public void TwoSampleKolmogorovSmirnovTestConstructorTest()
{
Accord.Math.Tools.SetupGenerator(0);
// Create a K-S test to verify if two samples have been
// drawn from different populations. In this example, we
// will first generate a number of samples from different
// distributions, and then check if the K-S test can indeed
// see the difference:
// Generate 15 points from a Normal distribution with mean 5 and sigma 2
double[] sample1 = new NormalDistribution(mean: 5, stdDev: 1).Generate(25);
// Generate 15 points from an uniform distribution from 0 to 10
double[] sample2 = new UniformContinuousDistribution(a: 0, b: 10).Generate(25);
// Now we can create a K-S test and test the unequal hypothesis:
var test = new TwoSampleKolmogorovSmirnovTest(sample1, sample2,
TwoSampleKolmogorovSmirnovTestHypothesis.SamplesDistributionsAreUnequal);
bool significant = test.Significant; // outputs true
Assert.IsTrue(test.Significant);
Assert.AreEqual(0.44, test.Statistic, 1e-15);
Assert.IsFalse(Double.IsNaN(test.Statistic));
Assert.AreEqual(0.00826, test.PValue, 1e-5);
}
/// <summary>
/// Creates a new Shapiro-Wilk distribution.
/// </summary>
///
/// <param name="samples">The number of samples.</param>
///
public ShapiroWilkDistribution(int samples)
{
if (samples < 4)
{
throw new ArgumentOutOfRangeException("samples",
"The number of samples must be higher than 3.");
}
this.NumberOfSamples = samples;
if (samples <= 11)
{
double n = samples;
double n2 = n * n;
double n3 = n2 * n;
this.g = w => -Math.Log(0.459 * n - 2.273 - Math.Log(1 - w));
double mean = -0.0006714 * n3 + 0.0250540 * n2 - 0.39978 * n + 0.54400;
double sigma = Math.Exp(-0.0020322 * n3 + 0.0627670 * n2 - 0.77857 * n + 1.38220);
this.normal = new NormalDistribution(mean, sigma);
}
else
{
double u = Math.Log(samples);
double u2 = u * u;
double u3 = u2 * u;
this.g = w => Math.Log(1.0 - w);
double mean = 0.00389150 * u3 - 0.083751 * u2 - 0.31082 * u - 1.5861; // 1.5861?
double sigma = Math.Exp(0.00303020 * u2 - 0.082676 * u - 0.48030);
this.normal = new NormalDistribution(mean, sigma);
}
}
public static HiddenMarkovClassifier<NormalDistribution> CreateModel1()
{
// Create a Continuous density Hidden Markov Model Sequence Classifier
// to detect a univariate sequence and the same sequence backwards.
double[][] sequences = new double[][]
{
new double[] { 0,1,2,3,4 }, // This is the first sequence with label = 0
new double[] { 4,3,2,1,0 }, // This is the second sequence with label = 1
};
// Labels for the sequences
int[] labels = { 0, 1 };
// Creates a sequence classifier containing 2 hidden Markov Models
// with 2 states and an underlying Normal distribution as density.
NormalDistribution density = new NormalDistribution();
var classifier = new HiddenMarkovClassifier<NormalDistribution>(2, new Ergodic(2), density);
// Configure the learning algorithms to train the sequence classifier
var teacher = new HiddenMarkovClassifierLearning<NormalDistribution>(classifier,
// Train each model until the log-likelihood changes less than 0.001
modelIndex => new BaumWelchLearning<NormalDistribution>(classifier.Models[modelIndex])
{
Tolerance = 0.0001,
Iterations = 0
}
);
// Train the sequence classifier using the algorithm
double logLikelihood = teacher.Run(sequences, labels);
return classifier;
}
public ObservationGenerationModel(NormalDistribution foveaPeripheryOperatingCharacteristic,
int fixation,
int location)
{
_foveaPeripheryOperatingCharacteristic = foveaPeripheryOperatingCharacteristic;
_fixation = fixation;
_location = location;
}
public void Initialise()
{
State = new double[7];
for (var i = 0; i < State.Length; i++)
{
State[i] = 1d/7d;
}
;
_foveaPeripheryOperatingCharacteristic = NormalDistribution.Standard;
}
private double[] GenerateObservations(int fixation, int[] visualArray)
{
_observationValues = new double[visualArray.Length];
for (var location = 0; location < visualArray.Length; location++)
{
if (visualArray[location] == 0)
{
_observationValues[location] = _standardDistribution.Generate();
}
else
{
//discriminability is explained in Butko and Movellan (2008) and is determined using FPOC and eceentricity from fixation.
var discriminability =
new ObservationGenerationModel(_standardDistribution, fixation, location)
.GenerateDiscriminabilityValue();
_observationValues[location] = new NormalDistribution(discriminability, 1.0).Generate();
}
}
return _observationValues;
}
/// <summary>
/// Generates a random vector of observations from the
/// Inverse Gaussian distribution with the given parameters.
/// </summary>
///
/// <param name="mean">The mean parameter mu.</param>
/// <param name="shape">The shape parameter lambda.</param>
/// <param name="samples">The number of samples to generate.</param>
/// <param name="result">The location where to store the samples.</param>
/// <param name="source">The random number generator to use as a source of randomness.
