/// <summary>
/// Returns a universal threshold which is used to zero small or insignificant wavelet coefficients.
/// See pages 15 & 16 of "Wavelets for kids"!!
/// The coefficients should be derived from the bottom row of the WPD tree.
/// I think n = the level number of the coefficients being thresholded.
/// In other words, the standard deviation is calculated from the bottom row of coeficients but is increased for the higher rows.
/// THis is because the coefficients in the lower rows have a lower SNR.
/// </summary>
/// <param name="n">level number</param>
/// <param name="coefficients"></param>
/// <returns></returns>
public static double CalculateUniversalThreshold(int n, double[] coefficients)
{
double factor = Math.Sqrt(2 * Math.Log10(n));
NormalDist.AverageAndSD(coefficients, out var av, out var sd);
return(factor * sd);
}
}// CrossCorrelation()
// =============================================================================
/// <summary>
/// Pearsons correlation coefficient.
/// Equals the covariance normalised by the sd's.
/// </summary>
/// <param name="seriesX"></param>
/// <param name="seriesY"></param>
/// <returns></returns>
public static double CorrelationCoefficient(double[] seriesX, double[] seriesY)
{
NormalDist.AverageAndSD(seriesX, out var meanX, out var sdX);
NormalDist.AverageAndSD(seriesX, out var meanY, out var sdY);
double covar = 0.0;
for (int i = 0; i < seriesX.Length; i++)
{
covar += (seriesX[i] - meanX) * (seriesY[i] - meanY);
}
covar /= sdX * sdY;
covar /= seriesX.Length - 1;
return(covar);
}
/// <summary>
/// generates numbers 1 - 100.
/// </summary>
public static void GetRandomDistancesInEuclidianSpace(int trialCount, int dimensions)
{
double[] distanceArray = new double[trialCount];
//int seed = 123456;
int seed = (int)DateTime.Now.Ticks;
var rn = new RandomNumber(seed);
for (int i = 0; i < trialCount; i++)
{
double[] v1 = GetRandomVector(dimensions, rn);
double[] v2 = GetRandomVector(dimensions, rn);
distanceArray[i] = DataTools.EuclideanDistance(v1, v2);
}
NormalDist.AverageAndSD(distanceArray, out var av, out var sd);
double[] avAndsd = { av, sd };
Console.WriteLine(NormalDist.formatAvAndSD(avAndsd, 5));
Console.WriteLine("Min --> Max: {0:f3} --> {1:f3}", distanceArray.Min(), distanceArray.Max());
} //GetRandomDistancesInEuclidianSpace()
