Adaptive integration with with algebraic-logarithmic singularities at the end-points (GSL) More...
#include <inte_qaws_gsl.h>
This class computes the weighted integral
where the parameters of the weight function must satisfy
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.
Public Member Functions | |
inte_qaws_gsl () | |
Initialize the adptive workspace as with the constructor inte_qag_gsl::inte_qag_gsl. More... | |
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") | |
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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... | |
Protected Member Functions | |
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. | |
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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 | |
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 . | |
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] |
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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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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... | |
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inline |
The default paramters of the weight function are all zero.
Definition at line 372 of file inte_qaws_gsl.h.
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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.
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inline |
The parameters determine the exponents of the weight function
and must satsify
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.
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