/// Default is to use <see cref="Accord.Math.Random.Generator.Random"/>.</param>
///
/// <returns>An array of double values sampled from the inverse Gaussian distribution.</returns>
///
public static double[] Random(double mean, double shape, int samples, double[] result, Random source)
{
NormalDistribution.Random(samples, result, source);
for (int i = 0; i < result.Length; i++)
{
double v = result[i];
double y = v * v;
double x = mean + (mean * mean * y) / (2 * shape) - (mean / (2 * shape)) * Math.Sqrt(4 * mean * shape * y + mean * mean * y * y);
double t = source.NextDouble();
if (t <= (mean) / (mean + x))
{
result[i] = x;
}
else
{
result[i] = (mean * mean) / x;
}
}
return(result);
}
private void init(int n, double[] ranks, bool?exact)
{
if (n <= 0)
{
throw new ArgumentOutOfRangeException("n", "The number of samples must be positive.");
}
this.n = n;
double mean = n * (n + 1.0) / 4.0;
double stdDev = Math.Sqrt((n * (n + 1.0) * (2.0 * n + 1.0)) / 24.0);
bool hasVectors = ranks != null;
// For small samples (< 12) the distribution can be exact
this.exact = hasVectors && (n <= 12);
if (exact.HasValue)
{
if (exact.Value && !hasVectors)
{
throw new ArgumentException("exact", "Cannot use exact method if rank vectors are not specified.");
}
this.exact = exact.Value; // force
}
if (hasVectors)
{
if (this.exact)
{
initExactMethod(ranks);
}
}
this.approximation = new NormalDistribution(mean, stdDev);
}
private void init(int n1, int n2, double[] ranks, bool?exact)
{
if (n1 <= 0)
{
throw new ArgumentOutOfRangeException("n1", "The number of observations in the first sample (n1) must be higher than zero.");
}
if (n2 <= 0)
{
throw new ArgumentOutOfRangeException("n2", "The number of observations in the second sample (n2) must be higher than zero.");
}
if (n1 > n2)
{
Trace.TraceWarning("Creating a MannWhitneyDistribution where the first sample is larger than the second sample. If possible, please re-organize your samples such that the first sample is smaller than the second sample.");
}
if (ranks != null)
{
if (ranks.Length <= 1)
{
throw new ArgumentOutOfRangeException("ranks", "The rank vector must contain a minimum of 2 elements.");
}
for (int i = 0; i < ranks.Length; i++)
{
if (ranks[i] < 0)
{
throw new ArgumentOutOfRangeException("The rank values cannot be negative.");
}
}
}
int n = n1 + n2;
this.n1 = n1;
this.n2 = n2;
// From https://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test: For large samples, U
// is approximately normally distributed. In that case, the standardized value is given
// by z = (U - mean) / stdDev where:
double mean = ((double)n1 * n2) / 2.0;
double stdDev = Math.Sqrt(((double)n1 * n2 * (n + 1)) / 12.0);
bool hasVectors = ranks != null;
// For small samples (< 30) the distribution can be exact
this.exact = hasVectors && (n1 <= 30 && n2 <= 30);
if (exact.HasValue)
{
if (exact.Value && !hasVectors)
{
throw new ArgumentException("exact", "Cannot use exact method if rank vectors are not specified.");
}
this.exact = exact.Value; // force
}
if (hasVectors)
{
// Apply correction to the variance
double correction = MannWhitneyDistribution.correction(ranks);
double a = ((double)n1 * n2) / 12.0;
double b = (n + 1.0) - correction;
stdDev = Math.Sqrt(a * b);
if (this.exact)
{
initExactMethod(ranks);
}
}
this.approximation = new NormalDistribution(mean, stdDev);
}
public static double BaumWelchLearning(double[][] data)
{
// Specify a initial normal distribution for the samples.
NormalDistribution density = new NormalDistribution();
// Creates a continuous hidden Markov Model with two states organized in a forward
// topology and an underlying univariate Normal distribution as probability density.
var model = new HiddenMarkovModel<NormalDistribution>(new Ergodic(2), density);
// Configure the learning algorithms to train the sequence classifier until the
// difference in the average log-likelihood changes only by as little as 0.0001
var teacher = new BaumWelchLearning<NormalDistribution>(model)
{
Tolerance = 0.001,
Iterations = 0,
};
// Fit the model
double likelihood = teacher.Run(data);
// See the log-probability of the sequences learned
double a1 = model.Evaluate(new[] { 0.999999999999928, 0 , 0.999999999999988 , 0 , 0.999999999999988 }); // -0.12799388666109757
return a1;
}
public void NormalTest()
{
var target = GeneralizedNormalDistribution.Normal(mean: 0.42, stdDev: 4.2);
