/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="WishartFromShapeAndRateOp"]/message_doc[@name="RateAverageLogarithm(Wishart, double, Wishart)"]/*'/>
public static Wishart RateAverageLogarithm([SkipIfUniform] Wishart sample, double shape, Wishart result)
{
int dimension = result.Dimension;
result.Shape = shape + 0.5 * (dimension + 1);
sample.GetMean(result.Rate);
return(result);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="ProductWishartOp"]/message_doc[@name="AAverageLogarithm(Wishart, double, Wishart)"]/*'/>
public static Wishart AAverageLogarithm([SkipIfUniform] Wishart Product, double B, Wishart result)
{
if (Product.IsPointMass)
{
return(AAverageLogarithm(Product.Point, B, result));
}
return(AAverageConditional(Product, B, result));
}
public void FailSCreateWishart(double nu, int order)
{
var matrix = MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(order);
matrix[0, 0] = 0.0;
var d = new Wishart(nu, matrix);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="WishartFromShapeAndRateOp"]/message_doc[@name="AverageLogFactor(Wishart, double, Wishart)"]/*'/>
public static double AverageLogFactor([Proper] Wishart sample, double shape, [Proper] Wishart rate)
{
// factor = (a-(d+1)/2)*logdet(X) -tr(X*B) + a*logdet(B) - GammaLn(a,d)
int dimension = sample.Dimension;
return((shape - (dimension + 1) * 0.5) * sample.GetMeanLogDeterminant() - Matrix.TraceOfProduct(sample.GetMean(), rate.GetMean()) + shape * rate.GetMeanLogDeterminant() -
MMath.GammaLn(shape, dimension));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="ProductWishartOp"]/message_doc[@name="BAverageConditional(Wishart, PositiveDefiniteMatrix)"]/*'/>
public static Gamma BAverageConditional([SkipIfUniform] Wishart Product, PositiveDefiniteMatrix A)
{
if (Product.IsPointMass)
{
return(BAverageConditional(Product.Point, A));
}
// det(ab)^(shape-(d+1)/2) exp(-tr(rate*(ab))) =propto b^((shape-(d+1)/2)*d) exp(-b*tr(rate*a))
return(Gamma.FromShapeAndRate(Product.Dimension * (Product.Shape - (Product.Dimension + 1) * 0.5) + 1, Matrix.TraceOfProduct(Product.Rate, A)));
}
/// <summary>EP message to <c>b</c>.</summary>
/// <param name="Product">Incoming message from <c>product</c>. Must be a proper distribution. If any element is uniform, the result will be uniform.</param>
/// <param name="A">Constant value for <c>a</c>.</param>
/// <returns>The outgoing EP message to the <c>b</c> argument.</returns>
/// <remarks>
/// <para>The outgoing message is a distribution matching the moments of <c>b</c> as the random arguments are varied. The formula is <c>proj[p(b) sum_(product) p(product) factor(product,a,b)]/p(b)</c>.</para>
/// </remarks>
/// <exception cref="ImproperMessageException">
/// <paramref name="Product" /> is not a proper distribution.</exception>
public static Gamma BAverageConditional([SkipIfUniform] Wishart Product, PositiveDefiniteMatrix A)
{
if (Product.IsPointMass)
{
return(BAverageLogarithm(Product.Point, A));
}
// (ab)^(shape-(d+1)/2) exp(-tr(rate*(ab)))
return(Gamma.FromShapeAndRate(Product.Shape + (1 - (Product.Dimension + 1) * 0.5), Matrix.TraceOfProduct(Product.Rate, A)));
}
private void VectorGaussianModel()
{
Vector mm = Vector.FromArray(0.1, 0.2);
Vector m = Factor.Random(VectorGaussian.FromMeanAndPrecision(mm, PositiveDefiniteMatrix.Identity(2)));
PositiveDefiniteMatrix p = Factor.Random(Wishart.FromShapeAndRate(2, 1.0, 1.0));
Vector c = Factor.VectorGaussian(m, p);
InferNet.Infer(c, nameof(c));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="ProductWishartOp"]/message_doc[@name="ProductAverageConditional(Wishart, double, Wishart)"]/*'/>
public static Wishart ProductAverageConditional([SkipIfUniform] Wishart A, double B, Wishart result)
{
if (A.IsPointMass)
{
