This class is useful for the Array-RQMC method, in the situation where the Markov chain has a multidimensional state, the RQMC points are sorted once for all, based on their first \(\ell\) coordinates, then these coordinates are removed and only the remaining coordinates are kept and randomized at each step. More...

Inheritance diagram for SortedAndCutPointSet:

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Collaboration diagram for SortedAndCutPointSet:

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Classes
class	SortedAndCutPointSetIterator

Public Member Functions
	SortedAndCutPointSet (PointSet p, MultiDimSort sort)
	Takes the first `dim` coordinates of the first `n` points of `p` and creates a `SortedAndCutPointSet` from these points by sorting them according to `sort`. More...

int	getDimension ()
	Returns the number of coordinates of each point, which is the dimension of the original point set minus the dimension of the sort.

MultiDimSort	getSort ()
	Returns the sort used.

PointSetIterator	iterator ()
	Constructs and returns a point set iterator which gets the values directly from the array.

void	addRandomShift (int d1, int d2, RandomStream stream)
	Add the shift to the contained point set.

void	randomize (PointSetRandomization rand)
	Randomizes the contained point (all coordinates) set using `rand`. More...

String	toString ()
	Formats a string that contains the information about this point set. More...

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 Member Functions
int []	makeIndex ()
	Sorts the cached points in x[][] according to the first cached coordinates (the dimension of the sort) and constructs an index that retains the permutation. More...

void	fillCacheByIndex (int fromDim, int dim)
	Called by the constructors and also by {randomize}. More...

Protected Member Functions inherited from CachedPointSet
void	fillCache (int fromDim, int dim)
	Caches the points, skipping `fromDim` coordinates and taking the next `dim` ones.

Protected Attributes
int []	index

MultiDimSort	sort

int	numSortCoord

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
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 is useful for the Array-RQMC method, in the situation where the Markov chain has a multidimensional state, the RQMC points are sorted once for all, based on their first \(\ell\) coordinates, then these coordinates are removed and only the remaining coordinates are kept and randomized at each step.

It builds a sorted point set based on a given original point set p. The original points are first sorted based on their first \(\ell\) coordinates, via a umontreal.ssj.util.MultiDimSort in \(\ell\) dimensions, and this is used to build an index that stores the corresponding permutation, once for all. Then those \(\ell\) coordinates are removed from the points and never seen again. After that, when the points are enumerated, only the remaining coordinates are used and the points are enumerated by following the index. When they are randomized, the randomization is applied to the original point set, but only the remaining coordinates are randomized. If the original point set has dimension \(d_0\), the retained point set will have dimension \(d_0 - \ell\).

In this implementation, the retained coordinates of the points are cached, and they are re-cached after reach randomization.

Remarks: Pierre: This could be inefficient (and unnecessary) for very large point sets. One could implement an iterator that uses directly the randomized points in p without caching them.

To perform the sort, we first cache only the sorting coordinates of the points, with an extra coordinate that holds the original number of each point, and we apply the sort to those cached points. This extra coordinate is used to recover the permutation made by the sort and to produce the index.

The CachedPointSet class also offers methods for multi-dimensional sort and for skipping coordinates.

Constructor & Destructor Documentation

◆ SortedAndCutPointSet()

SortedAndCutPointSet	(	PointSet	p,
		MultiDimSort	sort
	)

Takes the first dim coordinates of the first n points of p and creates a SortedAndCutPointSet from these points by sorting them according to sort.

If sort is a umontreal.ssj.util.MultiDimSort of dimension \(d_s\), then the ordering of the points is determined from this sort acting on the first \(d_s\) coordinates of the original subset. The dimension of the resulting SortedAndCutPointSet is toDim - fromDim. Typically, in Array-RQMC applications, fromDim will be the dimension used by the sort.

Parameters

p	point set to be cached
n	number of points from `p` to use
dim	dimension to use for the points of `p`, before sorting.
sort	umontreal.ssj.util.MultiDimSort to use for sorting

Member Function Documentation

◆ fillCacheByIndex()

void fillCacheByIndex	(	int	fromDim,
		int	dim
	)

protected

Called by the constructors and also by {randomize}.

Cache the points in x, skipping the first fromDim coordinates and taking the next dim ones. The points are enumerated by order of the index.

◆ makeIndex()

int [] makeIndex ( )

protected

Sorts the cached points in x[][] according to the first cached coordinates (the dimension of the sort) and constructs an index that retains the permutation.

The coordinate after those used by the sort is used to identify the original point number and recover the permutation.
After this, one must call fillCacheByIndex to restore the cached points in proper order in x[][].

◆ randomize()

void randomize ( PointSetRandomization rand )

Randomizes the contained point (all coordinates) set using rand.

Parameters

rand	PointSetRandomization to use

◆ toString()

String toString ( )

Formats a string that contains the information about this point set.

Returns: string representation of the point set information

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

SortedAndCutPointSet.java

Classes

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members