Lagrange.h

Note

The documentation on this page was automatically extracted from the DOLFIN C++ code and may need to be edited or expanded.

class Lagrange

Parent class(es)

• Variable

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)

Lagrange(std::size_t q)

Constructor

Lagrange(const Lagrange &p)

Copy constructor

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

Specify point @param i (std::size_t) @param x (double)

std::size_t size() const

Return number of points @return std::size_t

std::size_t degree() const

Return degree @return std::size_t

double point(std::size_t i) const

Return point @param i (std::size_t)

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

Return value of polynomial i at given point x @param i (std::size_t) @param x (double)

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

Return value of polynomial i at given point x @param i (std::size_t) @param x (double)

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

Return derivate of polynomial i at given point x @param i (std::size_t) @param x (double)

double dqdx(std::size_t i)

Return derivative q (a constant) of polynomial @param i (std::size_t)

std::string str(bool verbose) const

Return informal string representation (pretty-print) @param verbose (bool)

Verbosity of output string