ОТЧЕТ ПО МО
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(обязательное)
namespace MO22
{
public class Program
{
public static double D(double a, double b)
{
return b - a;
}
private static double DeFfirst(double X1, double X2)
{
return 402 * X1 + 200 * X2 - 1204;
}
private static double DeFsecond(double X1, double X2)
{
return 200 * X1 + 102 * X2 - 614;
}
private static double Function(double X1, double X2)
{
return (X1 - 2) * (X1 - 2) + (X2 - 7) * (X2 - 7) + 50 * (X2 + 2 * X1 - 6) * (X2 + 2 * X1 - 6) + 7.6;
}
private static void FastDown()
{
double X11 = 0; double X12 = 0; double epsilon = 0.001;
double border_a = -2000; double border_b = 2000; double Alfa = 0.618; double Beta = 0.382;
int count = 0; do
{
double t = Gold(border_a, border_b, Alfa, Beta, X11, X12); double tempX1 = X11;
double tempX2 = X12;
X11 = X11 - t * DeFfirst(tempX1, tempX2);
X12 = X12 - t * DeFsecond(tempX1, tempX2); count++;
Console.WriteLine(Math.Round(X11, 3) + " " + Math.Round(X12, 3) + " "
+ Math.Round(Function(X11, X12), 3) + " " + Math.Round(t, 3) + " " + count);
}while (Math.Abs(DeFfirst(X11, X12)) > epsilon && Math.Abs(DeFsecond(X11,
X12)) > epsilon);
}
private static void GelfCeit()
{
double t1, t2, X01 = 0, X02 = 0, GlobalCount = 0, Count1 = 0, Count2 = 0, G1, G2, Alf = 0.618, Bet = 1 - Alf;
do
{
do
{
if (Math.Abs(DeFfirst(X01, X02)) > 0.01)
{
G1 = DeFfirst(X01, X02);
}
else
G1 = 0;
if (Math.Abs(DeFsecond(X01, X02)) > 0.01)
{
G2 = DeFsecond(X01, X02);
}
else
G2 = 0;
t1 = Gold(-2000, 2000, Alf, Bet, X01, X02);
X01 -= t1 * G1;
X02 -= t1 * G2;
Count1++;
}while (Count1 < 10); Count1 = 0;
do
{
if (Math.Abs(DeFfirst(X01, X02)) > 0.01)
{
G1 = DeFfirst(X01, X02);
}
else
G1 = 0;
if (Math.Abs(DeFsecond(X01, X02)) > 0.01)
{
G2 = DeFsecond(X01, X02);
}
else
G2 = 0;
t2 = Gold(-2000, 2000, Alf, Bet, X01, X02); X01 -= t2 * G1;
X02 -= t2 * G2; Count2++;
}while (Count2 < 10);
Count2 = 0;
GlobalCount++;
Console.WriteLine(Math.Round(X01, 6) + " " + Math.Round(X02, 6) + " "
+ Math.Round(Function(X01, X02), 6) + " " + Math.Round(G1, 6) + " " + Math.Round(G2,
6) + " " + GlobalCount);
}while (GlobalCount < 50);
}
public static double Gold(double a, double b, double Alf, double Bet, double X11, double X12)
{
var count = 0; double XB; double XA; do
{
XB = a + Bet * D(a, b); XA = a + Alf * D(a, b);
if (T(X11, X12, XB) >= T(X11, X12, XA))
{
a = XB;
}
else
{
b = XA;
}
count++;
} while (D(a, b) >= 0.01);
if (T(X11, X12, XA) <= T(X11, X12, XB))
{
return XA;
}
else
{
return XB;
}
}
private static void Main(string[] args)
{