var normal = new NormalDistribution(mean: 0.42, stdDev: 4.2);
test(target, normal);
}
public static Bitmap AWGNNoise(Bitmap bmp, int intensity)
{
Bitmap img = new Bitmap(bmp.Width, bmp.Height);
var normal = new NormalDistribution(mean: 0, stdDev: 1);
double[] noise = normal.Generate(img.Width*img.Height);
int l = 0;
for (int i = 0; i < bmp.Height; i++)
{
for(int j = 0; j < bmp.Width; j++)
{
Color c = bmp.GetPixel(j, i);
int c1 = c.R + ((int)Math.Ceiling(noise[l]) * intensity);//(int)noise + intensity;//(int)Math.Sqrt(noise() * 255) + intensity;
int c2 = c.G + ((int)Math.Ceiling(noise[l]) * intensity);//(int)Math.Sqrt(noise() * 255) + intensity;
int c3 = c.B + ((int)Math.Ceiling(noise[l]) * intensity);//(int)Math.Sqrt(noise() * 255) + intensity;
c1 = c1 > 255 ? 255 : c1;
c1 = c1 < 0 ? 0 : c1;
c2 = c2 > 255 ? 255 : c2;
c2 = c2 < 0 ? 0 : c2;
c3 = c3 > 255 ? 255 : c3;
c3 = c3 < 0 ? 0 : c3;
Color newC = Color.FromArgb(c1, c2, c3);
img.SetPixel(j, i, newC);
l++;
}
}
return img;
}
public void DistributionFunctionPerComponent()
{
NormalDistribution[] components = new NormalDistribution[2];
components[0] = new NormalDistribution(2, 1);
components[1] = new NormalDistribution(5, 1);
double[] coefficients = { 0.4, 0.5 };
var mixture = new Mixture<NormalDistribution>(coefficients, components);
double expected = mixture.DistributionFunction(0, 0.42) +
mixture.DistributionFunction(1, 0.42);
double actual = mixture.DistributionFunction(0.42);
Assert.AreEqual(expected, actual);
}
public void ProbabilityDensityFunctionTest2()
{
double expected, actual;
// Test for small variance
NormalDistribution target = new NormalDistribution(4.2, double.Epsilon);
expected = 0;
actual = target.ProbabilityDensityFunction(0);
Assert.AreEqual(expected, actual);
expected = double.PositiveInfinity;
actual = target.ProbabilityDensityFunction(4.2);
Assert.AreEqual(expected, actual);
}
public void FitTest()
{
double[] coefficients = { 0.50, 0.50 };
NormalDistribution[] components = new NormalDistribution[2];
components[0] = new NormalDistribution(2, 1);
components[1] = new NormalDistribution(5, 1);
var target = new Mixture<NormalDistribution>(coefficients, components);
double[] values = { 0, 1, 1, 0, 1, 6, 6, 5, 7, 5 };
double[] part1 = values.Submatrix(0, 4);
double[] part2 = values.Submatrix(5, 9);
MixtureOptions options = new MixtureOptions() { Threshold = 1e-10 };
target.Fit(values, options);
var actual = target;
var mean1 = Accord.Statistics.Tools.Mean(part1);
var var1 = Accord.Statistics.Tools.Variance(part1);
Assert.AreEqual(mean1, actual.Components[0].Mean, 1e-6);
Assert.AreEqual(var1, actual.Components[0].Variance, 1e-6);
var mean2 = Accord.Statistics.Tools.Mean(part2);
var var2 = Accord.Statistics.Tools.Variance(part2);
Assert.AreEqual(mean2, actual.Components[1].Mean, 1e-6);
Assert.AreEqual(var2, actual.Components[1].Variance, 1e-5);
var expectedMean = Accord.Statistics.Tools.Mean(values);
var actualMean = actual.Mean;
Assert.AreEqual(expectedMean, actualMean, 1e-7);
var expectedVar = Accord.Statistics.Tools.Variance(values, false);
var actualVar = actual.Variance;
Assert.AreEqual(expectedVar, actualVar, 0.15);
}
public void LogProbabilityDensityFunction()
{
NormalDistribution[] components = new NormalDistribution[2];
components[0] = new NormalDistribution(2, 1);
components[1] = new NormalDistribution(5, 1);
double[] coefficients = { 0.4, 0.5 };
var mixture = new Mixture<NormalDistribution>(coefficients, components);
double expected = System.Math.Log(
0.4 * components[0].ProbabilityDensityFunction(0.42) +
0.5 * components[1].ProbabilityDensityFunction(0.42));
double actual = mixture.LogProbabilityDensityFunction(0.42);
Assert.AreEqual(expected, actual);
}
public void LogProbabilityDensityFunctionTest()
{
double x = 3;
double mean = 7;
double dev = 5;
NormalDistribution target = new NormalDistribution(mean, dev);
double expected = System.Math.Log(0.0579383105522966);
double actual = target.LogProbabilityDensityFunction(x);
Assert.IsFalse(double.IsNaN(actual));
Assert.AreEqual(expected, actual, 1e-15);
}
public void ConstructorTest0()
{
var original = new NormalDistribution(mean: 4, stdDev: 4.2);
var normal = new GeneralContinuousDistribution(
original.Support,
original.ProbabilityDensityFunction,
original.DistributionFunction);
testNormal(normal, 1);
}
public void DistributionFunctionTest()
