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Distributions: adapt continuous-uniform, add InvCDF

pull/163/head
Christoph Ruegg 13 years ago
parent
8075fd7f27
commit
6ee0dd032e
3 changed files with 128 additions and 73 deletions
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  1. 21
      src/Numerics/Distributions/Cauchy.cs
  2. 135
      src/Numerics/Distributions/ContinuousUniform.cs
  3. 45
      src/UnitTests/DistributionTests/Continuous/ContinuousUniformTests.cs

21
src/Numerics/Distributions/Cauchy.cs
View File

@ -258,7 +258,7 @@ namespace MathNet.Numerics.Distributions
/// <returns>A random number from this distribution.</returns>
public double Sample()
{
return SampleUnchecked(_random, _location, _scale);
return _location + _scale*Math.Tan(Constants.Pi*(_random.NextDouble() - 0.5));
}
/// <summary>
@ -269,23 +269,10 @@ namespace MathNet.Numerics.Distributions
{
while (true)
{
yield return SampleUnchecked(_random, _location, _scale);
yield return _location + _scale*Math.Tan(Constants.Pi*(_random.NextDouble() - 0.5));
}
}
/// <summary>
/// Samples the distribution.
/// </summary>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="location">The location (x0) of the distribution.</param>
/// <param name="scale">The scale (γ) of the distribution. Range: γ > 0.</param>
/// <returns>a random number from the distribution.</returns>
static double SampleUnchecked(System.Random rnd, double location, double scale)
{
var u = rnd.NextDouble();
return location + (scale*Math.Tan(Constants.Pi*(u - 0.5)));
}
/// <summary>
/// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
/// </summary>
@ -359,7 +346,7 @@ namespace MathNet.Numerics.Distributions
{
if (scale <= 0.0) throw new ArgumentOutOfRangeException("scale", Resources.InvalidDistributionParameters);
return SampleUnchecked(rnd, location, scale);
return location + scale*Math.Tan(Constants.Pi*(rnd.NextDouble() - 0.5));
}
/// <summary>
@ -375,7 +362,7 @@ namespace MathNet.Numerics.Distributions
while (true)
{
yield return SampleUnchecked(rnd, location, scale);
yield return location + scale*Math.Tan(Constants.Pi*(rnd.NextDouble() - 0.5));
}
}
}

