class matrix_col { 

 public:

  int i;
  double *ptr00, *ptr10, *ptr20;

  matrix_col(){

    ptr00 = new double[Grids];
    ptr10 = new double[Grids];
    ptr20 = new double[Grids];

    for(i = 0; i < (Grids); i++){

      ptr00[i] = 0;
      ptr10[i] = 0;
      ptr20[i] = 0;
    }
  }

  //copy constructor
  matrix_col(const matrix_col &a){

    int i;
 
    ptr00 = new double[Grids];
    ptr10 = new double[Grids];
    ptr20 = new double[Grids];

    for(i = 0; i < (Grids); i++){

      ptr00[i] = a.ptr00[i];
      ptr10[i] = a.ptr10[i];
      ptr20[i] = a.ptr20[i];
    }
  }

  ~matrix_col(){

    delete [] ptr00;
    delete [] ptr10;
    delete [] ptr20;

  }

  friend matrix_col operator+(const matrix_col &, const matrix_col &);

};


// Overload + for ob1 + ob2.

matrix_col operator+(const matrix_col &left, const matrix_col &right)
{

  int i;
  matrix_col temp;

  for (i = 0; i < Grids; i++){

    temp.ptr00[i] = left.ptr00[i] + right.ptr00[i];
    temp.ptr10[i] = left.ptr10[i] + right.ptr10[i];
    temp.ptr20[i] = left.ptr20[i] + right.ptr20[i];
 
 }

  return temp;
}

#ifndef MATRIX_H_INCLUDED
#define MATRIX_H_INCLUDED

#include <iostream>
#include <vector>
#include <memory>
#include "vector.h"

template < class T >
class Matrix
{
public:
    Matrix(unsigned int n_cols = 0, unsigned int n_rows = 0);
	Matrix(const Matrix& m);

	void Output( )
	{
		for(int j = 0; j < Rows; j++)
		{
			for(int i = 0; i < Cols; i++)
			{
				std::cout << Data[j][i];
			}
			std::cout << std::endl;
		}
	}

	void SetColElements(const std::vector< std::vector< T > >& v, unsigned int col);
	void SetRowElements(const std::vector< std::vector< T > >& v, unsigned int row);
	void SetElement(unsigned int col, unsigned int row, T val);

	void InterchangeRows(unsigned int row_1, unsigned int row_2);
	void InterchangeCols(unsigned int col_1, unsigned int col_2);

	bool LowerTriangle( ) const;
	bool UpperTriangle( ) const;
	bool DiagonalMatrix( ) const;
    bool SquareMatrix( ) const;

	T Determinant( );

	void GaussElim(const Vector< T >&);
	void GaussJordanElim(const Vector< T >&);

	static Matrix< T > IdentityMatrix(unsigned int size);
	static Matrix< T > NullMatrix(unsigned int size);

    Matrix< T > Minor(unsigned int col, unsigned int row);

	Matrix< T >& operator = (const Matrix< T >&);
	Matrix< T >& operator += (const Matrix< T >&);
	Matrix< T >& operator -= (const Matrix< T >&);
	Matrix< T > operator * (const Matrix< T >&) const;
	Matrix< T > operator * (const T&) const;
	Matrix< T > operator *= (const T&);
	Matrix< T > operator - (const Matrix< T >&) const;
	Matrix< T > operator + (const Matrix< T >&) const;
private:
	unsigned int Rows, Cols;
    std::vector< std::vector< T > > Data;
};

template < class T >
Matrix< T >::Matrix< T >(unsigned int n_cols, unsigned int n_rows)
	: Cols(n_cols), Rows(n_rows)
{
	if(Cols > 0 && Rows > 0)
	{
		Data.reserve(Rows);
		for(int i = 0; i < Rows; i++)
		{
			Data.push_back(std::vector< T >( ));