Console.WriteLine("\nДля ВТОРОЙ функции\n"); Console.WriteLine("\nМетод Нелдера-Мида\n"); NelderMid();
Console.WriteLine("\nМетод быстрого спуска\n"); FastDown();
Console.WriteLine("\nМетод Гельфанда-Цейтлина\n"); GelfCeit();
}
private static void NelderMid()
{
var n = 2;
var count = 1;
double Xh = 0, Xh1, Xh2, Xl = 0, Xl1, Xl2, t = 10, X11, X12, X21, X22, X31, X32, X61, X62, X71, X72, A, X51, X52, X41, X42, Max, Min;
var d2 = t * (Math.Pow(n + 1, 0.5) - 1) / (Math.Pow(2, 0.5) * n); var d1 = t * (Math.Pow(n + 1, 0.5) + n - 1) / (Math.Pow(2, 0.5) * n); X11 = 0;
X12 = 0;
X21 = d1;
X22 = d2;
X31 = d2;
X32 = d1;
Max = double.MinValue; Min = double.MaxValue;
if (Function(X11, X12) > Function(X21, X22) && Function(X11, X12) > Function(X31, X32))
{
Xh = Function(X11, X12); Xh1 = X11;
Xh2 = X12;
}
else if (Function(X21, X22) > Function(X11, X12) && Function(X21, X22) > Function(X31, X32))
{
Xh = Function(X21, X22); Xh1 = X21;
Xh2 = X22;
}
else
{
Xh = Function(X31, X32); Xh1 = X31;
Xh2 = X32;
}
if (Function(X11, X12) < Function(X21, X22) && Function(X11, X12) < Function(X31, X32))
{
Xl = Function(X11, X12); Xl1 = X11;
Xl2 = X12;
}
else if (Function(X21, X22) < Function(X11, X12) && Function(X21, X22) < Function(X31, X32))
{
Xl = Function(X21, X22); Xl1 = X21;
Xl2 = X22;
}
else
{
Xl = Function(X31, X32); Xl1 = X31;
Xl2 = X32;
}
do
{
Console.Write("(" + Math.Round(X11, 2) + ";" + Math.Round(X12, 2) + ") " + Math.Round(Function(X11, X12), 2)
+ " ");
Console.Write("(" + Math.Round(X21, 2) + ";" + Math.Round(X22, 2) + ") " + Math.Round(Function(X21, X22), 2)
+ " ");
Console.Write("(" + Math.Round(X31, 2) + ";" + Math.Round(X32, 2) + ") " + Math.Round(Function(X31, X32), 2)
+ " ");
Console.WriteLine(count); //смещенный центр тяжести if (Xh == Function(X11, X12))
{
X41 = (X21 + X31) / n;
X42 = (X22 + X32) / n;
}
else if (Xh == Function(X21, X22))
{
X41 = (X11 + X31) / n;
X42 = (X12 + X32) / n;
}
else
{
X41 = (X11 + X21) / n;
X42 = (X12 + X22) / n;
}
//точка отражения
X51 = 2 * X41 - Xh1;
X52 = 2 * X42 - Xh2;
if (Function(X51, X52) < Xl)
{
//точка растяжения
X61 = 2 * X51 - X41;
X62 = 2 * X52 - X42;
if (Function(X61, X62) < Xl)
{
Xh1 = X61;
Xh2 = X62;
Xh = Function(Xh1, Xh2);
}
else
{
Xh1 = X51;
Xh2 = X52;
Xh = Function(Xh1, Xh2);
}
}
else
{
if (Function(X51, X52) > Function(X11, X12) && Function(X51, X52) > Function(X21, X22) && Function(X51, X52) > Function(X31, X32))
{
if (Function(X51, X52) > Xh)
{
//редукция
X11 = 0.5 * Xl1 + 0.5 * X11;
X12 = 0.5 * Xl2 + 0.5 * X12;
X21 = 0.5 * Xl1 + 0.5 * X21;
X22 = 0.5 * Xl2 + 0.5 * X22;
X31 = 0.5 * Xl1 + 0.5 * X31;
X32 = 0.5 * Xl2 + 0.5 * X32;
