/// <summary>
/// Calculate a frequency distribution for the provided array of values.
/// 1) The minimum and maximum values are found.
/// 2) The resulting value range is divided into equal sized sub-ranges (categoryCount).
/// 3) The number of values that fall into each category is determined.
/// </summary>
public static HistogramData BuildHistogramData(double[] valArr, int categoryCount)
{
// Determine min/max.
MathArrayUtils.MinMax(valArr, out double min, out double max);
// Note. each bucket's range has interval [low,high), i.e. samples exactly equal to 'high'
// will fall into the next highest bucket. Therefore to prevent the maximum sample vAalue falling into the
// last bucket by itself, we inflate the range by a small proportion so that the max value falls just below
// the max range covered by the distribution.
double range = (max - min) * 1.01;
// Handle special case where the data series contains a single value.
if (0.0 == range)
{
return(new HistogramData(min, max, 0.0, new int[] { valArr.Length }));
}
// Loop values and for each one increment the relevant category's frequency count.
double incr = range / categoryCount;
int[] frequencyArr = new int[categoryCount];
for (int i = 0; i < valArr.Length; i++)
{
frequencyArr[(int)((valArr[i] - min) / incr)]++;
}
return(new HistogramData(min, max, incr, frequencyArr));
}
/// <summary>
/// Evaluate the provided black box against the function regression task,
/// and return its fitness score.
/// </summary>
/// <param name="box">The black box to evaluate.</param>
public FitnessInfo Evaluate(IBlackBox <double> box)
{
// Probe the black box over the full range of the input parameter.
_blackBoxProbe.Probe(box, _yArr);
// Calc gradients.
FuncRegressionUtils.CalcGradients(_paramSamplingInfo, _yArr, _gradientArr);
// Calc y position mean squared error (MSE), and apply weighting.
double yMse = MathArrayUtils.MeanSquaredDelta(_yArr, _yArrTarget);
yMse *= _yMseWeight;
// Calc gradient mean squared error.
double gradientMse = MathArrayUtils.MeanSquaredDelta(_gradientArr, _gradientArrTarget);
gradientMse *= _gradientMseWeight;
// Calc fitness as the inverse of MSE (higher value is fitter).
// Add a constant to avoid divide by zero, and to constrain the fitness range between bad and good solutions;
// this allows the selection strategy to select solutions that are mediocre and therefore helps preserve diversity.
double fitness = 20.0 / (yMse + gradientMse + 0.02);
return(new FitnessInfo(fitness));
}
private static void MinMax(UniformDistributionSampler sampler, int len)
{
// Alloc arrays and fill with uniform random noise.
double[] a = new double[len];
sampler.Sample(a);
// Calc results and compare.
MinMax(a, out double expectedMin, out double expectedMax);
MathArrayUtils.MinMax(a, out double actualMin, out double actualMax);
Assert.AreEqual(expectedMin, actualMin, 1e-10);
Assert.AreEqual(expectedMax, actualMax, 1e-10);
}
private static void SumSquaredDelta(UniformDistributionSampler sampler, int len)
{
// Alloc arrays and fill with uniform random noise.
double[] a = new double[len];
double[] b = new double[len];
sampler.Sample(a);
sampler.Sample(b);
// Calc results and compare.
double expected = SumSquaredDelta(a, b);
double actual = MathArrayUtils.SumSquaredDelta(a, b);
Assert.AreEqual(expected, actual, 1e-10);
}
private static void Clip(UniformDistributionSampler sampler, int len)
{
// Alloc array and fill with uniform random noise.
double[] x = new double[len];
sampler.Sample(x);
// Clip the elements of the array with the safe routine.
double[] expected = (double[])x.Clone();
Clip(expected, -1.1, 18.8);
// Clip the elements of the array.
double[] actual = (double[])x.Clone();
MathArrayUtils.Clip(actual, -1.1, 18.8);
// Compare expected with actual array.
Assert.IsTrue(ArrayUtils.Equals(expected, actual));
}
/// <summary>
/// Evaluate the provided IBlackBox against the XOR problem domain and return its fitness score.
/// </summary>
public FitnessInfo Evaluate(IBlackBox box)
{
int sampleCount = _paramSamplingInfo._sampleCount;
// TODO: We can avoid a memory allocation here by allocating at construction time, but this requires modification of
// ParallelGenomeListEvaluator to utilise multiple evaluators (one per thread).
double[] yArr = new double[sampleCount];
double[] gradientArr = new double[sampleCount];
// Probe the black box over the full range of the input parameter.
_blackBoxProbe.Probe(box, yArr);
// Calc gradients.
FnRegressionUtils.CalcGradients(_paramSamplingInfo, yArr, gradientArr);
// Calc y position mean squared error (MSE), and apply weighting.
double yMse = MathArrayUtils.MeanSquaredDelta(yArr, _yArrTarget);
yMse *= _yMseWeight;
// Calc gradient mean squared error.
double gradientMse = MathArrayUtils.MeanSquaredDelta(gradientArr, _gradientArrTarget);
gradientMse *= _gradientMseWeight;
// Calc fitness as the inverse of MSE (higher value is fitter).
// Add a constant to avoid divide by zero, and to constrain the fitness range between bad and good solutions;
// this allows the selection strategy to select solutions that are mediocre and therefore helps preserve diversity.
double fitness = 20.0 / (yMse + gradientMse + 0.02);
// Test for stopping condition (near perfect response).
if (fitness >= 100000.0)
{
_stopConditionSatisfied = true;
}
_evalCount++;
return(new FitnessInfo(fitness, fitness));
}