			Data[i].reserve(Cols);
			Data[i].insert(Data[i].begin(), Cols, 0);
		}
	}
	else if(Cols < 0 && Rows < 0)
	{
		Cols = Rows = 0;
	}
}

template < class T >
Matrix< T >::Matrix< T >(const Matrix& m)
{
	*this = m;
}

template < class T >
void Matrix< T >::SetColElements(const std::vector< std::vector< T > >& v, unsigned int col)
{
	if(ls.size() == Rows && Cols != 0 && Rows != 0 && col > 0 && col < Cols)
	{
		for(int j = 0; j < Rows; j++)
		{
			Data[j][col] = v[j];
		}
	}
}

template < class T >
void Matrix< T >::SetRowElements(const std::vector< std::vector< T > >& v, unsigned int row)
{
	if(ls.size() == Rows && Cols != 0 && Rows != 0 && row > 0 && row < Rows)
	{
		for(int i = 0; i < Cols; i++)
		{
			Data[row][i] = v[i];
		}
	}
}

template < class T >
void Matrix< T >::SetElement(unsigned int col, unsigned int row, T val)
{
	if(col >= 0 && row >= 0 && col < Cols && row < Rows)
	{
		Data[row][col] = val;
	}
}

template < class T >
void Matrix< T >::InterchangeRows(unsigned int row_1, unsigned int row_2)
{
	if(row_1 != row_2 && (row_1 >= 0 && row_2 >= 0))
	{
		Data[row_1].swap(Data[row_2]);
	}
}

template < class T>
void Matrix< T >::InterchangeCols(unsigned int col_1, unsigned int col_2)
{
	// Parentheses for easier reading only
	// Make sure both columns are different and range in [0, Cols[
	if((col_1 != col_2) && (col_1 >= 0) && (col_2 >= 0) && (col_1 < Cols) && (col_2 < Cols))
	{
		for(int j = 0; j < Rows; j++)
		{
			T tmp = Data[j][col_1];
			Data[j][col_1] = Data[j][col_2];
			Data[j][col_2] = tmp;
		}
	}
}

template < class T >
bool Matrix< T >::LowerTriangle( ) const
{
	// Only square matrixes bigger than 0,0
	if(SquareMatrix() && (Cols != 0 && Rows != 0))
	{
		for(int j = 0; j < Rows; j++)
		{
			for(int i = 0; i < Cols; i++)
			{
				if(i > j && Data[j][i] != 0)
				{
					return false;
				}
			}
		}
	}
	else
	{
		return false;
	}
	return true;
}

template < class T >
bool Matrix< T >::UpperTriangle( ) const
{
	// Only square matrixes bigger than 0,0
	if(SquareMatrix() && (Cols != 0 && Rows != 0))
	{
		for(int j = 0; j < Rows; j++)
		{
			for(int i = 0; i < Cols; i++)
			{
				if(i < j && Data[j][i] != 0)
				{
					return false;
				}
			}
		}
	}
	else
	{
		return false;
	}
	return true;
}

template < class T >
bool Matrix< T >::DiagonalMatrix( ) const
{
	return (UpperTriangle( ) && LowerTriangle( ));
}

template < class T >
bool Matrix< T >::SquareMatrix( ) const
{
    return (Rows == Cols);
}

template < class T >
T Matrix< T >::Determinant( )
{
	if(SquareMatrix( ))
	{
		if(Cols == 0 && Rows == 0)
		{
			return static_cast< T >(0);
		}
		if(Cols == 1 && Rows == 1)
		{
			return Data[0][0];
		}

		if(UpperTriangle( ) || LowerTriangle( ))
		{
			int total = 1;
			for(int i = 0; i < Cols; i++)
			{
				total *= Data[i][i];
			}
			return total;
		}

		if(Cols == 2 && Rows == 2)
		{
			return (Data[0][0] * Data[1][1] - Data[0][1] * Data[1][0]);
		}
		if(Cols == 3 && Rows == 3)
		{
			return (Data[0][0] * Data[1][1] * Data[2][2] +
					Data[0][2] * Data[1][0] * Data[2][1] +
					Data[0][1] * Data[1][2] * Data[2][0] -
					Data[0][2] * Data[1][1] * Data[2][0] -
					Data[0][0] * Data[1][2] * Data[2][1] -
					Data[0][1] * Data[1][0] * Data[2][2]);
		}
		// Let's use the M = LU decomposition method for faster processing
		else
		{
			
		}
	}
}

template < class T >
void Matrix< T >::GaussElim(const Vector< T >& solution)
{

}

template < class T >
void Matrix< T >::GaussJordanElim(const Vector< T >& solution)
{

