Browse Source

Partial Normal distribution implementation.

Signed-off-by: jvangael <jurgen.vangael@gmail.com>
pull/36/head
Jurgen Van Gael 17 years ago
parent
commit
ef0141298e
  1. 10000
      data/gamma-matlab.txt
  2. 156
      src/Managed.UnitTests/DistributionTests/Continuous/NormalTests.cs
  3. 5
      src/Managed.UnitTests/Managed.UnitTests.csproj
  4. 193
      src/Managed/Distributions/Continuous/Normal.cs
  5. 48
      src/Managed/Distributions/IContinuousDistribution.cs
  6. 80
      src/Managed/Distributions/IDiscreteDistribution.cs
  7. 73
      src/Managed/Distributions/IDistribution.cs
  8. 8
      src/Managed/Managed.csproj
  9. 35
      src/Managed/RandomSources/RandomSource.cs
  10. 7
      src/Native.UnitTests/Native.UnitTests.csproj
  11. 16
      src/Native/Native.csproj

10000
data/gamma-matlab.txt

File diff suppressed because it is too large

156
src/Managed.UnitTests/DistributionTests/Continuous/NormalTests.cs

@ -0,0 +1,156 @@
// <copyright file="Combinatorics.cs" company="Math.NET">
// Math.NET Numerics, part of the Math.NET Project
// http://mathnet.opensourcedotnet.info
//
// Copyright (c) 2009 Math.NET
//
// Permission is hereby granted, free of charge, to any person
// obtaining a copy of this software and associated documentation
// files (the "Software"), to deal in the Software without
// restriction, including without limitation the rights to use,
// copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following
// conditions:
//
// The above copyright notice and this permission notice shall be
// included in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
// OTHER DEALINGS IN THE SOFTWARE.
// </copyright>
namespace MathNet.Numerics.UnitTests
{
using System;
using MbUnit.Framework;
using MathNet.Numerics.Distributions;
[TestFixture]
public class NormalTests
{
[Test, MultipleAsserts]
public void CanCreateStandardNormal()
{
var n = new Normal();
AssertEx.AreEqual<double>(0.0, n.Mean);
AssertEx.AreEqual<double>(1.0, n.StdDev);
}
[Test, MultipleAsserts]
[Row(0.0, 0.0)]
[Row(0.0, 0.1)]
[Row(0.0, 1.0)]
[Row(0.0, 10.0)]
[Row(10.0, 1.0)]
[Row(-5.0, 100.0)]
[Row(0.0, Double.PositiveInfinity)]
public void CanCreateNormal(double mean, double sdev)
{
var n = new Normal(mean, sdev);
AssertEx.AreEqual<double>(mean, n.Mean);
AssertEx.AreEqual<double>(sdev, n.StdDev);
}
[Test]
[ExpectedException(typeof(ArgumentOutOfRangeException))]
public void NormalCreateFailsWithMeanIsNaN()
{
var n = new Normal(Double.NaN, 1.0);
}
[Test]
[ExpectedException(typeof(ArgumentOutOfRangeException))]
public void NormalCreateFailsWithStdDevIsNaN()
{
var n = new Normal(0.0, Double.NaN);
}
[Test, MultipleAsserts]
[Row(0.0, 0.0)]
[Row(0.0, 0.1)]
[Row(0.0, 1.0)]
[Row(0.0, 10.0)]
[Row(10.0, 1.0)]
[Row(-5.0, 100.0)]
[Row(0.0, Double.PositiveInfinity)]
public void CanCreateNormalFromMeanAndStdDev(double mean, double sdev)
{
var n = Normal.WithMeanStdDev(mean, sdev);
AssertEx.AreEqual<double>(mean, n.Mean);
AssertEx.AreEqual<double>(sdev, n.StdDev);
}
[Test, MultipleAsserts]
[Row(0.0, 0.0)]
[Row(0.0, 0.1)]
[Row(0.0, 1.0)]
[Row(0.0, 10.0)]
[Row(10.0, 1.0)]
[Row(-5.0, 100.0)]
[Row(0.0, Double.PositiveInfinity)]
public void CanCreateNormalFromMeanAndVariance(double mean, double var)
{
var n = Normal.WithMeanVariance(mean, var);
AssertEx.AreEqual<double>(mean, n.Mean);
AssertEx.AreEqual<double>(var, n.Variance);
}
[Test, MultipleAsserts]
[Row(0.0, 0.0)]
[Row(0.0, 0.1)]
[Row(0.0, 1.0)]
[Row(0.0, 10.0)]
[Row(10.0, 1.0)]
[Row(-5.0, 100.0)]
[Row(0.0, Double.PositiveInfinity)]
public void CanCreateNormalFromMeanAndPrecision(double mean, double prec)
{
var n = Normal.WithMeanAndPrecision(mean, prec);
AssertEx.AreEqual<double>(mean, n.Mean);
AssertEx.AreEqual<double>(prec, n.Precision);
}
[Test]
public void ToStringTest()
{
var n = new Normal(1.0, 2.0);
AssertEx.AreEqual<string>("Normal(Mean = 1, StdDev = 2)", n.ToString());
}
[Test]
public void CanGetRandomNumberGenerator()
{
var n = new Normal();
var rs = n.RandomNumberGenerator;
Assert.IsNotNull(rs);
}
[Test]
[Row(-0.0)]
[Row(0.0)]
[Row(0.1)]
[Row(1.0)]
[Row(10.0)]
[Row(0.0, Double.PositiveInfinity)]
public void CanSetRandomNumberGenerator(double prec)
{
var n = new Normal();
n.Precision = prec;
}
[Test]
[ExpectedException(typeof(ArgumentOutOfRangeException))]
public void SetPrecisionFailsWithNegativePrecision()
{
var n = new Normal();
n.Precision = -1.0;
}
}
}

