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

Adaptive integration for oscillatory integrals (GSL) More...

#include <inte_qawo_gsl.h>

Inheritance diagram for o2scl::inte_qawo_gsl_sin< 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 > o2scl::inte_qawf_gsl_sin< func_t > o2scl::inte_qawo_gsl_cos< func_t > o2scl::inte_qawf_gsl_cos< 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 omega
 The user-specified frequency (default 1.0)
size_t n_levels
 The number of bisection levels (default 10)
- 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 Member Functions

int qawo (func_t &func, const double a, const double epsabs, const double epsrel, inte_workspace_gsl *loc_w, gsl_integration_qawo_table *wf, double *result, double *abserr)
 The full GSL integration routine called by integ_err() More...
void qc25f (func_t &func, double a, double b, gsl_integration_qawo_table *wf, size_t level, double *result, double *abserr, double *resabs, double *resasc)
 25-point quadrature for oscillating functions
virtual double transform (double t, func_t &func)
 Add the oscillating part to the integrand.
const char * type ()
 Return string denoting type ("inte_qawo_gsl_sin")
- 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...

Protected Attributes

gsl_integration_qawo_table * otable
 The integration workspace.
- 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.

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...

Detailed Description

template<class func_t>
class o2scl::inte_qawo_gsl_sin< func_t >

The integral

\[ \int_a^b f(x) \sin (\omega x)~dx \]

is computed for some frequency parameter $ \omega $, stored in inte_qawo_gsl_sin::omega .

An adaptive algorithm together with an series-acceleration method like that of inte_qags_gsl is used. Those subintervals with "large" widths $ d \equiv b-a $ where $ d\omega > 4 $ are computed using a 25-point Clenshaw-Curtis integration rule to handle the oscillatory behavior. In order to work efficiently, the Chebyshev moments for the particular weight function $ W $ are computed in advance.

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

Definition at line 58 of file inte_qawo_gsl.h.

Member Function Documentation

◆ qawo()

template<class func_t >
int o2scl::inte_qawo_gsl_sin< func_t >::qawo ( func_t &  func,
const double  a,
const double  epsabs,
const double  epsrel,
inte_workspace_gsl loc_w,
gsl_integration_qawo_table *  wf,
double *  result,
double *  abserr 
Idea for Future:
Remove goto statements.

Definition at line 104 of file inte_qawo_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).