Class inte_qaws_gsl (o2scl)¶

template<class func_t = funct> class inte_qaws_gsl : public o2scl::inte_cheb_gsl<funct>¶

Adaptive integration with with algebraic-logarithmic singularities at the end-points (GSL)

This class computes the weighted integral

\[ \int_a^b f(x)(x - a)^\alpha (b - x)^\beta \log^\mu(x - a) \log^\nu(b - x)~dx \]

where the parameters of the weight function must satisfy

\[ \alpha > -1, \quad \beta > -1, \quad \mu \in \{0, 1\}, \quad \nu \in \{0, 1\}, \]

and which are set by set_weight(). Note that setting \( \mu=0 \) or \( \nu=0 \) removes the respective factor \( \log^mu(\ldots) \) or \( \log^\nu(\ldots) \) 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 details in the User’s guide for general information about the GSL integration classes.

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.

inline void initialise_qaws_table()¶

Set the array values ri, rj, rg, rh from the current values alpha and beta.

This is the function from the GSL source code integration/qmomo.c that initializes gsl_integration_qaws_table.

inline virtual double transform(double t, func_t &func)¶: Weighted integrand.

inline 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).

inline 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.

inline inte_qaws_gsl()¶

Initialize the adptive workspace as with the constructor inte_qag_gsl::inte_qag_gsl.

The default paramters \( \alpha, \beta, \mu, \nu \) of the weight function are all zero.

inline ~inte_qaws_gsl()¶

inline int set_weight(double u_alpha, double u_beta, int u_mu, int u_nu)¶

Sets the exponents of singularites of the weight function.

The parameters determine the exponents of the weight function

\[ W(x) = (x-a)^\alpha (b-x)^\beta \log^\mu(x-a) \log^\nu(b-x), \]

and must satsify

\[ \alpha > -1, \quad \beta > -1, \quad \mu \in \{0, 1\}, \quad \nu \in \{0, 1\}. \]

In order for the adaptive algorithm to run quickly, a table of Chebyshev weights for the particular parameters are computed in advance.

inline 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.

inline 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.

inline virtual const char *type()¶: Return string denoting type (“inte_qaws_gsl”)