/// <summary>
/// 获取多个随机整型
/// </summary>
/// <param name="count">整型个数</param>
/// <param name="minValue">最大值</param>
/// <param name="maxValue">最小值</param>
/// <param name="_Distribution">分布规律</param>
public static int[] Ints(int count, int minValue, int maxValue, DistributionFunction _Distribution = DistributionFunction.Uniform)
{
int[] ints = new int[count];
decimal a = 0, b = 0, c = 0;
if (_Distribution == DistributionFunction.Parabola)
{
decimal d = ((decimal)Math.Pow(maxValue, 3) - (decimal)Math.Pow(minValue, 3)) / 3 - (maxValue + minValue) * ((decimal)Math.Pow(maxValue, 2) - (decimal)Math.Pow(minValue, 2)) / 2 + (decimal)Math.Pow(maxValue + minValue, 2) * (maxValue - minValue) / 4;
a = 1 / d;
b = -a * (minValue + maxValue);
c = a * (decimal)Math.Pow(minValue + maxValue, 2) / 4;
}
for (int i = 0; i < count; i++)
{
switch (_Distribution)
{
case DistributionFunction.Uniform:
ints[i] = Int(minValue, maxValue + 1); break;
case DistributionFunction.Possion:
ints[i] = PossionVariable_Int((maxValue + minValue) / 2.0, minValue, maxValue); break;
case DistributionFunction.Parabola:
ints[i] = ParabolaVariable_Int(a, b, c, minValue, maxValue); break;
}
}
return(ints);
}
//For Puasson: 0, 0.220, 0.553, 0.805, 0.932, 0.980, 0.995, 1
private static IEnumerable <double> GetDistributionFunctionValues(DistributionFunction function, int amount)
{
for (int i = 0; i < amount + 1; i++)
{
yield return(function((double)i / amount));
}
}
public ContinuousDistribution(DistributionFunction pdf, float min, float max, DistributionFunction cdf = null)
{
this.pdf = pdf;
this.cdf = cdf;
this.min = min;
this.max = max;
}
public double[] GenerateSamples(int howMany)
{
var resArray = new double[howMany];
if (DistributionFunction == null)
{
return(new double[howMany]);
}
var res = DistributionFunction.Generate(howMany, resArray);
return(res);
}
internal WeaponBarrelsBase(BinaryReader binaryReader)
{
this.flags = (Flags)binaryReader.ReadInt32();
this.roundsPerSecond = binaryReader.ReadRange();
this.accelerationTimeSeconds = binaryReader.ReadSingle();
this.decelerationTimeSeconds = binaryReader.ReadSingle();
this.barrelSpinScale = binaryReader.ReadSingle();
this.blurredRateOfFire = binaryReader.ReadSingle();
this.shotsPerFire = binaryReader.ReadInt32();
this.fireRecoveryTimeSeconds = binaryReader.ReadSingle();
this.softRecoveryFraction = binaryReader.ReadSingle();
this.magazine = binaryReader.ReadShortBlockIndex1();
this.roundsPerShot = binaryReader.ReadInt16();
this.minimumRoundsLoaded = binaryReader.ReadInt16();
this.roundsBetweenTracers = binaryReader.ReadInt16();
this.optionalBarrelMarkerName = binaryReader.ReadStringID();
this.predictionType = (PredictionType)binaryReader.ReadInt16();
this.firingNoise = (FiringNoiseHowLoudThisWeaponAppearsToTheAI)binaryReader.ReadInt16();
this.accelerationTimeSeconds0 = binaryReader.ReadSingle();
this.decelerationTimeSeconds0 = binaryReader.ReadSingle();
this.damageError = binaryReader.ReadRange();
this.accelerationTimeSeconds1 = binaryReader.ReadSingle();
this.decelerationTimeSeconds1 = binaryReader.ReadSingle();
this.invalidName_ = binaryReader.ReadBytes(8);
this.minimumErrorDegrees = binaryReader.ReadSingle();
