    inline int getNumRows() const
    { return colOrdered_ ? minorDim_ : majorDim_; }

    /*! \brief A vector containing the elements in the packed matrix.
    
	Returns #elements_. Note that there might be gaps in this vector,
	entries that do not belong to any major-dimension vector. To get
	the actual elements one should look at this vector together with
	vectorStarts (#start_) and vectorLengths (#length_).
    */
    inline const double * getElements() const { return element_; }

    /*! \brief A vector containing the minor indices of the elements in
    	       the packed matrix.

	Returns #index_. Note that there might be gaps in this list,
	entries that do not belong to any major-dimension vector. To get
	the actual elements one should look at this vector together with
	vectorStarts (#start_) and vectorLengths (#length_).
    */
    inline const int * getIndices() const { return index_; }

    /*! \brief The size of the <code>vectorStarts</code> array

	See #start_.
    */
    inline int getSizeVectorStarts() const
    { return ((majorDim_ > 0)?(majorDim_+1):(0)) ; }

    /*! \brief The size of the <code>vectorLengths</code> array
    
        See #length_.
    */
    inline int getSizeVectorLengths() const { return majorDim_; }

    /*! \brief The positions where the major-dimension vectors start in
    	       elements and indices.

	See #start_.
    */
    inline const CoinBigIndex * getVectorStarts() const { return start_; }

    /*! \brief The lengths of the major-dimension vectors.
    
        See #length_.
    */
    inline const int * getVectorLengths() const { return length_; }

    /** The position of the first element in the i'th major-dimension vector.
     */
    CoinBigIndex getVectorFirst(const int i) const {
#ifndef COIN_FAST_CODE
      if (i < 0 || i >= majorDim_)
	throw CoinError("bad index", "vectorFirst", "CoinPackedMatrix");
#endif
      return start_[i];
    }
    /** The position of the last element (well, one entry <em>past</em> the
        last) in the i'th major-dimension vector. */
    CoinBigIndex getVectorLast(const int i) const {
#ifndef COIN_FAST_CODE
      if (i < 0 || i >= majorDim_)
	throw CoinError("bad index", "vectorLast", "CoinPackedMatrix");
#endif
      return start_[i] + length_[i];
    }
    /** The length of i'th vector. */
    inline int getVectorSize(const int i) const {
#ifndef COIN_FAST_CODE
      if (i < 0 || i >= majorDim_)
	throw CoinError("bad index", "vectorSize", "CoinPackedMatrix");
#endif
      return length_[i];
    }
#ifndef CLP_NO_VECTOR  
    /** Return the i'th vector in matrix. */
    const CoinShallowPackedVector getVector(int i) const {
#ifndef COIN_FAST_CODE
      if (i < 0 || i >= majorDim_)
	throw CoinError("bad index", "vector", "CoinPackedMatrix");
#endif
      return CoinShallowPackedVector(length_[i],
  				    index_ + start_[i],
  				    element_ + start_[i],
  				    false);
    }
#endif
    /** Returns an array containing major indices.  The array is
	  getNumElements long and if getVectorStarts() is 0,2,5 then
	  the array would start 0,0,1,1,1,2...
	  This method is provided to go back from a packed format
	  to a triple format.  It returns NULL if there are gaps in
	  matrix so user should use removeGaps() if there are any gaps.
	  It does this as this array has to match getElements() and 
	  getIndices() and because it makes no sense otherwise.
	  The returned array is allocated with <code>new int[]</code>,
	  free it with  <code>delete[]</code>. */
    int * getMajorIndices() const;
  //@}

  //---------------------------------------------------------------------------
  /**@name Modifying members */
  //@{
    /*! \brief Set the dimensions of the matrix.
    
      The method name is deceptive; the effect is to append empty columns
      and/or rows to the matrix to reach the specified dimensions.
      A negative number for either dimension means that that dimension
      doesn't change. An exception will be thrown if the specified dimensions
      are smaller than the current dimensions.
    */
    void setDimensions(int numrows, int numcols);
   
    /** Set the extra gap to be allocated to the specified value. */
    void setExtraGap(const double newGap);
    /** Set the extra major to be allocated to the specified value. */
    void setExtraMajor(const double newMajor);
#ifndef CLP_NO_VECTOR
    /*! Append a column to the end of the matrix.
    
