Namespace for numerical integration functions. More...

Classes
class	cquad_workspace
	Workspace for CQUAD quadrature routine. More...

class	fixed_workspace
	Workspace for integration_fixed. More...

class	glfixed_table
	Workspace for glfixed_table: used for Gauss–Legendre integration. More...

class	qawo_table
	A precomputed table of Chebychev moments. More...

class	qaws_table
	A precomputed table of Chebychev moments. More...

class	romberg_workspace
	Workspace for integration. More...

class	workspace
	Workspace for integration. More...

Enumerations
enum	qawo_enum { SINE = GSL_INTEG_SINE , COSINE = GSL_INTEG_COSINE }
	Enumerated type. More...

enum	qag_key { GAUSS15 = 1 , GAUSS21 = 2 , GAUSS31 = 3 , GAUSS41 = 4 , GAUSS51 = 5 , GAUSS61 = 6 }
	Keys used for qaq(). More...

Functions
int	qaws_table_set (qaws_table &t, double const alpha, double const beta, int const mu, int const nu)
	C++ version of gsl_integration_qaws_table_set(). More...

int	qawo_table_set (qawo_table &t, double const omega, double const L, qawo_enum const sine)
	C++ version of gsl_integration_qawo_table_set(). More...

int	qawo_table_set_length (qawo_table &t, double L)
	C++ version of gsl_integration_qawo_table_set_length(). More...

void	qk15 (function_scl const &f, double a, double b, double &result, double &abserr, double &resabs, double &resasc)
	C++ version of gsl_integration_qk15(). More...

void	qk21 (function_scl const &f, double a, double b, double &result, double &abserr, double &resabs, double &resasc)
	C++ version of gsl_integration_qk21(). More...

void	qk31 (function_scl const &f, double a, double b, double &result, double &abserr, double &resabs, double &resasc)
	C++ version of gsl_integration_qk31(). More...

void	qk41 (function_scl const &f, double a, double b, double &result, double &abserr, double &resabs, double &resasc)
	C++ version of gsl_integration_qk41(). More...

void	qk51 (function_scl const &f, double a, double b, double &result, double &abserr, double &resabs, double &resasc)
	C++ version of gsl_integration_qk51(). More...

void	qk61 (function_scl const &f, double a, double b, double &result, double &abserr, double &resabs, double &resasc)
	C++ version of gsl_integration_qk61(). More...

template<typename T >
void	qcheb (function_scl &f, double a, double b, T &cheb12, T &cheb24)
	C++ version of gsl_integration_qcheb(). More...

void	qk (int const n, double const xgk[], double const wg[], double const wgk[], double fv1[], double fv2[], function_scl const &f, double a, double b, double &result, double &abserr, double &resabs, double &resasc)
	C++ version of gsl_integration_qk(). More...

template<typename T >
void	qk (T const &xgk, T const &wg, T const &wgk, T &fv1, T &fv2, function_scl const &f, double a, double b, double &result, double &abserr, double &resabs, double &resasc)
	C++ version of gsl_integration_qk(). More...

int	qng (function_scl const &f, double a, double b, double epsabs, double epsrel, double &result, double &abserr, size_t &neval)
	C++ version of gsl_integration_qng(). More...

int	qag (function_scl &f, double const a, double const b, double const epsabs, double const epsrel, size_t const limit, qag_key const key, workspace &workspace, double &result, double &abserr)
	C++ version of gsl_integration_qag(). More...

int	qagi (function_scl &f, double const epsabs, double const epsrel, size_t const limit, workspace &workspace, double &result, double &abserr)
	C++ version of gsl_integration_qagi(). More...

int	qagiu (function_scl &f, double const a, double const epsabs, double const epsrel, size_t const limit, workspace &workspace, double &result, double &abserr)
	C++ version of gsl_integration_qagiu(). More...

int	qagil (function_scl &f, double const b, double const epsabs, double const epsrel, size_t const limit, workspace &workspace, double &result, double &abserr)
	C++ version of gsl_integration_qagil(). More...

int	qags (function_scl &f, double const a, double const b, double const epsabs, double const epsrel, size_t const limit, workspace &workspace, double &result, double &abserr)
	C++ version of gsl_integration_qags(). More...

int	qagp (function_scl &f, double const *pts, size_t const npts, double const epsabs, double const epsrel, size_t const limit, workspace &workspace, double &result, double &abserr)
	C++ version of gsl_integration_qagp(). More...