this.errorAngleDegrees = binaryReader.ReadRange();
this.dualWieldDamageScale = binaryReader.ReadSingle();
this.distributionFunction = (DistributionFunction)binaryReader.ReadInt16();
this.projectilesPerShot = binaryReader.ReadInt16();
this.distributionAngleDegrees = binaryReader.ReadSingle();
this.minimumErrorDegrees0 = binaryReader.ReadSingle();
this.errorAngleDegrees0 = binaryReader.ReadRange();
this.firstPersonOffsetWorldUnits = binaryReader.ReadVector3();
this.damageEffectReportingType = (DamageEffectReportingType)binaryReader.ReadByte();
this.invalidName_0 = binaryReader.ReadBytes(3);
this.projectile = binaryReader.ReadTagReference();
this.eh = new WeaponBarrelDamageEffectStructBlock(binaryReader);
this.ejectionPortRecoveryTime = binaryReader.ReadSingle();
this.illuminationRecoveryTime = binaryReader.ReadSingle();
this.heatGeneratedPerRound01 = binaryReader.ReadSingle();
this.ageGeneratedPerRound01 = binaryReader.ReadSingle();
this.overloadTimeSeconds = binaryReader.ReadSingle();
this.angleChangePerShot = binaryReader.ReadRange();
this.accelerationTimeSeconds2 = binaryReader.ReadSingle();
this.decelerationTimeSeconds2 = binaryReader.ReadSingle();
this.angleChangeFunction = (AngleChangeFunctionFunctionUsedToScaleBetweenInitialAndFinalAngleChangePerShot)binaryReader.ReadInt16();
this.invalidName_1 = binaryReader.ReadBytes(2);
this.invalidName_2 = binaryReader.ReadBytes(8);
this.invalidName_3 = binaryReader.ReadBytes(24);
this.firingEffects = ReadBarrelFiringEffectBlockArray(binaryReader);
}
private static void CheckPearsonCriteria(List <double> list, DistributionFunction function)
{
var distributionFunctionValues = GetDistributionFunctionValues(function, IntervalsAmount).ToList();
var probabilityFunctionValues = GetProbabilityFunctionValues(distributionFunctionValues).ToList();
var intervals = GetAmountByIntervals(list).ToList();
double value = 0;
for (int i = 0; i < IntervalsAmount; i++)
{
value += Math.Pow(intervals[i] - N * probabilityFunctionValues[i], 2) / (N * probabilityFunctionValues[i]);
}
Console.WriteLine($"Pearson criterion: {DisplayCriteriaResults(value, Pearson49Quantiles[Epsilon])}");
}
//生成无重复的多个整型
public static int[] Ints_Unrepeating(int count, int minValue, int maxValue, DistributionFunction _Distribution = DistributionFunction.Uniform)
{
int[] ints = new int[count]; //输出的整型数组
int[] ranges = new int[maxValue - minValue + 1]; //将取值范围内所有的数组都排列出来
for (int i = minValue; i <= maxValue; i++)
{
ranges[i - minValue] = i;
}
double lambda = 0;
if (_Distribution == DistributionFunction.Possion)
{
lambda = (minValue + maxValue) / 2.0;
}
for (int i = 0; i < count; i++)
{
int index = Int(minValue, maxValue) - minValue; //取值范围内的下标
if (_Distribution == DistributionFunction.Uniform)
{
index = Int(minValue, maxValue) - minValue; //取值范围内的下标
}
else if (_Distribution == DistributionFunction.Possion)
{
index = PossionVariable_Int(lambda, minValue, maxValue);
}
else
{
index = ParabolaVariable_Int(minValue, maxValue);
}
ints[i] = ranges[index]; //赋值给输出的数组
ranges[index] = ranges[maxValue - minValue]; //替换当前位置的值，防止重复
maxValue--;
}
return(ints);
}
public static void CDFSampling()
{
var cdfSampleTestCount = 2000000;
