[Serializable]
[DataContract]
[Quality(QualityBand.Experimental)]
public struct WrappedGaussian : IDistribution<double>, IDistribution, ICloneable, Diffable, SettableToUniform, HasPoint<double>, CanGetLogProb<double>, SettableTo<WrappedGaussian>, SettableToProduct<WrappedGaussian>, SettableToProduct<WrappedGaussian, WrappedGaussian>, SettableToRatio<WrappedGaussian>, SettableToRatio<WrappedGaussian, WrappedGaussian>, SettableToWeightedSum<WrappedGaussian>, SettableToPower<WrappedGaussian>, Sampleable<double>, CanGetLogAverageOf<WrappedGaussian>, CanGetLogAverageOfPower<WrappedGaussian>, CanGetAverageLog<WrappedGaussian>

Remarks

The distribution is represented by a unwrapped Gaussian and a period length L. To get the wrapped density, the unwrapped density is summed over all shifts by L, i.e. p(x) = sum_k N(x + Lk; m, v) over all integers k The wrapped density is automatically normalized over the range [0,L) because it simply moves the probability mass that was previously distributed over the real line to all lie in the interval [0,L).

Constructors

WrappedGaussian(Gaussian, Double)

Create a WrappedGaussian distribution

Declaration

[Construction(new string[]{"Gaussian", "Period"})]
public WrappedGaussian(Gaussian unwrapped, double period)

Parameters

Type	Name	Description
Gaussian	unwrapped
Double	period

WrappedGaussian(Double, Double, Double)

Create a WrappedGaussian distribution

Declaration

public WrappedGaussian(double unwrappedMean, double unwrappedVariance, double period = 6.2831853071795862)

Parameters

Type	Name	Description
Double	unwrappedMean
Double	unwrappedVariance
Double	period

Fields

Gaussian

The unwrapped Gaussian, with mean in [0,L)

Declaration

[DataMember]
public Gaussian Gaussian

Field Value

Type	Description
Gaussian

Period

The period length, greater than zero

Declaration

[DataMember]
public double Period

Field Value

Type	Description
Double

Properties

IsPointMass

True if the distribution is a point mass.

Declaration

[IgnoreDataMember]
public readonly bool IsPointMass { get; }

Property Value

Type	Description
Boolean

Point

Set this distribution to a point mass, or get its location

Declaration

[IgnoreDataMember]
public double Point { get; set; }

Property Value

Type	Description
Double

Methods

Clone()

Make a deep copy of this distribution.

Declaration

public object Clone()

Returns

Type	Description
Object

Equals(Object)

True if this distribution has the same parameters as that

Declaration

public override bool Equals(object that)

Parameters

Type	Name	Description
Object	that

Returns

Type	Description
Boolean

Overrides

ValueType.Equals(Object)

GetAverageLog(WrappedGaussian)

Get the average logarithm of that distribution under this distribution, i.e. int this(x) log( that(x) ) dx

Declaration

public double GetAverageLog(WrappedGaussian that)

Parameters

Type	Name	Description
WrappedGaussian	that

Returns

Type	Description
Double

Remarks

The result is approximate.

GetHashCode()

A hash of the distribution parameter values

Declaration

public override int GetHashCode()

Returns

Type	Description
Int32

Overrides

ValueType.GetHashCode()

GetLogAverageOf(WrappedGaussian)

Get the logarithm of the average value of that distribution under this distribution, i.e. log(int this(x) that(x) dx)

Declaration

public double GetLogAverageOf(WrappedGaussian that)

Parameters

Type	Name	Description
WrappedGaussian	that

Returns

Type	Description
Double

GetLogAverageOfPower(WrappedGaussian, Double)

Get the integral of this distribution times another distribution raised to a power.

Declaration

public double GetLogAverageOfPower(WrappedGaussian that, double power)

Parameters

Type	Name	Description
WrappedGaussian	that
Double	power

Returns

Type	Description
Double

GetLogProb(Double)

Get the log probability density at value.

