/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="WishartFromShapeAndRateOp_Laplace2"]/message_doc[@name="RateAverageConditional(Wishart, double, Wishart, Wishart, Wishart)"]/*'/>
public static Wishart RateAverageConditional([SkipIfUniform] Wishart sample, double shape, Wishart rate, Wishart to_rate, Wishart result)
{
if (sample.IsPointMass)
{
return(WishartFromShapeAndRateOp.RateAverageConditional(sample.Point, shape, result));
}
// f(Y,R) = |Y|^(a-c) |R|^a exp(-tr(YR))
// p(Y) = |Y|^(a_y-c) exp(-tr(YB_y)
// p(R) = |R|^(a_r-c) exp(-tr(RB_r)
// int_Y f(Y,R) p(Y) dY = |R|^a |R+B_y|^-(a+a_y-c)
int dim = sample.Dimension;
double c = 0.5 * (dim + 1);
double shape2 = shape - c + sample.Shape;
Wishart ratePost = rate * to_rate;
PositiveDefiniteMatrix r = ratePost.GetMean();
PositiveDefiniteMatrix rby = r + sample.Rate;
PositiveDefiniteMatrix invrby = rby.Inverse();
PositiveDefiniteMatrix rInvrby = rby;
rInvrby.SetToProduct(r, invrby);
double xxddlogp = Matrix.TraceOfProduct(rInvrby, rInvrby) * shape2;
double delta = -xxddlogp / dim;
PositiveDefiniteMatrix invR = r.Inverse();
PositiveDefiniteMatrix dlogp = invrby;
dlogp.Scale(-shape2);
LowerTriangularMatrix rChol = new LowerTriangularMatrix(dim, dim);
rChol.SetToCholesky(r);
result.SetDerivatives(rChol, invR, dlogp, xxddlogp, GammaFromShapeAndRateOp.ForceProper, shape);
return(result);
}
/// <summary>
/// Cholesky of Kernel matrix
/// </summary>
/// <param name="kf">Kernel function</param>
/// <param name="xData">Data with which to build the matrix</param>
/// <returns></returns>
public static LowerTriangularMatrix Cholesky(IKernelFunction kf, Dictionary <int, Vector> xData)
{
if (null == kf || null == xData)
{
throw new ArgumentException("Unexpected null arguments");
}
int nData = xData.Count;
// Allocate and fill the Kernel matrix.
PositiveDefiniteMatrix K = new PositiveDefiniteMatrix(nData, nData);
for (int i = 0; i < nData; i++)
{
for (int j = 0; j < nData; j++)
{
// Evaluate the kernel. All hyperparameters, including noise
// variance are handled in the kernel.
K[i, j] = kf.EvaluateX1X2(xData[i], xData[j]);
}
}
LowerTriangularMatrix chol = new LowerTriangularMatrix(nData, nData);
chol.SetToCholesky(K);
K = null;
GC.Collect(0);
return(chol);
}
static void begin(LowerTriangularMatrix <double> lt, int start, int antCount, double alpha,
double beta, double pheromoneEvaporationCoef, double pheromoneConstant, int maxIters,
Queue <IterationContext> cq)
{
AntColony ac = new AntColony(lt, start, antCount, alpha, beta, pheromoneEvaporationCoef,
pheromoneConstant, maxIters, cq);
ac.begin();
int currIter = 0;
while (currIter < maxIters - 1)
{
IterationContext it;
while (cq.TryDequeue(out it) == false)
{
;
}
currIter = it.currIter;
Console.WriteLine("" + it.currIter);
}
var path = string.Join("=>", ac.shortestPath);
var dist = ac.shrotestDistance;
Console.WriteLine($"Shortest path has length of {dist} and it is: {path}");
}
private static PositiveDefiniteMatrix GetInverse(PositiveDefiniteMatrix A)
{
PositiveDefiniteMatrix result = new PositiveDefiniteMatrix(A.Rows, A.Cols);
LowerTriangularMatrix L = new LowerTriangularMatrix(A.Rows, A.Cols);
L.SetToCholesky(A);
bool[] isZero = new bool[L.Rows];
for (int i = 0; i < L.Rows; i++)
{
if (L[i, i] == 0)
{
isZero[i] = true;
L[i, i] = 1;
}
}
L.SetToInverse(L);
result.SetToOuterTranspose(L);
for (int i = 0; i < isZero.Length; i++)
{
if (isZero[i])
{
result[i, i] = double.PositiveInfinity;
}
}
return(result);
}
#pragma warning disable 162
#endif
/// <summary>EP message to <c>b</c>.</summary>
/// <param name="product">Incoming message from <c>product</c>.</param>
/// <param name="A">Constant value for <c>a</c>.</param>
/// <param name="result">Modified to contain the outgoing message.</param>
/// <returns>
/// <paramref name="result" />
/// </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>
public static VectorGaussian BAverageConditional(VectorGaussian product, Matrix A, VectorGaussian result)
{
if (product.IsPointMass)
{
return(BAverageConditional(product.Point, A, result));
}
// (p.mean - A*B)'*p.prec*(p.mean - A*B)
// = B'*(A'*p.prec*A)*B - B'*A'*p.prec*p.mean - ...