5
src/Managed.UnitTests/Managed.UnitTests.csproj

@ -59,6 +59,7 @@
<ItemGroup>
<Compile Include="CombinatoricsTests\CombinatoricsCountingTest.cs" />
<Compile Include="ComplexTest.cs" />
<Compile Include="DistributionTests\Continuous\NormalTests.cs" />
<Compile Include="Properties\AssemblyInfo.cs" />
</ItemGroup>
<ItemGroup>
@ -67,6 +68,10 @@
<Name>Managed</Name>
</ProjectReference>
</ItemGroup>
<ItemGroup>
<Folder Include="DistributionTests\Discrete\" />
<Folder Include="DistributionTests\Multivariate\" />
</ItemGroup>
<Import Project="$(MSBuildToolsPath)\Microsoft.CSharp.targets" />
<!-- To modify your build process, add your task inside one of the targets below and uncomment it.
Other similar extension points exist, see Microsoft.Common.targets.

193
src/Managed/Distributions/Continuous/Normal.cs

@ -0,0 +1,193 @@
// <copyright file="Combinatorics.cs" company="Math.NET">
// Math.NET Numerics, part of the Math.NET Project
// http://mathnet.opensourcedotnet.info
//
// Copyright (c) 2009 Math.NET
//
// Permission is hereby granted, free of charge, to any person
// obtaining a copy of this software and associated documentation
// files (the "Software"), to deal in the Software without
// restriction, including without limitation the rights to use,
// copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following
// conditions:
//
// The above copyright notice and this permission notice shall be
// included in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
// OTHER DEALINGS IN THE SOFTWARE.
// </copyright>
namespace MathNet.Numerics.Distributions
{
using System;
using System.Collections.Generic;
/// <summary>
/// Implements the univariate Normal (or Gaussian) distribution.
/// </summary>
public class Normal : IContinuousDistribution
{
// Keeps track of the mean of the normal distribution.
private double mMean;
// Keeps track of the standard deviation of the normal distribution.
private double mStdDev;
/// <summary>
/// Constructs a standard normal distribution. This is a normal distribution with mean 0.0
/// and standard deviation 1.0.
/// </summary>
public Normal() : this(0.0, 1.0)
{
}
/// <summary>
/// Construct a normal distribution with a particular mean and standard deviation.
/// </summary>
/// <param name="mean">The mean of the normal distribution.</param>
/// <param name="stddev">The standard deviation of the normal distribution.</param>
public Normal(double mean, double stddev)
{
SetParameters(mean, stddev);
}
/// <summary>
/// Constructs a normal distribution from a mean and standard deviation.
/// </summary>
/// <param name="mean">The mean of the normal distribution.</param>
/// <param name="stddev">The standard deviation of the normal distribution.</param>
public static Normal WithMeanStdDev(double mean, double stddev)
{
return new Normal(mean, stddev);
}
/// <summary>
/// Constructs a normal distribution from a mean and variance.
/// </summary>
/// <param name="mean">The mean of the normal distribution.</param>
/// <param name="stddev">The variance of the normal distribution.</param>
public static Normal WithMeanVariance(double mean, double var)
{
return new Normal(mean, System.Math.Sqrt(var));
}
/// <summary>
/// Constructs a normal distribution from a mean and precision.
/// </summary>
