newmat.h

C++矩阵算法库

   Real NormFrobenius() const;
   virtual Real SumAbsoluteValue() const;
   virtual Real Sum() const;
   virtual Real MaximumAbsoluteValue() const;
   virtual Real MaximumAbsoluteValue1(int& i) const;
   virtual Real MaximumAbsoluteValue2(int& i, int& j) const;
   virtual Real MinimumAbsoluteValue() const;
   virtual Real MinimumAbsoluteValue1(int& i) const;
   virtual Real MinimumAbsoluteValue2(int& i, int& j) const;
   virtual Real Maximum() const;
   virtual Real Maximum1(int& i) const;
   virtual Real Maximum2(int& i, int& j) const;
   virtual Real Minimum() const;
   virtual Real Minimum1(int& i) const;
   virtual Real Minimum2(int& i, int& j) const;
   virtual Real Trace() const;
   Real Norm1() const;
   Real NormInfinity() const;
   virtual MatrixBandWidth BandWidth() const;  // bandwidths of band matrix
   virtual void CleanUp() {}                   // to clear store
   void IEQND() const;                         // called by ineq. ops
//   virtual ReturnMatrix Reverse() const;       // reverse order of elements


//protected:
//   BaseMatrix() : t(this), i(this) {}

   friend class GeneralMatrix;
   friend class Matrix;
   friend class nricMatrix;
   friend class RowVector;
   friend class ColumnVector;
   friend class SymmetricMatrix;
   friend class UpperTriangularMatrix;
   friend class LowerTriangularMatrix;
   friend class DiagonalMatrix;
   friend class CroutMatrix;
   friend class BandMatrix;
   friend class LowerBandMatrix;
   friend class UpperBandMatrix;
   friend class SymmetricBandMatrix;
   friend class AddedMatrix;
   friend class MultipliedMatrix;
   friend class SubtractedMatrix;
   friend class SPMatrix;
   friend class KPMatrix;
   friend class ConcatenatedMatrix;
   friend class StackedMatrix;
   friend class SolvedMatrix;
   friend class ShiftedMatrix;
   friend class NegShiftedMatrix;
   friend class ScaledMatrix;
   friend class TransposedMatrix;
   friend class ReversedMatrix;
   friend class NegatedMatrix;
   friend class InvertedMatrix;
   friend class RowedMatrix;
   friend class ColedMatrix;
   friend class DiagedMatrix;
   friend class MatedMatrix;
   friend class GetSubMatrix;
   friend class ReturnMatrixX;
   friend class LinearEquationSolver;
   friend class GenericMatrix;
   NEW_DELETE(BaseMatrix)
};


