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/*
* Declaration of class Ortho_poly and derived classes
*/
/*
* Copyright (c) 2005 Eric Gourgoulhon
*
* This file is part of LORENE.
*
* LORENE is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* LORENE is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with LORENE; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
/*
* $Id: ortho_poly.h,v 1.1 2005/11/14 01:57:00 e_gourgoulhon Exp $
* $Log: ortho_poly.h,v $
* Revision 1.1 2005/11/14 01:57:00 e_gourgoulhon
* First version
*
*
* $Header: /cvsroot/Lorene/School05/Monday/ortho_poly.h,v 1.1 2005/11/14 01:57:00 e_gourgoulhon Exp $
*
*/
#ifndef __ORTHO_POLY_H_
#define __ORTHO_POLY_H_
class Grid ;
//----------------------------------//
// class Ortho_poly //
//----------------------------------//
/** Base class for orthogonal polynomials on [-1,1]. \ingroup (poly)
* Storage of polynomials of an orthogonal family \f$(p_i)\f$ up to a
* given degree \e N.
* The class \c Ortho_poly is abstract: it cannot be instanciated.
*
*/
class Ortho_poly {
// Data :
// -----
protected:
const int nn ; ///< \e N = maximum degree of the polynomials
/** Pointer on the Gauss nodes
*/
mutable const Grid* p_gauss_nodes ;
/** Pointer on the Gauss weights
*/
mutable double* p_gauss_weights ;
/** Pointer on the gamma factors (squares of the polynomials with
* respect to the discrete scalar product associated with the
* Gauss nodes)
*/
mutable double* p_gauss_gamma ;
/** Pointer on the Gauss-Lobatto nodes
*/
mutable const Grid* p_gauss_lobatto_nodes ;
/** Pointer on the Gauss-Lobatto weights
*/
mutable double* p_gauss_lobatto_weights ;
/** Pointer on the gamma factors (square of the polynomials with
* respect to the discrete scalar product associated with the
* Gauss-Lobatto nodes)
*/
mutable double* p_gauss_lobatto_gamma ;
// Constructors - Destructor
// -------------------------
protected:
Ortho_poly(const Ortho_poly& ) ; ///< Copy constructor
/** Constructor to be used only by derived classes (hence protected)
* @param ni maximum degree \e N of the polynomials
*/
Ortho_poly(int ni) ;
public:
virtual ~Ortho_poly() ; ///< Destructor
// Mutators / assignment
// ---------------------
public:
/// Assignment to another Ortho_poly
void operator=(const Ortho_poly&) ;
// Accessors
// ---------
public:
int n() const ; ///< returns \e N, i.e. the maximum degree of the polynomials
// Computation
// -----------
public:
/** Weight function \f$w\f$.
*
* @param x point in [-1,1] where the weight function is to be evaluated
* @return value of \f$w(x)\f$
*/
virtual double weight(double x) const = 0 ;
/** Value of the polynomial \f$p_i\f$
*
* @param i no. of the polynomial
* @param x point in [-1,1] where the polynomial is to be evaluated
* @return value of \f$p_i(x)\f$
*
*/
virtual double operator()(int i, double x) const = 0 ;
/// Gauss nodes
virtual const Grid& gauss_nodes() const = 0 ;
/** Gauss weights
*
* @param i index of the weight
* @return weight \f$w_i\f$
*/
virtual double gauss_weight(int i) const = 0 ;
/** Gamma factor \f$\gamma_i\f$ (square of the polynomial
* number \e i with
* respect to the discrete scalar product associated with the
* Gauss nodes)
*/
virtual double gauss_gamma(int i) const = 0 ;
/// Gauss-Lobatto nodes
virtual const Grid& gauss_lobatto_nodes() const = 0 ;
/** Gauss-Lobatto weights
*
* @param i index of the weight
* @return weight \f$w_i\f$
*/
virtual double gauss_lobatto_weight(int i) const = 0 ;
/** Gamma factor \f$\gamma_i\f$ (square of the polynomial number
* \e i with
* respect to the discrete scalar product associated with the
* Gauss-Lobatto nodes)
*/
virtual double gauss_lobatto_gamma(int i) const = 0 ;
/** Coefficients of the interpolant polynomial through the
* Gauss nodes.