/// <param name="mean">The mean of the normal distribution.</param>
/// <param name="stddev">The precision of the normal distribution.</param>
public static Normal WithMeanAndPrecision(double mean, double prec)
{
return new Normal(mean, 1.0 / System.Math.Sqrt(prec));
}
/// <summary>
/// A string representation of the distribution.
/// </summary>
public override string ToString()
{
return "Normal(Mean = " + mMean + ", StdDev = " + mStdDev + ")";
}
/// <summary>
/// Checks whether the parameters of the distribution are valid.
/// </summary>
/// <param name="mean">The mean of the normal distribution.</param>
/// <param name="stddev">The standard deviation of the normal distribution.</param>
/// <returns>True when the parameters are valid, false otherwise.</returns>
private static bool IsValidParameterSet(double mean, double stddev)
{
if (stddev < 0.0)
{
return false;
}
else if (System.Double.IsNaN(mean))
{
return false;
}
else if (System.Double.IsNaN(stddev))
{
return false;
}
return true;
}
/// <summary>
/// Sets the parameters of the distribution after checking their validity.
/// </summary>
/// <param name="mean">The mean of the normal distribution.</param>
/// <param name="stddev">The standard deviation of the normal distribution.</param>
/// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
private void SetParameters(double mean, double stddev)
{
if (IsValidParameterSet(mean, stddev))
{
mMean = mean;
mStdDev = stddev;
}
else
{
throw new System.ArgumentOutOfRangeException("Invalid parameterization for the normal distribution.");
}
}
public double Precision
{
get { return 1.0 / (mStdDev * mStdDev); }
set { throw new NotImplementedException(); }
}
#region IDistribution implementation
public Random RandomNumberGenerator { get; set; }
public double Mean
{
get { return mMean; }
set { throw new NotImplementedException(); }
}
public double Variance
{
get { return mStdDev * mStdDev; }
set { throw new NotImplementedException(); }
}
public double StdDev
{
get { return mStdDev; }
set { throw new NotImplementedException(); }
}
public double Entropy { get { throw new NotImplementedException(); } }
public double Skewness { get { throw new NotImplementedException(); } }
#endregion
#region IContinuousDistribution implementation
public double Mode { get { throw new NotImplementedException(); } }
public double Median { get { throw new NotImplementedException(); } }
public double Minimum { get { throw new NotImplementedException(); } }
public double Maximum { get { throw new NotImplementedException(); } }
public double Density(double x) { throw new NotImplementedException(); }
public double DensityLn(double x) { throw new NotImplementedException(); }
public double CumulativeDistribution(double x) { throw new NotImplementedException(); }
public double Sample() { throw new NotImplementedException(); }
public IEnumerable<double> Samples() { throw new NotImplementedException(); }
#endregion
public double InverseCumulativeDistribution(double p)
{
throw new NotImplementedException();
}
public static double Sample(System.Random rng, double mean, double stddev) { throw new NotImplementedException(); }
public static IEnumerable<double> Samples(System.Random rng, double mean, double stddev) { throw new NotImplementedException(); }
}
}

