/// <summary> Takes a set of normal distributions and computes the probability that each one would produce the minimal value if
/// a point sample was taken from each. Integration is performed by Simpson's 3/8 rule. </summary>
/// <param name="distributions">The array of distributions to compare</param>
/// <param name="iterations">The number of iterations to use in Simpson's 3/8 Rule. Defaults to 150.</param>
/// <returns>An array of probabilities that each distribution will produce the minimum value if a point sample was taken from each.
/// [i] = P(X_i less than min(all X_j))</returns>
public static double[] Simpsons38RuleWithoutNegation(Normal[] distributions, int iterations = 150)
{
double[] complementProbs = new double[distributions.Length];
for (int i = 0; i < distributions.Length; i++)
{
Normal distribution_i = distributions[i];
Func <double, double> integrand = x =>
{
double product = distribution_i.Density(x);
for (int j = 0; j < distributions.Length; j++)
{
if (j != i)
{
product *= 1 - distributions[j].CumulativeDistribution(x);
}
}
return(product);
};
complementProbs[i] = NewtonCotes.Simpsons38Rule(integrand,
distribution_i.Mean - 8 * distribution_i.StdDev, distribution_i.Mean + 8 * distribution_i.StdDev, iterations);
//Console.WriteLine($"S38R[{i}]: {complementProbs[i]}");
}
return(complementProbs);
}
// Method for direct computation with gauss legendre
public static double[] ComputeDiscardComplementsGaussLegendre(Normal[] distributions)
{
double[] complementProbs = new double[distributions.Length];
for (int i = 0; i < distributions.Length; i++)
{
Normal distribution_i = distributions[i];
Func <double, double> integrand = x =>
{
double product = distribution_i.Density(x);
for (int j = 0; j < distributions.Length; j++)
{
if (j != i)
{
product *= 1 - distributions[j].CumulativeDistribution(x);
}
}
return(product);
};
complementProbs[i] = MathNet.Numerics.Integration.GaussLegendreRule.Integrate(integrand,
distribution_i.Mean - 8 * distribution_i.StdDev, distribution_i.Mean + 8 * distribution_i.StdDev, 96);
Console.WriteLine($"GL[{i}]: {complementProbs[i]}");
}
return(complementProbs);
}
public static double[] ComputeDiscardComplementsSimpsonAlt(Normal[] distributions, int iterations = 150)
{
double[] complementProbs = new double[distributions.Length];
distributions = NegateDistributions(distributions); // This change is local to this method
for (int i = 0; i < distributions.Length; i++)
{
Normal distribution_i = distributions[i];
Func <double, double> integrand = x =>
{
double product = distribution_i.Density(x);
for (int j = 0; j < distributions.Length; j++)
{
if (j != i)
{
product *= distributions[j].CumulativeDistribution(x);
}
}
return(product);
};
complementProbs[i] = Integration.SimpsonsRule.Integrate(integrand,
distribution_i.Mean - 8 * distribution_i.StdDev, distribution_i.Mean + 8 * distribution_i.StdDev, iterations);
//Console.WriteLine($"S38RAlt[{i}]: {complementProbs[i]}");
}
return(complementProbs);
}
/// <summary>
/// Theta = first derivative of price with respect to time to expiration.
/// </summary>
/// <returns>theta of the option</returns>
public static double BlackScholesTheta(this EuropeanOption option, Date valueDate, double spot, double vol, double rate, double div)
{
var dist = new Normal();
var T = (double)(option._exerciseDate - valueDate) / 365;
double d1 = D1(spot, option._strike, vol, rate, div, T);
double d2 = D2(spot, option._strike, vol, rate, div, T);
double theta;
var flag = (double)option._putOrCall;
double t1 = (Math.Exp(-div * T) * spot * dist.Density(d1) * vol * 0.5) / Math.Sqrt(T);
double t2 = div * Math.Exp(-div * T) * spot * dist.CumulativeDistribution(flag * d1);
double t3 = rate * option._strike * Math.Exp(-rate * T) * dist.CumulativeDistribution(flag * d2);
if (option._putOrCall == PutOrCall.Call)
{
theta = -t1 + t2 - t3;
}
else
{
theta = -t1 - t2 + t3;
}
return(theta);
}
public PointPairList getDensityCurve(IList <double> data, double bandwidth)
{
int intervals = 1000;
var result = new PointPairList {
Capacity = intervals
};
//generate a base line
var statistics = new DescriptiveStatistics(data);
double minValue = data.Min() - (2 * statistics.StandardDeviation);
double maxValue = data.Max() + (2 * statistics.StandardDeviation);
double interval = (maxValue - minValue) / intervals * 1.0;
for (int i = 0; i < intervals; i++)
{
