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Distributions: adapt InverseGamma

optimization-1
Christoph Ruegg 13 years ago
parent
e9adc7e563
commit
dc12629f83
2 changed files with 63 additions and 57 deletions
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  1. 101
      src/Numerics/Distributions/InverseGamma.cs
  2. 19
      src/UnitTests/DistributionTests/Continuous/InverseGammaTests.cs

101
src/Numerics/Distributions/InverseGamma.cs
View File

@ -30,6 +30,7 @@
using System;
using System.Collections.Generic;
using System.Linq;
using MathNet.Numerics.Properties;
namespace MathNet.Numerics.Distributions
@ -84,17 +85,6 @@ namespace MathNet.Numerics.Distributions
return "InverseGamma(α = " + _shape + ", β = " + _scale + ")";
}
/// <summary>
/// Checks whether the parameters of the distribution are valid.
/// </summary>
/// <param name="shape">The shape (α) of the distribution. Range: α > 0.</param>
/// <param name="scale">The scale (β) of the distribution. Range: β > 0.</param>
/// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
static bool IsValidParameterSet(double shape, double scale)
{
return shape > 0.0 && scale > 0.0;
}
/// <summary>
/// Sets the parameters of the distribution after checking their validity.
/// </summary>
@ -103,7 +93,7 @@ namespace MathNet.Numerics.Distributions
/// <exception cref="ArgumentOutOfRangeException">When the parameters are out of range.</exception>
void SetParameters(double shape, double scale)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(shape, scale))
if (shape <= 0.0 || scale <= 0.0 || Double.IsNaN(shape) || Double.IsNaN(scale))
{
throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
}
@ -241,14 +231,10 @@ namespace MathNet.Numerics.Distributions
/// </summary>
/// <param name="x">The location at which to compute the density.</param>
/// <returns>the density at <paramref name="x"/>.</returns>
/// <seealso cref="PDF"/>
public double Density(double x)
{
if (x >= 0.0)
{
return Math.Pow(_scale, _shape)*Math.Pow(x, -_shape - 1.0)*Math.Exp(-_scale/x)/SpecialFunctions.Gamma(_shape);
}
return 0.0;
return x < 0.0 ? 0.0 : Math.Pow(_scale, _shape)*Math.Pow(x, -_shape - 1.0)*Math.Exp(-_scale/x)/SpecialFunctions.Gamma(_shape);
}
/// <summary>
@ -256,6 +242,7 @@ namespace MathNet.Numerics.Distributions
/// </summary>
/// <param name="x">The location at which to compute the log density.</param>
/// <returns>the log density at <paramref name="x"/>.</returns>
/// <seealso cref="PDFLn"/>
public double DensityLn(double x)
{
return Math.Log(Density(x));
@ -266,42 +253,71 @@ namespace MathNet.Numerics.Distributions
/// </summary>
/// <param name="x">The location at which to compute the cumulative distribution function.</param>
/// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
/// <seealso cref="CDF"/>
public double CumulativeDistribution(double x)
{
return SpecialFunctions.GammaUpperRegularized(_shape, _scale/x);
}
/// <summary>
/// Samples the distribution.
/// Draws a random sample from the distribution.
/// </summary>
/// <returns>A random number from this distribution.</returns>
public double Sample()
{
return 1.0/Gamma.Sample(_random, _shape, _scale);
}
/// <summary>
/// Generates a sequence of samples from the Cauchy distribution.
/// </summary>
/// <returns>a sequence of samples from the distribution.</returns>
public IEnumerable<double> Samples()
{
return Gamma.Samples(_random, _shape, _scale).Select(z => 1.0/z);
}
/// <summary>
/// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
/// </summary>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="shape">The shape (α) of the distribution. Range: α > 0.</param>
/// <param name="scale">The scale (β) of the distribution. Range: β > 0.</param>
/// <returns>a random number from the distribution.</returns>
static double SampleUnchecked(System.Random rnd, double shape, double scale)
/// <param name="x">The location at which to compute the density.</param>
/// <returns>the density at <paramref name="x"/>.</returns>
/// <seealso cref="Density"/>
public static double PDF(double shape, double scale, double x)
{
return 1.0/Gamma.Sample(rnd, shape, scale);
if (shape <= 0.0 || scale <= 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
return x < 0.0 ? 0.0 : Math.Pow(scale, shape)*Math.Pow(x, -shape - 1.0)*Math.Exp(-scale/x)/SpecialFunctions.Gamma(shape);
}
/// <summary>
/// Draws a random sample from the distribution.
/// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
/// </summary>
/// <returns>A random number from this distribution.</returns>
public double Sample()
/// <param name="shape">The shape (α) of the distribution. Range: α > 0.</param>
/// <param name="scale">The scale (β) of the distribution. Range: β > 0.</param>
/// <param name="x">The location at which to compute the density.</param>
/// <returns>the log density at <paramref name="x"/>.</returns>
/// <seealso cref="DensityLn"/>
public static double PDFLn(double shape, double scale, double x)
{
return SampleUnchecked(_random, _shape, _scale);
return Math.Log(PDF(shape, scale, x));
}
/// <summary>
/// Generates a sequence of samples from the Cauchy distribution.
/// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
/// </summary>
/// <returns>a sequence of samples from the distribution.</returns>
public IEnumerable<double> Samples()
/// <param name="x">The location at which to compute the cumulative distribution function.</param>
/// <param name="shape">The shape (α) of the distribution. Range: α > 0.</param>
/// <param name="scale">The scale (β) of the distribution. Range: β > 0.</param>
/// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
/// <seealso cref="CumulativeDistribution"/>
public static double CDF(double shape, double scale, double x)
{
while (true)
{
yield return SampleUnchecked(_random, _shape, _scale);
}
if (shape <= 0.0 || scale <= 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
return SpecialFunctions.GammaUpperRegularized(shape, scale/x);
}
/// <summary>
@ -313,12 +329,9 @@ namespace MathNet.Numerics.Distributions
/// <returns>a sample from the distribution.</returns>
public static double Sample(System.Random rnd, double shape, double scale)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(shape, scale))
{
throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
}
if (shape <= 0.0 || scale <= 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
return SampleUnchecked(rnd, shape, scale);
return 1.0/Gamma.Sample(rnd, shape, scale);
}
/// <summary>
@ -330,15 +343,9 @@ namespace MathNet.Numerics.Distributions
/// <returns>a sequence of samples from the distribution.</returns>
public static IEnumerable<double> Samples(System.Random rnd, double shape, double scale)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(shape, scale))
{
throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
}
if (shape <= 0.0 || scale <= 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
while (true)
{
yield return SampleUnchecked(rnd, shape, scale);
}
return Gamma.Samples(rnd, shape, scale).Select(z => 1.0/z);
}
}
}