// B.prec = A'*p.prec*A
// B.precTimesMean = A'*p.precTimesMean
if (true)
{
// this method is slower but more numerically accurate
// L*L' = p.prec
int dim = product.Precision.Cols;
LowerTriangularMatrix L = new LowerTriangularMatrix(dim, dim);
L.SetToCholesky(product.Precision);
Matrix At = A.Transpose();
Matrix temp = At * L;
result.Precision.SetToOuter(temp);
}
else
{
Matrix temp = (product.Precision * A).Transpose();
result.Precision.SetToProduct(temp, A);
}
result.MeanTimesPrecision.SetToProduct(product.MeanTimesPrecision, A);
return(result);
}
public PositiveDefiniteMatrix Sample(PositiveDefiniteMatrix result)
{
Assert.IsTrue(result.Rows == Dimension);
LowerTriangularMatrix cholB = new LowerTriangularMatrix(Dimension, Dimension);
LowerTriangularMatrix cholX = new LowerTriangularMatrix(Dimension, Dimension);
Matrix cholXt = new Matrix(Dimension, Dimension);
return(Sample(result, cholB, cholX, cholXt));
}
public IterationContext(List <List <int> > antsRoutes, List <int> iterShortestPath,
LowerTriangularMatrix <double> pheromoneMatrix, int currIter,
int numOfIters)
{
this.antsRoutes = antsRoutes;
this.iterShortestPath = iterShortestPath;
this.pheromoneMatrix = new LowerTriangularMatrix <double>(pheromoneMatrix);
this.currIter = currIter;
this.numOfIters = numOfIters;
}
// Use this for initialization
void Start()
{
timeLeft = lengthOfAnimation;
cityControler = gameObject.GetComponent <CityControler>();
acoControler = gameObject.GetComponent <AcoControler>();
pathControler = gameObject.GetComponent <PathControler>();
pheromons = null;
antPefab = Resources.Load <GameObject>("CityTestScene/Prefab/Ant");
distanceControler = gameObject.GetComponent <DistanceControler>();
}
public LowerTriangularMatrix(LowerTriangularMatrix <T> other)
{
this.size = other.size;
data = new T[size * (size + 1) / 2];
//deep copy of array
for (int i = 0; i < this.size * (this.size + 1) / 2; ++i)
{
this.data[i] = other.data[i];
}
}
private static double GetSquaredLengthOfRow(LowerTriangularMatrix L, int row)
{
double sum = 0;
for (int col = 0; col <= row; col++)
{
double element = L[row, col];
sum += element * element;
}
return(sum);
}
private static double GetSquaredLengthOfColumn(LowerTriangularMatrix L, int column)
{
int rows = L.Rows;
double sum = 0;
for (int row = column; row < rows; row++)
{
double element = L[row, column];
sum += element * element;
}
return(sum);
}
public Ant(int start, List <int> notVisited, LowerTriangularMatrix <double> pheromoneMatrix,
LowerTriangularMatrix <double> distanceMatrix, double alpha, double beta, bool firstPass)
{
this.notVisited = notVisited;
this.pheromoneMatrix = pheromoneMatrix;
this.distanceMatrix = distanceMatrix;
this.alpha = alpha;
this.beta = beta;
this.firstPass = firstPass;
this.route = new List <int>();
updateRoute(start);
this.distanceTraveled = 0;
}
private void applyLinearScale(double a, double b, LowerTriangularMatrix <double> matrix)
{
for (int i = 0; i < matrix.size; ++i)
{
for (int j = i + 1; j < matrix.size; ++j)
{
if (matrix[i, j] != 0)
{
matrix[i, j] = a * matrix[i, j] + b;
}
}
}
}
private void calculateFitness(LowerTriangularMatrix <double> lt)
{
int threadNum = Environment.ProcessorCount * 2;
ConcurrentQueue <int> unservisedColonies =
new ConcurrentQueue <int>(Enumerable.Range(0, currentGeneration.Count));
Task[] tasks = new Task[threadNum];
for (int i = 0; i < threadNum; ++i)
{
tasks[i] = Task.Factory.StartNew(() => threadRun(unservisedColonies, lt));
}
Task.WaitAll(tasks);
}
public static void Main(string[] args)