result.Add(minValue + i * interval, 0);
}
if (bandwidth == 0)
{
bandwidth = 1.06 * statistics.StandardDeviation * Math.Pow(data.Count, -1.0 / 5);
}
var orderedData = data.OrderBy(o => o);
foreach (var value in orderedData)
{
Normal nD = new Normal(0, 1);
for (int q = 0; q < intervals; q++)
{
result[q].Y += (1 / (data.Count * bandwidth)) * nD.Density((value - result[q].X) / bandwidth);
}
}
return(result);
}
// Method with alt form using gauss legendre
public static double[] ComplementsLegendre(Normal[] distributions, int order)
{
double[] complementProbs = new double[distributions.Length];
distributions = NegateDistributions(distributions); // This change is local to this method
for (int i = 0; i < distributions.Length; i++)
{
Normal distribution_i = distributions[i];
Func <double, double> integrand = x =>
{
double product = distribution_i.Density(x);
for (int j = 0; j < distributions.Length; j++)
{
if (j != i)
{
product *= distributions[j].CumulativeDistribution(x);
}
}
return(product);
};
complementProbs[i] = GaussLegendre.Integrate(integrand,
distribution_i.Mean - 8 * distribution_i.StdDev, distribution_i.Mean + 8 * distribution_i.StdDev, order);
//complementProbs[i] = MathNet.Numerics.Integration.GaussLegendreRule.Integrate(integrand,
// distribution_i.Mean - 8 * distribution_i.StdDev, distribution_i.Mean + 8 * distribution_i.StdDev, 96);
//Console.WriteLine($"GL[{i}]: {complementProbs[i]}");
}
return(complementProbs);
}
/// <summary>
/// Imputes missing intensity value for each protein
/// </summary>
private void ImputeData(ProteinRowInfo proteinRowInfo, double[] samplesMeanIntensityValue, double[] samplesStandardDeviation,
List <string> samplesFileNames, double[] missingFactor, int[] numberOfIntensityValuesInSample, double meanFraction)
{
Dictionary <string, double> samplesintensityData = proteinRowInfo.SamplesIntensityData;
for (int i = 0; i < samplesFileNames.Count; i++)
{
if (samplesintensityData[samplesFileNames[i]] == 0)
{
double imputedFraction = missingFactor[i] / (numberOfIntensityValuesInSample[i] + missingFactor[i]);
if (imputedFraction <= 0.5)
{
double imputedProbability = imputedFraction / (1 - imputedFraction);
double standardDeviationFraction = Math.Max(2 * imputedFraction, 0.3);
double stdDevFraction = 0.6 * (1 - (imputedFraction * imputedFraction));
Normal probabilityDist = new Normal(samplesMeanIntensityValue[i], standardDeviationFraction);
double probabilitySetPoint = probabilityDist.Density(samplesMeanIntensityValue[i] + stdDevFraction * standardDeviationFraction);
double yCoordinate = imputedProbability * probabilitySetPoint;
double deltaX = standardDeviationFraction * stdDevFraction;
Normal xCoord = new Normal(samplesMeanIntensityValue[i], samplesStandardDeviation[i]);
double deltaMu = xCoord.InverseCumulativeDistribution(yCoordinate);
double meanDownshift = (deltaMu - deltaX * meanFraction);
Normal normalDist = new Normal(meanDownshift, standardDeviationFraction);
double imputeVal = normalDist.Sample();
samplesintensityData[samplesFileNames[i]] = imputeVal;
}
}
}
}
public static double[] ComplementsSimpsons38(Normal[] distributions, int steps = 150)
{
if (steps % 3 != 0)
{
steps += 3 - steps % 3; // Round up to a multiple of 3
}
double[] complementProbs = new double[distributions.Length];
distributions = NegateDistributions(distributions); // This change is local to this method
for (int i = 0; i < distributions.Length; i++)
{
Normal distribution_i = distributions[i];
Func <double, double> integrand = x =>
{
double product = distribution_i.Density(x);
for (int j = 0; j < distributions.Length; j++)
{
if (j != i)
{
product *= distributions[j].CumulativeDistribution(x);
}
}
return(product);
};
complementProbs[i] = NewtonCotes.Simpsons38Rule(integrand,
distribution_i.Mean - 8 * distribution_i.StdDev, distribution_i.Mean + 8 * distribution_i.StdDev, steps);
//Console.WriteLine($"S38[{i}]: {complementProbs[i]}");
}
return(complementProbs);
}
public void ValidateNormalDensityEquivalence(double location, double scale, double x)
{
var sgt = new SkewedGeneralizedT(location, scale, 0, 2, double.PositiveInfinity);
var n = new Normal(location, scale);
AssertHelpers.AlmostEqualRelative(n.Density(x), sgt.Density(x), 8);
AssertHelpers.AlmostEqualRelative(n.DensityLn(x), sgt.DensityLn(x), 8);
}
/// <summary>
/// Runs a playout with two given controllers and reports the result.
