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/*
* Declaration of class Grid 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: grid.h,v 1.1 2005/11/14 01:56:58 e_gourgoulhon Exp $
* $Log: grid.h,v $
* Revision 1.1 2005/11/14 01:56:58 e_gourgoulhon
* First version
*
*
* $Header: /cvsroot/Lorene/School05/Monday/grid.h,v 1.1 2005/11/14 01:56:58 e_gourgoulhon Exp $
*
*/
#ifndef __GRID_H_
#define __GRID_H_
//----------------------------------//
// class Grid //
//----------------------------------//
/** Set of nodes in the interval [-1,1]. \ingroup (grid)
*
*/
class Grid {
// Data :
// -----
protected:
const int nn ; ///< \e N = number of nodes - 1
double* xx ; ///< Values of the nodes (pointer to an array of size \c nn+1)
// Constructors - Destructor
// -------------------------
public:
/** Standard constructor.
* @param nb_nodes number of nodes
* @param xi array of size \c nb_nodes containing the abscissas of the nodes
*/
Grid(int nb_nodes, double* xi) ;
Grid(const Grid& ) ; ///< Copy constructor
protected:
/** Constructor to be used only by derived classes (hence protected)
* @param nb_nodes number of nodes
*/
Grid(int nb_nodes) ;
public:
virtual ~Grid() ; ///< Destructor
// Mutators / assignment
// ---------------------
public:
/// Assignment to another Grid
void operator=(const Grid&) ;
// Accessors
// ---------
public:
int n() const ; ///< returns \e N, i.e. the number of nodes - 1
double operator()(int i) const ; ///< returns value of node no. \c i
/** Graphical display of the node points.
*
* @param color color of the points (drawn as small circles) :
* \li 0 : black (background)
* \li 1 : white (default)
* \li 2 : red
* \li 3 : green
* \li 4 : blue
* \li 5 : cyan
* \li 6 : magenta
* \li 7 : yellow
* \li 8 : orange
* \li 9 : green + yellow
* \li 10 : green + cyan
* \li 11 : blue + cyan
* \li 12 : blue + magenta
* \li 13 : red + magenta
* \li 14 : dark gray
* \li 15 : light gray
* @param nfig index of the figure (in the range [0,99])
* to be used for the plot: if this figure does not exist,
* it will be created with the device name \c device provided by the last
* argument.
* @param ymin lower bound on y of the graphical window (used only if a new
* figure must be created)
* @param ymax upper bound on y of the graphical window (used only if a new
* figure must be created)
* @param title title of the figure (used only if a new figure must be created)
* @param label_y y legend of the figure (used only if a new
* figure must be created)
* @param device type of graphical device (default value = 0x0, will result in
* interactive choice) (used only if a new
* figure must be created)
*/
void plot(int color = 1, int nfig = 0, double ymin = -1.,
double ymax = 1., const char* title = 0x0,
const char* label_y = 0x0, const char* device = 0x0) const ;
// Computation
// -----------
public:
/** Lagrange polynomials (characteristic polynomials).
* The Lagrange polynomial no. \e i is the unique polynomial
* \f$\ell_i(x)\f$ of degree \e N such that
* \f$\ell_i(x_{j})=\delta_{ij}\f$. It is also called \e cardinal
* \e polynomial associated with the node \f$x_i\f$
* @param i number of Lagrange polynomial \f$\ell_i\f$
* @param x point \e x in [-1,1] where the Lagrange polynomial is to
* be evaluated
* @return value of \f$\ell_i(x)\f$
*/
double lagrange(int i, double x) const ;
/** Nodal polynomial.
* The nodal polynomoal is the unique polynomial of degree \e N + 1
* and leading coefficient 1, the roots of which are the \e N +1 nodes
* \f$x_i\f$.
*
* @param x point \e x in [-1,1] where the Lagrange polynomial is to
* be evaluated
* @return value of the nodal polynomial at \e x
*/
double nodal_polynomial(double x) const ;
/** Interpolation of a given function at the nodes
*
* @param (*f)(double) function to be interpolated
* @param x point \e x in [-1,1] where the interpolating polynomial
* associated with the nodes \f$x_i\f$ is to evaluated
* @return value of the interpolating polynomial at \e x
*/
double interpole(double (*f)(double), double x) const ;
/// Computes (an approximate value of) the Lebesgue constant
double lebesgue_constant() const ;
};
/// Display of an object of class \c Grid
ostream& operator<<(ostream& , const Grid& ) ;
//----------------------------------//
// class Grid_uniform //
//----------------------------------//
/** Uniform sampling of the interval [-1,1]. \ingroup (grid)
*
*/
class Grid_uniform : public Grid {
// Constructors - Destructor
// -------------------------
public:
/** Standard constructor.