135
src/Numerics/Distributions/ContinuousUniform.cs
View File

@ -92,17 +92,6 @@ namespace MathNet.Numerics.Distributions
return "ContinuousUniform(Lower = " + _lower + ", Upper = " + _upper + ")";
}
/// <summary>
/// Checks whether the parameters of the distribution are valid.
/// </summary>
/// <param name="lower">Lower bound. Range: lower ≤ upper.</param>
/// <param name="upper">Upper bound. Range: lower ≤ upper.</param>
/// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
static bool IsValidParameterSet(double lower, double upper)
{
return upper >= lower && !Double.IsNaN(upper) && !Double.IsNaN(lower);
}
/// <summary>
/// Sets the parameters of the distribution after checking their validity.
/// </summary>
@ -111,7 +100,7 @@ namespace MathNet.Numerics.Distributions
/// <exception cref="ArgumentOutOfRangeException">When the parameters are out of range.</exception>
void SetParameters(double lower, double upper)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(lower, upper))
if (upper < lower || Double.IsNaN(upper) || Double.IsNaN(lower))
{
throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
}
@ -227,14 +216,10 @@ 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 >= _lower && x <= _upper)
{
return 1.0/(_upper - _lower);
}
return 0.0;
return x < _lower || x > _upper ? 0.0 : 1.0/(_upper - _lower);
}
/// <summary>
@ -242,14 +227,10 @@ 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)
{
if (x >= _lower && x <= _upper)
{
return -Math.Log(_upper - _lower);
}
return Double.NegativeInfinity;
return x < _lower || x > _upper ? Double.NegativeInfinity : -Math.Log(_upper - _lower);
}
/// <summary>
@ -257,31 +238,22 @@ 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)
{
if (x <= _lower)
{
return 0.0;
}
if (x >= _upper)
{
return 1.0;
}
return (x - _lower)/(_upper - _lower);
return x <= _lower ? 0.0 : x >= _upper ? 1.0 : (x - _lower)/(_upper - _lower);
}
/// <summary>
/// Generates one sample from the <c>ContinuousUniform</c> distribution without parameter checking.
/// Computes the inverse of the cumulative distribution function (InvCDF) for the distribution
/// at the given probability. This is also known as the quantile or percent point function.
/// </summary>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="lower">Lower bound. Range: lower ≤ upper.</param>
/// <param name="upper">Upper bound. Range: lower ≤ upper.</param>
/// <returns>a uniformly distributed random number.</returns>
static double SampleUnchecked(System.Random rnd, double lower, double upper)
/// <param name="p">The location at which to compute the inverse cumulative density.</param>
/// <returns>the inverse cumulative density at <paramref name="p"/>.</returns>
/// <seealso cref="InvCDF"/>
public double InverseCumulativeDistribution(double p)
{
return lower + (rnd.NextDouble()*(upper - lower));
return p <= 0.0 ? _lower : p >= 1.0 ? _upper : _lower*(1.0 - p) + _upper*p;
}
/// <summary>
@ -290,7 +262,7 @@ namespace MathNet.Numerics.Distributions
/// <returns>a sample from the distribution.</returns>
public double Sample()
{
return SampleUnchecked(_random, _lower, _upper);
return _lower + _random.NextDouble()*(_upper - _lower);
}
/// <summary>
@ -301,10 +273,71 @@ namespace MathNet.Numerics.Distributions
{
while (true)
{
yield return SampleUnchecked(_random, _lower, _upper);
yield return _lower + _random.NextDouble()*(_upper - _lower);
}
}
/// <summary>
/// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
/// </summary>
/// <param name="lower">Lower bound. Range: lower ≤ upper.</param>
/// <param name="upper">Upper bound. Range: lower ≤ upper.</param>
/// <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 lower, double upper, double x)
{
if (upper < lower) throw new ArgumentOutOfRangeException("upper", Resources.InvalidDistributionParameters);
return x < lower || x > upper ? 0.0 : 1.0/(upper - lower);
}
/// <summary>
/// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
/// </summary>
/// <param name="lower">Lower bound. Range: lower ≤ upper.</param>
/// <param name="upper">Upper bound. Range: lower ≤ upper.</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 lower, double upper, double x)
{
if (upper < lower) throw new ArgumentOutOfRangeException("upper", Resources.InvalidDistributionParameters);
return x < lower || x > upper ? Double.NegativeInfinity : -Math.Log(upper - lower);
}
/// <summary>
/// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
/// </summary>
/// <param name="x">The location at which to compute the cumulative distribution function.</param>
/// <param name="lower">Lower bound. Range: lower ≤ upper.</param>
/// <param name="upper">Upper bound. Range: lower ≤ upper.</param>
/// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
/// <seealso cref="CumulativeDistribution"/>
public static double CDF(double lower, double upper, double x)
{
if (upper < lower) throw new ArgumentOutOfRangeException("upper", Resources.InvalidDistributionParameters);
return x <= lower ? 0.0 : x >= upper ? 1.0 : (x - lower)/(upper - lower);
}
/// <summary>
/// Computes the inverse of the cumulative distribution function (InvCDF) for the distribution
/// at the given probability. This is also known as the quantile or percent point function.
/// </summary>
/// <param name="p">The location at which to compute the inverse cumulative density.</param>
/// <param name="lower">Lower bound. Range: lower ≤ upper.</param>
/// <param name="upper">Upper bound. Range: lower ≤ upper.</param>
/// <returns>the inverse cumulative density at <paramref name="p"/>.</returns>
/// <seealso cref="InverseCumulativeDistribution"/>
public static double InvCDF(double lower, double upper, double p)
{
if (upper < lower) throw new ArgumentOutOfRangeException("upper", Resources.InvalidDistributionParameters);
return p <= 0.0 ? lower : p >= 1.0 ? upper : lower*(1.0 - p) + upper*p;
}
/// <summary>
/// Generates a sample from the <c>ContinuousUniform</c> distribution.
/// </summary>
@ -314,12 +347,9 @@ namespace MathNet.Numerics.Distributions
/// <returns>a uniformly distributed sample.</returns>
public static double Sample(System.Random rnd, double lower, double upper)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(lower, upper))
{
throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
}
if (upper < lower) throw new ArgumentOutOfRangeException("upper", Resources.InvalidDistributionParameters);
return SampleUnchecked(rnd, lower, upper);
return lower + rnd.NextDouble()*(upper - lower);
}
/// <summary>
@ -331,14 +361,11 @@ namespace MathNet.Numerics.Distributions
/// <returns>a sequence of uniformly distributed samples.</returns>
public static IEnumerable<double> Samples(System.Random rnd, double lower, double upper)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(lower, upper))
{
throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
}
if (upper < lower) throw new ArgumentOutOfRangeException("upper", Resources.InvalidDistributionParameters);
while (true)
{
yield return SampleUnchecked(rnd, lower, upper);
yield return lower + rnd.NextDouble()*(upper - lower);
}
}
}

