public void SparseGaussianListFactor()
{
SparseGaussianList.DefaultTolerance = 1e-10;
var calcSuffix = ": calculation differs between sparse and dense";
var sparsitySuffix = ": result is not sparse as expected";
var calcErrMsg = "";
var sparsityErrMsg = "";
var tolerance = 1e-10;
Rand.Restart(12347);
int listSize = 50;
// True distribution for the means
var sparseMeanDist = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(1, 2), tolerance);
sparseMeanDist[3] = Gaussian.FromMeanAndPrecision(4, 5);
sparseMeanDist[6] = Gaussian.FromMeanAndPrecision(7, 8);
var meanDist = sparseMeanDist.ToArray();
var sparseMeanPoint = SparseList <double> .Constant(listSize, 0.1);
sparseMeanPoint[3] = 0.7;
sparseMeanPoint[6] = 0.8;
var meanPoint = sparseMeanPoint.ToArray();
// True distribution for the precisions
var sparsePrecDist = SparseGammaList.Constant(listSize, Gamma.FromShapeAndRate(1.1, 1.2), tolerance);
sparsePrecDist[3] = Gamma.FromShapeAndRate(2.3, 2.4);
sparsePrecDist[6] = Gamma.FromShapeAndRate(3.4, 4.5);
var precDist = sparsePrecDist.ToArray();
var sparsePrecPoint = SparseList <double> .Constant(listSize, 0.1);
sparsePrecPoint[3] = 5.6;
sparsePrecPoint[6] = 0.5;
var precPoint = sparsePrecPoint.ToArray();
var sparseSampleDist = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(0.5, 1.5), tolerance);
sparseSampleDist[3] = Gaussian.FromMeanAndPrecision(-0.5, 2.0);
sparseSampleDist[9] = Gaussian.FromMeanAndPrecision(1.6, 0.4);
var sampleDist = sparseSampleDist.ToArray();
var sparseSamplePoint = SparseList <double> .Constant(listSize, 0.5);
sparseSamplePoint[3] = 0.1;
sparseSamplePoint[9] = 2.3;
var samplePoint = sparseSamplePoint.ToArray();
var toSparseSampleDist = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(-0.2, 0.3), tolerance);
toSparseSampleDist[3] = Gaussian.FromMeanAndPrecision(2.1, 3.2);
toSparseSampleDist[4] = Gaussian.FromMeanAndPrecision(1.3, 0.7);
var toSampleDist = toSparseSampleDist.ToArray();
var toSparsePrecDist = SparseGammaList.Constant(listSize, Gamma.FromShapeAndRate(2.3, 3.4), tolerance);
toSparsePrecDist[3] = Gamma.FromShapeAndRate(3.4, 4.5);
toSparsePrecDist[4] = Gamma.FromShapeAndRate(5.6, 6.7);
var toPrecDist = toSparsePrecDist.ToArray();
// ---------------------------
// Check average log factor
// ---------------------------
calcErrMsg = "Average log factor" + calcSuffix;
// Dist, dist, dist
var sparseAvgLog = SparseGaussianListOp.AverageLogFactor(sparseSampleDist, sparseMeanDist, sparsePrecDist);
var avgLog = Util.ArrayInit(listSize, i => GaussianOp.AverageLogFactor(sampleDist[i], meanDist[i], precDist[i])).Sum();
TAssert.True(System.Math.Abs(avgLog - sparseAvgLog) < tolerance, calcErrMsg);
// Dist, dist, point
sparseAvgLog = SparseGaussianListOp.AverageLogFactor(sparseSampleDist, sparseMeanDist, sparsePrecPoint);
avgLog = Util.ArrayInit(listSize, i => GaussianOp.AverageLogFactor(sampleDist[i], meanDist[i], precPoint[i])).Sum();
TAssert.True(System.Math.Abs(avgLog - sparseAvgLog) < tolerance, calcErrMsg);
// Dist, point, dist
sparseAvgLog = SparseGaussianListOp.AverageLogFactor(sparseSampleDist, sparseMeanPoint, sparsePrecDist);
avgLog = Util.ArrayInit(listSize, i => GaussianOp.AverageLogFactor(sampleDist[i], meanPoint[i], precDist[i])).Sum();
TAssert.True(System.Math.Abs(avgLog - sparseAvgLog) < tolerance, calcErrMsg);
// Dist, point, point
sparseAvgLog = SparseGaussianListOp.AverageLogFactor(sparseSampleDist, sparseMeanPoint, sparsePrecPoint);
avgLog = Util.ArrayInit(listSize, i => GaussianOp.AverageLogFactor(sampleDist[i], meanPoint[i], precPoint[i])).Sum();
TAssert.True(System.Math.Abs(avgLog - sparseAvgLog) < tolerance, calcErrMsg);
