MathPoly::detail Namespace Reference

Functions
void	EvaluatePolynomialWithDerivatives (const double *theCoeffs, int theDegree, std::complex< double > theX, std::complex< double > &theP, std::complex< double > &theDP, std::complex< double > &theD2P)
	Evaluate polynomial and its first two derivatives at x (complex version). Polynomial: c[n]*x^n + c[n-1]*x^(n-1) + ... + c[1]*x + c[0].
std::complex< double >	LaguerreIteration (const double *theCoeffs, int theDegree, std::complex< double > theX0, double theTol, int theMaxIter)
	Laguerre iteration to find one root of polynomial.
void	DeflateReal (double *theCoeffs, int &theDegree, double theRoot)
	Deflate polynomial by removing a real root. Divides p(x) by (x - root) to get q(x).
void	DeflateComplex (double *theCoeffs, int &theDegree, std::complex< double > theRoot)
	Deflate polynomial by removing a complex conjugate pair. Divides p(x) by (x^2 + b*x + c) where b = -2*Re(root), c = |root|^2.
double	RefineRealRoot (const double *theOrigCoeffs, int theOrigDegree, double theRoot)
	Refine a real root using Newton-Raphson.

Function Documentation

DeflateComplex()

void MathPoly::detail::DeflateComplex ( double * theCoeffs, int & theDegree, std::complex< double > theRoot )

inline

Deflate polynomial by removing a complex conjugate pair. Divides p(x) by (x^2 + b*x + c) where b = -2*Re(root), c = |root|^2.

Parameters

theCoeffs	input coefficients, output deflated coefficients
theDegree	polynomial degree (will be decremented by 2)
theRoot	complex root (its conjugate is also removed)

DeflateReal()

void MathPoly::detail::DeflateReal ( double * theCoeffs, int & theDegree, double theRoot )

inline

Deflate polynomial by removing a real root. Divides p(x) by (x - root) to get q(x).

Parameters

theCoeffs	input coefficients, output deflated coefficients
theDegree	polynomial degree (will be decremented)
theRoot	root to remove

EvaluatePolynomialWithDerivatives()

void MathPoly::detail::EvaluatePolynomialWithDerivatives ( const double * theCoeffs, int theDegree, std::complex< double > theX, std::complex< double > & theP, std::complex< double > & theDP, std::complex< double > & theD2P )

inline

Evaluate polynomial and its first two derivatives at x (complex version). Polynomial: c[n]*x^n + c[n-1]*x^(n-1) + ... + c[1]*x + c[0].

Parameters

theCoeffs	coefficients array (c[0] = constant term)
theDegree	polynomial degree
theX	evaluation point
theP	output: polynomial value P(x)
theDP	output: first derivative P'(x)
theD2P	output: second derivative P''(x)

LaguerreIteration()

std::complex< double > MathPoly::detail::LaguerreIteration ( const double * theCoeffs, int theDegree, std::complex< double > theX0, double theTol, int theMaxIter )

inline

Laguerre iteration to find one root of polynomial.

Parameters

theCoeffs	coefficients array
theDegree	polynomial degree
theX0	initial guess
theTol	convergence tolerance
theMaxIter	maximum iterations

Returns

refined root estimate

RefineRealRoot()

double MathPoly::detail::RefineRealRoot ( const double * theOrigCoeffs, int theOrigDegree, double theRoot )

inline

Refine a real root using Newton-Raphson.