var pdfSizes = new[] { 5, 10, 25, 50, 100, 250 };
var rnd = new RandomSystem(0);
foreach (var pz in pdfSizes)
{
var pdf = new double[pz].SetByIndex(i => rnd.UniformDouble());
var sum = pdf.Sum();
var cdf = new DistributionFunction(pdf);
Assert.True(cdf.Norm.ApproximateEquals(sum, 1e-10));
rnd.ReSeed(0);
var sc1 = new int[pdf.Length];
Report.BeginTimed("Sample Binary Search");
for (int i = 0; i < cdfSampleTestCount; i++)
{
var ind = cdf.Sample(rnd.UniformDouble());
sc1[ind]++;
}
Report.End();
rnd.ReSeed(0);
var sc2 = new int[pdf.Length];
Report.BeginTimed("Sample Linear Search");
for (int i = 0; i < cdfSampleTestCount; i++)
{
var ind = SamplePDFLinear(pdf, sum, rnd.UniformDouble());
sc2[ind]++;
}
Report.End();
for (int i = 0; i < pdf.Length; i++)
{
Assert.True(sc1[i] == sc2[i]);
}
}
}
private static void CheckKolmogorovCriteria(List <double> list, DistributionFunction function)
{
var distributionFunctionValues = GetDistributionFunctionValues(function, list.Count).ToList();
double maxDiff = 0;
for (int i = 0; i < list.Count; i++)
{
if (Math.Abs(list[i] - distributionFunctionValues[i]) > maxDiff)
{
maxDiff = Math.Abs(list[i] - distributionFunctionValues[i]);
}
if (Math.Abs(list[i] - distributionFunctionValues[i + 1]) > maxDiff)
{
maxDiff = Math.Abs(list[i] - distributionFunctionValues[i + 1]);
}
}
var value = maxDiff * Math.Sqrt(list.Count);
Console.WriteLine($"Kolmogorov criterion: {DisplayCriteriaResults(value, KolmogorovQuantiles[Epsilon])}");
}
/// <summary>
/// Shows a new chart in a default form.
/// </summary>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <remarks>
/// Equivalent to:
/// <code>
/// NMathStatsChart.Show( ToChart( dist, function ) );
/// </code>
/// </remarks>
public static void Show( PoissonDistribution dist, DistributionFunction function = DistributionFunction.PDF )
{
Show( ToChart( dist, function ) );
}
/// <summary>
/// Shows a new chart in a default form.
/// </summary>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <remarks>
/// Equivalent to:
/// <code>
/// NMathStatsChart.Show( ToChart( dist, function ) );
/// </code>
/// </remarks>
public static void Show( NegativeBinomialDistribution dist, DistributionFunction function = DistributionFunction.PDF )
{
Show( ToChart( dist, function ) );
}
/// <summary>
/// Shows a new chart in a default form.
/// </summary>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <remarks>
/// Equivalent to:
/// <code>
/// NMathStatsChart.Show( ToChart( dist, function ) );
/// </code>
/// </remarks>
public static void Show( GeometricDistribution dist, DistributionFunction function = DistributionFunction.PDF )
{
Show( ToChart( dist, function ) );
}
/// <summary>
/// Updates the given chart with the specified distribution.
/// </summary>
/// <param name="chart">A chart.</param>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <param name="numInterpolatedValues">The number of interpolated values.</param>
/// <returns>A new chart.</returns>
/// <remarks>
/// Plots the specified function of the given distribution for 0.0001 <= p <= 0.9999.
/// <br/>
/// Titles are added only if chart does not currently contain any titles.
/// <br/>
/// chart.Series[0] is replaced, or added if necessary.