       When compiled with COIN_DEBUG defined this method throws an exception
       if the column vector specifies a nonexistent row index.  Otherwise the
       method assumes that every index fits into the matrix.
    */
    void appendCol(const CoinPackedVectorBase& vec);
#endif
    /*! Append a column to the end of the matrix.
    
       When compiled with COIN_DEBUG defined this method throws an exception
       if the column vector specifies a nonexistent row index.  Otherwise the
       method assumes that every index fits into the matrix.
    */
    void appendCol(const int vecsize,
  		   const int *vecind, const double *vecelem);
#ifndef CLP_NO_VECTOR
    /*! Append a set of columns to the end of the matrix.

       When compiled with COIN_DEBUG defined this method throws an exception
       if any of the column vectors specify a nonexistent row index. Otherwise
       the method assumes that every index fits into the matrix.
    */
    void appendCols(const int numcols,
		    const CoinPackedVectorBase * const * cols);
#endif
    /*! Append a set of columns to the end of the matrix.
    
      Returns the number of errors (nonexistent or duplicate row index).
      No error checking is performed if \p numberRows < 0.
    */
    int appendCols(const int numcols,
		    const CoinBigIndex * columnStarts, const int * row,
                   const double * element, int numberRows=-1);
#ifndef CLP_NO_VECTOR
    /*! Append a row to the end of the matrix.
  
       When compiled with COIN_DEBUG defined this method throws an exception
       if the row vector specifies a nonexistent column index.  Otherwise the
       method assumes that every index fits into the matrix.
    */
    void appendRow(const CoinPackedVectorBase& vec);
#endif
    /*! Append a row to the end of the matrix.

       When compiled with COIN_DEBUG defined this method throws an exception
       if the row vector specifies a nonexistent column index.  Otherwise the
       method assumes that every index fits into the matrix.
    */
    void appendRow(const int vecsize,
  		  const int *vecind, const double *vecelem);
#ifndef CLP_NO_VECTOR
    /*! Append a set of rows to the end of the matrix.
    
       When compiled with COIN_DEBUG defined this method throws an exception
       if any of the row vectors specify a nonexistent column index. Otherwise
       the method assumes that every index fits into the matrix.
    */
    void appendRows(const int numrows,
		    const CoinPackedVectorBase * const * rows);
#endif
    /*! Append a set of rows to the end of the matrix.
    
      Returns the number of errors (nonexistent or duplicate column index).
      No error checking is performed if \p numberColumns < 0.
    */
    int appendRows(const int numrows,
		    const CoinBigIndex * rowStarts, const int * column,
                   const double * element, int numberColumns=-1);
  
    /** Append the argument to the "right" of the current matrix. Imagine this
        as adding new columns (don't worry about how the matrices are ordered,
        that is taken care of). An exception is thrown if the number of rows
        is different in the matrices. */
    void rightAppendPackedMatrix(const CoinPackedMatrix& matrix);
    /** Append the argument to the "bottom" of the current matrix. Imagine this
        as adding new rows (don't worry about how the matrices are ordered,
        that is taken care of). An exception is thrown if the number of columns
        is different in the matrices. */
    void bottomAppendPackedMatrix(const CoinPackedMatrix& matrix);
  
    /** Delete the columns whose indices are listed in <code>indDel</code>. */
    void deleteCols(const int numDel, const int * indDel);
    /** Delete the rows whose indices are listed in <code>indDel</code>. */
    void deleteRows(const int numDel, const int * indDel);

    /** Replace the elements of a vector.  The indices remain the same.
	At most the number specified will be replaced.
        The index is between 0 and major dimension of matrix */
    void replaceVector(const int index,
		       const int numReplace, const double * newElements);
    /** Modify one element of packed matrix.  An element may be added.
        This works for either ordering
	If the new element is zero it will be deleted unless
	keepZero true */
    void modifyCoefficient(int row, int column, double newElement,
			   bool keepZero=false);
    /** Return one element of packed matrix.
        This works for either ordering
	If it is not present will return 0.0 */
    double getCoefficient(int row, int column) const;

