pbat::math::polynomial Namespace Reference

The namespace for the Polynomial module. More...

Classes
struct	DivergenceFreeBasis
	Divergence-free polynomial basis \( \left\{ \mathbf{P}_i(X) \; \text{s.t.} \; \nabla_X \mathbf{P}_i = 0 \right\} \) in dimensions \( d \) and order \( p \). More...
struct	MonomialBasis
	Polynomial basis \( \left\{ \Pi_{i=1}^{d} \mathbf{X}_i^{p_i} \; \text{s.t.} \; 0 \leq \sum_{i=1}^d p_i \leq p \right\} \) in dimensions \( d \) and order \( p \). More...
struct	OrthonormalBasis
	Orthonormal polynomial basis \( \left\{ P_i(X) \right\} \) in dimensions \( d \) and order \( p \). More...

Concepts
concept	CBasis
concept	CVectorBasis

Functions
template<auto N, class TScalar = Scalar>
bool	HasRoot (std::array< TScalar, N+1 > const &coeffs, TScalar min=std::numeric_limits< TScalar >::lowest(), TScalar max=std::numeric_limits< TScalar >::max())
	Check if a polynomial has a root in the range [min,max].
template<auto N, class TScalar = Scalar>
std::array< TScalar, N >	Roots (std::array< TScalar, N+1 > const &coeffs, TScalar min=std::numeric_limits< TScalar >::lowest(), TScalar max=std::numeric_limits< TScalar >::max())
	Computes all real roots of a degree N polynomial in the range [min,max].
template<auto N, class FOnRoot, class TScalar = Scalar>
bool	ForEachRoot (FOnRoot &&fOnRoot, std::array< TScalar, N+1 > const &coeffs, TScalar min=std::numeric_limits< TScalar >::lowest(), TScalar max=std::numeric_limits< TScalar >::max())
	Computes the each real root of a degree N polynomial in the range [min,max] in increasing order.

Detailed Description

The namespace for the Polynomial module.

Function Documentation

ForEachRoot()

template<auto N, class FOnRoot, class TScalar = Scalar>

bool pbat::math::polynomial::ForEachRoot ( FOnRoot && fOnRoot, std::array< TScalar, N+1 > const & coeffs, TScalar min = std::numeric_limits<TScalar>::lowest(), TScalar max = std::numeric_limits<TScalar>::max() )

inline

Computes the each real root of a degree N polynomial in the range [min,max] in increasing order.

Note

We use the expensive but most accurate method from [16]

Template Parameters

N	Degree of the polynomial.
FOnRoot	Callable type with signature bool(TScalar root).
TScalar	Scalar type of the polynomial.

Parameters

fOnRoot	Callable object to be called for each root. If the callable returns true, the iteration stops.
coeffs	Coefficients of the polynomial.
min	Minimum value of the search range.
max	Maximum value of the search range.

Returns

true if root finding is terminated by fOnRoot. Otherwise, returns false.

HasRoot()

template<auto N, class TScalar = Scalar>

bool pbat::math::polynomial::HasRoot ( std::array< TScalar, N+1 > const & coeffs, TScalar min = std::numeric_limits<TScalar>::lowest(), TScalar max = std::numeric_limits<TScalar>::max() )

inline

Check if a polynomial has a root in the range [min,max].

Note

We use the expensive but most accurate method from [16]

Template Parameters

N	The degree of the polynomial.
TScalar	The scalar type of the polynomial.

Parameters

coeffs	The coefficients of the polynomial.
min	The minimum value of the search range.
max	The maximum value of the search range.

Returns

true if the polynomial has a root, false otherwise.

Roots()

template<auto N, class TScalar = Scalar>

std::array< TScalar, N > pbat::math::polynomial::Roots ( std::array< TScalar, N+1 > const & coeffs, TScalar min = std::numeric_limits<TScalar>::lowest(), TScalar max = std::numeric_limits<TScalar>::max() )

inline

Computes all real roots of a degree N polynomial in the range [min,max].

Note

We use the expensive but most accurate method from [16]

Template Parameters

N	Degree of the polynomial.
TScalar	Scalar type of the polynomial.

Parameters

coeffs	Coefficients of the polynomial.
min	Minimum value of the search range.
max	Maximum value of the search range.

Returns

The roots of the polynomial at the head of the returned array, NaNs at the tail.