/// </summary>
public static PlayoutResult Playout(GameInstance game, IMobController ai1, IMobController ai2)
{
var hub = new GameEventHub(game);
game.MobManager.Teams[TeamColor.Red] = ai1;
game.MobManager.Teams[TeamColor.Blue] = ai2;
const int maxIterations = 100;
int i = 0;
for (; i < maxIterations && !game.IsFinished; i++)
{
game.CurrentController.FastPlayTurn(hub);
ActionEvaluator.FNoCopy(game, UctAction.EndTurnAction());
}
float totalMaxHp = 0;
float totalCurrentHp = 0;
foreach (var mobId in game.MobManager.Mobs)
{
totalMaxHp += game.MobManager.MobInfos[mobId].MaxHp;
totalCurrentHp += Math.Max(0, game.State.MobInstances[mobId].Hp);
}
int red = 0;
int blue = 0;
Utils.Log(LogSeverity.Error, nameof(GameEvaluator),
$"Playout time limit reached at {maxIterations} rounds");
if (i < maxIterations && game.VictoryTeam.HasValue)
{
if (game.VictoryTeam.Value == TeamColor.Red)
{
red++;
}
else
{
blue++;
}
Accounting.IncrementWinner(game.VictoryController);
}
var gamePercentage = totalCurrentHp / totalMaxHp;
Debug.Assert(gamePercentage >= 0);
var mobsCount = game.MobManager.Mobs.Count;
var dis = new Normal(mobsCount * 2, mobsCount);
dis.Density(mobsCount * 2);
return(new PlayoutResult(i, gamePercentage, game.State.AllPlayed, i == maxIterations, red, blue));
}
public double GetNextProbability(int currentTick)
{
if (currentTick > (round + 1) * totalTicks)
{
//we start over.
round++;
}
return(normalDis.Density(currentTick - (round * totalTicks)));
}
/// <summary>
/// Vega = first derivative of price with respect to volatility.
/// </summary>
/// <returns>vega of the option</returns>
public static double BlackScholesVega(this EuropeanOption option, Date valueDate, double spot, double vol, double rate, double div)
{
var dist = new Normal();
var T = (double)(option._exerciseDate - valueDate) / 365;
double d1 = D1(spot, option._strike, vol, rate, div, T);
double vega;
vega = spot * Math.Exp(-div * T) * dist.Density(d1) * Math.Sqrt(T);
return(vega);
}
float calcSpeed(float angle_in)
{
// angle convert to speed
// angle: 1.2 ~ 3
// mean can set to 3
// standard deviation set to 1.2 with 1.2~3 as 1.5theta
Normal speed_pdf = new Normal(30, 2);
// input given and get the probability density(PDF)
double speed_out = speed_pdf.Density(10 * (double)angle_in);
//Debug.Log("angle_in" + angle_in);
//Debug.Log("speed_out: " + speed_out);
return((float)speed_out);
}
/// <summary>
/// Truncated N(0, 1) to (x1, x2), where P(X <= x1) = trim and P(X <= x2) = 1 - trim
/// </summary>
/// <param name="trim">tail probability</param>
/// <returns>approximately (E[X^2] = 1) / Et[X^2]</returns>
private static double InflationFactor(double trim)
{
var norm = new Normal(); // N(0, 1)
double a = norm.InverseCumulativeDistribution(1 - trim);
double step = 2 * a / 10000;
double[] x1s = Helper.Seq(-a + step / 2, a - step / 2, 10000);
// Truncated N(0, 1) to P(X <= x) = trim and P(X <= x) = 1 - trim
double eX2 = 0.0;
foreach (double x1 in x1s)
{
eX2 += (x1 * x1) * norm.Density(x1);
}
eX2 = eX2 * step / (1 - 2 * trim);
// eX2 now approximates Et[X^2]: E[X^2] of the truncated N(0, 1)
return(1 / eX2); // approx (E[X^2] = 1) / Et[X^2]
// == 1 / (1 + (-a * dnorm(-a) - a * dnorm(a)) / (1 - 2*trim) - ((dnorm(-1) - dnorm(a)) / (1 - 2* trim))^2)
// According to http://en.wikipedia.org/wiki/Truncated_normal_distribution
}
public int EstimateOverTime(int estimatedtime)
{
double mean = estimatedtime;
MathNet.Numerics.Distributions.Normal normalDist = new Normal(mean, _std);
double d = mean + 1.0;
double sum = 0;
while (true)
{
double density = normalDist.Density(d);
if (density < 1e-10)
{
break;
}
sum += d * density;
d = d + 1.0;
}
sum = Math.Round(sum, 0);
return((int)sum);
}
/// <summary> Uses Gauss-Hermite quadrature on the alternative integral form with an invariant to compute the probability that each of the distributions is the minimum </summary>