return(ProductAverageConditional(A.Point, B, result));
}
result.SetTo(A);
result.Rate.Scale(1 / B);
return(result);
}
public void ValidateDensity(double nu, double density)
{
var matrix = Matrix <double> .Build.Dense(1, 1, 1.0);
var x = Matrix <double> .Build.Dense(1, 1, 5.0);
var d = new Wishart(nu, matrix);
AssertHelpers.AlmostEqualRelative(density, d.Density(x), 16);
}
public static Wishart ProductAverageConditional([SkipIfUniform] Wishart A, double B, Wishart result)
{
if (A.IsPointMass) {
result.Rate.SetTo(A.Point);
result.Rate.Scale(B);
} else {
result.SetTo(A);
result.Rate.Scale(1/B);
}
return result;
}
public void MP_GetItemWishart()
{
InferenceEngine engine = new InferenceEngine();
ModelDefinitionMethod meth = new ModelDefinitionMethod(GetItemWishartModel);
var ca = engine.Compiler.CompileWithoutParams(
declaringType, meth.Method, new AttributeRegistry <object, ICompilerAttribute>(true));
ca.Execute(1);
Wishart cMarg = ca.Marginal <Wishart>("c");
DistributionArray <Wishart> dMarg = ca.Marginal <DistributionArray <Wishart> >("d");
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="ProductWishartOp"]/message_doc[@name="BAverageLogarithm(Wishart, Wishart)"]/*'/>
public static Gamma BAverageLogarithm([SkipIfUniform] Wishart Product, [Proper] Wishart A)
{
if (A.IsPointMass)
{
return(BAverageLogarithm(Product, A.Point));
}
if (Product.IsPointMass)
{
return(BAverageLogarithm(Product.Point, A));
}
return(BAverageConditional(Product, A.GetMean()));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="WishartFromShapeAndRateOp"]/message_doc[@name="LogAverageFactor(PositiveDefiniteMatrix, double, Wishart)"]/*'/>
public static double LogAverageFactor(PositiveDefiniteMatrix sample, double shape, Wishart rate)
{
// f(X,a,B) = |X|^(a-c) |B|^a/Gamma_d(a) exp(-tr(BX)) = |X|^(-2c) Gamma_d(a+c)/Gamma_d(a) W(B; a+c, X)
// p(B) = |B|^(a'-c) |B'|^(a')/Gamma_d(a') exp(-tr(BB'))
// int_B f p(B) dB = |X|^(a-c) Gamma_d(a+a')/Gamma_d(a)/Gamma_d(a') |B'|^(a') |B'+X|^(-(a+a'))
int dimension = sample.Rows;
double c = 0.5 * (dimension + 1);
Wishart to_rate = new Wishart(dimension);
to_rate = RateAverageConditional(sample, shape, to_rate);
return(rate.GetLogAverageOf(to_rate) - 2 * c * sample.LogDeterminant() + MMath.GammaLn(shape + c, dimension) - MMath.GammaLn(shape, dimension));
}
/// <summary>VMP message to <c>b</c>.</summary>
/// <param name="Product">Incoming message from <c>product</c>. Must be a proper distribution. If any element is uniform, the result will be uniform.</param>
/// <param name="A">Incoming message from <c>a</c>. Must be a proper distribution. If any element is uniform, the result will be uniform.</param>
/// <returns>The outgoing VMP message to the <c>b</c> argument.</returns>
/// <remarks>
/// <para>The outgoing message is the exponential of the average log-factor value, where the average is over all arguments except <c>b</c>. Because the factor is deterministic, <c>product</c> is integrated out before taking the logarithm. The formula is <c>exp(sum_(a) p(a) log(sum_product p(product) factor(product,a,b)))</c>.</para>
/// </remarks>
/// <exception cref="ImproperMessageException">
/// <paramref name="Product" /> is not a proper distribution.</exception>
/// <exception cref="ImproperMessageException">
/// <paramref name="A" /> is not a proper distribution.</exception>
public static Gamma BAverageLogarithm([SkipIfUniform] Wishart Product, [Proper] Wishart A)
{
if (A.IsPointMass)
{
return(BAverageLogarithm(Product, A.Point));
}
if (Product.IsPointMass)
{
return(BAverageLogarithm(Product.Point, A));
}
// (ab)^(shape-(d+1)/2) exp(-tr(rate*(ab)))
return(Gamma.FromShapeAndRate(Product.Shape + (1 - (Product.Dimension + 1) * 0.5), Matrix.TraceOfProduct(Product.Rate, A.GetMean())));
}
public void CanGetS()
{