{
double x = 3;
double mean = 7;
double dev = 5;
NormalDistribution target = new NormalDistribution(mean, dev);
double expected = 0.211855398583397;
double actual = target.DistributionFunction(x);
Assert.IsFalse(double.IsNaN(actual));
Assert.AreEqual(expected, actual, 1e-15);
}
public void MixtureFitTest()
{
var samples1 = new NormalDistribution(mean: -2, stdDev: 0.5).Generate(100000);
var samples2 = new NormalDistribution(mean: +4, stdDev: 0.5).Generate(100000);
// Mix the samples from both distributions
var samples = samples1.Concatenate(samples2);
// Create a new mixture distribution with two Normal components
var mixture = new Mixture<NormalDistribution>(new[] { 0.2, 0.8 },
new NormalDistribution(-1),
new NormalDistribution(+1));
// Estimate the distribution
mixture.Fit(samples, new MixtureOptions
{
Iterations = 50,
Threshold = 0
});
var result = mixture.ToString("N2", System.Globalization.CultureInfo.InvariantCulture);
Assert.AreEqual("Mixture(x; 0.50*N(x; μ = -2.00, σ² = 0.25) + 0.50*N(x; μ = 4.00, σ² = 0.25))", result);
}
public void DistributionFunctionTest3()
{
double expected, actual;
// Test small variance
NormalDistribution target = new NormalDistribution(1.0, double.Epsilon);
expected = 0;
actual = target.DistributionFunction(0);
Assert.AreEqual(expected, actual);
expected = 0.5;
actual = target.DistributionFunction(1.0);
Assert.AreEqual(expected, actual);
expected = 1.0;
actual = target.DistributionFunction(1.0 + 1e-15);
Assert.AreEqual(expected, actual);
expected = 0.0;
actual = target.DistributionFunction(1.0 - 1e-15);
Assert.AreEqual(expected, actual);
}
public void DistributionFunctionTest1()
{
var target = GeneralizedNormalDistribution.Normal(mean: 0.42, stdDev: 4.2);
var normal = new NormalDistribution(mean: 0.42, stdDev: 4.2);
for (double x = -10; x < 10; x += 0.0001)
{
double actual = target.DistributionFunction(x);
double expected = normal.DistributionFunction(x);
Assert.AreEqual(expected, actual, 1e-10);
Assert.IsFalse(Double.IsNaN(actual));
}
}
public void ZScoreTest()
{
double x = 5;
double mean = 3;
double dev = 6;
NormalDistribution target = new NormalDistribution(mean, dev);
double expected = (x - 3) / 6;
double actual = target.ZScore(x);
Assert.AreEqual(expected, actual);
}
public void NormalTest2()
{
var target = GeneralizedNormalDistribution.Normal(mean: 0.0, stdDev: 2 / Constants.Sqrt2);
var normal = new NormalDistribution(mean: 0.0, stdDev: 2 / Constants.Sqrt2);
test(target, normal);
var support = target.Support;
Assert.AreEqual(normal.Support.Min, support.Min);
Assert.AreEqual(normal.Support.Max, support.Max);
for (double i = 0.01; i <= 1; i += 0.01)
{
var actual = normal.GetRange(i);
var expected = normal.GetRange(i);
Assert.AreEqual(expected.Min, actual.Min);
Assert.AreEqual(expected.Max, actual.Max);
}
}
public void CloneTest()
{
NormalDistribution target = new NormalDistribution(0.5, 4.2);
NormalDistribution clone = (NormalDistribution)target.Clone();
Assert.AreNotSame(target, clone);
Assert.AreEqual(target.Entropy, clone.Entropy);
Assert.AreEqual(target.Mean, clone.Mean);
Assert.AreEqual(target.StandardDeviation, clone.StandardDeviation);
Assert.AreEqual(target.Variance, clone.Variance);
}
public Activation(NormalDistribution standardDistribution)
{
_standardDistribution = standardDistribution;
}
public void FitTest()
{
double expectedMean = 1.125;
double expectedSigma = 1.01775897605147;
NormalDistribution target;
target = new NormalDistribution();
double[] observations = { 0.10, 0.40, 2.00, 2.00 };
double[] weights = { 0.25, 0.25, 0.25, 0.25 };
target.Fit(observations, weights);
Assert.AreEqual(expectedMean, target.Mean);
Assert.AreEqual(expectedSigma, target.StandardDeviation, 1e-6);
target = new NormalDistribution();
double[] observations2 = { 0.10, 0.10, 0.40, 2.00 };
double[] weights2 = { 0.125, 0.125, 0.25, 0.50 };
target.Fit(observations2, weights2);
Assert.AreEqual(expectedMean, target.Mean);
// Assert.AreEqual(expectedSigma, target.StandardDeviation, 1e-6);
}
/// <summary>
/// Generates a random observation from the
/// Lognormal distribution with the given parameters.
/// </summary>
///
/// <param name="location">The distribution's location value.</param>
/// <param name="shape">The distribution's shape deviation.</param>
/// <param name="source">The random number generator to use as a source of randomness.