19
src/UnitTests/DistributionTests/Continuous/InverseGammaTests.cs
View File

@ -262,14 +262,9 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
public void ValidateDensity(double a, double b, double x)
{
var n = new InverseGamma(a, b);
if (x >= 0)
{
Assert.AreEqual(Math.Pow(b, a) * Math.Pow(x, -a - 1.0) * Math.Exp(-b / x) / SpecialFunctions.Gamma(a), n.Density(x));
}
else
{
Assert.AreEqual(0.0, n.Density(x));
}
double expected = Math.Pow(b, a)*Math.Pow(x, -a - 1.0)*Math.Exp(-b/x)/SpecialFunctions.Gamma(a);
Assert.AreEqual(expected, n.Density(x));
Assert.AreEqual(expected, InverseGamma.PDF(a, b, x));
}
/// <summary>
@ -290,7 +285,9 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
public void ValidateDensityLn(double a, double b, double x)
{
var n = new InverseGamma(a, b);
Assert.AreEqual(Math.Log(n.Density(x)), n.DensityLn(x));
double expected = Math.Log(Math.Pow(b, a)*Math.Pow(x, -a - 1.0)*Math.Exp(-b/x)/SpecialFunctions.Gamma(a));
Assert.AreEqual(expected, n.DensityLn(x));
Assert.AreEqual(expected, InverseGamma.PDFLn(a, b, x));
}
/// <summary>
@ -332,7 +329,9 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
public void ValidateCumulativeDistribution(double a, double b, double x)
{
var n = new InverseGamma(a, b);
Assert.AreEqual(SpecialFunctions.GammaUpperRegularized(a, b / x), n.CumulativeDistribution(x));
double expected = SpecialFunctions.GammaUpperRegularized(a, b/x);
Assert.AreEqual(expected, n.CumulativeDistribution(x));
Assert.AreEqual(expected, InverseGamma.CDF(a, b, x));
}
}
}

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