int order = 2;
var matrix = MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(order);
var d = new Wishart(1.0, matrix);
for (int i = 0; i < order; i++)
{
for (int j = 0; j < order; j++)
{
Assert.AreEqual <double>(matrix[i, j], d.S[i, j]);
}
}
}
public void ValidateMode(double nu, int order)
{
var d = new Wishart(nu, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(order));
var mode = d.Mode;
for (int i = 0; i < d.S.RowCount; i++)
{
for (int j = 0; j < d.S.ColumnCount; j++)
{
Assert.AreEqual((nu - d.S.RowCount - 1.0) * d.S[i, j], mode[i, j]);
}
}
}
public void ValidateVariance(double nu, int order)
{
var d = new Wishart(nu, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(order));
var variance = d.Variance;
for (var i = 0; i < d.S.RowCount; i++)
{
for (var j = 0; j < d.S.ColumnCount; j++)
{
Assert.AreEqual(nu * (d.S[i, j] * d.S[i, j] + d.S[i, i] * d.S[j, j]), variance[i, j]);
}
}
}
public void ValidateMean([Values(0.1, 1.0, 5.0)] double nu, [Values(2, 5)] int order)
{
var d = new Wishart(nu, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(order));
var mean = d.Mean;
for (var i = 0; i < d.S.RowCount; i++)
{
for (var j = 0; j < d.S.ColumnCount; j++)
{
Assert.AreEqual(nu * d.S[i, j], mean[i, j]);
}
}
}
public void ValidateMode(double nu, int order)
{
var d = new Wishart(nu, Matrix <double> .Build.RandomPositiveDefinite(order, 1));
var mode = d.Mode;
for (var i = 0; i < d.Scale.RowCount; i++)
{
for (var j = 0; j < d.Scale.ColumnCount; j++)
{
Assert.AreEqual((nu - d.Scale.RowCount - 1.0) * d.Scale[i, j], mode[i, j]);
}
}
}
public void ValidateVariance(double nu, int order)
{
var d = new Wishart(nu, Matrix <double> .Build.RandomPositiveDefinite(order, 1));
var variance = d.Variance;
for (var i = 0; i < d.Scale.RowCount; i++)
{
for (var j = 0; j < d.Scale.ColumnCount; j++)
{
Assert.AreEqual(nu * ((d.Scale[i, j] * d.Scale[i, j]) + (d.Scale[i, i] * d.Scale[j, j])), variance[i, j]);
}
}
}
public void ValidateMean(double nu, int order)
{
var d = new Wishart(nu, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(order));
var mean = d.Mean;
for (var i = 0; i < d.Scale.RowCount; i++)
{
for (var j = 0; j < d.Scale.ColumnCount; j++)
{
Assert.AreEqual(nu * d.Scale[i, j], mean[i, j]);
}
}
}
private static void ClusterizeAll(IReadOnlyList <float> series, int[] from, int[] to, ILogger logger)
{
foreach (var template in Wishart.GenerateTemplateForWishart(from, to))
{
var vectors = ZVectorBuilder.Build(series, template, 0);
var clusters = Clusterize(vectors);
var path = Path.Combine(Environment.GetFolderPath(Environment.SpecialFolder.DesktopDirectory),
"clusters", $"{template[0]}-{template[1]}-{template[2]}-{template[3]}.json");
using (var writer = new StreamWriter(path))
{
ServiceStack.Text.JsonSerializer.SerializeToWriter(clusters, writer);
}
}
}
public void CanGetS()
{
const int Order = 2;
var matrix = MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(Order);
var d = new Wishart(1.0, matrix);
for (var i = 0; i < Order; i++)
{
for (var j = 0; j < Order; j++)
{
Assert.AreEqual(matrix[i, j], d.Scale[i, j]);
}
}
}
private static void wishart_test08()
//****************************************************************************80
//
// Purpose:
//
// WISHART_TEST08 samples the unit Wishart and unit Wishart inverse matrices.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 11 October 2013
//
// Author:
//
// John Burkardt
//
{
Console.WriteLine("");
Console.WriteLine("WISHART_TEST08:");
Console.WriteLine(" Verify that, if using the same set of random numbers,");
Console.WriteLine(" inverse(W) = M,");
Console.WriteLine(" where");
Console.WriteLine(" W = Wishart.wishart_unit_sample ( n, df );");
Console.WriteLine(" M = Wishart.wishart_unit_sample_inverse ( n, df );");
//
// Set the parameters.
