Numerics.hh File Reference

#include <array>
#include <complex>
#include <functional>
#include <vector>
#include "Garfield/FundamentalConstants.hh"

Go to the source code of this file.

Namespaces
namespace	Garfield
namespace	Garfield::Numerics
	Collection of numerical routines.
namespace	Garfield::Numerics::QUADPACK
	Functions for performing numerical integration (quadrature).
namespace	Garfield::Numerics::CERNLIB
	Linear algebra routines from CERNLIB.

Functions
constexpr std::array< double, 2 >	Garfield::Numerics::GaussLegendreNodes2 ()
constexpr std::array< double, 2 >	Garfield::Numerics::GaussLegendreWeights2 ()
constexpr std::array< double, 3 >	Garfield::Numerics::GaussLegendreNodes3 ()
constexpr std::array< double, 3 >	Garfield::Numerics::GaussLegendreWeights3 ()
constexpr std::array< double, 4 >	Garfield::Numerics::GaussLegendreNodes4 ()
constexpr std::array< double, 4 >	Garfield::Numerics::GaussLegendreWeights4 ()
constexpr std::array< double, 5 >	Garfield::Numerics::GaussLegendreNodes5 ()
constexpr std::array< double, 5 >	Garfield::Numerics::GaussLegendreWeights5 ()
constexpr std::array< double, 6 >	Garfield::Numerics::GaussLegendreNodes6 ()
constexpr std::array< double, 6 >	Garfield::Numerics::GaussLegendreWeights6 ()
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.
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.
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.
int	Garfield::Numerics::CERNLIB::deqn (const int n, std::vector< std::vector< double > > &a, std::vector< double > &b)
	Replaces b by the solution x of Ax = b, after which A is undefined.
int	Garfield::Numerics::CERNLIB::deqinv (const int n, std::vector< std::vector< double > > &a, std::vector< double > &b)
	Replaces b by the solution x of Ax = b, and replace A by its inverse.
void	Garfield::Numerics::CERNLIB::dfact (const int n, std::vector< std::vector< double > > &a, std::vector< int > &ir, int &ifail, double &det, int &jfail)
void	Garfield::Numerics::CERNLIB::dfeqn (const int n, std::vector< std::vector< double > > &a, std::vector< int > &ir, std::vector< double > &b)
void	Garfield::Numerics::CERNLIB::dfinv (const int n, std::vector< std::vector< double > > &a, std::vector< int > &ir)
int	Garfield::Numerics::CERNLIB::dinv (const int n, std::vector< std::vector< double > > &a)
	Replace square matrix A by its inverse.
void	Garfield::Numerics::CERNLIB::cfact (const int n, std::vector< std::vector< std::complex< double > > > &a, std::vector< int > &ir, int &ifail, std::complex< double > &det, int &jfail)
void	Garfield::Numerics::CERNLIB::cfinv (const int n, std::vector< std::vector< std::complex< double > > > &a, std::vector< int > &ir)
int	Garfield::Numerics::CERNLIB::cinv (const int n, std::vector< std::vector< std::complex< double > > > &a)
	Replace square matrix A by its inverse.
void	Garfield::Numerics::CERNLIB::cfft (std::vector< std::complex< double > > &a, const int msign)
double	Garfield::Numerics::Legendre (const unsigned int n, const double x)
	Legendre polynomials.
double	Garfield::Numerics::BesselI0S (const double xx)
	Modified Bessel functions.
double	Garfield::Numerics::BesselI1S (const double xx)
double	Garfield::Numerics::BesselK0S (const double xx)
double	Garfield::Numerics::BesselK0L (const double xx)
double	Garfield::Numerics::BesselK1S (const double xx)
double	Garfield::Numerics::BesselK1L (const double xx)
double	Garfield::Numerics::Divdif (const std::vector< double > &f, const std::vector< double > &a, int nn, double x, int mm)
	C++ version of DIVDIF (CERN program library E105) which performs tabular interpolation using symmetrically placed argument points.
double	Garfield::Numerics::LinearInterpolation (const std::vector< double > &ytab, const std::vector< double > &xtab, const double x)
bool	Garfield::Numerics::Boxin2 (const std::vector< std::vector< double > > &value, const std::vector< double > &xAxis, const std::vector< double > &yAxis, const int nx, const int ny, const double xx, const double yy, double &f, const int iOrder)
	Interpolation of order 1 and 2 in an irregular rectangular two-dimensional grid.
bool	Garfield::Numerics::Boxin3 (const std::vector< std::vector< std::vector< double > > > &value, const std::vector< double > &xAxis, const std::vector< double > &yAxis, const std::vector< double > &zAxis, const int nx, const int ny, const int nz, const double xx, const double yy, const double zz, double &f, const int iOrder)
	Interpolation of order 1 and 2 in an irregular rectangular three-dimensional grid.
bool	Garfield::Numerics::LeastSquaresFit (std::function< double(double, const std::vector< double > &)> f, std::vector< double > &par, std::vector< double > &epar, const std::vector< double > &x, const std::vector< double > &y, const std::vector< double > &ey, const unsigned int nMaxIter, const double diff, double &chi2, const double eps, const bool debug, const bool verbose)
	Least-squares minimisation.