    /** Eliminate all elements in matrix whose 
	absolute value is less than threshold.
	The column starts are not affected.  Returns number of elements
	eliminated.  Elements eliminated are at end of each vector
    */
    int compress(double threshold);
    /** Eliminate all duplicate AND small elements in matrix 
	The column starts are not affected.  Returns number of elements
	eliminated.  
    */
    int eliminateDuplicates(double threshold);
    /** Sort all columns so indices are increasing.in each column */
    void orderMatrix();
    /** Really clean up matrix.
	a) eliminate all duplicate AND small elements in matrix 
	b) remove all gaps and set extraGap_ and extraMajor_ to 0.0
	c) reallocate arrays and make max lengths equal to lengths
	d) orders elements
	returns number of elements eliminated
    */
    int cleanMatrix(double threshold=1.0e-20);
  //@}

  //---------------------------------------------------------------------------
  /**@name Methods that reorganize the whole matrix */
  //@{
    /** Remove the gaps from the matrix if there were any
	Can also remove small elements fabs() <= removeValue*/
    void removeGaps(double removeValue=-1.0);
 
    /** Extract a submatrix from matrix. Those major-dimension vectors of
	the matrix comprise the submatrix whose indices are given in the
	arguments. Does not allow duplicates. */
    void submatrixOf(const CoinPackedMatrix& matrix,
		     const int numMajor, const int * indMajor);
    /** Extract a submatrix from matrix. Those major-dimension vectors of
	the matrix comprise the submatrix whose indices are given in the
	arguments. Allows duplicates and keeps order. */
    void submatrixOfWithDuplicates(const CoinPackedMatrix& matrix,
		     const int numMajor, const int * indMajor);
#if 0
    /** Extract a submatrix from matrix. Those major/minor-dimension vectors of
	the matrix comprise the submatrix whose indices are given in the
	arguments. */
    void submatrixOf(const CoinPackedMatrix& matrix,
		     const int numMajor, const int * indMajor,
		     const int numMinor, const int * indMinor);
#endif

    /** Copy method. This method makes an exact replica of the argument,
        including the extra space parameters. */
    void copyOf(const CoinPackedMatrix& rhs);
    /** Copy the arguments to the matrix. If <code>len</code> is a NULL pointer
        then the matrix is assumed to have no gaps in it and <code>len</code>
        will be created accordingly. */
    void copyOf(const bool colordered,
 	       const int minor, const int major, const CoinBigIndex numels,
 	       const double * elem, const int * ind,
 	       const CoinBigIndex * start, const int * len,
 	       const double extraMajor=0.0, const double extraGap=0.0);
    /** Copy method. This method makes an exact replica of the argument,
        including the extra space parameters. 
	If there is room it will re-use arrays */
    void copyReuseArrays(const CoinPackedMatrix& rhs);

    /*! \brief Make a reverse-ordered copy.
    
      This method makes an exact replica of the argument with the major
      vector orientation changed from row (column) to column (row).
      The extra space parameters are also copied and reversed.
      (Cf. #reverseOrdering, which does the same thing in place.)
    */
    void reverseOrderedCopyOf(const CoinPackedMatrix& rhs);

    /** Assign the arguments to the matrix. If <code>len</code> is a NULL
	pointer then the matrix is assumed to have no gaps in it and
	<code>len</code> will be created accordingly. <br>
        <strong>NOTE 1</strong>: After this method returns the pointers
        passed to the method will be NULL pointers! <br>
        <strong>NOTE 2</strong>: When the matrix is eventually destructed the
        arrays will be deleted by <code>delete[]</code>. Hence one should use
        this method ONLY if all array swere allocated by <code>new[]</code>! */
    void assignMatrix(const bool colordered,
 		     const int minor, const int major, 
		      const CoinBigIndex numels,
 		     double *& elem, int *& ind,
 		     CoinBigIndex *& start, int *& len,
 		     const int maxmajor = -1, const CoinBigIndex maxsize = -1);
 
 
 
    /** Assignment operator. This copies out the data, but uses the current
        matrix's extra space parameters. */
    CoinPackedMatrix & operator=(const CoinPackedMatrix& rhs);
 
    /*! \brief Reverse the ordering of the packed matrix.