//
int n = 5;
int df = 8;
double[] w = Wishart.wishart_unit_sample(n, df);
double[] m = Wishart.wishart_unit_sample_inverse(n, df);
//
// Compute W * M.
//
double[] wm = typeMethods.r8mat_mm_new(n, n, n, w, m);
//
// Compare M * W to I.
//
double[] ident = typeMethods.r8mat_identity_new(n);
double diff = typeMethods.r8mat_norm_fro_affine(n, n, wm, ident);
Console.WriteLine("");
Console.WriteLine(" Frobenius norm of error is " + diff + "");
}
public void CanCreateWishart([Values(0.1, 1.0, 5.0)] double nu, [Values(2, 5)] int order)
{
var matrix = MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(order);
var d = new Wishart(nu, matrix);
Assert.AreEqual(nu, d.Nu);
for (var i = 0; i < d.S.RowCount; i++)
{
for (var j = 0; j < d.S.ColumnCount; j++)
{
Assert.AreEqual(matrix[i, j], d.S[i, j]);
}
}
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="WishartFromShapeAndRateOp_Laplace2"]/message_doc[@name="LogAverageFactor(Wishart, double, Wishart, Wishart)"]/*'/>
public static double LogAverageFactor(Wishart sample, double shape, Wishart rate, [Fresh] Wishart to_sample)
{
// int_R f(Y,R) p(R) dR = |Y|^(a-c) |Y+B_r|^-(a+a_r) Gamma_d(a+a_r)/Gamma_d(a)/Gamma_d(a_r) |B_r|^a_r
int dim = sample.Dimension;
double c = 0.5 * (dim + 1);
double shape2 = shape + rate.Shape;
Wishart samplePost = sample * to_sample;
PositiveDefiniteMatrix y = samplePost.GetMean();
PositiveDefiniteMatrix yPlusBr = y + rate.Rate;
double result = (shape - c) * y.LogDeterminant() - shape2 * yPlusBr.LogDeterminant() + sample.GetLogProb(y) - samplePost.GetLogProb(y);
result += MMath.GammaLn(shape2, dim) - MMath.GammaLn(shape, dim) - MMath.GammaLn(rate.Shape, dim);
result += rate.Shape * rate.Rate.LogDeterminant();
return(result);
}
public void ValidateDensity(double nu, double density)
{
const int Order = 1;
var matrix = new DenseMatrix(Order);
matrix[0, 0] = 1;
var x = new DenseMatrix(Order);
x[0, 0] = 5;
var d = new Wishart(nu, matrix);
AssertHelpers.AlmostEqualRelative(density, d.Density(x), 16);
}
public void CanCreateWishart(double nu, int order)
{
var matrix = Matrix <double> .Build.RandomPositiveDefinite(order, 1);
var d = new Wishart(nu, matrix);
Assert.AreEqual(nu, d.DegreesOfFreedom);
for (var i = 0; i < d.Scale.RowCount; i++)
{
for (var j = 0; j < d.Scale.ColumnCount; j++)
{
Assert.AreEqual(matrix[i, j], d.Scale[i, j]);
}
}
}
public void CanGetS()
{
const int Order = 2;
var matrix = Matrix <double> .Build.RandomPositiveDefinite(Order, 1);
var d = new Wishart(1.0, matrix);
for (var i = 0; i < Order; i++)
{
for (var j = 0; j < Order; j++)
{
Assert.AreEqual(matrix[i, j], d.Scale[i, j]);
}
}
}
public void CanCreateWishart(double nu, int order)
{
var matrix = MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(order);
var d = new Wishart(nu, matrix);
Assert.AreEqual(nu, d.DegreesOfFreedom);
for (var i = 0; i < d.Scale.RowCount; i++)
{
for (var j = 0; j < d.Scale.ColumnCount; j++)
{
Assert.AreEqual(matrix[i, j], d.Scale[i, j]);
}
}
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="ProductWishartOp"]/message_doc[@name="AAverageLogarithm(Wishart, Gamma, Wishart)"]/*'/>
