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 void testSobol()
{
//("Testing Sobol sequences up to dimension "
// + PPMT_MAX_DIM + "...");
List<double> point;
double tolerance = 1.0e-15;
// testing max dimensionality
int dimensionality =(int)SobolRsg.PPMT_MAX_DIM;
ulong seed = 123456;
SobolRsg rsg=new SobolRsg(dimensionality, seed);
int points = 100, i;
for (i=0; i<points; i++)
{
point = rsg.nextSequence().value;
if (point.Count!=dimensionality) {
Assert.Fail("Sobol sequence generator returns "+
" a sequence of wrong dimensionality: " + point.Count
+ " instead of " + dimensionality);
}
}
// testing homogeneity properties
dimensionality = 33;
seed = 123456;
rsg = new SobolRsg(dimensionality, seed);
SequenceStatistics stat=new SequenceStatistics(dimensionality);
List<double> mean;
int k = 0;
for (int j=1; j<5; j++) { // five cycle
points = (int)(Utils.Pow(2.0, j)-1); // base 2
for (; k<points; k++) {
point = rsg.nextSequence().value;
stat.add(point);
}
mean = stat.mean();
for (i=0; i<dimensionality; i++) {
double error = Math.Abs(mean[i]-0.5);
if (error > tolerance) {
Assert.Fail(i+1 + " dimension: "
// + QL_FIXED
+ "mean (" + mean[i]
+ ") at the end of the " + j+1
+ " cycle in Sobol sequence is not " + 0.5
//+ QL_SCIENTIFIC
+ " (error = " + error + ")");
}
}
}
// testing first dimension (van der Corput sequence)
double[] vanderCorputSequenceModuloTwo= {
// first cycle (zero excluded)
0.50000,
// second cycle
0.75000, 0.25000,
// third cycle
0.37500, 0.87500, 0.62500, 0.12500,
// fourth cycle
0.18750, 0.68750, 0.93750, 0.43750, 0.31250, 0.81250, 0.56250, 0.06250,
// fifth cycle
0.09375, 0.59375, 0.84375, 0.34375, 0.46875, 0.96875, 0.71875, 0.21875,
0.15625, 0.65625, 0.90625, 0.40625, 0.28125, 0.78125, 0.53125, 0.03125
};
dimensionality = 1;
rsg = new SobolRsg(dimensionality);
points = (int)(Utils.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 Sobol sequence is not in the "
+ "van der Corput sequence modulo two: "
+ "it should have been "
+ vanderCorputSequenceModuloTwo[i]
//+ QL_SCIENTIFIC
+ " (error = " + error + ")");
}
}
}
public void testSobol()
{
//("Testing Sobol sequences up to dimension "
// + PPMT_MAX_DIM + "...");
List <double> point;
double tolerance = 1.0e-15;
// testing max dimensionality
int dimensionality = (int)SobolRsg.PPMT_MAX_DIM;
ulong seed = 123456;
SobolRsg rsg = new SobolRsg(dimensionality, seed);
int points = 100, i;
for (i = 0; i < points; i++)
{
point = rsg.nextSequence().value;
if (point.Count != dimensionality)
{
Assert.Fail("Sobol sequence generator returns " +
" a sequence of wrong dimensionality: " + point.Count
+ " instead of " + dimensionality);
}
}
// testing homogeneity properties
dimensionality = 33;
seed = 123456;
rsg = new SobolRsg(dimensionality, seed);
SequenceStatistics stat = new SequenceStatistics(dimensionality);
List <double> mean;
int k = 0;
for (int j = 1; j < 5; j++) // five cycle
{
points = (int)(Utils.Pow(2.0, j) - 1); // base 2
for (; k < points; k++)
{
point = rsg.nextSequence().value;
stat.add(point);
}
mean = stat.mean();
for (i = 0; i < dimensionality; i++)
{
double error = Math.Abs(mean[i] - 0.5);
if (error > tolerance)
{
Assert.Fail(i + 1 + " dimension: "
// + QL_FIXED
+ "mean (" + mean[i]
+ ") at the end of the " + j + 1
+ " cycle in Sobol sequence is not " + 0.5
//+ QL_SCIENTIFIC
+ " (error = " + error + ")");
}
}
}
// testing first dimension (van der Corput sequence)
double[] vanderCorputSequenceModuloTwo =
{
// first cycle (zero excluded)
0.50000,
// second cycle
0.75000, 0.25000,
// third cycle
0.37500, 0.87500, 0.62500, 0.12500,
// fourth cycle
0.18750, 0.68750, 0.93750, 0.43750, 0.31250, 0.81250, 0.56250, 0.06250,
// fifth cycle
0.09375, 0.59375, 0.84375, 0.34375, 0.46875, 0.96875, 0.71875, 0.21875,
0.15625, 0.65625, 0.90625, 0.40625, 0.28125, 0.78125, 0.53125, 0.03125
};
dimensionality = 1;
rsg = new SobolRsg(dimensionality);
points = (int)(Utils.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 Sobol sequence is not in the "
+ "van der Corput sequence modulo two: "
+ "it should have been "
+ vanderCorputSequenceModuloTwo[i]
//+ QL_SCIENTIFIC
+ " (error = " + error + ")");
}
}
}
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 + ")");
}
}
}