}

template < class T >
Matrix< T > Matrix< T >::IdentityMatrix(unsigned int size)
{
	Matrix< T > tmp(size, size);

	for(int j = 0; j < tmp.Rows; j++)
	{
		for(int i = 0; i < tmp.Cols; i++)
		{
			tmp.Data[j][i] = i == j ? 1 : 0;
		}
	}

	return tmp;
}

template < class T >
Matrix< T > Matrix< T >::NullMatrix(unsigned int size)
{
	return Matrix< T >(size, size);
}

template < class T >
Matrix< T > Matrix< T >::Minor(unsigned int col, unsigned int row)
{
	Matrix< T > tmp(col, row);

	if(SquareMatrix( ) && (Rows != 0 && Cols != 0))
	{
		int y = 0;

		// Move horizontally then down in the matrix
		for(int j = 0; j < Rows; j++)
		{

			if(j != row)
			{
				// We're on a new line...
				tmp.Data.push_back(std::vector< T >( ));
				for(int i = 0; i < Cols; i++)
				{
					if(i != col)
					{
						tmp.Data[y].push_back(Data[j][i]);
					}
				}
				y++;
			}
		}
		tmp.Cols = tmp.Data[0].size();
		tmp.Rows = tmp.Data.size();
	}

	return tmp;
}

template < class T >
Matrix< T >& Matrix< T >::operator = (const Matrix< T >& m)
{
	Rows = m.Rows;
	Cols = m.Cols;

	Data.assign(m.Data.begin(), m.Data.end());

	return *this;
}

template < class T >
Matrix< T >& Matrix< T >::operator += (const Matrix< T >& m)
{
	*this = *this + m;
	return *this;
}

template < class T >
Matrix< T >& Matrix< T >::operator -= (const Matrix< T >& m)
{
	*this = *this - m;
	return *this;
}

template < class T >
Matrix< T > Matrix< T >::operator * (const Matrix< T >& m) const
{
	// A Matrix A(a, b) and a matrix B(c, d) yield a matric C(b, c) when multiplied
	Matrix< T > tmp(Rows, m.Cols);

	if(Cols == m.Rows && Rows == m.Cols && Rows > 0 && Cols > 0)
	{
		for(int j_result = 0; j_result < Rows; j_result++)
		{
			for(int i_result = 0; i_result < m.Cols; i_result++)
			{
				int sum = 0;
				for(int j = 0, i = 0; j < m.Rows && i < Cols; j++, i++)
				{
					sum += Data[j_result][i] * m.Data[j][i_result];
				}
				tmp.Data[j_result][i_result] = sum;
			}
		}
	}

	return tmp;
}

template < class T >
Matrix< T > Matrix< T >::operator * (const T& val) const
{
	Matrix< T > tmp(Cols, Rows);
	tmp = *this;

	if(Rows > 0 && Cols > 0)
	{
		for(int j = 0; j < Rows; j++)
		{
			for(int i = 0; i < Cols; i++)
			{
				tmp.Data[j][i] *= val;
			}
		}
	}

	return tmp;
}

template < class T >
Matrix< T > Matrix< T >::operator *= (const T& val)
{
	// Slight overhead due to creation of temporary variable
	*this = *this * val;
	return *this;
}

template < class T >
Matrix< T > Matrix< T >::operator - (const Matrix< T >& m) const
{
	Matrix< T > tmp(Cols, Rows);

	if(Rows == m.Rows && Cols == m.Cols && Rows > 0 && Cols > 0)
	{
		for(int j = 0; j < Rows; j++)
		{
			for(int i = 0; i < Cols; i++)
			{
				tmp.Data[j][i] = Data[j][i] - m.Data[j][i];
			}
		}
	}

	return tmp;
}

template < class T >
Matrix< T > Matrix< T >::operator + (const Matrix< T >& m) const
{
	Matrix< T > tmp(Cols, Rows);

	if(Rows == m.Rows && Cols == m.Cols && Rows > 0 && Cols > 0)
	{
		for(int j = 0; j < Rows; j++)
		{
			for(int i = 0; i < Cols; i++)
			{
				tmp.Data[j][i] = Data[j][i] + m.Data[j][i];
			}
		}
	}

	return tmp;
}

#endif // MATRIX_H_INCLUDED