public static Wishart AAverageLogarithm([SkipIfUniform] Wishart Product, [Proper] Gamma B, Wishart result)
{
if (B.IsPointMass)
{
return(AAverageLogarithm(Product, B.Point, result));
}
if (Product.IsPointMass)
{
return(AAverageLogarithm(Product.Point, B, result));
}
// (ab)^(shape-1) exp(-rate*(ab))
result.Shape = Product.Shape;
result.Rate.SetToProduct(Product.Rate, B.GetMean());
return(result);
}
public void ValidateDensity(double nu, double density)
{
int order = 1;
var matrix = new DenseMatrix(order);
matrix[0, 0] = 1;
var X = new DenseMatrix(order);
X[0, 0] = 5;
var d = new Wishart(nu, matrix);
AssertHelpers.AlmostEqual(density, d.Density(X), 16);
}
public void CanCreateWishart(double nu, int order)
{
var matrix = MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(order);
var d = new Wishart(nu, matrix);
Assert.AreEqual <double>(nu, d.Nu);
for (int i = 0; i < d.S.RowCount; i++)
{
for (int j = 0; j < d.S.ColumnCount; j++)
{
Assert.AreEqual(matrix[i, j], d.S[i, j]);
}
}
}
public static VectorGaussianWishart Combine(VectorGaussian position, Wishart orientation, VectorGaussianWishart result)
{
if (orientation.IsUniform())
{
result.SetToUniform();
}
else if (position.IsUniform())
{
result.SetTo(orientation.Shape, orientation.Rate, Vector.Zero(2), 0);
}
else
{
PositiveDefiniteMatrix rateTimesPrecision = new PositiveDefiniteMatrix(2, 2);
rateTimesPrecision.SetToProduct(orientation.Rate, position.Precision);
double trace = MathHelpers.Invert(rateTimesPrecision).Trace();
Vector positionMean = position.MeanTimesPrecision * MathHelpers.Invert(position.Precision);
result.SetTo(orientation.Shape, orientation.Rate, positionMean, orientation.Dimension / (orientation.Shape * trace));
}
return result;
}
public static double LogEvidenceRatio(PositiveDefiniteMatrix product, Wishart a, double b)
{
throw new NotImplementedException();
}
public static Wishart AAverageConditional([SkipIfUniform] Wishart Product, double B, Wishart result)
{
result.SetTo(Product);
result.Rate.Scale(B);
return result;
}
public static Wishart ProductAverageConditional(Wishart Product, Wishart A, Gamma B, Wishart result)
{
}
/// <summary>
/// VMP message to 'precision'
/// </summary>
/// <param name="Sample">Incoming message from 'sample'. Must be a proper distribution. If any element is uniform, the result will be uniform.</param>
/// <param name="SampleMean">Buffer 'SampleMean'.</param>
/// <param name="SampleVariance">Buffer 'SampleVariance'.</param>
/// <param name="Mean">Incoming message from 'mean'. Must be a proper distribution. If any element is uniform, the result will be uniform.</param>
/// <param name="MeanMean">Buffer 'MeanMean'.</param>
/// <param name="MeanVariance">Buffer 'MeanVariance'.</param>
/// <param name="result">Modified to contain the outgoing message</param>
/// <returns><paramref name="result"/></returns>
/// <remarks><para>
/// The outgoing message is the exponential of the average log-factor value, where the average is over all arguments except 'precision'.
/// The formula is <c>exp(sum_(sample,mean) p(sample,mean) log(factor(sample,mean,precision)))</c>.
