HaltonUniformDistribution (ELKI: Environment for DeveLoping KDD-Applications Supported by Index-Structures)

java.lang.Object
- de.lmu.ifi.dbs.elki.math.statistics.distribution.HaltonUniformDistribution

All Implemented Interfaces:

Distribution
```
@Reference(title="Randomized halton sequences",
           authors="X. Wang, F. J. Hickernell",
           booktitle="Mathematical and Computer Modelling Vol. 32 (7)",
           url="https://doi.org/10.1016/S0895-7177(00)00178-3",
           bibkey="doi:10.1016/S0895-71770000178-3")
public class HaltonUniformDistribution
extends java.lang.Object
implements Distribution
```
Halton sequences are a pseudo-uniform distribution. The data is actually too regular for a true uniform distribution, but as such will of course often appear to be uniform.
Technically, they are based on Van der Corput sequence and the Von Neumann Katutani transformation. These produce a series of integers which then are converted to floating point values.
To randomize, we just choose a random starting position, as indicated by
Reference:
X. Wang, F. J. Hickernell
Randomized halton sequences
Mathematical and Computer Modelling Vol. 32 (7)
Important note: this code hasn't been double checked yet. While it probably works for some simple cases such as example data set generation, do not rely on it for e.g. quasi monte carlo methods without double-checking the quality, and looking at more advanced methods!
Let me repeat this: this code was written to generate toy datasets. It may have deficits for other uses! There is a high chance it will produce correlated data when used for more than one dimension. - for toy data sets, try different random seeds until you find one that works for you.
TODO: find an improved algorithm that takes care of a better randomization, for example by adding scrambling.

Since:

0.5.5

Author:

Erich Schubert

Nested Class Summary

Nested Classes
Modifier and Type	Class and Description
`static class`	`HaltonUniformDistribution.Parameterizer` Parameterization class TODO: allow manual parameterization of sequence parameters!

Field Summary

Fields
Modifier and Type	Field and Description
`private static double`	`ALMOST_ONE` Threshold
`(package private) short`	`base` Base value
`(package private) int`	`counter` Counter, for max iterations of fast function.
`(package private) double`	`current` Current value
`(package private) double`	`invbase` Inverse of base, for faster division by multiplication.
`(package private) long`	`inverse` Integer inverse
`private double`	`len` Len := max - min
`(package private) double`	`logbase` Logarithm of base.
`private double`	`max` Maximum
`private static int`	`MAXFAST` Maximum number of iterations of fast variant
`(package private) int`	`maxi` Maximum integer to use
`private double`	`min` Minimum

Constructor Summary

Constructors
Constructor and Description
`HaltonUniformDistribution(double min, double max)` Constructor for a halton pseudo uniform distribution on the interval [min, max[
`HaltonUniformDistribution(double min, double max, int base, double seed)` Constructor for a halton pseudo uniform distribution on the interval [min, max[
`HaltonUniformDistribution(double min, double max, java.util.Random rnd)` Constructor for a halton pseudo uniform distribution on the interval [min, max[
`HaltonUniformDistribution(double min, double max, RandomFactory rnd)` Constructor for a halton pseudo uniform distribution on the interval [min, max[

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double`	`cdf(double val)` Return the cumulative density function at the given value.
`private static int`	`choosePrime(java.util.Random rnd)` Choose a random prime.
`double`	`getMax()`
`double`	`getMin()`
`private long`	`inverse(double current)` Compute the inverse with respect to the given base.
`double`	`logpdf(double val)` Return the log density of an existing value
`private double`	`nextRadicalInverse()` Compute the next radical inverse.
`double`	`nextRandom()` Generate a new random value
`double`	`pdf(double val)` Return the density of an existing value
`double`	`quantile(double val)` Quantile aka probit (for normal) aka inverse CDF (invcdf, cdf^-1) function.
`private double`	`radicalInverse(long i)` Compute the radical inverse of i.
`java.lang.String`	`toString()` Describe the distribution

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Field Detail
  - min
```
private double min
```
    Minimum
  - max
```
private double max
```
    Maximum
  - len
```
private double len
```
    Len := max - min
  - MAXFAST
```
private static final int MAXFAST
```
    Maximum number of iterations of fast variant
    
    See Also:
    
    Constant Field Values
  - ALMOST_ONE
```
private static final double ALMOST_ONE
```
    Threshold
    
    See Also:
    
