public void testHalton()
{
//("Testing Halton sequences...");
List<double> point;
double tolerance = 1.0e-15;
// testing "high" dimensionality
int dimensionality = (int)SobolRsg.PPMT_MAX_DIM;
HaltonRsg rsg = new HaltonRsg(dimensionality, 0, false, false);
int points = 100, i, k;
for (i = 0; i < points; i++)
{
point = rsg.nextSequence().value;
if (point.Count != dimensionality)
{
Assert.Fail("Halton sequence generator returns "+
" a sequence of wrong dimensionality: " + point.Count
+ " instead of " + dimensionality)
;
}
}
// testing first and second dimension (van der Corput sequence)
double[] vanderCorputSequenceModuloTwo = {
// first cycle (zero excluded)
0.50000,
// second cycle
0.25000, 0.75000,
// third cycle
0.12500, 0.62500, 0.37500, 0.87500,
// fourth cycle
0.06250, 0.56250, 0.31250, 0.81250, 0.18750, 0.68750, 0.43750,
0.93750,
// fifth cycle
0.03125, 0.53125, 0.28125, 0.78125, 0.15625, 0.65625, 0.40625,
0.90625,
0.09375, 0.59375, 0.34375, 0.84375, 0.21875, 0.71875, 0.46875,
0.96875,
};
dimensionality = 1;
rsg = new HaltonRsg(dimensionality, 0, false, false);
points = (int) (Math.Pow(2.0, 5)) - 1; // five cycles
for (i = 0; i < points; i++)
{
point = rsg.nextSequence().value;
double error = Math.Abs(point[0] - vanderCorputSequenceModuloTwo[i]);
if (error > tolerance)
{
Assert.Fail(i + 1 + " draw ("
+ /*QL_FIXED*/ + point[0]
+ ") in 1-D Halton sequence is not in the "
+ "van der Corput sequence modulo two: "
+ "it should have been "
+ vanderCorputSequenceModuloTwo[i]
//+ QL_SCIENTIFIC
+ " (error = " + error + ")");
}
}
double[] vanderCorputSequenceModuloThree = {
// first cycle (zero excluded)
1.0/3, 2.0/3,
// second cycle
1.0/9, 4.0/9, 7.0/9, 2.0/9, 5.0/9, 8.0/9,
// third cycle
1.0/27, 10.0/27, 19.0/27, 4.0/27, 13.0/27, 22.0/27,
7.0/27, 16.0/27, 25.0/27, 2.0/27, 11.0/27, 20.0/27,
5.0/27, 14.0/27, 23.0/27, 8.0/27, 17.0/27, 26.0/27
};
dimensionality = 2;
rsg = new HaltonRsg(dimensionality, 0, false, false);
points = (int) (Math.Pow(3.0, 3)) - 1; // three cycles of the higher dimension
for (i = 0; i < points; i++)
{
point = rsg.nextSequence().value;
double error = Math.Abs(point[0] - vanderCorputSequenceModuloTwo[i]);
if (error > tolerance)
{
Assert.Fail("First component of " + i + 1
+ " draw (" + /*QL_FIXED*/ + point[0]
+ ") in 2-D Halton sequence is not in the "
+ "van der Corput sequence modulo two: "
+ "it should have been "
+ vanderCorputSequenceModuloTwo[i]
//+ QL_SCIENTIFIC
+ " (error = " + error + ")");
}
error = Math.Abs(point[1] - vanderCorputSequenceModuloThree[i]);
if (error > tolerance)
{
Assert.Fail("Second component of " + i + 1
+ " draw (" + /*QL_FIXED*/ + point[1]
+ ") in 2-D Halton sequence is not in the "
+ "van der Corput sequence modulo three: "
+ "it should have been "
+ vanderCorputSequenceModuloThree[i]
//+ QL_SCIENTIFIC
+ " (error = " + error + ")");
}
}
// testing homogeneity properties
dimensionality = 33;
rsg = new HaltonRsg(dimensionality, 0, false, false);
SequenceStatistics stat = new SequenceStatistics(dimensionality);
List<double> mean; //, stdev, variance, skewness, kurtosis;
k = 0;
int j;
for (j = 1; j < 5; j++)
{
// five cycle
points = (int) (Math.Pow(2.0, j)) - 1; // base 2
for (; k < points; k++)
{
point = rsg.nextSequence().value;
stat.add(point);
}
mean = stat.mean();
double error = Math.Abs(mean[0] - 0.5);
if (error > tolerance)
{
Assert.Fail("First dimension mean (" + /*QL_FIXED*/ + mean[0]
+ ") at the end of the " + j + 1
+ " cycle in Halton sequence is not " + 0.5
//+ QL_SCIENTIFIC
+ " (error = " + error + ")");