// ***************************** working classes **************************/

class GeneralMatrix : public BaseMatrix         // declarable matrix types
{
   virtual GeneralMatrix* Image() const;        // copy of matrix
protected:
   int tag;                                     // shows whether can reuse
   int nrows, ncols;                            // dimensions
   int storage;                                 // total store required
   Real* store;                                 // point to store (0=not set)
   GeneralMatrix();                             // initialise with no store
   GeneralMatrix(ArrayLengthSpecifier);         // constructor getting store
   void Add(GeneralMatrix*, Real);              // sum of GM and Real
   void Add(Real);                              // add Real to this
   void NegAdd(GeneralMatrix*, Real);           // Real - GM
   void NegAdd(Real);                           // this = this - Real
   void Multiply(GeneralMatrix*, Real);         // product of GM and Real
   void Multiply(Real);                         // multiply this by Real
   void Negate(GeneralMatrix*);                 // change sign
   void Negate();                               // change sign
   void ReverseElements();                      // internal reverse of elements
   void ReverseElements(GeneralMatrix*);        // reverse order of elements
   void operator=(Real);                        // set matrix to constant
   Real* GetStore();                            // get store or copy
   GeneralMatrix* BorrowStore(GeneralMatrix*, MatrixType);
                                                // temporarily access store
   void GetMatrix(const GeneralMatrix*);        // used by = and initialise
   void Eq(const BaseMatrix&, MatrixType);      // used by =
   void Eq(const BaseMatrix&, MatrixType, bool);// used by <<
   void Eq2(const BaseMatrix&, MatrixType);     // cut down version of Eq
   int search(const BaseMatrix*) const;
   virtual GeneralMatrix* Transpose(TransposedMatrix*, MatrixType);
   void CheckConversion(const BaseMatrix&);     // check conversion OK
   void ReSize(int, int, int);                  // change dimensions
   virtual short SimpleAddOK(const GeneralMatrix* gm) { return 0; }
             // see bandmat.cpp for explanation
public:
   GeneralMatrix* Evaluate(MatrixType mt=MatrixTypeUnSp);
   virtual MatrixType Type() const = 0;         // type of a matrix
   int Nrows() const { return nrows; }          // get dimensions
   int Ncols() const { return ncols; }
   int Storage() const { return storage; }
   Real* Store() const { return store; }
   virtual ~GeneralMatrix();                    // delete store if set
   void tDelete();                              // delete if tag permits
   bool reuse();                                // true if tag allows reuse
   void Protect() { tag=-1; }                   // cannot delete or reuse
   int Tag() const { return tag; }
   bool IsZero() const;                         // test matrix has all zeros
   void Release() { tag=1; }                    // del store after next use
   void Release(int t) { tag=t; }               // del store after t accesses
   void ReleaseAndDelete() { tag=0; }           // delete matrix after use
   void operator<<(const Real*);                // assignment from an array
   void operator<<(const BaseMatrix& X)
      { Eq(X,this->Type(),true); }              // = without checking type
   void Inject(const GeneralMatrix&);           // copy stored els only
   void operator+=(const BaseMatrix&);
   void operator-=(const BaseMatrix&);
   void operator*=(const BaseMatrix&);
   void operator|=(const BaseMatrix&);
   void operator&=(const BaseMatrix&);
   void operator+=(Real);
   void operator-=(Real r) { operator+=(-r); }
   void operator*=(Real);
   void operator/=(Real r) { operator*=(1.0/r); }
   virtual GeneralMatrix* MakeSolver();         // for solving
   virtual void Solver(MatrixColX&, const MatrixColX&) {}
   virtual void GetRow(MatrixRowCol&) = 0;      // Get matrix row
   virtual void RestoreRow(MatrixRowCol&) {}    // Restore matrix row
   virtual void NextRow(MatrixRowCol&);         // Go to next row
   virtual void GetCol(MatrixRowCol&) = 0;      // Get matrix col
   virtual void GetCol(MatrixColX&) = 0;        // Get matrix col
   virtual void RestoreCol(MatrixRowCol&) {}    // Restore matrix col
   virtual void RestoreCol(MatrixColX&) {}      // Restore matrix col
   virtual void NextCol(MatrixRowCol&);         // Go to next col
   virtual void NextCol(MatrixColX&);           // Go to next col
   Real SumSquare() const;
   Real SumAbsoluteValue() const;
   Real Sum() const;
   Real MaximumAbsoluteValue1(int& i) const;
   Real MinimumAbsoluteValue1(int& i) const;
   Real Maximum1(int& i) const;
   Real Minimum1(int& i) const;
   Real MaximumAbsoluteValue() const;
   Real MaximumAbsoluteValue2(int& i, int& j) const;
   Real MinimumAbsoluteValue() const;
   Real MinimumAbsoluteValue2(int& i, int& j) const;
   Real Maximum() const;
   Real Maximum2(int& i, int& j) const;
   Real Minimum() const;
   Real Minimum2(int& i, int& j) const;
   LogAndSign LogDeterminant() const;
   virtual bool IsEqual(const GeneralMatrix&) const;
                                                // same type, same values
   void CheckStore() const;                     // check store is non-zero
   virtual void SetParameters(const GeneralMatrix*) {}
                                                // set parameters in GetMatrix
   operator ReturnMatrix() const;               // for building a ReturnMatrix
   ReturnMatrix ForReturn() const;
   virtual bool SameStorageType(const GeneralMatrix& A) const;
   virtual void ReSizeForAdd(const GeneralMatrix& A, const GeneralMatrix& B);
   virtual void ReSizeForSP(const GeneralMatrix& A, const GeneralMatrix& B);
   virtual void ReSize(const GeneralMatrix& A);
   MatrixInput operator<<(Real);                // for loading a list
   MatrixInput operator<<(int f);
//   ReturnMatrix Reverse() const;                // reverse order of elements
   void CleanUp();                              // to clear store