    Constant Field Values
  - base
```
final short base
```
    Base value
  - invbase
```
final double invbase
```
    Inverse of base, for faster division by multiplication.
  - logbase
```
final double logbase
```
    Logarithm of base.
  - maxi
```
final int maxi
```
    Maximum integer to use
  - counter
```
int counter
```
    Counter, for max iterations of fast function.
  - current
```
double current
```
    Current value
  - inverse
```
long inverse
```
    Integer inverse
- Constructor Detail
  - HaltonUniformDistribution
```
public HaltonUniformDistribution(double min,
                                 double max,
                                 int base,
                                 double seed)
```
    Constructor for a halton pseudo uniform distribution on the interval [min, max[
    
    Parameters:
    
    min - Minimum value
    
    max - Maximum value
    
    base - Base value
    
    seed - Random seed (starting value)
  - HaltonUniformDistribution
```
public HaltonUniformDistribution(double min,
                                 double max)
```
    Constructor for a halton pseudo uniform distribution on the interval [min, max[
    
    Parameters:
    
    min - Minimum value
    
    max - Maximum value
  - HaltonUniformDistribution
```
public HaltonUniformDistribution(double min,
                                 double max,
                                 java.util.Random rnd)
```
    Constructor for a halton pseudo uniform distribution on the interval [min, max[
    
    Parameters:
    
    min - Minimum value
    
    max - Maximum value
    
    rnd - Random generator
  - HaltonUniformDistribution
```
public HaltonUniformDistribution(double min,
                                 double max,
                                 RandomFactory rnd)
```
    Constructor for a halton pseudo uniform distribution on the interval [min, max[
    
    Parameters:
    
    min - Minimum value
    
    max - Maximum value
    
    rnd - Random generator
- Method Detail
  - choosePrime
```
private static int choosePrime(java.util.Random rnd)
```
    Choose a random prime. We try to avoid the later primes, as they are known to cause too correlated data.
    
    Parameters:
    
    rnd - Random generator
    
    Returns:
    
    Prime
  - pdf
```
public double pdf(double val)
```
    Description copied from interface: Distribution
    
    Return the density of an existing value
    
    Specified by:
    
    pdf in interface Distribution
    
    Parameters:
    
    val - existing value
    
    Returns:
    
    distribution density
  - logpdf
```
public double logpdf(double val)
```
    Description copied from interface: Distribution
    
    Return the log density of an existing value
    
    Specified by:
    
    logpdf in interface Distribution
    
    Parameters:
    
    val - existing value
    
    Returns:
    
    log distribution density
  - cdf
```
public double cdf(double val)
```
    Description copied from interface: Distribution
    
    Return the cumulative density function at the given value.
    
    Specified by:
    
    cdf in interface Distribution
    
    Parameters:
    
    val - existing value
    
    Returns:
    
    cumulative density
  - quantile
```
public double quantile(double val)
```
    Description copied from interface: Distribution
    
    Quantile aka probit (for normal) aka inverse CDF (invcdf, cdf^-1) function.
    
    Specified by:
    
    quantile in interface Distribution
    
    Parameters:
    
    val - Quantile to find
    
    Returns:
    
    Quantile position
  - inverse
```
private long inverse(double current)
```
    Compute the inverse with respect to the given base.
    
    Parameters:
    
    current - Current value
    
    Returns:
    
    Integer inverse
  - radicalInverse
```
private double radicalInverse(long i)
```
    Compute the radical inverse of i.
    
    Parameters:
    
    i - Input long value
    
    Returns:
    
    Double radical inverse
  - nextRadicalInverse
```
private double nextRadicalInverse()
```
    Compute the next radical inverse.
    
    Returns:
    
    Next inverse
  - nextRandom
```
public double nextRandom()
```
    Description copied from interface: Distribution
    
    Generate a new random value
    
    Specified by:
    
    nextRandom in interface Distribution
    
    Returns:
    
    new random value
  - toString
```
public java.lang.String toString()
```
    Description copied from interface: Distribution
    
    Describe the distribution
    
    Specified by:
    
    toString in interface Distribution
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    
    description
  - getMin
```
public double getMin()
```
    Returns:
    
    the minimum value
  - getMax
```
public double getMax()
```
    Returns:
    
    the maximum value

Class HaltonUniformDistribution

Nested Class Summary

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

min

max

len

MAXFAST

ALMOST_ONE

base

invbase

logbase

maxi

counter

current

inverse

Constructor Detail

HaltonUniformDistribution

HaltonUniformDistribution

HaltonUniformDistribution

HaltonUniformDistribution

Method Detail

choosePrime

pdf

logpdf

cdf

quantile

inverse

radicalInverse

nextRadicalInverse

nextRandom

toString

getMin

getMax