48
src/Managed/Distributions/IContinuousDistribution.cs

@ -0,0 +1,48 @@
// <copyright file="Combinatorics.cs" company="Math.NET">
// Math.NET Numerics, part of the Math.NET Project
// http://mathnet.opensourcedotnet.info
//
// Copyright (c) 2009 Math.NET
//
// Permission is hereby granted, free of charge, to any person
// obtaining a copy of this software and associated documentation
// files (the "Software"), to deal in the Software without
// restriction, including without limitation the rights to use,
// copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following
// conditions:
//
// The above copyright notice and this permission notice shall be
// included in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
// OTHER DEALINGS IN THE SOFTWARE.
// </copyright>
namespace MathNet.Numerics.Distributions
{
using System.Collections.Generic;
/// <summary>
/// The interface for continuous univariate distributions.
/// </summary>
public interface IContinuousDistribution : IDistribution
{
double Mode { get; }
double Median { get; }
double Minimum { get; }
double Maximum { get; }
double Density(double x);
double DensityLn(double x);
double Sample();
IEnumerable<double> Samples();
}
}

80
src/Managed/Distributions/IDiscreteDistribution.cs

@ -0,0 +1,80 @@
// <copyright file="Combinatorics.cs" company="Math.NET">
// Math.NET Numerics, part of the Math.NET Project
// http://mathnet.opensourcedotnet.info
//
// Copyright (c) 2009 Math.NET
//
// Permission is hereby granted, free of charge, to any person
// obtaining a copy of this software and associated documentation
// files (the "Software"), to deal in the Software without
// restriction, including without limitation the rights to use,
// copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following
// conditions:
//
// The above copyright notice and this permission notice shall be
// included in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
// OTHER DEALINGS IN THE SOFTWARE.
// </copyright>
namespace MathNet.Numerics.Distributions
{
using System.Collections.Generic;
/// <summary>
/// The interface for discrete univariate distributions.
/// </summary>
public interface IDiscreteDistribution : IDistribution
{
/// <summary>
/// The mode of the distribution.
/// </summary>
int Mode { get; }
/// <summary>
/// The median of the distribution.
/// </summary>
int Median { get; }
/// <summary>
/// The smallest element in the domain of the distributions which can be represented by an integer.
/// </summary>
int Minimum { get; }
/// <summary>
/// The largest element in the domain of the distributions which can be represented by an integer.
/// </summary>
int Maximum { get; }
/// <summary>
/// Computes values of the probability mass function.
/// </summary>
/// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
double Probability(int k);
/// <summary>
/// Computes values of the log probability mass function.
/// </summary>
/// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
double ProbabilityLn(int k);
/// <summary>
/// Draws a random sample from the distribution.
/// </summary>
int Sample();
/// <summary>
/// Draws a sequence of random samples from the distribution.
/// </summary>
IEnumerable<int> Samples();
}
}

73
src/Managed/Distributions/IDistribution.cs

@ -0,0 +1,73 @@
// <copyright file="Combinatorics.cs" company="Math.NET">
// Math.NET Numerics, part of the Math.NET Project
// http://mathnet.opensourcedotnet.info
//
// Copyright (c) 2009 Math.NET
//
// Permission is hereby granted, free of charge, to any person
// obtaining a copy of this software and associated documentation
// files (the "Software"), to deal in the Software without
// restriction, including without limitation the rights to use,
// copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following
// conditions:
//
// The above copyright notice and this permission notice shall be
// included in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
// OTHER DEALINGS IN THE SOFTWARE.
// </copyright>
namespace MathNet.Numerics.Distributions
{
using System;
/// <summary>
/// The interface for univariate distributions.
/// </summary>
public interface IDistribution
{
/// <summary>
/// Gets or sets the random number generator which is used to generate random samples from the distribution.
/// </summary>
Random RandomNumberGenerator { get; set; }
/// <summary>
/// The mean of the distribution.
/// </summary>
double Mean { get; }
/// <summary>
/// The variance of the distribution.
/// </summary>
double Variance { get; }
/// <summary>
/// The standard deviation of the distribution.
/// </summary>
double StdDev { get; }
/// <summary>
/// The entropy of the distribution.
/// </summary>
double Entropy { get; }
/// <summary>
/// The skewness of the distribution.
/// </summary>
double Skewness { get; }
/// <summary>
/// Computes the cumulative distribution function (cdf) for this probability distribution.
/// </summary>
double CumulativeDistribution(double x);
}
}

