matrix.h

一个可进行矩阵计算的模版类,可实现大多数常用的矩阵计算功能

////////////////////////////////
// Matrix TCL Lite v1.13
// Copyright (c) 1997-2002 Techsoft Pvt. Ltd. (See License.Txt file.)
//
// Matrix.h: Matrix C++ template class include file 
// Web: http://www.techsoftpl.com/matrix/
// Email: [e-mail]
//

//////////////////////////////
// Installation:
//
// Copy this "matrix.h" file into include directory of your compiler.
//

//////////////////////////////
// Note: This matrix template class defines majority of the matrix
// operations as overloaded operators or methods. It is assumed that
// users of this class is familiar with matrix algebra. We have not
// defined any specialization of this template here, so all the instances
// of matrix will be created implicitly by the compiler. The data types
// tested with this class are float, double, long double, complex<float>,
// complex<double> and complex<long double>. Note that this class is not 
// optimized for performance.
//
// Since implementation of exception, namespace and template are still
// not standardized among the various (mainly old) compilers, you may 
// encounter compilation error with some compilers. In that case remove 
// any of the above three features by defining the following macros:
//
//  _NO_NAMESPACE:  Define this macro to remove namespace support.
//
//  _NO_EXCEPTION:  Define this macro to remove exception handling
//                  and use old style of error handling using function.
//
//  _NO_TEMPLATE:   If this macro is defined matrix class of double
//                  type will be generated by default. You can also
//                  generate a different type of matrix like float.
//
//  _SGI_BROKEN_STL: For SGI C++ v.7.2.1 compiler.
//
//  Since all the definitions are also included in this header file as
//  inline function, some compiler may give warning "inline function
//  can't be expanded". You may ignore/disable this warning using compiler
//  switches. All the operators/methods defined in this class have their
//  natural meaning except the followings:
//
//  Operator/Method                          Description
//  ---------------                          -----------
//   operator ()   :   This function operator can be used as a
//                     two-dimensional subscript operator to get/set
//                     individual matrix elements.
//
//   operator !    :   This operator has been used to calculate inversion
//                     of matrix.
//
//   operator ~    :   This operator has been used to return transpose of
//                     a matrix.
//
//   operator ^    :   It is used calculate power (by a scalar) of a matrix.
//                     When using this operator in a matrix equation, care
//                     must be taken by parenthesizing it because it has
//                     lower precedence than addition, subtraction,
//                     multiplication and division operators.
//
//   operator >>   :   It is used to read matrix from input stream as per
//                     standard C++ stream operators.
//
//   operator <<   :   It is used to write matrix to output stream as per
//                     standard C++ stream operators.
//
// Note that professional version of this package, Matrix TCL Pro 2.11
// is optimized for performance and supports many more matrix operations.
// It is available from our web site at <http://www.techsoftpl.com/matrix/>.
//

#ifndef __cplusplus
#error Must use C++ for the type matrix.
#endif

#if !defined(__STD_MATRIX_H)
#define __STD_MATRIX_H

//////////////////////////////
// First deal with various shortcomings and incompatibilities of
// various (mainly old) versions of popular compilers available.
//

#if defined(__BORLANDC__)
#pragma option -w-inl -w-pch
#endif

#if ( defined(__BORLANDC__) || _MSC_VER <= 1000 ) && !defined( __GNUG__ )
#  include <stdio.h>
#  include <stdlib.h>
#  include <math.h>
#  include <iostream.h>
#  include <string.h>
#else
#  include <cmath>
#  include <cstdio>
#  include <cstdlib>
#  include <string>
#  include <iostream>
#endif

#if defined(_MSC_VER) && _MSC_VER <= 1000
#  define _NO_EXCEPTION        // stdexception is not fully supported in MSVC++ 4.0
typedef int bool;
#  if !defined(false)
#    define false  0
#  endif
#  if !defined(true)
#    define true   1
#  endif
#endif

#if defined(__BORLANDC__) && !defined(__WIN32__)
#  define _NO_EXCEPTION        // std exception and namespace are not fully
#  define _NO_NAMESPACE        // supported in 16-bit compiler
#endif

