Functions
template<typename dtype >
auto	airy_ai (const NdArray< dtype > &inArray)

template<typename dtype >
auto	airy_ai (dtype inValue)

template<typename dtype >
auto	airy_ai_prime (const NdArray< dtype > &inArray)

template<typename dtype >
auto	airy_ai_prime (dtype inValue)

template<typename dtype >
auto	airy_bi (const NdArray< dtype > &inArray)

template<typename dtype >
auto	airy_bi (dtype inValue)

template<typename dtype >
auto	airy_bi_prime (const NdArray< dtype > &inArray)

template<typename dtype >
auto	airy_bi_prime (dtype inValue)

NdArray< double >	bernoilli (const NdArray< uint32 > &inArray)

double	bernoilli (uint32 n)

template<typename dtype1 , typename dtype2 >
auto	bessel_in (dtype1 inV, const NdArray< dtype2 > &inArrayX)

template<typename dtype1 , typename dtype2 >
auto	bessel_in (dtype1 inV, dtype2 inX)

template<typename dtype1 , typename dtype2 >
auto	bessel_in_prime (dtype1 inV, const NdArray< dtype2 > &inArrayX)

template<typename dtype1 , typename dtype2 >
auto	bessel_in_prime (dtype1 inV, dtype2 inX)

template<typename dtype1 , typename dtype2 >
auto	bessel_jn (dtype1 inV, const NdArray< dtype2 > &inArrayX)

template<typename dtype1 , typename dtype2 >
auto	bessel_jn (dtype1 inV, dtype2 inX)

template<typename dtype1 , typename dtype2 >
auto	bessel_jn_prime (dtype1 inV, const NdArray< dtype2 > &inArrayX)

template<typename dtype1 , typename dtype2 >
auto	bessel_jn_prime (dtype1 inV, dtype2 inX)

template<typename dtype1 , typename dtype2 >
auto	bessel_kn (dtype1 inV, const NdArray< dtype2 > &inArrayX)

template<typename dtype1 , typename dtype2 >
auto	bessel_kn (dtype1 inV, dtype2 inX)

template<typename dtype1 , typename dtype2 >
auto	bessel_kn_prime (dtype1 inV, const NdArray< dtype2 > &inArrayX)

template<typename dtype1 , typename dtype2 >
auto	bessel_kn_prime (dtype1 inV, dtype2 inX)

template<typename dtype1 , typename dtype2 >
auto	bessel_yn (dtype1 inV, const NdArray< dtype2 > &inArrayX)

template<typename dtype1 , typename dtype2 >
auto	bessel_yn (dtype1 inV, dtype2 inX)

template<typename dtype1 , typename dtype2 >
auto	bessel_yn_prime (dtype1 inV, const NdArray< dtype2 > &inArrayX)

template<typename dtype1 , typename dtype2 >
auto	bessel_yn_prime (dtype1 inV, dtype2 inX)

template<typename dtype1 , typename dtype2 >
auto	beta (const NdArray< dtype1 > &inArrayA, const NdArray< dtype2 > &inArrayB)

template<typename dtype1 , typename dtype2 >
auto	beta (dtype1 a, dtype2 b)

double	cnr (uint32 n, uint32 r)

template<typename dtype >
auto	comp_ellint_1 (const NdArray< dtype > &inArrayK)

template<typename dtype >
auto	comp_ellint_1 (dtype inK)

template<typename dtype >
auto	comp_ellint_2 (const NdArray< dtype > &inArrayK)

template<typename dtype >
auto	comp_ellint_2 (dtype inK)

template<typename dtype1 , typename dtype2 >
auto	comp_ellint_3 (const NdArray< dtype1 > &inArrayK, const NdArray< dtype2 > &inArrayV)

template<typename dtype1 , typename dtype2 >
auto	comp_ellint_3 (dtype1 inK, dtype2 inV)

template<typename dtype1 , typename dtype2 >
auto	cyclic_hankel_1 (dtype1 inV, const NdArray< dtype2 > &inX)

template<typename dtype1 , typename dtype2 >
auto	cyclic_hankel_1 (dtype1 inV, dtype2 inX)

template<typename dtype1 , typename dtype2 >
auto	cyclic_hankel_2 (dtype1 inV, const NdArray< dtype2 > &inX)