/// Default is to use <see cref="Accord.Math.Random.Generator.Random"/>.</param>
///
/// <returns>A random double value sampled from the specified Lognormal distribution.</returns>
///
public static double Random(double location, double shape, Random source)
{
return(Math.Exp(location + shape * NormalDistribution.Random(source)));
}
public void ConstructorTest2()
{
var original = new NormalDistribution(mean: 4, stdDev: 4.2);
var normal = GeneralContinuousDistribution.FromDensityFunction(
original.Support, original.ProbabilityDensityFunction);
for (double i = -10; i < +10; i += 0.1)
{
double expected = original.DistributionFunction(i);
double actual = normal.DistributionFunction(i);
double diff = Math.Abs(expected - actual) / expected;
Assert.IsTrue(diff < 1e-7);
}
testNormal(normal, 1);
}
public void ConstructorTest1()
{
NormalDistribution[] components = new NormalDistribution[2];
components[0] = new NormalDistribution(2, 1);
components[1] = new NormalDistribution(5, 1);
var mixture = new Mixture<NormalDistribution>(components);
double[] expected = { 0.5, 0.5 };
Assert.IsTrue(expected.IsEqual(mixture.Coefficients));
Assert.AreEqual(components, mixture.Components);
}
public void InverseDistributionFunctionTest()
{
double[] expected =
{
Double.NegativeInfinity, -4.38252, -2.53481, -1.20248,
-0.0640578, 1.0, 2.06406, 3.20248, 4.53481, 6.38252,
Double.PositiveInfinity
};
NormalDistribution original = new NormalDistribution(1.0, 4.2);
var target = GeneralContinuousDistribution.FromDistributionFunction(
original.Support, original.DistributionFunction);
for (int i = 0; i < expected.Length; i++)
{
double x = i / 10.0;
double actual = target.InverseDistributionFunction(x);
Assert.AreEqual(expected[i], actual, 1e-5);
Assert.IsFalse(Double.IsNaN(actual));
}
}
public void FitTest2()
{
double[] coefficients = { 0.50, 0.50 };
NormalDistribution[] components = new NormalDistribution[2];
components[0] = new NormalDistribution(2, 1);
components[1] = new NormalDistribution(5, 1);
var target = new Mixture<NormalDistribution>(coefficients, components);
double[] values = { 12512, 1, 1, 0, 1, 6, 6, 5, 7, 5 };
double[] weights = { 0, 1, 1, 1, 1, 1, 1, 1, 1, 1 };
weights = weights.Divide(weights.Sum());
double[] part1 = values.Submatrix(1, 4);
double[] part2 = values.Submatrix(5, 9);
MixtureOptions opt = new MixtureOptions()
{
Threshold = 0.000001
};
target.Fit(values, weights, opt);
var mean1 = Accord.Statistics.Tools.Mean(part1);
var var1 = Accord.Statistics.Tools.Variance(part1);
Assert.AreEqual(mean1, target.Components[0].Mean, 1e-5);
Assert.AreEqual(var1, target.Components[0].Variance, 1e-5);
var mean2 = Accord.Statistics.Tools.Mean(part2);
var var2 = Accord.Statistics.Tools.Variance(part2);
Assert.AreEqual(mean2, target.Components[1].Mean, 1e-5);
Assert.AreEqual(var2, target.Components[1].Variance, 1e-5);
var expectedMean = Accord.Statistics.Tools.WeightedMean(values, weights);
var actualMean = target.Mean;
Assert.AreEqual(expectedMean, actualMean, 1e-5);
}
public void MedianTest2()
{
NormalDistribution original = new NormalDistribution(0.4, 2.2);
var target = GeneralContinuousDistribution.FromDistributionFunction(
original.Support, original.DistributionFunction);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
Assert.AreEqual(target.Median, original.Median, 1e-10);
target = GeneralContinuousDistribution.FromDensityFunction(
original.Support, original.ProbabilityDensityFunction);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5), 1e-10);
Assert.AreEqual(target.Median, original.Median, 1e-10);
}
public void MixtureWeightsFitTest()
{
// Randomly initialize some mixture components
NormalDistribution[] components = new NormalDistribution[2];
components[0] = new NormalDistribution(2, 1);
components[1] = new NormalDistribution(5, 1);
// Create an initial mixture
Mixture<NormalDistribution> mixture = new Mixture<NormalDistribution>(components);
// Now, suppose we have a weighted data
// set. Those will be the input points:
double[] points = { 0, 3, 1, 7, 3, 5, 1, 2, -1, 2, 7, 6, 8, 6 }; // (14 points)
// And those are their respective unormalized weights:
double[] weights = { 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 3, 1, 1 }; // (14 weights)
// Let's normalize the weights so they sum up to one:
weights = weights.Divide(weights.Sum());
// Now we can fit our model to the data:
mixture.Fit(points, weights); // done!
// Our model will be:
double mean1 = mixture.Components[0].Mean; // 1.41126
double mean2 = mixture.Components[1].Mean; // 6.53301
// If we need the GaussianMixtureModel functionality, we can
// use the estimated mixture to initialize a new model:
GaussianMixtureModel gmm = new GaussianMixtureModel(mixture);
Assert.AreEqual(mean1, gmm.Gaussians[0].Mean[0]);
Assert.AreEqual(mean2, gmm.Gaussians[1].Mean[0]);
Assert.AreEqual(mean1, 1.4112610766836404, 1e-15);
Assert.AreEqual(mean2, 6.5330177004151082, 1e-14);
Assert.AreEqual(mixture.Coefficients[0], gmm.Gaussians[0].Proportion);
Assert.AreEqual(mixture.Coefficients[1], gmm.Gaussians[1].Proportion);
}
static void Main(string[] args)
{
Process _process = Process.GetCurrentProcess();
bool _takearguments = false;
// How many arguments have been stored in the game.
if (args.Length > 0)
{
Console.WriteLine("Arguments found.");
_takearguments = true;
HandleArguments(args);
}
string HostName = "localhost";
if (!_takearguments)
{
Console.WriteLine("Host name:");
HostName = Console.ReadLine();
Console.Clear();
Console.WriteLine("How many games do you wish to simulate?");
string _count = Console.ReadLine();
int _result = 0;
// Determine that the value that has been inputted is
// in fact valid.
while (!int.TryParse(_count, out _result))
{
Console.Clear();
Console.WriteLine("Please try again: ");
_count = Console.ReadLine();
}
// Set the new count of games that we want to simulate.
gamesToPlay = _result;
Console.Clear();
string _consoleoutput = "";
while (_consoleoutput != "n" && _consoleoutput != "y")
{
// Determine if we want to log output to be silence while we do this
Console.WriteLine("Silence output?");
_consoleoutput = Console.ReadLine();
}
if (_consoleoutput == "n")
{
m_RemainQuiet = false;
}
else if (_consoleoutput == "y")
{
m_RemainQuiet = true;
}
}
//RunGamesParallel();
//return;
// Get some strange invocation error here.
