ACDCGen is a general class for sampling multi-dimensional functions. More...

#include <ACDCGen.h>

Inheritance diagram for ACDCGenerator::ACDCGen< Rnd, FncPtr >:

Classes
struct	Level
	A helper struct representing a level of compensation. More...

struct	Slicer
	This is a help struct to perform the divide-and-conquer slicing of cells before starting the compensation procedure. More...

Public Types
typedef Rnd	RndType
	Template argument typedef. More...

typedef ACDCRandomTraits< RndType >	RndTraits
	Template argument typedef. More...

typedef FncPtr	FncPtrType
	Template argument typedef. More...

typedef vector< ACDCGenCell * >	CellVector
	A vector of cells. More...

typedef vector< FncPtrType >	FncVector
	A vector of function objects. More...

typedef vector< DimType >	DimVector
	A vector of integers. More...

typedef DimVector::size_type	size_type
	The size type of the vectors used. More...

typedef ACDCFncTraits< FncPtrType >	FncTraits
	Template argument typedef. More...

Public Member Functions
	ACDCGen (Rnd *r)
	Standard constructor requiring a random generator object to be used.

	ACDCGen ()
	Default Constructor.

	~ACDCGen ()
	Destructor.

bool	addFunction (DimType dim, FncPtrType f, double maxrat=-1.0)
	Add a function of a given dimension, dim, according to which points will be generated. More...

void	clear ()
	Remove all added functions and reset the generator;.

FncPtrType	generate ()
	Generate a point, choosing between the different functions specified. More...

void	reject ()
	Reject the last generated point. More...

const DVector &	lastPoint () const
	Return the last generated point. More...

double	lastF () const
	Return the value of the last chosen function in the last point.

FncPtrType	lastFunction () const
	Return the function chosen for the last generated point.

size_type	last () const
	return the index of the function chosen for the last generated point.

template<typename POStream >
void	output (POStream &) const
	This function is to be used in ThePEG for output to a persistent stream and will not work properly for normal ostreams.

template<typename PIStream >
void	input (PIStream &)
	This function is to be used in ThePEG for input from a persistent stream and will not work properly for normal istreams.

Functions influencing the efficiency of the generation.
void	eps (double newEps)
	Set the minimum cell size considered for this generation. More...

void	margin (double newMargin)
	Set the safety margin used to multiply the highest found function value in a cell when setting its overestimated value. More...

void	nTry (size_type newNTry)
	Set the number of points (with non-zero function value) used to initialize the tree of cells to use in the generation for each function.

void	maxTry (long)
	Set the maximum number of attempts to generate a phase space point, or to find non-zero points in the initialization.

Information about the current generation.
double	integral (FncPtrType f=FncPtrType()) const
	Return the current Monte Carlo estimate of the integral of the specified function (or all functions if NULL) over the unit volume.

double	integralErr (FncPtrType f=FncPtrType()) const
	Return the error on the current Monte Carlo estimate of the integral of the specified function (or all functions if NULL) over the unit volume.

long	n () const
	The number of accepted points so far.

long	N () const
	The number of calls to generate() so far. More...

double	efficiency () const
	The ratio of the number of accepted and number of tried points n()/N();.

int	nBins () const
	Return the number of active cells created so far.

int	depth () const
	Return the maximum depth of any tree of cells used.

double	maxInt () const
	Return the current overestimation of the full integral of all specified functions over the unit volume.

Access to member variables.
double	eps () const
	The minimum cell size considered for this generation.

double	margin () const
	The safety margin used to multiply the highest found function value in a cell when setting its overestimated value.

size_type	nTry () const
	The number of points used to initialize the tree of cells to use in the generation.

long	maxTry () const
	The maximum number of attempts to generate a phase space point, or to find non-zero points in the initialization.

bool	cheapRandom () const
	Returns true if generating random numbers are so cheap that a new one can be thrown everytime a sub-cell is chosen. More...

size_type	size () const
	The number of functions used.

bool	compensating ()
	Returns true if the generator is currently in a state of compensating an erroneous overestimation of one of the specified functions. More...

long	compleft () const
	Return an estimate of how many points need to be sampled before the generator finishes compensating.

vector< ACDCGenCellInfo >	extractCellInfo () const
	Return a vector with information about all cells.