      Change the major vector orientation of the matrix data structures from
      row (column) to column (row). (Cf. #reverseOrderedCopyOf, which does
      the same thing but produces a new matrix.)
    */
    void reverseOrdering();

    /*! \brief Transpose the matrix.

        \note
	If you start with a column-ordered matrix and invoke transpose, you
	will have a row-ordered transposed matrix. To change the major vector
	orientation (e.g., to transform a column-ordered matrix to a
	column-ordered transposed matrix), invoke transpose() followed by
	#reverseOrdering().
    */
    void transpose();
 
    /*! \brief Swap the content of two packed matrices. */
    void swap(CoinPackedMatrix& matrix);
   
  //@}

  //---------------------------------------------------------------------------
  /**@name Matrix times vector methods */
  //@{
    /** Return <code>A * x</code> in <code>y</code>.
        @pre <code>x</code> must be of size <code>numColumns()</code>
        @pre <code>y</code> must be of size <code>numRows()</code> */
    void times(const double * x, double * y) const;
#ifndef CLP_NO_VECTOR
    /** Return <code>A * x</code> in <code>y</code>. Same as the previous
        method, just <code>x</code> is given in the form of a packed vector. */
    void times(const CoinPackedVectorBase& x, double * y) const;
#endif
    /** Return <code>x * A</code> in <code>y</code>.
        @pre <code>x</code> must be of size <code>numRows()</code>
        @pre <code>y</code> must be of size <code>numColumns()</code> */
    void transposeTimes(const double * x, double * y) const;
#ifndef CLP_NO_VECTOR
    /** Return <code>x * A</code> in <code>y</code>. Same as the previous
        method, just <code>x</code> is given in the form of a packed vector. */
    void transposeTimes(const CoinPackedVectorBase& x, double * y) const;
#endif
  //@}

  //---------------------------------------------------------------------------
  /**@name Helper functions used internally, but maybe useful externally.

     These methods do not worry about testing whether the packed matrix is
     row or column major ordered; they operate under the assumption that the
     correct version is invoked. In fact, a number of other methods simply
     just call one of these after testing the ordering of the matrix. */
  //@{

    //-------------------------------------------------------------------------
    /**@name Queries */
    //@{
      /** Count the number of entries in every minor-dimension vector and
	  return an array containing these lengths. The returned array is
	  allocated with <code>new int[]</code>, free it with
	  <code>delete[]</code>. */
      int * countOrthoLength() const;
      /** Count the number of entries in every minor-dimension vector and
	  fill in an array containing these lengths.  */
      void countOrthoLength(int * counts) const;
      /** Major dimension. For row ordered matrix this would be the number of
          rows. */
      inline int getMajorDim() const { return majorDim_; }
      /** Set major dimension. For row ordered matrix this would be the number of
          rows. Use with great care.*/
      inline void setMajorDim(int value) { majorDim_ = value; }
      /** Minor dimension. For row ordered matrix this would be the number of
	  columns. */
      inline int getMinorDim() const { return minorDim_; }
      /** Set minor dimension. For row ordered matrix this would be the number of
          columns. Use with great care.*/
      inline void setMinorDim(int value) { minorDim_ = value; }
      /** Current maximum for major dimension. For row ordered matrix this many
          rows can be added without reallocating the vector related to the
	  major dimension (<code>start_</code> and <code>length_</code>). */
      inline int getMaxMajorDim() const { return maxMajorDim_; }

      /** Dump the matrix on stdout. When in dire straits this method can
	  help. */
      void dumpMatrix(const char* fname = NULL) const;

      /// Print a single matrix element.
      void printMatrixElement(const int row_val, const int col_val) const;
    //@}