template<typename T >
int	qagp (function_scl &f, T const &pts, double const epsabs, double const epsrel, size_t const limit, workspace &workspace, double &result, double &abserr)
	C++ version of gsl_integration_qagp(). More...

int	qawc (function_scl &f, double const a, double const b, double const c, double const epsabs, double const epsrel, size_t const limit, workspace &workspace, double &result, double &abserr)
	C++ version of gsl_integration_qawc(). More...

int	qaws (function_scl &f, double const a, double const b, qaws_table &t, double const epsabs, double const epsrel, size_t const limit, workspace &workspace, double &result, double &abserr)
	C++ version of gsl_integration_qaws(). More...

int	qawo (function_scl &f, double const a, double const epsabs, double const epsrel, size_t const limit, workspace &workspace, qawo_table &wf, double &result, double &abserr)
	C++ version of gsl_integration_qawo(). More...

int	qawf (function_scl &f, double const a, double const epsabs, size_t const limit, integration::workspace &workspace, integration::workspace &cycle_workspace, qawo_table &wf, double &result, double &abserr)
	C++ version of gsl_integration_qawf(). More...

double	glfixed (function_scl const &f, double const a, double const b, glfixed_table const &t)
	C++ version of gsl_integration_glfixed(). More...

int	glfixed_point (double const a, double const b, size_t const i, double &xi, double &wi, glfixed_table const &t)
	C++ version of gsl_integration_glfixed_point(). More...

int	cquad (function_scl const &f, double const a, double const b, double const epsabs, double const epsrel, cquad_workspace &ws, double &result, double &abserr, size_t &nevals)
	C++ version of gsl_integration_cquad(). More...

int	romberg (function_scl const &f, double const a, double const b, double const epsabs, double const epsrel, double &result, size_t &neval, romberg_workspace &w)
	C++ version of gsl_integration_romberg(). More...

size_t	fixed_n (fixed_workspace const &w)
	Get the number of quadrature nodes and weights. More...

double *	fixed_nodes (fixed_workspace const &w)
	Get a pointer to an array of nodes. More...

double *	fixed_weights (fixed_workspace const &w)
	Get a pointer to an array of weights. More...

int	fixed (function_scl const &func, double *result, fixed_workspace &w)
	C++ version of gsl_integration_fixed(). More...

Detailed Description

Namespace for numerical integration functions.

Enumeration Type Documentation

◆ qag_key

enum gsl::integration::qag_key

Keys used for qaq().

Enumerator
GAUSS15	use 15-point Gauss–Konrod rule
GAUSS21	use 21-point Gauss–Konrod rule
GAUSS31	use 31-point Gauss–Konrod rule
GAUSS41	use 41-point Gauss–Konrod rule
GAUSS51	use 51-point Gauss–Konrod rule
GAUSS61	use 61-point Gauss–Konrod rule

Definition at line 1329 of file integration.hpp.

◆ qawo_enum

enum gsl::integration::qawo_enum

Enumerated type.

Enumerator
SINE	use sine function in qawo_table
COSINE	use cosine function in qawo_table

Definition at line 670 of file integration.hpp.

Function Documentation

◆ cquad()

int gsl::integration::cquad	(	function_scl const &	f,
		double const	a,
		double const	b,
		double const	epsabs,
		double const	epsrel,
		cquad_workspace &	ws,
		double &	result,
		double &	abserr,
		size_t &	nevals
	)

inline

C++ version of gsl_integration_cquad().

Parameters

f	A function.
a	Lower limit of integration.
b	Upper limit of integration.
epsabs	Required absolute error in integral estimate.
epsrel	Required relative error in integral estimate.
ws	The cquad workspace.
result	The estimate of the integral.
abserr	An estimate of the absolute error in the estimate of the integral.
nevals	The number of evaluations required.

Returns: Error code on failure.

Definition at line 2274 of file integration.hpp.

References gsl::sf::mathieu::a(), gsl::sf::mathieu::b(), and gsl::integration::cquad_workspace::get().

◆ fixed()

int gsl::integration::fixed	(	function_scl const &	func,
		double *	result,
		fixed_workspace &	w
	)

inline

C++ version of gsl_integration_fixed().

Parameters

func	A function.
result	The result [returned]
w	A gsl::integration::romberg_workspace.

Definition at line 2560 of file integration.hpp.

References gsl::sf::hermite::func(), and gsl::integration::fixed_workspace::get().

