Numerical derivatives class. More...

#include <GDerivative.hpp>

Inheritance diagram for GDerivative:

Classes
class	tiny

Public Member Functions
	GDerivative (void)
	Void constructor. More...

	GDerivative (GFunction *func)
	Function constructor. More...

	GDerivative (const GDerivative &dx)
	Copy constructor. More...

virtual	~GDerivative (void)
	Destructor. More...

GDerivative &	operator= (const GDerivative &dx)
	Assignment operator. More...

void	clear (void)
	Clear derivative. More...

GDerivative *	clone (void) const
	Clone derivative. More...

std::string	classname (void) const
	Return class name. More...

void	max_iter (const int &max_iter)
	Set maximum number of iterations. More...

void	eps (const double &eps)
	Set precision. More...

void	step_frac (const double &fraction)
	Set step fraction. More...

void	silent (const bool &silent)
	Set silence flag. More...

const int &	iter (void) const
	Return number of iterations. More...

const int &	max_iter (void) const
	Return maximum number of iterations. More...

const double &	eps (void) const
	Get precision. More...

const double &	step_frac (void) const
	Get step fraction. More...

const bool &	silent (void) const
	Get silence flag. More...

void	function (GFunction *func)
	Set function. More...

const GFunction *	function (void) const
	Get function. More...

double	value (const double &x, const double &step=0.0)
	Returns derivative. More...

double	ridder (const double &x, const double &h, double *err)
	Returns derivative by Ridders' method. More...

double	minuit2 (const double &x, double *err)
	Returns derivative using Minuit2 algorithm. More...

double	difference (const double &x, const double &h)
	Returns gradient computed from symmetric function difference. More...

double	left_difference (const double &x, const double &h)
	Returns gradient computed from left-sided function difference. More...

double	right_difference (const double &x, const double &h)
	Returns gradient computed from right-sided function difference. More...

double	smooth_robust (const double &x, const double &h, const int &degree=2, const int &length=5)
	Returns smooth noise-robust derivative. More...

std::string	print (const GChatter &chatter=NORMAL) const
	Print derivative information. More...

Public Member Functions inherited from GBase
virtual	~GBase (void)
	Destructor. More...

Protected Member Functions
void	init_members (void)
	Initialise class members. More...

void	copy_members (const GDerivative &dx)
	Copy class members. More...

void	free_members (void)
	Delete class members. More...

void	set_tiny (void)
	Compute tiny number for Minuit2. More...

Protected Attributes
GFunction *	m_func
	Pointer to function. More...

double	m_eps
	Derivative precision. More...

double	m_step_frac
	Value fraction to use for initial step. More...

double	m_tiny
	Tiny number for minuit2. More...

int	m_max_iter
	Maximum number of iterations. More...

int	m_iter
	Number of iterations used. More...

bool	m_silent
	Suppress warnings. More...

Detailed Description

Numerical derivatives class.

This class allows to compute numerical derivatives using various methods. The function to be derived is implemented by the abstract GFunction class.

Definition at line 45 of file GDerivative.hpp.

Constructor & Destructor Documentation

GDerivative::GDerivative ( void )

Void constructor.

Definition at line 60 of file GDerivative.cpp.

References init_members().

Referenced by clone().

GDerivative::GDerivative ( GFunction * func )

explicit

Function constructor.

Parameters

[in] func Function pointer.

Construct class instance from single parameter function. Note that the function is not copied but just a pointer to it is stored. The function should thus not be destroyed before computation of derivatives is finished.

Definition at line 80 of file GDerivative.cpp.

References init_members().

GDerivative::GDerivative ( const GDerivative & dx )

Copy constructor.

Parameters

[in] dx Derivative.

Definition at line 98 of file GDerivative.cpp.

References copy_members(), and init_members().

GDerivative::~GDerivative ( void )

virtual

Destructor.

Definition at line 114 of file GDerivative.cpp.

References free_members().

Member Function Documentation

std::string GDerivative::classname ( void ) const

inlinevirtual

Return class name.

Returns: String containing the class name ("GDerivative").

Implements GBase.

Definition at line 119 of file GDerivative.hpp.

void GDerivative::clear ( void )

virtual

Clear derivative.

Implements GBase.

Definition at line 166 of file GDerivative.cpp.

References free_members(), and init_members().