*
* @param (*f)(double) function to be interpolated
* @param cf [output] array containing the \e N+1 coefficients
* of the expansion of the interpolant on the basis polynomials.
* This array must be of size at least \e N+1 and must have
* been allocated by the user prior to the call of this method.
*/
void coef_interpolant_Gauss(double (*f)(double), double* cf) const ;
/** Coefficients of the interpolant polynomial through the
* Gauss-Lobatto nodes.
*
* @param (*f)(double) function to be interpolated
* @param cf [output] array containing the \e N+1 coefficients
* of the expansion of the interpolant on the basis polynomials.
* This array must be of size at least \e N+1 and must have
* been allocated by the user prior to the call of this method.
*/
void coef_interpolant_GL(double (*f)(double), double* cf) const ;
/** Coefficients of the expansion over the basis polynomials of the
* orthogonal projection on the space of polynomials of maximum
* degree \e N.
*
* @param (*f)(double) function to be projected
* @param cf [output] array containing the \e N+1 coefficients of the
* expansion over the basis polynomials of the
* orthogonal projection on the space of polynomials of maximum
* degree \e N.
* This array must be of size at least \e N+1 and must have
* been allocated by the user prior to the call of this method.
*/
virtual void coef_projection(double (*f)(double), double* cf) const = 0 ;
/** Value of some expansion over the polynomials:
* \f$\sum_{i=0}^N a_i\, p_i(x)\f$
*
* @param a array of size at least \e N+1 and storing the \e N+1
* coefficients \f$a_i\f$ of the expansion on the basis
* polynomials \f$p_i(x)\f$.
* For an interpolant polynomial, \e a is the array \c cf
* computed by the method
* \c coef_interpolant_Gauss (Gauss nodes) or
* \c coef_interpolant_GL (Gauss-Lobatto nodes)
* @param x point in [-1,1] where the series is to be evaluated
* @return value of \f$\sum_{i=0}^N a_i\, p_i(x)\f$
*/
double series(const double* a, double x) const ;
};
//----------------------------------//
// class Chebyshev_poly //
//----------------------------------//
/** Chebyshev polynomials. \ingroup (poly)
* Each instance of this class represents a family of Chebyshev polynomials
* \f$(T_i)\f$ up to a given degree \e N.
*
*/
class Chebyshev_poly : public Ortho_poly {
// Constructors - Destructor
// -------------------------
public:
/** Standard constructor
* @param ni maximum degree of the polynomials
*/
Chebyshev_poly(int ni ) ;
Chebyshev_poly(const Chebyshev_poly& ) ; ///< Copy constructor
public:
virtual ~Chebyshev_poly() ; ///< Destructor
// Mutators / assignment
// ---------------------
public:
/// Assignment to another Chebyshev_poly
void operator=(const Chebyshev_poly&) ;
// Computation
// -----------
public:
/** Weight function \f$w\f$.
*
* @param x point in [-1,1] where the weight function is to be evaluated
* @return \f$w(x)=1/\sqrt{1-x^2}\f$
*/
virtual double weight(double x) const ;
/** Value of the polynomial \f$p_i\f$
*
* @param i no. of the polynomial
* @param x point in [-1,1] where the polynomial is to be evaluated
* @return value of \f$p_i(x)\f$
*
*/
virtual double operator()(int i, double x) const ;
/// Gauss nodes
virtual const Grid& gauss_nodes() const ;
/** Gauss weights
*
* @param i index of the weight
* @return weight \f$w_i\f$
*/
virtual double gauss_weight(int i) const ;
/** Gamma factor \f$\gamma_i\f$ (square of the polynomial no. \e i with
* respect to the discrete scalar product associated with the
* Gauss nodes)
*/
virtual double gauss_gamma(int i) const ;
/// Gauss-Lobatto nodes
virtual const Grid& gauss_lobatto_nodes() const ;
/** Gauss-Lobatto weights
*
* @param i index of the weight
* @return weight \f$w_i\f$
*/
virtual double gauss_lobatto_weight(int i) const ;
/** Gamma factor \f$\gamma_i\f$ (square of the polynomial no. \e i with
* respect to the discrete scalar product associated with the
* Gauss-Lobatto nodes)
*/
virtual double gauss_lobatto_gamma(int i) const ;
/** Coefficients of the interpolant polynomial through the
* Gauss-Lobatto nodes via a FFT.