8
src/Managed/Managed.csproj

@ -43,6 +43,10 @@
<ItemGroup>
<Compile Include="Combinatorics.cs" />
<Compile Include="Complex.cs" />
<Compile Include="Distributions\Continuous\Normal.cs" />
<Compile Include="Distributions\IContinuousDistribution.cs" />
<Compile Include="Distributions\IDiscreteDistribution.cs" />
<Compile Include="Distributions\IDistribution.cs" />
<Compile Include="Properties\AssemblyInfo.cs" />
<Compile Include="Properties\Resources.Designer.cs">
<AutoGen>True</AutoGen>
@ -61,6 +65,10 @@
<Link>MathNet.Numerics.snk</Link>
</None>
</ItemGroup>
<ItemGroup>
<Folder Include="Distributions\Discrete\" />
<Folder Include="Distributions\Multivariate\" />
</ItemGroup>
<Import Project="$(MSBuildToolsPath)\Microsoft.CSharp.targets" />
<!-- To modify your build process, add your task inside one of the targets below and uncomment it.
Other similar extension points exist, see Microsoft.Common.targets.

35
src/Managed/RandomSources/RandomSource.cs

@ -0,0 +1,35 @@
using System;
namespace Pnl.RandomSources
{
// Do we want to inherit from System.Random so people can plugin any RNG not from our library?
public abstract class RandomSource /* : System.Random */
{
protected RandomSource(bool threadSafe) { }
public abstract int Next();
public abstract int Next(int maxValue);
public abstract int Next(int minValue, int maxValue);
public abstract double NextDouble();
public abstract double NextDouble(double maxValue);
public abstract double NextDouble(double minValue, double maxValue);
public abstract bool NextBoolean();
public abstract void NextBytes(byte[] buffer);
// Do we want Reset() or just a SetSeed kind of method?
public abstract void Reset();
public abstract bool CanReset
{
get;
}
public virtual long NextInt64()
{
throw new NotImplementedException();
}
public virtual decimal NextDecimal()
{
throw new NotImplementedException();
}
}
}

7
src/Native.UnitTests/Native.UnitTests.csproj

@ -63,6 +63,9 @@
<Compile Include="..\Managed.UnitTests\ComplexTest.cs">
<Link>ComplexTest.cs</Link>
</Compile>
<Compile Include="..\Managed.UnitTests\DistributionTests\Continuous\NormalTests.cs">
<Link>DistributionTests\Continuous\NormalTests.cs</Link>
</Compile>
<Compile Include="Properties\AssemblyInfo.cs" />
</ItemGroup>
<ItemGroup>
@ -71,6 +74,10 @@
<Name>Native</Name>
</ProjectReference>
</ItemGroup>
<ItemGroup>
<Folder Include="DistributionTests\Discrete\" />
<Folder Include="DistributionTests\Multivariate\" />
</ItemGroup>
<Import Project="$(MSBuildToolsPath)\Microsoft.CSharp.targets" />
<!-- To modify your build process, add your task inside one of the targets below and uncomment it.
Other similar extension points exist, see Microsoft.Common.targets.

16
src/Native/Native.csproj

@ -44,6 +44,18 @@
<Compile Include="..\Managed\Complex.cs">
<Link>Complex.cs</Link>
</Compile>
<Compile Include="..\Managed\Distributions\Continuous\Normal.cs">
<Link>Distributions\Continuous\Normal.cs</Link>
</Compile>
<Compile Include="..\Managed\Distributions\IContinuousDistribution.cs">
<Link>Distributions\IContinuousDistribution.cs</Link>
</Compile>
<Compile Include="..\Managed\Distributions\IDiscreteDistribution.cs">
<Link>Distributions\IDiscreteDistribution.cs</Link>
</Compile>
<Compile Include="..\Managed\Distributions\IDistribution.cs">
<Link>Distributions\IDistribution.cs</Link>
</Compile>
<Compile Include="..\Managed\Properties\Resources.Designer.cs">
<Link>Properties\Resources.Designer.cs</Link>
</Compile>
@ -59,6 +71,10 @@
<Link>MathNet.Numerics.snk</Link>
</None>
</ItemGroup>
<ItemGroup>
<Folder Include="Distributions\Discrete\" />
<Folder Include="Distributions\Multivariate\" />
</ItemGroup>
<Import Project="$(MSBuildToolsPath)\Microsoft.CSharp.targets" />
<!-- To modify your build process, add your task inside one of the targets below and uncomment it.
Other similar extension points exist, see Microsoft.Common.targets.

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