Declaration

public double GetLogProb(double value)

Parameters

Type	Name	Description
Double	value

Returns

Type	Description
Double

IsUniform()

True if the distribution is uniform

Declaration

public bool IsUniform()

Returns

Type	Description
Boolean

MaxDiff(Object)

The maximum difference between the parameters of this distribution and that

Declaration

public double MaxDiff(object thatd)

Parameters

Type	Name	Description
Object	thatd

Returns

Type	Description
Double

Mod(Double)

Return x modulo the period

Declaration

public double Mod(double x)

Parameters

Type	Name	Description
Double	x

Returns

Type	Description
Double

Mod(Double, Double)

Return x modulo the period

Declaration

public static double Mod(double x, double period)

Parameters

Type	Name	Description
Double	x
Double	period

Returns

Type	Description
Double

Normalize()

Declaration

public void Normalize()

PointMass(Double, Double)

Create a WrappedGaussian distribution with all mass on a single point

Declaration

[Construction(new string[]{"Point", "Period"}, UseWhen = "IsPointMass")]
public static WrappedGaussian PointMass(double point, double period = 6.2831853071795862)

Parameters

Type	Name	Description
Double	point
Double	period

Returns

Type	Description
WrappedGaussian

Sample()

Sample from the distribution

Declaration

public double Sample()

Returns

Type	Description
Double	The sample value

Sample(Double)

Sample from the distribution

Declaration

public double Sample(double result)

Parameters

Type	Name	Description
Double	result	Ignored

Returns

Type	Description
Double	The sample value

SetTo(WrappedGaussian)

Set this distribution equal to value

Declaration

public void SetTo(WrappedGaussian value)

Parameters

Type	Name	Description
WrappedGaussian	value

SetToPower(WrappedGaussian, Double)

Set this equal to (dist)^exponent

Declaration

public void SetToPower(WrappedGaussian dist, double exponent)

Parameters

Type	Name	Description
WrappedGaussian	dist
Double	exponent

SetToProduct(WrappedGaussian, WrappedGaussian)

Set this distribution equal to the approximate product of a and b

Declaration

public void SetToProduct(WrappedGaussian a, WrappedGaussian b)

Parameters

Type	Name	Description
WrappedGaussian	a
WrappedGaussian	b

Remarks

Since WrappedGaussians are not closed under multiplication, the result is approximate.

SetToRatio(WrappedGaussian, WrappedGaussian, Boolean)

Set this equal to numerator/denominator

Declaration

public void SetToRatio(WrappedGaussian numerator, WrappedGaussian denominator, bool forceProper = false)

Parameters

Type	Name	Description
WrappedGaussian	numerator
WrappedGaussian	denominator
Boolean	forceProper

SetToSum(Double, WrappedGaussian, Double, WrappedGaussian)

Set the parameters to match the moments of a mixture distribution.

Declaration

public void SetToSum(double weight1, WrappedGaussian value1, double weight2, WrappedGaussian value2)

Parameters

Type	Name	Description
Double	weight1	The first weight
WrappedGaussian	value1	The first distribution
Double	weight2	The second weight
WrappedGaussian	value2	The second distribution

SetToUniform()

Set the distribution to uniform, keeping the same period

Declaration

public void SetToUniform()

ToString()

A human-readable string containing the parameters of the distribution

Declaration

public override string ToString()

Returns

Type	Description
String

Overrides

ValueType.ToString()

Uniform(Double)

Create a uniform WrappedGaussian distribution

Declaration

[Construction(new string[]{"Period"}, UseWhen = "IsUniform")]
public static WrappedGaussian Uniform(double period = 6.2831853071795862)

Parameters

Type	Name	Description
Double	period

Returns

Type	Description
WrappedGaussian

Operators

Equality(WrappedGaussian, WrappedGaussian)

Equals operator

Declaration

public static bool operator ==(WrappedGaussian a, WrappedGaussian b)

Parameters

Type	Name	Description
WrappedGaussian	a
WrappedGaussian	b

Returns

Type	Description
Boolean

Inequality(WrappedGaussian, WrappedGaussian)

Not equals operator

Declaration

public static bool operator !=(WrappedGaussian a, WrappedGaussian b)

Parameters

Type	Name	Description
WrappedGaussian	a
WrappedGaussian	b

Returns

Type	Description
Boolean

Multiply(WrappedGaussian, WrappedGaussian)

Creates a new WrappedGaussian which is the product of two other WrappedGaussians

Declaration

public static WrappedGaussian operator *(WrappedGaussian a, WrappedGaussian b)

Parameters

Type	Name	Description
WrappedGaussian	a	First WrappedGaussian
WrappedGaussian	b	Second WrappedGaussian

Returns

Type	Description
WrappedGaussian	Result

Implements

IDistribution<T>

IDistribution

System.ICloneable

Diffable

SettableToUniform

HasPoint<T>

CanGetLogProb<T>

SettableTo<T>

SettableToProduct<T>

SettableToProduct<T, U>

SettableToRatio<T>

SettableToRatio<T, U>

SettableToWeightedSum<T>

SettableToPower<T>

Sampleable<T>

CanGetLogAverageOf<T>

CanGetLogAverageOfPower<T>

CanGetAverageLog<T>