    //-------------------------------------------------------------------------
    /*! @name Append vectors

       \details
       When compiled with COIN_DEBUG defined these methods throw an exception
       if the major (minor) vector contains an index that's invalid for the
       minor (major) dimension. Otherwise the methods assume that every index
       fits into the matrix.
    */
    //@{
#ifndef CLP_NO_VECTOR
      /** Append a major-dimension vector to the end of the matrix. */
      void appendMajorVector(const CoinPackedVectorBase& vec);
#endif
      /** Append a major-dimension vector to the end of the matrix. */
      void appendMajorVector(const int vecsize, const int *vecind,
			     const double *vecelem);
#ifndef CLP_NO_VECTOR
      /** Append several major-dimensonvectors to the end of the matrix */
      void appendMajorVectors(const int numvecs,
			      const CoinPackedVectorBase * const * vecs);

      /** Append a minor-dimension vector to the end of the matrix. */
      void appendMinorVector(const CoinPackedVectorBase& vec);
#endif
      /** Append a minor-dimension vector to the end of the matrix. */
      void appendMinorVector(const int vecsize, const int *vecind,
			     const double *vecelem);
#ifndef CLP_NO_VECTOR
      /** Append several minor-dimension vectors to the end of the matrix */
      void appendMinorVectors(const int numvecs,
			      const CoinPackedVectorBase * const * vecs);
#endif
    /*! \brief Append a set of rows (columns) to the end of a column (row)
    	       ordered matrix.
    
      This case is when we know there are no gaps and majorDim_ will not
      change.

      \todo
      This method really belongs in the group of protected methods with
      #appendMinor; there are no safeties here even with COIN_DEBUG.
      Apparently this method was needed in ClpPackedMatrix and giving it
      proper visibility was too much trouble. Should be moved.
    */
    void appendMinorFast(const int number,
		    const CoinBigIndex * starts, const int * index,
                    const double * element);
    //@}

    //-------------------------------------------------------------------------
    /*! \name Append matrices

      \details
      We'll document these methods assuming that the current matrix is
      column major ordered (Hence in the <code>...SameOrdered()</code>
      methods the argument is column ordered, in the
      <code>OrthoOrdered()</code> methods the argument is row ordered.)
    */
    //@{
      /** Append the columns of the argument to the right end of this matrix.
	  @pre <code>minorDim_ == matrix.minorDim_</code> <br>
	  This method throws an exception if the minor dimensions are not the
	  same. */
      void majorAppendSameOrdered(const CoinPackedMatrix& matrix);
      /** Append the columns of the argument to the bottom end of this matrix.
	  @pre <code>majorDim_ == matrix.majorDim_</code> <br>
	  This method throws an exception if the major dimensions are not the
	  same. */
      void minorAppendSameOrdered(const CoinPackedMatrix& matrix);
      /** Append the rows of the argument to the right end of this matrix.
	  @pre <code>minorDim_ == matrix.majorDim_</code> <br>
	  This method throws an exception if the minor dimension of the
	  current matrix is not the same as the major dimension of the
	  argument matrix. */
      void majorAppendOrthoOrdered(const CoinPackedMatrix& matrix);
      /** Append the rows of the argument to the bottom end of this matrix.
	  @pre <code>majorDim_ == matrix.minorDim_</code> <br>
	  This method throws an exception if the major dimension of the
	  current matrix is not the same as the minor dimension of the
	  argument matrix. */
      void minorAppendOrthoOrdered(const CoinPackedMatrix& matrix);
      //@}

      //-----------------------------------------------------------------------
      /**@name Delete vectors */
      //@{
      /** Delete the major-dimension vectors whose indices are listed in
	  <code>indDel</code>. */
      void deleteMajorVectors(const int numDel, const int * indDel);
      /** Delete the minor-dimension vectors whose indices are listed in
	  <code>indDel</code>. */
      void deleteMinorVectors(const int numDel, const int * indDel);
      //@}