◆ fixed_n()

size_t gsl::integration::fixed_n ( fixed_workspace const & w )

inline

Get the number of quadrature nodes and weights.

Parameters

w	A gsl::integration::fixed_workspace.

Returns: The number of quadrature nodes and weights

Definition at line 2537 of file integration.hpp.

References gsl::integration::fixed_workspace::get().

◆ fixed_nodes()

double * gsl::integration::fixed_nodes ( fixed_workspace const & w )

inline

Get a pointer to an array of nodes.

Parameters

w	A gsl::integration::fixed_workspace.

Returns: A pointer to an array of nodes

Definition at line 2544 of file integration.hpp.

References gsl::integration::fixed_workspace::get().

◆ fixed_weights()

double * gsl::integration::fixed_weights ( fixed_workspace const & w )

inline

Get a pointer to an array of weights.

Parameters

w	A gsl::integration::fixed_workspace.

Returns: A pointer to an array of weights

Definition at line 2551 of file integration.hpp.

References gsl::integration::fixed_workspace::get().

◆ glfixed()

double gsl::integration::glfixed	(	function_scl const &	f,
		double const	a,
		double const	b,
		glfixed_table const &	t
	)

inline

C++ version of gsl_integration_glfixed().

Parameters

f	A function.
a	Lower limit of integration.
b	Upper limit of integration.
t	The glfixed_table.

Returns: Error code on failure.

Definition at line 2012 of file integration.hpp.

References gsl::sf::mathieu::a(), gsl::sf::mathieu::b(), and gsl::integration::glfixed_table::get().

◆ glfixed_point()

int gsl::integration::glfixed_point	(	double const	a,
		double const	b,
		size_t const	i,
		double &	xi,
		double &	wi,
		glfixed_table const &	t
	)

inline

C++ version of gsl_integration_glfixed_point().

Parameters

a	Lower limit of integration.
b	Upper limit of integration.
i	Index i.
xi	ith Gauss–Legendre point.
wi	ith Gauss–Legendre weight.
t	The glfixed_table.

Returns: Error code on failure.

Definition at line 2055 of file integration.hpp.

References gsl::sf::mathieu::a(), gsl::sf::mathieu::b(), and gsl::integration::glfixed_table::get().

◆ qag()

int gsl::integration::qag	(	function_scl &	f,
		double const	a,
		double const	b,
		double const	epsabs,
		double const	epsrel,
		size_t const	limit,
		qag_key const	key,
		workspace &	workspace,
		double &	result,
		double &	abserr
	)

inline

C++ version of gsl_integration_qag().

Parameters

f	A function.
a	Lower limit of integration.
b	Upper limit of integration.
epsabs	Required absolute error in integral estimate.
epsrel	Required relative error in integral estimate.
limit	The maximum number of subintervals: limited to and typically identical to workspace.size()
key	A qag_key to determine the rule.
workspace	An integration::workspace.
result	The estimate of the integral.
abserr	An estimate of the absolute error in the estimate of the integral.

Returns: Error code on failure.

Definition at line 1353 of file integration.hpp.

References gsl::sf::mathieu::a(), gsl::sf::mathieu::b(), gsl::integration::workspace::get(), and gsl::exception::GSL_EFAILED.

◆ qagi()

int gsl::integration::qagi	(	function_scl &	f,
		double const	epsabs,
		double const	epsrel,
		size_t const	limit,
		workspace &	workspace,
		double &	result,
		double &	abserr
	)

inline

C++ version of gsl_integration_qagi().

Parameters

f	A function.
epsabs	Required absolute error in integral estimate.
epsrel	Required relative error in integral estimate.
limit	The maximum number of subintervals.
workspace	A gsl::integration workspace.
result	The estimate of the integral.
abserr	An estimate of the absolute error in the estimate of the integral.

Returns: Error code on failure.

Definition at line 1404 of file integration.hpp.

References gsl::integration::workspace::get().

◆ qagil()

int gsl::integration::qagil	(	function_scl &	f,
		double const	b,
		double const	epsabs,
		double const	epsrel,
		size_t const	limit,
		workspace &	workspace,
		double &	result,
		double &	abserr
	)

inline

C++ version of gsl_integration_qagil().

Parameters

f	A function.
b	Upper limit of integration.
epsabs	Required absolute error in integral estimate.
epsrel	Required relative error in integral estimate.
limit	The maximum number of subintervals.
workspace	A gsl::integration workspace.
result	The estimate of the integral.
abserr	An estimate of the absolute error in the estimate of the integral.