/// </para></remarks>
/// <exception cref="ImproperMessageException"><paramref name="Sample"/> is not a proper distribution</exception>
/// <exception cref="ImproperMessageException"><paramref name="Mean"/> is not a proper distribution</exception>
public static Wishart PrecisionAverageLogarithm(
[Proper] VectorGaussian Sample,
[Fresh] Vector SampleMean,
[Fresh] PositiveDefiniteMatrix SampleVariance,
[Proper] VectorGaussian Mean,
[Fresh] Vector MeanMean,
[Fresh] PositiveDefiniteMatrix MeanVariance,
Wishart result)
{
if (Sample.IsPointMass) return PrecisionAverageLogarithm(Sample.Point, Mean, MeanMean, MeanVariance, result);
if (Mean.IsPointMass) return PrecisionAverageLogarithm(Sample, SampleMean, SampleVariance, Mean.Point, result);
// The formula is exp(int_x int_mean p(x) p(mean) log N(x;mean,1/prec)) =
// exp(-0.5 prec E[(x-mean)^2] + 0.5 log(prec)) =
// Gamma(prec; 0.5, 0.5*E[(x-mean)^2])
// E[(x-mean)^2] = E[x^2] - 2 E[x] E[mean] + E[mean^2] = var(x) + (E[x]-E[mean])^2 + var(mean)
if (result == default(Wishart)) result = new Wishart(Sample.Dimension);
result.Shape = 0.5 * (result.Dimension + 2);
Vector diff = SampleMean - MeanMean;
result.Rate.SetToOuter(diff, diff);
result.Rate.SetToSum(result.Rate, SampleVariance);
result.Rate.SetToSum(result.Rate, MeanVariance);
result.Rate.Scale(0.5);
return result;
}
public static double AverageLogFactor(Wishart product) { return 0.0; }
/// <summary>
/// VMP message to 'precision'
/// </summary>
/// <param name="Sample">Constant value for 'sample'.</param>
/// <param name="Mean">Constant value for 'mean'.</param>
/// <param name="result">Modified to contain the outgoing message</param>
/// <returns><paramref name="result"/></returns>
/// <remarks><para>
/// The outgoing message is the factor viewed as a function of 'precision' conditioned on the given values.
/// </para></remarks>
public static Wishart PrecisionAverageLogarithm(Vector Sample, Vector Mean, Wishart result)
{
return PrecisionConditional(Sample, Mean, result);
}
public void FailSetRandomSourceWithNullReference()
{
var d = new Wishart(1.0, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(2));
Assert.Throws<ArgumentNullException>(() => d.RandomSource = null);
}
public void ValidateDensity(double nu, double density)
{
const int Order = 1;
var matrix = new DenseMatrix(Order);
matrix[0, 0] = 1;
var x = new DenseMatrix(Order);
x[0, 0] = 5;
var d = new Wishart(nu, matrix);
AssertHelpers.AlmostEqualRelative(density, d.Density(x), 16);
}
public static double LogEvidenceRatio(Wishart product, Wishart a, double b) { return 0.0; }
public void ValidateMode(double nu, int order)
{
var d = new Wishart(nu, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(order));
var mode = d.Mode;
for (var i = 0; i < d.Scale.RowCount; i++)
{
for (var j = 0; j < d.Scale.ColumnCount; j++)
{
Assert.AreEqual((nu - d.Scale.RowCount - 1.0) * d.Scale[i, j], mode[i, j]);
}
}
}
public void ValidateVariance(double nu, int order)
{
var d = new Wishart(nu, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(order));
var variance = d.Variance;
for (var i = 0; i < d.Scale.RowCount; i++)
{
for (var j = 0; j < d.Scale.ColumnCount; j++)
{
Assert.AreEqual(nu * ((d.Scale[i, j] * d.Scale[i, j]) + (d.Scale[i, i] * d.Scale[j, j])), variance[i, j]);
}
}
}
public void CanGetS()
{
const int Order = 2;
var matrix = MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(Order);
var d = new Wishart(1.0, matrix);
for (var i = 0; i < Order; i++)
{
for (var j = 0; j < Order; j++)
{
Assert.AreEqual(matrix[i, j], d.Scale[i, j]);
}
}
}
public void CanGetNu(double nu)
{
var d = new Wishart(nu, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(2));
Assert.AreEqual(nu, d.DegreesOfFreedom);
}
public void ValidateToString()
{
var d = new Wishart(1.0, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(2));
Assert.AreEqual("Wishart(DegreesOfFreedom = 1, Rows = 2, Columns = 2)", d.ToString());
}
/// <summary>
/// VMP message to 'a'
/// </summary>
/// <param name="Product">Constant value for 'product'.</param>
/// <param name="B">Constant value for 'b'.</param>
/// <returns>The outgoing VMP message to the 'a' argument</returns>
/// <remarks><para>
/// The outgoing message is the factor viewed as a function of 'a' conditioned on the given values.