GDerivative * GDerivative::clone ( void ) const

virtual

Clone derivative.

Returns: Pointer to deep copy of derivative.

Implements GBase.

Definition at line 184 of file GDerivative.cpp.

References GDerivative().

void GDerivative::copy_members ( const GDerivative & dx )

protected

Copy class members.

Parameters

[in] dx Derivative.

Definition at line 816 of file GDerivative.cpp.

References m_eps, m_func, m_iter, m_max_iter, m_silent, m_step_frac, and m_tiny.

Referenced by GDerivative(), and operator=().

double GDerivative::difference	(	const double &	x,
		const double &	h
	)

Returns gradient computed from symmetric function difference.

Parameters

[in]	x	Function value.
[in]	h	Step size.

This is the most simple and dumb gradient computation method we can think of. It does a reasonable good job if the problem is well controlled, and in particular, if the step size is known in advance.

Definition at line 514 of file GDerivative.cpp.

References GFunction::eval(), and m_func.

void GDerivative::eps ( const double & eps )

inline

Set precision.

Parameters

[in] eps Precision.

Definition at line 168 of file GDerivative.hpp.

References eps(), and m_eps.

const double & GDerivative::eps ( void ) const

inline

Get precision.

Returns: Precision.

Definition at line 181 of file GDerivative.hpp.

References m_eps.

Referenced by eps(), minuit2(), and print().

void GDerivative::free_members ( void )

protected

Delete class members.

Definition at line 835 of file GDerivative.cpp.

Referenced by clear(), operator=(), and ~GDerivative().

void GDerivative::function ( GFunction * function )

inline

Set function.

Parameters

[in] function Function.

Sets the function for which the derivative should be determined.

Definition at line 245 of file GDerivative.hpp.

References m_func.

const GFunction * GDerivative::function ( void ) const

inline

Get function.

Returns: Function.

Definition at line 258 of file GDerivative.hpp.

References m_func.

void GDerivative::init_members ( void )

protected

Initialise class members.

Definition at line 792 of file GDerivative.cpp.

References m_eps, m_func, m_iter, m_max_iter, m_silent, m_step_frac, and m_tiny.

Referenced by clear(), GDerivative(), and operator=().

const int & GDerivative::iter ( void ) const

inline

Return number of iterations.

Returns: Number of iterations.

Definition at line 131 of file GDerivative.hpp.

References m_iter.

double GDerivative::left_difference	(	const double &	x,
		const double &	h
	)

Returns gradient computed from left-sided function difference.

Parameters

[in]	x	Function value.
[in]	h	Step size.

This is the most simple and dumb gradient computation method we can think of. It does a reasonable good job if the problem is well controlled, and in particular, if the step size is known in advance.

Definition at line 536 of file GDerivative.cpp.

References GFunction::eval(), and m_func.

void GDerivative::max_iter ( const int & max_iter )

inline

Set maximum number of iterations.

Parameters

[in] max_iter Maximum number of iterations.

Definition at line 143 of file GDerivative.hpp.

References m_max_iter, and max_iter().

const int & GDerivative::max_iter ( void ) const

inline

Return maximum number of iterations.

Returns: Maximum number of iterations.

Definition at line 156 of file GDerivative.hpp.

References m_max_iter.

Referenced by max_iter(), and print().

double GDerivative::minuit2	(	const double &	x,
		double *	err
	)

Returns derivative using Minuit2 algorithm.

Parameters

[in]	x	Function value.
[out]	err	Estimated error in the derivative.

This method has been inspired by corresponding code in the Minuit2 package. Please check the following files in Minuit2 for more information:

Numerical2PGradientCalculator.cxx for the main code MnStrategy.cxx for the definition of algorithm parameters MnMachinePrecision.h for the definition of eps and eps2 InitialGradientCalculator.cxx for the Minuit2 way of estimating initial gradients.

The exact value of fcnup has little impact on the results.

Definition at line 380 of file GDerivative.cpp.

References abs(), eps(), GFunction::eval(), G_MINUIT2, m_func, m_iter, max(), silent(), sqrt(), gammalib::str(), and gammalib::warning().

GDerivative & GDerivative::operator= ( const GDerivative & dx )

Assignment operator.

Parameters

[in] dx Derivative.

Returns: Derivative.

Definition at line 136 of file GDerivative.cpp.