* @param nb_nodes number of nodes
*/
Grid_uniform(int nb_nodes) ;
Grid_uniform(const Grid_uniform& ) ; ///< Copy constructor
virtual ~Grid_uniform() ; ///< Destructor
// Mutators / assignment
// ---------------------
public:
/// Assignment to another Grid_uniform
void operator=(const Grid_uniform&) ;
};
/// Display of an object of class \c Grid_uniform
ostream& operator<<(ostream& , const Grid_uniform& ) ;
//----------------------------------//
// class Grid_Legendre_Gauss //
//----------------------------------//
/** Legendre Gauss nodes in the interval [-1,1]. \ingroup (grid)
*
*/
class Grid_Legendre_Gauss : public Grid {
// Constructors - Destructor
// -------------------------
public:
/** Standard constructor.
* @param nb_nodes number of nodes
*/
Grid_Legendre_Gauss(int nb_nodes) ;
Grid_Legendre_Gauss(const Grid_Legendre_Gauss& ) ; ///< Copy constructor
virtual ~Grid_Legendre_Gauss() ; ///< Destructor
// Mutators / assignment
// ---------------------
public:
/// Assignment to another Grid_Legendre_Gauss
void operator=(const Grid_Legendre_Gauss&) ;
};
/// Display of an object of class \c Grid_Legendre_Gauss
ostream& operator<<(ostream& , const Grid_Legendre_Gauss& ) ;
//----------------------------------//
// class Grid_Legendre_GL //
//----------------------------------//
/** Legendre Gauss-Lobatto nodes in the interval [-1,1]. \ingroup (grid)
*
*/
class Grid_Legendre_GL : public Grid {
// Constructors - Destructor
// -------------------------
public:
/** Standard constructor.
* @param nb_nodes number of nodes
*/
Grid_Legendre_GL(int nb_nodes) ;
Grid_Legendre_GL(const Grid_Legendre_GL& ) ; ///< Copy constructor
virtual ~Grid_Legendre_GL() ; ///< Destructor
// Mutators / assignment
// ---------------------
public:
/// Assignment to another Grid_Legendre_GL
void operator=(const Grid_Legendre_GL&) ;
};
/// Display of an object of class \c Grid_Legendre_GL
ostream& operator<<(ostream& , const Grid_Legendre_GL& ) ;
//----------------------------------//
// class Grid_Chebyshev_Gauss //
//----------------------------------//
/** Chebyshev Gauss nodes in the interval [-1,1]. \ingroup (grid)
*
*/
class Grid_Chebyshev_Gauss : public Grid {
// Constructors - Destructor
// -------------------------
public:
/** Standard constructor.
* @param nb_nodes number of nodes
*/
Grid_Chebyshev_Gauss(int nb_nodes) ;
Grid_Chebyshev_Gauss(const Grid_Chebyshev_Gauss& ) ; ///< Copy constructor
virtual ~Grid_Chebyshev_Gauss() ; ///< Destructor
// Mutators / assignment
// ---------------------
public:
/// Assignment to another Grid_Chebyshev_Gauss
void operator=(const Grid_Chebyshev_Gauss&) ;
};
/// Display of an object of class \c Grid_Chebyshev_Gauss
ostream& operator<<(ostream& , const Grid_Chebyshev_Gauss& ) ;
//----------------------------------//
// class Grid_Chebyshev_GL //
//----------------------------------//
/** Chebyshev Gauss-Lobatto nodes in the interval [-1,1]. \ingroup (grid)
*
*/
class Grid_Chebyshev_GL : public Grid {
// Constructors - Destructor
// -------------------------
public:
/** Standard constructor.
* @param nb_nodes number of nodes
*/
Grid_Chebyshev_GL(int nb_nodes) ;
Grid_Chebyshev_GL(const Grid_Chebyshev_GL& ) ; ///< Copy constructor
virtual ~Grid_Chebyshev_GL() ; ///< Destructor
// Mutators / assignment
// ---------------------
public:
/// Assignment to another Grid_Chebyshev_GL
void operator=(const Grid_Chebyshev_GL&) ;
};
/// Display of an object of class \c Grid_Chebyshev_GL
ostream& operator<<(ostream& , const Grid_Chebyshev_GL& ) ;
#endif
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