libdeal.ii-dev 6.3.1-1.1 / usr / include / deal.II / base / polynomials_p.h

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//---------------------------------------------------------------------------
//    $Id: polynomials_p.h 20162 2009-11-25 04:24:45Z kanschat $
//    Version: $Name$
//
//    Copyright (C) 2004, 2005, 2006, 2009 by the deal.II authors
//
//    This file is subject to QPL and may not be  distributed
//    without copyright and license information. Please refer
//    to the file deal.II/doc/license.html for the  text  and
//    further information on this license.
//
//---------------------------------------------------------------------------
#ifndef __deal2__polynomials_P_h
#define __deal2__polynomials_P_h


#include <base/config.h>
#include <base/exceptions.h>
#include <base/tensor.h>
#include <base/point.h>
#include <base/polynomial.h>
#include <base/polynomial_space.h>
#include <base/table.h>

#include <vector>

DEAL_II_NAMESPACE_OPEN
/**
 * @addtogroup Polynomials
 * @{
 */

/**
 * This class implements the polynomial space of degree <tt>p</tt>
 * based on the monomials ${1,x,x^2,...}$. I.e. in <tt>d</tt>
 * dimensions it constructs all polynomials of the form $\prod_{i=1}^d
 * x_i^{n_i}$, where $\sum_i n_i\leq p$. The base polynomials are
 * given a specific ordering, e.g. in 2 dimensions:
 * ${1,x,y,xy,x^2,y^2,x^2y,xy^2,x^3,y^3,...}$. The ordering of the
 * monomials in $P_k1$ matches the ordering of the monomials in $P_k2$
 * for $k2>k1$.
 *
 * @author Ralf Hartmann, 2004
 */
template <int dim>
class PolynomialsP: public PolynomialSpace<dim>
{
  public:
				     /**
				      * Access to the dimension of
				      * this object, for checking and
				      * automatic setting of dimension
				      * in other classes.
				      */
    static const unsigned int dimension = dim;
    
				     /**
				      * Constructor. Creates all basis
				      * functions of $P_p$.
				      * @arg p: the degree of the
				      * polynomial space
				      */
    PolynomialsP (const unsigned int p);

				     /**
				      * Returns the degree <tt>p</tt>
				      * of the polynomial space
				      * <tt>P_p</tt>.
				      *
				      * Note, that this number is
				      * <tt>PolynomialSpace::degree()-1</tt>,
				      * compare definition in
				      * PolynomialSpace.
				      */
    unsigned int degree() const;

				     /**
				      * For the <tt>n</tt>th
				      * polynomial $p_n(x,y,z)=x^i y^j
				      * z^k$ this function gives the
				      * degrees i,j,k in the x,y,z
				      * directions.
				      */
    void directional_degrees(unsigned int n,
			     unsigned int (&degrees)[dim]) const;
    
  private:

				     /**
				      * Fills the <tt>index_map</tt>.
				      */
    void create_polynomial_ordering(std::vector<unsigned int> &index_map) const;

				     /**
				      * Degree <tt>p</tt> of the
				      * polynomial space $P_p$,
				      * i.e. the number <tt>p</tt>
				      * which was given to the
				      * constructor.
				      */
    const unsigned int p;
};

/** @} */

template <int dim>
inline unsigned int
PolynomialsP<dim>::degree() const
{
  return p;
}


template <int dim>
inline void
PolynomialsP<dim>::directional_degrees(unsigned int n,
				       unsigned int (&degrees)[dim]) const
{
  this->compute_index(n,degrees);
}

DEAL_II_NAMESPACE_CLOSE

#endif

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