public void ExpOpGammaPowerTest()
{
Assert.True(!double.IsNaN(ExpOp.ExpAverageConditional(GammaPower.Uniform(-1), Gaussian.FromNatural(0.046634157098979417, 0.00078302234897204242), Gaussian.Uniform()).Rate));
Assert.True(!double.IsNaN(ExpOp.ExpAverageConditional(GammaPower.Uniform(-1), Gaussian.FromNatural(0.36153121930654075, 0.0005524890062312658), Gaussian.Uniform()).Rate));
Assert.True(ExpOp.DAverageConditional(GammaPower.PointMass(0, -1), new Gaussian(0, 1), Gaussian.Uniform()).Point < double.MinValue);
ExpOp.ExpAverageConditional(GammaPower.FromShapeAndRate(-1, 283.673, -1), Gaussian.FromNatural(0.004859823703146038, 6.6322755562737905E-06), Gaussian.FromNatural(0.00075506803981220758, 8.24487022054953E-07));
GammaPower exp = GammaPower.FromShapeAndRate(0, 0, -1);
Gaussian[] ds = new[]
{
Gaussian.FromNatural(-1.6171314269768655E+308, 4.8976001759138024),
Gaussian.FromNatural(-0.037020622891705768, 0.00034989765084474117),
Gaussian.PointMass(double.NegativeInfinity),
};
foreach (var d in ds)
{
Gaussian to_d = ExpOp.DAverageConditional(exp, d, Gaussian.Uniform());
Gaussian to_d_slow = ExpOp_Slow.DAverageConditional(exp, d);
Assert.True(to_d_slow.MaxDiff(to_d) < 1e-10);
to_d = Gaussian.FromNatural(1, 0);
GammaPower to_exp = ExpOp.ExpAverageConditional(exp, d, to_d);
//Trace.WriteLine($"{to_exp}");
}
ExpOp.ExpAverageConditional(GammaPower.FromShapeAndRate(-1, 883.22399999999993, -1), Gaussian.FromNatural(0.0072160312702854888, 8.1788482512051846E-06), Gaussian.FromNatural(0.00057861649495666474, 5.6316164560235272E-07));
}
public void ExpOpGammaPower_PointExp()
{
double power = -1;
double vd = 1e-4;
vd = 1e-3;
Gaussian d = new Gaussian(0, vd);
Gaussian uniform = Gaussian.Uniform();
GammaPower expPoint = GammaPower.PointMass(2, power);
GammaPower to_exp_point = ExpOp.ExpAverageConditional(expPoint, d, uniform);
Gaussian to_d_point = ExpOp.DAverageConditional(expPoint, d, uniform);
double to_exp_oldError = double.PositiveInfinity;
double to_d_oldError = double.PositiveInfinity;
for (int i = 0; i < 100; i++)
{
double ve = System.Math.Pow(10, -i);
GammaPower exp = GammaPower.FromMeanAndVariance(2, ve, power);
GammaPower to_exp = ExpOp.ExpAverageConditional(exp, d, uniform);
Gaussian to_d = ExpOp.DAverageConditional(exp, d, uniform);
double to_exp_error = to_exp.MaxDiff(to_exp_point);
double to_d_error = System.Math.Abs(to_d.GetMean() - to_d_point.GetMean());
Trace.WriteLine($"ve={ve}: to_exp={to_exp} error={to_exp_error} to_d={to_d} error={to_d_error}");
Assert.True(to_exp_error <= to_exp_oldError);
to_exp_oldError = to_exp_error;
Assert.True(to_d_error <= to_d_oldError);
to_d_oldError = to_d_error;
}
}
public void ExpOpTest()
{
Assert.True(ExpOp.ExpAverageConditional(Gamma.FromShapeAndRate(3.302758272196654, 0.00060601537137241492), Gaussian.FromNatural(55.350150233321628, 6.3510247863590683), Gaussian.FromNatural(27.960892513144643, 3.4099170930572216)).Rate > 0);
Gamma exp = new Gamma(1, 1);
Gaussian[] ds = new[]
{
Gaussian.FromNatural(-1.6171314269768655E+308, 4.8976001759138024),
Gaussian.PointMass(double.NegativeInfinity),
};
foreach (var d in ds)
{
Gamma to_exp = ExpOp.ExpAverageConditional(exp, d, Gaussian.Uniform());
Gaussian to_d = ExpOp.DAverageConditional(exp, d, Gaussian.Uniform());
Gaussian to_d_slow = ExpOp_Slow.DAverageConditional(exp, d);
Trace.WriteLine($"{to_d}");
Trace.WriteLine($"{to_d_slow}");
Assert.True(to_d_slow.MaxDiff(to_d) < 1e-10);
}
