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Object-oriented Scientific Computing Library: Version 0.910
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Base class for integrating a function with a singularity (GSL) More...
#include <gsl_inte_singular.h>
This class contains the extrapolation table mechanics and the base integration function for singular integrals from GSL. The casual end-user should use the classes explained in the Integration section of the User's guide.
Definition at line 50 of file gsl_inte_singular.h.
Data Structures | |
struct | extrapolation_table |
A structure for extrapolation for gsl_inte_qags. More... | |
Public Types | |
typedef struct gsl_inte_singular::extrapolation_table | extrap_table |
A structure for extrapolation for gsl_inte_qags. | |
Protected Member Functions | |
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. | |
int | large_interval (gsl_inte_workspace *workspace) |
Determine if an interval is large. | |
void | reset_nrmax (gsl_inte_workspace *workspace) |
Reset workspace to work on the interval with the largest error. | |
int | increase_nrmax (gsl_inte_workspace *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. |
typedef struct gsl_inte_singular::extrapolation_table gsl_inte_singular< func_t >::extrap_table |
void gsl_inte_singular< func_t >::qelg | ( | struct extrapolation_table * | table, |
double * | result, | ||
double * | abserr | ||
) | [inline, protected] |
For certain convergent series whose error term
is well behaved, it is possible to find a transformation of the sequence that yields a faster converging series to the same limit. This method of extrapolation applies to some sequences of adaptive-approximation and error-estimation for numerical integration. This function implements the
-algorithm (Wynn56, Piessens83) for an extrapolation table stored in
table
.
Quadpack documentation
c c list of major variables c ----------------------- c e0 - the 4 elements on which the computation of a new c e1 element in the epsilon table is based c e2 c e3 e0 c e3 e1 new c e2 c newelm - number of elements to be computed in the new c diagonal c error - error = abs(e1-e0)+abs(e2-e1)+abs(new-e2) c result - the element in the new diagonal with least value c of error c c machine dependent constants c --------------------------- c c epmach is the largest relative spacing. c oflow is the largest positive magnitude. c limexp is the maximum number of elements the epsilon c table can contain. if this number is reached, the upper c diagonal of the epsilon table is deleted. c
Definition at line 136 of file gsl_inte_singular.h.
int gsl_inte_singular< func_t >::qags | ( | func_t & | func, |
const double | a, | ||
const double | b, | ||
const double | l_epsabs, | ||
const double | l_epsrel, | ||
double * | result, | ||
double * | abserr | ||
) | [inline, protected] |
Definition at line 344 of file gsl_inte_singular.h.
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