/// </remarks>
public static void Update( ref ChartControl chart, GammaDistribution dist, DistributionFunction function = DistributionFunction.PDF, int numInterpolatedValues = 100 )
{
List<string> titles = new List<string>()
{
"GammaDistribution",
String.Format("\u03B1={0}, \u03B2={1}", dist.Alpha, dist.Beta)
};
UpdateContinuousDistribution( ref chart, dist, titles, function, numInterpolatedValues );
}
/// <summary>
/// Updates the given chart with the specified distribution.
/// </summary>
/// <param name="chart">A chart.</param>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <param name="numInterpolatedValues">The number of interpolated values.</param>
/// <returns>A new chart.</returns>
/// <remarks>
/// Plots the specified function of the given distribution for 0.0001 <= p <= 0.9999.
/// <br/>
/// Titles are added only if chart does not currently contain any titles.
/// <br/>
/// chart.Series[0] is replaced, or added if necessary.
/// </remarks>
public static void Update( ref ChartControl chart, TDistribution dist, DistributionFunction function = DistributionFunction.PDF, int numInterpolatedValues = 100 )
{
List<string> titles = new List<string>()
{
"TDistribution",
String.Format("df={0}", dist.DegreesOfFreedom)
};
UpdateContinuousDistribution( ref chart, dist, titles, function, numInterpolatedValues );
}
/// <summary>
/// Updates the given chart with the specified distribution.
/// </summary>
/// <param name="chart">A chart.</param>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <returns>A new chart.</returns>
/// <remarks>
/// Plots the specified function of the given distribution for 0.0001 <= p <= 0.9999.
/// <br/>
/// Titles are added only if chart does not currently contain any titles.
/// <br/>
/// chart.Series[0] is replaced, or added if necessary.
/// </remarks>
public static void Update( ref ChartControl chart, PoissonDistribution dist, DistributionFunction function = DistributionFunction.PDF )
{
List<string> titles = new List<string>()
{
"PoissonDistribution",
String.Format("\u03BB={0}", dist.Mean)
};
UpdateDiscreteDistribution( ref chart, dist, titles, function );
}
/// <summary>
/// Updates the given chart with the specified distribution.
/// </summary>
/// <param name="chart">A chart.</param>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <param name="numInterpolatedValues">The number of interpolated values.</param>
/// <returns>A new chart.</returns>
/// <remarks>
/// Plots the specified function of the given distribution for 0.0001 <= p <= 0.9999.
/// <br/>
/// Titles are added only if chart does not currently contain any titles.
/// <br/>
/// chart.Series[0] is replaced, or added if necessary.
/// </remarks>
public static void Update( ref ChartControl chart, NormalDistribution dist, DistributionFunction function = DistributionFunction.PDF, int numInterpolatedValues = 100 )
{
List<string> titles = new List<string>()
{
"NormalDistribution",
String.Format("\u03BC={0}, \u03C3\u00B2={1}", dist.Mean, dist.Variance)
};
UpdateContinuousDistribution( ref chart, dist, titles, function, numInterpolatedValues );
}
/// <summary>
/// Updates the given chart with the specified distribution.
/// </summary>
/// <param name="chart">A chart.</param>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <returns>A new chart.</returns>
/// <remarks>
/// Plots the specified function of the given distribution for 0.0001 <= p <= 0.9999.
/// <br/>
/// Titles are added only if chart does not currently contain any titles.
/// <br/>
/// chart.Series[0] is replaced, or added if necessary.
/// </remarks>
public static void Update( ref ChartControl chart, NegativeBinomialDistribution dist, DistributionFunction function = DistributionFunction.PDF )
{
List<string> titles = new List<string>()
{
"NegativeBinomialDistribution",
String.Format("n={0}, p={1}", dist.N, dist.P)
};
UpdateDiscreteDistribution( ref chart, dist, titles, function );
}
/// <summary>
/// Updates the given chart with the specified distribution.
/// </summary>
/// <param name="chart">A chart.</param>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <param name="numInterpolatedValues">The number of interpolated values.</param>
/// <returns>A new chart.</returns>
/// <remarks>
/// Plots the specified function of the given distribution for 0.0001 <= p <= 0.9999.