   friend class Matrix;
   friend class nricMatrix;
   friend class SymmetricMatrix;
   friend class UpperTriangularMatrix;
   friend class LowerTriangularMatrix;
   friend class DiagonalMatrix;
   friend class CroutMatrix;
   friend class RowVector;
   friend class ColumnVector;
   friend class BandMatrix;
   friend class LowerBandMatrix;
   friend class UpperBandMatrix;
   friend class SymmetricBandMatrix;
   friend class BaseMatrix;
   friend class AddedMatrix;
   friend class MultipliedMatrix;
   friend class SubtractedMatrix;
   friend class SPMatrix;
   friend class KPMatrix;
   friend class ConcatenatedMatrix;
   friend class StackedMatrix;
   friend class SolvedMatrix;
   friend class ShiftedMatrix;
   friend class NegShiftedMatrix;
   friend class ScaledMatrix;
   friend class TransposedMatrix;
   friend class ReversedMatrix;
   friend class NegatedMatrix;
   friend class InvertedMatrix;
   friend class RowedMatrix;
   friend class ColedMatrix;
   friend class DiagedMatrix;
   friend class MatedMatrix;
   friend class GetSubMatrix;
   friend class ReturnMatrixX;
   friend class LinearEquationSolver;
   friend class GenericMatrix;
   NEW_DELETE(GeneralMatrix)
};



class Matrix : public GeneralMatrix             // usual rectangular matrix
{
   GeneralMatrix* Image() const;                // copy of matrix
public:
   Matrix() {}
   ~Matrix() {}
   Matrix(int, int);                            // standard declaration
   Matrix(const BaseMatrix&);                   // evaluate BaseMatrix
   void operator=(const BaseMatrix&);
   void operator=(Real f) { GeneralMatrix::operator=(f); }
   void operator=(const Matrix& m) { operator=((const BaseMatrix&)m); }
   MatrixType Type() const;
   Real& operator()(int, int);                  // access element
   Real& element(int, int);                     // access element
   Real operator()(int, int) const;            // access element
   Real element(int, int) const;               // access element
#ifdef SETUP_C_SUBSCRIPTS
   Real* operator[](int m) { return store+m*ncols; }
   const Real* operator[](int m) const { return store+m*ncols; }
#endif
   Matrix(const Matrix& gm) { GetMatrix(&gm); }
   GeneralMatrix* MakeSolver();
   Real Trace() const;
   void GetRow(MatrixRowCol&);
   void GetCol(MatrixRowCol&);
   void GetCol(MatrixColX&);
   void RestoreCol(MatrixRowCol&);
   void RestoreCol(MatrixColX&);
   void NextRow(MatrixRowCol&);
   void NextCol(MatrixRowCol&);
   void NextCol(MatrixColX&);
   virtual void ReSize(int,int);           // change dimensions
      // virtual so we will catch it being used in a vector called as a matrix
   void ReSize(const GeneralMatrix& A);
   Real MaximumAbsoluteValue2(int& i, int& j) const;
   Real MinimumAbsoluteValue2(int& i, int& j) const;
   Real Maximum2(int& i, int& j) const;
   Real Minimum2(int& i, int& j) const;
   friend Real DotProduct(const Matrix& A, const Matrix& B);
   NEW_DELETE(Matrix)
};