{
Queue <IterationContext> cq = new Queue <IterationContext>();
int start = 0;
int antCount = 100;
double alpha = .27;
double beta = 8.8;
double pheromoneEvaporationCoef = 0.7;
double pheromoneConstant = 250;
int maxIters = 100;
if (args[0] == "-genarate")
{
int numOfGraphs = 1;
int maxNodes = 20;
int minNodes = 5;
int maxWeight = 3000;
int minWeight = 500;
Generator g = new Generator(numOfGraphs, maxNodes, minNodes, maxWeight, minWeight);
var graphs = g.generate(); //array of matricies of graphs
Console.WriteLine("Graphs generated");
foreach (LowerTriangularMatrix <double> lt in graphs)
{
lt.writeToFile("test.txt");
Console.WriteLine(lt.size);
begin(lt, start, antCount, alpha, beta, pheromoneEvaporationCoef, pheromoneConstant
, maxIters, cq);
}
}
else if (args[0] == "-run")
{
LowerTriangularMatrix <double> lt = new LowerTriangularMatrix <double>(0);
lt.readFromFile(args[1]);
begin(lt, start, antCount, alpha, beta, pheromoneEvaporationCoef, pheromoneConstant
, maxIters, cq);
}
else if (args[0] == "-genetic")
{
GeneticAlg g = new GeneticAlg(5000);
g.start();
}
else
{
Console.WriteLine("Need an option besides [-generate,-genetic,-run <path>]? Add it :D");
return;
}
}
public static PositiveDefiniteMatrix Sample(double shape, PositiveDefiniteMatrix scale, PositiveDefiniteMatrix result)
{
int dimension = scale.Rows;
LowerTriangularMatrix cholB = new LowerTriangularMatrix(dimension, dimension);
cholB.SetToCholesky(scale);
LowerTriangularMatrix cholX = new LowerTriangularMatrix(dimension, dimension);
Rand.Wishart(shape, cholX);
cholX.SetToProduct(cholB, cholX);
UpperTriangularMatrix cholXt = cholX.Transpose();
result.SetToProduct(cholX, cholXt);
return(result);
}
public void RandWishart()
{
// multivariate Gamma
double a = 2.7;
int d = 3;
PositiveDefiniteMatrix mTrue = new PositiveDefiniteMatrix(d, d);
mTrue.SetToIdentity();
mTrue.SetToProduct(mTrue, a);
LowerTriangularMatrix L = new LowerTriangularMatrix(d, d);
PositiveDefiniteMatrix X = new PositiveDefiniteMatrix(d, d);
PositiveDefiniteMatrix m = new PositiveDefiniteMatrix(d, d);
m.SetAllElementsTo(0);
double s = 0;
for (int i = 0; i < nsamples; i++)
{
Rand.Wishart(a, L);
X.SetToProduct(L, L.Transpose());
m = m + X;
s = s + X.LogDeterminant();
}
double sTrue = 0;
for (int i = 0; i < d; i++)
{
sTrue += MMath.Digamma(a - i * 0.5);
}
m.Scale(1.0 / nsamples);
s = s / nsamples;
Console.WriteLine("");
Console.WriteLine("Multivariate Gamma");
Console.WriteLine("-------------------");
Console.WriteLine("m = \n{0}", m);
double dError = m.MaxDiff(mTrue);
if (dError > TOLERANCE)
{
Assert.True(false, String.Format("Wishart({0}) mean: (should be {0}*I), error = {1}", a, dError));
}
if (System.Math.Abs(s - sTrue) > TOLERANCE)
{
Assert.True(false, string.Format("E[logdet]: {0} (should be {1})", s, sTrue));
}
}
void loadDistances()
{
distance_ = new LowerTriangularMatrix <float>(cc.citys.Length);
var file = Resources.Load <TextAsset>("CityTestScene/Data/distances");
var tmp = JsonUtility.FromJson <JsonArray <Distance> >(file.text).array;
foreach (var x in tmp)
{
int i = cc.mapNameToIndex(x.from);
int j = cc.mapNameToIndex(x.to);
distance_[i, j] = x.distance;
//Debug.Log(i + " " + j +" " + x.distance);
}
}
public void start()
{
int iterCount = 200;
int iter = 0;
init();
LowerTriangularMatrix <double> lt = new LowerTriangularMatrix <double>(0);
lt.readFromFile("../data/cities_dist.txt");
for (iter = 0; iter < iterCount; ++iter)
{
Console.WriteLine("iteration: " + iter);
calculateFitness(lt);
crossingSpecies();
