StratifiedUnitCube Class Reference

This class implements a stratification of the unit cube in rectangular boxes of same size and orientation. More...

Inheritance diagram for StratifiedUnitCube:

Collaboration diagram for StratifiedUnitCube:

Public Member Functions
	StratifiedUnitCube (int[] k, int dim)
	Builds a stratified points set in dim dimensions, with k[j] intervals in dimension j. More...
	StratifiedUnitCube (int k, int dim)
	Same as StratifiedUnitCube (int[] k, int dim) with all coordinates of the vector k equal to the integer k. More...
void	randomize (RandomStream stream)
	This randomization generates one point randomly in its corresponding box, for each of the \(n\) boxes. More...
void	addRandomShift (int fromDim, int toDim, RandomStream stream)
	Random shifts and partial randomizations are irrelevant here, so this method is redefined to be equivalent to randomize (stream). More...
void	randomize (PointSetRandomization rand)
	Randomizes the points using stratification, regardless of what rand is. More...
String	toString ()
Public Member Functions inherited from CachedPointSet
	CachedPointSet (PointSet p, int fromPoint, int toPoint, int fromDim, int toDim)
	Creates a new PointSet object that contains an array storing the coordinates fromDim (inclusive) to toDim (exclusive) of the points numbered fromPoint (inclusive) to toPoint (exclusive) of p. More...
	CachedPointSet (PointSet p, int n, int dim)
	Same as CachedPointSet(p, 0, n, 0, dim).
	CachedPointSet (PointSet p)
	Creates a new PointSet object that contains an array storing the points of p. More...
PointSetIterator	iterator ()
	Constructs and returns a point set iterator which gets the values directly from the array.
void	setRandomizeParent (boolean randomizeParent)
	If randomizeParent is true, calls to randomize() will be defered to the parent point set (this is the default); otherwise, the randomize method of the PointSetRandomization instance is invoked with this CachedPointSet instance as its argument.
void	addRandomShift (int d1, int d2, RandomStream stream)
	Generates a random shift, adds it to the contained point set, and re-caches the points. More...
void	randomize (PointSetRandomization rand)
	Randomizes the underlying point set using rand and re-caches the points. More...
void	sortByCoordinate (int j)
	Sorts the cached points by increasing order of coordinate j. More...
void	stripCoordinates (int d)
	Removes the first d coordinates of each cached point. More...
String	toString ()
double	getCoordinate (int i, int j)
double [][]	getArray ()
PointSet	getParentPointSet ()
	Returns the reference point set that was passed to the constructor.
Public Member Functions inherited from PointSet
int	getDimension ()
	Returns the dimension (number of available coordinates) of the points. More...
int	getNumPoints ()
	Returns the number of points. More...
abstract double	getCoordinate (int i, int j)
	Returns \(u_{i,j}\), the coordinate \(j\) of the point \(i\). More...
PointSetIterator	iterator ()
	Constructs and returns a point set iterator. More...
void	randomize (PointSetRandomization rand)
	Randomizes this point set using the given rand. More...
void	addRandomShift (int d1, int d2, RandomStream stream)
	By default, this method generates a random shift in the protected double[] array shift, to be used eventually for a random shift modulo 1. More...
void	addRandomShift (RandomStream stream)
	Same as addRandomShift(0, dim, stream), where dim is the dimension of the point set. More...
void	addRandomShift (int d1, int d2)
	Refreshes the random shift (generates new uniform values for the random shift coordinates) for coordinates d1 to d2-1, using the saved shiftStream.
void	addRandomShift ()
	Same as addRandomShift(0, dim), where dim is the dimension of the point set.
void	clearRandomShift ()
	Erases the current random shift, if any.
String	toString ()
	Formats a string that contains information about the point set. More...
String	formatPoints ()
	Same as invoking formatPoints(n, d) with \(n\) and \(d\) equal to the number of points and the dimension of this object, respectively. More...
String	formatPoints (int n, int d)
	Formats a string that displays the same information as returned by toString, together with the first \(d\) coordinates of the first \(n\) points. More...
String	formatPoints (PointSetIterator iter)
	Same as invoking formatPoints(iter, n, d) with \(n\) and \(d\) equal to the number of points and the dimension, respectively. More...
String	formatPoints (PointSetIterator iter, int n, int d)
	Same as invoking formatPoints(n, d), but prints the points by calling iter repeatedly. More...
String	formatPointsBase (int b)
	Similar to formatPoints(), but the points coordinates are printed in base \(b\). More...
String	formatPointsBase (int n, int d, int b)
	Similar to formatPoints(n, d), but the points coordinates are printed in base \(b\). More...
String	formatPointsBase (PointSetIterator iter, int b)
	Similar to formatPoints(iter), but the points coordinates are printed in base \(b\). More...
String	formatPointsBase (PointSetIterator iter, int n, int d, int b)
	Similar to formatPoints(iter, n, d), but the points coordinates are printed in base \(b\). More...
String	formatPointsNumbered ()
	Same as invoking formatPointsNumbered(n, d) with \(n\) and \(d\) equal to the number of points and the dimension, respectively. More...
String	formatPointsNumbered (int n, int d)
	Same as invoking formatPoints(n,d), except that the points are numbered. More...

