org.nd4j.linalg.api.rng.distribution.impl

Class OrthogonalDistribution

java.lang.Object

org.nd4j.linalg.api.rng.distribution.BaseDistribution

org.nd4j.linalg.api.rng.distribution.impl.OrthogonalDistribution

All Implemented Interfaces:

Distribution

public class OrthogonalDistribution
extends BaseDistribution

Limited Orthogonal distribution implementation

Author:

[email protected]

Field Summary

Fields

Modifier and Type	Field and Description
static double	DEFAULT_INVERSE_ABSOLUTE_ACCURACY Default inverse cumulative probability accuracy.

Fields inherited from class org.nd4j.linalg.api.rng.distribution.BaseDistribution

random, solverAbsoluteAccuracy

Constructor Summary

Constructors

Constructor and Description
OrthogonalDistribution(double gain)

Method Summary

Modifier and Type	Method and Description
double	cumulativeProbability(double x) For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
double	cumulativeProbability(double x0, double x1) Deprecated. See org.apache.commons.math3.distribution.RealDistribution#cumulativeProbability(double, double)
double	density(double x) Returns the probability density function (PDF) of this distribution evaluated at the specified point x.
double	getMean() Access the mean.
double	getNumericalMean() Use this method to get the numerical value of the mean of this distribution.
double	getNumericalVariance() Use this method to get the numerical value of the variance of this distribution.
protected double	getSolverAbsoluteAccuracy() Returns the solver absolute accuracy for inverse cumulative computation.
double	getStandardDeviation() Access the standard deviation.
double	getSupportLowerBound() Access the lower bound of the support.
double	getSupportUpperBound() Access the upper bound of the support.
double	inverseCumulativeProbability(double p) Computes the quantile function of this distribution.
boolean	isSupportConnected() Use this method to get information about whether the support is connected, i.e.
boolean	isSupportLowerBoundInclusive() Whether or not the lower bound of support is in the domain of the density function.
boolean	isSupportUpperBoundInclusive() Whether or not the upper bound of support is in the domain of the density function.
double	probability(double x0, double x1) For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).
double	sample() Generate a random value sampled from this distribution.
INDArray	sample(INDArray target) Fill the target array by sampling from the distribution
INDArray	sample(int[] shape) Sample the given shape
INDArray	sample(long[] shape)

Methods inherited from class org.nd4j.linalg.api.rng.distribution.BaseDistribution

probability, reseedRandomGenerator, sample

Methods inherited from class java.lang.Object

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

Field Detail

DEFAULT_INVERSE_ABSOLUTE_ACCURACY

public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY

Default inverse cumulative probability accuracy.

Since:

2.1

See Also:

Constant Field Values

Constructor Detail

OrthogonalDistribution

public OrthogonalDistribution(double gain)

Method Detail

getMean

public double getMean()

Access the mean.

Returns:

the mean for this distribution.

getStandardDeviation

public double getStandardDeviation()

Access the standard deviation.

Returns:

the standard deviation for this distribution.

density

public double density(double x)

Returns the probability density function (PDF) of this distribution evaluated at the specified point x. In general, the PDF is the derivative of the CDF. If the derivative does not exist at x, then an appropriate replacement should be returned, e.g. Double.POSITIVE_INFINITY, Double.NaN, or the limit inferior or limit superior of the difference quotient.

Parameters:

x - the point at which the PDF is evaluated

Returns:

the value of the probability density function at point x

cumulativeProbability

public double cumulativeProbability(double x)

For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x). In other words, this method represents the (cumulative) distribution function (CDF) for this distribution.

If x is more than 40 standard deviations from the mean, 0 or 1 is returned, as in these cases the actual value is within Double.MIN_VALUE of 0 or 1.

Parameters:

x - the point at which the CDF is evaluated

Returns:

the probability that a random variable with this distribution takes a value less than or equal to x

inverseCumulativeProbability

public double inverseCumulativeProbability(double p)
                                    throws org.apache.commons.math3.exception.OutOfRangeException

Computes the quantile function of this distribution. For a random variable X distributed according to this distribution, the returned value is

• inf{x in R | P(X<=x) >= p} for 0 < p <= 1,
• inf{x in R | P(X<=x) > 0} for p = 0.

The default implementation returns

• Distribution.getSupportLowerBound() for p = 0,
• Distribution.getSupportUpperBound() for p = 1.