if (Function(X11, X12) > Function(X21, X22) &&
Function(X11, X12) > Function(X31, X32) && Function(X11, X12) > Max)
{
Xh = Function(X11, X12); Xh1 = X11;
Xh2 = X12;
}
else if (Function(X21, X22) > Function(X11, X12) &&
Function(X21, X22) > Function(X31, X32) && Function(X21, X22) > Max)
{
Xh = Function(X21, X22); Xh1 = X21;
Xh2 = X22;
}
else
{
Xh = Function(X31, X32); Xh1 = X31;
Xh2 = X32;
}
if (Function(X11, X12) < Function(X21, X22) &&
Function(X11, X12) < Function(X31, X32) && Function(X11, X12) < Min)
{
Xl = Function(X11, X12); Xl1 = X11;
Xl2 = X12;
}
else if (Function(X21, X22) < Function(X11, X12) &&
Function(X21, X22) < Function(X31, X32) && Function(X21, X22) < Min)
{
Xl = Function(X21, X22); Xl1 = X21;
Xl2 = X22;
}
else
{
Xl = Function(X31, X32); Xl1 = X31;
Xl2 = X32;
}
}
else
{
//Сжатие
X71 = 0.5 * X51 - X41;
X72 = 0.5 * X52 - X42;
if (Function(X71, X72) > Xh)
{
//редукция
X11 = 0.5 * Xl1 + 0.5 * X11;
X12 = 0.5 * Xl2 + 0.5 * X12;
X21 = 0.5 * Xl1 + 0.5 * X21;
X22 = 0.5 * Xl2 + 0.5 * X22;
X31 = 0.5 * Xl1 + 0.5 * X31;
X32 = 0.5 * Xl2 + 0.5 * X32;
if (Function(X11, X12) > Function(X21, X22) &&
Function(X11, X12) > Function(X31, X32) && Function(X11, X12) > Max)
{
Xh = Function(X11, X12); Xh1 = X11;
Xh2 = X12;
}
else if (Function(X21, X22) > Function(X11, X12) &&
Function(X21, X22) > Function(X31, X32) && Function(X21, X22) > Max)
{
Xh = Function(X21, X22); Xh1 = X21;
Xh2 = X22;
}
else
{
Xh = Function(X31, X32); Xh1 = X31;
Xh2 = X32;
}
if (Function(X11, X12) < Function(X21, X22) &&
Function(X11, X12) < Function(X31, X32) && Function(X11, X12) < Min)
{
Xl = Function(X11, X12); Xl1 = X11;
Xl2 = X12;
}
else if (Function(X21, X22) < Function(X11, X12) &&
Function(X21, X22) < Function(X31, X32) && Function(X21, X22) < Min)
{
Xl = Function(X21, X22); Xl1 = X21;
Xl2 = X22;
}
else
{
Xl = Function(X31, X32); Xl1 = X31;
Xl2 = X32;
}
}
else
{
Xh1 = X71;
Xh2 = X72;
Xh = Function(Xh1, Xh2);
}
}
}
else
{
Xh1 = X51;
Xh2 = X52;
Xh = Function(Xh1, Xh2);
}
}
count++;
A = (Math.Pow(Function(X11, X12) - Function(X41, X42), 2) +
Math.Pow(Function(X21, X22) - Function(X41, X42), 2) + Math.Pow(Function(X31, X32) - Function(X41, X42), 2)) / (n + 1);
} while (A >= 0.01); Console.WriteLine();
}
public static double T(double X11, double X12, double t)
{
return (X11 - t * DeFfirst(X11, X12) - 2) * (X11 - t * DeFfirst(X11, X12) - 2)
+ (X12 - t * DeFsecond(X11, X12) - 7) * (X12 - t * DeFsecond(X11, X12) - 7) + 50
*(X12 - t * DeFsecond(X11, X12) + 2 * (X11 - t * DeFfirst(X11, X12)) - 6) * (X12 - t
*DeFsecond(X11, X12) + 2 * (X11 - t * DeFfirst(X11, X12)) - 6) + 7.6;
}
}
}