#ifndef ZERNIKE_H
#define ZERNIKE_H

/**
 @author Richard J. Mathar
 @since 2007-03-23
 <a href="http://www.strw.leidenuniv.nl/~mathar">Richard J. Mathar homepage</a>.
*/
#include <cmath>
#include <vector>

using namespace std ;

/** Representation of Noll's radial terms of Zernike polynomials.
* \latexonly
* See \cite{NollJOSA66}.
* \endlatexonly
* The normalization is
* \f$ \int_0^{1/2}x dx [Z_n^m(x)]^2 =1\f$, which implies that
* \f$ Z_n^m(x)= 2\sqrt{2(n+1)}R_n^m(2r)\f$ in Noll's \f$R\f$ notation
* with \f$ x=2r\f$.
* @since 2007-03-23
*/
class Zernike {
public:

	/** the quantum number. Also the maximum power of
	* the power basis (polynomial) expansion
	*/
	int n;

	Zernike(const int nodaln) ;

	double at(const double x, const int m) const ;

#if 0
	static double at(const double x, const int n, const int m) ;
#endif

	double powcoef(const int m, const int i) const ;

	double intgrl(const int m, const double xlo, const double xhi) const ;

	double Overl(const int m, const Zernike & oth, const int othm) const ;

	double gradOverl(const int m, const Zernike & oth, const int othm) const ;

#if 0
	static double powcoef(const int n, const int m, const int i) ;
#endif
	
protected:
private:

	/** the expansion coefficients in a polynomial basis, sorted
	* as coef[0]+coef[1]*x+coef[2]*x^2... The first m ones (which are zero)
	* are not stored, nor those others which vanish also.
	* @warn these refer to the \f$x\f$ interval between 0 and 1/2, not to
	* Noll's \f$r\f$ intervall from 0 to 1, where \f$r=2x\f$.
	*/
	vector<vector<double> > coef ;

	static double binom(const int n, int m) ;

} ; /* Zernike */

/** A collection of Zernike polynomials up to some maximum power in the
* radial variable.
* @since 2007-03-23
*/
class ZernikeBase {
public:

	/** the set of radial basis functions, Z[0] for n=0, Z[1] for n=1 etc
	*/
	static vector<Zernike> Z ;

	ZernikeBase() ;

	double at(const double x, const int n, const int m) ;

	double at(const double x, const vector<double> & coe, const int m) ;

	double Overl(const int n, const int m, const int nprime, const int mprime) ;

	double Overl(const int m, const vector<double> & coe, const int mprime, const vector<double> &coeprime) ;

	double gradOverl(const int n, const int m, const int nprime, const int mprime) ;

	double gradOverl(const int m, const vector<double> & coe, const int mprime, const vector<double> &coeprime) ;

	double powcoef(const int n, const int m, const int i) ;

	double intgrl(const int n, const int m, const double xlo, const double xhi) ;
	
protected:
private:
	void growto(const int n) ;
} ; /* ZernikeBase */

#endif /* ZERNIKE_H */