// Point, dist, dist
sparseAvgLog = SparseGaussianListOp.AverageLogFactor(sparseSamplePoint, sparseMeanDist, sparsePrecDist);
avgLog = Util.ArrayInit(listSize, i => GaussianOp.AverageLogFactor(samplePoint[i], meanDist[i], precDist[i])).Sum();
TAssert.True(System.Math.Abs(avgLog - sparseAvgLog) < tolerance, calcErrMsg);
// Point, dist, point
sparseAvgLog = SparseGaussianListOp.AverageLogFactor(sparseSamplePoint, sparseMeanDist, sparsePrecPoint);
avgLog = Util.ArrayInit(listSize, i => GaussianOp.AverageLogFactor(samplePoint[i], meanDist[i], precPoint[i])).Sum();
TAssert.True(System.Math.Abs(avgLog - sparseAvgLog) < tolerance, calcErrMsg);
// Point, point, dist
sparseAvgLog = SparseGaussianListOp.AverageLogFactor(sparseSamplePoint, sparseMeanPoint, sparsePrecDist);
avgLog = Util.ArrayInit(listSize, i => GaussianOp.AverageLogFactor(samplePoint[i], meanPoint[i], precDist[i])).Sum();
TAssert.True(System.Math.Abs(avgLog - sparseAvgLog) < tolerance, calcErrMsg);
// Point, point, point
sparseAvgLog = SparseGaussianListOp.AverageLogFactor(sparseSamplePoint, sparseMeanPoint, sparsePrecPoint);
avgLog = Util.ArrayInit(listSize, i => GaussianOp.AverageLogFactor(samplePoint[i], meanPoint[i], precPoint[i])).Sum();
TAssert.True(System.Math.Abs(avgLog - sparseAvgLog) < tolerance, calcErrMsg);
// ---------------------------
// Check log average factor
// ---------------------------
calcErrMsg = "Log average factor" + calcSuffix;
var sparseLogAvg = SparseGaussianListOp.LogAverageFactor(sparseSampleDist, sparseMeanDist, sparsePrecDist, toSparsePrecDist);
var logAvg = Util.ArrayInit(listSize, i => GaussianOp.LogAverageFactor(sampleDist[i], meanDist[i], precDist[i], toPrecDist[i])).Sum();
TAssert.True(System.Math.Abs(logAvg - sparseLogAvg) < tolerance, calcErrMsg);
// Dist, dist, point
sparseLogAvg = SparseGaussianListOp.LogAverageFactor(sparseSampleDist, sparseMeanDist, sparsePrecPoint);
logAvg = Util.ArrayInit(listSize, i => GaussianOp.LogAverageFactor(sampleDist[i], meanDist[i], precPoint[i])).Sum();
TAssert.True(System.Math.Abs(logAvg - sparseLogAvg) < tolerance, calcErrMsg);
// Dist, point, dist
sparseLogAvg = SparseGaussianListOp.LogAverageFactor(sparseSampleDist, sparseMeanPoint, sparsePrecDist, toSparsePrecDist);
logAvg = Util.ArrayInit(listSize, i => GaussianOp.LogAverageFactor(sampleDist[i], meanPoint[i], precDist[i], toPrecDist[i])).Sum();
TAssert.True(System.Math.Abs(logAvg - sparseLogAvg) < tolerance, calcErrMsg);
// Dist, point, point
sparseLogAvg = SparseGaussianListOp.LogAverageFactor(sparseSampleDist, sparseMeanPoint, sparsePrecPoint);
logAvg = Util.ArrayInit(listSize, i => GaussianOp.LogAverageFactor(sampleDist[i], meanPoint[i], precPoint[i])).Sum();
TAssert.True(System.Math.Abs(logAvg - sparseLogAvg) < tolerance, calcErrMsg);
// Point, dist, dist
sparseLogAvg = SparseGaussianListOp.LogAverageFactor(sparseSamplePoint, sparseMeanDist, sparsePrecDist, toSparsePrecDist);
logAvg = Util.ArrayInit(listSize, i => GaussianOp.LogAverageFactor(samplePoint[i], meanDist[i], precDist[i], toPrecDist[i])).Sum();
TAssert.True(System.Math.Abs(logAvg - sparseLogAvg) < tolerance, calcErrMsg);
// Point, dist, point
sparseLogAvg = SparseGaussianListOp.LogAverageFactor(sparseSamplePoint, sparseMeanDist, sparsePrecPoint);
logAvg = Util.ArrayInit(listSize, i => GaussianOp.LogAverageFactor(samplePoint[i], meanDist[i], precPoint[i])).Sum();
TAssert.True(System.Math.Abs(logAvg - sparseLogAvg) < tolerance, calcErrMsg);
// Point, point, dist
sparseLogAvg = SparseGaussianListOp.LogAverageFactor(sparseSamplePoint, sparseMeanPoint, sparsePrecDist);
