ug4
Public Member Functions | Static Public Member Functions | Protected Member Functions | List of all members
ug::BoundedEquidistantLagrange1D Class Reference

#include <lagrange1d.h>

+ Inheritance diagram for ug::BoundedEquidistantLagrange1D:

Public Member Functions

 BoundedEquidistantLagrange1D (const size_t i, const size_t degree, const size_t bound)
 
- Public Member Functions inherited from ug::Polynomial1D
size_t degree () const
 
Polynomial1D derivative () const
 returns the derivative of this polynomial as a polynomial More...
 
Polynomial1D & operator*= (const Polynomial1D &v)
 multiply by a polynomial More...
 
Polynomial1D & operator*= (number scale)
 multiply by a scalar More...
 
 Polynomial1D (const std::vector< number > &a)
 Constructor passing coefficients for the polynomial. More...
 
 Polynomial1D (size_t degree=0)
 Constructor producing zero polynomial of degree 'degree'. More...
 
number value (const number x) const
 evaluate the value of the polynom at x More...
 

Static Public Member Functions

static number position (const size_t i, const size_t degree)
 returns the position of the i'th interpolation point More...
 

Protected Member Functions

void compute_coeffs (const int i, const int p, const int b)
 computes the coefficients for passed interpolation points More...
 
- Protected Member Functions inherited from ug::Polynomial1D
void set_coefficients (const std::vector< number > &a)
 

Detailed Description

Bounded EquiDistant Lagrange Function

Creates for given order p, interpolation point i and upper bound 0 <= b <= p the polynomial

\[ \prod_{\substack{j=0\\j\neq i}}^{b} \frac{x - \frac{j}{p}}{\frac{i}{p} - \frac{j}{p}} \]

Thus, it is a polynomial of order b.

Constructor & Destructor Documentation

◆ BoundedEquidistantLagrange1D()

ug::BoundedEquidistantLagrange1D::BoundedEquidistantLagrange1D ( const size_t  i,
const size_t  degree,
const size_t  bound 
)
inline

creates a lagrange polynomial with equidistant interpolation points

Parameters
[in]inumber of interpolation point, where polynom is 1
[in]degreedegree of polynom
[in]boundPoint until lagrange points are included

References compute_coeffs(), ug::Polynomial1D::degree(), and UG_ASSERT.

Member Function Documentation

◆ compute_coeffs()

void ug::BoundedEquidistantLagrange1D::compute_coeffs ( const int  i,
const int  p,
const int  b 
)
inlineprotected

computes the coefficients for passed interpolation points

References p, and ug::Polynomial1D::set_coefficients().

Referenced by BoundedEquidistantLagrange1D().

◆ position()

static number ug::BoundedEquidistantLagrange1D::position ( const size_t  i,
const size_t  degree 
)
inlinestatic

returns the position of the i'th interpolation point

References ug::Polynomial1D::degree(), and UG_ASSERT.

The documentation for this class was generated from the following file: