Class inte_qawc_gsl (o2scl)

O2scl : Class List

template<class func_t>
class inte_qawc_gsl : public o2scl::inte_cheb_gsl<func_t>

Adaptive Cauchy principal value integration (GSL)

The Cauchy principal value of the integral of

\[ \int_a^b \frac{f(x)}{x-c}~dx = \lim_{\epsilon\to 0^+} \left\{ \int_a^{c-\epsilon} \frac{f(x)}{x-c}~dx + \int_{c+\epsilon}^b \frac{f(x)}{x-c}~dx \right\}. \]

over \( (a,b), \) with a singularity at \( c, \) is computed. The adaptive refinement algorithm described for inte_qag_gsl is used with modifications to ensure that subdivisions do not occur at the singular point \( x = c\) . When a subinterval contains the point \( x = c \) or is close to it, a special 25-point modified Clenshaw-Curtis rule is used to control the singularity. Further away from the singularity the algorithm uses a Gauss-Kronrod integration rule.

The location of the singularity must be specified before-hand in inte_qawc_gsl::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 not be specified in the argument func to integ(). Note that this is different from how the inte_cauchy_cern operates.

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

Idea for Future:

Make inte_cauchy_cern and this class consistent in the way which they require the user to provide the denominator in the integrand

Public Functions

inline inte_qawc_gsl()

inline virtual ~inte_qawc_gsl()

inline 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 Members

double s

The singularity.

Protected Functions

inline int qawc(func_t &func, const double a, const double b, const double c, const double epsabs, const double epsrel, double *result, double *abserr)

The full GSL integration routine called by integ_err()

inline void qc25c(func_t &func, double a, double b, double c, double *result, double *abserr, int *err_reliable)

25-point quadrature for Cauchy principal values

inline virtual double transform(double t, func_t &func)

Add the singularity to the function.

inline virtual const char *type()

Return string denoting type (“inte_qawc_gsl”)