SSJ
3.3.1
Stochastic Simulation in Java

This abstract class represents a general point set. More...
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...  
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 d21 , 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  
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...  
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 twodimensional 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 innerclass 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 highlyuniform 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. Builtin 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 reimplemented 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.
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 d21
. The variable shiftStream
is also set to this stream
. Allowing an arbitrary range d1
to d21
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 ArrayRQMC method.
This method is reimplemented 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.
stream  random number stream used to generate uniforms for the random shift 
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.
UnsupportedOperationException  if the number of points or dimension of the point set is infinite 
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.
n  number of points 
d  dimension 
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.
iter  iterator associated to the point set 
UnsupportedOperationException  if the number of points or dimension of the point set is infinite 
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.
iter  iterator associated to the point set 
n  number of points 
d  dimension 
String formatPointsBase  (  int  b  ) 
Similar to formatPoints(), but the points coordinates are printed in base \(b\).
b  base 
UnsupportedOperationException  if the number of points or dimension of the point set is infinite 
String formatPointsBase  (  int  n, 
int  d,  
int  b  
) 
Similar to formatPoints(n, d), but the points coordinates are printed in base \(b\).
n  number of points 
d  dimension 
b  base 
String formatPointsBase  (  PointSetIterator  iter, 
int  b  
) 
Similar to formatPoints(iter), but the points coordinates are printed in base \(b\).
iter  iterator associated to the point set 
b  base 
UnsupportedOperationException  if the number of points or dimension of the point set is infinite 
String formatPointsBase  (  PointSetIterator  iter, 
int  n,  
int  d,  
int  b  
) 
Similar to formatPoints(iter, n, d), but the points coordinates are printed in base \(b\).
iter  iterator associated to the point set 
n  number of points 
d  dimension 
b  base 
String formatPointsNumbered  (  ) 
Same as invoking formatPointsNumbered(n, d) with \(n\) and \(d\) equal to the number of points and the dimension, respectively.
UnsupportedOperationException  if the number of points or dimension of the point set is infinite 
String formatPointsNumbered  (  int  n, 
int  d  
) 
Same as invoking formatPoints(n,d), except that the points are numbered.
n  number of points 
d  dimension 

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. Fautil que toutes les getCoordinate
implémentent le random shift quand il existe? Oui.
i  index of the point to look for 
j  index of the coordinate to look for 
int getDimension  (  ) 
Returns the dimension (number of available coordinates) of the points.
If the dimension is actually infinite, Integer.MAX_VALUE
is returned.
Integer.MAX_VALUE
if it is infinite int getNumPoints  (  ) 
Returns the number of points.
If this number is actually infinite, Integer.MAX_VALUE
is returned.
Integer.MAX_VALUE
if the point set has infinity cardinality. 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.
void randomize  (  PointSetRandomization  rand  ) 
Randomizes this point set using the given rand
.
Use the equivalent rand.randomize(this)
instead.
rand  PointSetRandomization to use 
String toString  (  ) 
Formats a string that contains information about the point set.

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

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.

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.

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.