/// </para></remarks>
public static Wishart AAverageLogarithm(PositiveDefiniteMatrix Product, double B, Wishart result)
{
result.Point = Product;
result.Point.Scale(1/B);
return result;
}
/// <summary>
/// Gibbs message to 'precision'
/// </summary>
/// <param name="Sample">Constant value for 'sample'.</param>
/// <param name="Mean">Constant value for 'mean'.</param>
/// <param name="result">Modified to contain the outgoing message</param>
/// <returns><paramref name="result"/></returns>
/// <remarks><para>
/// The outgoing message is the factor viewed as a function of 'precision' conditioned on the given values.
/// </para></remarks>
public static Wishart PrecisionConditional(Vector Sample, Vector Mean, Wishart result)
{
Vector workspace = Vector.Zero(Sample.Count);
return PrecisionConditional(Sample, Mean, result, workspace);
}
/// <summary>
/// VMP message to 'a'
/// </summary>
/// <param name="Product">Incoming message from 'product'. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <param name="B">Constant value for 'b'.</param>
/// <returns>The outgoing VMP message to the 'a' argument</returns>
/// <remarks><para>
/// The outgoing message is the factor viewed as a function of 'a' with 'product' integrated out.
/// The formula is <c>sum_product p(product) factor(product,a,b)</c>.
/// </para></remarks>
/// <exception cref="ImproperMessageException"><paramref name="Product"/> is not a proper distribution</exception>
public static Wishart AAverageLogarithm([SkipIfUniform] Wishart Product, double B, Wishart result)
{
if (Product.IsPointMass) return AAverageLogarithm(Product.Point, B, result);
return AAverageConditional(Product, B, result);
}
/// <summary>
/// VMP message to 'precision'
/// </summary>
/// <param name="Sample">Incoming message from 'sample'. Must be a proper distribution. If any element is uniform, the result will be uniform.</param>
/// <param name="SampleMean">Buffer 'SampleMean'.</param>
/// <param name="SampleVariance">Buffer 'SampleVariance'.</param>
/// <param name="Mean">Constant value for 'mean'.</param>
/// <param name="result">Modified to contain the outgoing message</param>
/// <returns><paramref name="result"/></returns>
/// <remarks><para>
/// The outgoing message is the exponential of the average log-factor value, where the average is over all arguments except 'precision'.
/// The formula is <c>exp(sum_(sample) p(sample) log(factor(sample,mean,precision)))</c>.
/// </para></remarks>
/// <exception cref="ImproperMessageException"><paramref name="Sample"/> is not a proper distribution</exception>
public static Wishart PrecisionAverageLogarithm(
[Proper] VectorGaussian Sample,
[Fresh] Vector SampleMean,
[Fresh] PositiveDefiniteMatrix SampleVariance,
Vector Mean, Wishart result)
{
return PrecisionAverageLogarithm(Mean, Sample, SampleMean, SampleVariance, result);
}
public static Wishart AAverageLogarithm(PositiveDefiniteMatrix Product, [Proper] Gamma B, Wishart result)
{
throw new NotSupportedException(GaussianProductVmpOp.NotSupportedMessage);
}
public void HasRandomSource()
{
var d = new Wishart(1.0, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(2));
Assert.IsNotNull(d.RandomSource);
}
public void CanSample()
{
var d = new Wishart(1.0, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(2));
d.Sample();
}
/// <summary>
/// VMP message to 'product'
/// </summary>
/// <param name="B">Constant value for 'a'.</param>
/// <param name="A">Incoming message from 'b'. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <returns>The outgoing VMP message to the 'product' argument</returns>
/// <remarks><para>
/// The outgoing message is a distribution matching the moments of 'product' as the random arguments are varied.