      //-----------------------------------------------------------------------
      /**@name Various dot products. */
      //@{
      /** Return <code>A * x</code> (multiplied from the "right" direction) in
	  <code>y</code>.
	  @pre <code>x</code> must be of size <code>majorDim()</code>
	  @pre <code>y</code> must be of size <code>minorDim()</code> */
      void timesMajor(const double * x, double * y) const;
#ifndef CLP_NO_VECTOR
      /** Return <code>A * x</code> (multiplied from the "right" direction) in
	  <code>y</code>. Same as the previous method, just <code>x</code> is
	  given in the form of a packed vector. */
      void timesMajor(const CoinPackedVectorBase& x, double * y) const;
#endif
      /** Return <code>A * x</code> (multiplied from the "right" direction) in
	  <code>y</code>.
	  @pre <code>x</code> must be of size <code>minorDim()</code>
	  @pre <code>y</code> must be of size <code>majorDim()</code> */
      void timesMinor(const double * x, double * y) const;
#ifndef CLP_NO_VECTOR
      /** Return <code>A * x</code> (multiplied from the "right" direction) in
	  <code>y</code>. Same as the previous method, just <code>x</code> is
	  given in the form of a packed vector. */
      void timesMinor(const CoinPackedVectorBase& x, double * y) const;
#endif
      //@}
   //@}

   //--------------------------------------------------------------------------
   /**@name Logical Operations. */
   //@{
#ifndef CLP_NO_VECTOR
   /*! \brief Test for equivalence.

       Two matrices are equivalent if they are both row- or column-ordered,
       they have the same dimensions, and each (major) vector is equivalent.
       The operator used to test for equality can be specified using the
       \p FloatEqual template parameter.
   */
   template <class FloatEqual> bool 
   isEquivalent(const CoinPackedMatrix& rhs, const FloatEqual& eq) const
   {
      // Both must be column order or both row ordered and must be of same size
      if ((isColOrdered() ^ rhs.isColOrdered()) ||
	  (getNumCols() != rhs.getNumCols()) ||
	  (getNumRows() != rhs.getNumRows()) ||
	  (getNumElements() != rhs.getNumElements()))
	 return false;
     
      for (int i=getMajorDim()-1; i >= 0; --i) {
        CoinShallowPackedVector pv = getVector(i);
        CoinShallowPackedVector rhsPv = rhs.getVector(i);
        if ( !pv.isEquivalent(rhsPv,eq) )
          return false;
      }
      return true;
   }

  /*! \brief Test for equivalence and report differences

    Equivalence is defined as for #isEquivalent. In addition, this method will
    print differences to std::cerr. Intended for use in unit tests and
    for debugging.
  */
  bool isEquivalent2(const CoinPackedMatrix& rhs) const;
#else
   /*! \brief Test for equivalence.

       Two matrices are equivalent if they are both row- or column-ordered,
       they have the same dimensions, and each (major) vector is equivalent.
       This method is optimised for speed. CoinPackedVector#isEquivalent is
       replaced with more efficient code for repeated comparison of
       equal-length vectors. The CoinRelFltEq operator is used. 
   */
  bool isEquivalent(const CoinPackedMatrix& rhs, const CoinRelFltEq & eq) const;
#endif
   /*! \brief Test for equivalence.
   
     The test for element equality is the default CoinRelFltEq operator.
   */
   bool isEquivalent(const CoinPackedMatrix& rhs) const;
   //@}

   //--------------------------------------------------------------------------
   /*! \name Non-const methods

     These are to be used with great care when doing column generation, etc.
   */
   //@{
    /** A vector containing the elements in the packed matrix. Note that there
	might be gaps in this list, entries that do not belong to any
	major-dimension vector. To get the actual elements one should look at
	this vector together with #start_ and #length_. */
    inline double * getMutableElements() const { return element_; }
    /** A vector containing the minor indices of the elements in the packed
        matrix. Note that there might be gaps in this list, entries that do not
        belong to any major-dimension vector. To get the actual elements one
        should look at this vector together with #start_ and
        #length_. */
    inline int * getMutableIndices() const { return index_; }