References copy_members(), free_members(), and init_members().

std::string GDerivative::print ( const GChatter & chatter = NORMAL ) const

virtual

Print derivative information.

Parameters

[in] chatter Chattiness (defaults to NORMAL).

Returns: String containing derivative information.

Implements GBase.

Definition at line 750 of file GDerivative.cpp.

References eps(), max_iter(), gammalib::parformat(), SILENT, silent(), step_frac(), and gammalib::str().

double GDerivative::ridder	(	const double &	x,
		const double &	h,
		double *	err
	)

Returns derivative by Ridders' method.

Parameters

[in]	x	Function value.
[in]	h	Estimated initial step size.
[out]	err	Estimated error in the derivative.

Exceptions

GException::invalid_argument Step size of 0 has been specified.

Returns the derivative of a function at point x by Ridders's method of polynomial extrapolation. The value h is input as an estimated initial stepsize; it needs not to be small, but rather should be an increment in x over which the function changes substantially.

This method has been adopted from Numerical Recipes, 3rd edition, page 321f.

Definition at line 290 of file GDerivative.cpp.

References abs(), GFunction::eval(), G_RIDDER, and m_func.

Referenced by value().

double GDerivative::right_difference	(	const double &	x,
		const double &	h
	)

Returns gradient computed from right-sided function difference.

Parameters

[in]	x	Function value.
[in]	h	Step size.

This is the most simple and dumb gradient computation method we can think of. It does a reasonable good job if the problem is well controlled, and in particular, if the step size is known in advance.

Definition at line 558 of file GDerivative.cpp.

References GFunction::eval(), and m_func.

void GDerivative::set_tiny ( void )

protected

Compute tiny number for Minuit2.

On fermi gives m_tiny = 8.88178e-16 for i=51.

Definition at line 847 of file GDerivative.cpp.

References m_tiny.

void GDerivative::silent ( const bool & silent )

inline

Set silence flag.

Parameters

[in] silent Silence flag.

Definition at line 218 of file GDerivative.hpp.

References m_silent, and silent().

const bool & GDerivative::silent ( void ) const

inline

Get silence flag.

Returns: True is class is silent, false otherwise.

Definition at line 231 of file GDerivative.hpp.

References m_silent.

Referenced by minuit2(), print(), silent(), and value().

double GDerivative::smooth_robust	(	const double &	x,
		const double &	h,
		const int &	degree = `2`,
		const int &	length = `5`
	)

Returns smooth noise-robust derivative.

Parameters

[in]	x	Function value.
[in]	h	Step size.
[in]	degree	Differentiator degree (default: 2).
[in]	length	Filter length (default: 5).

Compute a smooth noise-robust numerical derivative using the method proposed by Pavel Holoborodko (http://www.holoborodko.com/pavel/numerical-methods/) Formulae for the following filter lengths and degrees have been implemented:

degree=2 length=5,7,9,11
degree=4 length=7,9,11

Definition at line 587 of file GDerivative.cpp.

References GFunction::eval(), G_SMOOTH_ROBUST, m_func, and gammalib::str().

void GDerivative::step_frac ( const double & fraction )

inline

Set step fraction.

Parameters

[in] fraction Step fraction.

Definition at line 193 of file GDerivative.hpp.

References m_step_frac.

const double & GDerivative::step_frac ( void ) const

inline

Get step fraction.

Returns: Step fraction.

Definition at line 206 of file GDerivative.hpp.

References m_step_frac.

Referenced by print().

double GDerivative::value	(	const double &	x,
		const double &	step = `0.0`
	)

Returns derivative.

Parameters

[in]	x	Function value.
[in]	step	Initial step size (default: automatic)

Computes derivative using the Ridders' method. If the specified initial step size is non-zero, the method starts with this step size and iteratively decreases the step size until the error becomes less than a threshold defined with the eps() method (by default the threshold is set to 1e-6). If the initial step size is zero, the method takes \(h={\tt m\_step\_frac} |x|\) as initial step size. The maximum number of iterations is controlled by the max_iter() method (by default, the maximum is set to 5).

Definition at line 205 of file GDerivative.cpp.

References abs(), G_VALUE, m_eps, m_iter, m_max_iter, m_step_frac, ridder(), silent(), gammalib::str(), and gammalib::warning().