Returns: Error code on failure.

Definition at line 1471 of file integration.hpp.

References gsl::sf::mathieu::b(), and gsl::integration::workspace::get().

◆ qagiu()

int gsl::integration::qagiu	(	function_scl &	f,
		double const	a,
		double const	epsabs,
		double const	epsrel,
		size_t const	limit,
		workspace &	workspace,
		double &	result,
		double &	abserr
	)

inline

C++ version of gsl_integration_qagiu().

Parameters

f	A function.
a	Lower limit of integration.
epsabs	Required absolute error in integral estimate.
epsrel	Required relative error in integral estimate.
limit	The maximum number of subintervals.
workspace	A gsl::integration workspace.
result	The estimate of the integral.
abserr	An estimate of the absolute error in the estimate of the integral.

Returns: Error code on failure.

Definition at line 1437 of file integration.hpp.

References gsl::sf::mathieu::a(), and gsl::integration::workspace::get().

◆ qagp() [1/2]

int gsl::integration::qagp	(	function_scl &	f,
		double const *	pts,
		size_t const	npts,
		double const	epsabs,
		double const	epsrel,
		size_t const	limit,
		workspace &	workspace,
		double &	result,
		double &	abserr
	)

inline

C++ version of gsl_integration_qagp().

Parameters

f	A function.
pts	An array of known singular points: the first and last elements should be the lower and upper integration limits
npts	The number of singular points
epsabs	Required absolute error in integral estimate.
epsrel	Required relative error in integral estimate.
limit	The maximum number of subintervals.
workspace	A gsl::integration workspace.
result	The estimate of the integral.
abserr	An estimate of the absolute error in the estimate of the integral.

Returns: Error code on failure.

Definition at line 1549 of file integration.hpp.

References gsl::integration::workspace::get().

◆ qagp() [2/2]

template<typename T >

int gsl::integration::qagp	(	function_scl &	f,
		T const &	pts,
		double const	epsabs,
		double const	epsrel,
		size_t const	limit,
		workspace &	workspace,
		double &	result,
		double &	abserr
	)

inline

C++ version of gsl_integration_qagp().

This version works with std::vector<double> and gsl::vector.

Parameters

f	A function.
pts	An array of known singular points: the first and last elements should be the lower and upper integration limits
epsabs	Required absolute error in integral estimate.
epsrel	Required relative error in integral estimate.
limit	The maximum number of subintervals.
workspace	A gsl::integration workspace.
result	The estimate of the integral.
abserr	An estimate of the absolute error in the estimate of the integral.

Returns: Error code on failure.

Definition at line 1592 of file integration.hpp.

References gsl::integration::workspace::get(), and gsl::exception::GSL_EFAILED.

◆ qags()

int gsl::integration::qags	(	function_scl &	f,
		double const	a,
		double const	b,
		double const	epsabs,
		double const	epsrel,
		size_t const	limit,
		workspace &	workspace,
		double &	result,
		double &	abserr
	)

inline

C++ version of gsl_integration_qags().

Parameters

f	A function.
a	Lower limit of integration.
b	Upper limit of integration.
epsabs	Required absolute error in integral estimate.
epsrel	Required relative error in integral estimate.
limit	The maximum number of subintervals.
workspace	A gsl::integration workspace.
result	The estimate of the integral.
abserr	An estimate of the absolute error in the estimate of the integral.

Returns: Error code on failure.

Definition at line 1508 of file integration.hpp.

References gsl::sf::mathieu::a(), gsl::sf::mathieu::b(), and gsl::integration::workspace::get().

◆ qawc()

int gsl::integration::qawc	(	function_scl &	f,
		double const	a,
		double const	b,
		double const	c,
		double const	epsabs,
		double const	epsrel,
		size_t const	limit,
		workspace &	workspace,
		double &	result,
		double &	abserr
	)

inline

C++ version of gsl_integration_qawc().

Parameters

f	A function.
a	Lower limit of integration.
b	Upper limit of integration.
c	Singularity point.
epsabs	Required absolute error in Cauchy principal value.
epsrel	Required relative error in Cauchy principal value.
limit	The maximum number of subintervals.
workspace	A gsl::integration workspace.
result	The estimate of the Cauchy principal value of the integral.
abserr	An estimate of the absolute error in the estimate of the Cauchy principal value.

