nc::polynomial Namespace Reference

Data Structures
class	Poly1d

Functions
template<typename dtype >
NdArray< double >	chebyshev_t (uint32 n, const NdArray< dtype > &inArrayX)
template<typename dtype >
double	chebyshev_t (uint32 n, dtype x)
template<typename dtype >
NdArray< double >	chebyshev_u (uint32 n, const NdArray< dtype > &inArrayX)
template<typename dtype >
double	chebyshev_u (uint32 n, dtype x)
template<typename dtype >
NdArray< double >	hermite (uint32 n, const NdArray< dtype > &inArrayX)
template<typename dtype >
double	hermite (uint32 n, dtype x)
template<typename dtype >
NdArray< double >	laguerre (uint32 n, const NdArray< dtype > &inArrayX)
template<typename dtype >
double	laguerre (uint32 n, dtype x)
template<typename dtype >
NdArray< double >	laguerre (uint32 n, uint32 m, const NdArray< dtype > &inArrayX)
template<typename dtype >
double	laguerre (uint32 n, uint32 m, dtype x)
template<typename dtype >
NdArray< double >	legendre_p (uint32 m, uint32 n, const NdArray< dtype > &inArrayX)
template<typename dtype >
double	legendre_p (uint32 m, uint32 n, dtype x)
template<typename dtype >
NdArray< double >	legendre_p (uint32 n, const NdArray< dtype > &inArrayX)
template<typename dtype >
double	legendre_p (uint32 n, dtype x)
template<typename dtype >
NdArray< double >	legendre_q (int32 n, const NdArray< dtype > &inArrayX)
template<typename dtype >
double	legendre_q (int32 n, dtype x)
template<typename dtype1 , typename dtype2 >
std::complex< double >	spherical_harmonic (uint32 n, int32 m, dtype1 theta, dtype2 phi)
template<typename dtype1 , typename dtype2 >
double	spherical_harmonic_i (uint32 n, int32 m, dtype1 theta, dtype2 phi)
template<typename dtype1 , typename dtype2 >
double	spherical_harmonic_r (uint32 n, int32 m, dtype1 theta, dtype2 phi)

Function Documentation

chebyshev_t() [1/2]

template<typename dtype >

NdArray< double > nc::polynomial::chebyshev_t	(	uint32	n,
		const NdArray< dtype > &	inArrayX
	)

Chebyshev Polynomial of the first kind. NOTE: Use of this function requires using the Boost includes.

Parameters

n	the order of the chebyshev polynomial
inArrayX	the input value

Returns

NdArray<double>

chebyshev_t() [2/2]

template<typename dtype >

double nc::polynomial::chebyshev_t	(	uint32	n,
		dtype	x
	)

Chebyshev Polynomial of the first kind. NOTE: Use of this function requires using the Boost includes.

Parameters

n	the order of the chebyshev polynomial
x	the input value

Returns

double

chebyshev_u() [1/2]

template<typename dtype >

NdArray< double > nc::polynomial::chebyshev_u	(	uint32	n,
		const NdArray< dtype > &	inArrayX
	)

Chebyshev Polynomial of the second kind. NOTE: Use of this function requires using the Boost includes.

Parameters

n	the order of the chebyshev polynomial
inArrayX	the input value

Returns

NdArray<double>

chebyshev_u() [2/2]

template<typename dtype >

double nc::polynomial::chebyshev_u	(	uint32	n,
		dtype	x
	)

Chebyshev Polynomial of the second kind. NOTE: Use of this function requires using the Boost includes.

Parameters

n	the order of the chebyshev polynomial
x	the input value

Returns

double

hermite() [1/2]

template<typename dtype >

NdArray< double > nc::polynomial::hermite	(	uint32	n,
		const NdArray< dtype > &	inArrayX
	)

Hermite Polynomial. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

n	the order of the hermite polynomial
inArrayX	the input value

Returns

NdArray<double>

hermite() [2/2]

template<typename dtype >

double nc::polynomial::hermite	(	uint32	n,
		dtype	x
	)

Hermite Polynomial NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

n	the order of the hermite polynomial
x	the input value

Returns

double

laguerre() [1/4]

template<typename dtype >

NdArray< double > nc::polynomial::laguerre	(	uint32	n,
		const NdArray< dtype > &	inArrayX
	)

Laguerre Polynomial. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

n	the order of the leguerre polynomial
inArrayX	the input value

Returns

NdArray<double>

laguerre() [2/4]

template<typename dtype >

double nc::polynomial::laguerre	(	uint32	n,
		dtype	x
	)

Laguerre Polynomial. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

n	the order of the leguerre polynomial
x	the input value

Returns

double

laguerre() [3/4]

template<typename dtype >

NdArray< double > nc::polynomial::laguerre	(	uint32	n,
		uint32	m,
		const NdArray< dtype > &	inArrayX
	)