logAvg = Util.ArrayInit(listSize, i => GaussianOp.LogAverageFactor(samplePoint[i], meanPoint[i], precDist[i])).Sum();
TAssert.True(System.Math.Abs(logAvg - sparseLogAvg) < tolerance, calcErrMsg);
// Point, point, point
sparseLogAvg = SparseGaussianListOp.LogAverageFactor(sparseSamplePoint, sparseMeanPoint, sparsePrecPoint);
logAvg = Util.ArrayInit(listSize, i => GaussianOp.LogAverageFactor(samplePoint[i], meanPoint[i], precPoint[i])).Sum();
TAssert.True(System.Math.Abs(logAvg - sparseLogAvg) < tolerance, calcErrMsg);
// ---------------------------
// Check log evidence ratio
// ---------------------------
calcErrMsg = "Log evidence ratio" + calcSuffix;
var sparseEvidRat = SparseGaussianListOp.LogEvidenceRatio(sparseSampleDist, sparseMeanDist, sparsePrecDist, toSparseSampleDist, toSparsePrecDist);
var evidRat = Util.ArrayInit(listSize, i => GaussianOp.LogEvidenceRatio(sampleDist[i], meanDist[i], precDist[i], toSampleDist[i], toPrecDist[i])).Sum();
TAssert.True(System.Math.Abs(evidRat - sparseEvidRat) < tolerance, calcErrMsg);
// Dist, dist, point
sparseEvidRat = SparseGaussianListOp.LogEvidenceRatio(sparseSampleDist, sparseMeanDist, sparsePrecPoint);
evidRat = Util.ArrayInit(listSize, i => GaussianOp.LogEvidenceRatio(sampleDist[i], meanDist[i], precPoint[i])).Sum();
TAssert.True(System.Math.Abs(evidRat - sparseEvidRat) < tolerance, calcErrMsg);
// Dist, point, dist
sparseEvidRat = SparseGaussianListOp.LogEvidenceRatio(sparseSampleDist, sparseMeanPoint, sparsePrecDist, toSparseSampleDist, toSparsePrecDist);
evidRat = Util.ArrayInit(listSize, i => GaussianOp.LogEvidenceRatio(sampleDist[i], meanPoint[i], precDist[i], toSampleDist[i], toPrecDist[i])).Sum();
TAssert.True(System.Math.Abs(evidRat - sparseEvidRat) < tolerance, calcErrMsg);
// Dist, point, point
sparseEvidRat = SparseGaussianListOp.LogEvidenceRatio(sparseSampleDist, sparseMeanPoint, sparsePrecPoint);
evidRat = Util.ArrayInit(listSize, i => GaussianOp.LogEvidenceRatio(sampleDist[i], meanPoint[i], precPoint[i])).Sum();
TAssert.True(System.Math.Abs(evidRat - sparseEvidRat) < tolerance, calcErrMsg);
// Point, dist, dist
sparseEvidRat = SparseGaussianListOp.LogEvidenceRatio(sparseSamplePoint, sparseMeanDist, sparsePrecDist, toSparsePrecDist);
evidRat = Util.ArrayInit(listSize, i => GaussianOp.LogEvidenceRatio(samplePoint[i], meanDist[i], precDist[i], toPrecDist[i])).Sum();
TAssert.True(System.Math.Abs(evidRat - sparseEvidRat) < tolerance, calcErrMsg);
// Point, dist, point
sparseEvidRat = SparseGaussianListOp.LogEvidenceRatio(sparseSamplePoint, sparseMeanDist, sparsePrecPoint);
evidRat = Util.ArrayInit(listSize, i => GaussianOp.LogEvidenceRatio(samplePoint[i], meanDist[i], precPoint[i])).Sum();
TAssert.True(System.Math.Abs(evidRat - sparseEvidRat) < tolerance, calcErrMsg);
// Point, point, dist
sparseEvidRat = SparseGaussianListOp.LogEvidenceRatio(sparseSamplePoint, sparseMeanPoint, sparsePrecDist);
evidRat = Util.ArrayInit(listSize, i => GaussianOp.LogEvidenceRatio(samplePoint[i], meanPoint[i], precDist[i])).Sum();
TAssert.True(System.Math.Abs(evidRat - sparseEvidRat) < tolerance, calcErrMsg);
// Point, point, point
sparseEvidRat = SparseGaussianListOp.LogEvidenceRatio(sparseSamplePoint, sparseMeanPoint, sparsePrecPoint);
evidRat = Util.ArrayInit(listSize, i => GaussianOp.LogEvidenceRatio(samplePoint[i], meanPoint[i], precPoint[i])).Sum();
TAssert.True(System.Math.Abs(evidRat - sparseEvidRat) < tolerance, calcErrMsg);
// ---------------------------
// Check SampleAverageConditional
// ---------------------------
calcErrMsg = "SampleAverageConditional" + calcSuffix;
sparsityErrMsg = "SampleAverageConditional" + sparsitySuffix;
// Use different common value to ensure this gets properly set