Returns: Error code on failure.

Definition at line 1651 of file integration.hpp.

References gsl::sf::mathieu::a(), gsl::sf::mathieu::b(), and gsl::integration::workspace::get().

◆ qawf()

int gsl::integration::qawf	(	function_scl &	f,
		double const	a,
		double const	epsabs,
		size_t const	limit,
		integration::workspace &	workspace,
		integration::workspace &	cycle_workspace,
		qawo_table &	wf,
		double &	result,
		double &	abserr
	)

inline

C++ version of gsl_integration_qawf().

Parameters

f	A function.
a	Lower limit of integration.
epsabs	Required absolute error in integral estimate.
limit	The maximum number of subintervals.
workspace	A gsl::integration workspace.
cycle_workspace	A gsl::integration workspace for subintervals.
wf	The qawo_table.
result	The estimate of the integral.
abserr	An estimate of the absolute error in the estimate of the integral.

Returns: Error code on failure.

Definition at line 1774 of file integration.hpp.

References gsl::sf::mathieu::a(), gsl::integration::workspace::get(), and gsl::integration::qawo_table::get().

◆ qawo()

int gsl::integration::qawo	(	function_scl &	f,
		double const	a,
		double const	epsabs,
		double const	epsrel,
		size_t const	limit,
		workspace &	workspace,
		qawo_table &	wf,
		double &	result,
		double &	abserr
	)

inline

C++ version of gsl_integration_qawo().

Parameters

f	A function.
a	Lower limit of integration.
epsabs	Required absolute error in integral estimate.
epsrel	Required relative error in integral estimate.
limit	The maximum number of subintervals.
workspace	A gsl::integration workspace.
wf	A qawo_table.
result	The estimate of the integral.
abserr	An estimate of the absolute error in the estimate of the integral.

Returns: Error code on failure.

Definition at line 1734 of file integration.hpp.

References gsl::sf::mathieu::a(), gsl::integration::workspace::get(), and gsl::integration::qawo_table::get().

◆ qawo_table_set()

int gsl::integration::qawo_table_set	(	qawo_table &	t,
		double const	omega,
		double const	L,
		qawo_enum const	sine
	)

inline

C++ version of gsl_integration_qawo_table_set().

Parameters

t	The qawo_table.
omega	\(\omega\).
L	length of the integral over which the function will be evaluated.
sine	gsl::integration::SINE or gsl::integration::COSINE.

Returns: Error code on failure.

Definition at line 892 of file integration.hpp.

References gsl::integration::qawo_table::get().

◆ qawo_table_set_length()

int gsl::integration::qawo_table_set_length	(	qawo_table &	t,
		double	L
	)

inline

C++ version of gsl_integration_qawo_table_set_length().

Parameters

t	The qawo_table.
L	New interval length.

Returns: Error code on failure.

Definition at line 903 of file integration.hpp.

References gsl::integration::qawo_table::get().

◆ qaws()

int gsl::integration::qaws	(	function_scl &	f,
		double const	a,
		double const	b,
		qaws_table &	t,
		double const	epsabs,
		double const	epsrel,
		size_t const	limit,
		workspace &	workspace,
		double &	result,
		double &	abserr
	)

inline

C++ version of gsl_integration_qaws().

Parameters

f	A function.
a	Lower limit of integration.
b	Upper limit of integration.
t	The qaws_table.
epsabs	Required absolute error in integral estimate.
epsrel	Required relative error in integral estimate.
limit	The maximum number of subintervals.
workspace	A gsl::integration workspace.
result	The estimate of the integral.
abserr	An estimate of the absolute error in the estimate of the integral.

Returns: Error code on failure.

Definition at line 1693 of file integration.hpp.

References gsl::sf::mathieu::a(), gsl::sf::mathieu::b(), gsl::integration::workspace::get(), and gsl::integration::qaws_table::get().

◆ qaws_table_set()

int gsl::integration::qaws_table_set	(	qaws_table &	t,
		double const	alpha,
		double const	beta,
		int const	mu,
		int const	nu
	)

inline

C++ version of gsl_integration_qaws_table_set().

Parameters

t	The qaws_table
alpha	\(\alpha\).
beta	\(\beta\).
mu	\(\mu\).
nu	\(\nu\).

Returns: Erro code on failure.

Definition at line 663 of file integration.hpp.