/// <br/>
/// Titles are added only if chart does not currently contain any titles.
/// <br/>
/// chart.Series[0] is replaced, or added if necessary.
/// </remarks>
public static void Update( ref ChartControl chart, JohnsonDistribution dist, DistributionFunction function = DistributionFunction.PDF, int numInterpolatedValues = 100 )
{
List<string> titles = new List<string>()
{
"JohnsonDistribution",
String.Format("\u03B3={0}, \u03B4={1}, \u03BE={2}, \u03BB={3}", dist.Gamma, dist.Delta, dist.Xi, dist.Lambda)
};
UpdateContinuousDistribution( ref chart, dist, titles, function, numInterpolatedValues );
}
/// <summary>
/// Updates the given chart with the specified distribution.
/// </summary>
/// <param name="chart">A chart.</param>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <returns>A new chart.</returns>
/// <remarks>
/// Plots the specified function of the given distribution for 0.0001 <= p <= 0.9999.
/// <br/>
/// Titles are added only if chart does not currently contain any titles.
/// <br/>
/// chart.Series[0] is replaced, or added if necessary.
/// </remarks>
public static void Update( ref ChartControl chart, GeometricDistribution dist, DistributionFunction function = DistributionFunction.PDF )
{
List<string> titles = new List<string>()
{
"GeometricDistribution",
String.Format("p={0}", dist.P)
};
UpdateDiscreteDistribution( ref chart, dist, titles, function );
}
/// <summary>
/// Shows a new chart in a default form.
/// </summary>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <param name="numInterpolatedValues">The number of interpolated values.</param>
/// <remarks>
/// Equivalent to:
/// <code>
/// NMathStatsChart.Show( ToChart( dist, function, numInterpolatedValues ) );
/// </code>
/// </remarks>
public static void Show( WeibullDistribution dist, DistributionFunction function = DistributionFunction.PDF, int numInterpolatedValues = 100 )
{
Show( ToChart( dist, function, numInterpolatedValues ) );
}
/// <summary>
/// Updates the given chart with the specified distribution.
/// </summary>
/// <param name="chart">A chart.</param>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <param name="numInterpolatedValues">The number of interpolated values.</param>
/// <returns>A new chart.</returns>
/// <remarks>
/// Plots the specified function of the given distribution for 0.0001 <= p <= 0.9999.
/// <br/>
/// Titles are added only if chart does not currently contain any titles.
/// <br/>
/// chart.Series[0] is replaced, or added if necessary.
/// </remarks>
public static void Update( ref ChartControl chart, UniformDistribution dist, DistributionFunction function = DistributionFunction.PDF, int numInterpolatedValues = 100 )
{
List<string> titles = new List<string>()
{
"UniformDistribution",
String.Format("lower={0}, upper={1}", dist.LowerLimit, dist.UpperLimit)
};
UpdateContinuousDistribution( ref chart, dist, titles, function, numInterpolatedValues );
}
public override string ToString()
{
return($"Distribution: {DistributionFunction?.GetType()}, Mean: {Mean}, STD: {StDeviation}");
}
/// <summary>
/// Returns a new line chart plotting the specified function of the given distribution for 0.0001 <= p <= 0.9999.
