public void build_prob_map()
{
Normal N_x = new Normal(X / 2, STD_X);
Normal N_y = new Normal(Y / 2, STD_Y);
DenseMatrix M_x = new DenseMatrix(Y, X, 0.0);
DenseMatrix M_y = new DenseMatrix(Y, X, 0.0);
DenseVector V_x = new DenseVector(X);
for (int i = 0; i < X; i++)
{
V_x[i] = N_x.Density(i);
}
for (int j = 0; j < Y; j++)
{
M_x.SetRow(j, V_x);
}
DenseVector V_y = new DenseVector(Y);
for (int i = 0; i < Y; i++)
{
V_y[i] = N_y.Density(i);
}
for (int j = 0; j < X; j++)
{
M_y.SetColumn(j, V_y);
}
DenseMatrix MULT = (DenseMatrix)M_x.PointwiseMultiply(M_y);
double s = MULT.Data.Sum();
MULT = (DenseMatrix)MULT.PointwiseDivide(new DenseMatrix(Y, X, s));
//this.dataGridView1.DataSource = MULT;
//Console.WriteLine(MULT.Data.Sum());
PROB_MAP_ORIG = MULT;
s = MULT[Y / 2, X / 2];
MULT = (DenseMatrix)MULT.PointwiseDivide(new DenseMatrix(Y, X, s));
/*
for (int i = 0; i < Y; i++)
{
Console.Write(i + " - ");
for (int j = 0; j < X; j++)
{
Console.Write(MULT[i, j] + " ");
}
Console.WriteLine();
Console.WriteLine();
}
*/
PROB_MAP = MULT;
}
/// <summary>
/// Computes the density of the Student t-distribution.
/// </summary>
/// <param name="x">The location at which to compute the density.</param>
/// <returns>the density at <paramref name="x"/>.</returns>
public double Density(double x)
{
// TODO JVG we can probably do a better job for Cauchy special case
if (_dof >= 1e+8d)
{
return(Normal.Density(_location, _scale, x));
}
var d = (x - _location) / _scale;
return(Math.Exp(SpecialFunctions.GammaLn((_dof + 1.0) / 2.0) - SpecialFunctions.GammaLn(_dof / 2.0))
* Math.Pow(1.0 + (d * d / _dof), -0.5 * (_dof + 1.0))
/ Math.Sqrt(_dof * Math.PI)
/ _scale);
}
/// <summary>
/// Computes the density of the Student t-distribution.
/// </summary>
/// <param name="x">The location at which to compute the density.</param>
/// <returns>the density at <paramref name="x"/>.</returns>
public double Density(double x)
{
// TODO JVG we can probably do a better job for Cauchy special case
if (Double.IsPositiveInfinity(_dof))
{
return(Normal.Density(_location, _scale, x));
}
var d = (x - _location) / _scale;
return(SpecialFunctions.Gamma((_dof + 1.0) / 2.0)
* Math.Pow(1.0 + (d * d / _dof), -0.5 * (_dof + 1.0))
/ SpecialFunctions.Gamma(_dof / 2.0)
/ Math.Sqrt(_dof * Math.PI)
/ _scale);
}
private void disp_button_Click(object sender, EventArgs e)
{
/*
Normal N = new Normal(0.0, 1.0);
DenseVector VALS = new DenseVector(20, 0);
for (int i = -10; i < 10; i++)
{
VALS[i + 10] = N.Density(i);
Console.WriteLine(VALS[i + 10]);
}
*/
/*
//double[] d = new double[]{0,0};
DenseMatrix mu = new DenseMatrix(2, 1, new[] { 0.0, 0.0 });
DenseMatrix K = new DenseMatrix(1, 1, new[] { 1.0 });
DenseMatrix V = new DenseMatrix(2,2, new[] {4.0, 0.0, 0.0, 1.0 });
MatrixNormal mN = new MatrixNormal(mu, V, K);
Console.WriteLine(mu.RowCount);
Console.WriteLine(mu.ColumnCount);
Console.WriteLine(mN.Sample());
Console.WriteLine(mN.Sample());
DenseMatrix sample_pt = new DenseMatrix(2, 1, new[] { 0.0, 0.1 });
double pt = mN.Density(sample_pt);
*/
int M = 150;
int N = 200;
Normal N_x = new Normal(N/2, 50);
Normal N_y = new Normal(M/2, 30);
DenseMatrix M_x = new DenseMatrix(M, N, 0.0);
DenseMatrix M_y = new DenseMatrix(M, N, 0.0);
DenseVector V_x = new DenseVector(N);
for (int i = 0; i < N; i++)
{
V_x[i] = N_x.Density(i);
}
for (int j = 0; j < M; j++)
{
M_x.SetRow(j, V_x);
}
DenseVector V_y = new DenseVector(M);
for (int i = 0; i < M; i++)
{
V_y[i] = N_y.Density(i);
}