References gsl::ran::beta(), and gsl::integration::qaws_table::get().

◆ qcheb()

template<typename T >

void gsl::integration::qcheb	(	function_scl &	f,
		double	a,
		double	b,
		T &	cheb12,
		T &	cheb24
	)

inline

C++ version of gsl_integration_qcheb().

This version works with std::vector<double> and gsl::vector.

Parameters

f	A function.
a	Lower limit.
b	Upper limit.
cheb12	A vector of dimension 13 containing the Chebyshev coefficients for degree 12.
cheb24	A vector of dimension 25 containing the Chebyshev coefficients for degree 24.

Definition at line 1120 of file integration.hpp.

References gsl::sf::mathieu::a(), gsl::sf::mathieu::b(), and gsl::exception::GSL_EFAILED.

◆ qk() [1/2]

void gsl::integration::qk	(	int const	n,
		double const	xgk[],
		double const	wg[],
		double const	wgk[],
		double	fv1[],
		double	fv2[],
		function_scl const &	f,
		double	a,
		double	b,
		double &	result,
		double &	abserr,
		double &	resabs,
		double &	resasc
	)

inline

C++ version of gsl_integration_qk().

Parameters

n	An integer
xgk	An array of length n.
wg	An array of length n.
wgk	An array of length n.
fv1	An array of length n (return value).
fv2	An array of length n (return value).
f	A function.
a	Lower limit of integration.
b	Upper limit of integration.
result	The estimate of the integral.
abserr	An estimate of the absolute error in the estimate of the integral.
resabs	Approximation to the integral of abs(f).
resasc	Approximation to the integral of abs(f - integral / (b - a) ).

Returns: Error code on failure.

Definition at line 1183 of file integration.hpp.

References gsl::sf::mathieu::a(), gsl::sf::mathieu::b(), and gsl::rstat::n().

◆ qk() [2/2]

template<typename T >

void gsl::integration::qk	(	T const &	xgk,
		T const &	wg,
		T const &	wgk,
		T &	fv1,
		T &	fv2,
		function_scl const &	f,
		double	a,
		double	b,
		double &	result,
		double &	abserr,
		double &	resabs,
		double &	resasc
	)

inline

C++ version of gsl_integration_qk().

This version works with std::vector<double> and gsl::vector of size n.

Parameters

xgk	An array of length n.
wg	An array of length n.
wgk	An array of length n.
fv1	An array of length n (return value).
fv2	An array of length n (return value).
f	A function.
a	Lower limit of integration.
b	Upper limit of integration.
result	Approximation to the integral.
abserr	Estimate of the absolute size of the absolute error.
resabs	Approximation to the integral of abs(f).
resasc	Approximation to the integral of abs(f - integral / (b - a) ).

Definition at line 1231 of file integration.hpp.

References gsl::sf::mathieu::a(), gsl::sf::mathieu::b(), gsl::exception::GSL_EFAILED, and gsl::rstat::n().

◆ qk15()

void gsl::integration::qk15	(	function_scl const &	f,
		double	a,
		double	b,
		double &	result,
		double &	abserr,
		double &	resabs,
		double &	resasc
	)

inline

C++ version of gsl_integration_qk15().

Parameters

f	Function to be integrated.
a	Lower limit of integration.
b	Upper limit of integration.
result	Approximation to the integral.
abserr	Estimate of the absolute size of the absolute error.
resabs	Approximation to the integral of abs(f).
resasc	Approximation to the integral of abs(f - integral / (b - a) ).

Definition at line 916 of file integration.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ qk21()

void gsl::integration::qk21	(	function_scl const &	f,
		double	a,
		double	b,
		double &	result,
		double &	abserr,
		double &	resabs,
		double &	resasc
	)

inline

C++ version of gsl_integration_qk21().

Parameters

f	Function to be integrated.
a	Lower limit of integration.
b	Upper limit of integration.
result	Approximation to the integral.
abserr	Estimate of the absolute size of the absolute error.
resabs	Approximation to the integral of abs(f).
resasc	Approximation to the integral of abs(f - integral / (b - a) ).

Definition at line 946 of file integration.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ qk31()

void gsl::integration::qk31	(	function_scl const &	f,
		double	a,
		double	b,
		double &	result,
		double &	abserr,
		double &	resabs,
		double &	resasc
	)

inline

C++ version of gsl_integration_qk31().