/// <param name="distributions"> The set of distributions to consider </param>
/// <param name="evalPoints"> The set of evaluation points </param>
/// <param name="weights"> The set of weights, in the same order as the eval points </param>
/// <returns> An array of probabilities indexed to match the distribution array </returns>
/// <remarks> This will require up to 3NV special function evaluations, where N is the number of distributions and V is the number of evaluation points. </remarks>
public static double[] ComputeDiscardComplementsGaussHermiteAltInvariant(Normal[] distributions, double[] evalPoints, double[] weights)
{
if (evalPoints.Length != weights.Length)
{
throw new ArgumentException("Error: Evaluation points must have same length as weights.");
}
distributions = NegateDistributions(distributions); // This change is local to this method
// Compute the interval of integration
double minMean = distributions[0].Mean;
double maxMean = distributions[0].Mean;
double maxStdev = 0;
for (int i = 0; i < distributions.Length; i++)
{
if (distributions[i].Mean < minMean)
{
minMean = distributions[i].Mean;
}
if (distributions[i].Mean > maxMean)
{
maxMean = distributions[i].Mean;
}
if (distributions[i].StdDev > maxStdev)
{
maxStdev = distributions[i].StdDev;
}
}
//double a = (minMean + maxMean) / 2; // Original
double a = maxMean;
//double b = (maxMean - minMean) / Math.Sqrt(2); // Original
//double b = Math.Sqrt(2) * Math.Min((maxMean - minMean) / 2, maxStdev); // Worse
double b = Math.Sqrt(2) * Math.Min(maxMean, maxStdev); // Better than original
Normal U = new Normal(a, b); // Original
//Normal U = new Normal(a, Math.Min((maxMean - minMean) / 2, maxStdev)); // Worse
//Normal U = new Normal(a, Math.Min(maxMean, maxStdev)); // Better than the original
// Compute the change of variable function
Func <double, double> xOfz = z => b * z + a;
// Compute the vector of constants
double[] C = new double[evalPoints.Length];
double[] X = new double[evalPoints.Length];
for (int i = 0; i < C.Length; i++)
{
X[i] = xOfz(evalPoints[i]);
C[i] = weights[i] / U.Density(X[i]);
for (int j = 0; j < distributions.Length; j++)
{
C[i] *= distributions[j].CumulativeDistribution(X[i]);
}
}
// --- Perform the Integration ---
double[] complementProbs = new double[distributions.Length];
for (int i = 0; i < distributions.Length; i++)
{
complementProbs[i] = 0;
for (int j = 0; j < C.Length; j++)
{
double CDFij = distributions[i].CumulativeDistribution(X[j]);
if (CDFij > 0)
{
complementProbs[i] += distributions[i].Density(X[j]) * C[j] / CDFij;
}
}
complementProbs[i] /= Math.Sqrt(Math.PI);
Console.WriteLine($"GHAltInv[{i}]: {complementProbs[i]}");
}
return(complementProbs);
}
/// <summary>
/// Run example
/// </summary>
/// <a href="http://en.wikipedia.org/wiki/Normal_distribution">Normal distribution</a>
public void Run()
{
// 1. Initialize the new instance of the Normal distribution class with parameters Mean = 0, StdDev = 1
var normal = new Normal(0, 1);
Console.WriteLine(@"1. Initialize the new instance of the Normal distribution class with parameters Mean = {0}, StdDev = {1}", normal.Mean, normal.StdDev);
Console.WriteLine();
// 2. Distributuion properties:
Console.WriteLine(@"2. {0} distributuion properties:", normal);
// Cumulative distribution function
Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", normal.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000"));
// Probability density
Console.WriteLine(@"{0} - Probability density at location '0.3'", normal.Density(0.3).ToString(" #0.00000;-#0.00000"));
// Log probability density
Console.WriteLine(@"{0} - Log probability density at location '0.3'", normal.DensityLn(0.3).ToString(" #0.00000;-#0.00000"));
// Entropy
Console.WriteLine(@"{0} - Entropy", normal.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
Console.WriteLine(@"{0} - Largest element in the domain", normal.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
