public static double[] ComplementsSimpsons38(Normal[] distributions, int steps = 150)
{
if (steps % 3 != 0)
{
steps += 3 - steps % 3; // Round up to a multiple of 3
}
double[] complementProbs = new double[distributions.Length];
distributions = NegateDistributions(distributions); // This change is local to this method
for (int i = 0; i < distributions.Length; i++)
{
Normal distribution_i = distributions[i];
Func <double, double> integrand = x =>
{
double product = distribution_i.Density(x);
for (int j = 0; j < distributions.Length; j++)
{
if (j != i)
{
product *= distributions[j].CumulativeDistribution(x);
}
}
return(product);
};
complementProbs[i] = NewtonCotes.Simpsons38Rule(integrand,
distribution_i.Mean - 8 * distribution_i.StdDev, distribution_i.Mean + 8 * distribution_i.StdDev, steps);
//Console.WriteLine($"S38[{i}]: {complementProbs[i]}");
}
return(complementProbs);
}
/// <summary> Takes a set of normal distributions and computes the probability that each one would produce the minimal value if
/// a point sample was taken from each. Integration is performed by Simpson's 3/8 rule. </summary>
/// <param name="distributions">The array of distributions to compare</param>
/// <param name="iterations">The number of iterations to use in Simpson's 3/8 Rule. Defaults to 150.</param>
/// <returns>An array of probabilities that each distribution will produce the minimum value if a point sample was taken from each.
/// [i] = P(X_i less than min(all X_j))</returns>
public static double[] Simpsons38RuleWithoutNegation(Normal[] distributions, int iterations = 150)
{
double[] complementProbs = new double[distributions.Length];
for (int i = 0; i < distributions.Length; i++)
{
Normal distribution_i = distributions[i];
Func <double, double> integrand = x =>
{
double product = distribution_i.Density(x);
for (int j = 0; j < distributions.Length; j++)
{
if (j != i)
{
product *= 1 - distributions[j].CumulativeDistribution(x);
}
}
return(product);
};
complementProbs[i] = NewtonCotes.Simpsons38Rule(integrand,
distribution_i.Mean - 8 * distribution_i.StdDev, distribution_i.Mean + 8 * distribution_i.StdDev, iterations);
//Console.WriteLine($"S38R[{i}]: {complementProbs[i]}");
}
return(complementProbs);
}
void App_Startup(object sender, StartupEventArgs e)
{
Func <double, double> function = null;
int funSelection = 0;
bool isParsable = false;
bool isBetween = false;
do
{
Console.WriteLine("Wybierz wariant funkcji do całkowania:");
Console.WriteLine("(1). f(x) = 4x^4 -2x^3 + 4x^2 -4x +1 ");
Console.WriteLine("(2). f(x) = 4sin(2x) ");
Console.WriteLine("(3). f(x) = 2|x^3|");
isParsable = Int32.TryParse(Console.ReadLine(), out funSelection);
isBetween = funSelection.IsBetween(1, 3);
} while(!(isParsable && isBetween));
switch (funSelection)
{
case 1:
function = Example.Polynomial;
break;
case 2:
function = Example.Sinus;
break;
case 3:
function = Example.Absolute;
break;
}
Console.Write("Nieskończone przedziały? (t/*)");
bool isInifniteRange = Console.ReadKey().IsKey('t');
Console.WriteLine();
double a, b;
if (isInifniteRange)
{
a = double.NegativeInfinity;
b = double.PositiveInfinity;
}
else
{
bool isNumber = false;
bool isCorrect = false;
do
{
Console.WriteLine("Określ przedziały całkowania:");
Console.Write("a:");
isNumber = double.TryParse(Console.ReadLine(), NumberStyles.Any, CultureInfo.InvariantCulture, out a);
Console.Write("b:");
isNumber = double.TryParse(Console.ReadLine(), NumberStyles.Any, CultureInfo.InvariantCulture, out b);
isCorrect = a < b;
} while (!isNumber || !isCorrect);
}
double epsilon = 0;
bool isEpsilonCorrect = false;
do
{
Console.Write("Określ dokładność obliczeń: ");
isEpsilonCorrect = double.TryParse(Console.ReadLine(), NumberStyles.Any, CultureInfo.InvariantCulture, out epsilon);
} while (!isEpsilonCorrect);
if (double.IsInfinity(a) || double.IsInfinity(b))
{
a = Utilis.CalculateLimit(0, -2, Example.Exponent(function));
b = Utilis.CalculateLimit(0, 2, Example.Exponent(function));
}
Newton_Cotes NewtonCotes;
Gauss_Hermite GaussHermite;
if (isInifniteRange)
{
NewtonCotes = new Newton_Cotes(Example.Exponent(function), a, b, epsilon);
GaussHermite = new Gauss_Hermite(function, epsilon);
}
else
{
NewtonCotes = new Newton_Cotes(Example.Exponent(function), a, b, epsilon);
GaussHermite = null;
}
Console.WriteLine("Całka obliczona przy użyciu metody Newtona-Cotesa wynosi: " + NewtonCotes.GetResult());
Console.WriteLine("Liczba węzłów: " + NewtonCotes.GetIterationsCount());
if (!(GaussHermite is null))
{
Console.WriteLine("Całka obliczona przy użyciu kwadratury Gaussa wynosi: " + GaussHermite.GetResult());
Console.WriteLine("Liczba węzłów: " + GaussHermite.GetIterationsCount());
}
MainWindow mainWindow = new MainWindow();
mainWindow.Plot.NewtonCotesValues = NewtonCotes.GetNodes();
mainWindow.Plot.Values = NewtonCotes.GetValues();
mainWindow.Show();
}
