/// <summary>
/// Creates a new Gaussian which is the product of two other Gaussians
/// </summary>
/// <param name="a">First Gaussian</param>
/// <param name="b">Second Gaussian</param>
/// <returns>Result</returns>
public static Gaussian operator*(Gaussian a, Gaussian b)
{
Gaussian result = new Gaussian();
result.SetToProduct(a, b);
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>
/// Set this distribution equal to the approximate product of a and b
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <remarks>
/// Since WrappedGaussians are not closed under multiplication, the result is approximate.
/// </remarks>
public void SetToProduct(WrappedGaussian a, WrappedGaussian b)
{
if (a.Period < b.Period)
{
SetToProduct(b, a);
return;
}
// a.Period >= b.Period
if (a.IsUniform())
{
SetTo(b);
return;
}
if (b.IsUniform())
{
SetTo(a);
return;
}
if (a.IsPointMass)
{
if (b.IsPointMass && !a.Point.Equals(b.Point))
{
throw new AllZeroException();
}
Point = a.Point;
return;
}
if (b.IsPointMass)
{
Point = b.Point;
return;
}
// (a,b) are not uniform or point mass
double ratio = a.Period / b.Period;
int intRatio = (int)Math.Round(ratio);
if (Math.Abs(ratio - intRatio) > a.Period * 1e-4)
{
throw new ArgumentException("a.Period (" + a.Period + ") is not a multiple of b.Period (" + b.Period + ")");
}
this.Period = a.Period;
// a.Period = k*b.Period, k >= 1
// because one period is a multiple of the other, we only need to sum over one set of shifts.
// otherwise, we would need to sum over two sets of shifts.
double ma, va, mb, vb;
a.Gaussian.GetMeanAndVariance(out ma, out va);
b.Gaussian.GetMeanAndVariance(out mb, out vb);
double diff = (ma - mb) / b.Period;
#if true
// approximate using only the one best shift
int k = (int)Math.Round(diff);
Gaussian bShifted = new Gaussian(mb + k * b.Period, vb);
Gaussian.SetToProduct(a.Gaussian, bShifted);
#else
// we will sum over shifts from kMin to kMax, numbering intRatio in total
int kMin, kMax;
if (intRatio % 2 == 1)
{
// odd number of shifts
int kMid = (int)Math.Round(diff);
int halfRatio = intRatio / 2;
kMin = kMid - halfRatio;
kMax = kMid + halfRatio;
}
else
{
// even number of shifts
int kMid = (int)Math.Floor(diff);
int halfRatio = intRatio / 2;
kMin = kMid - halfRatio + 1;
kMax = kMid + halfRatio;
}
if (kMax - kMin != intRatio - 1)
{
throw new ApplicationException("kMax - kMin != intRatio-1");
}
// exclude shifts that are too far away
double sa = Math.Sqrt(va + vb);
double lowerBound = ma - 5 * sa;
double upperBound = ma + 5 * sa;
// find the largest k such that (mb + k*Lb <= lowerBound)
double kLower = Math.Floor((lowerBound - mb) / b.Period);
if (kLower > kMin)
{
kMin = (int)kLower;
}
// find the smallest k such that (mb + k*Lb >= upperBound)
double kUpper = Math.Ceiling((upperBound - mb) / b.Period);
if (kUpper < kMax)
{
kMax = (int)kUpper;
}
if (kMax - kMin > 100)
{
throw new ApplicationException("kMax - kMin = " + (kMax - kMin));
}
double totalWeight = Double.NegativeInfinity;
for (int k = kMin; k <= kMax; k++)
{
Gaussian bShifted = new Gaussian(mb + k * b.Period, vb);
Gaussian product = a.Gaussian * bShifted;
double weight = a.Gaussian.GetLogAverageOf(bShifted);
if (double.IsNegativeInfinity(totalWeight))
{
Gaussian.SetTo(product);
totalWeight = weight;
}
else
{
Gaussian.SetToSum(1.0, Gaussian, Math.Exp(weight - totalWeight), product);
totalWeight = MMath.LogSumExp(totalWeight, weight);
}
}
#endif
if (double.IsNaN(Gaussian.MeanTimesPrecision))
{
throw new ApplicationException("result is nan");
}
Normalize();
}