Functions for performing numerical integration (quadrature). More...

Functions
void	qagi (std::function< double(double)> f, double bound, const int inf, const double epsabs, const double epsrel, double &result, double &abserr, unsigned int &status)
	Estimates an integral over a semi-infinite or infinite interval.
void	qk15i (std::function< double(double)> f, double bound, const int inf, const double a, const double b, double &result, double &abserr, double &resabs, double &resasc)
	15-point Gauss-Kronrod integration with (semi-)infinite integration range.
void	qk15 (std::function< double(double)> f, const double a, const double b, double &result, double &abserr, double &resabs, double &resasc)
	15-point Gauss-Kronrod integration with finite integration range.

Detailed Description

Functions for performing numerical integration (quadrature).

Reimplemented from QUADPACK.

R. Piessens, E. de Doncker-Kapenger, C. Ueberhuber, D. Kahaner, QUADPACK, a Subroutine Package for Automatic Integration, Springer, 1983

Function Documentation

void Garfield::Numerics::QUADPACK::qagi	(	std::function< double(double)>	f,
		double	bound,
		const int	inf,
		const double	epsabs,
		const double	epsrel,
		double &	result,
		double &	abserr,
		unsigned int &	status )

Estimates an integral over a semi-infinite or infinite interval.

Calculates an approximation to an integral

$I = \int_{a}^{\infty} f\left(x\right) dx,$

or

$I = \int_{-\infty}^{a} f\left(x\right) dx,$

or

$I = \int_{-\infty}^{\infty} f\left(x\right) dx$

hopefully satisfying

$\left| I - \mathrm{RESULT} \right| \leq \max(\varepsilon_{\mathrm{abs}}, \varepsilon_{\mathrm{rel}} \left|I\right|).$

Parameters

f	function to be integrated.
bound	value of the finite endpoint of the integration range (if any).
inf	indicates the type of integration range. 1: ( bound, +Infinity) -1: (-Infinity, bound) 2: (-Infinity, +Infinity)
epsabs	requested absolute accuracy
epsrel	requested relative accuracy
result	the estimated value of the integral
abserr	estimated error
status	error flag 0: normal and reliable termination, requested accuracy has been achieved. > 0: abnormal termination, estimates for result and error are less reliable. 1: maximum number of subdivisions reached. 2: occurance of roundoff error prevents the requested tolerance from being achieved. Error may be underestimated. 3: extremely bad integrand behaviour at some points of the integration interval. 4: algorithm does not converge, roundoff error is detected in the extrapolation table. It is assumed that the requested tolerance cannot be achieved and that the returned result is the best that can be obtained. 5: integral is probably divergent, or slowly convergent. 6: invalid input.

void Garfield::Numerics::QUADPACK::qk15	(	std::function< double(double)>	f,
		const double	a,
		const double	b,
		double &	result,
		double &	abserr,
		double &	resabs,
		double &	resasc )

15-point Gauss-Kronrod integration with finite integration range.

void Garfield::Numerics::QUADPACK::qk15i	(	std::function< double(double)>	f,
		double	bound,
		const int	inf,
		const double	a,
		const double	b,
		double &	result,
		double &	abserr,
		double &	resabs,
		double &	resasc )

15-point Gauss-Kronrod integration with (semi-)infinite integration range.

Parameters

f	function to be integrated.
bound	finite bound of original integration range (0 if inf = 2).
inf	indicates the type of integration range.
a	lower limit for integration over subrange of (0, 1).
b	upper limit for integration over subrange of (0, 1).
result	approximation to the integral.
abserr	estimate of the modulus of the absolute error.
resabs	approximation to the integral over $\left\|f\right\|$ .
resasc	approximation to the integral of $\left\|f - I / (b-a)\right\|$ over .