Package org.apache.commons.rng.sampling.distribution

Class LargeMeanPoissonSampler

java.lang.Object

org.apache.commons.rng.sampling.distribution.LargeMeanPoissonSampler

All Implemented Interfaces:

DiscreteSampler, SharedStateDiscreteSampler, SharedStateSampler<SharedStateDiscreteSampler>

public class LargeMeanPoissonSampler
extends Object
implements SharedStateDiscreteSampler

Sampler for the Poisson distribution.

• For large means, we use the rejection algorithm described in

  Devroye, Luc. (1981).The Computer Generation of Poisson Random Variables
  Computing vol. 26 pp. 197-207.

This sampler is suitable for mean >= 40.

Sampling uses:

• UniformRandomProvider.nextLong()
• UniformRandomProvider.nextDouble()

Since:

1.1

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
(package private) static final class	LargeMeanPoissonSampler.LargeMeanPoissonSamplerState	Encapsulate the state of the sampler.

Field Summary

Fields

Modifier and Type	Field	Description
private final double	c1	Algorithm constant: 1 / (8 * lambda).
private final double	delta	Algorithm constant: Math.sqrt(lambda * Math.log(32 * lambda / Math.PI + 1)).
private final SharedStateContinuousSampler	exponential	Exponential.
private final InternalUtils.FactorialLog	factorialLog	Local class to compute log(n!).
private final SharedStateContinuousSampler	gaussian	Gaussian.
private final double	halfDelta	Algorithm constant: delta / 2.
private final double	lambda	Algorithm constant: Math.floor(mean).
private final double	logLambda	Algorithm constant: Math.log(lambda).
private final double	logLambdaFactorial	Algorithm constant: factorialLog((int) lambda).
private static final double	MAX_MEAN	Upper bound to avoid truncation.
private static final InternalUtils.FactorialLog	NO_CACHE_FACTORIAL_LOG	Class to compute log(n!).
private static final SharedStateDiscreteSampler	NO_SMALL_MEAN_POISSON_SAMPLER	Used when there is no requirement for a small mean Poisson sampler.
private final double	p1	Algorithm constant: a1 / aSum.
private final double	p2	Algorithm constant: a2 / aSum.
private final UniformRandomProvider	rng	Underlying source of randomness.
private final SharedStateDiscreteSampler	smallMeanPoissonSampler	The internal Poisson sampler for the lambda fraction.
private final double	sqrtLambdaPlusHalfDelta	Algorithm constant: Math.sqrt(lambda + halfDelta).
private final double	twolpd	Algorithm constant: 2 * lambda + delta.

Constructor Summary

Constructors

Modifier	Constructor	Description
private	LargeMeanPoissonSampler(double mean, UniformRandomProvider rng)
private	LargeMeanPoissonSampler(LargeMeanPoissonSampler.LargeMeanPoissonSamplerState state, double lambdaFractional, UniformRandomProvider rng)	Instantiates a sampler using a precomputed state.
	LargeMeanPoissonSampler(UniformRandomProvider rng, double mean)	Create an instance.
private	LargeMeanPoissonSampler(UniformRandomProvider rng, LargeMeanPoissonSampler source)
(package private)	LargeMeanPoissonSampler(UniformRandomProvider rng, LargeMeanPoissonSampler.LargeMeanPoissonSamplerState state, double lambdaFractional)	Instantiates a sampler using a precomputed state.

Method Summary

Modifier and Type	Method	Description
private double	getFactorialLog(int n)	Compute the natural logarithm of the factorial of n.
(package private) LargeMeanPoissonSampler.LargeMeanPoissonSamplerState	getState()	Gets the initialisation state of the sampler.
static SharedStateDiscreteSampler	of(UniformRandomProvider rng, double mean)	Creates a new Poisson distribution sampler.
int	sample()	Creates an int sample.
String	toString()
SharedStateDiscreteSampler	withUniformRandomProvider(UniformRandomProvider rng)	Create a new instance of the sampler with the same underlying state using the given uniform random provider as the source of randomness.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface org.apache.commons.rng.sampling.distribution.DiscreteSampler

samples, samples

Field Details

MAX_MEAN

private static final double MAX_MEAN

Upper bound to avoid truncation.

See Also:

• Constant Field Values

NO_CACHE_FACTORIAL_LOG

private static final InternalUtils.FactorialLog NO_CACHE_FACTORIAL_LOG

Class to compute log(n!). This has no cached values.

