namespace for Numerical integration with Sector Decomposition method More...

Classes
class	ChengWu
	class to manipulate with Cheng-Wu theorem More...

class	CppFormat
	class to export GiNaC expression to cpp format More...

class	cse_Parser

class	cseParser
	class for Common SubExpression Parser More...

class	ErrMin
	ErrMin with HookeJeeves. More...

class	ExFormat

struct	FeynmanParameter
	wrap parameters for loop integrals More...

class	HCubature
	numerical integrator using HCubature More...

class	HCubatureMP
	numerical integrator using HCubatureMP More...

class	HookeJeeves
	class to minimize a function using HookeJeeves More...

class	IntegratorBase
	base for numerical integrator More...

class	MinimizeBase
	base for class to minimize a function More...

class	QuadMP
	numerical integrator using TanhSinhMP More...

class	SecDec
	SecDec the main class to use Sector Decompostion method. More...

class	SecDecBase
	base class of SecDec More...

class	SecDecG
	SecDec by geometric method. More...

class	TanhSinhMP
	numerical integrator using TanhSinhMP More...

struct	XIntegrand
	wrap parameters for generic parameter integrals More...

Typedefs
typedef long double	dREAL

typedef complex< dREAL >	dCOMPLEX

typedef __float128	qREAL

typedef __complex128	qCOMPLEX

typedef mpfr::mpreal	mpREAL

typedef complex< mpREAL >	mpCOMPLEX

Functions
void	ex_print_power (const power &p, const ExFormat &c, unsigned level)

	REGISTER_FUNCTION (PL, do_not_evalf_params().expl_derivative_func(zd1D).derivative_func(zp1D)) REGISTER_FUNCTION(FTX

	do_not_evalf_params ().expl_derivative_func(zd2D).derivative_func(zp2D)) REGISTER_FUNCTION(CT

exvector	get_xy_from (ex pol)

exvector	get_x_from (ex pol)

exvector	get_y_from (ex pol)

exvector	get_z_from (ex pol)

exvector	get_pl_from (ex pol)

ex	VESimplify (ex expr)

ex	VEResult (ex expr)

ex	VEResult2 (ex expr)

ex	VEMaxErr (ex expr)

int	x_free_index (ex expr)

int	y_free_index (ex expr)

int	epsRank (ex expr_in, ex epi)

int	vsRank (ex expr_in)

ex	Factor (const ex expr_in)

ex	FactorOutX (const ex expr)

ex	FactorFT (const ex &expr)

ex	exp_simplify (const ex expr_in)

ex	pow_simplify (const ex expr_in)

ex	xyz_pow_simplify (const ex expr_in)

void	Replacement2 (exmap &repl)

vector< matrix >	Triangularize (const lst &fs_in, const ex &xs_in, const lst &nsubs)
	to Triangularize the domain with each xi from 0 to +infinity

void	Triangularize (exvector &FunExp, const lst &fs, const ex &xs, const lst &nsubs)
	to Triangularize the domain with each xi from 0 to +infinity, and update FunExp directly

vector< int >	zero_row_index (const matrix &mat)

matrix	mat_sub (matrix mat, int r, int nr, int c, int nc)

bool	is_zero_row (const matrix &mat, int r)

matrix	remove_zero_rows (const matrix &mat)

vector< vector< int > >	QHull (const matrix &dc, int dim)

Variables
int	VEO_Digits = 10

Detailed Description

namespace for Numerical integration with Sector Decomposition method

Typedef Documentation

◆ dCOMPLEX

typedef complex<dREAL> HepLib::SD::dCOMPLEX

Definition at line 123 of file SD.h.

◆ dREAL

typedef long double HepLib::SD::dREAL

Definition at line 122 of file SD.h.

◆ mpCOMPLEX

typedef complex<mpREAL> HepLib::SD::mpCOMPLEX

Definition at line 127 of file SD.h.

◆ mpREAL

typedef mpfr::mpreal HepLib::SD::mpREAL

Definition at line 126 of file SD.h.

◆ qCOMPLEX

typedef __complex128 HepLib::SD::qCOMPLEX

Definition at line 125 of file SD.h.

◆ qREAL

typedef __float128 HepLib::SD::qREAL

Definition at line 124 of file SD.h.

Function Documentation

◆ do_not_evalf_params()

HepLib::SD::do_not_evalf_params ( )

◆ epsRank()

int HepLib::SD::epsRank	(	ex	expr_in,
		ex	epi
	)

Definition at line 195 of file Helpers.cpp.

◆ ex_print_power()

void HepLib::SD::ex_print_power	(	const power &	p,
		const ExFormat &	c,
		unsigned	level
	)

Definition at line 74 of file ExFormat.cpp.

◆ exp_simplify()

ex HepLib::SD::exp_simplify ( const ex expr_in )

Definition at line 315 of file Helpers.cpp.

◆ Factor()

ex HepLib::SD::Factor ( const ex expr_in )

Definition at line 244 of file Helpers.cpp.

◆ FactorFT()

ex HepLib::SD::FactorFT ( const ex & expr )

Definition at line 302 of file Helpers.cpp.

◆ FactorOutX()

ex HepLib::SD::FactorOutX ( const ex expr )

Definition at line 278 of file Helpers.cpp.

◆ get_pl_from()

exvector HepLib::SD::get_pl_from ( ex pol )

Definition at line 74 of file Helpers.cpp.