class nricMatrix : public Matrix                // for use with Numerical
                                                // Recipes in C
{
   GeneralMatrix* Image() const;                // copy of matrix
   Real** row_pointer;                          // points to rows
   void MakeRowPointer();                       // build rowpointer
   void DeleteRowPointer();
public:
   nricMatrix() {}
   nricMatrix(int m, int n)                     // standard declaration
      :  Matrix(m,n) { MakeRowPointer(); }
   nricMatrix(const BaseMatrix& bm)             // evaluate BaseMatrix
      :  Matrix(bm) { MakeRowPointer(); }
   void operator=(const BaseMatrix& bm)
      { DeleteRowPointer(); Matrix::operator=(bm); MakeRowPointer(); }
   void operator=(Real f) { GeneralMatrix::operator=(f); }
   void operator=(const nricMatrix& m) { operator=((const BaseMatrix&)m); }
   void operator<<(const BaseMatrix& X)
      { DeleteRowPointer(); Eq(X,this->Type(),true); MakeRowPointer(); }
   nricMatrix(const nricMatrix& gm) { GetMatrix(&gm); MakeRowPointer(); }
   void ReSize(int m, int n)               // change dimensions
      { DeleteRowPointer(); Matrix::ReSize(m,n); MakeRowPointer(); }
   void ReSize(const GeneralMatrix& A);
   ~nricMatrix() { DeleteRowPointer(); }
   Real** nric() const { CheckStore(); return row_pointer-1; }
   void CleanUp();                                // to clear store
   NEW_DELETE(nricMatrix)
};

class SymmetricMatrix : public GeneralMatrix
{
   GeneralMatrix* Image() const;                // copy of matrix
public:
   SymmetricMatrix() {}
   ~SymmetricMatrix() {}
   SymmetricMatrix(ArrayLengthSpecifier);
   SymmetricMatrix(const BaseMatrix&);
   void operator=(const BaseMatrix&);
   void operator=(Real f) { GeneralMatrix::operator=(f); }
   void operator=(const SymmetricMatrix& m) { operator=((const BaseMatrix&)m); }
   Real& operator()(int, int);                  // access element
   Real& element(int, int);                     // access element
   Real operator()(int, int) const;             // access element
   Real element(int, int) const;                // access element
#ifdef SETUP_C_SUBSCRIPTS
   Real* operator[](int m) { return store+(m*(m+1))/2; }
   const Real* operator[](int m) const { return store+(m*(m+1))/2; }
#endif
   MatrixType Type() const;
   SymmetricMatrix(const SymmetricMatrix& gm) { GetMatrix(&gm); }
   Real SumSquare() const;
   Real SumAbsoluteValue() const;
   Real Sum() const;
   Real Trace() const;
   void GetRow(MatrixRowCol&);
   void GetCol(MatrixRowCol&);
   void GetCol(MatrixColX&);
   void RestoreCol(MatrixRowCol&) {}
   void RestoreCol(MatrixColX&);
	GeneralMatrix* Transpose(TransposedMatrix*, MatrixType);
   void ReSize(int);                       // change dimensions
   void ReSize(const GeneralMatrix& A);
   NEW_DELETE(SymmetricMatrix)
};

class UpperTriangularMatrix : public GeneralMatrix
{
   GeneralMatrix* Image() const;                // copy of matrix
public:
   UpperTriangularMatrix() {}
   ~UpperTriangularMatrix() {}
   UpperTriangularMatrix(ArrayLengthSpecifier);
   void operator=(const BaseMatrix&);
   void operator=(const UpperTriangularMatrix& m)
      { operator=((const BaseMatrix&)m); }
   UpperTriangularMatrix(const BaseMatrix&);
   UpperTriangularMatrix(const UpperTriangularMatrix& gm) { GetMatrix(&gm); }
   void operator=(Real f) { GeneralMatrix::operator=(f); }
   Real& operator()(int, int);                  // access element
   Real& element(int, int);                     // access element
   Real operator()(int, int) const;             // access element
   Real element(int, int) const;                // access element
#ifdef SETUP_C_SUBSCRIPTS
   Real* operator[](int m) { return store+m*ncols-(m*(m+1))/2; }