Functions related to the random number generator.
void	cheapRandom (bool b)
	Set to true if generating random numbers are so cheap that a new one can be thrown everytime a sub-cell is chosen. More...

void	setRnd (Rnd *r)
	Set a new random number generator.

double	rnd () const
	Double precision number in the interval ]0,1[.

double	rnd (double lo, double up) const
	Double precision number in the interval ]lo,up[.

void	rnd (const DVector &lo, const DVector &up, DVector &r) const
	Fill the r vector with doubles r[i] in the interval ]lo[i],up[i][.

void	rnd (DimType D, DVector &r) const
	Fill the D first elements in the r vector with doubles in the interval ]0,1[.

long	rndInt (long x) const
	Integer in the interval [0,x[.

Static Public Attributes
static size_type	maxsize
	The maximum recursion depth of the compensation so far. More...

Private Types
typedef vector< Level >	LevelVector
	A vector (stack) of levels.

Private Member Functions
double	doMaxInt ()
	Calculate the overestimated integral for all functions.

const FncVector &	functions () const
	Return the vector of functions.

FncPtrType	function (size_type i) const
	Return the i'th function.

const DimVector &	dimensions () const
	Return a vector with the dimensions of all functions.

DimType	dimension (size_type i) const
	Return the dimension of the i'th function.

DimType	lastDimension () const
	Return the dimension of the function chosen for the last generated point.

const CellVector &	cells () const
	Return the roots of all cell trees.

ACDCGenCell *	cell (size_type i) const
	Return the root cell for the i'th function.

ACDCGenCell *	lastPrimary () const
	Return the root cell for the function chosen for the last generated point.

const DVector &	sumMaxInts () const
	Return a vector with the incremental sum of overestimated integrals for each function.

ACDCGenCell *	lastCell () const
	Return the cell chosen for the last generated point.

void	chooseCell (DVector &lo, DVector &up)
	Choose a function according to its overestimated integral and choose a cell to generate a point in.

void	compensate (const DVector &lo, const DVector &up)
	Start the compensation procedure for the last chosen cell when a function velue has been found which exceeds the previous overestimation.

	ACDCGen (const ACDCGen &)
	Copy constructor is private and not implemented.

ACDCGen &	operator= (const ACDCGen &)=delete
	Assignment is private and not implemented.

Private Attributes
RndType *	theRnd
	The random number generator to be used for this Generator.

long	theNAcc
	The number of accepted points (weight > 0) so far.

long	theN
	The number of attempted points so far.

vector< long >	theNI
	The number of attempts per function so far.

DVector	theSumW
	The summed weights per function so far.

DVector	theSumW2
	The summed squared weights per function so far.

double	theEps
	The smallest possible division allowed.

double	theMargin
	The factor controlling the loss of efficiency when compensating.

size_type	theNTry
	The number of points to use to find initial average.

long	theMaxTry
	The maximum number of attempts to generate a phase space point, or to find non-zero points in the initialization.

bool	useCheapRandom
	True if generating random numbers are so cheap that a new one can be thrown everytime a sub-cell is chosen. More...

FncVector	theFunctions
	A vector of functions.

DimVector	theDimensions
	The dimensions of the functions in theFunctions.

CellVector	thePrimaryCells
	The root of the cell tree for the functions in theFunctions.

DVector	theSumMaxInts
	The accumulated sum of overestimated integrals of the functions in theFunctions.

size_type	theLast
	The last index chosen.

ACDCGenCell *	theLastCell
	The last cell chosen.

DVector	theLastPoint
	The last point generated.

double	theLastF
	The function value of the last point.

LevelVector	levels
	The vector (stack) of levels.

Detailed Description

template<typename Rnd, typename FncPtr>
class ACDCGenerator::ACDCGen< Rnd, FncPtr >

ACDCGen is a general class for sampling multi-dimensional functions.