template<typename dtype1 , typename dtype2 >
auto	cyclic_hankel_2 (dtype1 inV, dtype2 inX)

template<typename dtype >
auto	digamma (const NdArray< dtype > &inArray)

template<typename dtype >
auto	digamma (dtype inValue)

template<typename dtype1 , typename dtype2 >
auto	ellint_1 (const NdArray< dtype1 > &inArrayK, const NdArray< dtype2 > &inArrayP)

template<typename dtype1 , typename dtype2 >
auto	ellint_1 (dtype1 inK, dtype2 inP)

template<typename dtype1 , typename dtype2 >
auto	ellint_2 (const NdArray< dtype1 > &inArrayK, const NdArray< dtype2 > &inArrayP)

template<typename dtype1 , typename dtype2 >
auto	ellint_2 (dtype1 inK, dtype2 inP)

template<typename dtype1 , typename dtype2 , typename dtype3 >
auto	ellint_3 (const NdArray< dtype1 > &inArrayK, const NdArray< dtype2 > &inArrayV, const NdArray< dtype3 > &inArrayP)

template<typename dtype1 , typename dtype2 , typename dtype3 >
auto	ellint_3 (dtype1 inK, dtype2 inV, dtype3 inP)

template<typename dtype >
auto	erf (const NdArray< dtype > &inArray)

template<typename dtype >
auto	erf (dtype inValue)

template<typename dtype >
auto	erf_inv (const NdArray< dtype > &inArray)

template<typename dtype >
auto	erf_inv (dtype inValue)

template<typename dtype >
auto	erfc (const NdArray< dtype > &inArray)

template<typename dtype >
auto	erfc (dtype inValue)

template<typename dtype >
auto	erfc_inv (const NdArray< dtype > &inArray)

template<typename dtype >
auto	erfc_inv (dtype inValue)

template<typename dtype >
auto	expint (const NdArray< dtype > &inArrayX)

template<typename dtype >
auto	expint (dtype inX)

NdArray< double >	factorial (const NdArray< uint32 > &inArray)

double	factorial (uint32 inValue)

template<typename dtype >
auto	gamma (const NdArray< dtype > &inArray)

template<typename dtype >
auto	gamma (dtype inValue)

template<typename dtype >
auto	gamma1pm1 (const NdArray< dtype > &inArray)

template<typename dtype >
auto	gamma1pm1 (dtype inValue)

template<typename dtype >
auto	log_gamma (const NdArray< dtype > &inArray)

template<typename dtype >
auto	log_gamma (dtype inValue)

double	pnr (uint32 n, uint32 r)

template<typename dtype >
auto	polygamma (uint32 n, const NdArray< dtype > &inArray)

template<typename dtype >
auto	polygamma (uint32 n, dtype inValue)

NdArray< uint32 >	prime (const NdArray< uint32 > &inArray)

uint32	prime (uint32 n)

template<typename dtype >
auto	riemann_zeta (const NdArray< dtype > &inArray)

template<typename dtype >
auto	riemann_zeta (dtype inValue)

template<typename dtype >
NdArray< double >	softmax (const NdArray< dtype > &inArray, Axis inAxis=Axis::NONE)

template<typename dtype >
auto	spherical_bessel_jn (uint32 inV, const NdArray< dtype > &inArrayX)

template<typename dtype >
auto	spherical_bessel_jn (uint32 inV, dtype inX)

template<typename dtype >
auto	spherical_bessel_yn (uint32 inV, const NdArray< dtype > &inArrayX)

template<typename dtype >
auto	spherical_bessel_yn (uint32 inV, dtype inX)

template<typename dtype1 , typename dtype2 >
auto	spherical_hankel_1 (dtype1 inV, const NdArray< dtype2 > &inArray)

template<typename dtype1 , typename dtype2 >
auto	spherical_hankel_1 (dtype1 inV, dtype2 inX)

template<typename dtype1 , typename dtype2 >
auto	spherical_hankel_2 (dtype1 inV, const NdArray< dtype2 > &inArray)

template<typename dtype1 , typename dtype2 >
std::complex< double >	spherical_hankel_2 (dtype1 inV, dtype2 inX)

template<typename dtype >
auto	trigamma (const NdArray< dtype > &inArray)

template<typename dtype >
auto	trigamma (dtype inValue)

Function Documentation

◆ airy_ai() [1/2]

template<typename dtype >

auto nc::special::airy_ai ( const NdArray< dtype > & inArray )

The first linearly independent solution to the differential equation y'' - yz = 0. http://mathworld.wolfram.com/AiryFunctions.html NOTE: Use of this function requires using the Boost includes.

