//	vektors.hh

/**
	@param	i	index
	@return		1/(i+1)^2
*/
double fu(const int i);

/**
	@param	n	vector length
	@param	i	index
	@return		sin(4*PI*(i-1)/(n-1)
*/
double fw(const int n, const int i);

/**	Calculates the inner product of two vectors.
	We assume that both vectors have the same length.
	@param	n	vector length
	@param	x	vector
	@param	y	vector
	@return		inner product
*/
double InnerProd( const int n, const double x[], const double y[] );

/**	Calculates Euclidian norm of a vector.
	@param	n	vector length
	@param	x	vector
	@return		Euclidian norm
*/
double EuklidNorm( const int n, const double x[] );

/**	Calculation of vector z via

	z[odd] = alpha*u + w  und  z[even] = u + beta*w
	@param	n	vector length
	@param	z	output vector
	@param  alpha	scalar
	@param	beta	scalar
	@param	x	input vector
	@param	y	input vector
*/
void Calc_z(const int n, double z[], const double alpha, const double beta,
		   const double x[], const double y[]);

/**
	Prints the first 40 components of a vector or
	the first two and the last two components of it
	if the vector is to long.
	@param	n	vector length
	@param	z	vector
*/
void Print(const int n, const double z[]);