tridiag.h

常用算法与数据结构原代码

// tridiagonal matrix

#ifndef Tridiagonal_
#define Tridiagonal_


#include <stdlib.h>
#include <iostream.h>
#include "xcept.h"


template<class T>
class TridiagonalMatrix {
	friend ostream& operator<<(ostream&, const TridiagonalMatrix<T>&);
	friend istream& operator>>(istream&, TridiagonalMatrix<T>&);
   public:
	   TridiagonalMatrix(int size = 10)
	   {
		   n = size; 
		   t = new T [3*n-2];
	   }
	   ~TridiagonalMatrix() 
	   {
		   delete [] t;
	   }
	   TridiagonalMatrix<T>& Store(const T& x, int i, int j);
	   T Retrieve(int i, int j) const;
	   TridiagonalMatrix(const TridiagonalMatrix<T>& x);
	   // copy constructor
	   TridiagonalMatrix<T>& operator=(const TridiagonalMatrix<T>& x);
	   TridiagonalMatrix<T> operator+() const; // unary +
	   TridiagonalMatrix<T> operator+(const TridiagonalMatrix<T>& x) const;
	   TridiagonalMatrix<T> operator-() const; // unary minus
	   TridiagonalMatrix<T> operator-(const TridiagonalMatrix<T>& x) const;
	   TridiagonalMatrix<T>& operator+=(const T& x);
	   TridiagonalMatrix<T> Transpose();
   private:
	   int n; // matrix dimension
	   T *t;  // 1D array for tridiagonal
};

template<class T>
TridiagonalMatrix<T>& TridiagonalMatrix<T>::Store(const T& x, int i, int j)
{// Store x as T(i,j)
	if ( i < 1 || j < 1 || i > n || j > n)
		throw OutOfBounds();
	
	switch (i - j) 
	{
	case 1: // lower diagonal
		t[i - 2] = x; 
		break;
	case 0: // main diagonal
		t[n + i - 2] = x; 
		break;
	case -1: // upper diagonal
		t[2 * n + i - 2] = x; 
		break;
	default: 
		if(x != 0)
			throw MustBeZero();
	}
	return *this;
}

template <class T>
T TridiagonalMatrix<T>::Retrieve(int i, int j) const
{// Retrieve T(i,j)
	if ( i < 1 || j < 1 || i > n || j > n)
		throw OutOfBounds();
    
	switch (i - j) 
	{
	case 1: // lower diagonal
		return t[i - 2];
	case 0: // main diagonal
		return t[n + i - 2];
	case -1: // upper diagonal
		return t[2 * n + i - 2];
	default: 
		return 0;
	}
}

template<class T>
TridiagonalMatrix<T>::TridiagonalMatrix(const TridiagonalMatrix<T>& x)
{// Copy constructor for tridiagonal matrices.
	n = x.n;
	t = new T[3 * n - 2];               // get space
	for (int i = 0; i < 3 * n - 2; i++) // copy elements
		t[i] = x.t[i];
}


template<class T>
TridiagonalMatrix<T>& TridiagonalMatrix<T>::operator=(const TridiagonalMatrix<T>& x)
{// Overload assignment operator.
	if (this != &x)
	{// not self-assignment
		n = x.n;
		delete [] t; // free old space
		t = new T[3 * n - 2];      // get right amount
		for (int i = 0; i < 3 * n - 2; i++) // copy elements
			t[i] = x.t[i];
	}
	return *this;
}

template<class T>
TridiagonalMatrix<T> TridiagonalMatrix<T>::operator+(const TridiagonalMatrix<T>& x) const
{// Return w = (*this) + x.
	if (n != x.n) 
		throw SizeMismatch();
	
	// create result array w
	TridiagonalMatrix<T> w(n);
	for (int i = 0; i < 3 * n - 2; i++)
		w.t[i] = t[i] + x.t[i];
	
	return w;
}

template<class T>
TridiagonalMatrix<T> TridiagonalMatrix<T>::operator-(const TridiagonalMatrix<T>& x) const
{// Return w = (*this) - x.
	if (n != x.n) 
		throw SizeMismatch();
	
	// create result array w
	TridiagonalMatrix<T> w(n);
	for (int i = 0; i < 3 * n - 2; i++)
		w.t[i] = t[i] - x.t[i];
	
	return w;
}

template<class T>
TridiagonalMatrix<T> TridiagonalMatrix<T>::operator-() const
{// Return w = -(*this).
	// create result array w
	TridiagonalMatrix<T> w(n);
	for (int i = 0; i < 3 * n - 2; i++)
		w.t[i] = -t[i];
	
	return w;
}

template<class T>
TridiagonalMatrix<T>& TridiagonalMatrix<T>::operator+=(const T& x)
{// Add x to each element of (*this).
	for (int i = 0; i < 3 * n - 2; i++)
		t[i] += x;
	return *this;
}


template<class T>
TridiagonalMatrix<T> TridiagonalMatrix<T>::Transpose()
{// Compute the transpose of *this.
	
	// create result array w
	TridiagonalMatrix<T> w(n);
	// copy lower diagonal of *this to
	// upper diagonal of w and upper of
	// *this to lower of w
	for (int i = 0; i < n - 1; i++) 
	{
		w.t[2 * n - 1 + i] = t[i];
		w.t[i] = t[2 * n - 1 + i];
	}
	
	// copy main diagonal of *this to
	// main diagonal of w
	for (i = n - 1; i < 2 * n - 1; i++)
		w.t[i] = t[i];
	
	return w;
}


template<class T>
ostream& operator<<(ostream& out, const TridiagonalMatrix<T>& x)
{// Put the elements of x into the stream out.
	out << "Lower diagonal is" << endl;
	for (int i = 0; i < x.n - 1; i++)
		out << x.t[i] << "  ";
	out << endl;
	
	out << "Main diagonal is" << endl;
	for (i = x.n - 1; i < 2 * x.n - 1; i++)
		out << x.t[i] << "  ";
	out << endl;
	
	out << "Upper diagonal is" << endl;
	for (i = 2 * x.n - 1; i < 3 * x.n - 2; i++)
		out << x.t[i] << "  ";
	out << endl;
	
	return out;
}

// overload >>
template<class T>
istream& operator>>(istream& in, TridiagonalMatrix<T>& x)
{// Input the tridiagonal matrix.
	
	cout << "Enter number of rows"
        << endl;
	in >> x.n;
	if (x.n < 0) 
		throw BadInput();
	
	// input terms
	cout << "Enter lower diagonal" << endl;
	for (int i = 0; i < x.n - 1; i++)
		in >> x.t[i];
	
	cout << "Enter main diagonal" << endl;
	for (i = x.n - 1; i < 2 * x.n - 1; i++)
		in >> x.t[i];
	
	cout << "Enter upper diagonal" << endl;
	for (i = 2 * x.n - 1; i < 3 * x.n - 2; i++)
		in >> x.t[i];
	
	return in;
}

#endif