Parameters

inArray

Returns: NdArray

◆ airy_ai() [2/2]

template<typename dtype >

auto nc::special::airy_ai ( dtype inValue )

The first linearly independent solution to the differential equation y'' - yz = 0. http://mathworld.wolfram.com/AiryFunctions.html NOTE: Use of this function requires using the Boost includes.

Parameters

inValue

Returns: calculated-result-type

◆ airy_ai_prime() [1/2]

template<typename dtype >

auto nc::special::airy_ai_prime ( const NdArray< dtype > & inArray )

The derivative of the first linearly independent solution to the differential equation y'' - yz = 0. http://mathworld.wolfram.com/AiryFunctions.html NOTE: Use of this function requires using the Boost includes.

Parameters

inArray

Returns: NdArray

◆ airy_ai_prime() [2/2]

template<typename dtype >

auto nc::special::airy_ai_prime ( dtype inValue )

The derivative of the first linearly independent solution to the differential equation y'' - yz = 0. http://mathworld.wolfram.com/AiryFunctions.html NOTE: Use of this function requires using the Boost includes.

Parameters

inValue

Returns: calculated-result-type

◆ airy_bi() [1/2]

template<typename dtype >

auto nc::special::airy_bi ( const NdArray< dtype > & inArray )

The second linearly independent solution to the differential equation y'' - yz = 0. http://mathworld.wolfram.com/AiryFunctions.html NOTE: Use of this function requires using the Boost includes.

Parameters

inArray

Returns: NdArray

◆ airy_bi() [2/2]

template<typename dtype >

auto nc::special::airy_bi ( dtype inValue )

The second linearly independent solution to the differential equation y'' - yz = 0. http://mathworld.wolfram.com/AiryFunctions.html NOTE: Use of this function requires using the Boost includes.

Parameters

inValue

Returns: calculated-result-type

◆ airy_bi_prime() [1/2]

template<typename dtype >

auto nc::special::airy_bi_prime ( const NdArray< dtype > & inArray )

The derivative of the second linearly independent solution to the differential equation y'' - yz = 0. http://mathworld.wolfram.com/AiryFunctions.html NOTE: Use of this function requires using the Boost includes.

Parameters

inArray

Returns: NdArray

◆ airy_bi_prime() [2/2]

template<typename dtype >

auto nc::special::airy_bi_prime ( dtype inValue )

The derivative of the second linearly independent solution to the differential equation y'' - yz = 0. http://mathworld.wolfram.com/AiryFunctions.html NOTE: Use of this function requires using the Boost includes.

Parameters

inValue

Returns: calculated-result-type

◆ bernoilli() [1/2]

NdArray< double > nc::special::bernoilli ( const NdArray< uint32 > & inArray )

inline

Both return the nth Bernoulli number B2n. NOTE: Use of this function requires using the Boost includes.

Parameters

inArray

Returns: NdArray<double>

◆ bernoilli() [2/2]

double nc::special::bernoilli ( uint32 n )

inline

Both return the nth Bernoulli number B2n. NOTE: Use of this function requires using the Boost includes.

Parameters

n

Returns: double

◆ bessel_in() [1/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::bessel_in	(	dtype1	inV,
		const NdArray< dtype2 > &	inArrayX
	)

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

Parameters

inV	the order of the bessel function
inArrayX	the input values

Returns: NdArray

◆ bessel_in() [2/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::bessel_in	(	dtype1	inV,
		dtype2	inX
	)

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

Parameters

inV	the order of the bessel function
inX	the input value

Returns: calculated-result-type

◆ bessel_in_prime() [1/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::bessel_in_prime	(	dtype1	inV,
		const NdArray< dtype2 > &	inArrayX
	)

Derivcative of the Modified Cylindrical Bessel function of the first kind. NOTE: Use of this function requires using the Boost includes.

