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	PolynomialView Class Template Reference

#include "vigra/polynomial.hxx"

Inheritance diagram for PolynomialView:

Public Types
typedef T	value_type
typedef NumericTraits< T >::RealPromote	RealPromote
typedef NumericTraits< RealPromote >::ValueType	Real
typedef NumericTraits< RealPromote >::ComplexPromote	Complex
typedef T *	iterator
typedef T const *	const_iterator
Public Methods
	PolynomialView (T *coeffs, unsigned int order, double epsilon=1.0e-14)
T &	operator[] (unsigned int i)
	Access the coefficient of x^i.
T const &	operator[] (unsigned int i) const
	Access the coefficient of x^i.
template<class V> PromoteTraits< T, V >::Promote	operator() (V v) const
void	differentiate (unsigned int n=1)
void	deflate (T const &r, unsigned int multiplicity=1)
void	forwardDeflate (T const &v)
void	forwardBackwardDeflate (T v)
void	backwardDeflate (T v)
void	deflateConjugatePair (Complex const &v)
void	minimizeOrder (double epsilon=0.0)
void	normalize ()
iterator	begin ()
iterator	end ()
const_iterator	begin () const
const_iterator	end () const
unsigned int	size () const
unsigned int	order () const
double	epsilon () const
void	setEpsilon (double eps)

Detailed Description

template<class T>
class vigra::PolynomialView< T >

Polynomial interface for an externally managed array.

The coefficient type T can be either a scalar or complex (compatible to std::complex) type.

See also:

vigra::Polynomial, vigra::StaticPolynomial, polynomialRoots()

#include "vigra/polynomial.hxx"
Namespace: vigra

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Member Typedef Documentation

typedef NumericTraits<RealPromote>::ComplexPromote Complex

Complex type associated with RealPromote Reimplemented in Polynomial, and StaticPolynomial.

typedef T const* const_iterator

Const iterator for the coefficient sequence Reimplemented in Polynomial, and StaticPolynomial.

typedef T* iterator

Iterator for the coefficient sequence Reimplemented in Polynomial, and StaticPolynomial.

typedef NumericTraits<RealPromote>::ValueType Real

Scalar type associated with RealPromote Reimplemented in Polynomial, and StaticPolynomial.

typedef NumericTraits<T>::RealPromote RealPromote

Promote type of value_type used for polynomial calculations

typedef T value_type

Coefficient type of the polynomial Reimplemented in Polynomial, and StaticPolynomial.

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Constructor & Destructor Documentation

PolynomialView (  T *    coeffs, unsigned int    order, double    epsilon = 1.0e-14 )  [inline]

Construct from a coefficient array of given order. The externally managed array must have length order+1 and is interpreted as representing the polynomial: coeffs[0] + x * coeffs[1] + x * x * coeffs[2] + ... The coefficients are not copied, we only store a pointer to the array.epsilon (default: 1.0e-14) determines the precision of subsequent algorithms (especially root finding) performed on the polynomial.

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Member Function Documentation

void backwardDeflate (  T    v )

Backward-deflate the polynomial at the root r. The behavior of this function is undefined if r is not a root. Backward deflation is best if r is the snallest root (by magnitude).

const_iterator begin (    )  const [inline]

Get const_iterator for the coefficient sequence.

iterator begin (    )  [inline]

Get iterator for the coefficient sequence.

void deflate (  T const &    r, unsigned int    multiplicity = 1 )

Deflate the polynomial at the root r with the given multiplicity. The behavior of this function is undefined if r is not a root with at least the given multiplicity. This function calls forwardBackwardDeflate().

void deflateConjugatePair (  Complex const &    v )

Deflate the polynomial with the complex conjugate roots r and conj(r). The behavior of this function is undefined if these are not roots.

void differentiate (  unsigned int    n = 1 )

Differentiate the polynomial n times.

const_iterator end (    )  const [inline]

Get end const_iterator for the coefficient sequence.

iterator end (    )  [inline]

Get end iterator for the coefficient sequence.

double epsilon (    )  const [inline]

Get requested precision for polynomial algorithms (especially root finding).

void forwardBackwardDeflate (  T    v )

Forward/backward eflate the polynomial at the root r. The behavior of this function is undefined if r is not a root. Combined forward/backward deflation is best if r is an ontermediate root or we don't know r's relation to the other roots of the polynomial.

void forwardDeflate (  T const &    v )

Forward-deflate the polynomial at the root r. The behavior of this function is undefined if r is not a root. Forward deflation is best if r is the biggest root (by magnitude).

void minimizeOrder (  double    epsilon = 0.0 )

Adjust the polynomial's order if the highest coefficients are near zero. The order is reduced as long as the absolute value does not exceed the given epsilon.

void normalize (    )

Normalize the polynomial, i.e. dived by the highest coefficient.

PromoteTraits< T, U >::Promote operator() (  V    v )  const

Evaluate the polynomial at the point v Multiplication must be defined between the types V and PromoteTraits<T, V>Promote. If both V and V are scalar, the result will be a scalar, otherwise it will be complex.

unsigned int order (    )  const [inline]

Get order of the polynomial.

void setEpsilon (  double    eps )  [inline]

Set requested precision for polynomial algorithms (especially root finding).

unsigned int size (    )  const [inline]

Get length of the coefficient sequence (order() + 1).

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

• vigra/polynomial.hxx

© Ullrich Köthe (koethe@informatik.uni-hamburg.de) Cognitive Systems Group, University of Hamburg, Germany

html generated using doxygen and Python VIGRA 1.5.0 (7 Dec 2006)