    /** The positions where the major-dimension vectors start in #element_ and
        #index_. */
    inline CoinBigIndex * getMutableVectorStarts() const { return start_; }
    /** The lengths of the major-dimension vectors. */
    inline int * getMutableVectorLengths() const { return length_; }
    /// Change the size of the bulk store after modifying - be careful
    inline void setNumElements(CoinBigIndex value)
    { size_ = value;}
    /*! NULLify element array
    
      Used when space is very tight. Does not free the space!
    */
    inline void nullElementArray() {element_=NULL;}

    /*! NULLify start array
    
      Used when space is very tight. Does not free the space!
    */
    inline void nullStartArray() {start_=NULL;}

    /*! NULLify length array
    
      Used when space is very tight. Does not free the space!
    */
    inline void nullLengthArray() {length_=NULL;}

    /*! NULLify index array
    
      Used when space is very tight. Does not free the space!
    */
    inline void nullIndexArray() {index_=NULL;}
   //@}

   //--------------------------------------------------------------------------
   /*! \name Constructors and destructors */
   //@{
   /// Default Constructor creates an empty column ordered packed matrix
   CoinPackedMatrix();

   /// A constructor where the ordering and the gaps are specified
   CoinPackedMatrix(const bool colordered,
		   const double extraMajor, const double extraGap);

   CoinPackedMatrix(const bool colordered,
		   const int minor, const int major, const CoinBigIndex numels,
		   const double * elem, const int * ind,
		   const CoinBigIndex * start, const int * len,
		   const double extraMajor, const double extraGap);

   CoinPackedMatrix(const bool colordered,
		   const int minor, const int major, const CoinBigIndex numels,
		   const double * elem, const int * ind,
		   const CoinBigIndex * start, const int * len);

   /** Create packed matrix from triples.
       If colordered is true then the created matrix will be column ordered.
       Duplicate matrix elements are allowed. The created matrix will have 
       the sum of the duplicates. <br>
       For example if: <br>
         rowIndices[0]=2; colIndices[0]=5; elements[0]=2.0 <br>
         rowIndices[1]=2; colIndices[1]=5; elements[1]=0.5 <br>
       then the created matrix will contain a value of 2.5 in row 2 and column 5.<br>
       The matrix is created without gaps.
   */
   CoinPackedMatrix(const bool colordered,
     const int * rowIndices, 
     const int * colIndices, 
     const double * elements, 
     CoinBigIndex numels ); 

   /// Copy constructor 
   CoinPackedMatrix(const CoinPackedMatrix& m);

  /*! \brief Copy constructor with fine tuning
  
    This constructor allows for the specification of an exact amount of extra
    space and/or reverse ordering.

    \p extraForMajor is the exact number of spare major vector slots after
    any possible reverse ordering. If \p extraForMajor < 0, all gaps and small
    elements will be removed from the copy, otherwise gaps and small elements
    are preserved.

    \p extraElements is the exact number of spare element entries.

    The usual multipliers, #extraMajor_ and #extraGap_, are set to zero.
  */
  CoinPackedMatrix(const CoinPackedMatrix &m,
  		   int extraForMajor, int extraElements,
		   bool reverseOrdering = false) ;

  /** Subset constructor (without gaps).  Duplicates are allowed
      and order is as given */
  CoinPackedMatrix (const CoinPackedMatrix & wholeModel,
		    int numberRows, const int * whichRows,
		    int numberColumns, const int * whichColumns);

   /// Destructor 
   virtual ~CoinPackedMatrix();    
   //@}

  /*! \name Debug Utilities */
  //@{
    /*! \brief Scan the matrix for anomalies.

	Returns the number of anomalies. Scans the structure for gaps,
	obviously bogus indices and coefficients, and inconsistencies. Gaps
	are not an error unless #hasGaps() says the matrix should be
	gap-free. Zeroes are not an error unless \p zeroesAreError is set to
	true.
	
	Values for verbosity are:
	- 0: No messages, just the return value
	- 1: Messages about errors
	- 2: If there are no errors, a message indicating the matrix was
	     checked is printed (positive confirmation).
	- 3: Adds a bit more information about the matrix.
	- 4: Prints warnings about zeroes even if they're not considered
	     errors.

