Namespace for elliptic integrals. More...

Functions
int	Kcomp_e (double k, mode_t mode, result &result)
	C++ version of gsl_sf_ellint_Kcomp_e(). More...

double	Kcomp (double k, mode_t mode)
	C++ version of gsl_sf_ellint_Kcomp(). More...

int	Ecomp_e (double k, mode_t mode, result &result)
	C++ version of gsl_sf_ellint_Ecomp_e(). More...

double	Ecomp (double k, mode_t mode)
	C++ version of gsl_sf_ellint_Ecomp(). More...

int	Pcomp_e (double k, double n, mode_t mode, result &result)
	C++ version of gsl_sf_ellint_Pcomp_e(). More...

double	Pcomp (double k, double n, mode_t mode)
	C++ version of gsl_sf_ellint_Pcomp(). More...

int	Dcomp_e (double k, mode_t mode, result &result)
	C++ version of gsl_sf_ellint_Dcomp_e(). More...

double	Dcomp (double k, mode_t mode)
	C++ version of gsl_sf_ellint_Dcomp(). More...

int	F_e (double phi, double k, mode_t mode, result &result)
	C++ version of gsl_sf_ellint_F_e(). More...

double	F (double phi, double k, mode_t mode)
	C++ version of gsl_sf_ellint_F(). More...

int	E_e (double phi, double k, mode_t mode, result &result)
	C++ version of gsl_sf_ellint_E_e(). More...

double	E (double phi, double k, mode_t mode)
	C++ version of gsl_sf_ellint_E(). More...

int	P_e (double phi, double k, double n, mode_t mode, result &result)
	C++ version of gsl_sf_ellint_P_e(). More...

double	P (double phi, double k, double n, mode_t mode)
	C++ version of gsl_sf_ellint_P(). More...

int	D_e (double phi, double k, mode_t mode, result &result)
	C++ version of gsl_sf_ellint_D_e(). More...

double	D (double phi, double k, mode_t mode)
	C++ version of gsl_sf_ellint_D(). More...

int	RC_e (double x, double y, mode_t mode, result &result)
	C++ version of gsl_sf_ellint_RC_e(). More...

double	RC (double x, double y, mode_t mode)
	C++ version of gsl_sf_ellint_RC(). More...

int	RD_e (double x, double y, double z, mode_t mode, result &result)
	C++ version of gsl_sf_ellint_RD_e(). More...

double	RD (double x, double y, double z, mode_t mode)
	C++ version of gsl_sf_ellint_RD(). More...

int	RF_e (double x, double y, double z, mode_t mode, result &result)
	C++ version of gsl_sf_ellint_RF_e(). More...

double	RF (double x, double y, double z, mode_t mode)
	C++ version of gsl_sf_ellint_RF(). More...

int	RJ_e (double x, double y, double z, double p, mode_t mode, result &result)
	C++ version of gsl_sf_ellint_RJ_e(). More...

double	RJ (double x, double y, double z, double p, mode_t mode)
	C++ version of gsl_sf_ellint_RJ(). More...

Detailed Description

Namespace for elliptic integrals.

Function Documentation

◆ D()

double gsl::sf::ellint::D	(	double	phi,
		double	k,
		mode_t	mode
	)

inline

C++ version of gsl_sf_ellint_D().

D(phi,k,n) = R_D(1-Sin[phi]^2, 1-k^2 Sin[phi]^2, 1.0)

Parameters

phi	A real number
k	A real number
mode	The mode

Returns: The function value

Definition at line 203 of file sf_ellint.hpp.

Referenced by gsl::linalg::balance_accum(), gsl::linalg::balance_columns(), gsl::linalg::balance_matrix(), gsl::linalg::cholesky_decomp_unit(), gsl::linalg::ldlt_band_unpack(), and gsl::linalg::QR_UD_decomp().

◆ D_e()

int gsl::sf::ellint::D_e	(	double	phi,
		double	k,
		mode_t	mode,
		result &	result
	)

inline

C++ version of gsl_sf_ellint_D_e().