◆ get_x_from()

exvector HepLib::SD::get_x_from ( ex pol )

Definition at line 29 of file Helpers.cpp.

◆ get_xy_from()

exvector HepLib::SD::get_xy_from ( ex pol )

Definition at line 14 of file Helpers.cpp.

◆ get_y_from()

exvector HepLib::SD::get_y_from ( ex pol )

Definition at line 44 of file Helpers.cpp.

◆ get_z_from()

exvector HepLib::SD::get_z_from ( ex pol )

Definition at line 59 of file Helpers.cpp.

◆ is_zero_row()

bool HepLib::SD::is_zero_row	(	const matrix &	mat,
		int	r
	)

inline

Definition at line 38 of file SecDecG.cpp.

◆ mat_sub()

matrix HepLib::SD::mat_sub	(	matrix	mat,
		int	r,
		int	nr,
		int	c,
		int	nc
	)

inline

Definition at line 28 of file SecDecG.cpp.

◆ pow_simplify()

ex HepLib::SD::pow_simplify ( const ex expr_in )

Definition at line 330 of file Helpers.cpp.

◆ QHull()

vector< vector< int > > HepLib::SD::QHull	(	const matrix &	dc,
		int	dim
	)

inline

Definition at line 63 of file SecDecG.cpp.

◆ REGISTER_FUNCTION()

HepLib::SD::REGISTER_FUNCTION	(	PL	,
		do_not_evalf_params().expl_derivative_func(zd1D).derivative_func(zp1D)
	)

◆ remove_zero_rows()

matrix HepLib::SD::remove_zero_rows ( const matrix & mat )

inline

Definition at line 46 of file SecDecG.cpp.

◆ Replacement2()

void HepLib::SD::Replacement2 ( exmap & repl )

Definition at line 21 of file InitEval.cpp.

◆ Triangularize() [1/2]

vector< matrix > HepLib::SD::Triangularize	(	const lst &	fs_in,
		const ex &	xs_in,
		const lst &	nsubs
	)

to Triangularize the domain with each xi from 0 to +infinity

Parameters

fs_in	is the list containing the liner equations w.r.t. xs_in
xs_in	is a list of x's in Delta function
subs	to replace the parameters with numerical values

Returns: vector of tranformation matrixes. for each matrix M, one has X = M.Y, with Y the new variables

Definition at line 77 of file Triangularize.cpp.

◆ Triangularize() [2/2]

void HepLib::SD::Triangularize	(	exvector &	FunExp,
		const lst &	fs,
		const ex &	xs,
		const lst &	nsubs
	)

to Triangularize the domain with each xi from 0 to +infinity, and update FunExp directly

Parameters

FunExp	the same as FunExp in SecDec class, will be updated
fs	is the list containing the liner equations w.r.t. xs_in
xs	is a list of x's in Delta function
subs	to replace the parameters with numerical values

Returns: vector of tranformation matrixes. for each matrix M, one has X = M.Y, with Y the new variables

Definition at line 224 of file Triangularize.cpp.

◆ VEMaxErr()

ex HepLib::SD::VEMaxErr ( ex expr )

Definition at line 131 of file Helpers.cpp.

◆ VEResult()

ex HepLib::SD::VEResult ( ex expr )

Definition at line 123 of file Helpers.cpp.

◆ VEResult2()

ex HepLib::SD::VEResult2 ( ex expr )

Definition at line 127 of file Helpers.cpp.

◆ VESimplify()

ex HepLib::SD::VESimplify ( ex expr )

Definition at line 92 of file Helpers.cpp.

◆ vsRank()

int HepLib::SD::vsRank ( ex expr_in )

Definition at line 211 of file Helpers.cpp.

◆ x_free_index()

int HepLib::SD::x_free_index ( ex expr )

Definition at line 165 of file Helpers.cpp.

◆ xyz_pow_simplify()

ex HepLib::SD::xyz_pow_simplify ( const ex expr_in )

Definition at line 349 of file Helpers.cpp.

◆ y_free_index()

int HepLib::SD::y_free_index ( ex expr )

Definition at line 180 of file Helpers.cpp.

◆ zero_row_index()

vector< int > HepLib::SD::zero_row_index ( const matrix & mat )

inline

Definition at line 13 of file SecDecG.cpp.

Variable Documentation

◆ VEO_Digits

int HepLib::SD::VEO_Digits = 10

extern

Definition at line 182 of file Init.cpp.

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ dCOMPLEX

◆ dREAL

◆ mpCOMPLEX

◆ mpREAL

◆ qCOMPLEX

◆ qREAL

Function Documentation

◆ do_not_evalf_params()

◆ epsRank()

◆ ex_print_power()

◆ exp_simplify()

◆ Factor()

◆ FactorFT()

◆ FactorOutX()

◆ get_pl_from()

◆ get_x_from()

◆ get_xy_from()

◆ get_y_from()

◆ get_z_from()

◆ is_zero_row()

◆ mat_sub()

◆ pow_simplify()

◆ QHull()

◆ REGISTER_FUNCTION()

◆ remove_zero_rows()

◆ Replacement2()

◆ Triangularize() [1/2]

◆ Triangularize() [2/2]

◆ VEMaxErr()

◆ VEResult()

◆ VEResult2()

◆ VESimplify()

◆ vsRank()

◆ x_free_index()

◆ xyz_pow_simplify()

◆ y_free_index()

◆ zero_row_index()

Variable Documentation

◆ VEO_Digits