vnl_real_polynomial Class Reference

#include <vnl_real_polynomial.h>

List of all members.

Detailed Description

Evaluation of real polynomials at real and complex points.

vnl_real_polynomial represents a univariate polynomial with real coefficients, stored as a vector of doubles. This allows evaluation of the polynomial $p(x)$ at given values of $x$ , or of its derivative $p'(x)$ .

Roots may be extracted using the roots() method.

Definition at line 34 of file vnl_real_polynomial.h.

Public Member Functions

vnl_real_polynomial (vnl_vector< double > const &a)

Initialize polynomial.

vnl_real_polynomial (double const *a, unsigned len)

Initialize polynomial from C vector.

vnl_real_polynomial (double a)

Initialize polynomial from double.

vnl_real_polynomial (int d)

Initialize polynomial of a given degree.

bool operator== (vnl_real_polynomial const &p) const

comparison operator.

double evaluate (double x) const

Evaluate polynomial at value x.

double evaluate_integral (double x) const

Evaluate integral at x (assuming constant of integration is zero).

double evaluate_integral (double x1, double x2) const

Evaluate integral between x1 and x2.

double devaluate (double x) const

Evaluate derivative at value x.

vcl_complex< double > evaluate (vcl_complex< double > const &x) const

Evaluate polynomial at complex value x.

vcl_complex< double > devaluate (vcl_complex< double > const &x) const

Evaluate derivative at complex value x.

vnl_real_polynomial derivative () const

Return derivative of this polynomial.

vnl_real_polynomial primitive () const

Return primitive function (inverse derivative) of this polynomial.

int degree () const

Return the degree (highest power of x) of the polynomial.

double & operator[] (int i)

Access to the polynomial coefficients.

double operator[] (int i) const

Access to the polynomial coefficients.

const vnl_vector< double > & coefficients () const

Return the vector of coefficients.

vnl_vector< double > & coefficients ()

Return the vector of coefficients.

void set_coefficients (vnl_vector< double > const &coeffs)

void print (vcl_ostream &os) const

Print this polynomial to stream.

Protected Attributes

vnl_vector< double > coeffs_

The coefficients of the polynomial.

Related Functions

(Note that these are not member functions.)

vnl_real_polynomial operator+ (const vnl_real_polynomial &f1, const vnl_real_polynomial &f2)

Returns polynomial which is sum of two polynomials f1(x)+f2(x).

vnl_real_polynomial operator- (const vnl_real_polynomial &f1, const vnl_real_polynomial &f2)

Returns polynomial which is different of two polynomials f1(x)-f2(x).

double vnl_rms_difference (const vnl_real_polynomial &f1, const vnl_real_polynomial &f2, double x1, double x2)

Returns RMS difference between f1 and f2 over range [x1,x2].

Constructor & Destructor Documentation

vnl_real_polynomial::vnl_real_polynomial ( vnl_vector< double > const & a ) [inline]

Initialize polynomial.
The polynomial is $a[0] x^d + a[1] x^{d-1} + \cdots + a[d] = 0$ .
Definition at line 39 of file vnl_real_polynomial.h.

vnl_real_polynomial::vnl_real_polynomial ( double const * a,

unsigned len

) [inline]

Initialize polynomial from C vector.
The parameter len is the number of coefficients, one greater than the degree.
Definition at line 46 of file vnl_real_polynomial.h.

vnl_real_polynomial::vnl_real_polynomial ( double a ) [inline]

Initialize polynomial from double.
Useful when adding or multiplying a polynomial and a number.
Definition at line 52 of file vnl_real_polynomial.h.

vnl_real_polynomial::vnl_real_polynomial ( int d ) [inline]

Initialize polynomial of a given degree.

Definition at line 55 of file vnl_real_polynomial.h.

Member Function Documentation

vnl_vector<double>& vnl_real_polynomial::coefficients ( ) [inline]

Return the vector of coefficients.

Definition at line 99 of file vnl_real_polynomial.h.

const vnl_vector<double>& vnl_real_polynomial::coefficients ( ) const [inline]

Return the vector of coefficients.

Definition at line 97 of file vnl_real_polynomial.h.

int vnl_real_polynomial::degree ( ) const [inline]

Return the degree (highest power of x) of the polynomial.

Definition at line 89 of file vnl_real_polynomial.h.

vnl_real_polynomial vnl_real_polynomial::derivative ( ) const

Return derivative of this polynomial.

Definition at line 176 of file vnl_real_polynomial.cxx.

vcl_complex< double > vnl_real_polynomial::devaluate ( vcl_complex< double > const & x ) const

Evaluate derivative at complex value x.

Definition at line 71 of file vnl_real_polynomial.cxx.

double vnl_real_polynomial::devaluate ( double x ) const

Evaluate derivative at value x.

Definition at line 64 of file vnl_real_polynomial.cxx.

vcl_complex<double> vnl_real_polynomial::evaluate ( vcl_complex< double > const & x ) const

Evaluate polynomial at complex value x.

double vnl_real_polynomial::evaluate ( double x ) const

Evaluate polynomial at value x.

double vnl_real_polynomial::evaluate_integral ( double x1,

double x2

) const

Evaluate integral between x1 and x2.

