/// Computes the absolute difference between two Gaussians
public static double AbsoluteDifference(GaussianDistribution left, GaussianDistribution right)
{
return Math.Max(
Math.Abs(left.PrecisionMean - right.PrecisionMean),
Math.Sqrt(Math.Abs(left.Precision - right.Precision)));
}
public GaussianDistribution Clone()
{
var result = new GaussianDistribution();
result.Mean = Mean;
result.StandardDeviation = StandardDeviation;
result.Variance = Variance;
result.Precision = Precision;
result.PrecisionMean = PrecisionMean;
return result;
}
public static double LogProductNormalization(GaussianDistribution left, GaussianDistribution right)
{
if ((left.Precision == 0) || (right.Precision == 0))
{
return 0;
}
double varianceSum = left.Variance + right.Variance;
double meanDifference = left.Mean - right.Mean;
double logSqrt2Pi = Math.Log(Math.Sqrt(2*Math.PI));
return -logSqrt2Pi - (Math.Log(varianceSum)/2.0) - (Square(meanDifference)/(2.0*varianceSum));
}
public static double LogRatioNormalization(GaussianDistribution numerator, GaussianDistribution denominator)
{
if ((numerator.Precision == 0) || (denominator.Precision == 0))
{
return 0;
}
double varianceDifference = denominator.Variance - numerator.Variance;
double meanDifference = numerator.Mean - denominator.Mean;
double logSqrt2Pi = Math.Log(Math.Sqrt(2*Math.PI));
return Math.Log(denominator.Variance) + logSqrt2Pi - Math.Log(varianceDifference)/2.0 +
Square(meanDifference)/(2*varianceDifference);
}
public static GaussianDistribution FromPrecisionMean(double precisionMean, double precision)
{
var gaussianDistribution = new GaussianDistribution();
gaussianDistribution.Precision = precision;
gaussianDistribution.PrecisionMean = precisionMean;
gaussianDistribution.Variance = 1.0/precision;
gaussianDistribution.StandardDeviation = Math.Sqrt(gaussianDistribution.Variance);
gaussianDistribution.Mean = gaussianDistribution.PrecisionMean/gaussianDistribution.Precision;
return gaussianDistribution;
}