Parameters

inV	the order of the bessel function
inArrayX	the input values

Returns: NdArray

◆ bessel_in_prime() [2/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::bessel_in_prime	(	dtype1	inV,
		dtype2	inX
	)

Derivcative of the Modified Cylindrical Bessel function of the first kind. NOTE: Use of this function requires using the Boost includes.

Parameters

inV	the order of the bessel function
inX	the input value

Returns: calculated-result-type

◆ bessel_jn() [1/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::bessel_jn	(	dtype1	inV,
		const NdArray< dtype2 > &	inArrayX
	)

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

Parameters

inV	the order of the bessel function
inArrayX	the input values

Returns: NdArray

◆ bessel_jn() [2/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::bessel_jn	(	dtype1	inV,
		dtype2	inX
	)

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

Parameters

inV	the order of the bessel function
inX	the input value

Returns: calculated-result-type

◆ bessel_jn_prime() [1/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::bessel_jn_prime	(	dtype1	inV,
		const NdArray< dtype2 > &	inArrayX
	)

Derivcative of the Cylindrical Bessel function of the first kind. NOTE: Use of this function requires using the Boost includes.

Parameters

inV	the order of the bessel function
inArrayX	the input values

Returns: NdArray

◆ bessel_jn_prime() [2/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::bessel_jn_prime	(	dtype1	inV,
		dtype2	inX
	)

Derivcative of the Cylindrical Bessel function of the first kind. NOTE: Use of this function requires using the Boost includes.

Parameters

inV	the order of the bessel function
inX	the input value

Returns: calculated-result-type

◆ bessel_kn() [1/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::bessel_kn	(	dtype1	inV,
		const NdArray< dtype2 > &	inArrayX
	)

Modified Cylindrical Bessel function of the second kind. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

inV	the order of the bessel function
inArrayX	the input values

Returns: NdArray

◆ bessel_kn() [2/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::bessel_kn	(	dtype1	inV,
		dtype2	inX
	)

Modified Cylindrical Bessel function of the second kind. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

inV	the order of the bessel function
inX	the input value

Returns: calculated-result-type

◆ bessel_kn_prime() [1/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::bessel_kn_prime	(	dtype1	inV,
		const NdArray< dtype2 > &	inArrayX
	)

Derivcative of the Modified Cylindrical Bessel function of the second kind NOTE: Use of this function requires using the Boost includes.

Parameters

inV	the order of the bessel function
inArrayX	the input values

Returns: NdArray

◆ bessel_kn_prime() [2/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::bessel_kn_prime	(	dtype1	inV,
		dtype2	inX
	)

Derivcative of the Modified Cylindrical Bessel function of the second kind. NOTE: Use of this function requires using the Boost includes.

Parameters

inV	the order of the bessel function
inX	the input value

Returns: calculated-result-type

◆ bessel_yn() [1/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::bessel_yn	(	dtype1	inV,
		const NdArray< dtype2 > &	inArrayX
	)

Cylindrical Bessel function of the second kind. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

inV	the order of the bessel function
inArrayX	the input values

Returns: NdArray

◆ bessel_yn() [2/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::bessel_yn	(	dtype1	inV,
		dtype2	inX
	)

Cylindrical Bessel function of the second kind. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

inV	the order of the bessel function
inX	the input value

Returns: calculated-result-type

◆ bessel_yn_prime() [1/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::bessel_yn_prime	(	dtype1	inV,
		const NdArray< dtype2 > &	inArrayX
	)

Derivcative of the Cylindrical Bessel function of the second kind. NOTE: Use of this function requires using the Boost includes.

Parameters

inV	the order of the bessel function
inArrayX	the input values

Returns: NdArray

◆ bessel_yn_prime() [2/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::bessel_yn_prime	(	dtype1	inV,
		dtype2	inX
	)

Derivcative of the Cylindrical Bessel function of the second kind. NOTE: Use of this function requires using the Boost includes.

