honey::Vegas< Dim, DimRes, Real__, BinCount > Class Template Reference

Monte Carlo (random-based) method to approximate the integral of a function over any number of dimensions. More...

#include <Vegas.h>

Public Types
typedef Real__	Real
typedef Vec< dimRes, Real >	VecRes
typedef Vec< dim, Real >	Vec
typedef function< VecRes(const Vec &)>	Func

Public Member Functions
	Vegas (const Func &func, RandomGen &gen, const Vec &lower, const Vec &upper, sdt sampleCount=1000, Real warmUp=0.1, sdt iterCount=5, Real alpha=1.5)
	Constructor, set up constants for all integration calls. More...
	~Vegas ()
const VecRes &	integrate (Real progressDelta=1)
	Perform integral calculation. The calculation can be split up over multiple calls. More...
Real	progress () const
	Current progress of calculation, from 0 (start) to 1 (complete). More...
const VecRes &	result () const
	Get current result of integration (same value returned by Integrate) More...
const VecRes &	chiSqr () const
	Get chi-square statistic for integral. A value that differs significantly from 1 (eg. diff > 0.5) indicates an unreliable result and more samples or iterations are required. More...
const VecRes &	stdDev () const
	Estimate of standard deviation of integral result. Indicative of +- error range in result. More...

Static Public Attributes
static const sdt	dim = Dim
static const sdt	dimRes = DimRes

Detailed Description

template<sdt Dim = 1, sdt DimRes = 1, class Real__ = Real, sdt BinCount = 100>
class honey::Vegas< Dim, DimRes, Real__, BinCount >

Monte Carlo (random-based) method to approximate the integral of a function over any number of dimensions.

Example: Find the mass of a sphere with radius 2 and density 0.5

//Functor takes a 3D coordinate and returns a 1D density sample
typedef Vegas<3, 1> Vegas;
struct Func { Vegas::VecRes operator()(const Vegas::Vec& coord)   { return coord.length() <= 2 ? 0.5 : 0; }  };

//Integrate over 3D bounding box [-2, 2]
Real mass = Vegas(Func(), Chacha(), Vegas::Vec(-2), Vegas::Vec(2)).integrate();
//mass =~ 16.7

Template Parameters

Dim	The dimension of the function input, number of variables that func operates on
DimRes	The dimension of the function result, each dimension of the result will be averaged separately over the integration region
BinCount	Tunable param, each dimension of the input (Dim) will be divided into BinCount separate bins. Higher bin counts provide more accuracy. At the default bin count of 100 a Vegas instance can fit on the stack, providing better performance.

Algorithm from: "VEGAS: An Adaptive Multi-dimensional Integration Program", G.P. Lepage, 1980.
Code adapted from C implementation by Richard Kreckel.

Member Typedef Documentation

template<sdt Dim = 1, sdt DimRes = 1, class Real__ = Real, sdt BinCount = 100>

typedef function<VecRes (const Vec&)> honey::Vegas< Dim, DimRes, Real__, BinCount >::Func

template<sdt Dim = 1, sdt DimRes = 1, class Real__ = Real, sdt BinCount = 100>

typedef Real__ honey::Vegas< Dim, DimRes, Real__, BinCount >::Real

template<sdt Dim = 1, sdt DimRes = 1, class Real__ = Real, sdt BinCount = 100>

typedef Vec<dim,Real> honey::Vegas< Dim, DimRes, Real__, BinCount >::Vec

template<sdt Dim = 1, sdt DimRes = 1, class Real__ = Real, sdt BinCount = 100>

typedef Vec<dimRes,Real> honey::Vegas< Dim, DimRes, Real__, BinCount >::VecRes

Constructor & Destructor Documentation

template<sdt Dim = 1, sdt DimRes = 1, class Real__ = Real, sdt BinCount = 100>

honey::Vegas< Dim, DimRes, Real__, BinCount >::Vegas ( const Func &  func, RandomGen &  gen, const Vec &  lower, const Vec &  upper, sdt  sampleCount = 1000, Real  warmUp = 0.1, sdt  iterCount = 5, Real  alpha = 1.5  )

inline

Constructor, set up constants for all integration calls.

Parameters

func	Function to integrate
gen	Random generator
lower	Lower bound of the region over which to integrate (has dimension Dim)
upper	Upper bound of the region over which to integrate (has dimension Dim)
sampleCount	Number of functor calls per iteration. If results are not reliable then increase the sample count (check stdDev() or chiSqr())
warmUp	Tunable param, percentage of samples (range >= 0) to use for warming up the grid. These are extra samples, results are discarded.
iterCount	Tunable param, number of iterations, functor will be called roughly sampleCount times per iteration.
alpha	Tunable param, represents stiffness of the grid rebinning algorithm. Range is usually [1,2], no rebinning will occur at 0.

template<sdt Dim = 1, sdt DimRes = 1, class Real__ = Real, sdt BinCount = 100>

honey::Vegas< Dim, DimRes, Real__, BinCount >::~Vegas ( )

inline

Member Function Documentation

template<sdt Dim = 1, sdt DimRes = 1, class Real__ = Real, sdt BinCount = 100>

const VecRes& honey::Vegas< Dim, DimRes, Real__, BinCount >::chiSqr ( ) const

inline

Get chi-square statistic for integral. A value that differs significantly from 1 (eg. diff > 0.5) indicates an unreliable result and more samples or iterations are required.

template<sdt Dim, sdt DimRes, class Real , sdt BinCount>

const Vegas< Dim, DimRes, Real, BinCount >::VecRes & honey::Vegas< Dim, DimRes, Real, BinCount >::integrate

(

Real

progressDelta = 1

)

Perform integral calculation. The calculation can be split up over multiple calls.

Parameters

progressDelta

Percentage of progress to complete in this call. Range [0,1]

Returns

Result of integration so far. Accuracy increases with progress.

template<sdt Dim = 1, sdt DimRes = 1, class Real__ = Real, sdt BinCount = 100>

Real honey::Vegas< Dim, DimRes, Real__, BinCount >::progress ( ) const

inline

Current progress of calculation, from 0 (start) to 1 (complete).

template<sdt Dim = 1, sdt DimRes = 1, class Real__ = Real, sdt BinCount = 100>

const VecRes& honey::Vegas< Dim, DimRes, Real__, BinCount >::result ( ) const

inline

Get current result of integration (same value returned by Integrate)

template<sdt Dim = 1, sdt DimRes = 1, class Real__ = Real, sdt BinCount = 100>

const VecRes& honey::Vegas< Dim, DimRes, Real__, BinCount >::stdDev ( ) const

inline

Estimate of standard deviation of integral result. Indicative of +- error range in result.

Member Data Documentation

template<sdt Dim = 1, sdt DimRes = 1, class Real__ = Real, sdt BinCount = 100>

const sdt honey::Vegas< Dim, DimRes, Real__, BinCount >::dim = Dim

static

template<sdt Dim = 1, sdt DimRes = 1, class Real__ = Real, sdt BinCount = 100>

const sdt honey::Vegas< Dim, DimRes, Real__, BinCount >::dimRes = DimRes

static

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

• src/common/Honey/Math/Random/Vegas.h