SSJ  3.3.1 Stochastic Simulation in Java
PointSet Class Referenceabstract

This abstract class represents a general point set. More...

Inheritance diagram for PointSet:
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Collaboration diagram for PointSet:
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## Classes

class  DefaultPointSetIterator
This class implements a default point set iterator. More...

## Public Member Functions

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...

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.

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

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...

## Static Protected Attributes

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...

## Detailed Description

This abstract class represents a general point set.

It defines some basic methods for accessing and manipulating the points and other properties of the point set. Conceptually, a point set can be viewed as a two-dimensional array, whose element $$(i,j)$$ contains $$u_{i,j}$$, the coordinate $$j$$ of point $$i$$, for $$i\geq 0$$ and $$j\geq 0$$. Each coordinate $$u_{i,j}$$ is assumed to be in the unit interval $$[0,1]$$. Whether the values 0 and 1 can occur or not may depend on the actual implementation of the point set. In general, when the points are randomized, after the randomization we add (internally, when the points or coordinates are requested) $$\epsilon/2$$ to each coordinate for a very small $$\epsilon > 0$$, so that 0 never occurs in the output. By default, in this PointSet class, we have $$\epsilon = 2^{-54}$$.

All points have the same number of coordinates (their dimension) and this number can be queried by getDimension. The number of points is queried by getNumPoints. The points and coordinates are both numbered starting from 0 and their number can actually be infinite.

The iterator method provides a PointSetIterator object which can enumerate the points and their coordinates. Several iterators over the same point set can coexist at any given time. However, in the current implementation they will all enumerate the same randomized points when the points are randomized, because the randomizations are integrated in the point sets and not in the iterators. These iterators are instances of a hidden inner-class that implements the PointSetIterator interface. The default implementation of iterator provided here relies on the method getCoordinate to access the coordinates directly. However, this approach is rarely efficient. (One exception is in a CachedPointSet.) Specialized implementations that dramatically improve the performance are provided in subclasses of PointSet. The PointSetIterator interface actually extends the umontreal.ssj.rng.RandomStream interface, so that the iterator can also be seen as a umontreal.ssj.rng.RandomStream and used wherever such a stream is required for generating uniform random numbers. This permits one to easily replace pseudorandom numbers by the coordinates of a selected set of highly-uniform points, i.e., to replace Monte Carlo by QMC or RQMC in a simulation program.

The present abstract class has only one abstract method: getCoordinate. Providing an implementation for this method is already sufficient for the subclass to work. However, in most cases, efficiency can be dramatically improved by overwriting iterator to provide a custom iterator that does not necessarily rely on getCoordinate. Direct use of getCoordinate to access the coordinates is generally discouraged. One should access the points and coordinates via the iterators. Built-in range checks when generating the points require some extra time and also assume that nobody ever uses negative indices. If getCoordinate is never accessed directly by the user, it may be implemented without range checks.

In this abstract class, the addRandomShift() methods generate a double[] array to be used eventually to add a random shift modulo 1, but this random shift is not used here. It can be used in subclasses when generating coordinates.
In subclasses, addRandomShift (d1, d2, stream) can also be optionally re-implemented to produce something else than a double[] array, for example when we want the random shift to be digital. There are also some types of point sets that do not use at all such a random shift.

## Member Function Documentation

 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.

This random shift will be added (modulo 1) to all the points when they are enumerated by the iterator.
The random shift is generated using the stream to generate the uniform random numbers, one for each of the coordinates d1 to d2-1. The variable shiftStream is also set to this stream. Allowing an arbitrary range d1 to d2-1 permits one to extends the random shift to additional coordinates when needed, e.g., when the number of coordinates that we need is unknown a priori. There are also other situations in which we may want to randomize only specific coordinates, e.g., in the Array-RQMC method.

This method is re-implemented in subclasses for which a different form of shift is appropriate, e.g., should produce a random digital shift in base $$b$$ for a #DigitalNet, a binary digital shift for a #DigitalNetBase2, etc.

These methods are used internally by randomizations. For example, calling RandomShift.randomize(PointSet) calls addRandomShift. Normally, one should not call them directly, but use #PointSetRandomization objects instead.

 void addRandomShift ( RandomStream stream )

Same as addRandomShift(0, dim, stream), where dim is the dimension of the point set.

Parameters
 stream random number stream used to generate uniforms for the random shift

## ◆ formatPoints() [1/4]

 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.

Returns
string representation of all the points in the point set
Exceptions
 UnsupportedOperationException if the number of points or dimension of the point set is infinite

## ◆ formatPoints() [2/4]

 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.

If $$n$$ is larger than the number of points in the point set, it is reset to that number. If $$d$$ is larger than the dimension of the points, it is reset to that dimension. The points are printed in the simplest format, separated by spaces, by calling the default iterator repeatedly.

Parameters
 n number of points d dimension
Returns
string representation of first d coordinates of first n points in the point set

## ◆ formatPoints() [3/4]

 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.

