lsst::afw::math::details Namespace Reference

Classes
struct	AuxFunc1
	Auxiliary struct 1. More...
struct	AuxFunc2
class	binder2_1
class	Int2DAuxType
class	binder3_1
class	Int3DAuxType

Functions
template<class T>
T	norm (const T &x)
template<class T>
T	real (const T &x)
template<class T>
T	Epsilon ()
template<class T>
T	MinRep ()
template<class T>
T	rescale_error (T err, T const &resabs, T const &resasc)
template<typename UnaryFunctionT, typename Arg>
bool	intGKPNA (UnaryFunctionT func, IntRegion< Arg > &reg, Arg const epsabs, Arg const epsrel, std::map< Arg, Arg > *fxmap=nullptr)
	Non-adaptive integration of the function f over the region 'reg'.
template<typename UnaryFunctionT, typename Arg>
void	intGKP (UnaryFunctionT func, IntRegion< Arg > &reg, Arg const epsabs, Arg const epsrel, std::map< Arg, Arg > *fxmap=nullptr)
	An adaptive integration algorithm which computes the integral of f over the region reg.
template<class UF>
AuxFunc1< UF >	Aux1 (UF uf)
	Auxiliary function 1.
template<class UF>
AuxFunc2< UF >	Aux2 (UF uf)
	Auxiliary function 2.
template<class BF, class Tp>
binder2_1< BF >	bind21 (const BF &oper, const Tp &x)
template<class TF, class Tp>
binder3_1< TF >	bind31 (const TF &oper, const Tp &x)
int	gkp_n (int level)
template<class T>
const std::vector< T > &	gkp_x (int level)
template<class T>
const std::vector< T > &	gkp_wa (int level)
template<class T>
const std::vector< T > &	gkp_wb (int level)

Function Documentation

Aux1()

template<class UF>

AuxFunc1< UF > lsst::afw::math::details::Aux1 ( UF uf )

inline

Auxiliary function 1.

Definition at line 587 of file Integrate.h.

Aux2()

template<class UF>

AuxFunc2< UF > lsst::afw::math::details::Aux2 ( UF uf )

inline

Auxiliary function 2.

Definition at line 608 of file Integrate.h.

bind21()

template<class BF, class Tp>

binder2_1< BF > lsst::afw::math::details::bind21 ( const BF & oper, const Tp & x )

inline

Definition at line 628 of file Integrate.h.

bind31()

template<class TF, class Tp>

binder3_1< TF > lsst::afw::math::details::bind31 ( const TF & oper, const Tp & x )

inline

Definition at line 670 of file Integrate.h.

Epsilon()

template<class T>

T lsst::afw::math::details::Epsilon ( )

inline

Definition at line 244 of file Integrate.h.

gkp_n()

int lsst::afw::math::details::gkp_n ( int level )

inline

Definition at line 47 of file IntGKPData10.h.

gkp_wa()

template<class T>

const std::vector< T > & lsst::afw::math::details::gkp_wa ( int level )

inline

Definition at line 116 of file IntGKPData10.h.

gkp_wb()

template<class T>

const std::vector< T > & lsst::afw::math::details::gkp_wb ( int level )

inline

Definition at line 171 of file IntGKPData10.h.

gkp_x()

template<class T>

const std::vector< T > & lsst::afw::math::details::gkp_x ( int level )

inline

Definition at line 54 of file IntGKPData10.h.

intGKP()

template<typename UnaryFunctionT, typename Arg>

void lsst::afw::math::details::intGKP ( UnaryFunctionT func, IntRegion< Arg > & reg, Arg const epsabs, Arg const epsrel, std::map< Arg, Arg > * fxmap = nullptr )

inline

An adaptive integration algorithm which computes the integral of f over the region reg.

Note

First the non-adaptive GKP algorithm is tried. If that is not accurate enough (according to the absolute and relative accuracies, epsabs and epsrel), the region is split in half, and each new region is integrated. The routine continues by successively splitting the subregion which gave the largest absolute error until the integral converges.

The area and estimated error are returned as reg.Area() and reg.Err() If desired, *retx and *retf return std::vectors of x,f(x) respectively They only include the evaluations in the non-adaptive pass, so they do not give an accurate estimate of the number of function evaluations.

Definition at line 426 of file Integrate.h.

intGKPNA()

template<typename UnaryFunctionT, typename Arg>

bool lsst::afw::math::details::intGKPNA ( UnaryFunctionT func, IntRegion< Arg > & reg, Arg const epsabs, Arg const epsrel, std::map< Arg, Arg > * fxmap = nullptr )

inline

Non-adaptive integration of the function f over the region 'reg'.

Note

The algorithm computes first a Gaussian quadrature value then successive Kronrod/Patterson extensions to this result. The functions terminates when the difference between successive approximations (rescaled according to rescale_error) is less than either epsabs or epsrel * I, where I is the latest estimate of the integral. The order of the Gauss/Kronron/Patterson scheme is determined by which file is included above. Currently schemes starting with order 1 and order 10 are calculated. There seems to be little practical difference in the integration times using the two schemes, so I haven't bothered to calculate any more.

Definition at line 298 of file Integrate.h.

MinRep()

template<class T>

T lsst::afw::math::details::MinRep ( )

inline

Definition at line 248 of file Integrate.h.

norm()

template<class T>

T lsst::afw::math::details::norm ( const T & x )

inline

Definition at line 160 of file Integrate.h.

real()

template<class T>

T lsst::afw::math::details::real ( const T & x )

inline

Definition at line 165 of file Integrate.h.

rescale_error()

template<class T>

T lsst::afw::math::details::rescale_error ( T err, T const & resabs, T const & resasc )

inline

Definition at line 264 of file Integrate.h.