#include <jacobi.hpp>
1D Jacobi polynomial
(excerpt from Karniadakis/Sherwin Appendix A) Jacobi polynomials are a family of polynomial to the singular Sturm-Liouville problem. A significant feature of these polynomials is that they are orthogonal in the interval
with respect to the function
Several functions related to the one-dimensional jacobi polynomials: Evaluation, evaluation of derivatives, plus computation of the roots via Newton's method.
Public Types | |
Typedefs | |
typedef T | value_type |
typedef Jacobi< N, T > | self_type |
Public Member Functions | |
Constructors, destructor | |
Jacobi (value_type a=value_type(0.0), value_type b=value_type(0.0)) | |
Jacobi (Jacobi const &p) | |
~Jacobi () | |
Operator overloads | |
self_type & | operator= (self_type const &p) |
value_type | operator() (value_type const &x) const |
Accessors | |
uint16_type | degree () const |
Methods | |
value_type | value (value_type const &x) const |
value_type | derivate (value_type const &x) const |
Static Public Attributes | |
Static values | |
static const int | order = N |
static const int | nOrder = N |
|
inline |
default values for a and b give the special case of Legendre polynomials
Jacobi< N, T >::value_type Feel::Jacobi< N, T >::operator() | ( | value_type const & | x | ) | const |
Evaluates the nth jacobi polynomial with weight parameters a,b at a point x. Recurrence relations implemented from the pseudocode given in Karniadakis and Sherwin, Appendix B
a and b are defaulted to 0 and the Jacobi polynomial is then the Legendre polynomial
x | point for polynomial evaluation |
x
|
inline |
Evaluates the nth jacobi polynomial with weight parameters a,b at a point x. Recurrence relations implemented from the pseudocode given in Karniadakis and Sherwin, Appendix B
a and b are defaulted to 0 and the Jacobi polynomial is then the Legendre polynomial
x | point for polynomial evaluation |
x
References Feel::Jacobi< N, T >::operator()().