Parameters

f	Function to be integrated.
a	Lower limit of integration.
b	Upper limit of integration.
result	Approximation to the integral.
abserr	Estimate of the absolute size of the absolute error.
resabs	Approximation to the integral of abs(f).
resasc	Approximation to the integral of abs(f - integral / (b - a) ).

Definition at line 976 of file integration.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ qk41()

void gsl::integration::qk41	(	function_scl const &	f,
		double	a,
		double	b,
		double &	result,
		double &	abserr,
		double &	resabs,
		double &	resasc
	)

inline

C++ version of gsl_integration_qk41().

Parameters

f	Function to be integrated.
a	Lower limit of integration.
b	Upper limit of integration.
result	Approximation to the integral.
abserr	Estimate of the absolute size of the absolute error.
resabs	Approximation to the integral of abs(f).
resasc	Approximation to the integral of abs(f - integral / (b - a) ).

Definition at line 1006 of file integration.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ qk51()

void gsl::integration::qk51	(	function_scl const &	f,
		double	a,
		double	b,
		double &	result,
		double &	abserr,
		double &	resabs,
		double &	resasc
	)

inline

C++ version of gsl_integration_qk51().

Parameters

f	Function to be integrated.
a	Lower limit of integration.
b	Upper limit of integration.
result	Approximation to the integral.
abserr	Estimate of the absolute size of the absolute error.
resabs	Approximation to the integral of abs(f).
resasc	Approximation to the integral of abs(f - integral / (b - a) ).

Definition at line 1036 of file integration.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ qk61()

void gsl::integration::qk61	(	function_scl const &	f,
		double	a,
		double	b,
		double &	result,
		double &	abserr,
		double &	resabs,
		double &	resasc
	)

inline

C++ version of gsl_integration_qk61().

Parameters

f	Function to be integrated.
a	Lower limit of integration.
b	Upper limit of integration.
result	Approximation to the integral.
abserr	Estimate of the absolute size of the absolute error.
resabs	Approximation to the integral of abs(f).
resasc	Approximation to the integral of abs(f - integral / (b - a) ).

Definition at line 1066 of file integration.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ qng()

int gsl::integration::qng	(	function_scl const &	f,
		double	a,
		double	b,
		double	epsabs,
		double	epsrel,
		double &	result,
		double &	abserr,
		size_t &	neval
	)

inline

C++ version of gsl_integration_qng().

Parameters

f	A function.
a	Lower limit of integration.
b	Upper limit of integration.
epsabs	Absolute error limit.
epsrel	Relative error limit.
result	Estimate of integral.
abserr	Estimate of absolute error (return value).
neval	Number of function evaluations used (return value).

Returns: Error code on failure.

Definition at line 1304 of file integration.hpp.

References gsl::sf::mathieu::a(), and gsl::sf::mathieu::b().

◆ romberg()

int gsl::integration::romberg	(	function_scl const &	f,
		double const	a,
		double const	b,
		double const	epsabs,
		double const	epsrel,
		double &	result,
		size_t &	neval,
		romberg_workspace &	w
	)

inline

C++ version of gsl_integration_romberg().

Parameters

f	A function.
a	Lower limit of integration.
b	Upper limit of integration.
epsabs	Required absolute error in integral estimate.
epsrel	Required relative error in integral estimate.
result	The result [returned]
neval	The total number of function evaluations [returned]
w	A gsl::integration::romberg_workspace.

Definition at line 2511 of file integration.hpp.

References gsl::sf::mathieu::a(), gsl::sf::mathieu::b(), and gsl::integration::romberg_workspace::get().

Classes

Enumerations

Functions

Detailed Description

Enumeration Type Documentation

◆ qag_key

◆ qawo_enum

Function Documentation

◆ cquad()

◆ fixed()

◆ fixed_n()

◆ fixed_nodes()

◆ fixed_weights()

◆ glfixed()

◆ glfixed_point()

◆ qag()

◆ qagi()

◆ qagil()

◆ qagiu()

◆ qagp() [1/2]

◆ qagp() [2/2]

◆ qags()

◆ qawc()

◆ qawf()

◆ qawo()

◆ qawo_table_set()

◆ qawo_table_set_length()

◆ qaws()

◆ qaws_table_set()

◆ qcheb()

◆ qk() [1/2]

◆ qk() [2/2]

◆ qk15()

◆ qk21()

◆ qk31()

◆ qk41()

◆ qk51()

◆ qk61()

◆ qng()

◆ romberg()