	Obviously bogus coefficients are coefficients that are NaN or have
	absolute value greater than 1e50. Zeros have absolute value less
	than 1e-50.
      */
    int verifyMtx(int verbosity = 1, bool zeroesAreError = false) const ;
  //@}

  //--------------------------------------------------------------------------
protected:
   void gutsOfDestructor();
   void gutsOfCopyOf(const bool colordered,
		     const int minor, const int major, const CoinBigIndex numels,
		     const double * elem, const int * ind,
		     const CoinBigIndex * start, const int * len,
		     const double extraMajor=0.0, const double extraGap=0.0);
   /// When no gaps we can do faster
   void gutsOfCopyOfNoGaps(const bool colordered,
		     const int minor, const int major,
		     const double * elem, const int * ind,
                           const CoinBigIndex * start);
   void gutsOfOpEqual(const bool colordered,
		      const int minor, const int major, const CoinBigIndex numels,
		      const double * elem, const int * ind,
		      const CoinBigIndex * start, const int * len);
   void resizeForAddingMajorVectors(const int numVec, const int * lengthVec);
   void resizeForAddingMinorVectors(const int * addedEntries);

    /*! \brief Append a set of rows (columns) to the end of a row (colum)
    	       ordered matrix.
	
      If \p numberOther > 0 the method will check if any of the new rows
      (columns) contain duplicate indices or invalid indices and return the
      number of errors. A valid minor index must satisfy
      \code 0 <= k < numberOther \endcode
      If \p numberOther < 0 no checking is performed.
    */
    int appendMajor(const int number,
		    const CoinBigIndex * starts, const int * index,
                    const double * element, int numberOther=-1);
    /*! \brief Append a set of rows (columns) to the end of a column (row)
    	       ordered matrix.
    
      If \p numberOther > 0 the method will check if any of the new rows
      (columns) contain duplicate indices or indices outside the current
      range for the major dimension and return the number of violations.
      If \p numberOther <= 0 the major dimension will be expanded as
      necessary and there are no checks for duplicate indices.
    */
    int appendMinor(const int number,
		    const CoinBigIndex * starts, const int * index,
                    const double * element, int numberOther=-1);

private:
   inline CoinBigIndex getLastStart() const {
      return majorDim_ == 0 ? 0 : start_[majorDim_];
   }

   //--------------------------------------------------------------------------
protected:
   /**@name Data members
      The data members are protected to allow access for derived classes. */
   //@{
   /** A flag indicating whether the matrix is column or row major ordered. */
   bool     colOrdered_;
   /** This much times more space should be allocated for each major-dimension
       vector (with respect to the number of entries in the vector) when the
       matrix is resized. The purpose of these gaps is to allow fast insertion
       of new minor-dimension vectors. */
   double   extraGap_;
   /** his much times more space should be allocated for major-dimension
       vectors when the matrix is resized. The purpose of these gaps is to
       allow fast addition of new major-dimension vectors. */
   double   extraMajor_;

   /** List of nonzero element values. The entries in the gaps between
       major-dimension vectors are undefined. */
   double  *element_;
   /** List of nonzero element minor-dimension indices. The entries in the gaps
       between major-dimension vectors are undefined. */
   int     *index_;
   /** Starting positions of major-dimension vectors. */
   CoinBigIndex     *start_;
   /** Lengths of major-dimension vectors. */
   int     *length_;

   /// number of vectors in matrix
   int majorDim_;
   /// size of other dimension
   int minorDim_;
   /// the number of nonzero entries
   CoinBigIndex size_;

   /// max space allocated for major-dimension
   int maxMajorDim_;
   /// max space allocated for entries
   CoinBigIndex maxSize_;
   //@}
};

//#############################################################################
/*! \brief Test the methods in the CoinPackedMatrix class.

    The only reason for it not to be a member method is that this way
    it doesn't have to be compiled into the library. And that's a gain,
    because the library should be compiled with optimization on, but this
    method should be compiled with debugging.
*/
void
CoinPackedMatrixUnitTest();

#endif