Console.WriteLine(@"{0} - Smallest element in the domain", normal.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
Console.WriteLine(@"{0} - Mean", normal.Mean.ToString(" #0.00000;-#0.00000"));
// Median
Console.WriteLine(@"{0} - Median", normal.Median.ToString(" #0.00000;-#0.00000"));
// Mode
Console.WriteLine(@"{0} - Mode", normal.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
Console.WriteLine(@"{0} - Variance", normal.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
Console.WriteLine(@"{0} - Standard deviation", normal.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
Console.WriteLine(@"{0} - Skewness", normal.Skewness.ToString(" #0.00000;-#0.00000"));
Console.WriteLine();
// 3. Generate 10 samples
Console.WriteLine(@"3. Generate 10 samples");
for (var i = 0; i < 10; i++)
{
Console.Write(normal.Sample().ToString("N05") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Generate 100000 samples of the Normal(0, 1) distribution and display histogram
Console.WriteLine(@"4. Generate 100000 samples of the Normal(0, 1) distribution and display histogram");
var data = new double[100000];
for (var i = 0; i < data.Length; i++)
{
data[i] = normal.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 5. Generate 100000 samples of the Normal(-10, 0.2) distribution and display histogram
Console.WriteLine(@"5. Generate 100000 samples of the Normal(-10, 0.01) distribution and display histogram");
normal.Mean = -10;
normal.StdDev = 0.01;
for (var i = 0; i < data.Length; i++)
{
data[i] = normal.Sample();
}
ConsoleHelper.DisplayHistogram(data);
}
public IEnumerable <double> SolveOptimizationProblemWithOutliersFiltering(out List <List <double> > parametersHistory, out List <List <SpacePointsType> > filteredEventsListsHistory, double precision = 1.0e-8d)
{
parametersHistory = new List <List <double> >();
filteredEventsListsHistory = new List <List <SpacePointsType> >();
int startingEventsSetLength = mEventsSpaceVector.Count();
int prevEventsSetLength = mEventsSpaceVector.Count();
int newEventsSetLength = mEventsSpaceVector.Count();
int epoch = 0;
bool success = false;
while (!success)
{
nParametersSpacePoint = SolveOptimizationProblem(precision);
parametersHistory.Add(nParametersSpacePoint.ToList());
// find outliers indexes
List <double> funcDevVector = this.ObjectiveDeviations(nParametersSpacePoint).ToList();
#region debugging presentations
#if DEBUG
//HistogramDataAndProperties hist = new HistogramDataAndProperties(
// DenseVector.OfEnumerable(funcDevVector), 50);
//HistogramCalcAndShowForm histForm = new HistogramCalcAndShowForm("", null);
//histForm.HistToRepresent = hist;
//histForm.Represent();
//histForm.SaveToImage("D:\\_gulevlab\\SkyImagesAnalysis_appData\\RV-ANS-31-test\\hist_" + epoch.ToString("D3") + ".jpg");
#endif
#endregion debugging presentations
List <bool> lIsOutlier = mEventsSpaceVector.ToList().ConvertAll <bool>(val => false);
Normal normDistrib = Normal.Estimate(funcDevVector, null);
lIsOutlier = funcDevVector.ConvertAll <bool>(devVal => normDistrib.Density(devVal) <= 0.2d * normDistrib.Density(normDistrib.Mean));
#region DEBUG: manually set 0.03 fraction of set to true
//List<int> lOutliersIndexes = RandPerm(mEventsSpaceVector.Count()).ToList();
//int maxOutlierPosition = Convert.ToInt32(Math.Floor(0.03d*lOutliersIndexes.Count) + 1);
//for (int i = 0; i < maxOutlierPosition; i++)
//{
// lIsOutlier[lOutliersIndexes[i]] = true;
//}
#endregion DEBUG: manually set 0.03 fraction of set to true
// filter outliers
mEventsSpaceVector = new List <SpacePointsType>(mEventsSpaceVector.Where((val, idx) => !lIsOutlier[idx]));
mFittingValuesVector = new List <double>(mFittingValuesVector.Where((val, idx) => !lIsOutlier[idx]));
filteredEventsListsHistory.Add(mEventsSpaceVector.ToList());
newEventsSetLength = mEventsSpaceVector.Count();
if ((double)Math.Abs(newEventsSetLength - prevEventsSetLength) / (double)prevEventsSetLength <= 0.005)
