/// <summary>
/// Operator overload for exponentation
/// </summary>
/// <param name="dist"></param>
/// <param name="exponent"></param>
/// <returns></returns>
public static TruncatedGaussian operator ^(TruncatedGaussian dist, double exponent)
{
var result = new TruncatedGaussian();
result.SetToPower(dist, exponent);
return(result);
}
/// <summary>
/// Get the average logarithm of that distribution under this distribution, i.e. int this(x) log( that(x) ) dx
/// </summary>
/// <param name="that"></param>
/// <returns></returns>
public double GetAverageLog(TruncatedGaussian that)
{
if (IsPointMass)
{
if (that.IsPointMass && this.Point == that.Point)
{
return(0.0);
}
else
{
return(that.GetLogProb(this.Point));
}
}
else if (this.LowerBound < that.LowerBound || this.UpperBound > that.UpperBound)
{
return(double.NegativeInfinity);
}
else if (that.IsPointMass)
{
return(Double.NegativeInfinity);
}
else if (!IsProper())
{
throw new ImproperDistributionException(this);
}
else
{
double m, v;
GetMeanAndVariance(out m, out v);
return(-0.5 * that.Gaussian.Precision * (m * m + v) + that.Gaussian.MeanTimesPrecision * m - that.GetLogNormalizer());
}
}
/// <summary>
/// Operator overload for division
/// </summary>
/// <param name="numerator"></param>
/// <param name="denominator"></param>
/// <returns></returns>
public static TruncatedGaussian operator /(TruncatedGaussian numerator, TruncatedGaussian denominator)
{
var result = new TruncatedGaussian();
result.SetToRatio(numerator, denominator);
return(result);
}
/// <summary>
/// Operator overload for product.
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static TruncatedGaussian operator *(TruncatedGaussian a, TruncatedGaussian b)
{
TruncatedGaussian result = new TruncatedGaussian();
result.SetToProduct(a, b);
return(result);
}
/// <summary>
/// Construct a uniform truncated Gaussian. This is mathematically equivalent to
/// a uniform Gaussian.
/// </summary>
/// <returns></returns>
public static TruncatedGaussian Uniform()
{
var result = new TruncatedGaussian();
result.SetToUniform();
return(result);
}
public static IEnumerable <double> SampleTruncatedGaussian(this IPolyrand random, double mean, double σ, double lower, double upper)
{
var dist = new Dist.TruncatedGaussian(Dist.Gaussian.FromMeanAndVariance(mean, σ * σ), lower, upper);
while (true)
{
yield return(dist.Sample(random));
}
}
/// <summary>
/// Create a point mass distribution.
/// </summary>
/// <param name="point">The location of the point mass</param>
/// <returns>A new TruncatedGaussian with all probability concentrated on the given point.</returns>
public static TruncatedGaussian PointMass(double point)
{
var result = new TruncatedGaussian();
result.Point = point;
result.LowerBound = double.NegativeInfinity;
result.UpperBound = double.PositiveInfinity;
return(result);
}
/// <summary>
/// Set this distribution equal to the product of a and b
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
public void SetToProduct(TruncatedGaussian a, TruncatedGaussian b)
{
LowerBound = Math.Max(a.LowerBound, b.LowerBound);
UpperBound = Math.Min(a.UpperBound, b.UpperBound);
if (LowerBound > UpperBound)
{
throw new AllZeroException();
}
Gaussian.SetToProduct(a.Gaussian, b.Gaussian);
}
/// <summary>
/// The maximum difference between the parameters of this distribution and that
/// </summary>
/// <param name="thatd"></param>
/// <returns></returns>
public double MaxDiff(object thatd)
{
if (!(thatd is TruncatedGaussian))
{
return(Double.PositiveInfinity);
}
TruncatedGaussian that = (TruncatedGaussian)thatd;
double diff1 = Gaussian.MaxDiff(that.Gaussian);
double diff3 = MMath.AbsDiff(LowerBound, that.LowerBound);
double diff4 = MMath.AbsDiff(UpperBound, that.UpperBound);
return(Math.Max(diff1, Math.Max(diff3, diff4)));
}
/// <summary>
/// Set the parameters to match the moments of a mixture distribution.