var sparseSampleAvgConditional = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(0.5, 0.6), tolerance);
sparseSampleAvgConditional = SparseGaussianListOp.SampleAverageConditional(sparseSampleDist, sparseMeanDist, sparsePrecDist, toSparsePrecDist, sparseSampleAvgConditional);
var sampleAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.SampleAverageConditional(sampleDist[i], meanDist[i], precDist[i], toPrecDist[i]));
TAssert.True(3 == sparseSampleAvgConditional.SparseCount, sparsityErrMsg);
TAssert.True(sparseSampleAvgConditional.MaxDiff(sampleAvgConditional) < tolerance, calcErrMsg);
sparseSampleAvgConditional = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(0.5, 0.6), tolerance);
sparseSampleAvgConditional = SparseGaussianListOp.SampleAverageConditional(sparseSampleDist, sparseMeanPoint, sparsePrecDist, toSparsePrecDist, sparseSampleAvgConditional);
sampleAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.SampleAverageConditional(sampleDist[i], meanPoint[i], precDist[i], toPrecDist[i]));
TAssert.True(3 == sparseSampleAvgConditional.SparseCount, sparsityErrMsg);
TAssert.True(sparseSampleAvgConditional.MaxDiff(sampleAvgConditional) < tolerance, calcErrMsg);
sparseSampleAvgConditional = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(0.5, 0.6), tolerance);
sparseSampleAvgConditional = SparseGaussianListOp.SampleAverageConditional(sparseMeanDist, sparsePrecPoint, sparseSampleAvgConditional);
sampleAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.SampleAverageConditional(meanDist[i], precPoint[i]));
TAssert.True(2 == sparseSampleAvgConditional.SparseCount, sparsityErrMsg);
TAssert.True(sparseSampleAvgConditional.MaxDiff(sampleAvgConditional) < tolerance, calcErrMsg);
sparseSampleAvgConditional = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(0.5, 0.6), tolerance);
sparseSampleAvgConditional = SparseGaussianListOp.SampleAverageConditional(sparseMeanPoint, sparsePrecPoint, sparseSampleAvgConditional);
sampleAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.SampleAverageConditional(meanPoint[i], precPoint[i]));
TAssert.True(2 == sparseSampleAvgConditional.SparseCount, sparsityErrMsg);
TAssert.True(sparseSampleAvgConditional.MaxDiff(sampleAvgConditional) < tolerance, calcErrMsg);
// ---------------------------
// Check MeanAverageConditional
// ---------------------------
calcErrMsg = "MeanAverageConditional" + calcSuffix;
sparsityErrMsg = "MeanAverageConditional" + sparsitySuffix;
// Use different common value to ensure this gets properly set
var sparseMeanAvgConditional = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(0.5, 0.6), tolerance);
sparseMeanAvgConditional = SparseGaussianListOp.MeanAverageConditional(sparseSampleDist, sparseMeanDist, sparsePrecDist, toSparsePrecDist, sparseMeanAvgConditional);
var meanAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.MeanAverageConditional(sampleDist[i], meanDist[i], precDist[i], toPrecDist[i]));
TAssert.True(3 == sparseMeanAvgConditional.SparseCount, sparsityErrMsg);
TAssert.True(sparseMeanAvgConditional.MaxDiff(meanAvgConditional) < tolerance, calcErrMsg);
sparseMeanAvgConditional = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(0.5, 0.6), tolerance);
sparseMeanAvgConditional = SparseGaussianListOp.MeanAverageConditional(sparseSamplePoint, sparseMeanDist, sparsePrecDist, toSparsePrecDist, sparseMeanAvgConditional);
meanAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.MeanAverageConditional(samplePoint[i], meanDist[i], precDist[i], toPrecDist[i]));
TAssert.True(3 == sparseMeanAvgConditional.SparseCount, sparsityErrMsg);
