Public Member Functions | Protected Member Functions | List of all members
o2scl::inte_qag_gsl< func_t > Class Template Reference

Adaptive numerical integration of a function (without singularities) on a bounded interval (GSL) More...

#include <inte_qag_gsl.h>

Inheritance diagram for o2scl::inte_qag_gsl< func_t >:
o2scl::inte_kronrod_gsl< func_t > o2scl::inte_gsl o2scl::inte< func_t >

Public Member Functions

 inte_qag_gsl ()
 Create an integrator with the specified rule.
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. More...
const char * type ()
 Return string denoting type ("inte_qag_gsl")
- Public Member Functions inherited from o2scl::inte_kronrod_gsl< func_t >
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.
double get_error ()
 Return the numerically estimated error in the result from the last call to integ() More...

Protected Member Functions

int qag (func_t &func, const double a, const double b, const double l_epsabs, const double l_epsrel, double *result, double *abserr)
 Perform an adaptive integration given the coefficients, and returning result. 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...

Additional Inherited Members

- Public Attributes inherited from o2scl::inte< func_t >
int verbose
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 Attributes inherited from o2scl::inte_kronrod_gsl< func_t >
 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.

Detailed Description

template<class func_t = funct11>
class o2scl::inte_qag_gsl< func_t >

Adaptive integration of a univariate function requires two main procedures: approximating the integral on a bounded interval, and estimating the approximation error. The algorithm recursively refines the interval, computing the integral and its error estimate on each subinterval, until the total error estimate over all subintervals falls within the user-specified tolerance. The value returned is the sum of the (approximated) integrals over all subintervals.

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

Idea for Future:

There are a few fine-tuned parameters which should be re-expressed as data members in the convergence tests.

Should QUADPACK parameters in round-off tests be subject to adjustments by the end user?

Add functions to examine the contents of the workspace to detect regions where the integrand may be problematic; possibly call these functions automatically depending on verbosity settings.

Definition at line 80 of file inte_qag_gsl.h.

Member Function Documentation

◆ integ_err()

template<class func_t = funct11>
virtual int o2scl::inte_qag_gsl< func_t >::integ_err ( func_t &  func,
double  a,
double  b,
double &  res,
double &  err 

Implements o2scl::inte< func_t >.

Definition at line 95 of file inte_qag_gsl.h.

◆ qag()

template<class func_t = funct11>
int o2scl::inte_qag_gsl< func_t >::qag ( func_t &  func,
const double  a,
const double  b,
const double  l_epsabs,
const double  l_epsrel,
double *  result,
double *  abserr 
Idea for Future:
Just move this function to integ_err().

Definition at line 109 of file inte_qag_gsl.h.

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

Documentation generated with Doxygen. Provided under the GNU Free Documentation License (see License Information).