Class inte_adapt_cern_tl (o2scl)¶

O2scl : Class List

template<class fp_25_t = o2fp_25, class fp_35_t = o2fp_35, class fp_50_t = o2fp_50, class fp_100_t = o2fp_100> class inte_adapt_cern_tl¶

Adaptive integration (CERNLIB)

Uses a base integration object (default is inte_gauss56_cern) to perform adaptive integration by automatically subdividing the integration interval. At each step, the interval with the largest absolute uncertainty is divided in half. The routine succeeds if the absolute tolerance is less than tol_abs or if the relative tolerance is less than tol_rel, i.e.

\[ \mathrm{err}\leq\mathrm{tol\_abs}~\mathrm{or}~ \mathrm{err}\leq\mathrm{tol\_rel}\cdot|I| \]

where \( I \) is the current estimate for the integral and \( \mathrm{err} \) is the current estimate for the uncertainty. If the number of subdivisions exceeds the template parameter nsub, the error handler is called, since the integration may not have been successful. The number of subdivisions used in the last integration can be obtained from get_nsubdivisions().

The template parameter nsub, is the maximum number of subdivisions. It is automatically set to 100 in the original CERNLIB routine, and defaults to 100 here. The default base integration object is of type inte_gauss56_cern. This is the CERNLIB default, but can be modified by calling set_inte().

This class is based on the CERNLIB routines RADAPT and DADAPT which are documented at http://wwwasdoc.web.cern.ch/wwwasdoc/shortwrupsdir/d102/top.html

Idea for Future:

Allow user to set the initial subdivisions?
It might be interesting to directly compare the performance of this class to o2scl::inte_qag_gsl .
There is a fixme entry in the code which could be resolved.
Output the point where most subdividing was required?

Integration settings

int nsub¶: The number of subdivisions for the next integration.

double tol_rel_multip¶: The maximum relative uncertainty for multipreicsion integrals (default \( -1 \))

double pow_tol_func¶: Power for tolerance of function evaluations in multiprecision integrations (default 1.33)

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 \( 10^{-8} \))

int verbose¶: Verbosity parameter.

bool err_nonconv¶: If true, call the error handler if the integration does not succeed (default true)

int last_iter¶: The last number of required iterations.

inline void set_nsub(int n)¶: Set the number of subdivisions for the next integration.

Subdivisions

size_t nsubdiv¶

Number of subdivisions.

The options are

0: Use previous binning and do not subdivide further
1: Automatic - adapt until tolerance is attained (default)
n: (n>1) split first in n equal subdivisions, then adapt until tolerance is obtained.

Internal integration functions [protected]

template<typename func_t, class fp_t> inline int integ_err_funct(func_t &func, fp_t a, fp_t b, fp_t &res, fp_t &err, double target_tol, double integ_tol, inte_subdiv<fp_t> &is)¶: Integrate function func from a to b giving result res and error err.

template<typename func_t, class fp_t> inline int integ_iu_err_int(func_t &&func, fp_t a, fp_t &res, fp_t &err, double target_tol, double integ_tol, double func_tol)¶: Desc.

template<typename func_t, class fp_t> inline int integ_il_err_int(func_t &&func, fp_t b, fp_t &res, fp_t &err, double target_tol, double integ_tol, double func_tol)¶: Desc.

template<typename func_t, class fp_t> inline int integ_i_err_int(func_t &&func, fp_t &res, fp_t &err, double target_tol, double integ_tol, double func_tol)¶: Desc.

template<typename func_t, class fp_t> inline int integ_err_int(func_t &&func, fp_t a, fp_t b, fp_t &res, fp_t &err, double target_tol, double integ_tol, double func_tol)¶: Internal version of integration function.

Constructor

inline inte_adapt_cern_tl()¶

Integration functions

template<typename func_t, class fp_t> inline int integ_err(func_t &func, fp_t a, fp_t b, fp_t &res, fp_t &err)¶: Integrate function func from a to b and place the result in res and the error in err.

template<typename func_t, class fp_t> inline int integ_il_err(func_t &func, fp_t b, fp_t &res, fp_t &err)¶: Integrate function func from a to b and place the result in res and the error in err.

template<typename func_t, class fp_t> inline int integ_iu_err(func_t &func, fp_t a, fp_t &res, fp_t &err)¶: Integrate function func from a to b and place the result in res and the error in err.

template<typename func_t, class fp_t> inline int integ_i_err(func_t &func, fp_t &res, fp_t &err)¶: Integrate function func from a to b and place the result in res and the error in err.

template<typename func_t, class fp_t> inline fp_t integ(func_t &func, fp_t a, fp_t b)¶: Integrate function func from a to b.

Integration specifying subdivision

template<typename func_t, class fp_t> inline int integ_err_is(func_t &func, fp_t a, fp_t b, fp_t &res, fp_t &err, inte_subdiv<fp_t> &is)¶: Integrate function func from a to b and place the result in res and the error in err.

template<typename func_t, class fp_t> inline int integ_il_err_is(func_t &func, fp_t b, fp_t &res, fp_t &err, inte_subdiv<fp_t> &is)¶: Integrate function func from a to b and place the result in res and the error in err.

template<typename func_t, class fp_t> inline int integ_iu_err_is(func_t &func, fp_t a, fp_t &res, fp_t &err, inte_subdiv<fp_t> &is)¶: Integrate function func from a to b and place the result in res and the error in err.

template<typename func_t, class fp_t> inline int integ_i_err_is(func_t &func, fp_t &res, fp_t &err, inte_subdiv<fp_t> &is)¶: Integrate function func from a to b and place the result in res and the error in err.

Multipreicison integration functions

template<typename func_t, class fp_t> inline int integ_err_multip(func_t &&func, fp_t a, fp_t b, fp_t &res, fp_t &err, double integ_tol = -1.0)¶: Integrate function func from a to b using multiprecision, placing the result in res and the error in err.

template<typename func_t, class fp_t> inline int integ_iu_err_multip(func_t &&func, fp_t a, fp_t &res, fp_t &err, double integ_tol = -1.0)¶: Integrate function func from a to b using multiprecision, placing the result in res and the error in err.

template<typename func_t, class fp_t> inline int integ_il_err_multip(func_t &&func, fp_t b, fp_t &res, fp_t &err, double integ_tol = -1.0)¶: Integrate function func from a to b using multiprecision, placing the result in res and the error in err.

template<typename func_t, class fp_t> inline int integ_i_err_multip(func_t &&func, fp_t &res, fp_t &err, double integ_tol = -1.0)¶: Integrate function func from a to b using multiprecision, placing the result in res and the error in err.