NO_SMALL_MEAN_POISSON_SAMPLER

private static final SharedStateDiscreteSampler NO_SMALL_MEAN_POISSON_SAMPLER

Used when there is no requirement for a small mean Poisson sampler.

rng

private final UniformRandomProvider rng

Underlying source of randomness.

exponential

private final SharedStateContinuousSampler exponential

Exponential.

gaussian

private final SharedStateContinuousSampler gaussian

Gaussian.

factorialLog

private final InternalUtils.FactorialLog factorialLog

Local class to compute log(n!). This may have cached values.

lambda

private final double lambda

Algorithm constant: Math.floor(mean).

logLambda

private final double logLambda

Algorithm constant: Math.log(lambda).

logLambdaFactorial

private final double logLambdaFactorial

Algorithm constant: factorialLog((int) lambda).

delta

private final double delta

Algorithm constant: Math.sqrt(lambda * Math.log(32 * lambda / Math.PI + 1)).

halfDelta

private final double halfDelta

Algorithm constant: delta / 2.

sqrtLambdaPlusHalfDelta

private final double sqrtLambdaPlusHalfDelta

Algorithm constant: Math.sqrt(lambda + halfDelta).

twolpd

private final double twolpd

Algorithm constant: 2 * lambda + delta.

p1

private final double p1

Algorithm constant: a1 / aSum.

• a1 = Math.sqrt(Math.PI * twolpd) * Math.exp(c1)
• aSum = a1 + a2 + 1

p2

private final double p2

Algorithm constant: a2 / aSum.

• a2 = (twolpd / delta) * Math.exp(-delta * (1 + delta) / twolpd)
• aSum = a1 + a2 + 1

c1

private final double c1

Algorithm constant: 1 / (8 * lambda).

smallMeanPoissonSampler

private final SharedStateDiscreteSampler smallMeanPoissonSampler

The internal Poisson sampler for the lambda fraction.

Constructor Details

LargeMeanPoissonSampler

public LargeMeanPoissonSampler(UniformRandomProvider rng,
 double mean)

Create an instance.

Parameters:

rng - Generator of uniformly distributed random numbers.

mean - Mean.

Throws:

IllegalArgumentException - if mean < 1 or mean > 0.5 * Integer.MAX_VALUE.

LargeMeanPoissonSampler

LargeMeanPoissonSampler(UniformRandomProvider rng,
 LargeMeanPoissonSampler.LargeMeanPoissonSamplerState state,
 double lambdaFractional)

Instantiates a sampler using a precomputed state.

Parameters:

rng - Generator of uniformly distributed random numbers.

state - The state for lambda = (int)Math.floor(mean).

lambdaFractional - The lambda fractional value (mean - (int)Math.floor(mean)).

Throws:

IllegalArgumentException - if lambdaFractional < 0 || lambdaFractional >= 1.

LargeMeanPoissonSampler

private LargeMeanPoissonSampler(double mean,
 UniformRandomProvider rng)

Parameters:

mean - Mean.

rng - Generator of uniformly distributed random numbers.

LargeMeanPoissonSampler

private LargeMeanPoissonSampler(LargeMeanPoissonSampler.LargeMeanPoissonSamplerState state,
 double lambdaFractional,
 UniformRandomProvider rng)

Instantiates a sampler using a precomputed state.

Parameters:

state - The state for lambda = (int)Math.floor(mean).

lambdaFractional - The lambda fractional value (mean - (int)Math.floor(mean)).

rng - Generator of uniformly distributed random numbers.

LargeMeanPoissonSampler

private LargeMeanPoissonSampler(UniformRandomProvider rng,
 LargeMeanPoissonSampler source)

Parameters:

rng - Generator of uniformly distributed random numbers.

source - Source to copy.

Method Details

sample

public int sample()

Creates an int sample.

Specified by:

sample in interface DiscreteSampler

Returns:

a sample.

getFactorialLog

private double getFactorialLog(int n)

Compute the natural logarithm of the factorial of n.

Parameters:

n - Argument.

Returns:

log(n!)

Throws:

IllegalArgumentException - if n < 0.

toString

public String toString()

Overrides:

toString in class Object

withUniformRandomProvider

public SharedStateDiscreteSampler withUniformRandomProvider(UniformRandomProvider rng)

Create a new instance of the sampler with the same underlying state using the given uniform random provider as the source of randomness.

Specified by:

withUniformRandomProvider in interface SharedStateSampler<SharedStateDiscreteSampler>

Parameters:

rng - Generator of uniformly distributed random numbers.

Returns:

the sampler

Since:

1.3

of

public static SharedStateDiscreteSampler of(UniformRandomProvider rng,
 double mean)

Creates a new Poisson distribution sampler.

Parameters:

rng - Generator of uniformly distributed random numbers.

mean - Mean.

Returns:

the sampler

Throws:

IllegalArgumentException - if mean < 1 or mean > 0.5 * Integer.MAX_VALUE.

Since:

1.3

getState

LargeMeanPoissonSampler.LargeMeanPoissonSamplerState getState()

Gets the initialisation state of the sampler.

The state is computed using an integer lambda value of lambda = (int)Math.floor(mean).

The state will be suitable for reconstructing a new sampler with a mean in the range lambda <= mean < lambda+1 using LargeMeanPoissonSampler(UniformRandomProvider, LargeMeanPoissonSamplerState, double).

Returns:

the state