Template Class poly¶

Defined in File opoly.hh

Inheritance Relationships¶

Derived Types¶

public opoly::Chebyshev< INT, REAL > (Template Class Chebyshev)
public opoly::Hermite< INT, REAL > (Template Class Hermite)
public opoly::Jacobi< INT, REAL > (Template Class Jacobi)
public opoly::Laguerre< INT, REAL > (Template Class Laguerre)
public opoly::Legendre< INT, REAL > (Template Class Legendre)

Class Documentation¶

template<typename INT, typename REAL> class opoly::poly¶

Base class defining an orthogonal polynomial

INT is a integer type, can be also unsigned
REAL is a floating point type, can be float or a high precision number class

Subclassed by opoly::Chebyshev< INT, REAL >, opoly::Hermite< INT, REAL >, opoly::Jacobi< INT, REAL >, opoly::Laguerre< INT, REAL >, opoly::Legendre< INT, REAL >

Public Types

typedef INT int_type¶

typedef int_type *int_pointer¶

typedef int_type const *int_const_pointer¶

typedef int_type int_reference¶

typedef int_type const &int_const_reference¶

typedef REAL real_type¶

typedef real_type *pointer¶

typedef real_type const *const_pointer¶

typedef real_type &reference¶

typedef real_type const &const_reference¶

Public Functions

inline poly()¶

inline virtual ~poly()¶

virtual real_type operator()(int_type n, const_reference x) const = 0¶

Evaluate the polynomial

Parameters

n – [in] the degree op the polynomial
x – [in] the value at which the polynomial is evaluated

Returns

the value \( p(x) \)

virtual int_type svar(int_type n, const_reference x) const = 0¶

Evaluate the sign variation of the corresponding sturm sequence.

Parameters

n – [in] the degree op the polynomial
x – [in] the value at which the polynomial is evaluated

Returns

the number of sign variations

virtual int_type eval(int_type n, const_reference x, reference p) const = 0¶

Evaluate the polynomial and the sign variation of the corresponding sturm sequence.

Parameters

n – [in] the degree op the polynomial
x – [in] the value at which the polynomial is evaluated
p – [out] the value \( p(x) \)

Returns

the number of sign variations

virtual int_type eval(int_type n, const_reference x, reference p, reference dp) const = 0¶

Evaluate the polynomial and its derivative. Moreover return the sign variation of the corresponding sturm sequence.

Parameters

n – [in] the degree op the polynomial
x – [in] the value at which the polynomial is evaluated
p – [out] the value \( p(x) \)
dp – [out] the value \( p'(x) \)

Returns

the number of sign variations

virtual int_type sequence(int_type n, const_reference x, pointer pvec) const = 0¶

Evaluate the Sturm sequence

Parameters

n – [in] the degree of the polynomial
x – [in] the value at which the polynomial is evaluated
pvec – [out] the sequence \( p_0(x) \), \( p_1(x) \), …, \( p_n(x) \) of the 3 term recurrence

Returns

the number of sign variations

virtual real_type weight(const_reference x) const = 0¶

Weight function of the orthogonal polynomial

Parameters: x – [in] the value at which the weight is evaluated