Parameters

inV	the order of the bessel function
inX	the input value

Returns: calculated-result-type

◆ beta() [1/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::beta	(	const NdArray< dtype1 > &	inArrayA,
		const NdArray< dtype2 > &	inArrayB
	)

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

Parameters

inArrayA
inArrayB

Returns: NdArray

◆ beta() [2/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::beta	(	dtype1	a,
		dtype2	b
	)

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

Parameters

a
b

Returns: calculated-result-type

◆ cnr()

double nc::special::cnr	(	uint32	n,
		uint32	r
	)

inline

Returns the number of combinations of n choose r. C(n, r)

Parameters

n	the total number of items
r	the number of items taken

Returns: double

◆ comp_ellint_1() [1/2]

template<typename dtype >

auto nc::special::comp_ellint_1 ( const NdArray< dtype > & inArrayK )

Computes the complete elliptic integral of the first kind of k. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

inArrayK elliptic modulus or eccentricity

Returns: NdArray

◆ comp_ellint_1() [2/2]

template<typename dtype >

auto nc::special::comp_ellint_1 ( dtype inK )

Computes the complete elliptic integral of the first kind of k. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

inK	elliptic modulus or eccentricity

Returns: calculated-result-type

◆ comp_ellint_2() [1/2]

template<typename dtype >

auto nc::special::comp_ellint_2 ( const NdArray< dtype > & inArrayK )

Computes the complete elliptic integral of the second kind of k. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

inArrayK elliptic modulus or eccentricity

Returns: NdArray

◆ comp_ellint_2() [2/2]

template<typename dtype >

auto nc::special::comp_ellint_2 ( dtype inK )

Computes the complete elliptic integral of the second kind of k. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

inK	elliptic modulus or eccentricity

Returns: calculated-result-type

◆ comp_ellint_3() [1/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::comp_ellint_3	(	const NdArray< dtype1 > &	inArrayK,
		const NdArray< dtype2 > &	inArrayV
	)

Computes the complete elliptic integral of the third kind of k and p. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

inArrayK	the order of the bessel function
inArrayV	elliptic characteristic

Returns: NdArray

◆ comp_ellint_3() [2/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::comp_ellint_3	(	dtype1	inK,
		dtype2	inV
	)

Computes the complete elliptic integral of the third kind of k and v. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

inK	elliptic modulus or eccentricity
inV	elliptic characteristic

Returns: calculated-result-type

◆ cyclic_hankel_1() [1/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::cyclic_hankel_1	(	dtype1	inV,
		const NdArray< dtype2 > &	inX
	)

Hankel funcion of the first kind. NOTE: Use of this function requires using the Boost includes.

Parameters

inV	the order of the bessel function
inX	the input array

Returns: NdArray<std::complex>

◆ cyclic_hankel_1() [2/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::cyclic_hankel_1	(	dtype1	inV,
		dtype2	inX
	)

Hankel funcion of the first kind. NOTE: Use of this function requires using the Boost includes.

Parameters

inV	the order of the bessel function
inX	the input value

Returns: std::complex<double>

◆ cyclic_hankel_2() [1/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::cyclic_hankel_2	(	dtype1	inV,
		const NdArray< dtype2 > &	inX
	)

Hankel funcion of the second kind. NOTE: Use of this function requires using the Boost includes.

Parameters

inV	the order of the bessel function
inX	the input array

Returns: NdArray<std::complex>

◆ cyclic_hankel_2() [2/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::cyclic_hankel_2	(	dtype1	inV,
		dtype2	inX
	)

Hankel funcion of the second kind. NOTE: Use of this function requires using the Boost includes.

Parameters

inV	the order of the bessel function
inX	the input value

Returns: std::complex<>

◆ digamma() [1/2]

template<typename dtype >

auto nc::special::digamma ( const NdArray< dtype > & inArray )

Returns the digamma or psi function of values in inArray. Digamma is defined as the logarithmic derivative of the gamma function. NOTE: Use of this function requires using the Boost includes.

Parameters

inArray

Returns: NdArray

◆ digamma() [2/2]

template<typename dtype >

auto nc::special::digamma ( dtype inValue )

Returns the digamma or psi function of inValue. Digamma is defined as the logarithmic derivative of the gamma function. NOTE: Use of this function requires using the Boost includes.

