Polynomial< ftype, N > Class Template Reference

Detailed Description

template<typename ftype, int N>
class cy::Polynomial< ftype, N >

A general-purpose polynomial class.

This class can be used for easily generating and manipulating polynomials. It also offers interfaces to the polynomial evaluation and root finding functions.

#include <cyPolynomial.h>

Public Member Functions
ftype const &	operator[] (int i) const
	Access to the coefficients of the polynomial.
ftype &	operator[] (int i)
	Access to the coefficients of the polynomial.
ftype	operator() (ftype x) const
	Evaluates the polynomial at the given x value.
ftype	Eval (ftype x) const
	Evaluates the polynomial at x.
ftype	EvalWithDeriv (ftype &deriv, ftype x) const
	Evaluates the polynomial and its derivative at x.
Polynomial< ftype, N >	operator+ (Polynomial< ftype, N > const &p) const
	Adds two polynomials.
Polynomial< ftype, N >	operator- (Polynomial< ftype, N > const &p) const
	Subtracts two polynomials.
Polynomial< ftype, N >	operator* (ftype s) const
	Multiplies the polynomial with a scalar.
void	operator+= (Polynomial< ftype, N > const &p)
	Adds another polynomial to this one.
void	operator-= (Polynomial< ftype, N > const &p)
	Subtracts another polynomial from this one.
void	operator*= (ftype s)
	Multiplies this polynomial with a scalar.
template<int M>
Polynomial< ftype, N+M >	operator* (Polynomial< ftype, M > const &p) const
	Multiplies two polynomials and returns the resulting polynomial.
Polynomial< ftype, 2 *N >	Squared () const
	Multiplies the polynomial with itself and returns the resulting polynomial.
Polynomial< ftype, N-1 >	Derivative () const
	Returns the derivative of the polynomial.
Polynomial< ftype, N-1 >	Deflate (ftype root) const
	Returns the deflation of the polynomial with the given root.
Polynomial< ftype, N+1 >	Inflate (ftype root) const
	Returns the inflated polynomial using the given root.
template<bool boundError = false>
int	Roots (ftype roots[N], ftype xError=DefaultError()) const
	Finds all roots of the polynomial and returns the number of roots found.
template<bool boundError = false>
bool	FirstRoot (ftype &root, ftype xError=DefaultError()) const
	Finds the first root of the polynomial and returns true if a root is found.
template<bool boundError = false>
bool	HasRoot (ftype xError=DefaultError()) const
	Returns true if the polynomial has a root.
template<bool boundError = false, typename RootCallback >
void	ForEachRoot (RootCallback c, ftype xError=DefaultError()) const
	Calls the given callback function for each root of the polynomial.
template<bool boundError = false>
int	Roots (ftype roots[N], ftype xMin, ftype xMax, ftype xError=DefaultError()) const
	Finds all roots of the polynomial between xMin and xMax and returns the number of roots found.
template<bool boundError = false>
bool	FirstRoot (ftype &root, ftype xMin, ftype xMax, ftype xError=DefaultError()) const
	Finds the first root of the polynomial between xMin and xMax and returns true if a root is found.
template<bool boundError = false>
bool	HasRoot (ftype xMin, ftype xMax, ftype xError=DefaultError()) const
	Returns true if the polynomial has a root between xMin and xMax.
template<bool boundError = false, typename RootCallback >
void	ForEachRoot (RootCallback c, ftype xMin, ftype xMax, ftype xError=DefaultError()) const
	Calls the given callback function for each root of the polynomial between xMin and xMax.
bool	IsFinite () const
	Returns true if all coefficients are finite real numbers.

Public Attributes
ftype	coef [N+1]
	The coefficients of the polynomial.

Static Protected Member Functions
static ftype	DefaultError ()
	Returns the default error threshold for numerical root finding.