for (int j = 0; j < N; j++)
{
M_y.SetColumn(j, V_y);
}
DenseMatrix MULT = (DenseMatrix)M_x.PointwiseMultiply(M_y);
double s = MULT.Data.Sum();
MULT = (DenseMatrix)MULT.PointwiseDivide(new DenseMatrix(M,N,s));
//this.dataGridView1.DataSource = MULT;
//Console.WriteLine(MULT.Data.Sum());
s = MULT[M / 2, N / 2];
MULT = (DenseMatrix)MULT.PointwiseDivide(new DenseMatrix(M, N, s));
/*
for (int i = 0; i < M; i++)
{
Console.Write(i + " - ");
for (int j = 0; j < N; j++)
{
Console.Write(MULT[i, j] + " ");
}
Console.WriteLine();
Console.WriteLine();
}
*/
Console.WriteLine(Environment.ProcessorCount);
}
/// <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
}
/// <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);
}
/// <summary>
/// Sets up A similarity function to indicate correlation
/// </summary>
/// <param name="distance">The distance between two nodes</param>
/// <returns>The data similarity "PDF"</returns>
private double SimilarityPDF(double distance)
{
var Gaussian = new Normal(0, Simulation.Default.Sigma);
double normalizer = Gaussian.Density(0);
return Gaussian.Density(distance) / normalizer;
}
/// <summary>
/// Initializes the Data of the field
/// </summary>
private void Init()
{
//Generate random data to the network. These are partially correlated.
//Console.WriteLine("Initiating Data network..");
var Gaussian = new Normal(Simulation.Default.Data_Initial_Mean, Simulation.Default.Data_Initial_Sigma);
for (int i = 0; i < Data.Length; i++)
{
for (int j = 0; j < Data[i].Length; j++)
{
Data[i][j] = Gaussian.Density(new Random(i * Data[i].Length + j).NextDouble()) / Gaussian.Density(0) * Simulation.Default.Data_Initial_Mean;
}
}
//Setup data correlation changes
//Console.WriteLine("Setting up " + Simulation.Default.Data_Changes + " data changes..");
for (int i = 0; i < Simulation.Default.Data_Changes; i++)
{
GenerateChange();
}
}
public PlotModel createHistogPlotModel(IEnumerable<double> data, String varname)
{
if (data == null)
{
return null;
}
double[] oAr = data.ToArray();
int n = oAr.Length;
if (n < 2)
{
return null;
}
ColumnSeries s2 = new ColumnSeries();
DescriptiveStatistics st = new DescriptiveStatistics(oAr);
double mean = st.Mean;
double dev = st.StandardDeviation;
if (dev <= 0.0)
{
return null;
}
var histog = new Histogram(oAr, 11);
int nc = histog.BucketCount;
Normal dist = new Normal();
Collection<HistogItem> items = new Collection<HistogItem>();
for (int i = 0; i < nc; ++i)
{
HistogItem item = new HistogItem();
var b = histog[i];
double x = (b.LowerBound + b.UpperBound) / 2.0;
String label = String.Format("{0}", myconvert(x));
int nx = (int)(dist.Density((x - mean) / dev) * n);
item.Label = label;
item.Value1 = b.Count;
item.Value2 = nx;
items.Add(item);
}// i
var model = new PlotModel(varname)
{
LegendPlacement = LegendPlacement.Outside,
LegendPosition = LegendPosition.RightTop,
LegendOrientation = LegendOrientation.Vertical
};
// Add the axes, note that MinimumPadding and AbsoluteMinimum should be set on the value axis.
model.Axes.Add(new CategoryAxis { ItemsSource = items, LabelField = "Label" });
model.Axes.Add(new LinearAxis(AxisPosition.Left) { MinimumPadding = 0, AbsoluteMinimum = 0 });
model.Series.Add(new ColumnSeries { Title = varname, ItemsSource = items, ValueField = "Value1" });
model.Series.Add(new ColumnSeries { Title = "DistributionNormale", ItemsSource = items, ValueField = "Value2" });
return model;
}
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;
}