Parameters

inValue

Returns: calculated-result-type

◆ ellint_1() [1/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::ellint_1	(	const NdArray< dtype1 > &	inArrayK,
		const NdArray< dtype2 > &	inArrayP
	)

Computes the incomplete elliptic integral of the first kind of k and p. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

inArrayK	elliptic modulus or eccentricity
inArrayP	Jacobi amplitude (measured in radians)

Returns: NdArray

◆ ellint_1() [2/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::ellint_1	(	dtype1	inK,
		dtype2	inP
	)

Computes the incomplete elliptic integral of the first kind of k and p. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

inK	elliptic modulus or eccentricity
inP	Jacobi amplitude (measured in radians)

Returns: calculated-result-type

◆ ellint_2() [1/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::ellint_2	(	const NdArray< dtype1 > &	inArrayK,
		const NdArray< dtype2 > &	inArrayP
	)

Computes the incomplete elliptic integral of the second kind of k and p. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

inArrayK	elliptic modulus or eccentricity
inArrayP	Jacobi amplitude (measured in radians)

Returns: NdArray

◆ ellint_2() [2/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::ellint_2	(	dtype1	inK,
		dtype2	inP
	)

Computes the incomplete elliptic integral of the second kind of k and p. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

inK	elliptic modulus or eccentricity
inP	Jacobi amplitude (measured in radians)

Returns: calculated-result-type

◆ ellint_3() [1/2]

template<typename dtype1 , typename dtype2 , typename dtype3 >

auto nc::special::ellint_3	(	const NdArray< dtype1 > &	inArrayK,
		const NdArray< dtype2 > &	inArrayV,
		const NdArray< dtype3 > &	inArrayP
	)

Computes the incomplete elliptic integral of the second kind of k, v, and p. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

inArrayK	the order of the bessel function
inArrayV	elliptic characteristic
inArrayP	Jacobi amplitude (measured in radians)

Returns: NdArray

◆ ellint_3() [2/2]

template<typename dtype1 , typename dtype2 , typename dtype3 >

auto nc::special::ellint_3	(	dtype1	inK,
		dtype2	inV,
		dtype3	inP
	)

Computes the incomplete elliptic integral of the second kind of k, v, and p. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

inK	elliptic modulus or eccentricity
inV	elliptic characteristic
inP	Jacobi amplitude (measured in radians)

Returns: calculated-result-type

◆ erf() [1/2]

template<typename dtype >

auto nc::special::erf ( const NdArray< dtype > & inArray )

Calculate the error function of all elements in the input array. Integral (from [-x, x]) of np.exp(np.power(-t, 2)) dt, multiplied by 1/np.pi. NOTE: Use of this function requires using the Boost includes.

Parameters

inArray

Returns: NdArray

◆ erf() [2/2]

template<typename dtype >

auto nc::special::erf ( dtype inValue )

Calculate the error function of all elements in the input array. Integral (from [-x, x]) of np.exp(np.power(-t, 2)) dt, multiplied by 1/np.pi. NOTE: Use of this function requires using the Boost includes.

Parameters

inValue

Returns: calculated-result-type

◆ erf_inv() [1/2]

template<typename dtype >

auto nc::special::erf_inv ( const NdArray< dtype > & inArray )

Returns the inverse error function of z, that is a value x such that: z = erf(x). NOTE: Use of this function requires using the Boost includes.

Parameters

inArray

Returns: NdArray

◆ erf_inv() [2/2]

template<typename dtype >

auto nc::special::erf_inv ( dtype inValue )

Returns the inverse error function of z, that is a value x such that: z = erf(x). NOTE: Use of this function requires using the Boost includes.

Parameters

inValue

Returns: calculated-result-type

◆ erfc() [1/2]

template<typename dtype >

auto nc::special::erfc ( const NdArray< dtype > & inArray )

Returns the element-wise complement of the error function of inValue. NOTE: Use of this function requires using the Boost includes.

Parameters

inArray

Returns: NdArray

◆ erfc() [2/2]

template<typename dtype >

auto nc::special::erfc ( dtype inValue )

Returns the complement of the error function of inValue. NOTE: Use of this function requires using the Boost includes.

Parameters

inValue

Returns: calculated-result-type

◆ erfc_inv() [1/2]

template<typename dtype >

auto nc::special::erfc_inv ( const NdArray< dtype > & inArray )

Returns the inverse complementary error function of z, that is a value x such that: z = erfc(x). NOTE: Use of this function requires using the Boost includes.

Parameters

inArray

Returns: NdArray

◆ erfc_inv() [2/2]

template<typename dtype >

auto nc::special::erfc_inv ( dtype inValue )

Returns the inverse complentary error function of z, that is a value x such that: z = erfc(x). NOTE: Use of this function requires using the Boost includes.