{
success = true;
epoch++;
#region debugging presentations
#if DEBUG
//hist = new HistogramDataAndProperties(DenseVector.OfEnumerable(funcDevVector), 50);
//histForm.HistToRepresent = hist;
//histForm.Represent();
//histForm.SaveToImage("D:\\_gulevlab\\SkyImagesAnalysis_appData\\RV-ANS-31-test\\hist_" + epoch.ToString("D3") + ".jpg");
#endif
#endregion debugging presentations
}
prevEventsSetLength = newEventsSetLength;
epoch++;
}
return(nParametersSpacePoint);
}
public static void TestNumericalIntegration(Random rand)
{
BogaertGLWrapper.Initialize();
/*
* double[] nodesAndWeightsRaw = BogaertGLWrapper.GetGLNodesAndWeights(10000000);
*
* // Count how many can be culled
* int count = 0;
* for (int i = 0; i < nodesAndWeightsRaw.Length / 2; i++)
* {
* double x = nodesAndWeightsRaw[2 * i];
* double w = nodesAndWeightsRaw[2 * i + 1];
* if (x < 0 && w * Normal.CDF(0, 1.0 / 8, x) < 10E-18) { count++; }
* else if (x > 0 && w * Normal.PDF(0, 1.0 / 8, x) < 10E-18) { count++; }
* }
* Console.WriteLine($"Could cull {count} out of {nodesAndWeightsRaw.Length / 2} evaluation points.");
*
* Console.ReadKey();
*/
// Parameters
int numberOfDistributions = 20;
double minMeanFitness = 8;
double maxMeanFitness = 60;
double minStDev = 6;
double maxStDev = 25;
// Computed values
double fitnessRange = maxMeanFitness - minMeanFitness;
double stDevRange = maxStDev - minStDev;
// Set up the distributions and pick the one with the biggest mean to be i
Normal[] distributions = new Normal[numberOfDistributions];
Normal distribution_i = new Normal();
double minMean = -1 * minMeanFitness, maxMean = -1 * maxMeanFitness; // Starting points for finding min and max in the set (not an error)
for (int i = 0; i < distributions.Length; i++)
{
distributions[i] = new Normal(-1 * (minMeanFitness + fitnessRange * rand.NextDouble()), minStDev + stDevRange * rand.NextDouble());
if (distributions[i].Mean > maxMean)
{
maxMean = distributions[i].Mean;
}
if (distributions[i].Mean < minMean)
{
minMean = distributions[i].Mean; distribution_i = distributions[i];
}
Console.WriteLine($"Dist {i}: mean {distributions[i].Mean}, stdev {distributions[i].StdDev}");
}
Func <double, double> altForm = x =>
{
double cdfi = distribution_i.CumulativeDistribution(x);
if (cdfi == 0 || double.IsNaN(cdfi))
{
return(0);
}
double product = distribution_i.Density(x) / cdfi;
for (int i = 0; i < distributions.Length; i++)
{
product *= distributions[i].CumulativeDistribution(x);
}
return(product);
};
/*
* double correctResult = SimpsonsRule.Integrate(altForm, minMean - 3 * maxStDev, maxMean + 3 * maxStDev, 600);
* Console.WriteLine($"Simp 3/8 (600): 1 - P(D_i) = {correctResult}");
*
* double gaussLegendreResult = MathNet.Numerics.Integration.GaussLegendreRule.Integrate(altForm, minMean - 3 * maxStDev, maxMean + 3 * maxStDev, 128);
* Console.WriteLine($"Gauss-Legendre 128: 1 - P(D_i) = {gaussLegendreResult}");
*/
double[] discardProbs = new double[distributions.Length];
/*
* for (int i = 0; i < distributions.Length; i++)
* {
* distribution_i = distributions[i];
* discardProbs[i] = SimpsonsRule.Integrate(altForm, minMean - 8 * maxStDev, maxMean + 8 * maxStDev, 1500);
* Console.WriteLine($"Simp 3/8 (1500): 1 - P(D_{i}) = {discardProbs[i]}");
* }*/
List <double> discardProbList = new List <double>(discardProbs);
discardProbList.Sort();
double sum = 0;
for (int i = 0; i < discardProbList.Count; i++)
{
//Console.WriteLine($"Sorted: {discardProbList[i]}");
sum += discardProbList[i];
}
// Console.WriteLine($"Sum of probabilities is {sum}");
/*
* NormalComparison.ComputeDiscardComplementsSimpson(distributions);
* NormalComparison.ComputeDiscardComplementsGaussHermite(distributions);
* NormalComparison.ComputeDiscardComplementsGaussLegendre(distributions);
* NormalComparison.ComputeDiscardComplementsSimpsonAlt(distributions);
* NormalComparison.ComputeDiscardComplementsGaussHermiteAlt(distributions);
