public double Integration(FormulaExecutor integrand, double a, double b, double eps)
{
//заменим особые предельные точки на точки из окрестности
if (Double.IsNaN(integrand.Execute(a)) || Double.IsInfinity(integrand.Execute(a)))
{
a += 0.0001 * eps * (b - a);
}
if (Double.IsNaN(integrand.Execute(b)) || Double.IsInfinity(integrand.Execute(b)))
{
b -= 0.0001 * eps * (b - a);
}
//последовательно посчитаем производные до 4 порядка на 100 точках
int n = 1000;
//первая производная
double[] deriv = new double[n];
deriv[0] = (integrand.Execute(a + (b - a) / (n - 1)) - integrand.Execute(a)) / ((b - a) / (n - 1));
for (int i = 1; i < n; ++i)
{
deriv[i] = (integrand.Execute(a + i * (b - a) / (n - 1)) - integrand.Execute(a + (i - 1) * (b - a) / (n - 1))) / ((b - a) / (n - 1));
}
//вторая производная
double[] secDeriv = new double[n];
secDeriv[0] = (deriv[1] - deriv[0]) / ((b - a) / (n - 1));
for (int i = 1; i < n; ++i)
{
secDeriv[i] = (deriv[i] - deriv[i - 1]) / ((b - a) / (n - 1));
}
//третья производная
double[] thirdDeriv = new double[n];
thirdDeriv[0] = (secDeriv[1] - secDeriv[0]) / ((b - a) / (n - 1));
for (int i = 1; i < n; ++i)
{
thirdDeriv[i] = (secDeriv[i] - secDeriv[i - 1]) / ((b - a) / (n - 1));
}
//четвертая производная
double[] fourthDeriv = new double[n];
fourthDeriv[0] = (thirdDeriv[1] - thirdDeriv[0]) / ((b - a) / (n - 1));
double maxFourthDeriv = Math.Abs(fourthDeriv[0]);
for (int i = 1; i < n; ++i)
{
fourthDeriv[i] = (thirdDeriv[i] - thirdDeriv[i - 1]) / ((b - a) / (n - 1));
if (Math.Abs(fourthDeriv[i]) > maxFourthDeriv)
{
maxFourthDeriv = Math.Abs(fourthDeriv[i]);
}
}
//определим шаг разбиения h для метода
double h = (b - a) / Math.Ceiling(Math.Pow(maxFourthDeriv * Math.Pow(b - a, 5) / (2880 * eps), 0.25));
//найдем значение интеграла
double sum = 0;
for (int i = 0; i *h < (b - a); ++i)
{
sum += h / 6 * (integrand.Execute(a + i * h) + 4 * integrand.Execute(a + i * h + h / 2) + integrand.Execute(a + (i + 1) * h));
}
return(sum);
}
private (int time, bool hasSpecialCharacter) ParseCalculationPattern(Time time, string calculationPattern)
{
var splittedPattern = calculationPattern.Split(':');
if (splittedPattern.Length != 2)
{
throw new FormatException("Calculation format. Expected [S].");
}
var timePattern = splittedPattern.FirstOrDefault();
int concreteTime = GetTimeFromTimePattern(time, timePattern);
var formulaPattern = splittedPattern.LastOrDefault();
IFormulaExecutor formula = new FormulaExecutor();
(int formulaResult, int formulaValue, string specialCharacter) = formula.Execute(concreteTime, formulaPattern);
if (specialCharacter == null)
{
SubtractTime(time, formulaValue * formulaResult, timePattern);
}
return(formulaResult, specialCharacter != null);
}
public double Integration(FormulaExecutor integrand, double a, double b, double eps)
{
//заменим особые предельные точки на точки из окрестности
if (Double.IsNaN(integrand.Execute(a)) || Double.IsInfinity(integrand.Execute(a)))
{
a += 0.0001 * eps * (b - a);
}
if (Double.IsNaN(integrand.Execute(b)) || Double.IsInfinity(integrand.Execute(b)))
{
b -= 0.0001 * eps * (b - a);
}
//посчитаем производную на 100 точках и определим шаг разбиения h для метода
int n = 100;
double[] deriv = new double[n];
deriv[0] = (integrand.Execute(a + (b - a) / (n - 1)) - integrand.Execute(a)) / ((b - a) / (n - 1));
double maxDeriv = Math.Abs(deriv[0]);
for (int i = 1; i < n; ++i)
{
deriv[i] = (integrand.Execute(a + i * (b - a) / (n - 1)) - integrand.Execute(a + (i - 1) * (b - a) / (n - 1))) / ((b - a) / (n - 1));
if (Math.Abs(deriv[i]) > maxDeriv)
{
maxDeriv = Math.Abs(deriv[i]);
}
}
double h = (b - a) / Math.Ceiling(0.5 * maxDeriv * (b - a) * (b - a) / eps);
//найдем значение интеграла
double sum = 0;
for (int i = 0; i *h < (b - a); ++i)
{
sum += integrand.Execute(a + i * h);
}
return(sum * h);
}
public double Integration(FormulaExecutor integrand, double a, double b, double eps)
{
//заменим особые предельные точки на точки из окрестности
if (Double.IsNaN(integrand.Execute(a)) || Double.IsInfinity(integrand.Execute(a)))
{
a += 0.0001 * eps * (b - a);
}
if (Double.IsNaN(integrand.Execute(b)) || Double.IsInfinity(integrand.Execute(b)))
{
b -= 0.0001 * eps * (b - a);
}
//посчитаем производную на 100 точках и определим шаг разбиения h для метода
int n = 1000;
double[] deriv = new double[n];
deriv[0] = (integrand.Execute(a + (b - a) / (n - 1)) - integrand.Execute(a)) / ((b - a) / (n - 1));
for (int i = 1; i < n; ++i)
{
deriv[i] = (integrand.Execute(a + i * (b - a) / (n - 1)) - integrand.Execute(a + (i - 1) * (b - a) / (n - 1))) / ((b - a) / (n - 1));
}
//по значению производной посчитаем значение второй производной и определим шаг разбиения h для метода
double[] secDeriv = new double[n];
secDeriv[0] = (deriv[1] - deriv[0]) / ((b - a) / (n - 1));
double maxSecDeriv = Math.Abs(secDeriv[0]);
for (int i = 1; i < n; ++i)
{
secDeriv[i] = (deriv[i] - deriv[i - 1]) / ((b - a) / (n - 1));
if (Math.Abs(secDeriv[i]) > maxSecDeriv)
{
maxSecDeriv = Math.Abs(secDeriv[i]);
}
}
double h = (b - a) / Math.Ceiling(Math.Sqrt(maxSecDeriv * Math.Pow(b - a, 3) / (12 * eps)));
//найдем значение интеграла
double sum = integrand.Execute(a) + integrand.Execute(b);
for (int i = 1; i *h < (b - a); ++i)
{
sum += 2 * integrand.Execute(a + i * h);
}
return(0.5 * h * sum);
}