Adaptive integration for oscillatory integrals (GSL) More...
#include <inte_qawo_gsl.h>
The integral
is computed for some frequency parameter , 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 where
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
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.
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 . | |
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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. | |
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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... | |
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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) | |
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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 ![]() | |
double | tol_abs |
The maximum absolute uncertainty in the value of the integral (default ![]() | |
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") | |
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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... | |
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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 ![]() | |
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... | |
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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. | |
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inte_workspace_gsl * | w |
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. | |
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double | interror |
The uncertainty for the last integration computation. | |
Additional Inherited Members | |
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typedef struct o2scl::inte_singular_gsl::extrapolation_table | extrap_table |
A structure for extrapolation for inte_qags_gsl. More... | |
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inlineprotected |
Definition at line 104 of file inte_qawo_gsl.h.
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