// Sample a pre-determined number of points using the given generator and grid and return the average function value.
private static double Integrate_MonteCarlo_Cycle(MultiFunctor f, CoordinateTransform[] map, VectorGenerator g, LePageGrid grid, int n)
{
double sum = 0.0;
for (int i = 0; i < n; i++)
{
double[] x = g.NextVector();
//sum += f.Evaluate(x);
sum += grid.Evaluate(f, map, x);
}
return(sum / n);
}
// Sample a pre-determined number of points using the given generator and grid and return the average function value.
private static double Integrate_MonteCarlo_Cycle(MultiFunctor f, CoordinateTransform[] map, VectorGenerator g, LePageGrid grid, int n)
{
double sum = 0.0;
for (int i = 0; i < n; i++) {
double[] x = g.NextVector();
//sum += f.Evaluate(x);
sum += grid.Evaluate(f, map, x);
}
return (sum / n);
}
private static UncertainValue Integrate_MonteCarlo(MultiFunctor f, CoordinateTransform[] map, IList <Interval> box, EvaluationSettings settings)
{
int d = box.Count;
// Use a Sobol quasi-random sequence. This give us 1/N accuracy instead of 1/\sqrt{N} accuracy.
//VectorGenerator g = new RandomVectorGenerator(d, new Random(314159265));
VectorGenerator g = new SobolVectorGenerator(d);
// Start with a trivial Lepage grid.
// We will increase the grid size every few cycles.
// My tests indicate that trying to increase every cycle or even every other cycle is too often.
// This makes sense, because we have no reason to believe our new grid will be better until we
// have substantially more evaluations per grid cell than we did for the previous grid.
LePageGrid grid = new LePageGrid(box, 1);
int refineCount = 0;
// Start with a reasonable number of evaluations per cycle that increases with the dimension.
int cycleCount = 8 * d;
//double lastValue = Integrate_MonteCarlo_Cycle(f, map, g, grid, cycleCount);
// Each cycle consists of three sets of evaluations.
// At first I did this with just two set and used the difference between the two sets as an error estimate.
// I found that it was pretty common for that difference to be low just by chance, causing error underestimatation.
double value1 = Integrate_MonteCarlo_Cycle(f, map, g, grid, cycleCount);
double value2 = Integrate_MonteCarlo_Cycle(f, map, g, grid, cycleCount);
double value3 = Integrate_MonteCarlo_Cycle(f, map, g, grid, cycleCount);
while (f.EvaluationCount < settings.EvaluationBudget)
{
// Take the largest deviation as the error.
double value = (value1 + value2 + value3) / 3.0;
double error = Math.Max(Math.Abs(value1 - value3), Math.Max(Math.Abs(value1 - value2), Math.Abs(value2 - value3)));
Debug.WriteLine("{0} {1} {2}", f.EvaluationCount, value, error);
// Check for convergence.
if ((error <= settings.AbsolutePrecision) || (error <= Math.Abs(value) * settings.RelativePrecision))
{
return(new UncertainValue(value, error));
}
// Do more cycles. In order for new sets to be equal-sized, one of those must be at the current count and the next at twice that.
double smallValue = Integrate_MonteCarlo_Cycle(f, map, g, grid, cycleCount);
cycleCount *= 2;
double bigValue = Integrate_MonteCarlo_Cycle(f, map, g, grid, cycleCount);
// Combine all the cycles into new ones with twice the number of evaluations each.
value1 = (value1 + value2) / 2.0;
value2 = (value3 + smallValue) / 2.0;
value3 = bigValue;
//double currentValue = Integrate_MonteCarlo_Cycle(f, map, g, grid, cycleCount);
//double error = Math.Abs(currentValue - lastValue);
//double value = (currentValue + lastValue) / 2.0;
//lastValue = value;
// Increase the number of evaluations for the next cycle.
//cycleCount *= 2;
// Refine the grid for the next cycle.
refineCount++;
if (refineCount == 2)
{
Debug.WriteLine("Replacing grid with {0} bins after {1} evaluations", grid.BinCount, grid.EvaluationCount);
grid = grid.ComputeNewGrid(grid.BinCount * 2);
refineCount = 0;
}
}
throw new NonconvergenceException();
}
private static UncertainValue Integrate_MonteCarlo(MultiFunctor f, CoordinateTransform[] map, IList<Interval> box, EvaluationSettings settings)
{
int d = box.Count;
// Use a Sobol quasi-random sequence. This give us 1/N accuracy instead of 1/\sqrt{N} accuracy.
//VectorGenerator g = new RandomVectorGenerator(d, new Random(314159265));
VectorGenerator g = new SobolVectorGenerator(d);
// Start with a trivial Lepage grid.
// We will increase the grid size every few cycles.
// My tests indicate that trying to increase every cycle or even every other cycle is too often.
// This makes sense, because we have no reason to believe our new grid will be better until we
// have substantially more evaluations per grid cell than we did for the previous grid.
LePageGrid grid = new LePageGrid(box, 1);
int refineCount = 0;
// Start with a reasonable number of evaluations per cycle that increases with the dimension.
int cycleCount = 8 * d;
//double lastValue = Integrate_MonteCarlo_Cycle(f, map, g, grid, cycleCount);
// Each cycle consists of three sets of evaluations.
// At first I did this with just two set and used the difference between the two sets as an error estimate.
// I found that it was pretty common for that difference to be low just by chance, causing error underestimatation.
double value1 = Integrate_MonteCarlo_Cycle(f, map, g, grid, cycleCount);
double value2 = Integrate_MonteCarlo_Cycle(f, map, g, grid, cycleCount);
double value3 = Integrate_MonteCarlo_Cycle(f, map, g, grid, cycleCount);
while (f.EvaluationCount < settings.EvaluationBudget) {
// Take the largest deviation as the error.
double value = (value1 + value2 + value3) / 3.0;
double error = Math.Max(Math.Abs(value1 - value3), Math.Max(Math.Abs(value1 - value2), Math.Abs(value2 - value3)));
Debug.WriteLine("{0} {1} {2}", f.EvaluationCount, value, error);
// Check for convergence.
if ((error <= settings.AbsolutePrecision) || (error <= Math.Abs(value) * settings.RelativePrecision)) {
return (new UncertainValue(value, error));
}
// Do more cycles. In order for new sets to be equal-sized, one of those must be at the current count and the next at twice that.
double smallValue = Integrate_MonteCarlo_Cycle(f, map, g, grid, cycleCount);
cycleCount *= 2;
double bigValue = Integrate_MonteCarlo_Cycle(f, map, g, grid, cycleCount);
// Combine all the cycles into new ones with twice the number of evaluations each.
value1 = (value1 + value2) / 2.0;
value2 = (value3 + smallValue) / 2.0;
value3 = bigValue;
//double currentValue = Integrate_MonteCarlo_Cycle(f, map, g, grid, cycleCount);
//double error = Math.Abs(currentValue - lastValue);
//double value = (currentValue + lastValue) / 2.0;
//lastValue = value;
// Increase the number of evaluations for the next cycle.
//cycleCount *= 2;
// Refine the grid for the next cycle.
refineCount++;
if (refineCount == 2) {
Debug.WriteLine("Replacing grid with {0} bins after {1} evaluations", grid.BinCount, grid.EvaluationCount);
grid = grid.ComputeNewGrid(grid.BinCount * 2);
refineCount = 0;
}
}
throw new NonconvergenceException();
}