mutateSpecies();
swapWorstParents();
if (allTimeBest.fitness >
this.currentGeneration[this.currentGeneration.Count - 1].fitness)
{
//saving all time best
Console.WriteLine("New All time best!");
allTimeBest = new Colony(this.currentGeneration[this.currentGeneration.Count - 1]);
}
Console.WriteLine("fitness: " + this.currentGeneration[this.currentGeneration.Count - 1]
.fitness);
Console.WriteLine("length: " + this.currentGeneration[this.currentGeneration.Count - 1]
.shorestDistance);
Console.WriteLine("time: " + this.currentGeneration[this.currentGeneration.Count - 1].time);
Console.WriteLine(string.Join(" ", allTimeBest.parameters));
// if(iter % 10 == 0){
// Console.WriteLine("fitness: " + this.currentGeneration[this.currentGeneration.Count -1].fitness);
// }
this.newGeneration.Clear();
}
Console.WriteLine("fitness: " + allTimeBest.fitness);
Console.WriteLine("path: " + allTimeBest.shorestDistance);
Console.WriteLine("time: " + allTimeBest.time);
string outputString = string.Join(" ", allTimeBest.parameters);
Console.WriteLine(outputString);
string[] lines = new string[1];
lines.Append(outputString);
System.IO.File.WriteAllLines("ACO_parameters.txt", lines);
}
public void reset()
{
pheromons = null;
for (int i = 0; i < cityControler.activeCitysIndex.Length; ++i)
{
int tmp = cityControler.activeCitysIndex[i];
for (int j = i + 1; j < cityControler.activeCitysIndex.Length; ++j)
{
int tmp1 = cityControler.activeCitysIndex[j];
if (pathControler.pathMatrix[tmp, tmp1])
{
pathControler.pathMatrix[tmp, tmp1].startWidth = 0;
pathControler.pathMatrix[tmp, tmp1].endWidth = 0;
}
}
}
}
private static void GetProductMoments(Matrix A, Vector BMean, PositiveDefiniteMatrix BVariance, Vector mean, PositiveDefiniteMatrix variance)
{
// P.mean = A*B.mean
// P.var = A*B.var*A'
mean.SetToProduct(A, BMean);
if (UseAccurateMethod)
{
int dim = BVariance.Rows;
LowerTriangularMatrix cholesky = new LowerTriangularMatrix(dim, dim);
cholesky.SetToCholesky(BVariance);
Matrix AL = A * cholesky;
variance.SetToOuter(AL);
}
else
{
variance.SetToProduct(A, (A * BVariance).Transpose());
variance.Symmetrize();
}
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="WishartFromShapeAndRateOp_Laplace2"]/message_doc[@name="SampleAverageConditional(Wishart, double, Wishart, Wishart, Wishart, Wishart)"]/*'/>
public static Wishart SampleAverageConditional([NoInit] Wishart sample, double shape, [Proper] Wishart rate, [NoInit] Wishart to_rate, [NoInit] Wishart to_sample, Wishart result)
{
if (sample.IsUniform())
{
return(SampleAverageConditional2(shape, rate, to_rate, result));
}
// f(Y,R) = |Y|^(a-c) |R|^a exp(-tr(YR))
// p(Y) = |Y|^(a_y-c) exp(-tr(YB_y)
// p(R) = |R|^(a_r-c) exp(-tr(RB_r)
// int_R f(Y,R) p(R) dR = |Y|^(a-c) |Y+B_r|^-(a+a_r)
int dim = sample.Dimension;
double c = 0.5 * (dim + 1);
double shape2 = shape + rate.Shape;
Wishart samplePost = sample * to_sample;
if (!samplePost.IsProper())
{
return(SampleAverageConditional2(shape, rate, to_rate, result));
}
PositiveDefiniteMatrix y = samplePost.GetMean();
PositiveDefiniteMatrix yPlusBr = y + rate.Rate;
PositiveDefiniteMatrix invyPlusBr = yPlusBr.Inverse();
PositiveDefiniteMatrix yInvyPlusBr = yPlusBr;
yInvyPlusBr.SetToProduct(y, invyPlusBr);
double xxddlogf = shape2 * Matrix.TraceOfProduct(yInvyPlusBr, yInvyPlusBr);
PositiveDefiniteMatrix invY = y.Inverse();
//double delta = -xxddlogf / dim;
//result.Shape = delta + shape;
//result.Rate.SetToSum(delta, invY, shape2, invyPlusBr);
LowerTriangularMatrix yChol = new LowerTriangularMatrix(dim, dim);
