Gaussian quadrature (CERNLIB) More...
#include <inte_gauss_cern.h>
For any interval , we define
and
to be the 8- and 16-point Gaussian quadrature approximations to
and define
The function integ() returns given by
where and
and the subdivision points
are given by
where is the first number in the sequence
for which
If, at any stage, the ratio
is so small so that is indistinguishable from unity, then the accuracy is required is not reachable and the error handler is called.
Unless there is severe cancellation, inte::tol_rel may be considered as specifying a bound on the relative error of the integral in the case that and an absolute error if
. More precisely, if
is the number of subintervals from above, and if
then
will nearly always be true when no error is returned. For functions with no singualarities in the interval, the accuracy will usually be higher than this.
If the desired accuracy is not achieved, the integration functions will call the error handler and return the best guess, unless inte::err_nonconv is false, in which case the error handler is not called.
This function is based on the CERNLIB routines GAUSS and DGAUSS which are documented at http://wwwasdoc.web.cern.ch/wwwasdoc/shortwrupsdir/d103/top.html
cst
? Definition at line 96 of file inte_gauss_cern.h.
Public Member Functions | |
virtual int | integ_err (func_t &func, double a, double b, double &res, double &err) |
Integrate function func from a to b . | |
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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... | |
virtual const char * | type () |
Return string denoting type ("inte") | |
Protected Attributes | |
Integration constants (Set in the constructor) | |
double | x [12] |
double | w [12] |
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double | interror |
The uncertainty for the last integration computation. | |
Additional Inherited Members | |
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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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