ACDCGen can sample several functions simultaneously, selecting different functions according to the relative probabilities determined by their total integrals. The functions are sampled on a unit hypercube. Function object of any class can be used as long as the ACDCFncTraits class is specialized correctly. ACDCFncTraits can also be used to rescale values in the unit hypercube to any desired range. ACDCGen needs a random number generator. Again, random number generators of any class can be used as long as the ACDCRandomTraits class is specialized correctly.

To give an unweighted samlpe ACDCGen uses a compensating algorithm. Before the production sampling begins, the functions are sampled randomly in the hypercube a user-defined number of times to find an approximate maxumum value. The hypercube is then divided into cells each of which have an approximate maximum value of the function, to enable efficient sampling. The maxima are only approximate though and, if a function value is found above the maximum in a cell the ACDCGen will go into a compensating mode. The cell is then first subdivided further and in the following this cell will be over-sampled to compensate for that fact that it was under-sampled before. In this way the probability of obtaining a biased sample is reduced. Also rather functions with large peaks are then sampled rather efficiently. Functions with narrow peaks should, however, be avoided since there is no guarantee that the peack is actually hit.

Definition at line 49 of file ACDCGen.h.

Member Typedef Documentation

◆ CellVector

template<typename Rnd, typename FncPtr>

typedef vector<ACDCGenCell*> ACDCGenerator::ACDCGen< Rnd, FncPtr >::CellVector

A vector of cells.

Definition at line 60 of file ACDCGen.h.

◆ DimVector

template<typename Rnd, typename FncPtr>

typedef vector<DimType> ACDCGenerator::ACDCGen< Rnd, FncPtr >::DimVector

A vector of integers.

Definition at line 64 of file ACDCGen.h.

◆ FncPtrType

template<typename Rnd, typename FncPtr>

typedef FncPtr ACDCGenerator::ACDCGen< Rnd, FncPtr >::FncPtrType

Template argument typedef.

Definition at line 58 of file ACDCGen.h.

◆ FncTraits

template<typename Rnd, typename FncPtr>

typedef ACDCFncTraits<FncPtrType> ACDCGenerator::ACDCGen< Rnd, FncPtr >::FncTraits

Template argument typedef.

Definition at line 68 of file ACDCGen.h.

◆ FncVector

template<typename Rnd, typename FncPtr>

typedef vector<FncPtrType> ACDCGenerator::ACDCGen< Rnd, FncPtr >::FncVector

A vector of function objects.

Definition at line 62 of file ACDCGen.h.

◆ RndTraits

template<typename Rnd, typename FncPtr>

typedef ACDCRandomTraits<RndType> ACDCGenerator::ACDCGen< Rnd, FncPtr >::RndTraits

Template argument typedef.

Definition at line 56 of file ACDCGen.h.

◆ RndType

template<typename Rnd, typename FncPtr>

typedef Rnd ACDCGenerator::ACDCGen< Rnd, FncPtr >::RndType

Template argument typedef.

Definition at line 54 of file ACDCGen.h.

◆ size_type

template<typename Rnd, typename FncPtr>

typedef DimVector::size_type ACDCGenerator::ACDCGen< Rnd, FncPtr >::size_type

The size type of the vectors used.

Definition at line 66 of file ACDCGen.h.

Member Function Documentation

◆ addFunction()

template<typename Rnd, typename FncPtr>

bool ACDCGenerator::ACDCGen< Rnd, FncPtr >::addFunction	(	DimType	dim,
		FncPtrType	f,
		double	maxrat = `-1.0`
	)

inline

Add a function of a given dimension, dim, according to which points will be generated.

Note that each function, f, added like this will have its own tree of cells. The maxrat argument determines the lowest ratio of values allowed between the cell with lowest and highest value. If negative it is given by 1/nTry().

◆ cheapRandom() [1/2]

template<typename Rnd, typename FncPtr>

bool ACDCGenerator::ACDCGen< Rnd, FncPtr >::cheapRandom ( ) const

inline

Returns true if generating random numbers are so cheap that a new one can be thrown everytime a sub-cell is chosen.