* NormalComparison.ComputeDiscardComplementsGaussLegendreAlt(distributions);
*/
List <double> output;
sum = 0;
output = new List <double>(NormalComparison.ComputeDiscardComplementsSimpson38AltInvariant(distributions, 450));
output.Sort();
for (int i = 0; i < output.Count; i++)
{
sum += output[i];
}
Console.WriteLine($"Sum of probabilities is {sum}");
/*
* Console.WriteLine($"Dist 1 : 1/sqrt3 & 2 : 1/sqrt3");
* distributions = new Normal[] { new Normal(1, 1.0/Math.Sqrt(3)), new Normal(2, 1.0/ Math.Sqrt(3)) };
* Console.WriteLine($"Exact = {NormalComparison.ComputeDiscardProbabilityPairwiseExact(distributions[0], distributions[1])}");
* NormalComparison.ComputeDiscardComplementsGaussLegendreAlt(distributions);
* NormalComparison.ComputeDiscardComplementsSimpson38AltInvariant(distributions, 210);
* Console.WriteLine($"4 Dists 1 : 1 & 2 : 1");
* distributions = new Normal[10];
* for (int i = 0; i < distributions.Length - 1; i++) { distributions[i] = new Normal(1, 1); }
* distributions[distributions.Length - 1] = new Normal(2, 1);
*/
/*
* NormalComparison.ComputeDiscardComplementsGaussLegendreAlt(distributions);
* output = new List<double>(NormalComparison.ComputeDiscardComplementsSimpson38AltInvariant(distributions, 210));
* output.Sort();
* sum = 0;
* for (int i = 0; i < output.Count; i++)
* {
* sum += output[i];
* }
* Console.WriteLine($"Sum of probabilities is {sum}");
*/
output = new List <double>(NormalComparison.ComputeDiscardComplementsGaussLegendreAltInvariant(distributions, GaussLegendre.evalPoints75opt, GaussLegendre.weights75opt));
output.Sort();
sum = 0;
for (int i = 0; i < output.Count; i++)
{
sum += output[i];
}
Console.WriteLine($"Sum of probabilities is {sum}");
output = new List <double>(NormalComparison.ComputeDiscardComplementsGaussHermiteAltInvariant(distributions, GaussHermite.evaluationPoints70opt, GaussHermite.weights70opt));
output.Sort();
sum = 0;
for (int i = 0; i < output.Count; i++)
{
sum += output[i];
}
Console.WriteLine($"Sum of probabilities is {sum}");
output = new List <double>(NormalComparison.ComputeDiscardComplementsClenshawCurtisAltInvariant(distributions, 450));
output.Sort();
sum = 0;
for (int i = 0; i < output.Count; i++)
{
sum += output[i];
}
Console.WriteLine($"Sum of probabilities is {sum}");
System.Diagnostics.Stopwatch watch = new System.Diagnostics.Stopwatch();
watch.Start();
double[] bigTest = NormalComparison.ComputeDiscardComplementsClenshawCurtisAltInvariantAutomatic(distributions);
watch.Stop();
sum = 0;
for (int i = 0; i < bigTest.Length; i++)
{
//Console.WriteLine($"CCAltInvAuto[{i}]: {bigTest[i]}");
sum += bigTest[i];
}
Console.WriteLine($"Sum of probabilities is {sum}");
Console.WriteLine($"Total Error lower bound: {Math.Abs(sum - 1)}");
Console.WriteLine($"Time: {watch.Elapsed.TotalMilliseconds}ms");
discardProbList = new List <double>(bigTest);
discardProbList.Sort();
{
double certainty = 1;
int idx = 0;
while (true)
{
double newval = certainty - discardProbList[idx];
if (newval < 0.95)
{
break;
}
certainty = newval;
idx++;
}
Console.WriteLine($"Can discard {idx} distributions with 95% certainty");
}
watch.Restart();
bigTest = NormalComparison.ComputeDiscardComplementsSimpson38AltInvariantAutomatic(distributions);
watch.Stop();
output = new List <double>(bigTest);
output.Sort();
sum = 0;
for (int i = 0; i < output.Count; i++)
{
sum += output[i];
}
Console.WriteLine($"S38 Sum of probabilities is {sum}");
Console.WriteLine($"S38 Time: {watch.Elapsed.TotalMilliseconds}ms");
}
public void UpdateDistributionChart(CartesianChart inChart, List <double> inVals)
{
// Clears the chart's X Labels
inChart.AxisX[0].Labels.Clear();
ColumnSeries colSeries = inChart.Series.FirstOrDefault(a => a is ColumnSeries) as ColumnSeries;
// Clears the chart's Series' data
colSeries.Values.Clear();
// Nothing in the list
if (inVals.Count < 2) // 0 or 1
{
// Hides the chart.