Specified by:

inverseCumulativeProbability in interface Distribution

Overrides:

inverseCumulativeProbability in class BaseDistribution

Parameters:

p - the cumulative probability

Returns:

the smallest p-quantile of this distribution (largest 0-quantile for p = 0)

Throws:

org.apache.commons.math3.exception.OutOfRangeException - if p < 0 or p > 1

Since:

3.2

cumulativeProbability

@Deprecated
public double cumulativeProbability(double x0,
                                                double x1)
                                         throws org.apache.commons.math3.exception.NumberIsTooLargeException

Deprecated. See org.apache.commons.math3.distribution.RealDistribution#cumulativeProbability(double, double)

For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).

Parameters:

x0 - the exclusive lower bound

x1 - the inclusive upper bound

Returns:

the probability that a random variable with this distribution takes a value between x0 and x1, excluding the lower and including the upper endpoint

Throws:

org.apache.commons.math3.exception.NumberIsTooLargeException - if x0 > x1

probability

public double probability(double x0,
                          double x1)
                   throws org.apache.commons.math3.exception.NumberIsTooLargeException

For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).

Overrides:

probability in class BaseDistribution

Parameters:

x0 - Lower bound (excluded).

x1 - Upper bound (included).

Returns:

the probability that a random variable with this distribution takes a value between x0 and x1, excluding the lower and including the upper endpoint.

Throws:

org.apache.commons.math3.exception.NumberIsTooLargeException - if x0 > x1.

The default implementation uses the identity P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)

getSolverAbsoluteAccuracy

protected double getSolverAbsoluteAccuracy()

Returns the solver absolute accuracy for inverse cumulative computation. You can override this method in order to use a Brent solver with an absolute accuracy different from the default.

Overrides:

getSolverAbsoluteAccuracy in class BaseDistribution

Returns:

the maximum absolute error in inverse cumulative probability estimates

getNumericalMean

public double getNumericalMean()

Use this method to get the numerical value of the mean of this distribution.

For mean parameter mu, the mean is mu.

Returns:

the mean or Double.NaN if it is not defined

getNumericalVariance

public double getNumericalVariance()

Use this method to get the numerical value of the variance of this distribution.

For standard deviation parameter s, the variance is s^2.

Returns:

the variance (possibly Double.POSITIVE_INFINITY as for certain cases in org.apache.commons.math3.distribution.TDistribution) or Double.NaN if it is not defined

getSupportLowerBound

public double getSupportLowerBound()

Access the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0). In other words, this method must return

inf {x in R | P(X <= x) > 0}.

The lower bound of the support is always negative infinity no matter the parameters.

Returns:

lower bound of the support (always Double.NEGATIVE_INFINITY)

getSupportUpperBound

public double getSupportUpperBound()

Access the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1). In other words, this method must return

inf {x in R | P(X <= x) = 1}.

The upper bound of the support is always positive infinity no matter the parameters.

Returns:

upper bound of the support (always Double.POSITIVE_INFINITY)

isSupportLowerBoundInclusive

public boolean isSupportLowerBoundInclusive()

Whether or not the lower bound of support is in the domain of the density function. Returns true iff getSupporLowerBound() is finite and density(getSupportLowerBound()) returns a non-NaN, non-infinite value.

Returns:

true if the lower bound of support is finite and the density function returns a non-NaN, non-infinite value there

isSupportUpperBoundInclusive

public boolean isSupportUpperBoundInclusive()

Whether or not the upper bound of support is in the domain of the density function. Returns true iff getSupportUpperBound() is finite and density(getSupportUpperBound()) returns a non-NaN, non-infinite value.

Returns:

true if the upper bound of support is finite and the density function returns a non-NaN, non-infinite value there

isSupportConnected

public boolean isSupportConnected()

Use this method to get information about whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support.

The support of this distribution is connected.

Returns:

true

sample

public double sample()

Generate a random value sampled from this distribution.

The default implementation uses the inversion method.

Specified by:

sample in interface Distribution

Overrides:

sample in class BaseDistribution

Returns:

a random value.

sample

public INDArray sample(int[] shape)

Description copied from interface: Distribution

Sample the given shape

Specified by:

sample in interface Distribution

Overrides:

sample in class BaseDistribution

Parameters:

shape - the given shape

Returns:

an ndarray with random samples from this distribution

sample

public INDArray sample(long[] shape)

Specified by:

sample in interface Distribution

Overrides:

sample in class BaseDistribution

sample

public INDArray sample(INDArray target)

Description copied from interface: Distribution

Fill the target array by sampling from the distribution

Specified by:

sample in interface Distribution

Overrides:

sample in class BaseDistribution

Parameters:

target - target array

Returns:

an ndarray with random samples from this distribution