cbm::algo::kf::math Namespace Reference

Functions
constexpr size_t	NofPolCoefficients (size_t N, size_t M)
	Number of coefficients in a polynomial.
template<size_t N, typename T >
constexpr T	Horner (const T *c, const T &x)
	Horner's scheme for a 1D-polynomial estimation.
template<size_t N, typename T , typename... Args>
constexpr T	Horner (const T *c, const T &x1, Args... xI)
	Horner's scheme for a multidvariable polynomial estimation.

Function Documentation

Horner() [1/2]

template<size_t N, typename T >

T cbm::algo::kf::math::Horner ( const T * c, const T & x )

constexpr

Horner's scheme for a 1D-polynomial estimation.

Template Parameters

T	Underlying data type
N	Degree of the polynomial

Parameters

c	Pointer to the first element of the polynomial coefficients
x	Variable, for which the polynomial is to be estimated

The polynomial coefficients are indexed as follows:

P<N>(x) = x * (... * (x * (x * c[0] + c[1]) + c[2]) + ...) + c[N] = c[0] * x^N + c[1] * x^(N-1) + ... + c[N - 1] * x + c[N]

Definition at line 35 of file KfMath.h.

References Horner(), and x.

Referenced by Horner(), and Horner().

Horner() [2/2]

template<size_t N, typename T , typename... Args>

T cbm::algo::kf::math::Horner ( const T * c, const T & x1, Args... xI )

constexpr

Horner's scheme for a multidvariable polynomial estimation.

Template Parameters

T	Underlying data type
N	Degree of the polynomial

Parameters

c	Pointer to the first element of the polynomial coefficients
x1	First variable of the polynomial
xI	Other variables: x2, ..., xM

Example of the polynomial coefficient indexing for N = 4, M = 3:

P(x,y,z) = c[0] * x4 +

c[1] * x3y + c[2] * x3z + c[3] * x3 +

c[4] * x2y2 + c[5] * x2yz + c[6] * x2y + c[7] * x2z2 + c[8] * x2z + c[9] * x2 +

c[10] * xy3 + c[11] * xy2z + c[12] * xy2 + c[13] * xyz2 + c[14] * xyz + c[15] * xy + c[16] * xz3 + c[17] * xz2 + c[18] * xz + c[19] * x +

c[20] * y4 + c[21] * y3z + c[22] * y3 + c[23] * y2z2 + c[24] * y2z + c[25] * y2 + c[26] * yz3 + c[27] * yz2 + c[28] * yz + c[29] * y + c[30] * z4 + c[31] * z3 + c[32] * z2 + c[33] * z + c[34];

Definition at line 75 of file KfMath.h.

References Horner(), and NofPolCoefficients().

NofPolCoefficients()

size_t cbm::algo::kf::math::NofPolCoefficients ( size_t N, size_t M )

constexpr

Number of coefficients in a polynomial.

Parameters

N	Degree of the polynomial
M	Number of dimensions

Definition at line 19 of file KfMath.h.

References NofPolCoefficients().

Referenced by Horner(), and NofPolCoefficients().