// Author:  Douglas Wilhelm Harder
// Copyright (c) 2009 by Douglas Wilhelm Harder.  All rights reserved.

#ifdef CA_UWATERLOO_ALUMNI_DWHARDER_SPARSE_SYSTEMS

template <int N, Orientation D>
class Vector {
	private:
		double array[N];

	public:
		// Vector Mechanics
		Vector( double x = 0.0 );
		Vector( Vector const & );

		static Vector random();

		Vector &operator=( Vector const & );

		double &operator()( int );
		double operator()( int ) const;

		// Vector Functions
		double norm() const;
		double norm( int ) const;

		// Vector-Vector Functions
		Vector &operator+=( Vector const & );
		Vector &operator-=( Vector const & );
		Vector &operator*=( Vector const & );
		Vector &operator/=( Vector const & );

		// Vector-Scalar Functions
		Vector &operator+=( double );
		Vector &operator-=( double );
		Vector &operator*=( double );
		Vector &operator/=( double );

		// Vector Streaming/Printing
		void details() const;
		void matlab( std::string const & ) const;

	// Vector Functions

	template <int Nt>
	friend Vector<Nt, COLUMN> transpose( Vector<Nt, ROW> const & );

	template <int Nt>
	friend Vector<Nt, ROW> transpose( Vector<Nt, COLUMN> const & );

	// Matrix-Vector Functions

	template <int Mt, int Nt>
	friend Vector<Nt, ROW> operator*( Vector<Mt, ROW> const &, Matrix<Mt, Nt> const & );

	template <int Mt, int Nt>
	friend Vector<Mt, COLUMN> operator*( Matrix<Mt, Nt> const &, Vector<Nt, COLUMN> const & );

	template <int Nt>
	friend Vector<Nt, COLUMN> &operator*=( Matrix<Nt, Nt> const &, Vector<Nt, COLUMN> & );

	template <int Nt>
	friend Vector<Nt, ROW> operator*=( Vector<Nt, ROW> &, Matrix<Nt, Nt> const & );

	template <int Mt, int Nt>
	friend Vector<Mt, COLUMN> matrix_vector_product( Matrix<Mt, Nt> const &, Vector<Nt, COLUMN> const &, Product );

	template <int Mt, int Nt>
	friend Vector<Nt, ROW> vector_matrix_product( Vector<Mt, ROW> const &, Matrix<Mt, Nt> const &, Product );

	// Vector-Vector Functions

	template <int Nt>
	friend double operator*( Vector<Nt, ROW> const &, Vector<Nt, COLUMN> const & );

	// Vector-Scalar Functions
	template <int Nt, Orientation Dt>
	friend Vector<Nt, Dt> operator-( double, Vector<Nt, Dt> const & );

	template <int Nt, Orientation Dt>
	friend Vector<Nt, Dt> operator/( double, Vector<Nt, Dt> const & );

	// Matrix Solvers

	template <int Nt>
	friend Vector<Nt, COLUMN> diagonal_solve( Matrix<Nt, Nt> const &, Vector<Nt, COLUMN> const & );

	template <int Nt>
	friend Vector<Nt, COLUMN> backward_substitution( Matrix<Nt, Nt> const &, Vector<Nt, COLUMN> const &, bool = false );

	template <int Nt>
	friend Vector<Nt, COLUMN> forward_substitution( Matrix<Nt, Nt> const &, Vector<Nt, COLUMN> const &, bool = false );

	template <int Nt>
	friend Vector<Nt, COLUMN> jacobi( Matrix<Nt, Nt> const &, Vector<Nt, COLUMN> const &, int, double );

	template <int Nt>
	friend Vector<Nt, COLUMN> gauss_seidel( Matrix<Nt, Nt> const &, Vector<Nt, COLUMN> const &, int, double );

	// Vector Streaming

	template <int Nt>
	friend std::ostream &operator<<( std::ostream &, Vector<Nt, ROW> const & );

	template <int Nt>
	friend std::ostream &operator<<( std::ostream &, Vector<Nt, COLUMN> const & );

	template <int Mt, int Nt>
	friend class Matrix;
};

#include "vector_mechanics.cpp"
#include "vector_functions.cpp"
#include "vector_scalar_operations.cpp"
#include "vector_vector_operations.cpp"
#include "vector_streaming.cpp"

#endif