yChol.SetToCholesky(y);
PositiveDefiniteMatrix dlogp = invyPlusBr;
dlogp.Scale(-shape2);
result.SetDerivatives(yChol, invY, dlogp, xxddlogf, GammaFromShapeAndRateOp.ForceProper, shape - c);
if (result.Rate.Any(x => double.IsNaN(x)))
{
throw new Exception("result.Rate is nan");
}
return(result);
}
private LowerTriangularMatrix <double> getMatrix()
{
LowerTriangularMatrix <double> matrix =
new LowerTriangularMatrix <double>(cityControler.activeCitysIndex.Length);
for (int i = 0; i < matrix.size; ++i)
{
int tmp = cityControler.activeCitysIndex[i];
for (int j = i + 1; j < matrix.size; ++j)
{
int tmp1 = cityControler.activeCitysIndex[j];
matrix[i, j] = distanceControler.distanceMatrix[tmp, tmp1];
}
}
return(matrix);
}
/// <summary>
/// Gets the normalizer for a Wishart density function specified by shape and rate matrix
/// </summary>
/// <param name="shape">Shape parameter</param>
/// <param name="rate">rate matrix</param>
/// <returns></returns>
public static double GetLogNormalizer(double shape, PositiveDefiniteMatrix rate)
{
int dimension = rate.Rows;
// inline call to IsProper()
if (!(shape > 0.5 * (dimension - 1)))
{
return(0.0);
}
LowerTriangularMatrix rateChol = new LowerTriangularMatrix(dimension, dimension);
bool isPosDef = rateChol.SetToCholesky(rate);
if (!isPosDef)
{
return(0.0);
}
// LogDeterminant(rate) = 2*L.TraceLn()
return(MMath.GammaLn(shape, dimension) - shape * 2 * rateChol.TraceLn());
}
private void findMinMax(LowerTriangularMatrix <double> matrix, out double min, out double max)
{
min = double.MaxValue;
max = double.MinValue;
for (int i = 0; i < matrix.size; ++i)
{
for (int j = i + 1; j < matrix.size; ++j)
{
if (matrix[i, j] < min)
{
min = matrix[i, j];
}
if (max < matrix[i, j])
{
max = matrix[i, j];
}
}
}
}
public PositiveDefiniteMatrix Sample(PositiveDefiniteMatrix result,
LowerTriangularMatrix cholB, LowerTriangularMatrix cholX, Matrix cholXt)
{
if (IsPointMass)
{
result.SetTo(Point);
return(result);
}
// Algorithm:
// X = chol(inv(B))*W*chol(inv(B))' where W is std Wishart
// chol(inv(B)) = inv(chol(B)')
cholB.SetToCholesky(rate);
UpperTriangularMatrix cholBt = UpperTriangularMatrix.TransposeInPlace(cholB);
Rand.Wishart(Shape, cholX);
cholX.PredivideBy(cholBt);
// cholX is no longer LowerTriangular
cholXt.SetToTranspose(cholX);
result.SetToProduct(cholX, cholXt);
return(result);
}
private void threadRun(ConcurrentQueue <int> unservisedColonies, LowerTriangularMatrix <double> lt)
{
while (!unservisedColonies.IsEmpty)
{
int index;
Queue <IterationContext> cq = new Queue <IterationContext>();//unused here
unservisedColonies.TryDequeue(out index);
Colony tmp = currentGeneration[index];
Stopwatch sw = new Stopwatch();
//since ACO is nondeterministic, we will repeat algoritam few times and take average
double[] dists = new double[this.numberOfRepetitions];
int[] times = new int[this.numberOfRepetitions];
for (int i = 0; i < this.numberOfRepetitions; ++i)
{
sw.Start();
AntColony ac = new AntColony(lt, 0, (int)tmp.parameters[0], tmp.parameters[1], tmp.parameters[2],
tmp.parameters[3], tmp.parameters[4], (int)tmp.parameters[5], cq);
ac.mainLoop();
sw.Stop();
dists[i] = ac.shrotestDistance;
times[i] = (int)sw.ElapsedMilliseconds;
}
double averageDist = dists.Sum() / dists.Length;
int averageTime = times.Sum() / times.Length;
int time = (int)sw.ElapsedMilliseconds;
currentGeneration[index].fitness = fitnessFunction(averageDist, averageTime);
currentGeneration[index].shorestDistance = averageDist;