}
}
// reset generator and gaussianstatistics
rsg = new HaltonRsg(dimensionality, 0, false, false);
stat.reset(dimensionality);
k = 0;
for (j = 1; j < 3; j++)
{
// three cycle
points = (int) (Math.Pow(3.0, j)) - 1; // base 3
for (; k < points; k++)
{
point = rsg.nextSequence().value;
stat.add(point);
}
mean = stat.mean();
double error = Math.Abs(mean[1] - 0.5);
if (error > tolerance)
{
Assert.Fail("Second dimension mean (" + /*QL_FIXED*/ + mean[1]
+ ") at the end of the " + j + 1
+ " cycle in Halton sequence is not " + 0.5
//+ QL_SCIENTIFIC
+ " (error = " + error + ")");
}
}
}
public override void update()
{
this.coeff_.updateModelInstance();
// we should also check that y contains positive values only
// we must update weights if it is vegaWeighted
if (vegaWeighted_)
{
coeff_.weights_.Clear();
double weightsSum = 0.0;
for (int i = 0; i < xBegin_.Count; i++)
{
double stdDev = Math.Sqrt((yBegin_[i]) * (yBegin_[i]) * this.coeff_.t_);
coeff_.weights_.Add(coeff_.model_.weight(xBegin_[i], forward_, stdDev, this.coeff_.addParams_));
weightsSum += coeff_.weights_.Last();
}
// weight normalization
for (int i = 0; i < coeff_.weights_.Count; i++)
{
coeff_.weights_[i] /= weightsSum;
}
}
// there is nothing to optimize
if (coeff_.paramIsFixed_.Aggregate((a, b) => b && a))
{
coeff_.error_ = interpolationError();
coeff_.maxError_ = interpolationMaxError();
coeff_.XABREndCriteria_ = EndCriteria.Type.None;
return;
}
else
{
XABRError costFunction = new XABRError(this);
Vector guess = new Vector(coeff_.model_.dimension());
for (int i = 0; i < guess.size(); ++i)
{
guess[i] = coeff_.params_[i].Value;
}
int iterations = 0;
int freeParameters = 0;
double bestError = double.MaxValue;
Vector bestParameters = new Vector();
for (int i = 0; i < coeff_.model_.dimension(); ++i)
{
if (!coeff_.paramIsFixed_[i])
{
++freeParameters;
}
}
HaltonRsg halton = new HaltonRsg(freeParameters, 42);
EndCriteria.Type tmpEndCriteria;
double tmpInterpolationError;
do
{
if (iterations > 0)
{
Sample <List <double> > s = halton.nextSequence();
coeff_.model_.guess(guess, coeff_.paramIsFixed_, forward_, coeff_.t_, s.value, coeff_.addParams_);
for (int i = 0; i < coeff_.paramIsFixed_.Count; ++i)
{
if (coeff_.paramIsFixed_[i])
{
guess[i] = coeff_.params_[i].Value;
}
}
}
Vector inversedTransformatedGuess = new Vector(coeff_.model_.inverse(guess, coeff_.paramIsFixed_, coeff_.params_, forward_));
ProjectedCostFunction rainedXABRError = new ProjectedCostFunction(costFunction, inversedTransformatedGuess,
coeff_.paramIsFixed_);
Vector projectedGuess = new Vector(rainedXABRError.project(inversedTransformatedGuess));
NoConstraint raint = new NoConstraint();
Problem problem = new Problem(rainedXABRError, raint, projectedGuess);
tmpEndCriteria = optMethod_.minimize(problem, endCriteria_);
Vector projectedResult = new Vector(problem.currentValue());
Vector transfResult = new Vector(rainedXABRError.include(projectedResult));
Vector result = coeff_.model_.direct(transfResult, coeff_.paramIsFixed_, coeff_.params_, forward_);
tmpInterpolationError = useMaxError_ ? interpolationMaxError()
: interpolationError();
if (tmpInterpolationError < bestError)
{
bestError = tmpInterpolationError;
bestParameters = result;
coeff_.XABREndCriteria_ = tmpEndCriteria;
}
} while (++iterations < maxGuesses_ &&
tmpInterpolationError > errorAccept_);
for (int i = 0; i < bestParameters.size(); ++i)
{
coeff_.params_[i] = bestParameters[i];
}
coeff_.error_ = interpolationError();
coeff_.maxError_ = interpolationMaxError();
}
}