#if defined(_MSC_VER) && !defined(_WIN32)
#  define _NO_EXCEPTION
#endif

#if defined(_NO_EXCEPTION)
#  define _NO_THROW
#  define _THROW_MATRIX_ERROR
#else
#  if defined(_MSC_VER)
#    if _MSC_VER >= 1020
#      include <stdexcept>
#    else
#      include <stdexcpt.h>
#    endif
#  elif defined(__MWERKS__)
#      include <stdexcept>
#  elif (__GNUC__ >= 2 || (__GNUC__ == 2 && __GNUC_MINOR__ >= 8))
#     include <stdexcept>
#  else
#     include <stdexcep>
#  endif
#  define _NO_THROW               throw ()
#  define _THROW_MATRIX_ERROR     throw (matrix_error)
#endif

#ifndef __MINMAX_DEFINED
#  define max(a,b)    (((a) > (b)) ? (a) : (b))
#  define min(a,b)    (((a) < (b)) ? (a) : (b))
#endif

#if defined(_MSC_VER)
#undef _MSC_EXTENSIONS      // To include overloaded abs function definitions!
#endif

#if ( defined(__BORLANDC__) || _MSC_VER ) && !defined( __GNUG__ ) 
inline float abs (float v) { return (float)fabs( v); } 
inline double abs (double v) { return fabs( v); } 
inline long double abs (long double v) { return fabsl( v); }
#endif

#if defined(__GNUG__) || defined(__MWERKS__) || (defined(__BORLANDC__) && (__BORLANDC__ >= 0x540))
#define FRIEND_FUN_TEMPLATE <>
#else
#define FRIEND_FUN_TEMPLATE
#endif

#if defined(_MSC_VER) && _MSC_VER <= 1020   // MSVC++ 4.0/4.2 does not
#  define _NO_NAMESPACE                     // support "std" namespace
#endif

#if !defined(_NO_NAMESPACE)
#if defined( _SGI_BROKEN_STL )              // For SGI C++ v.7.2.1 compiler
namespace std { }
#endif
using namespace std;
#endif

#ifndef _NO_NAMESPACE
namespace math {
#endif

#if !defined(_NO_EXCEPTION)
class matrix_error : public logic_error
{
    public:
	matrix_error (const string& what_arg) : logic_error( what_arg) {}
};
#define REPORT_ERROR(ErrormMsg)  throw matrix_error( ErrormMsg);
#else
inline void _matrix_error (const char* pErrMsg)
{
    cout << pErrMsg << endl;
    exit(1);
}
#define REPORT_ERROR(ErrormMsg)  _matrix_error( ErrormMsg);
#endif

#if !defined(_NO_TEMPLATE)
#  define MAT_TEMPLATE  template <class T>
#  define matrixT  matrix<T>
#else
#  define MAT_TEMPLATE
#  define matrixT  matrix
#  ifdef MATRIX_TYPE
     typedef MATRIX_TYPE T;
#  else
     typedef double T;
#  endif
#endif


MAT_TEMPLATE
class matrix
{
public:
   // Constructors
   matrix (const matrixT& m);
   matrix (size_t row = 6, size_t col = 6);

   // Destructor
   ~matrix ();

   // Assignment operators
   matrixT& operator = (const matrixT& m) _NO_THROW;

   // Value extraction method
   size_t RowNo () const { return _m->Row; }
   size_t ColNo () const { return _m->Col; }

   // Subscript operator
   T& operator () (size_t row, size_t col) _THROW_MATRIX_ERROR;
   T  operator () (size_t row, size_t col) const _THROW_MATRIX_ERROR;

   // Unary operators
   matrixT operator + () _NO_THROW { return *this; }
   matrixT operator - () _NO_THROW;

   // Combined assignment - calculation operators
   matrixT& operator += (const matrixT& m) _THROW_MATRIX_ERROR;
   matrixT& operator -= (const matrixT& m) _THROW_MATRIX_ERROR;
   matrixT& operator *= (const matrixT& m) _THROW_MATRIX_ERROR;
   matrixT& operator *= (const T& c) _NO_THROW;
   matrixT& operator /= (const T& c) _NO_THROW;
   matrixT& operator ^= (const size_t& pow) _THROW_MATRIX_ERROR;

   // Miscellaneous -methods
   void Null (const size_t& row, const size_t& col) _NO_THROW;
   void Null () _NO_THROW;
   void Unit (const size_t& row) _NO_THROW;
   void Unit () _NO_THROW;
   void SetSize (size_t row, size_t col) _NO_THROW;