currentGeneration[index].time = averageTime;
// Console.WriteLine("index: " + index + " fitness: " + currentGeneration[index].fitness
// +" for " + time + "ms");
}
}
public AntColony(LowerTriangularMatrix <double> matrix, int start, int antCount, double alpha, double beta,
double pheromoneEvaporationCoef, double pheromoneConstant, int numOfIters,
Queue <IterationContext> cq)
{
this.matrix = new LowerTriangularMatrix <double>(matrix);
this.start = start;
this.antCount = antCount;
this.alpha = alpha;
this.beta = beta;
this.pheromoneMatrix = new LowerTriangularMatrix <double>(matrix.size);
this.pheromoneMatrixCopy = new LowerTriangularMatrix <double>(matrix.size);
this.pheromoneEvaporationCoef = pheromoneEvaporationCoef;
this.pheromoneConstant = pheromoneConstant;
this.numOfIters = numOfIters;
ants = new Ant[antCount];
this.firstPass = true;
this.shortestPath = null;
this.shrotestDistance = -1;
initAnts();
this.resultQueue = cq;
this.running = true;
this.sendingStep = 5;//CAREFULL WHEN CHANGING THIS, numOfIters % sendingStep == 0(this must be true!)
}
/// <summary>
/// Cholesky of Kernel matrix
/// </summary>
/// <param name="kf">Kernel function</param>
/// <param name="xData">Data with which to build the matrix</param>
/// <returns></returns>
public static LowerTriangularMatrix Cholesky(IKernelFunction kf, Dictionary<int, Vector> xData)
{
if (null == kf || null == xData)
throw new ArgumentException("Unexpected null arguments");
int nData = xData.Count;
// Allocate and fill the Kernel matrix.
PositiveDefiniteMatrix K = new PositiveDefiniteMatrix(nData, nData);
for (int i = 0; i < nData; i++) {
for (int j = 0; j < nData; j++) {
// Evaluate the kernel. All hyperparameters, including noise
// variance are handled in the kernel.
K[i, j] = kf.EvaluateX1X2(xData[i], xData[j]);
}
}
LowerTriangularMatrix chol = new LowerTriangularMatrix(nData, nData);
chol.SetToCholesky(K);
K = null;
#if !SILVERLIGHT
GC.Collect(0);
#endif
return chol;
}
public static Wishart ShapeOrientationAverageConditional(
Vector point, Bernoulli label, Gaussian shapeX, Gaussian shapeY, Wishart shapeOrientation, Wishart result)
{
if (shapeOrientation.IsPointMass && shapeX.IsPointMass && shapeY.IsPointMass)
{
double labelProbTrue = label.GetProbTrue();
double labelProbFalse = 1.0 - labelProbTrue;
double probDiff = labelProbTrue - labelProbFalse;
Vector shapeLocation = Vector.FromArray(shapeX.Point, shapeY.Point);
Vector diff = shapeLocation - point;
Matrix diffOuter = diff.Outer(diff);
Matrix orientationTimesDiffOuter = shapeOrientation.Point * diffOuter;
double trace = orientationTimesDiffOuter.Trace();
double factorValue = Math.Exp(-0.5 * shapeOrientation.Point.QuadraticForm(diff));
double funcValue = factorValue * probDiff + labelProbFalse;
PositiveDefiniteMatrix dLogFunc = new PositiveDefiniteMatrix(diffOuter * (-0.5 * probDiff * factorValue / funcValue));
double xxddLogFunc =
-0.5 * probDiff * (-0.5 * labelProbFalse * factorValue * trace * trace / (funcValue * funcValue) + factorValue * trace / funcValue);
LowerTriangularMatrix cholesky = new LowerTriangularMatrix(2, 2);
cholesky.SetToCholesky(shapeOrientation.Point);
PositiveDefiniteMatrix inverse = shapeOrientation.Point.Inverse();
result.SetDerivatives(cholesky, inverse, dLogFunc, xxddLogFunc, forceProper: true);
return result;
}
else
{
throw new NotSupportedException();
}
}
public static Wishart MatrixAverageConditional(Wishart matrix, Gaussian angle, Gaussian logScaleX, Gaussian logScaleY, Wishart result)
{
if (!matrix.IsPointMass)
{
