ACDCGenerator::ACDCGen< Rnd, FncPtr > Class Template Reference

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

#include <ACDCGen.h>

List of all members.

Public Types

typedef Rnd RndType

Template argument typedef.

typedef ACDCRandomTraits< RndType > RndTraits

Template argument typedef.

typedef FncPtr FncPtrType

Template argument typedef.

typedef vector< ACDCGenCell * > CellVector

A vector of cells.

typedef vector< FncPtrType > FncVector

A vector of function objects.

typedef vector< DimType > DimVector

A vector of integers.

typedef DimVector::size_type size_type

The size type of the vectors used.

typedef ACDCFncTraits< FncPtrType > FncTraits

Template argument typedef.

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.

void clear ()

Remove all added functions and reset the generator;.

FncPtrType generate ()

Generate a point, choosing between the different functions specified.

void reject ()

Reject the last generated point.

const DVector & lastPoint () const

Return the last generated point.

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.

void margin (double newMargin)

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

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.

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.

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.

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.

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.

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 &)

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.

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.

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...

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 48 of file ACDCGen.h.