Basic Gauss-Kronrod integration class (GSL) More...

#include <inte_kronrod_gsl.h>

Inheritance diagram for o2scl::inte_kronrod_gsl< func_t >:

Detailed Description

template<class func_t>
class o2scl::inte_kronrod_gsl< func_t >

This class provides the basic Gauss-Kronrod integration function and integration workspace for some of the GSL-based integration classes.

The main function of interest is set_rule(), which sets the integration rule for the GSL integration classes which inherit from this base class. The argument to set rule should be selected from the following list:

1: 15-point Gauss-Kronrod integration rule (default)
2: 21-point rule
3: 31-point rule
4: 41-point rule
5: 51-point rule
6: 61-point rule Any value other than 1-6 forces the error handler to be called. All classes default to the 15-point rule, except for o2scl::inte_qags_gsl which defaults to the 21-point rule for singularities.

The integration coefficients for use with this class and associated children are stored in the o2scl_inte_gk_coeffs namespace.

Idea for Future:: Convert 'double *' objects to ubvector

Definition at line 614 of file inte_kronrod_gsl.h.

Public Member Functions
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...

template<class func2_t >
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 (func_t &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< func_t >
virtual double	integ (func_t &func, double a, double b)
	Integrate function `func` from `a` to `b`.

virtual int	integ_err (func_t &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...

virtual const char *	type ()
	Return string denoting type ("inte")

Protected Attributes
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< func_t >
double	interror
	The uncertainty for the last integration computation.

Additional Inherited Members
Public Attributes inherited from o2scl::inte< func_t >
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 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...

Member Function Documentation

◆ gauss_kronrod_base()

template<class func_t >

template<class func2_t >

void o2scl::inte_kronrod_gsl< func_t >::gauss_kronrod_base	(	func2_t &	func,
		double	a,
		double	b,
		double *	result,
		double *	abserr,
		double *	resabs,
		double *	resasc
	)

inline

Given abcissas and weights, this performs the integration of func between a and b, providing a result with uncertainties.

The Gauss-Kronrod rule uses $ 2m+1 $ abscissae $x_1, \ldots, x_{2m+1} \in (a, b)$ to estimate the integral of a function as a linear combination of values,

$\int_a^b f~dx \; \approx \; Q_m^{GK}f \; \equiv \; \sum_{k=1}^{2m+1} \beta_k f(x_k),$

where the weights $\beta_1,\ldots, \beta_{2m+1}$ are intrinsic to the abscissae. The data are designed so that the even-indexed abscissae yield a coarser estimate,

$Q_m^{G}f \; \equiv \; \sum_{j=1}^{m} \alpha_j f(x_{2j}),$

and their difference $|Q_m^Gf - Q_m^{GK}f|$ is the "raw" error estimate. The various quantities that the function computes are

$\begin{eqnarray*} \mathtt{result} &=& Q_m^{GK}f, \\ \mathtt{resabs} &=& Q_m^{GK}|f|, \\ \mathtt{resasc} &=& Q_m^{GK}(|f| - \mu), \quad \mu \equiv \frac{Q_m^{GK}f}{b - a}. \end{eqnarray*}$

The "absolute" error abserr is computed from the raw error value using the function inte_gsl::rescale_error.

This function is designed for use with the values given in the o2scl_inte_gk_coeffs namespace.

This function never calls the error handler.

Idea for Future:: This function, in principle, is an integration object in and of itself, and could be implemented separately as an object of type o2scl::inte.

Definition at line 798 of file inte_kronrod_gsl.h.

◆ get_rule()

template<class func_t >

int o2scl::inte_kronrod_gsl< func_t >::get_rule ( )

inline

This returns the index of the GSL integration rule a number between 1 and 6 (inclusive)

Definition at line 663 of file inte_kronrod_gsl.h.

◆ set_limit()

template<class func_t >

int o2scl::inte_kronrod_gsl< func_t >::set_limit ( size_t lim )

inline

If the value of size is zero, the error handler will be called.

Definition at line 745 of file inte_kronrod_gsl.h.

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

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

Detailed Description

template<class func_t> class o2scl::inte_kronrod_gsl< func_t >

Public Member Functions

Protected Attributes

Additional Inherited Members

Member Function Documentation

◆ gauss_kronrod_base()

◆ get_rule()

◆ set_limit()

template<class func_t>
class o2scl::inte_kronrod_gsl< func_t >