D(phi,k,n) = R_D(1-Sin[phi]^2, 1-k^2 Sin[phi]^2, 1.0)

Parameters

phi	A real number
k	A real number
mode	The mode
result	The result as a `gsl::sf::result` object

Returns: Error code on failure

Definition at line 193 of file sf_ellint.hpp.

◆ Dcomp()

double gsl::sf::ellint::Dcomp	(	double	k,
		mode_t	mode
	)

inline

C++ version of gsl_sf_ellint_Dcomp().

Parameters

k	A real number
mode	The mode

Returns: The function value

Definition at line 117 of file sf_ellint.hpp.

◆ Dcomp_e()

int gsl::sf::ellint::Dcomp_e	(	double	k,
		mode_t	mode,
		result &	result
	)

inline

C++ version of gsl_sf_ellint_Dcomp_e().

Parameters

k	A real number
mode	The mode
result	The result as a `gsl::sf::result` object

Returns: Error code on failure

Definition at line 109 of file sf_ellint.hpp.

◆ E()

double gsl::sf::ellint::E	(	double	phi,
		double	k,
		mode_t	mode
	)

inline

C++ version of gsl_sf_ellint_E().

E(phi,k) = Integral[ Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]

Parameters

phi	A real number
k	A real number
mode	The mode

Returns: The function value

Definition at line 159 of file sf_ellint.hpp.

◆ E_e()

int gsl::sf::ellint::E_e	(	double	phi,
		double	k,
		mode_t	mode,
		result &	result
	)

inline

C++ version of gsl_sf_ellint_E_e().

E(phi,k) = Integral[ Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]

Parameters

phi	A real number
k	A real number
mode	The mode
result	The result as a `gsl::sf::result` object

Returns: Error code on failure

Definition at line 149 of file sf_ellint.hpp.

◆ Ecomp()

double gsl::sf::ellint::Ecomp	(	double	k,
		mode_t	mode
	)

inline

C++ version of gsl_sf_ellint_Ecomp().

Legendre form of complete elliptic integrals

E(k) = Integral[ Sqrt[1 - k^2 Sin[t]^2], {t, 0, Pi/2}]

Parameters

k	A real number
mode	The mode

Returns: The function value

Definition at line 81 of file sf_ellint.hpp.

◆ Ecomp_e()

int gsl::sf::ellint::Ecomp_e	(	double	k,
		mode_t	mode,
		result &	result
	)

inline

C++ version of gsl_sf_ellint_Ecomp_e().

Legendre form of complete elliptic integrals

E(k) = Integral[ Sqrt[1 - k^2 Sin[t]^2], {t, 0, Pi/2}]

Parameters

k	A real number
mode	The mode
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 69 of file sf_ellint.hpp.

◆ F()

double gsl::sf::ellint::F	(	double	phi,
		double	k,
		mode_t	mode
	)

inline

C++ version of gsl_sf_ellint_F().

F(phi,k) = Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]

Parameters

phi	A real number
k	A real number
mode	The mode

Returns: The function value

Definition at line 138 of file sf_ellint.hpp.

Referenced by gsl::movstat::workspace::apply(), gsl::movstat::apply(), gsl::multiroot::fdjacobian(), gsl::fn_eval(), gsl::fn_fdf_eval_df(), gsl::fn_fdf_eval_f(), and gsl::sf::coulomb::wave_FG_e().

◆ F_e()

int gsl::sf::ellint::F_e	(	double	phi,
		double	k,
		mode_t	mode,
		result &	result
	)

inline

C++ version of gsl_sf_ellint_F_e().

F(phi,k) = Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]

Parameters

phi	A real number
k	A real number
mode	The mode
result	The result as a `gsl::sf::result` object

Returns: Error code on failure

Definition at line 128 of file sf_ellint.hpp.

◆ Kcomp()

double gsl::sf::ellint::Kcomp	(	double	k,
		mode_t	mode
	)

inline

C++ version of gsl_sf_ellint_Kcomp().