throw new NotImplementedException();
}
Func<Matrix, double> logF =
p =>
{
double lsx, lsy, a;
ExtractScaleAngle(p, out lsx, out lsy, out a);
return angle.GetLogProb(a) + logScaleX.GetLogProb(lsx) + logScaleY.GetLogProb(lsy);
};
Func<Matrix, double> trXdLogF =
p =>
{
return (p * MatrixDerivative(p, logF)).Trace();
};
Matrix dLogF = MatrixDerivative(matrix.Point, logF);
Matrix dTrXdLogF = MatrixDerivative(matrix.Point, trXdLogF);
double trXdTrXdLogF = (matrix.Point * dTrXdLogF).Trace();
LowerTriangularMatrix cholesky = new LowerTriangularMatrix(2, 2);
cholesky.SetToCholesky(matrix.Point);
PositiveDefiniteMatrix inverse = matrix.Point.Inverse();
result.SetDerivatives(cholesky, inverse, new PositiveDefiniteMatrix(dLogF), trXdTrXdLogF, forceProper: true);
return result;
}
/// <summary>
/// Evidence message for EP
/// </summary>
/// <param name="sample">Constant value for 'sample'.</param>
/// <param name="mean">Constant value for 'mean'.</param>
/// <param name="precision">Constant value for 'precision'.</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(factor(sample,mean,precision))</c>.
/// </para></remarks>
public static double LogAverageFactor(Vector sample, Vector mean, PositiveDefiniteMatrix precision)
{
int Dimension = sample.Count;
LowerTriangularMatrix precL = new LowerTriangularMatrix(Dimension, Dimension);
Vector iLb = Vector.Zero(Dimension);
Vector precisionTimesMean = precision * mean;
return VectorGaussian.GetLogProb(sample, precisionTimesMean, precision, precL, iLb);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="ArrayFromVectorOp"]/message_doc[@name="ArrayAverageConditional{GaussianList}(IList{Gaussian}, VectorGaussian, GaussianList)"]/*'/>
/// <typeparam name="GaussianList">The type of the resulting array.</typeparam>
public static GaussianList ArrayAverageConditional <GaussianList>(
[NoInit] IList <Gaussian> array, [SkipIfUniform] VectorGaussian vector, GaussianList result)
where GaussianList : IList <Gaussian>
{
if (result.Count != vector.Dimension)
{
throw new ArgumentException("vector.Dimension (" + vector.Dimension + ") != result.Count (" + result.Count + ")");
}
int length = result.Count;
bool allPointMass = array.All(g => g.IsPointMass);
if (allPointMass)
{
// efficient special case
for (int i = 0; i < length; i++)
{
double x = array[i].Point;
// -prec*(x-m) = -prec*x + prec*m
double dlogp = vector.MeanTimesPrecision[i];
for (int j = 0; j < length; j++)
{
dlogp -= vector.Precision[i, j] * array[j].Point;
}
double ddlogp = -vector.Precision[i, i];
result[i] = Gaussian.FromDerivatives(x, dlogp, ddlogp, false);
}
}
else if (vector.IsPointMass)
{
// efficient special case
Vector mean = vector.Point;
for (int i = 0; i < length; i++)
{
result[i] = Gaussian.PointMass(mean[i]);
}
}
else if (vector.IsUniform())
{
for (int i = 0; i < length; i++)
{
result[i] = Gaussian.Uniform();
}
}
else if (array.Any(g => g.IsPointMass))
{
// Z = N(m1; m2, V1+V2)
// logZ = -0.5 (m1-m2)'inv(V1+V2)(m1-m2)
// dlogZ = (m1-m2)'inv(V1+V2) dm2
// ddlogZ = -dm2'inv(V1+V2) dm2
Vector mean = Vector.Zero(length);
PositiveDefiniteMatrix variance = new PositiveDefiniteMatrix(length, length);
vector.GetMeanAndVariance(mean, variance);
for (int i = 0; i < length; i++)
{
if (array[i].IsUniform())
{
continue;
}
double m, v;
array[i].GetMeanAndVariance(out m, out v);
variance[i, i] += v;
mean[i] -= m;
}
PositiveDefiniteMatrix precision = variance.Inverse();
Vector meanTimesPrecision = precision * mean;
for (int i = 0; i < length; i++)
{
if (array[i].IsUniform())
{