Definition at line 95 of file vnl_real_polynomial.cxx.

double vnl_real_polynomial::evaluate_integral ( double x ) const

Evaluate integral at x (assuming constant of integration is zero).

Definition at line 77 of file vnl_real_polynomial.cxx.

bool vnl_real_polynomial::operator== ( vnl_real_polynomial const & p ) const [inline]

comparison operator.

Definition at line 58 of file vnl_real_polynomial.h.

double vnl_real_polynomial::operator[] ( int i ) const [inline]

Access to the polynomial coefficients.

Definition at line 94 of file vnl_real_polynomial.h.

double& vnl_real_polynomial::operator[] ( int i ) [inline]

Access to the polynomial coefficients.

Definition at line 92 of file vnl_real_polynomial.h.

vnl_real_polynomial vnl_real_polynomial::primitive ( ) const

Return primitive function (inverse derivative) of this polynomial.
Since a primitive function is not unique, the one with constant = 0 is returned
Definition at line 188 of file vnl_real_polynomial.cxx.

void vnl_real_polynomial::print ( vcl_ostream & os ) const

Print this polynomial to stream.

Definition at line 199 of file vnl_real_polynomial.cxx.

void vnl_real_polynomial::set_coefficients ( vnl_vector< double > const & coeffs ) [inline]

Definition at line 101 of file vnl_real_polynomial.h.

Friends And Related Function Documentation

vnl_real_polynomial operator+ ( const vnl_real_polynomial & f1,

const vnl_real_polynomial & f2

) [related]

Returns polynomial which is sum of two polynomials f1(x)+f2(x).

Definition at line 101 of file vnl_real_polynomial.cxx.

vnl_real_polynomial operator- ( const vnl_real_polynomial & f1,

const vnl_real_polynomial & f2

) [related]

Returns polynomial which is different of two polynomials f1(x)-f2(x).

Definition at line 123 of file vnl_real_polynomial.cxx.

double vnl_rms_difference ( const vnl_real_polynomial & f1,

const vnl_real_polynomial & f2,

double x1,

double x2

) [related]

Returns RMS difference between f1 and f2 over range [x1,x2].
$\frac1{\sqrt{|x_2-x_1|}}\,\sqrt{\int_{x_1}^{x_2}\left(f_1(x)-f_2(x)\right)^2\,dx}$
Definition at line 163 of file vnl_real_polynomial.cxx.

Member Data Documentation

vnl_vector<double> vnl_real_polynomial::coeffs_ [protected]

The coefficients of the polynomial.
coeffs_.back() is the const term. coeffs_[n] is the coefficient of the x^(d-n) term, where d=coeffs_.size()-1
Invariant:
coeffs_size() >= 1;

Definition at line 112 of file vnl_real_polynomial.h.

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

core/vnl/vnl_real_polynomial.h
core/vnl/vnl_real_polynomial.cxx

Generated on Thu Jan 10 14:37:40 2008 for core/vnl by

1.4.4


Public Member Functions
	vnl_real_polynomial (vnl_vector< double > const &a)
	Initialize polynomial.
	vnl_real_polynomial (double const *a, unsigned len)
	Initialize polynomial from C vector.
	vnl_real_polynomial (double a)
	Initialize polynomial from double.
	vnl_real_polynomial (int d)
	Initialize polynomial of a given degree.
bool	operator== (vnl_real_polynomial const &p) const
	comparison operator.
double	evaluate (double x) const
	Evaluate polynomial at value x.
double	evaluate_integral (double x) const
	Evaluate integral at x (assuming constant of integration is zero).
double	evaluate_integral (double x1, double x2) const
	Evaluate integral between x1 and x2.
double	devaluate (double x) const
	Evaluate derivative at value x.
vcl_complex< double >	evaluate (vcl_complex< double > const &x) const
	Evaluate polynomial at complex value x.
vcl_complex< double >	devaluate (vcl_complex< double > const &x) const
	Evaluate derivative at complex value x.
vnl_real_polynomial	derivative () const
	Return derivative of this polynomial.
vnl_real_polynomial	primitive () const
	Return primitive function (inverse derivative) of this polynomial.
int	degree () const
	Return the degree (highest power of x) of the polynomial.
double &	operator[] (int i)
	Access to the polynomial coefficients.
double	operator[] (int i) const
	Access to the polynomial coefficients.
const vnl_vector< double > &	coefficients () const
	Return the vector of coefficients.
vnl_vector< double > &	coefficients ()
	Return the vector of coefficients.
void	set_coefficients (vnl_vector< double > const &coeffs)
void	print (vcl_ostream &os) const
	Print this polynomial to stream.
Protected Attributes
vnl_vector< double >	coeffs_
	The coefficients of the polynomial.
Related Functions
(Note that these are not member functions.)
vnl_real_polynomial	operator+ (const vnl_real_polynomial &f1, const vnl_real_polynomial &f2)
	Returns polynomial which is sum of two polynomials f1(x)+f2(x).
vnl_real_polynomial	operator- (const vnl_real_polynomial &f1, const vnl_real_polynomial &f2)
	Returns polynomial which is different of two polynomials f1(x)-f2(x).
double	vnl_rms_difference (const vnl_real_polynomial &f1, const vnl_real_polynomial &f2, double x1, double x2)
	Returns RMS difference between f1 and f2 over range [x1,x2].