Parameters

inValue

Returns: calculated-result-type

◆ expint() [1/2]

template<typename dtype >

auto nc::special::expint ( const NdArray< dtype > & inArrayX )

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

Parameters

inArrayX value

Returns: NdArray

◆ expint() [2/2]

template<typename dtype >

auto nc::special::expint ( dtype inX )

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

Parameters

inX value

Returns: calculated-result-type

◆ factorial() [1/2]

NdArray< double > nc::special::factorial ( const NdArray< uint32 > & inArray )

inline

Returns the factorial of the input value

Parameters

inArray

Returns: NdArray<double>

◆ factorial() [2/2]

double nc::special::factorial ( uint32 inValue )

inline

Returns the factorial of the input value

Parameters

inValue

Returns: double

◆ gamma() [1/2]

template<typename dtype >

auto nc::special::gamma ( const NdArray< dtype > & inArray )

Returns the "true gamma" of values in array. NOTE: Use of this function requires using the Boost includes.

Parameters

inArray

Returns: NdArray

◆ gamma() [2/2]

template<typename dtype >

auto nc::special::gamma ( dtype inValue )

Returns the "true gamma" of value z. NOTE: Use of this function requires using the Boost includes.

Parameters

inValue

Returns: calculated-result-type

◆ gamma1pm1() [1/2]

template<typename dtype >

auto nc::special::gamma1pm1 ( const NdArray< dtype > & inArray )

Returns the true gamma(dz + 1) - 1 of values in array. NOTE: Use of this function requires using the Boost includes.

Parameters

inArray

Returns: NdArray

◆ gamma1pm1() [2/2]

template<typename dtype >

auto nc::special::gamma1pm1 ( dtype inValue )

Returns the true gamma(dz + 1) - 1 of value z. NOTE: Use of this function requires using the Boost includes.

Parameters

inValue

Returns: calculated-result-type

◆ log_gamma() [1/2]

template<typename dtype >

auto nc::special::log_gamma ( const NdArray< dtype > & inArray )

Returns natural log of the true gamma of values in array. NOTE: Use of this function requires using the Boost includes.

Parameters

inArray

Returns: NdArray

◆ log_gamma() [2/2]

template<typename dtype >

auto nc::special::log_gamma ( dtype inValue )

Returns natural log of the true gamma of value z. NOTE: Use of this function requires using the Boost includes.

Parameters

inValue

Returns: calculated-result-type

◆ pnr()

double nc::special::pnr	(	uint32	n,
		uint32	r
	)

inline

Returns the number of permutaions of n choose r. P(n, r)

Parameters

n	the total number of items
r	the number of items taken

Returns: double

◆ polygamma() [1/2]

template<typename dtype >

auto nc::special::polygamma	(	uint32	n,
		const NdArray< dtype > &	inArray
	)

Returns the polygamma function of the values in inArray. Polygamma is defined as the n'th derivative of the digamma function. NOTE: Use of this function requires using the Boost includes.

Parameters

n	the nth derivative
inArray

Returns: NdArray

◆ polygamma() [2/2]

template<typename dtype >

auto nc::special::polygamma	(	uint32	n,
		dtype	inValue
	)

Returns the polygamma function of inValue. Polygamma is defined as the n'th derivative of the digamma function. NOTE: Use of this function requires using the Boost includes.

Parameters

n	the nth derivative
inValue

Returns: calculated-result-type

◆ prime() [1/2]

NdArray< uint32 > nc::special::prime ( const NdArray< uint32 > & inArray )

inline

The function prime provides fast table lookup to the first 10000 prime numbers (starting from 2 as the zeroth prime: as 1 isn't terribly useful in practice). NOTE: Use of this function requires using the Boost includes.

Parameters

inArray

Returns: NdArray<uint32>

◆ prime() [2/2]

uint32 nc::special::prime ( uint32 n )

inline

The function prime provides fast table lookup to the first 10000 prime numbers (starting from 2 as the zeroth prime: as 1 isn't terribly useful in practice). NOTE: Use of this function requires using the Boost includes.