// tryLoadController(_agentName);
gs = new GameState(125);
gs.GameOver += new EventHandler(GameOverHandler);
gs.StartPlay();
BasePacman controller = new LucPacScripted();
Console.WriteLine("Choose an AI agent to control Pacman:");
Console.WriteLine(" 1 - LucPacScripted");
Console.WriteLine(" 2 - LucPac (MCTS)");
Console.WriteLine(" 3 - MMLocPac (Evolved Neural Network) from .nn file");
Console.WriteLine(" 5 - SimRandom");
int Selection = int.Parse(Console.ReadKey().KeyChar.ToString());
switch (Selection)
{
case 1:
controller = new LucPacScripted();
break;
case 2:
controller = new LucPac();
break;
case 3:
controller = new MMPac.MMLocPac("NeuralNetworkLocPac.nn");
break;
default:
controller = new RandomPac();
break;
}
var GR = new GameRunner();
var Base = new double[9] {
3.0, 2.8, 2.8, 2.8, 2.8, 1.5, 1.5, 1.5, 1.5
};
var Params = new double[9] {
0.07, 0.01, 0.02, -0.16, 0.06, -0.05, 0, 0.06, -0.09
};
//var Params = new double[9] { -0.17, 0.01, 0.02, -0.16, 0.06, -0.05, 0, 0.06, -0.09 };
// Params = Params.Add(Base);
string TestAgent = "PacmanAI.UncertainAgent,PacmanAI";
var GRR = GR.RunGamesOnline(HostName, gamesToPlay,
controller.GetType().Name
//TestAgent
, new Random().Next(),
//null
new List <double>(Params)
);
var NewScores = new List <double>();
NewScores.AddRange(GRR.scores);
for (int i = 0; i < NewScores.Count; i++)
{
NewScores[i] += 9000;
}
NewScores.AddRange(GRR.scores);
var ZeroScores = new List <double>();
for (int i = 0; i < 100; i++)
{
ZeroScores.Add(0);
}
Console.WriteLine("Done - " + GRR.scores.Average() + " " + GRR.gamesPlayed);
Console.WriteLine("Scores over 1600: " + GRR.scores.Where(s => s >= 1600).Count());
Console.WriteLine("Done (Altered) - " + NewScores.Average() + " " + GRR.gamesPlayed);
Console.WriteLine("Scores over 1500 (Altered): " + NewScores.Where(s => s >= 1500).Count());
/*Console.WriteLine("Evaluation score via distribution evaluation: " + new DistributionWeightEvaluation(null).CalculateFitnessScore(GRR.scores, 5000, 1));
* Console.WriteLine("Evaluation score via average evaluation: " + new AccurateThresholdEvaluation(null).CalculateFitnessScore(GRR.scores, 5000, 1));
*
*
* Console.WriteLine("Evaluation score via distribution evaluation (All zeroes): " + new DistributionWeightEvaluation(null).CalculateFitnessScore(ZeroScores, 1500, 1));
* Console.WriteLine("Evaluation score via average evaluation (All zeroes): " + new AccurateThresholdEvaluation(null).CalculateFitnessScore(ZeroScores, 1500, 1));
*
* Console.WriteLine("Evaluation score via distribution evaluation (Altered scores): " + new DistributionWeightEvaluation(null).CalculateFitnessScore(NewScores, 5000, 1));
* Console.WriteLine("Evaluation score via average evaluation (Altered scores): " + new AccurateThresholdEvaluation(null).CalculateFitnessScore(NewScores, 5000, 1));
*
* var gaussianDist = new Accord.Statistics.Distributions.Univariate.NormalDistribution(2000, 10);
*
* Console.WriteLine("Evaluation score via distribution evaluation (Gaussian scores): " + new DistributionWeightEvaluation(null).CalculateFitnessScore(gaussianDist.Generate(100).ToList(), 2000, 1));
* Console.WriteLine("Evaluation score via average evaluation (Gaussian scores): " + new AccurateThresholdEvaluation(null).CalculateFitnessScore(gaussianDist.Generate(100).ToList(), 2000, 1));
*/
Accord.Statistics.Distributions.Univariate.EmpiricalDistribution rdb = new Accord.Statistics.Distributions.Univariate.EmpiricalDistribution(GRR.scores.ToArray(), 25);
Accord.Controls.DataSeriesBox.Show("Pacman score distribution", rdb.ProbabilityDensityFunction, new Accord.DoubleRange(-2000, 12000));
Accord.Statistics.Distributions.Univariate.EmpiricalDistribution rdb2 = new Accord.Statistics.Distributions.Univariate.EmpiricalDistribution(NewScores.ToArray());
Accord.Controls.DataSeriesBox.Show("Pacman score distribution (Altered)", rdb2.ProbabilityDensityFunction, new Accord.DoubleRange(-2000, 12000));
double[] coef = { 4, 1 };
var skewNormal = new Mixture <NormalDistribution>(coef, new NormalDistribution(2000, 1500), new NormalDistribution(7000, 1500));// new SkewNormalDistribution(4500, 3000, 7.2);
Accord.Controls.DataSeriesBox.Show("Skew Normal", skewNormal.ProbabilityDensityFunction, new Accord.DoubleRange(-2000, 12000));
Console.ReadKey();
return;
// DEFINE CONTROLLER //
//BasePacman controller = new MMMCTSCode.MMMCTS();
//BasePacman controller = new RandomPac();
//BasePacman controller = new LucPacScripted();
//BasePacman controller = new LucPac();
