// Метод для поиска минимума методом золотого сечения (Algo8-1.c).
// Возвращает значение аргумента:
public static double Optimum_1(Functional_1 fun,
// fun - минимизируемая функция (функционал)
double A, double B, //границы интервала
double Delta, double Epsilon)
{ // точности по абсциссе и ординате
double Rone = (Math.Sqrt(5.0) - 1.0) / 2.0; // Determine constants
double Rtwo = Rone * Rone; /* for golden search */
double YA, YB; /* function values at A and B */
double C, D; /* interior points */
double H; /* width of interval */
double P, YC, YD, YP; /* minimum and function values */
YA = fun(A);
YB = fun(B);
H = B - A;
C = A + Rtwo * H;
YC = fun(C);
D = A + Rone * H;
YD = fun(D);
while (Math.Abs(YA - YB) > Epsilon || H > Delta)
{
if (YC < YD)
{
B = D;
YB = YD;
D = C;
YD = YC;
H = B - A;
C = A + Rtwo * H;
YC = fun(C);
}
else
{
A = C;
YA = YC;
C = D;
YC = YD;
H = B - A;
D = A + Rone * H;
YD = fun(D);
}
}
P = A;
YP = YA;
if (YB < YA)
{
P = B;
YP = YB;
}
return(P);
}//Optimum_1
/// <summary>
/// Find minimum's point.
/// </summary>
/// <param name="fun"> Function </param>
/// <param name="left"> Left bound </param>
/// <param name="right"> Right bound </param>
/// <param name="delta"> Eps X </param>
/// <param name="epsilon"> Eps Y </param>
/// <returns> Minimum's point </returns>
public static double Optimum_1(Functional_1 fun, double left, double right,
double delta, double epsilon)
{
if (fun is null || right < left || delta < 0 || epsilon < 0)
{
throw new Exception("Error passing parameters");
}
// Declare require variable.
var rOne = (Math.Sqrt(5) - 1) / 2.0;
var rTwo = rOne * rOne;
double yLeft, yRight;
double h;
// Можно было делать обычное присваивание, но так лаконичней.
// Set value in variables.
(yLeft, yRight, h) = (fun(left), fun(right), right - left);
var c = left + rTwo * h;
var yC = fun(c);
var d = left + rOne * h;
var yD = fun(d);
// Function start.
while (Math.Abs(yLeft - yRight) > epsilon || h > delta)
{
if (yC < yD)
{
(right, yRight) = (d, yD);
(d, yD, h) = (c, yC, right - left);
c = left + rTwo * h;
yC = fun(c);
}
else
{
(left, yLeft, c, yC) = (c, yC, d, yD);
h = right - left;
d = left + rOne * h;
yD = fun(d);
}
}
return((yRight < yLeft) ? right : left);
}