}
//[Fact]
//[Trait("Category", "ModifiesGlobals")]
internal void ExpOp_CompareToSampling()
{
int sampleCount = 1_000_000;
for (int i = 1; i < 10; i++)
{
double ve = System.Math.Pow(10, -i);
Gamma exp = Gamma.FromMeanAndVariance(1, ve);
Gaussian d = Gaussian.FromMeanAndVariance(0, 1);
Gaussian to_d = ExpOp.DAverageConditional(exp, d, Gaussian.Uniform());
var importanceSampler = new ImportanceSampler(sampleCount, d.Sample, x => System.Math.Exp(exp.GetLogProb(System.Math.Exp(x))));
double mean = importanceSampler.GetExpectation(x => x);
double Ex2 = importanceSampler.GetExpectation(x => x * x);
Gaussian to_d_is = new Gaussian(mean, Ex2 - mean * mean) / d;
var exp2 = Gamma.FromShapeAndRate(exp.Shape - 1, exp.Rate);
importanceSampler = new ImportanceSampler(sampleCount, exp2.Sample, x => System.Math.Exp(d.GetLogProb(System.Math.Log(x))));
mean = importanceSampler.GetExpectation(x => System.Math.Log(x));
Ex2 = importanceSampler.GetExpectation(x => System.Math.Log(x) * System.Math.Log(x));
Gaussian to_d_is2 = new Gaussian(mean, Ex2 - mean * mean) / d;
Trace.WriteLine($"{ve}\t{to_d.GetMean()}\t{to_d_is.GetMean()}\t{to_d_is2.GetMean()}");
Gamma to_exp = ExpOp.ExpAverageConditional(exp, d, Gaussian.Uniform());
importanceSampler = new ImportanceSampler(sampleCount, d.Sample, x => System.Math.Exp(exp.GetLogProb(System.Math.Exp(x))));
double Ey = importanceSampler.GetExpectation(x => System.Math.Exp(x));
double Elogy = importanceSampler.GetExpectation(x => x);
var to_exp_is1 = Gamma.FromMeanAndMeanLog(Ey, Elogy) / exp;
importanceSampler = new ImportanceSampler(sampleCount, exp2.Sample, x => System.Math.Exp(d.GetLogProb(System.Math.Log(x))));
Ey = importanceSampler.GetExpectation(x => x);
Elogy = importanceSampler.GetExpectation(x => System.Math.Log(x));
var to_exp_is2 = Gamma.FromMeanAndMeanLog(Ey, Elogy) / exp;
double is1_mean = to_exp_is1.IsProper() ? to_exp_is1.GetMean() : double.NaN;
double is2_mean = to_exp_is2.IsProper() ? to_exp_is2.GetMean() : double.NaN;
Trace.WriteLine($"to_exp: Quad {to_exp.GetMean()} IS1: {is1_mean} IS2: {is2_mean}");
}
}
public void ExpOp_PointExp()
{
using (TestUtils.TemporarilyChangeQuadratureNodeCount(21))
{
double vd = 1e-4;
vd = 1e-3;
Gaussian d = new Gaussian(0, vd);
double ve = 2e-3;
//ve = 1;
Gaussian uniform = Gaussian.Uniform();
Gamma expPoint = Gamma.PointMass(2);
Gamma to_exp_point = ExpOp.ExpAverageConditional(expPoint, d, uniform);
Gaussian to_d_point = ExpOp.DAverageConditional(expPoint, d, uniform);
double to_exp_oldError = double.PositiveInfinity;
double to_d_oldError = double.PositiveInfinity;
for (int i = 5; i < 100; i++)
{
ve = System.Math.Pow(10, -i);
Gamma exp = Gamma.FromMeanAndVariance(2, ve);
Gamma to_exp = ExpOp.ExpAverageConditional(exp, d, uniform);
Gaussian to_d = ExpOp.DAverageConditional(exp, d, uniform);
double to_exp_error = to_exp.MaxDiff(to_exp_point);
double to_d_error = System.Math.Abs(to_d.GetMean() - to_d_point.GetMean());
Trace.WriteLine($"ve={ve}: to_exp={to_exp} error={to_exp_error} to_d={to_d} error={to_d_error}");
Assert.True(to_exp_error <= to_exp_oldError);
to_exp_oldError = to_exp_error;
Assert.True(to_d_error <= to_d_oldError);
to_d_oldError = to_d_error;
}
Trace.WriteLine(ExpOp.DAverageConditional(Gamma.FromMeanAndVariance(1, ve), d, uniform));
using (TestUtils.TemporarilyChangeQuadratureShift(true))
{
Trace.WriteLine(ExpOp.DAverageConditional(Gamma.FromMeanAndVariance(1, ve), d, uniform));
}
}
}