//BasePacman controller = new MMPac.MMPac("NeuralNetwork.nn");
//BasePacman controller = new MMPac.MMPac(Weights);
//BasePacman controller = new MMPac.MMLocPac("NeuralNetworkLocPac.nn");
// Turn off the logging
if (controller.GetType() == typeof(LucPac) && m_RemainQuiet)
{
LucPac.REMAIN_QUIET = true;
}
if (controller.GetType() == typeof(LucPacScripted) && m_RemainQuiet)
{
LucPacScripted.REMAIN_QUIET = true;
}
//BasePacman controller = new SmartDijkstraPac();
gs.Controller = controller;
Stopwatch watch = new Stopwatch();
int percentage = -1;
int lastUpdate = 0;
watch.Start();
while (gamesPlayed < gamesToPlay)
{
int newPercentage = (int)Math.Floor(((float)gamesPlayed / gamesToPlay) * 100);
if (newPercentage != percentage || gamesPlayed - lastUpdate >= 100)
{
lastUpdate = gamesPlayed;
percentage = newPercentage;
Console.Clear();
Console.WriteLine("Simulating ... " + percentage + "% (" + gamesPlayed + " : " + gamesToPlay + ")");
Console.WriteLine(" - Elapsed: " + (watch.ElapsedMilliseconds / 1000.0) + "ms");
Console.WriteLine(" - Current best: " + highestScore);
Console.WriteLine(" - Current worst: " + lowestScore);
if (gamesPlayed > 0)
{
Console.WriteLine(" - Current avg.: " + (totalScore / gamesPlayed));
}
}
// update gamestate
Direction direction = controller.Think(gs);
gs.Pacman.SetDirection(direction);
// update game
gs.Update();
ms += GameState.MSPF;
}
watch.Stop();
// shut down controller
controller.SimulationFinished();
// output results
Console.Clear();
long seconds = ms / 1000;
Console.WriteLine("Games played: " + gamesPlayed);
Console.WriteLine("Avg. score: " + (totalScore / gamesPlayed));
Console.WriteLine("Highest score: " + highestScore + " points");
Console.WriteLine("Lowest score: " + lowestScore + " points");
Console.WriteLine("Max Pills Eaten: " + maxPillsEaten);
Console.WriteLine("Min Pills Eaten: " + minPillsEaten);
Console.WriteLine("Average Pills Eaten: " + pillsEatenTotal / gamesPlayed);
Console.WriteLine("Max Ghosts Eaten: " + maxGhostsEaten);
Console.WriteLine("Min Ghosts Eaten: " + minGhostsEaten);
Console.WriteLine("Average Ghosts Eaten: " + totalGhostsEaten / gamesPlayed);
Console.WriteLine("Longest game: " + ((float)longestGame / 1000.0f) + " seconds");
Console.WriteLine("Total simulated time: " + (seconds / 60 / 60 / 24) + "d " + ((seconds / 60 / 60) % 24) + "h " + ((seconds / 60) % 60) + "m " + (seconds % 60) + "s");
Console.WriteLine("Avg. simulated time pr. game: " + ((float)ms / 1000.0f / gamesPlayed) + " seconds");
Console.WriteLine("Simulation took: " + (watch.ElapsedMilliseconds / 1000.0f) + " seconds");
Console.WriteLine("Speed: " + (ms / watch.ElapsedMilliseconds) + " (" + ((ms / watch.ElapsedMilliseconds) / 60) + "m " + ((ms / watch.ElapsedMilliseconds) % 60) + " s) simulated seconds pr. second");
Console.WriteLine("For a total of: " + gamesPlayed / (watch.ElapsedMilliseconds / 1000.0f) + " games pr. second");
Console.WriteLine();
//Calculate standard deviation
double mean = totalScore / gamesPlayed;
double totalsqdif = 0;
foreach (var val in scores)
{
totalsqdif += (val - mean) * (val - mean);
}
double variance = totalsqdif / gamesPlayed;
double stddev = Math.Sqrt(variance);
Console.WriteLine("Standard deviation of: " + stddev);
Console.WriteLine("Standard deviation of (Accord): " + scores.ToArray().StandardDeviation());
//Generates a distribution from existing data
Accord.Statistics.Distributions.Univariate.EmpiricalDistribution db = new Accord.Statistics.Distributions.Univariate.EmpiricalDistribution(scores.ToArray());
//Calculates standard deviation
Console.WriteLine("Standard deviation of (Accord 2): " + db.StandardDeviation);
double[] sample =
//{ 1000, 960, 1000, 960, 1000, 600, 100, 1000, 1500};
{ 2000, 2500, 2100, 9000, 1900, 2000, 150, 2100 };
//{ 60000, 70000, 80000, 90000, 40000, 100000, 200000, 15000, 500000, 44444 };
//scores.Take(20).ToArray();
double[] sample2 =
scores.Take(100).ToArray();
//Shapiro Wilk test to see if distribution is normal
var swT = new Accord.Statistics.Testing.ShapiroWilkTest(scores.ToArray());
Console.WriteLine("Shapiro Wilk Test on all scores: Statistic - " + swT.Statistic + " , PValue - " + swT.PValue + " , Significant - " + swT.Significant);
var normalDist = new Accord.Statistics.Distributions.Univariate.NormalDistribution(950, 1200);
var swT2 = new Accord.Statistics.Testing.ShapiroWilkTest(normalDist.Generate(1000));
Console.WriteLine("Shapiro Wilk Test on normal dist: Statistic - " + swT2.Statistic + " , PValue - " + swT2.PValue + " , Significant - " + swT2.Significant);
