public void SynthethicModelStudy(string fileName)
{
// start from full configuration
int fullLength = this.N;
int[] input = new int[fullLength];
for (int i = 0; i < fullLength; i++)
input[i] = i;
bool first = true;
// for each possible length combination
for (int l = 1; l <= fullLength; l++)
{
Combinations<int> combinations = new Combinations<int>(input, l);
foreach (int[] combination in combinations)
{
// copy of the full configuration
LineSegmentConfiguration c = new LineSegmentConfiguration(this);
// find the complement set
List<int> complement = new List<int>(input);
for (int i = 0; i < l; i++)
complement.Remove(combination[i]);
// get the configuration according the combination
for (int i = 0; i < fullLength - l; i++)
c.RemoveAtIndex(complement[i]);
// calculate Up, Ud, U an H of the current configuration
c.CalculateUP();
c.CalculateUD();
c.CalculateU();
c.CalculateH();
// output line segment details
if (first)
{
first = false;
c.WriteDebugDetails(fileName);
}
else
{
c.WriteDebugDetails(fileName, FileMode.Append, FileAccess.Write);
}
}
}
}
public LineSegmentConfiguration(LineSegmentConfiguration c)
{
_configuration = new List<LineSegment>(c._configuration);
_joinedConfiguration = new List<LineSegment>(c._joinedConfiguration);
_n = c._n;
_nfe = c._nfe;
_nf = c._nf;
_pC = c._pC;
_pCPair = c._pCPair;
if (c._pC == null)
_pC = null;
else
_pC = new List<double>(c._pC);
if (c._pCPair == null)
_pCPair = null;
else
{
_pCPair = new double[_n, _n];
Array.Copy(c._pCPair, _pCPair, c._pCPair.Length);
}
_totalL = c._totalL;
_averageL = c._averageL;
_sumPC = c._sumPC;
_sumPL = c._sumPL;
_sumPG = c._sumPG;
_sumPI = c._sumPI;
_srcImage = c._srcImage;
_gvfU = c._gvfU;
_gvfV = c._gvfV;
_gvfMagnitude = c._gvfMagnitude;
// prior model
_w1 = c._w1;
_w2 = c._w2;
_w3 = c._w3;
_wC = c._wC;
_wL = c._wL;
_thetaMax = c._thetaMax;
// data term
_It = c._It;
_kI = c._kI;
_Gt = c._Gt;
_wG = c._wG;
_wI = c._wI;
_Up = c._Up;
_Ud = c._Ud;
}
/// <summary>
/// death accept probability
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <returns></returns>
private double DeathAcceptProbability(LineSegmentConfiguration x, LineSegmentConfiguration y)
{
double R;
double evaY = _GMTargetDistribution.Evaluate(y);
double evaX = _GMTargetDistribution.Evaluate(x);
R = evaY * x.N
/ evaX / _vS;
//R = evaX / evaY;
return R < 1.0 ? R : 1.0;
}
/// <summary>
/// birth accept probability (birth accept rate)
/// </summary>
/// <returns></returns>
private double BirthAcceptProbability(LineSegmentConfiguration x, LineSegmentConfiguration y)
{
// calculate birth accept probability
double R;
double evaY = _GMTargetDistribution.Evaluate(y);
double evaX = _GMTargetDistribution.Evaluate(x);
R = evaY * _vS
/ evaX / y.N;
//R = evaX / evaY;
return R < 1.0 ? R : 1.0;
}
/// <summary>
/// do accept rejection sampling
/// </summary>
/// <returns></returns>
public List<LineSegmentConfiguration> Sample()
{
if (_GMTargetDistribution == null)
throw new ApplicationException("GVFThinningSampler::Sample(), Candidate generating distribution or Instrumental distribution is not delegated.");
// initial work space
long seed = DateTime.Now.Millisecond;
