Stein's fractional Brownian motion context. More...

#include <libfbm.hpp>

Inheritance diagram for libfbm::FBMSteinContext:

Public Member Functions
	FBMSteinContext (double H, size_t dim, size_t size, double Rhint=-1, bool mapDim=true)
	Construct the Stein's FBM context object of size size^dim.
double	cov (const zvec &zvec)
	Covariance function.
void	disablePostProcessing ()
double	getR () const
	Get the parameter R described in [3].
Public Member Functions inherited from libfbm::SGPContext
	SGPContext (const zvec &fieldDim, const zvec &userDim, const std::string &cacheName)
	Constructor.
virtual	~SGPContext ()
const zvec &	getDim () const
	Get the usable dimension of the generated field.
const zvec &	getFieldDim () const
	Get the physical dimension of the generated field.
void	setCacheDir (const std::string &cacheDir)
	Set the cache directory.
size_t	badEigenCount () const
	Return the number of bad eigenvalues encountered.
bool	initCache (bool forceRecalc=false)
	Initialize the cache.

Static Public Member Functions
static size_t	userSize2FieldSize (size_t size, double R)
	Get the required field size for the given usable user size and R.
static size_t	fieldSize2UserSize (size_t size, double R)
	Map the field dimension into the resulting usable fBm field dimension.
static double	getRForH (double H, size_t dim, double Rhint=-1)
	Get the precomputed R value for the given H.

Protected Member Functions
void	postProcess (Field &field, GaussianGenerator &rng)
	Postprocessor called after field generation.
Protected Member Functions inherited from libfbm::SGPContext
void	setScaleResult (double f)
	Scale the output values by factor f.

Detailed Description

Stein's fractional Brownian motion context.

Stein [3] defines fBm as a random process Z with a power-law increment variance:

$\mbox{Var}\!\left(\left| Z\!\left(\mathbf{x}\right)-Z\!\left(\mathbf{y}\right)\right|^2\right)\propto\left|\mathbf{x}-\mathbf{y}\right|^{2H},$

however, the covariance does not match that of a "standard" fBm. Indeed, for Stein it is actually

$\mbox{Cov}\!\left(Z\!\left(\mathbf{x}\right),Z\!\left(\mathbf{y}\right)\right)=c0-\left|\mathbf{x}-\mathbf{y}\right|^{2H}+c_2\left(\left|\mathbf{x}\right|^2+\left|\mathbf{y}^2\right|\right).$

The FBMSteinContext changes the actual genereated field dimension. However, only part of it, that is the dimension given at construction is usable, the rest is used for the Stein's embedding method. This means the getDim() and getFieldDim() may have different values. The Field::getDim() reflects the usable area.

Definition at line 931 of file libfbm.hpp.

Constructor & Destructor Documentation

libfbm::FBMSteinContext::FBMSteinContext	(	double	H,
		size_t	dim,
		size_t	size,
		double	Rhint = `-1`,
		bool	mapDim = `true`
	)

Construct the Stein's FBM context object of size size^dim.

Parameters:

H	The Hurst exponent.
dim	Dimensionality of the field wanted (1D, 2D, 3D, etc.).
size	Request field of size^dim.
Rhint	Hint that overrides the self-determined R (see getRforH()). See [3] for details but in general 1<=R<=2. Larger R wastes more space and takes more time to calculate; smaller R may result in negative eigenvalues and a failed calculation. So one strives towards smallest R possible that works (no negative eigenvalues). As field size is increased (or field dimension), R must also increase. If left negative, the program attempts to estimate the value based on parameter H and dimensionality, but this estimate is conservative.
mapDim	Expand dimension so that the resulting usable field is the size requested. True by default.

The automatic R detections seems to work well for 2D case. For higher-dimensional cases you may have to fiddle with it manually.

Member Function Documentation

double libfbm::FBMSteinContext::cov ( const zvec & p )

virtual

Covariance function.

Implements libfbm::SGPContext.

void libfbm::FBMSteinContext::disablePostProcessing ( )

static size_t libfbm::FBMSteinContext::fieldSize2UserSize	(	size_t	size,
		double	R
	)

static

Map the field dimension into the resulting usable fBm field dimension.

double libfbm::FBMSteinContext::getR ( ) const

inline

Get the parameter R described in [3].

Definition at line 961 of file libfbm.hpp.

static double libfbm::FBMSteinContext::getRForH	(	double	H,
		size_t	dim,
		double	Rhint = `-1`
	)

static

Get the precomputed R value for the given H.

This function is quantized, so is not optimal. Also R depends a bit on the size of the field. This here is conservative. However, it could be it fails for some cases, then you need to provide your own correct R. The returned value is a very conservative 2.0 when dim >= 3, so for 3D and higher-dimensional cases it makes sense to find your own optimal R value.

Parameters:

Rhint If equal or greater than 1, return Rhint.

void libfbm::FBMSteinContext::postProcess	(	Field &	field,
		GaussianGenerator &	rng
	)

protectedvirtual

Postprocessor called after field generation.

This is called automatically by Field::generate().

Reimplemented from libfbm::SGPContext.

static size_t libfbm::FBMSteinContext::userSize2FieldSize	(	size_t	size,
		double	R
	)

static

Get the required field size for the given usable user size and R.

Stein's method [2] requires a larger field to generate a field for the required initial dimensions. This size depends on the chosen R. For 2D and H <= 0.75, R is always 1.0. For H > 0.75, R must be increased. It is proven that the methdod works with R=2.0. However, in practice R=1.3 at H=0.999 works just fine.

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

libfbm.hpp

Public Member Functions

Static Public Member Functions

Protected Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation