Class inte_cauchy_cern (o2scl)

O2scl : Class List

template<class func_t, class fp_t = double, class weights_t = inte_gauss_coeffs_double>
class inte_cauchy_cern : public o2scl::inte<func_t, double>

Cauchy principal value integration (CERNLIB)

The location of the singularity must be specified before-hand in inte_cauchy_cern::s, and the singularity must not be at one of the endpoints. Note that when integrating a function of the form \( \frac{f(x)}{(x-s)} \), the denominator \( (x-s) \) must be specified in the argument func to integ(). This is different from how the inte_qawc_gsl operates.

The method from [Longman58] is used for the decomposition of the integral, and the resulting integrals are computed using a user-specified base integration object.

The uncertainty in the integral is not calculated, and is always given as zero. The default base integration object is of type inte_gauss_cern. This is the CERNLIB default, but can be modified by calling set_inte(). If the singularity is outside the region of integration, then the result from the base integration object is returned without calling the error handler.

Possible errors for integ() and integ_err():

• exc_einval - Singularity is on an endpoint

• exc_efailed - Could not reach requested accuracy (occurs only if inte::err_nonconv is true)

This function is based on the CERNLIB routines RCAUCH and DCAUCH which are documented at http://wwwasdoc.web.cern.ch/wwwasdoc/shortwrupsdir/d104/top.html

Note

Currently supports only types double and long double for the floating point type fp_t .

Public Functions

inline inte_cauchy_cern()

inline int set_inte(inte<func_t, fp_t> &i)

Set the base integration object to use (default is inte_cauchy_cern::def_inte of type inte_gauss_cern)

inline virtual 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.

Public Members

const fp_t *w

const fp_t *x

weights_t wgts

fp_t s

The singularity (must be set before calling integ() or integ_err())

inte_gauss_cern<func_t, fp_t> def_inte

Default integration object.

Protected Attributes

inte<func_t, fp_t> *it

The base integration object.