result[i] = Gaussian.FromMeanAndVariance(mean[i], variance[i, i]);
}
else
{
double alpha = meanTimesPrecision[i];
double beta = precision[i, i];
result[i] = GaussianOp.GaussianFromAlphaBeta(array[i], alpha, beta, false);
}
}
}
else
{
// Compute inv(V1+V2)*(m1-m2) as inv(V2)*inv(inv(V1) + inv(V2))*(inv(V1)*m1 + inv(V2)*m2) - inv(V2)*m2 = inv(V2)*(m - m2)
// Compute inv(V1+V2) as inv(V2)*inv(inv(V1) + inv(V2))*inv(V2) - inv(V2)
PositiveDefiniteMatrix precision = (PositiveDefiniteMatrix)vector.Precision.Clone();
Vector meanTimesPrecision = vector.MeanTimesPrecision.Clone();
for (int i = 0; i < length; i++)
{
Gaussian g = array[i];
precision[i, i] += g.Precision;
meanTimesPrecision[i] += g.MeanTimesPrecision;
}
bool fastMethod = true;
if (fastMethod)
{
bool isPosDef;
// this destroys precision
LowerTriangularMatrix precisionChol = precision.CholeskyInPlace(out isPosDef);
if (!isPosDef)
{
throw new PositiveDefiniteMatrixException();
}
// variance = inv(precisionChol*precisionChol') = inv(precisionChol)'*inv(precisionChol) = varianceChol*varianceChol'
// this destroys meanTimesPrecision
var mean = meanTimesPrecision.PredivideBy(precisionChol);
mean = mean.PredivideByTranspose(precisionChol);
var varianceCholTranspose = precisionChol;
// this destroys precisionChol
varianceCholTranspose.SetToInverse(precisionChol);
for (int i = 0; i < length; i++)
{
Gaussian g = array[i];
double variance_ii = GetSquaredLengthOfColumn(varianceCholTranspose, i);
// works when g is uniform, but not when g is point mass
result[i] = Gaussian.FromMeanAndVariance(mean[i], variance_ii) / g;
}
}
else
{
// equivalent to above, but slower
PositiveDefiniteMatrix variance = precision.Inverse();
var mean = variance * meanTimesPrecision;
for (int i = 0; i < length; i++)
{
Gaussian g = array[i];
// works when g is uniform, but not when g is point mass
result[i] = Gaussian.FromMeanAndVariance(mean[i], variance[i, i]) / g;
}
}
}
return(result);
}
void makePaths()
{
int n = cityControler.citys.Length;
paths = new LowerTriangularMatrix <LineRenderer>(n);
//Debug.Log(n);
for (int i = 0; i < n; ++i)
{
GameObject city1 = cityControler.citys[i];
if (!city1)
{
continue;
}
for (int j = i + 1; j < n; ++j)
{
GameObject city2 = cityControler.citys[j];
if (!city2)
{
continue;
}
//Debug.Log("Drawing from " + i + "to " + j + " " + city1.name + "_" + city2.name);
Transform child1 = findDeepChild(city1.transform, "Outter");
Transform child2 = findDeepChild(city2.transform, "Outter");
if (!child1 || !child2)
{
return;
}
GameObject path = new GameObject();
path.name = "Path_" + city1.name + "_" + city2.name;
LineRenderer line = path.AddComponent <LineRenderer>();
line.material = new Material(Shader.Find("Sprites/Default"));
line.startColor = new Color(1, 0, 0, 1);
line.endColor = new Color(1, 0, 0, 1);
paths[i, j] = line;
line.startWidth = 0f;
line.endWidth = 0f;
int segments = 50;
float xRadius = (child1.position - child2.position).magnitude / 2;
float yRadius = xRadius / 2;
float angle = 270f;
line.positionCount = segments / 2 + 1;
for (int point = 0; point <= segments / 2; ++point)
{
float x = Mathf.Sin(Mathf.Deg2Rad * angle) * xRadius;
float z = Mathf.Cos(Mathf.Deg2Rad * angle) * yRadius;
line.useWorldSpace = false;
line.SetPosition(point, new Vector3(x, z, 0));
angle += (360f / segments);
}
path.transform.position = child1.position + (child2.position - child1.position) / 2;
var rot = Quaternion.FromToRotation(path.transform.right,
child2.position - child1.position);
path.transform.rotation = rot;
}
}
}