inChart.Visibility = Visibility.Hidden;
return;
}
double mean = inVals.Mean();
double stDev = inVals.StandardDeviation();
double max = inVals.Max();
double min = inVals.Min();
if (double.IsNaN(mean) || double.IsNaN(stDev) || max == min)
{
// Hides the chart.
inChart.Visibility = Visibility.Hidden;
return;
}
// Displays the chart
inChart.Visibility = Visibility.Visible;
double fullRange = max - min;
int colDivs = 20;
Dictionary <double, int> colValDict = new Dictionary <double, int>();
// Initializes the dictionary
for (int i = 0; i < colDivs; i++)
{
double rMin = min + ((fullRange / colDivs) * (double)i);
double rMax = min + ((fullRange / colDivs) * (double)(i + 1));
double rMid = ((rMax - rMin) / 2d) + rMin;
colValDict.Add(rMid, 0);
}
// Counts the number of elements in each bracket
foreach (double val in inVals)
{
// Finds the closest column
var kvp = colValDict.AsEnumerable().OrderBy(inPair => Math.Abs(val - inPair.Key)).First();
colValDict[kvp.Key]++;
}
// Sets the labels of the X axis
inChart.AxisX[0].Separator.Step = 1;
inChart.AxisX[0].LabelsRotation = -90d;
((List <string>)inChart.AxisX[0].Labels).AddRange(colValDict.Keys.Select(b => $"{b:+0.0e+00;-0.0e+00;0.0}"));
// Sets the column chart' data
colSeries.Values.AddRange(colValDict.Values.Cast <object>());
// Deletes the previous Normal Distribution Line Data From the Chart
if (inChart.Series.Count > 1)
{
inChart.Series.RemoveAt(1);
}
if (inChart.AxisY.Count > 1)
{
inChart.AxisY.RemoveAt(1);
}
if (inChart.AxisX.Count > 1)
{
inChart.AxisX.RemoveAt(1);
}
// Working with the normal distribution
Normal n = new Normal(mean, stDev);
ChartValues <ObservablePoint> normalValDict = new ChartValues <ObservablePoint>();
// Fills the dictionary
int normCount = (colDivs * 2);
double normStepSize = (max - min) / normCount;
for (int i = 0; i < (normCount + 1); i++)
{
double val = min + normStepSize * i;
normalValDict.Add(new ObservablePoint(val, n.Density(val)));
}
inChart.AxisX.Add(new Axis()
{
//Labels = new List<string>(),
ShowLabels = false,
Separator = new Separator()
{
IsEnabled = false
},
Sections = new SectionsCollection()
{
new AxisSection()
{
Value = mean - stDev,
SectionWidth = stDev,
Fill = new SolidColorBrush()
{
Color = Colors.DarkOrange, Opacity = 0.3
},
//Stroke = new SolidColorBrush(){ Color = Colors.DarkRed, Opacity = 1d},
//StrokeThickness = 2d,
},
new AxisSection()
{
Value = mean + stDev,
SectionWidth = -stDev,
Fill = new SolidColorBrush()
{
Color = Colors.DarkOrange, Opacity = 0.3
},
//Stroke = new SolidColorBrush(){ Color = Colors.DarkRed, Opacity = 1d},
//StrokeThickness = 2d,
},
new AxisSection()
{
Value = mean,
Stroke = new SolidColorBrush()
{
Color = Colors.DarkRed, Opacity = 1d
},
StrokeThickness = 2d,
}
},
MinValue = min,
MaxValue = max,
});
inChart.AxisY.Add(new Axis()
{
Position = AxisPosition.RightTop,
ShowLabels = false,
Separator = new Separator()
{
IsEnabled = false
},
});
inChart.Series.Add(new LineSeries()
{
Values = normalValDict,
PointForeground = AppSS.FirstReferencedWindow.Resources["EmsPanelBorder_Green"] as SolidColorBrush,
Foreground = AppSS.FirstReferencedWindow.Resources["EmsPanelBorder_Green"] as SolidColorBrush,
Stroke = AppSS.FirstReferencedWindow.Resources["EmsPanelBorder_Green"] as SolidColorBrush,
StrokeThickness = 1d,
Fill = new SolidColorBrush()
{
Opacity = 0d
},
PointGeometrySize = 0d,
LineSmoothness = 0.5d,
ScalesYAt = 1,
ScalesXAt = 1,
});
}