/// The formula is <c>proj[sum_(b) p(b) factor(product,a,b)]</c>.
/// </para></remarks>
/// <exception cref="ImproperMessageException"><paramref name="A"/> is not a proper distribution</exception>
public static Wishart ProductAverageLogarithm([SkipIfUniform] Wishart A, double B, Wishart result)
{
return ProductAverageConditional(A, B, result);
}
public static Wishart AAverageLogarithm([SkipIfUniform] Wishart Product, [Proper] Gamma B, Wishart result)
{
if (B.IsPointMass) return AAverageLogarithm(Product, B.Point, result);
if (Product.IsPointMass) return AAverageLogarithm(Product.Point, B, result);
// (ab)^(shape-1) exp(-rate*(ab))
result.Shape = Product.Shape;
result.Rate.SetToProduct(Product.Rate, B.GetMean());
return result;
}
/// <summary>
/// VMP message to 'product'
/// </summary>
/// <param name="B">Incoming message from 'a'. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <param name="A">Incoming message from 'b'. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <returns>The outgoing VMP message to the 'product' argument</returns>
/// <remarks><para>
/// The outgoing message is a distribution matching the moments of 'product' as the random arguments are varied.
/// The formula is <c>proj[sum_(a,b) p(a,b) factor(product,a,b)]</c>.
/// </para></remarks>
/// <exception cref="ImproperMessageException"><paramref name="B"/> is not a proper distribution</exception>
/// <exception cref="ImproperMessageException"><paramref name="A"/> is not a proper distribution</exception>
public static Wishart ProductAverageLogarithm([SkipIfUniform] Wishart A, [SkipIfUniform] Gamma B, Wishart result)
{
if (B.IsPointMass) return ProductAverageLogarithm(A, B.Point, result);
// E[x] = E[a]*E[b]
// E[log(x)] = E[log(a)]+E[log(b)]
PositiveDefiniteMatrix m = new PositiveDefiniteMatrix(A.Dimension, A.Dimension);
A.GetMean(m);
m.Scale(B.GetMean());
double meanLogDet = A.Dimension*B.GetMeanLog() + A.GetMeanLogDeterminant();
if (m.LogDeterminant() < meanLogDet) throw new MatrixSingularException(m);
return Wishart.FromMeanAndMeanLogDeterminant(m, meanLogDet, result);
}
/// <summary>
/// Gibbs message to 'precision'
/// </summary>
/// <param name="Sample">Constant value for 'sample'.</param>
/// <param name="Mean">Constant value for 'mean'.</param>
/// <param name="result">Modified to contain the outgoing message</param>
/// <returns><paramref name="result"/></returns>
/// <remarks><para>
/// The outgoing message is the factor viewed as a function of 'precision' conditioned on the given values.
/// </para></remarks>
public static Wishart PrecisionConditional(Vector Sample, Vector Mean, Wishart result, Vector diff)
{
if (result == default(Wishart)) result = new Wishart(Sample.Count);
diff.SetToDifference(Sample, Mean);
const double SQRT_HALF = 0.70710678118654752440084436210485;
diff.Scale(SQRT_HALF);
result.Rate.SetToOuter(diff, diff);
result.Shape = 0.5 * (result.Dimension + 2);
return result;
}
/// <summary>
/// Evidence message for EP
/// </summary>
/// <param name="sample">Incoming message from 'sample'.</param>
/// <param name="to_sample">Outgoing message to 'sample'.</param>
/// <returns>Logarithm of the factor's average value across the given argument distributions</returns>
/// <remarks><para>
/// The formula for the result is <c>log(sum_(sample) p(sample) factor(sample,shape,scale))</c>.
/// </para></remarks>
public static double LogAverageFactor(Wishart sample, [Fresh] Wishart to_sample)
{
return to_sample.GetLogAverageOf(sample);
}