UniformDistribution randomSample = new UniformDistribution(seed + 10); // sample for accept/reject
double uSample;
UniformDistribution randomPool = new UniformDistribution(seed + 30); // sample for birth from pool
double uPool;
UniformDistribution randomBirth = new UniformDistribution(seed + 40); // birth/death probability
double uBirth;
double uDeath;
UniformDistribution randomRemove = new UniformDistribution(seed + 50); // sample for remove line segment
double uRemove;
double acceptProbability;
// MCMC interation
int n = 0;
_hits = 0;
int Nm1 = _n - 1;
double hMax = Double.MinValue;
while (n < _n)
{
// get current coinfiguration
LineSegmentConfiguration X = new LineSegmentConfiguration(_totalSamples[n]);
int xLength = X.N;
bool death = false;
bool reject = false;
// count hits of line segments
int sourceLength = _sourceLineSegmentList.N;
for (int s = 0; s < xLength; s++)
{
int lineSegmentIndex = X.Configure[s].Index;
_sourceLineSegmentList.Configure[lineSegmentIndex].Hit++;
//for (int si = 0; si < sourceLength; si++)
//{
// if (_sourceLineSegmentList.Configure[si].Index == lineSegmentIndex)
// {
// _sourceLineSegmentList.Configure[si].Hit++;
// continue;
// }
//}
}
/// Birth or Death ?
#region Birth or Death ?
uBirth = randomBirth.Sample();
if (xLength > 0 && xLength < _totalLineSegment)
uDeath = 1 - uBirth;
else if (xLength == 0)
// only birth
{
uBirth = 1.0;
uDeath = 0.0;
}
else
// only death
{
uDeath = 1.0;
uBirth = 0.0;
}
#endregion
if (uBirth > uDeath)
// Birth
#region Birth
{
death = false;
// sample a new line segment from pool
uPool = System.Math.Floor(randomPool.Sample() * _lineSegmentPool.N);
LineSegment addedLineSegment = _lineSegmentPool.Configure[(int)uPool];
// propose Y
LineSegmentConfiguration Y = new LineSegmentConfiguration(X);
Y.Add(addedLineSegment);
// debug
#region debug
//double temphy = _GMTargetDistribution.Evaluate(Y);
//double temphx = _GMTargetDistribution.Evaluate(X);
//temphy = _GMTargetDistribution.Evaluate(Y);
//temphx = _GMTargetDistribution.Evaluate(X);
#endregion
// accept probability
acceptProbability = BirthAcceptProbability(X, Y);
_sumAcceptProbability += acceptProbability;
uSample = randomSample.Sample();
if (uSample <= acceptProbability)
// accept Y
{
reject = false;
_hits++;
if (n < Nm1)
// add Y to totalSample;
_totalSamples.Add(Y);
if (n >= _n0)
// add Y to targetSample
_targetSamples.Add(Y);
// remove l from pool
_lineSegmentPool.RemoveAt((int)uPool);
//_totalLineSegment--;
}
else
// reject Y
{
reject = true;
if (n < Nm1)
_totalSamples.Add(X);
if (n >= _n0)
_targetSamples.Add(X);
}
}
#endregion
else
// Death
#region Death
{
death = true;
// uniformly remove v from X
uRemove = (int)System.Math.Floor(randomRemove.Sample() * xLength);
// propose Y
LineSegmentConfiguration Y = new LineSegmentConfiguration(X);
LineSegment removedLineSegment = Y.Configure[(int)uRemove];
Y.RemoveAt((int)uRemove);
// accept probability
acceptProbability = DeathAcceptProbability(X, Y);
_sumAcceptProbability += acceptProbability;
uSample = randomSample.Sample();
if (uSample <= acceptProbability)
// accept Y
{
reject = false;
_hits++;
if (n < Nm1)