Parameters
 iter iterator associated to the point set
Returns
string representation of all the points in the point set
Exceptions
 UnsupportedOperationException if the number of points or dimension of the point set is infinite

## ◆ formatPoints() [4/4]

 String formatPoints ( PointSetIterator iter, int n, int d )

Same as invoking formatPoints(n, d), but prints the points by calling iter repeatedly.

The order of the printed points may be different than the one resulting from the default iterator.

Parameters
 iter iterator associated to the point set n number of points d dimension
Returns
string representation of first d coordinates of first n points in the point set

## ◆ formatPointsBase() [1/4]

 String formatPointsBase ( int b )

Similar to formatPoints(), but the points coordinates are printed in base $$b$$.

Parameters
 b base
Returns
string representation of all the points in the point set
Exceptions
 UnsupportedOperationException if the number of points or dimension of the point set is infinite

## ◆ formatPointsBase() [2/4]

 String formatPointsBase ( int n, int d, int b )

Similar to formatPoints(n, d), but the points coordinates are printed in base $$b$$.

Parameters
 n number of points d dimension b base
Returns
string representation of first d coordinates of first n points in the point set

## ◆ formatPointsBase() [3/4]

 String formatPointsBase ( PointSetIterator iter, int b )

Similar to formatPoints(iter), but the points coordinates are printed in base $$b$$.

Parameters
 iter iterator associated to the point set b base
Returns
string representation of all the points in the point set
Exceptions
 UnsupportedOperationException if the number of points or dimension of the point set is infinite

## ◆ formatPointsBase() [4/4]

 String formatPointsBase ( PointSetIterator iter, int n, int d, int b )

Similar to formatPoints(iter, n, d), but the points coordinates are printed in base $$b$$.

Parameters
 iter iterator associated to the point set n number of points d dimension b base
Returns
string representation of first d coordinates of first n points in the point set

## ◆ formatPointsNumbered() [1/2]

 String formatPointsNumbered ( )

Same as invoking formatPointsNumbered(n, d) with $$n$$ and $$d$$ equal to the number of points and the dimension, respectively.

Returns
string representation of all the points in the point set
Exceptions
 UnsupportedOperationException if the number of points or dimension of the point set is infinite

## ◆ formatPointsNumbered() [2/2]

 String formatPointsNumbered ( int n, int d )

Same as invoking formatPoints(n,d), except that the points are numbered.

Parameters
 n number of points d dimension
Returns
string representation of first d coordinates of first n points in the point set

## ◆ getCoordinate()

 abstract double getCoordinate ( int i, int j )
abstract

Returns $$u_{i,j}$$, the coordinate $$j$$ of the point $$i$$.

When the points are randomized (e.g., a random shift is added), the values returned by this method should incorporate the randomizations. Richard: La méthode getCoordinate de certaines classes ne tient pas compte du random shift, contrairement à l’itérateur de la même classe. Faut-il que toutes les getCoordinate implémentent le random shift quand il existe? Oui.

Parameters
 i index of the point to look for j index of the coordinate to look for
Returns
the value of $$u_{i,j}$$

## ◆ getDimension()

 int getDimension ( )

Returns the dimension (number of available coordinates) of the points.

If the dimension is actually infinite, Integer.MAX_VALUE is returned.

Returns
the dimension of the point set or Integer.MAX_VALUE if it is infinite

## ◆ getNumPoints()

 int getNumPoints ( )

Returns the number of points.

If this number is actually infinite, Integer.MAX_VALUE is returned.

Returns
the number of points in the point set or Integer.MAX_VALUE if the point set has infinity cardinality.

## ◆ iterator()

 PointSetIterator iterator ( )

Constructs and returns a point set iterator.

The default implementation returns an iterator that uses the method getCoordinate(i,j) to iterate over the points and coordinates, but subclasses can reimplement it for better efficiency.

Returns
point set iterator for the point set

## ◆ randomize()

 void randomize ( PointSetRandomization rand )

Randomizes this point set using the given rand.

Use the equivalent rand.randomize(this) instead.

Parameters
 rand PointSetRandomization to use

## ◆ toString()

 String toString ( )

Formats a string that contains information about the point set.

Returns
string representation of the point set information

## ◆ dimShift

 int dimShift = 0
protected

Current dimension of the shift.

This is useful mostly for the case where the points have an unlimited number of coordinates.

## ◆ MAXBITS

 final int MAXBITS = 31
staticprotected

Since Java has no unsigned type, the 32nd bit cannot be used efficiently, so we have only 31 bits.

This mainly affects digit scrambling and bit vectors. This also limits the maximum number of columns for the generating matrices of digital nets in base 2.

## ◆ shift

 double [] shift
protected

This is the shift vector as a double[] array, which contains the current random shift in case we apply a random shift modulo 1.

It is initially null.

## ◆ shiftStream

 RandomStream shiftStream
protected

Stream used to generate the random shifts.

This stream is saved from the last time we have called addRandomShift, in case this method has to be called again internally by an iterator. This may happen for example if the points have unbounded dimension and we need to extend the random shift to additional coordinates.

The documentation for this class was generated from the following file:
• PointSet.java