   // Utility methods
   matrixT Solve (const matrixT& v) const _THROW_MATRIX_ERROR;
   matrixT Adj () _THROW_MATRIX_ERROR;
   matrixT Inv () _THROW_MATRIX_ERROR;
   T Det () const _THROW_MATRIX_ERROR;
   T Norm () _NO_THROW;
   T Cofact (size_t row, size_t col) _THROW_MATRIX_ERROR;
   T Cond () _NO_THROW;

   // Type of matrices
   bool IsSquare () _NO_THROW { return (_m->Row == _m->Col); } 
   bool IsSingular () _NO_THROW;
   bool IsDiagonal () _NO_THROW;
   bool IsScalar () _NO_THROW;
   bool IsUnit () _NO_THROW;
   bool IsNull () _NO_THROW;
   bool IsSymmetric () _NO_THROW;
   bool IsSkewSymmetric () _NO_THROW;
   bool IsUpperTriangular () _NO_THROW;
   bool IsLowerTriangular () _NO_THROW;

private:
    struct base_mat
    {
	T **Val;
	size_t Row, Col, RowSiz, ColSiz;
	int Refcnt;

	base_mat (size_t row, size_t col, T** v)
	{
	    Row = row; RowSiz = row;
	    Col = col; ColSiz = col;
	    Refcnt = 1;

	    Val = new T* [row];
	    size_t rowlen = col * sizeof(T);

	    for (size_t i=0; i < row; i++)
	    {
		Val[i] = new T [col];
		if (v) memcpy( Val[i], v[i], rowlen);
	    }
	}
	~base_mat ()
	{
	    for (size_t i=0; i < RowSiz; i++)
		delete [] Val[i];
	    delete [] Val;
	}
    };
    base_mat *_m;

    void clone ();
    void realloc (size_t row, size_t col);
    int pivot (size_t row);
};

#if defined(_MSC_VER) && _MSC_VER <= 1020
#  undef  _NO_THROW               // MSVC++ 4.0/4.2 does not support 
#  undef  _THROW_MATRIX_ERROR     // exception specification in definition
#  define _NO_THROW
#  define _THROW_MATRIX_ERROR
#endif

// constructor
MAT_TEMPLATE inline
matrixT::matrix (size_t row, size_t col)
{
  _m = new base_mat( row, col, 0);
}

// copy constructor
MAT_TEMPLATE inline
matrixT::matrix (const matrixT& m)
{
    _m = m._m;
    _m->Refcnt++;
}

// Internal copy constructor
MAT_TEMPLATE inline void
matrixT::clone ()
{
    _m->Refcnt--;
    _m = new base_mat( _m->Row, _m->Col, _m->Val);
}

// destructor
MAT_TEMPLATE inline
matrixT::~matrix ()
{
   if (--_m->Refcnt == 0) delete _m;
}

// assignment operator
MAT_TEMPLATE inline matrixT&
matrixT::operator = (const matrixT& m) _NO_THROW
{
    m._m->Refcnt++;
    if (--_m->Refcnt == 0) delete _m;
    _m = m._m;
    return *this;
}

//  reallocation method
MAT_TEMPLATE inline void 
matrixT::realloc (size_t row, size_t col)
{
   if (row == _m->RowSiz && col == _m->ColSiz)
   {
      _m->Row = _m->RowSiz;
      _m->Col = _m->ColSiz;
      return;
   }

   base_mat *m1 = new base_mat( row, col, NULL);
   size_t colSize = min(_m->Col,col) * sizeof(T);
   size_t minRow = min(_m->Row,row);

   for (size_t i=0; i < minRow; i++)
      memcpy( m1->Val[i], _m->Val[i], colSize);

   if (--_m->Refcnt == 0) 
       delete _m;
   _m = m1;

   return;
}

// public method for resizing matrix
MAT_TEMPLATE inline void
matrixT::SetSize (size_t row, size_t col) _NO_THROW
{
   size_t i,j;
   size_t oldRow = _m->Row;
   size_t oldCol = _m->Col;

   if (row != _m->RowSiz || col != _m->ColSiz)
      realloc( row, col);

   for (i=oldRow; i < row; i++)
      for (j=0; j < col; j++)
	 _m->Val[i][j] = T(0);

   for (i=0; i < row; i++)                      
      for (j=oldCol; j < col; j++)
	 _m->Val[i][j] = T(0);

   return;
}

// subscript operator to get/set individual elements
MAT_TEMPLATE inline T&
matrixT::operator () (size_t row, size_t col) _THROW_MATRIX_ERROR
{
   if (row >= _m->Row || col >= _m->Col)
      REPORT_ERROR( "matrixT::operator(): Index out of range!");
   if (_m->Refcnt > 1) clone();
   return _m->Val[row][col];
}