Legendre form of complete elliptic integrals

K(k) = Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, Pi/2}]

Parameters

k	A real number
mode	The mode

Returns: function value

Definition at line 56 of file sf_ellint.hpp.

◆ Kcomp_e()

int gsl::sf::ellint::Kcomp_e	(	double	k,
		mode_t	mode,
		result &	result
	)

inline

C++ version of gsl_sf_ellint_Kcomp_e().

Legendre form of complete elliptic integrals

K(k) = Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, Pi/2}]

Parameters

k	A real number
mode	The mode
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 44 of file sf_ellint.hpp.

◆ P()

double gsl::sf::ellint::P	(	double	phi,
		double	k,
		double	n,
		mode_t	mode
	)

inline

C++ version of gsl_sf_ellint_P().

P(phi,k,n) = Integral[(1 + n Sin[t]^2)^(-1)/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]

Parameters

phi	A real number
k	A real number
n	A real number
mode	The mode

Returns: The function value

Definition at line 182 of file sf_ellint.hpp.

References gsl::rstat::n().

Referenced by gsl::cdf::beta_Pinv(), gsl::cdf::cauchy_Pinv(), gsl::cdf::chisq_Pinv(), gsl::ran::discrete_t::discrete_t(), gsl::blas::drotm(), gsl::blas::drotmg(), gsl::cdf::exponential_Pinv(), gsl::cdf::fdist_Pinv(), gsl::cdf::flat_Pinv(), gsl::cdf::gamma_Pinv(), gsl::cdf::gaussian_Pinv(), gsl::cdf::gumbel1_Pinv(), gsl::cdf::gumbel2_Pinv(), gsl::cdf::laplace_Pinv(), gsl::cdf::logistic_Pinv(), gsl::cdf::lognormal_Pinv(), gsl::cdf::pareto_Pinv(), gsl::cdf::rayleigh_Pinv(), gsl::blas::srotm(), gsl::blas::srotmg(), gsl::cdf::tdist_Pinv(), gsl::cdf::ugaussian_Pinv(), and gsl::cdf::weibull_Pinv().

◆ P_e()

int gsl::sf::ellint::P_e	(	double	phi,
		double	k,
		double	n,
		mode_t	mode,
		result &	result
	)

inline

C++ version of gsl_sf_ellint_P_e().

P(phi,k,n) = Integral[(1 + n Sin[t]^2)^(-1)/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]

Parameters

phi	A real number
k	A real number
n	A real number
mode	The mode
result	The result as a `gsl::sf::result` object

Returns: Error code on failure

Definition at line 171 of file sf_ellint.hpp.

References gsl::rstat::n().

◆ Pcomp()

double gsl::sf::ellint::Pcomp	(	double	k,
		double	n,
		mode_t	mode
	)

inline

C++ version of gsl_sf_ellint_Pcomp().

Parameters

k	A real number
n	A real number
mode	The mode

Returns: The function value

Definition at line 100 of file sf_ellint.hpp.

References gsl::rstat::n().

◆ Pcomp_e()

int gsl::sf::ellint::Pcomp_e	(	double	k,
		double	n,
		mode_t	mode,
		result &	result
	)

inline

C++ version of gsl_sf_ellint_Pcomp_e().

Parameters

k	A real number
n	A real number
mode	The mode
result	The result as a `gsl::sf::result` object

Returns: Error code on failure

Definition at line 91 of file sf_ellint.hpp.

References gsl::rstat::n().

◆ RC()

double gsl::sf::ellint::RC	(	double	x,
		double	y,
		mode_t	mode
	)

inline

C++ version of gsl_sf_ellint_RC().

Carlson's symmetric basis of functions

RC(x,y) = 1/2 Integral[(t+x)^(-1/2) (t+y)^(-1)], {t,0,Inf}]

Parameters

x	A real number
y	A real number
mode	The mode

Returns: The function value

Definition at line 228 of file sf_ellint.hpp.