/// </summary>
/// <param name="dist1">The first distribution</param>
/// <param name="weight1">The first weight</param>
/// <param name="dist2">The second distribution</param>
/// <param name="weight2">The second weight</param>
public void SetToSum(double weight1, TruncatedGaussian dist1, double weight2, TruncatedGaussian dist2)
{
if (weight1 + weight2 == 0)
{
SetToUniform();
}
else if (weight1 + weight2 < 0)
{
throw new ArgumentException("weight1 (" + weight1 + ") + weight2 (" + weight2 + ") < 0");
}
else if (weight1 == 0)
{
SetTo(dist2);
}
else if (weight2 == 0)
{
SetTo(dist1);
}
// if dist1 == dist2 then we must return dist1, with no roundoff error
else if (dist1.Equals(dist2))
{
SetTo(dist1);
}
else if (double.IsPositiveInfinity(weight1))
{
if (double.IsPositiveInfinity(weight2))
{
throw new ArgumentException("both weights are infinity");
}
else
{
SetTo(dist1);
}
}
else if (double.IsPositiveInfinity(weight2))
{
SetTo(dist2);
}
else if (dist1.LowerBound == dist2.LowerBound && dist1.UpperBound == dist2.UpperBound)
{
Gaussian.SetToSum(weight1, dist1.Gaussian, weight2, dist2.Gaussian);
}
else
{
throw new NotImplementedException();
}
}
/// <summary>
/// Get the logarithm of the average value of that distribution under this distribution, i.e. log(int this(x) that(x) dx)
/// </summary>
/// <param name="that"></param>
/// <returns></returns>
public double GetLogAverageOf(TruncatedGaussian that)
{
if (IsPointMass)
{
return(that.GetLogProb(Point));
}
else if (that.IsPointMass)
{
return(GetLogProb(that.Point));
}
else
{
// neither this nor that is a point mass.
TruncatedGaussian product = this * that;
return(product.GetLogNormalizer() - this.GetLogNormalizer() - that.GetLogNormalizer());
}
}
/// <summary>
/// Set this equal to (dist)^exponent
/// </summary>
/// <param name="dist"></param>
/// <param name="exponent"></param>
public void SetToPower(TruncatedGaussian dist, double exponent)
{
if (exponent == 0)
{
SetToUniform();
}
else
{
if (exponent < 0 && !(double.IsNegativeInfinity(dist.LowerBound) && double.IsPositiveInfinity(dist.UpperBound)))
{
throw new DivideByZeroException("The exponent is negative and the bounds are finite");
}
LowerBound = dist.LowerBound;
UpperBound = dist.UpperBound;
Gaussian.SetToPower(dist.Gaussian, exponent);
}
}
/// <summary>
/// Set this equal to numerator/denominator
/// </summary>
/// <param name="numerator"></param>
/// <param name="denominator"></param>
/// <param name="forceProper"></param>
public void SetToRatio(TruncatedGaussian numerator, TruncatedGaussian denominator, bool forceProper = false)
{
if (numerator.IsPointMass)
{
if (denominator.IsPointMass)
{
if (numerator.Point.Equals(denominator.Point))
{
SetToUniform();
}
else
{
throw new DivideByZeroException();
}
}
else
{
if (denominator.LowerBound < numerator.Point && numerator.Point < denominator.UpperBound)
{
Point = numerator.Point;
}
else
{
throw new DivideByZeroException();
}
}
}
else if (denominator.IsPointMass)
{
throw new DivideByZeroException();
}
else
{
if (numerator.LowerBound >= denominator.LowerBound && numerator.UpperBound <= denominator.UpperBound)
{
LowerBound = numerator.LowerBound;
UpperBound = numerator.UpperBound;
Gaussian.SetToRatio(numerator.Gaussian, denominator.Gaussian, forceProper);
}
else
{
throw new DivideByZeroException();
}
}
}
/// <summary>
/// Get the integral of this distribution times another distribution raised to a power.
/// </summary>
/// <param name="that"></param>
/// <param name="power"></param>
/// <returns></returns>
public double GetLogAverageOfPower(TruncatedGaussian that, double power)
{
if (IsPointMass)
{
return(power * that.GetLogProb(Point));
}
else if (that.IsPointMass)
{
if (power < 0)
{
throw new DivideByZeroException("The exponent is negative and the distribution is a point mass");
}
return(this.GetLogProb(that.Point));
}
else
{
var product = this * (that ^ power);
return(product.GetLogNormalizer() - this.GetLogNormalizer() - power * that.GetLogNormalizer());
}
}
/// <summary>
/// Create a new TruncatedGaussian distribution equal to that
/// </summary>
/// <param name="that"></param>
public TruncatedGaussian(TruncatedGaussian that)
: this()
{
SetTo(that);
}
/// <summary>
/// Set this distribution equal to value.
/// </summary>
/// <param name="value"></param>
public void SetTo(TruncatedGaussian value)
{
Gaussian.SetTo(value.Gaussian);
LowerBound = value.LowerBound;
UpperBound = value.UpperBound;
}