Detailed Description

template<class func_t>
class o2scl::inte_qawo_gsl_sin< func_t >

The integral

$\int_a^b f(x) \sin (\omega x)~dx$

is computed for some frequency parameter $\omega$ , stored in o2scl::inte_qawo_gsl_sin::omega .

An adaptive algorithm together with an series-acceleration method like that of o2scl::inte_qags_gsl is used. Those subintervals with "large" widths $d \equiv b-a$ where $d\omega > 4$ are computed using a 25-point Clenshaw-Curtis integration rule to handle the oscillatory behavior. In order to work efficiently, the Chebyshev moments for the particular weight function $ W $ are computed in advance.

See GSL-based integration routines in the User's guide for general information about the GSL integration classes.

Definition at line 58 of file inte_qawo_gsl.h.

Public Member Functions
virtual int	integ_err (func_t &func, double a, double b, double &res, double &err)
	Integrate function `func` from `a` to `b` and place the result in `res` and the error in `err`.

Public Member Functions inherited from o2scl::inte_transform_gsl< func_t >
virtual void	gauss_kronrod (func_t &func, double a, double b, double result, double abserr, double resabs, double resasc)
	Integration wrapper for internal transformed function type.

Public Member Functions inherited from o2scl::inte_kronrod_gsl< funct >
int	get_rule ()
	Get the Gauss-Kronrod integration rule. More...

void	set_rule (int rule)
	Set the Gauss-Kronrod integration rule to be used.

int	set_limit (size_t lim)
	Set the limit for the number of subdivisions of the integration region (default 1000) More...

void	gauss_kronrod_base (func2_t &func, double a, double b, double result, double abserr, double resabs, double resasc)
	The base Gauss-Kronrod integration function template. More...

virtual void	gauss_kronrod (funct &func, double a, double b, double result, double abserr, double resabs, double resasc)
	Integration wrapper for user-specified function type.

Public Member Functions inherited from o2scl::inte< funct >
virtual double	integ (funct &func, double a, double b)
	Integrate function `func` from `a` to `b`.

virtual int	integ_err (funct &func, double a, double b, double &res, double &err)=0
	Integrate function `func` from `a` to `b` and place the result in `res` and the error in `err`.

double	get_error ()
	Return the numerically estimated error in the result from the last call to integ() More...

Public Attributes
double	omega
	The user-specified frequency (default 1.0)

size_t	n_levels
	The number of bisection levels (default 10)

Public Attributes inherited from o2scl::inte< funct >
int	verbose
	Verbosity.

size_t	last_iter
	The most recent number of iterations taken.

double	tol_rel
	The maximum relative uncertainty in the value of the integral (default $10^{-8}$ )

double	tol_abs
	The maximum absolute uncertainty in the value of the integral (default $10^{-8}$ )

bool	err_nonconv
	If true, call the error handler if the routine does not converge or reach the desired tolerance (default true) More...

Protected Member Functions
int	qawo (func_t &func, const double a, const double epsabs, const double epsrel, inte_workspace_gsl loc_w, gsl_integration_qawo_table wf, double result, double abserr)
	The full GSL integration routine called by integ_err() More...

void	qc25f (func_t &func, double a, double b, gsl_integration_qawo_table wf, size_t level, double result, double abserr, double resabs, double *resasc)
	25-point quadrature for oscillating functions

virtual double	transform (double t, func_t &func)
	Add the oscillating part to the integrand.

const char *	type ()
	Return string denoting type ("inte_qawo_gsl_sin")

Protected Member Functions inherited from o2scl::inte_cheb_gsl< func_t >
void	compute_moments (double cc, double *moment)
	Compute the Chebyshev moments.

template<class func2_t >
void	inte_cheb_series (func2_t &f, double a, double b, double cheb12, double cheb24)
	Compute Chebyshev series expansion using a FFT method. More...

Protected Member Functions inherited from o2scl::inte_singular_gsl< funct >
void	initialise_table (struct extrapolation_table *table)
	Initialize the table.

void	append_table (struct extrapolation_table *table, double y)
	Append a result to the table.

int	test_positivity (double result, double resabs)
	Test if the integrand satisfies .

void	qelg (struct extrapolation_table table, double result, double *abserr)
	Determines the limit of a given sequence of approximations. More...

int	large_interval (inte_workspace_gsl *workspace)
	Determine if an interval is large.

void	reset_nrmax (inte_workspace_gsl *workspace)
	Reset workspace to work on the interval with the largest error.

int	increase_nrmax (inte_workspace_gsl *workspace)
	Increase workspace.

int	qags (funct &func, const double a, const double b, const double l_epsabs, const double l_epsrel, double result, double abserr)
	Integration function. More...

Protected Member Functions inherited from o2scl::inte_gsl
double	rescale_error (double err, const double result_abs, const double result_asc)
	QUADPACK's nonlinear rescaling of the absolute-error estimate. More...

Protected Attributes
gsl_integration_qawo_table *	otable
	The integration workspace.

Protected Attributes inherited from o2scl::inte_kronrod_gsl< funct >
inte_workspace_gsl *	w
	The integration workspace.

int	n_gk
	Size of Gauss-Kronrod arrays.

const double *	x_gk
	Gauss-Kronrod abscissae pointer.

const double *	w_g
	Gauss weight pointer.

const double *	w_gk
	Gauss-Kronrod weight pointer.

double *	f_v1
	Scratch space.

double *	f_v2
	Scratch space.

Protected Attributes inherited from o2scl::inte< funct >
double	interror
	The uncertainty for the last integration computation.

Additional Inherited Members
Public Types inherited from o2scl::inte_singular_gsl< funct >
typedef struct o2scl::inte_singular_gsl::extrapolation_table	extrap_table
	A structure for extrapolation for o2scl::inte_qags_gsl. More...

Member Function Documentation

◆ qawo()

template<class func_t >

int o2scl::inte_qawo_gsl_sin< func_t >::qawo	(	func_t &	func,
		const double	a,
		const double	epsabs,
		const double	epsrel,
		inte_workspace_gsl *	loc_w,
		gsl_integration_qawo_table *	wf,
		double *	result,
		double *	abserr
	)

inlineprotected

Idea for Future:: Remove goto statements.

Definition at line 104 of file inte_qawo_gsl.h.

The documentation for this class was generated from the following file:

/home/awsteiner/wcs/o2scl/src/inte/inte_qawo_gsl.h

Detailed Description

template<class func_t> class o2scl::inte_qawo_gsl_sin< func_t >

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Additional Inherited Members

Member Function Documentation

◆ qawo()

template<class func_t>
class o2scl::inte_qawo_gsl_sin< func_t >