*
* @param (*f)(double) function to be interpolated
* @param cf [output] array of size containing the \e N+1 coefficients
* of the expansion of the interpolant on the Chebyshev
* polynomials.
* This array must be of size at least \e N+1 and must have
* allocated by the user prior to the call of this method.
*/
void coef_interpolant_GL_FFT(double (*f)(double), double* cf) const ;
/** Coefficients of the expansion over the Chebyshev polynomials of the
* orthogonal projection on the space of polynomials of maximum
* degree \e N.
*
* @param (*f)(double) function to be projected
* @param cf [output] array containing the \e N+1 coefficients of the
* expansion over the Chebyshev polynomials of the
* orthogonal projection on the space of polynomials of maximum
* degree \e N.
* This array must be of size at least \e N+1 and must have
* been allocated by the user prior to the call of this method.
*/
virtual void coef_projection(double (*f)(double), double* cf) const ;
};
/// Display of an object of class \c Chebyshev_poly
ostream& operator<<(ostream& , const Chebyshev_poly& ) ;
//----------------------------------//
// class Legendre_poly //
//----------------------------------//
/** Legendre polynomials. \ingroup (poly)
* Each instance of this class represents a family of Legendre polynomials
* \f$(T_i)\f$ up to a given degree \e N.
*
*/
class Legendre_poly : public Ortho_poly {
// Constructors - Destructor
// -------------------------
public:
/** Standard constructor
* @param ni maximum degree of the polynomials
*/
Legendre_poly(int ni ) ;
Legendre_poly(const Legendre_poly& ) ; ///< Copy constructor
public:
virtual ~Legendre_poly() ; ///< Destructor
// Mutators / assignment
// ---------------------
public:
/// Assignment to another Legendre_poly
void operator=(const Legendre_poly&) ;
// Computation
// -----------
public:
/** Weight function \f$w\f$.
*
* @param x point in [-1,1] where the weight function is to be evaluated
* @return \f$w(x)=1\f$ (= constant value 1 for Legendre polynomials)
*/
virtual double weight(double x) const ;
/** Value of the polynomial \f$p_i\f$
*
* @param i no. of the polynomial
* @param x point in [-1,1] where the polynomial is to be evaluated
* @return value of \f$p_i(x)\f$
*
*/
virtual double operator()(int i, double x) const ;
/// Gauss nodes
virtual const Grid& gauss_nodes() const ;
/** Gauss weights
*
* @param i index of the weight
* @return weight \f$w_i\f$
*/
virtual double gauss_weight(int i) const ;
/** Gamma factor \f$\gamma_i\f$ (square of the polynomial no. \e i with
* respect to the discrete scalar product associated with the
* Gauss nodes)
*/
virtual double gauss_gamma(int i) const ;
/// Gauss-Lobatto nodes
virtual const Grid& gauss_lobatto_nodes() const ;
/** Gauss-Lobatto weights
*
* @param i index of the weight
* @return weight \f$w_i\f$
*/
virtual double gauss_lobatto_weight(int i) const ;
/** Gamma factor \f$\gamma_i\f$ (square of the polynomial no. \e i with
* respect to the discrete scalar product associated with the
* Gauss-Lobatto nodes)
*/
virtual double gauss_lobatto_gamma(int i) const ;
/** Coefficients of the expansion over the Legendre polynomials of the
* orthogonal projection on the space of polynomials of maximum
* degree \e N.
*
* @param (*f)(double) function to be projected
* @param cf [output] array containing the \e N+1 coefficients of the
* expansion over the Legendre polynomials of the
* orthogonal projection on the space of polynomials of maximum
* degree \e N.
* This array must be of size at least \e N+1 and must have
* been allocated by the user prior to the call of this method.
*/
virtual void coef_projection(double (*f)(double), double* cf) const ;
};
/// Display of an object of class \c Legendre_poly
ostream& operator<<(ostream& , const Legendre_poly& ) ;
#endif
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