45
src/UnitTests/DistributionTests/Continuous/ContinuousUniformTests.cs
View File

@ -275,11 +275,13 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
var x = i - 5.0;
if (x >= lower && x <= upper)
{
Assert.AreEqual(1.0 / (upper - lower), n.Density(x));
Assert.AreEqual(1.0/(upper - lower), n.Density(x));
Assert.AreEqual(1.0/(upper - lower), ContinuousUniform.PDF(lower, upper, x));
}
else
{
Assert.AreEqual(0.0, n.Density(x));
Assert.AreEqual(0.0, ContinuousUniform.PDF(lower, upper, x));
}
}
}
@ -304,10 +306,12 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
if (x >= lower && x <= upper)
{
Assert.AreEqual(-Math.Log(upper - lower), n.DensityLn(x));
Assert.AreEqual(-Math.Log(upper - lower), ContinuousUniform.PDFLn(lower, upper, x));
}
else
{
Assert.AreEqual(double.NegativeInfinity, n.DensityLn(x));
Assert.AreEqual(double.NegativeInfinity, ContinuousUniform.PDFLn(lower, upper, x));
}
}
}
@ -390,14 +394,51 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
if (x <= lower)
{
Assert.AreEqual(0.0, n.CumulativeDistribution(x));
Assert.AreEqual(0.0, ContinuousUniform.CDF(lower, upper, x));
}
else if (x >= upper)
{
Assert.AreEqual(1.0, n.CumulativeDistribution(x));
Assert.AreEqual(1.0, ContinuousUniform.CDF(lower, upper, x));
}
else
{
Assert.AreEqual((x - lower) / (upper - lower), n.CumulativeDistribution(x));
Assert.AreEqual((x - lower)/(upper - lower), n.CumulativeDistribution(x));
Assert.AreEqual((x - lower)/(upper - lower), ContinuousUniform.CDF(lower, upper, x));
}
}
}
/// <summary>
/// Validate inverse cumulative distribution.
/// </summary>
/// <param name="lower">Lower bound.</param>
/// <param name="upper">Upper bound.</param>
[TestCase(0.0, 0.0)]
[TestCase(0.0, 0.1)]
[TestCase(0.0, 1.0)]
[TestCase(0.0, 10.0)]
[TestCase(-5.0, 100.0)]
public void ValidateInverseCumulativeDistribution(double lower, double upper)
{
var n = new ContinuousUniform(lower, upper);
for (var i = 0; i < 11; i++)
{
var x = i - 5.0;
if (x <= lower)
{
Assert.AreEqual(lower, n.InverseCumulativeDistribution(0.0), 1e-12);
Assert.AreEqual(lower, ContinuousUniform.InvCDF(lower, upper, 0.0), 1e-12);
}
else if (x >= upper)
{
Assert.AreEqual(upper, n.InverseCumulativeDistribution(1.0), 1e-12);
Assert.AreEqual(upper, ContinuousUniform.InvCDF(lower, upper, 1.0), 1e-12);
}
else
{
Assert.AreEqual(x, n.InverseCumulativeDistribution((x - lower)/(upper - lower)), 1e-12);
Assert.AreEqual(x, ContinuousUniform.InvCDF(lower, upper, (x - lower)/(upper - lower)), 1e-12);
}
}
}

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