C API

The C library contains a selection numerical integration functions based on equivalents in the GSL numerical integration package. To use these functions the lintegrate.h header file must be included.

For all these functions the input gsl_function f should return the natural logarithm of the required integrand. The outputs will include the natural logarithm of the resulting integral.

QNG non-adaptive Gauss-Kronrod integration

int lintegration_qng (const gsl_function *f, double a, double b, double epsabs, double epsrel, double * result, double * abserr, size_t * neval)

This is the equivalent of the GSL gsl_integration_qng() function (see the link for a description of the arguments and return values). It applies a non-adaptive procedure which applied the Gauss-Kronrod integration rules. The output will include the natural logarithm of the resulting integral.

int lintegration_qng_split (const gsl_function *f, double *splitpts, size_t npts, double epsabs, double epsrel, double * result, double * abserr, size_t * neval)

In some cases it might be necessary to split the integral into multiple segments that are integrated separately and then combined. For example, if there is a large dynamic range for the abscissa variable. The “split” version of lintegration_qng() takes in an array of values splitpts giving the bounds (including of the upper bound point) and the length of that array npts. The other arguments are the same as for lintegration_qng().

QAG adaptive integration

int lintegration_qag (const gsl_function *f, double a, double b, double epsabs, double epsrel, size_t limit, int key, gsl_integration_workspace * workspace, double * result, double * abserr)

This is the equivalent of the GSL gsl_integration_qag() function (see the links for a description of the arguments and return values). It applies a simple adaptive integration procedure. The integration region is divided into subintervals, and on each iteration the subinterval with the largest estimated error is bisected.

int lintegration_qag_split (const gsl_function *f, double *splitpts, size_t npts, double epsabs, double epsrel, size_t limit, int key, double * result, double * abserr)

In some cases it might be necessary to split the integral into multiple segments that are integrated separately and then combined. For example, if there is a large dynamic range for the abscissa variable. The “split” version of lintegration_qag() takes in an array of values splitpts giving the bounds (including of the upper bound point) and the length of that array npts. The other arguments are the same as for lintegration_qag() except that is does not require a gsl_integration_workspace.

CQUAD doubly-adaptive integration

int lintegration_cquad (const gsl_function * f, double a, double b, double epsabs, double epsrel, gsl_integration_cquad_workspace * ws, double *result, double *abserr, size_t * nevals)

This is the equivalent of the GSL gsl_integration_cquad() function (see the links for a description of the arguments and return values). The algorithm uses a doubly-adaptive scheme in which Clenshaw-Curtis quadrature rules of increasing degree are used to compute the integral in each interval. It can handle most types of singularities, non-numerical function values such as Inf or NaN, as well as some divergent integrals.

int lintegration_cquad_split (const gsl_function * f, double *splitpts, size_t npts, double epsabs, double epsrel, size_t wsints, double *result, double *abserr, size_t * nevals)

In some cases it might be necessary to split the integral into multiple segments that are integrated separately and then combined. For example, if there is a large dynamic range for the abscissa variable. The “split” version of lintegration_cquad() takes in an array of values splitpts giving the bounds (including of the upper bound point) and the length of that array npts. The other arguments are the same as for lintegration_cquad(). It does not require a gsl_integration_cquad_workspace, but does take in wsints to set the maximum number of intervals for each gsl_integration_cquad_workspace allocated via gsl_integration_cquad_workspace_alloc().