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

Adaptive Cauchy principal value integration (GSL) More...

#include <inte_qawc_gsl.h>

Inheritance diagram for o2scl::inte_qawc_gsl< func_t >:
o2scl::inte_cheb_gsl< func_t > o2scl::inte_transform_gsl< func_t > o2scl::inte_singular_gsl< func_t > o2scl::inte_kronrod_gsl< func_t > o2scl::inte_gsl o2scl::inte< func_t >

Public Member Functions

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 Member Functions inherited from o2scl::inte_transform_gsl< func_t >
virtual void gauss_kronrod (func_t &func, double a, double b, double *result, double *abserr, double *resabs, double *resasc)
 Integration wrapper for internal transformed function type.
 
- 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...
 
- 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...
 

Public Attributes

double s
 The singularity.
 
- 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

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()
 
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
 
virtual double transform (double t, func_t &func)
 Add the singularity to the function.
 
const char * type ()
 Return string denoting type ("inte_qawc_gsl")
 
- Protected Member Functions inherited from o2scl::inte_cheb_gsl< func_t >
void compute_moments (double cc, double *moment)
 Compute the Chebyshev moments.
 
template<class func2_t >
void inte_cheb_series (func2_t &f, double a, double b, double *cheb12, double *cheb24)
 Compute Chebyshev series expansion using a FFT method. More...
 
- Protected Member Functions inherited from o2scl::inte_singular_gsl< func_t >
void initialise_table (struct extrapolation_table *table)
 Initialize the table.
 
void append_table (struct extrapolation_table *table, double y)
 Append a result to the table.
 
int test_positivity (double result, double resabs)
 Test if the integrand satisfies $ f = |f| $.
 
void qelg (struct extrapolation_table *table, double *result, double *abserr)
 Determines the limit of a given sequence of approximations. More...
 
int large_interval (inte_workspace_gsl *workspace)
 Determine if an interval is large.
 
void reset_nrmax (inte_workspace_gsl *workspace)
 Reset workspace to work on the interval with the largest error.
 
int increase_nrmax (inte_workspace_gsl *workspace)
 Increase workspace.
 
int qags (func_t &func, const double a, const double b, const double l_epsabs, const double l_epsrel, double *result, double *abserr)
 Integration function. 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 Types inherited from o2scl::inte_singular_gsl< func_t >
typedef struct o2scl::inte_singular_gsl::extrapolation_table extrap_table
 A structure for extrapolation for inte_qags_gsl. More...
 
- Protected Attributes inherited from o2scl::inte_kronrod_gsl< func_t >
inte_workspace_gslw
 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>
class o2scl::inte_qawc_gsl< func_t >

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 routines 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

Definition at line 351 of file inte_qawc_gsl.h.


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

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