Parameters

n	the nth prime number to return

Returns: uint32

◆ riemann_zeta() [1/2]

template<typename dtype >

auto nc::special::riemann_zeta ( const NdArray< dtype > & inArray )

The Riemann Zeta function https://en.wikipedia.org/wiki/Riemann_zeta_function NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

inArray

Returns: NdArray

◆ riemann_zeta() [2/2]

template<typename dtype >

auto nc::special::riemann_zeta ( dtype inValue )

The Riemann Zeta function https://en.wikipedia.org/wiki/Riemann_zeta_function NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

inValue

Returns: calculated-result-type

◆ softmax()

template<typename dtype >

NdArray< double > nc::special::softmax	(	const NdArray< dtype > &	inArray,
		Axis	inAxis = `Axis::NONE`
	)

The softmax function transforms each element of a collection by computing the exponential of each element divided by the sum of the exponentials of all the elements. That is, if x is a one-dimensional numpy array: softmax(x) = np.exp(x)/sum(np.exp(x))

Parameters

inArray
inAxis	(Optional, default NONE)

Returns: NdArray<double>

◆ spherical_bessel_jn() [1/2]

template<typename dtype >

auto nc::special::spherical_bessel_jn	(	uint32	inV,
		const NdArray< dtype > &	inArrayX
	)

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

Parameters

inV	the order of the bessel function
inArrayX	the input values

Returns: NdArray

◆ spherical_bessel_jn() [2/2]

template<typename dtype >

auto nc::special::spherical_bessel_jn	(	uint32	inV,
		dtype	inX
	)

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

Parameters

inV	the order of the bessel function
inX	the input value

Returns: calculated-result-type

◆ spherical_bessel_yn() [1/2]

template<typename dtype >

auto nc::special::spherical_bessel_yn	(	uint32	inV,
		const NdArray< dtype > &	inArrayX
	)

Spherical Bessel function of the second kind. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

inV	the order of the bessel function
inArrayX	the input values

Returns: NdArray

◆ spherical_bessel_yn() [2/2]

template<typename dtype >

auto nc::special::spherical_bessel_yn	(	uint32	inV,
		dtype	inX
	)

Spherical Bessel function of the second kind. NOTE: Use of this function requires either using the Boost includes or a C++17 compliant compiler.

Parameters

inV	the order of the bessel function
inX	the input value

Returns: calculated-result-type

◆ spherical_hankel_1() [1/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::spherical_hankel_1	(	dtype1	inV,
		const NdArray< dtype2 > &	inArray
	)

Spherical Hankel funcion of the first kind. NOTE: Use of this function requires using the Boost includes.

Parameters

inV	the order of the bessel function
inArray	the input values

Returns: NdArray

◆ spherical_hankel_1() [2/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::spherical_hankel_1	(	dtype1	inV,
		dtype2	inX
	)

Spherical Hankel funcion of the first kind. NOTE: Use of this function requires using the Boost includes.

Parameters

inV	the order of the bessel function
inX	the input value

Returns: calculated-result-type

◆ spherical_hankel_2() [1/2]

template<typename dtype1 , typename dtype2 >

auto nc::special::spherical_hankel_2	(	dtype1	inV,
		const NdArray< dtype2 > &	inArray
	)

Spherical Hankel funcion of the second kind. NOTE: Use of this function requires using the Boost includes.

Parameters

inV	the order of the bessel function
inArray	the input value

Returns: NdArray

◆ spherical_hankel_2() [2/2]

template<typename dtype1 , typename dtype2 >

std::complex< double > nc::special::spherical_hankel_2	(	dtype1	inV,
		dtype2	inX
	)

Spherical Hankel funcion of the second kind. NOTE: Use of this function requires using the Boost includes.

Parameters

inV	the order of the bessel function
inX	the input value

Returns: double

◆ trigamma() [1/2]

template<typename dtype >

auto nc::special::trigamma ( const NdArray< dtype > & inArray )

Returns the trigamma function of x. Trigamma is defined as the derivative of the digamma function. NOTE: Use of this function requires using the Boost includes.

Parameters

inArray

Returns: NdArray

◆ trigamma() [2/2]

template<typename dtype >

auto nc::special::trigamma ( dtype inValue )

Returns the trigamma function of x. Trigamma is defined as the derivative of the digamma function. NOTE: Use of this function requires using the Boost includes.

Parameters

inValue

Returns: calculated-result-type