TAssert.True(sparseMeanAvgConditional.MaxDiff(meanAvgConditional) < tolerance, calcErrMsg);
sparseMeanAvgConditional = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(0.5, 0.6), tolerance);
sparseMeanAvgConditional = SparseGaussianListOp.MeanAverageConditional(sparseSampleDist, sparsePrecPoint, sparseMeanAvgConditional);
meanAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.MeanAverageConditional(sampleDist[i], precPoint[i]));
TAssert.True(3 == sparseMeanAvgConditional.SparseCount, sparsityErrMsg);
TAssert.True(sparseMeanAvgConditional.MaxDiff(meanAvgConditional) < tolerance, calcErrMsg);
sparseMeanAvgConditional = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(0.5, 0.6), tolerance);
sparseMeanAvgConditional = SparseGaussianListOp.MeanAverageConditional(sparseSamplePoint, sparsePrecPoint, sparseMeanAvgConditional);
meanAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.MeanAverageConditional(samplePoint[i], precPoint[i]));
TAssert.True(3 == sparseMeanAvgConditional.SparseCount, sparsityErrMsg);
TAssert.True(sparseMeanAvgConditional.MaxDiff(meanAvgConditional) < tolerance, calcErrMsg);
// ---------------------------
// Check PrecisionAverageConditional
// ---------------------------
calcErrMsg = "PrecisionAverageConditional" + calcSuffix;
sparsityErrMsg = "PrecisionAverageConditional" + sparsitySuffix;
// Use different common value to ensure this gets properly set
var sparsePrecAvgConditional = SparseGammaList.Constant(listSize, Gamma.FromShapeAndRate(2.1, 3.2), tolerance);
sparsePrecAvgConditional = SparseGaussianListOp.PrecisionAverageConditional(sparseSampleDist, sparseMeanDist, sparsePrecDist, sparsePrecAvgConditional);
var precAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.PrecisionAverageConditional(sampleDist[i], meanDist[i], precDist[i]));
TAssert.True(3 == sparsePrecAvgConditional.SparseCount, sparsityErrMsg);
TAssert.True(sparsePrecAvgConditional.MaxDiff(precAvgConditional) < tolerance, calcErrMsg);
sparsePrecAvgConditional = SparseGammaList.Constant(listSize, Gamma.FromShapeAndRate(2.1, 3.2), tolerance);
sparsePrecAvgConditional = SparseGaussianListOp.PrecisionAverageConditional(sparseSamplePoint, sparseMeanDist, sparsePrecDist, sparsePrecAvgConditional);
precAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.PrecisionAverageConditional(Gaussian.PointMass(samplePoint[i]), meanDist[i], precDist[i]));
TAssert.True(3 == sparsePrecAvgConditional.SparseCount, sparsityErrMsg);
TAssert.True(sparsePrecAvgConditional.MaxDiff(precAvgConditional) < tolerance, calcErrMsg);
sparsePrecAvgConditional = SparseGammaList.Constant(listSize, Gamma.FromShapeAndRate(2.1, 3.2), tolerance);
sparsePrecAvgConditional = SparseGaussianListOp.PrecisionAverageConditional(sparseSampleDist, sparseMeanPoint, sparsePrecDist, sparsePrecAvgConditional);
precAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.PrecisionAverageConditional(sampleDist[i], Gaussian.PointMass(meanPoint[i]), precDist[i]));
TAssert.True(3 == sparsePrecAvgConditional.SparseCount, sparsityErrMsg);
TAssert.True(sparsePrecAvgConditional.MaxDiff(precAvgConditional) < tolerance, calcErrMsg);
sparsePrecAvgConditional = SparseGammaList.Constant(listSize, Gamma.FromShapeAndRate(2.1, 3.2), tolerance);
sparsePrecAvgConditional = SparseGaussianListOp.PrecisionAverageConditional(sparseSamplePoint, sparseMeanPoint, sparsePrecAvgConditional);
precAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.PrecisionAverageConditional(samplePoint[i], meanPoint[i]));
TAssert.True(3 == sparsePrecAvgConditional.SparseCount, sparsityErrMsg);
TAssert.True(sparsePrecAvgConditional.MaxDiff(precAvgConditional) < tolerance, calcErrMsg);
}