◆ RC_e()

int gsl::sf::ellint::RC_e	(	double	x,
		double	y,
		mode_t	mode,
		result &	result
	)

inline

C++ version of gsl_sf_ellint_RC_e().

Carlson's symmetric basis of functions

RC(x,y) = 1/2 Integral[(t+x)^(-1/2) (t+y)^(-1)], {t,0,Inf}]

Parameters

x	A real number
y	A real number
mode	The mode
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 216 of file sf_ellint.hpp.

◆ RD()

double gsl::sf::ellint::RD	(	double	x,
		double	y,
		double	z,
		mode_t	mode
	)

inline

C++ version of gsl_sf_ellint_RD().

Carlson's symmetric basis of functions

RD(x,y,z) = 3/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-3/2), {t,0,Inf}]

Parameters

x	A real number
y	A real number
z	A real number
mode	The mode

Returns: The function value

Definition at line 255 of file sf_ellint.hpp.

◆ RD_e()

int gsl::sf::ellint::RD_e	(	double	x,
		double	y,
		double	z,
		mode_t	mode,
		result &	result
	)

inline

C++ version of gsl_sf_ellint_RD_e().

Carlson's symmetric basis of functions

RD(x,y,z) = 3/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-3/2), {t,0,Inf}]

Parameters

x	A real number
y	A real number
z	A real number
mode	The mode
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 242 of file sf_ellint.hpp.

◆ RF()

double gsl::sf::ellint::RF	(	double	x,
		double	y,
		double	z,
		mode_t	mode
	)

inline

C++ version of gsl_sf_ellint_RF().

Carlson's symmetric basis of functions

RF(x,y,z) = 1/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2), {t,0,Inf}]

Parameters

x	A real number
y	A real number
z	A real number
mode	The mode

Returns: The function value

Definition at line 282 of file sf_ellint.hpp.

◆ RF_e()

int gsl::sf::ellint::RF_e	(	double	x,
		double	y,
		double	z,
		mode_t	mode,
		result &	result
	)

inline

C++ version of gsl_sf_ellint_RF_e().

Carlson's symmetric basis of functions

RF(x,y,z) = 1/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2), {t,0,Inf}]

Parameters

x	A real number
y	A real number
z	A real number
mode	The mode
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 269 of file sf_ellint.hpp.

◆ RJ()

double gsl::sf::ellint::RJ	(	double	x,
		double	y,
		double	z,
		double	p,
		mode_t	mode
	)

inline

C++ version of gsl_sf_ellint_RJ().

Carlson's symmetric basis of functions

RJ(x,y,z,p) = 3/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2) (t+p)^(-1), {t,0,Inf}]

Parameters

x	A real number
y	A real number
z	A real number
p	A real number
mode	The mode

Returns: The function value

Definition at line 311 of file sf_ellint.hpp.

◆ RJ_e()

int gsl::sf::ellint::RJ_e	(	double	x,
		double	y,
		double	z,
		double	p,
		mode_t	mode,
		result &	result
	)

inline

C++ version of gsl_sf_ellint_RJ_e().

Carlson's symmetric basis of functions

RJ(x,y,z,p) = 3/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2) (t+p)^(-1), {t,0,Inf}]

Parameters

x	A real number
y	A real number
z	A real number
p	A real number
mode	The mode
result	The result as a `gsl::sf::result` object

Returns: GSL_SUCCESS or GSL_EDOM

Definition at line 297 of file sf_ellint.hpp.

Functions

Detailed Description

Function Documentation

◆ D()

◆ D_e()

◆ Dcomp()

◆ Dcomp_e()

◆ E()

◆ E_e()

◆ Ecomp()

◆ Ecomp_e()

◆ F()

◆ F_e()

◆ Kcomp()

◆ Kcomp_e()

◆ P()

◆ P_e()

◆ Pcomp()

◆ Pcomp_e()

◆ RC()

◆ RC_e()

◆ RD()

◆ RD_e()

◆ RF()

◆ RF_e()

◆ RJ()

◆ RJ_e()