// add Y to totalSample;
_totalSamples.Add(Y);
if (n >= _n0)
// add Y to targetSample
_targetSamples.Add(Y);
// add l back to pool
_lineSegmentPool.Add(removedLineSegment);
//_totalLineSegment++;
}
else
// reject Y
{
reject = true;
if (n < Nm1)
_totalSamples.Add(X);
if (n >= _n0)
_targetSamples.Add(X);
}
}
#endregion
n++;
// debug output
#region debug
_averageAcceptProbability = _sumAcceptProbability / (double)n;
double h = _GMTargetDistribution.Evaluate(_totalSamples[n - 1]);
if (h > hMax)
{
hMax = h;
_indexMax = n - 1;
}
Console.Write("n = " + (n - 1));
if (death)
Console.Write(" Death");
else
Console.Write(" Birth");
if (reject)
Console.Write(" Reject");
else
Console.Write(" Accept");
Console.Write(" # = " + _totalSamples[n - 1].N);
Console.Write(" h(x) = " + String.Format("{0:0.0000e+00}", h));
Console.Write(" accept rate = " + String.Format("{0:0.0000e+00}", acceptProbability));
Console.WriteLine(" average accept rate " + String.Format("{0:f}", _averageAcceptProbability));
#endregion
} // end of while
#region debug
Console.Write("hx max = " + String.Format("{0:0.0000}", hMax) + " index = " + _indexMax);
_averageAcceptProbability = _sumAcceptProbability / (double)_n;
#endregion
return _targetSamples;
}
/// <summary>
/// init MCMC
/// data term has been assigned to the pool
/// </summary>
public void Init(LineSegmentConfiguration pool)
{
// source line segment list
_sourceLineSegmentList = new LineSegmentConfiguration(pool);
// line segment pool
_lineSegmentPool = new LineSegmentConfiguration(pool);
_lineSegmentPool.Empty();
// RJMCMC starts from full line segment configuration
LineSegmentConfiguration startList = new LineSegmentConfiguration(pool);
_totalSamples.Add(startList);
// v(S)
_vS = LebesgueMeasure(_lamda, _width, _height);
_totalLineSegment = pool.N;
}
/// <summary>
/// example target distribution function
/// </summary>
/// <returns></returns>
public static double ExampleDensityFunction(LineSegmentConfiguration x)
{
// calculate hp
x.FreeEndsFreeSegments();
x.JoinSegments();
x.CalculatePC();
x.CalculateSumPC();
x.CalculateTotalL();
x.CalculateAverageL();
// explicitly calculate sum(pL(s)), sum(pG(s)), and sum(pI(s)) for the efficiency sake
int count = x.Configure.Count;
double sumPL = 0.0;
double sumPG = 0.0;
double sumPI = 0.0;
for (int s = 0; s < count; s++)
{
// calculate sum(pL(s))
x.Configure[s].CalculatePL(x.TotalLength, x.AverageLength);
// try different weight
double pL = x.Configure[s].PL;
if (pL < 0.0)
sumPL += pL * 100;
else
sumPL += pL;
x.SumPL = sumPL;
// calculate sum(pG(s))
x.Configure[s].CalculatePG(x.Gt);
double pG = x.Configure[s].PG;
if (pG < 0.0)
sumPG += pG * 100;
else
sumPG += pG;
x.SumPG = sumPG;
// calculate sum(pI(s))
x.Configure[s].CalculatePI(x.It, x.KI);
double pI = x.Configure[s].PI;
if (pI < 0.0)
sumPI += pI * 10000;
else
sumPI += pI;
x.SumPI = sumPI;
}
double up = x.W1 * x.N + x.W2 * x.NF + x.W3 * x.NFE +
x.WC * x.SumPC + x.WL * x.SumPL;
// calculate hd
double ud = x.WG * x.SumPG + x.WI * x.SumPI;
// h = hp + hd;
double u = up + ud;
//return 1 / h;
// density function U = exp(-h);
double h = System.Math.Exp(-1.0 * u);
return h;
}