Otherwise random numbers used for this will be reused.

◆ cheapRandom() [2/2]

template<typename Rnd, typename FncPtr>

void ACDCGenerator::ACDCGen< Rnd, FncPtr >::cheapRandom ( bool b )

inline

Set to true if generating random numbers are so cheap that a new one can be thrown everytime a sub-cell is chosen.

Otherwise random numbers used for this will be reused.

◆ compensating()

template<typename Rnd, typename FncPtr>

bool ACDCGenerator::ACDCGen< Rnd, FncPtr >::compensating ( )

inline

Returns true if the generator is currently in a state of compensating an erroneous overestimation of one of the specified functions.

If so, the integral and the generated points are not statistically correct.

◆ eps()

template<typename Rnd, typename FncPtr>

void ACDCGenerator::ACDCGen< Rnd, FncPtr >::eps ( double newEps )

inline

Set the minimum cell size considered for this generation.

The default is the machine limit for double precision times a hundred.

◆ generate()

template<typename Rnd, typename FncPtr>

FncPtrType ACDCGenerator::ACDCGen< Rnd, FncPtr >::generate ( )

inline

Generate a point, choosing between the different functions specified.

The chosen function is returned, while the generated point is obtained by the function lastPoint().

◆ lastPoint()

template<typename Rnd, typename FncPtr>

const DVector& ACDCGenerator::ACDCGen< Rnd, FncPtr >::lastPoint ( ) const

inline

Return the last generated point.

Returns: a vector of doubles, each in the interval ]0,1[.

◆ margin()

template<typename Rnd, typename FncPtr>

void ACDCGenerator::ACDCGen< Rnd, FncPtr >::margin ( double newMargin )

inline

Set the safety margin used to multiply the highest found function value in a cell when setting its overestimated value.

(Default is 1.1.)

◆ N()

template<typename Rnd, typename FncPtr>

long ACDCGenerator::ACDCGen< Rnd, FncPtr >::N ( ) const

inline

The number of calls to generate() so far.

Note that the number of calls to the specified functions may be larger. It is up to the user to keep track of those.

◆ reject()

template<typename Rnd, typename FncPtr>

void ACDCGenerator::ACDCGen< Rnd, FncPtr >::reject ( )

inline

Reject the last generated point.

Only used in the evaluation of the total integral.

Member Data Documentation

◆ maxsize

template<typename Rnd, typename FncPtr>

size_type ACDCGenerator::ACDCGen< Rnd, FncPtr >::maxsize

static

The maximum recursion depth of the compensation so far.

Definition at line 745 of file ACDCGen.h.

◆ useCheapRandom

template<typename Rnd, typename FncPtr>

bool ACDCGenerator::ACDCGen< Rnd, FncPtr >::useCheapRandom

private

True if generating random numbers are so cheap that a new one can be thrown everytime a sub-cell is chosen.

Otherwise random numbers used for this will be reused.

Definition at line 472 of file ACDCGen.h.

The documentation for this class was generated from the following file:

ACDCGen.h

Classes

Public Types

Public Member Functions

Static Public Attributes

Private Types

Private Member Functions

Private Attributes

Detailed Description

template<typename Rnd, typename FncPtr> class ACDCGenerator::ACDCGen< Rnd, FncPtr >

Member Typedef Documentation

◆ CellVector

◆ DimVector

◆ FncPtrType

◆ FncTraits

◆ FncVector

◆ RndTraits

◆ RndType

◆ size_type

Member Function Documentation

◆ addFunction()

◆ cheapRandom() [1/2]

◆ cheapRandom() [2/2]

◆ compensating()

◆ eps()

◆ generate()

◆ lastPoint()

◆ margin()

◆ N()

◆ reject()

Member Data Documentation

◆ maxsize

◆ useCheapRandom

template<typename Rnd, typename FncPtr>
class ACDCGenerator::ACDCGen< Rnd, FncPtr >