17 #ifndef __deal2__polynomial_h
18 #define __deal2__polynomial_h
22 #include <deal.II/base/config.h>
24 #include <deal.II/base/subscriptor.h>
25 #include <deal.II/base/point.h>
26 #include <deal.II/base/std_cxx1x/shared_ptr.h>
30 DEAL_II_NAMESPACE_OPEN
53 template <
typename number>
80 const unsigned int evaluation_point);
93 number
value (
const number x)
const;
104 void value (
const number x,
105 std::vector<number> &values)
const;
112 unsigned int degree ()
const;
121 void scale (
const number factor);
138 template <
typename number2>
139 void shift (
const number2 offset);
180 void print(std::ostream &out)
const;
186 template <
class Archive>
187 void serialize (Archive &ar,
const unsigned int version);
194 static void scale (std::vector<number> &coefficients,
195 const number factor);
200 template <
typename number2>
201 static void shift (std::vector<number> &coefficients,
202 const number2 shift);
207 static void multiply (std::vector<number> &coefficients,
208 const number factor);
253 template <
typename number>
264 const double coefficient = 1.);
279 std::vector<Polynomial<number> >
286 static std::vector<number>
make_vector(
unsigned int n,
287 const double coefficient);
318 const unsigned int support_point);
329 std::vector<Polynomial<double> >
341 const unsigned int support_point,
342 std::vector<double> &a);
353 std::vector<Polynomial<double> >
394 std::vector<Polynomial<double> >
439 static const std::vector<double> &
473 Lobatto (
const unsigned int p = 0);
482 static std::vector<Polynomial<double> >
565 std::vector<Polynomial<double> >
581 static const std::vector<double> &
652 static std::vector<Polynomial<double> >
662 namespace Polynomials
664 template <
typename number>
668 in_lagrange_product_form (false),
674 template <
typename number>
679 if (in_lagrange_product_form ==
true)
681 return lagrange_support_points.size();
686 return coefficients.size() - 1;
692 template <
typename number>
697 if (in_lagrange_product_form ==
false)
702 const unsigned int m=coefficients.size();
703 number value = coefficients.back();
704 for (
int k=m-2; k>=0; --k)
705 value = value*x + coefficients[k];
711 const unsigned int m = lagrange_support_points.size();
713 for (
unsigned int j=0; j<m; ++j)
714 value *= x-lagrange_support_points[j];
715 value *= lagrange_weight;
722 template <
typename number>
723 template <
class Archive>
731 ar &in_lagrange_product_form;
732 ar &lagrange_support_points;
737 DEAL_II_NAMESPACE_CLOSE
void serialize(Archive &ar, const unsigned int version)
void scale(const number factor)
void transform_into_standard_form()
LagrangeEquidistant(const unsigned int n, const unsigned int support_point)
void shift(const number2 offset)
static std::vector< Polynomial< number > > generate_complete_basis(const unsigned int degree)
Legendre(const unsigned int p)
Polynomial< number > & operator-=(const Polynomial< number > &p)
static std::vector< std_cxx1x::shared_ptr< const std::vector< double > > > recursive_coefficients
static void compute_coefficients(const unsigned int p)
Monomial(const unsigned int n, const double coefficient=1.)
bool in_lagrange_product_form
Polynomial< number > primitive() const
bool operator==(const Polynomial< number > &p) const
number value(const number x) const
Polynomial< number > & operator*=(const double s)
static std::vector< Polynomial< double > > generate_complete_basis(const unsigned int degree)
#define Assert(cond, exc)
::ExceptionBase & ExcEmptyObject()
static std::vector< number > make_vector(unsigned int n, const double coefficient)
HermiteInterpolation(const unsigned int p)
std::vector< double > compute_coefficients(const unsigned int p)
Lobatto(const unsigned int p=0)
std::vector< Polynomial< double > > generate_complete_Lagrange_basis(const std::vector< Point< 1 > > &points)
Hierarchical(const unsigned int p)
static std::vector< Polynomial< double > > generate_complete_basis(const unsigned int degree)
static std::vector< std_cxx1x::shared_ptr< const std::vector< double > > > recursive_coefficients
Polynomial< number > derivative() const
std::vector< number > coefficients
static std::vector< Polynomial< double > > generate_complete_basis(const unsigned int degree)
void print(std::ostream &out) const
static const std::vector< double > & get_coefficients(const unsigned int k)
static void compute_coefficients(const unsigned int n, const unsigned int support_point, std::vector< double > &a)
std::vector< number > lagrange_support_points
static void compute_coefficients(const unsigned int p)
static const std::vector< double > & get_coefficients(const unsigned int p)
unsigned int degree() const
static std::vector< Polynomial< double > > generate_complete_basis(const unsigned int p)
static std::vector< std_cxx1x::shared_ptr< const std::vector< double > > > shifted_coefficients
static void multiply(std::vector< number > &coefficients, const number factor)
Polynomial< number > & operator+=(const Polynomial< number > &p)
static std::vector< Polynomial< double > > generate_complete_basis(const unsigned int p)