Adaptive integration with with algebraic-logarithmic singularities at the end-points (GSL) More...
#include <inte_qaws_gsl.h>
Inheritance diagram for o2scl::inte_qaws_gsl< func_t >:
Detailed Description
template<class func_t = funct>
class o2scl::inte_qaws_gsl< func_t >
This class computes the weighted integral
![\[ \int_a^b f(x)(x - a)^\alpha (b - x)^\beta \log^\mu(x - a) \log^\nu(b - x)~dx \]](form_238.png)
where the parameters of the weight function must satisfy
![\[ \alpha > -1, \quad \beta > -1, \quad \mu \in \{0, 1\}, \quad \nu \in \{0, 1\}, \]](form_239.png)
and which are set by set_weight(). Note that setting 
or 
removes the respective factor 
or 
from the weight.
The adaptive refinement algorithm described for inte_qag_gsl is used. When a subinterval contains one of the endpoints, a special 25-point modified Clenshaw-Curtis rule is used to control the singularities. For subintervals which do not include the endpoints, a Gauss-Kronrod integration rule is used.
See GSL-based integration routines in the User's guide for general information about the GSL integration classes.
Definition at line 80 of file inte_qaws_gsl.h.
Data from \c gsl_integration_qaws_table | |
| double | alpha |
| double | beta |
| int | mu |
| int | nu |
| double | ri [25] |
| double | rj [25] |
| double | rg [25] |
| double | rh [25] |
| bool | fn_qaws_R |
True if algebraic-logarithmic singularity is present at the right endpoint in the definition f_trans. | |
| bool | fn_qaws_L |
True if algebraic-logarithmic singularity is present at the left endpoint in the definition f_trans. | |
| double | left_endpoint |
Left endpoint in definition of f_trans. | |
| double | right_endpoint |
Right endpoint in definition of f_trans. | |
| void | initialise_qaws_table () |
Set the array values ri, rj, rg, rh from the current values alpha and beta. More... | |
| virtual double | transform (double t, func_t &func) |
| Weighted integrand. | |
| void | qc25s (func_t &func, double a, double b, double a1, double b1, double &result, double &abserr, int &err_reliable) |
| Clenshaw-Curtis 25-point integration and error estimator for functions with an algebraic-logarithmic singularity at the endpoint(s). | |
| void | compute_result (double *r, double *cheb12, double *cheb24, double &result12, double &result24) |
| Compute the 13-point and 25-point approximations from the Chebyshev moments and coefficients. | |
| inte_qaws_gsl () | |
| Initialize the adptive workspace as with the constructor inte_qag_gsl::inte_qag_gsl. More... | |
| ~inte_qaws_gsl () | |
| int | set_weight (double u_alpha, double u_beta, int u_mu, int u_nu) |
| Sets the exponents of singularites of the weight function. More... | |
| void | get_weight (double &u_alpha, double &u_beta, int &u_mu, int &u_nu) |
| Returns the current values (via reference) of the weight-function's parameters. | |
| virtual int | integ_err (func_t &func, double a, double b, double &result, double &abserr) |
Integrate the function func on the interval (a, b) returning the result and error estimate abserr. | |
| const char * | type () |
| Return string denoting type ("inte_qaws_gsl") | |
Additional Inherited Members | |
 Public Types inherited from o2scl::inte_singular_gsl< funct > | |
| typedef struct o2scl::inte_singular_gsl::extrapolation_table | extrap_table |
| A structure for extrapolation for o2scl::inte_qags_gsl. More... | |
| Public Member Functions inherited from o2scl::inte_transform_gsl< funct > | |
| virtual double | transform (double t, funct &func)=0 |
| The transformation to apply to the user-supplied function. | |
| virtual void | gauss_kronrod (funct &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< funct > | |
| 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... | |
| 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< funct > | |
| virtual double | integ (funct &func, double a, double b) |
Integrate function func from a to b. | |
| virtual int | integ_err (funct &func, double a, double b, double &res, double &err)=0 |
Integrate function func from a to b and place the result in res and the error in err. | |
| double | get_error () |
| Return the numerically estimated error in the result from the last call to integ() More... | |
| Public Attributes inherited from o2scl::inte< funct > | |
| 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 inherited from o2scl::inte_cheb_gsl< funct > | |
| void | compute_moments (double cc, double *moment) |
| Compute the Chebyshev moments. | |
| 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< funct > | |
| 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 (funct &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 inherited from o2scl::inte_kronrod_gsl< funct > | |
| 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. | |
| Protected Attributes inherited from o2scl::inte< funct > | |
| double | interror |
| The uncertainty for the last integration computation. | |
Constructor & Destructor Documentation
◆ inte_qaws_gsl()
template<class func_t = funct>
|
inline |
The default paramters 
of the weight function are all zero.
Definition at line 372 of file inte_qaws_gsl.h.
Member Function Documentation
◆ initialise_qaws_table()
template<class func_t = funct>
|
inlineprotected |
This is the function from the GSL source code integration/qmomo.c that initializes gsl_integration_qaws_table.
Definition at line 107 of file inte_qaws_gsl.h.
◆ set_weight()
template<class func_t = funct>
|
inline |
The parameters determine the exponents of the weight function
![\[ W(x) = (x-a)^\alpha (b-x)^\beta \log^\mu(x-a) \log^\nu(b-x), \]](form_245.png)
and must satsify
![\[ \alpha > -1, \quad \beta > -1, \quad \mu \in \{0, 1\}, \quad \nu \in \{0, 1\}. \]](form_246.png)
In order for the adaptive algorithm to run quickly, a table of Chebyshev weights for the particular parameters are computed in advance.
Definition at line 393 of file inte_qaws_gsl.h.
The documentation for this class was generated from the following file:
- /home/awsteiner/wcs/o2scl/src/inte/inte_qaws_gsl.h