/// </summary>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <param name="numInterpolatedValues">The number of interpolated values.</param>
/// <returns>A new chart.</returns>
public static ChartControl ToChart( WeibullDistribution dist, DistributionFunction function = DistributionFunction.PDF, int numInterpolatedValues = 100 )
{
ChartControl chart = GetDefaultChart();
Update( ref chart, dist, function, numInterpolatedValues );
return chart;
}
/// <summary></summary>
protected static void UpdateContinuousDistribution( ref ChartControl chart, ProbabilityDistribution dist, List<string> titles, DistributionFunction function, int numInterpolatedValues )
{
string xTitle = "x";
string yTitle;
double xmin = dist.InverseCDF( 0.0001 );
double xmax = dist.InverseCDF( 0.9999 );
OneVariableFunction f;
if( function == DistributionFunction.PDF )
{
yTitle = "Probability Density Function";
f = new OneVariableFunction( new Func<double, double> ( delegate( double x ) { return dist.PDF( x ); } ) );
}
else
{
yTitle = "Cumulative Distribution Function";
f = new OneVariableFunction( new Func<double, double> ( delegate( double x ) { return dist.CDF( x ); } ) );
}
ChartSeries series = BindXY( f, xmin, xmax, numInterpolatedValues, ChartSeriesType.Line, ChartSymbolShape.None );
Update( ref chart, series, titles, xTitle, yTitle );
}
/// <summary>
/// Returns a new line chart plotting the specified function of the given distribution for 0.0001 <= p <= 0.9999.
/// </summary>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <returns>A new chart.</returns>
public static ChartControl ToChart( PoissonDistribution dist, DistributionFunction function = DistributionFunction.PDF )
{
ChartControl chart = GetDefaultChart();
Update( ref chart, dist, function );
return chart;
}
/// <summary></summary>
protected static void UpdateDiscreteDistribution( ref ChartControl chart, ProbabilityDistribution dist, List<string> titles, DistributionFunction function )
{
string xTitle = "x";
string yTitle;
int xmin = (int)Math.Floor( dist.InverseCDF( 0.0001 ) );
int xmax = (int)Math.Ceiling( dist.InverseCDF( 0.9999 ) );
DoubleVector x = new DoubleVector( xmax - xmin + 1, xmin, 1 );
DoubleVector y;
if( function == DistributionFunction.PDF )
{
yTitle = "Probability Mass Function";
y = x.Apply( new Func<double, double>( dist.PDF ) );
}
else
{
yTitle = "Cumulative Distribution Function";
y = x.Apply( new Func<double, double>( dist.CDF ) );
}
ChartSeries series = BindXY( x, y, ChartSeriesType.Column, ChartSymbolShape.None );
Update( ref chart, series, titles, xTitle, yTitle );
}
/// <summary>
/// Updates the given chart with the specified distribution.
/// </summary>
/// <param name="chart">A chart.</param>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <param name="numInterpolatedValues">The number of interpolated values.</param>
/// <returns>A new chart.</returns>
/// <remarks>
/// Plots the specified function of the given distribution for 0.0001 <= p <= 0.9999.
/// <br/>
/// Titles are added only if chart does not currently contain any titles.
/// <br/>
/// chart.Series[0] is replaced, or added if necessary.
/// </remarks>
public static void Update( ref ChartControl chart, WeibullDistribution dist, DistributionFunction function = DistributionFunction.PDF, int numInterpolatedValues = 100 )
{
List<string> titles = new List<string>()
{
"WeibullDistribution",
String.Format("scale={0}, shape={1}", dist.Scale, dist.Shape)
};
UpdateContinuousDistribution( ref chart, dist, titles, function, numInterpolatedValues );
}
/// <summary>
/// Updates the given chart with the specified distribution.
/// </summary>
/// <param name="chart">A chart.</param>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <param name="numInterpolatedValues">The number of interpolated values.</param>
/// <returns>A new chart.</returns>
/// <remarks>
/// Plots the specified function of the given distribution for 0.0001 <= p <= 0.9999.
/// <br/>
/// Titles are added only if chart does not currently contain any titles.
/// <br/>
/// chart.Series[0] is replaced, or added if necessary.
/// </remarks>
public static void Update( ref ChartControl chart, ExponentialDistribution dist, DistributionFunction function = DistributionFunction.PDF, int numInterpolatedValues = 100 )
{
List<string> titles = new List<string>()
{
"ExponentialDistribution",
String.Format("\u03BB={0}", dist.Lambda)
};
UpdateContinuousDistribution( ref chart, dist, titles, function, numInterpolatedValues );
}