dolfin::Lagrange Class Reference

#include <Lagrange.h>

Inheritance diagram for dolfin::Lagrange:

Collaboration diagram for dolfin::Lagrange:

Public Member Functions
	Lagrange (std::size_t q)
	Constructor.
	Lagrange (const Lagrange &p)
	Copy constructor.
void	set (std::size_t i, double x)
std::size_t	size () const
std::size_t	degree () const
double	point (std::size_t i) const
double	operator() (std::size_t i, double x)
double	eval (std::size_t i, double x)
double	ddx (std::size_t i, double x)
double	dqdx (std::size_t i)
std::string	str (bool verbose) const
Public Member Functions inherited from dolfin::Variable
	Variable ()
	Create unnamed variable.
	Variable (const std::string name, const std::string label)
	Create variable with given name and label.
	Variable (const Variable &variable)
	Copy constructor.
virtual	~Variable ()
	Destructor.
const Variable &	operator= (const Variable &variable)
	Assignment operator.
void	rename (const std::string name, const std::string label)
	Rename variable.
std::string	name () const
	Return name.
std::string	label () const
	Return label (description)
std::size_t	id () const

Additional Inherited Members
Public Attributes inherited from dolfin::Variable
Parameters	parameters
	Parameters.

Detailed Description

Lagrange polynomial (basis) with given degree q determined by n = q + 1 nodal points.

Example: q = 1 (n = 2)

Lagrange p(1); p.set(0, 0.0); p.set(1, 1.0);

It is the callers responsibility that the points are distinct.

This creates a Lagrange polynomial (actually two Lagrange polynomials):

p(0,x) = 1 - x (one at x = 0, zero at x = 1) p(1,x) = x (zero at x = 0, one at x = 1)

Member Function Documentation

ddx()

double Lagrange::ddx	(	std::size_t	i,
		double	x
	)

Return derivate of polynomial i at given point x

Parameters

i	(std::size_t)
x	(double)

degree()

std::size_t Lagrange::degree

(

)

const

Return degree

Returns

std::size_t

dqdx()

double Lagrange::dqdx

(

std::size_t

i

)

Return derivative q (a constant) of polynomial

Parameters

i	(std::size_t)

eval()

double Lagrange::eval	(	std::size_t	i,
		double	x
	)

Return value of polynomial i at given point x

Parameters

i	(std::size_t)
x	(double)

operator()()

double Lagrange::operator()	(	std::size_t	i,
		double	x
	)

Return value of polynomial i at given point x

Parameters

i	(std::size_t)
x	(double)

point()

double Lagrange::point

(

std::size_t

i

)

const

Return point

Parameters

i	(std::size_t)

set()

void Lagrange::set	(	std::size_t	i,
		double	x
	)

Specify point

Parameters

i	(std::size_t)
x	(double)

size()

std::size_t Lagrange::size

(

)

const

Return number of points

Returns

std::size_t

str()

std::string Lagrange::str ( bool  verbose ) const

virtual

Return informal string representation (pretty-print)

Parameters

verbose

(bool) Verbosity of output string

Reimplemented from dolfin::Variable.

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

• /home/fenics/shared/dolfin/dolfin/math/Lagrange.h
• /home/fenics/shared/dolfin/dolfin/math/Lagrange.cpp