//Accord.Statistics.Testing.KolmogorovSmirnovTest ks = new Accord.Statistics.Testing.KolmogorovSmirnovTest(sample, db);
//Console.WriteLine("KS Test: Statistic - " + ks.Statistic + " , PValue - " + ks.PValue + " , Significant - " + ks.Significant);
//Probability that the given scores were sampled from the previous distribution
Accord.Statistics.Testing.ZTest ts = new Accord.Statistics.Testing.ZTest(sample, totalScore / gamesPlayed);
/*sample.Average(),
* db.StandardDeviation,
* sample.Length,
* totalScore / gamesPlayed);
*/
Console.WriteLine("Z Test: Statistic - " + ts.Statistic + " , PValue - " + ts.PValue + " , Significant - " + ts.Significant);
Accord.Statistics.Testing.ZTest ts2 = new Accord.Statistics.Testing.ZTest(sample2, totalScore / gamesPlayed);
/*sample2.Average(),
* //Accord.Statistics.Tools.StandardDeviation(sample2.ToArray()),
* db.StandardDeviation,
* sample2.Length,
* totalScore / gamesPlayed);
*/
Console.WriteLine("Z Test 2: Statistic - " + ts2.Statistic + " , PValue - " + ts2.PValue + " , Significant - " + ts2.Significant);
//% of values that are between given ranges
Console.WriteLine("Distribution function 0 - 1000: " + db.DistributionFunction(0, 1000));
Console.WriteLine("Distribution function 1000 - 11000: " + db.DistributionFunction(1000, 11000));
Console.WriteLine("Distribution function 0 - 500: " + db.DistributionFunction(0, 500));
Console.WriteLine("Distribution function 1500 - 11000: " + db.DistributionFunction(1500, 11000));
//MannWhitneyWilcoxon test on whether 2 samples are from the same distribution - high P value = likely same distribution
Accord.Statistics.Testing.MannWhitneyWilcoxonTest mwTest = new Accord.Statistics.Testing.MannWhitneyWilcoxonTest(scores.ToArray(), sample2);
Console.WriteLine("MWW Test: Statistic - " + mwTest.Statistic + " , PValue - " + mwTest.PValue + " , Significant - " + mwTest.Significant);
Accord.Statistics.Testing.MannWhitneyWilcoxonTest mwTest2 = new Accord.Statistics.Testing.MannWhitneyWilcoxonTest(normalDist.Generate(1000), scores.ToArray());
Console.WriteLine("MWW Test 2 (actual scores versus normal dist): Statistic - " + mwTest2.Statistic + " , PValue - " + mwTest2.PValue + " , Significant - " + mwTest2.Significant);
//Accord.Controls.HistogramBox.Show(scores.ToArray());
//Guess what distribution this is
var analysis = new Accord.Statistics.Analysis.DistributionAnalysis(scores.ToArray());
// Compute the analysis
analysis.Compute();
// Get the most likely distribution (first)
var mostLikely = analysis.GoodnessOfFit[0];
var result = mostLikely.Distribution.ToString();
Console.WriteLine(result);
//Plots the distributions
Accord.Controls.DataSeriesBox.Show("Pacman score distribution", db.ProbabilityDensityFunction, new Accord.DoubleRange(-2000, highestScore));
Accord.Controls.DataSeriesBox.Show("Normal distribution", normalDist.ProbabilityDensityFunction, new Accord.DoubleRange(-2000, highestScore));
Accord.Controls.DataSeriesBox.Show("Gamma distribution", mostLikely.Distribution.ProbabilityFunction, new Accord.DoubleRange(-2000, highestScore));
//Calculate some CDF related malarkey
//top 20 scores - 1 empirical
//next 20 scores - 2nd empirical
//calculate cdf of both
//calculate cdf of cumulative
int games1 = 80;
int games2 = 20;
Accord.Statistics.Distributions.Univariate.EmpiricalDistribution edb = new Accord.Statistics.Distributions.Univariate.EmpiricalDistribution(scores.GetRange(0, games1).ToArray());
Accord.Statistics.Distributions.Univariate.EmpiricalDistribution edb2 = new Accord.Statistics.Distributions.Univariate.EmpiricalDistribution(scores.GetRange(games1, games2).ToArray());
Accord.Statistics.Distributions.Univariate.EmpiricalDistribution edbC = new Accord.Statistics.Distributions.Univariate.EmpiricalDistribution(scores.GetRange(0, games1 + games2).ToArray());
var cdf1 = edb.DistributionFunction(800);
var cdf2 = edb2.DistributionFunction(800);
var cdfC = edbC.DistributionFunction(800);
Console.WriteLine("CDF1 = " + cdf1 + ", CDF2 = " + cdf2 + ", Guess = " + (cdf1 * games1 + cdf2 * games2) / (games1 + games2) + ", Actual = " + cdfC);
//Convolution
var ScoresA = scores.GetRange(0, games1).ToArray();
var ScoresB = scores.GetRange(games1, games1).ToArray();
//var Convolution = ScoresA.Convolve(ScoresB);
double[] Convolution = new double[games1];
Accord.Math.Transforms.FourierTransform2.Convolve(ScoresA, ScoresB, Convolution);
Console.ReadLine();
}