Associated Laguerre Polynomial. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

n	the order of the leguerre polynomial
m	the degree of the legendre polynomial
inArrayX	the input value

Returns

NdArray<double>

laguerre() [4/4]

template<typename dtype >

double nc::polynomial::laguerre	(	uint32	n,
		uint32	m,
		dtype	x
	)

Associated Laguerre Polynomial. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

n	the order of the leguerre polynomial
m	the degree of the legendre polynomial
x	the input value

Returns

double

legendre_p() [1/4]

template<typename dtype >

NdArray< double > nc::polynomial::legendre_p	(	uint32	m,
		uint32	n,
		const NdArray< dtype > &	inArrayX
	)

Associated Legendre Polynomial of the first kind. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

m	the order of the legendre polynomial
n	the degree of the legendre polynomial
inArrayX	the input value. Requires -1 <= x <= 1

Returns

NdArray<double>

legendre_p() [2/4]

template<typename dtype >

double nc::polynomial::legendre_p	(	uint32	m,
		uint32	n,
		dtype	x
	)

Associated Legendre Polynomial of the first kind. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

m	the order of the legendre polynomial
n	the degree of the legendre polynomial
x	the input value. Requires -1 <= x <= 1

Returns

double

legendre_p() [3/4]

template<typename dtype >

NdArray< double > nc::polynomial::legendre_p	(	uint32	n,
		const NdArray< dtype > &	inArrayX
	)

Legendre Polynomial of the first kind. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

n	the degree of the legendre polynomial
inArrayX	the input value. Requires -1 <= x <= 1

Returns

NdArray<double>

legendre_p() [4/4]

template<typename dtype >

double nc::polynomial::legendre_p	(	uint32	n,
		dtype	x
	)

Legendre Polynomial of the first kind. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

n	the degree of the legendre polynomial
x	the input value. Requires -1 <= x <= 1

Returns

double

legendre_q() [1/2]

template<typename dtype >

NdArray< double > nc::polynomial::legendre_q	(	int32	n,
		const NdArray< dtype > &	inArrayX
	)

Legendre Polynomial of the second kind. NOTE: Use of this function requires using the Boost includes.

Parameters

n	the order of the legendre polynomial
inArrayX	the input value. Requires -1 <= x <= 1

Returns

NdArray<double>

legendre_q() [2/2]

template<typename dtype >

double nc::polynomial::legendre_q	(	int32	n,
		dtype	x
	)

Legendre Polynomial of the second kind. NOTE: Use of this function requires using the Boost includes.

Parameters

n	the order of the legendre polynomial
x	the input value. Requires -1 <= x <= 1

Returns

double

spherical_harmonic()

template<typename dtype1 , typename dtype2 >

std::complex< double > nc::polynomial::spherical_harmonic	(	uint32	n,
		int32	m,
		dtype1	theta,
		dtype2	phi
	)

Returns the value of the Spherical Harmonic Ynm(theta, phi). The spherical harmonics Ynm(theta, phi) are the angular portion of the solution to Laplace's equation in spherical coordinates where azimuthal symmetry is not present. NOTE: Use of this function requires using the Boost includes.

Parameters

n	order of the harmonic
m	degree of the harmonic
theta	Azimuthal (longitudinal) coordinate; must be in [0, 2*pi].
phi	Polar (colatitudinal) coordinate; must be in [0, pi].

Returns

double

spherical_harmonic_i()

template<typename dtype1 , typename dtype2 >

double nc::polynomial::spherical_harmonic_i	(	uint32	n,
		int32	m,
		dtype1	theta,
		dtype2	phi
	)

Returns the imaginary part of the Spherical Harmonic Ynm(theta, phi). The spherical harmonics Ynm(theta, phi) are the angular portion of the solution to Laplace's equation in spherical coordinates where azimuthal symmetry is not present. NOTE: Use of this function requires using the Boost includes.

Parameters

n	order of the harmonic
m	degree of the harmonic
theta	Azimuthal (longitudinal) coordinate; must be in [0, 2*pi].
phi	Polar (colatitudinal) coordinate; must be in [0, pi].

Returns

double

spherical_harmonic_r()

template<typename dtype1 , typename dtype2 >

double nc::polynomial::spherical_harmonic_r	(	uint32	n,
		int32	m,
		dtype1	theta,
		dtype2	phi
	)

Returns the real part of the Spherical Harmonic Ynm(theta, phi). The spherical harmonics Ynm(theta, phi) are the angular portion of the solution to Laplace's equation in spherical coordinates where azimuthal symmetry is not present. NOTE: Use of this function requires using the Boost includes.

Parameters

n	order of the harmonic
m	degree of the harmonic
theta	Azimuthal (longitudinal) coordinate; must be in [0, 2*pi].
phi	Polar (colatitudinal) coordinate; must be in [0, pi].

Returns

double