Protected Attributes
int []	numDiv
	Number of divisions in each dimension, numDiv[j] for coordinate j.
double []	delta
	Size of divisions in each dimension, delta[j] = 1/numDiv[j].
Protected Attributes inherited from CachedPointSet
PointSet	P
double	x [][]
Protected Attributes inherited from PointSet
double	EpsilonHalf = 1.0 / Num.TWOEXP[55]
	To avoid 0 for nextCoordinate when random shifting, we add this to each coordinate.
int	dim = 0
	Dimension of the points.
int	numPoints = 0
	Number of points.
int	dimShift = 0
	Current dimension of the shift. More...
int	capacityShift = 0
	Number of array elements in the shift vector, always >= dimShift.
double []	shift
	This is the shift vector as a double[] array, which contains the current random shift in case we apply a random shift modulo 1. More...
RandomStream	shiftStream
	Stream used to generate the random shifts. More...

Additional Inherited Members
Protected Member Functions inherited from CachedPointSet
void	fillCache (int fromDim, int dim)
	Caches the points, skipping fromDim coordinates and taking the next dim ones.
Static Protected Attributes inherited from PointSet
static final int	MAXBITS = 31
	Since Java has no unsigned type, the 32nd bit cannot be used efficiently, so we have only 31 bits. More...
Package Functions inherited from CachedPointSet
public< T > void	sort (MultiDimSort< T > sort)
	Sorts the cached points (only) with the given umontreal.ssj.util.MultiDimSort sorting algorithm sort. More...
Package Attributes inherited from CachedPointSet
int	fromPoint = 0
int	fromDim = 0
boolean	randomizeParent = true

Detailed Description

This class implements a stratification of the unit cube in rectangular boxes of same size and orientation.

In \(s\) dimensions, it divides the \(j\)th axis in \(k_j \ge1\) equal parts of length \(d_j = 1/k_j\), for \(j=0,…,s-1\). This partitions the unit cube \([0,1)^s\) into \(n = k_0\cdots k_{s-1}\) rectangular boxes of the same size. The point set is defined by generating one random point uniformly in each of those \(n\) boxes.

We number the boxes (or strata) as follows: The box determined by the interval \([c_j d_j, (c_j+1)d_j)\) for \(j=0,…,s-1\) has number \(i = c_0 + c_1 k_0 + \cdots+ c_{s-1} k_0 \cdots k_{s-2}\). By default, the points are enumerated by order of their box number. One can also create iterators that enumerate the points by order of any given coordinate.

Although this class extends CachedPointSet, here there is no underlying point set p that is cached.

Constructor & Destructor Documentation

StratifiedUnitCube() [1/2]

StratifiedUnitCube	(	int []	k,
		int	dim
	)

Builds a stratified points set in dim dimensions, with k[j] intervals in dimension j.

Parameters

k	number of intervals in each dimension
dim	integer, dimension of the points set

StratifiedUnitCube() [2/2]

StratifiedUnitCube	(	int	k,
		int	dim
	)

Same as StratifiedUnitCube (int[] k, int dim) with all coordinates of the vector k equal to the integer k.

This gives \(n = k^s\) strata (and points), with \(s = {\mathtt{dim}}\).

Member Function Documentation

addRandomShift()

void addRandomShift	(	int	fromDim,
		int	toDim,
		RandomStream	stream
	)

Random shifts and partial randomizations are irrelevant here, so this method is redefined to be equivalent to randomize (stream).

The parameters fromDim and toDim are not used.

randomize() [1/2]

void randomize

(

RandomStream

stream

)

This randomization generates one point randomly in its corresponding box, for each of the \(n\) boxes.

The stratified points are defined only after this method has been called.

Parameters

stream

Random stream to generate the \(n\times{\mathtt{dim}}\) uniforms required to randomize the points

randomize() [2/2]

void randomize

(

PointSetRandomization

rand

)

Randomizes the points using stratification, regardless of what rand is.

Equivalent to randomize (rand.getStream).

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

• StratifiedUnitCube.java