/// <summary>
/// Creates a new <see cref="NonLinearRankFitnessFunction{TProgram}" /> with the given parameters.
/// </summary>
/// <param name="programComparer">The object used to compare programs and determine their ranking.</param>
/// <param name="population">The list of programs whose fitness can be computed by this function.</param>
/// <param name="selectivePressure">
/// The probability of the best individual being selected compared to the average probability of selection of all
/// individuals.
/// </param>
public NonLinearRankFitnessFunction(
IComparer <TProgram> programComparer, IPopulation <TProgram> population, double selectivePressure)
: base(programComparer, population)
{
var n = population.Count;
this.SelectivePressure = Math.Max(1d, Math.Min(n - 2d, selectivePressure));
// finds the root of the polynomial
try
{
this._root = Brent.FindRootExpand(this.Polynomial, -n, n, 1E-08, 1000);
this._rootFound = true;
}
catch (NonConvergenceException)
{
}
// stores the exponential sum
this._rootFactor = 0d;
var pow = 1d;
for (var i = 0; i < n; i++)
{
this._rootFactor += pow;
pow *= this._root;
}
this._rootFactor = n / this._rootFactor;
}
/// <summary>
/// Find first miss count achievable with at least probability p
/// </summary>
private static double getMissCount(double p, double[] missProbabilities)
{
var distribution = new PoissonBinomial(missProbabilities);
Func <double, double> cdfMinusProb = missCount => distribution.Cdf(missCount) - p;
return(Brent.FindRootExpand(cdfMinusProb, -100, 1000));
}
/// <summary>
/// Find first miss count achievable with at least probability p
/// </summary>
private static double getMissCount(double p, double[] missProbabilities)
{
if (missProbabilities.Sum() == 0)
{
return(0);
}
var distribution = new PoissonBinomial(missProbabilities);
double cdfMinusProb(double missCount) => distribution.CDF(missCount) - p;
return(Brent.FindRootExpand(cdfMinusProb, -100, 1000));
}
public static double inv_m1_beta_black_brent(double beta, double f, double sigma)
{
var guess = inv_m1_beta_black_convexity(beta, f, sigma);
var shift = 1.5e-8 * (Math.Max(1.0, Math.Abs(guess)));
var lo = guess - shift;
var hi = guess + shift;
var rf = FS.fun((double mu) =>
{
var rr = m1_beta_black(beta, mu, sigma);
return(rr - f);
});
return(Brent.FindRootExpand(rf, lo, hi));
}
public void BrentMultipleRoots()
{
// Roots at -2, 2
double F1(double x) => x * x - 4;
Assert.AreEqual(0, F1(Brent.FindRoot(F1, 1, 5, 1e-14)));
Assert.AreEqual(0, F1(Brent.FindRootExpand(F1, 3, 5, 1e-14)));
Assert.AreEqual(-2, Brent.FindRoot(F1, -5, -1, 1e-14));
Assert.AreEqual(2, Brent.FindRoot(F1, 1, 4, 1e-14));
Assert.AreEqual(0, F1(Brent.FindRoot(x => - F1(x), 1, 5, 1e-14)));
Assert.AreEqual(-2, Brent.FindRoot(x => - F1(x), -5, -1, 1e-14));
Assert.AreEqual(2, Brent.FindRoot(x => - F1(x), 1, 4, 1e-14));
// Roots at 3, 4
double F2(double x) => (x - 3) * (x - 4);
Assert.AreEqual(0, F2(Brent.FindRoot(F2, -5, 3.5, 1e-14)));
Assert.AreEqual(3, Brent.FindRoot(F2, -5, 3.5, 1e-14));
Assert.AreEqual(4, Brent.FindRoot(F2, 3.2, 5, 1e-14));
Assert.AreEqual(3, Brent.FindRoot(F2, 2.1, 3.9, 0.001, 50), 0.001);
Assert.AreEqual(3, Brent.FindRoot(F2, 2.1, 3.4, 0.001, 50), 0.001);
}
public void MultipleRoots()
{
// Roots at -2, 2
Func <double, double> f1 = x => x * x - 4;
Assert.AreEqual(0, f1(Brent.FindRoot(f1, 1, 5, 1e-14, 100)));
Assert.AreEqual(0, f1(Brent.FindRootExpand(f1, 3, 5, 1e-14, 100)));
Assert.AreEqual(-2, Brent.FindRoot(f1, -5, -1, 1e-14, 100));
Assert.AreEqual(2, Brent.FindRoot(f1, 1, 4, 1e-14, 100));
Assert.AreEqual(0, f1(Brent.FindRoot(x => - f1(x), 1, 5, 1e-14, 100)));
Assert.AreEqual(-2, Brent.FindRoot(x => - f1(x), -5, -1, 1e-14, 100));
Assert.AreEqual(2, Brent.FindRoot(x => - f1(x), 1, 4, 1e-14, 100));
// Roots at 3, 4
Func <double, double> f2 = x => (x - 3) * (x - 4);
Assert.AreEqual(0, f2(Brent.FindRoot(f2, -5, 3.5, 1e-14, 100)));
Assert.AreEqual(3, Brent.FindRoot(f2, -5, 3.5, 1e-14, 100));
Assert.AreEqual(4, Brent.FindRoot(f2, 3.2, 5, 1e-14, 100));
Assert.AreEqual(3, Brent.FindRoot(f2, 2.1, 3.9, 0.001, 50), 0.001);
Assert.AreEqual(3, Brent.FindRoot(f2, 2.1, 3.4, 0.001, 50), 0.001);
}