// subscript operator to get/set individual elements
MAT_TEMPLATE inline T
matrixT::operator () (size_t row, size_t col) const _THROW_MATRIX_ERROR
{
   if (row >= _m->Row || col >= _m->Col)
      REPORT_ERROR( "matrixT::operator(): Index out of range!");
   return _m->Val[row][col];
}

// input stream function
MAT_TEMPLATE inline istream&
operator >> (istream& istrm, matrixT& m)
{
   for (size_t i=0; i < m.RowNo(); i++)
      for (size_t j=0; j < m.ColNo(); j++)
      {
         T x;
         istrm >> x;
         m(i,j) = x;
      }
   return istrm;
}

// output stream function
MAT_TEMPLATE inline ostream&
operator << (ostream& ostrm, const matrixT& m)
{
   for (size_t i=0; i < m.RowNo(); i++)
   {
      for (size_t j=0; j < m.ColNo(); j++)
      {
         T x = m(i,j);
         ostrm << x << '\t';
      }
      ostrm << endl;
   }
   return ostrm;
}


// logical equal-to operator
MAT_TEMPLATE inline bool
operator == (const matrixT& m1, const matrixT& m2) _NO_THROW
{
   if (m1.RowNo() != m2.RowNo() || m1.ColNo() != m2.ColNo())
      return false;

   for (size_t i=0; i < m1.RowNo(); i++)
      for (size_t j=0; j < m1.ColNo(); j++)
	      if (m1(i,j) != m2(i,j))
	         return false;

   return true;
}

// logical no-equal-to operator
MAT_TEMPLATE inline bool
operator != (const matrixT& m1, const matrixT& m2) _NO_THROW
{
    return (m1 == m2) ? false : true;
}

// combined addition and assignment operator
MAT_TEMPLATE inline matrixT&
matrixT::operator += (const matrixT& m) _THROW_MATRIX_ERROR
{
   if (_m->Row != m._m->Row || _m->Col != m._m->Col)
      REPORT_ERROR( "matrixT::operator+= : Inconsistent matrix sizes in addition!");
   if (_m->Refcnt > 1) clone();
   for (size_t i=0; i < m._m->Row; i++)
      for (size_t j=0; j < m._m->Col; j++)
	 _m->Val[i][j] += m._m->Val[i][j];
   return *this;
}

// combined subtraction and assignment operator
MAT_TEMPLATE inline matrixT&
matrixT::operator -= (const matrixT& m) _THROW_MATRIX_ERROR
{
   if (_m->Row != m._m->Row || _m->Col != m._m->Col)
      REPORT_ERROR( "matrixT::operator-= : Inconsistent matrix sizes in subtraction!");
   if (_m->Refcnt > 1) clone();
   for (size_t i=0; i < m._m->Row; i++)
      for (size_t j=0; j < m._m->Col; j++)
	 _m->Val[i][j] -= m._m->Val[i][j];
   return *this;
}

// combined scalar multiplication and assignment operator
MAT_TEMPLATE inline matrixT&
matrixT::operator *= (const T& c) _NO_THROW
{
    if (_m->Refcnt > 1) clone();
    for (size_t i=0; i < _m->Row; i++)
	for (size_t j=0; j < _m->Col; j++)
	    _m->Val[i][j] *= c;
    return *this;
}

// combined matrix multiplication and assignment operator
MAT_TEMPLATE inline matrixT&
matrixT::operator *= (const matrixT& m) _THROW_MATRIX_ERROR
{
   if (_m->Col != m._m->Row)
      REPORT_ERROR( "matrixT::operator*= : Inconsistent matrix sizes in multiplication!");

   matrixT temp(_m->Row,m._m->Col);

   for (size_t i=0; i < _m->Row; i++)
      for (size_t j=0; j < m._m->Col; j++)
      {
         temp._m->Val[i][j] = T(0);
         for (size_t k=0; k < _m->Col; k++)
            temp._m->Val[i][j] += _m->Val[i][k] * m._m->Val[k][j];
      }
   *this = temp;