public static double GoldenCut_Calculation(double a, double b)
{
FileLine header = new FileLine();
int n = 1;
//Console.WriteLine("f(x) = x ** 2");
//Console.WriteLine("f(x) = cosh(x)");
//header.X = "f(x) = cosh(x)";
//header.X = "f(x) = x ** 2";
//Output.Add(header);
double tau = (1 + Math.Sqrt(5)) / 2;
//tau = Math.Round(tau, B);
double x1 = b - (b - a) / tau;
bool flipflag = false;
double d, x2, f1, f2;
x2 = a + b - x1;
double fn = F(a);
f1 = F(x1);
f2 = F(x2);
while (Math.Abs(b - a) > delta)
{
FileLine line = new FileLine();
//Print(n);
line.Iteration_number = n.ToString();
if (flipflag)
{
x1 = b - (b - a) / tau;
f1 = F(x1);
}
else
{
x2 = (b - a) / tau + a;
f2 = F(x2);
}
//line.X_left = x1.ToString();
//line.X_right = x2.ToString();
d = 0.00001;
//line.Func_left = f1.ToString();
//line.Func_right = f2.ToString();
if (f1 < f2)
{
b = x2;
x2 = x1;
f2 = f1;
flipflag = true;
//line.Comp = "<";
}
else
{
a = x1;
x1 = x2;
f1 = f2;
flipflag = false;
//line.Comp = ">";
}
line.a = a.ToString();
line.b = b.ToString();
n++;
Console.WriteLine();
//Output.Add(line);
}
double x = (b + a) / 2;
FileLine Down_header = new FileLine();
//Down_header.X = "x_min = ";
//Down_header.X_left = x.ToString();
//Down_header.X_right = "f(x_min) = ";
//Down_header.Func_left = F(x).ToString();
//Output.Add(Down_header);
//sigma = 0;
//SaveToCSV("X_cosh_test_golden_calculation");
return(x);
}
public double SquareApproximation(double a, double b)
{
FileLine header = new FileLine();
header.X_prev = "y = 5x^3 - 3x^5";
Output.Add(header);
double h, x1, x2, x3, F1, F2, F3, x_min, F_min;
x2 = (a + b) / 2;
x1 = a;
x3 = b;
h = delta;
int n = 0;
x_min = x2;
F_min = F(x_min);
int intervals = 10;
do
{
FileLine line = new FileLine();
n++;
//x1 = (a + b) / 2;
h = (x3 - x1) / (intervals + 1);
Tuple <double, double>[] points = new Tuple <double, double> [intervals + 1];
for (int i = 1; i <= intervals; i++)
{
points[i] = new Tuple <double, double>(x1 + h * i, F(x1 + h * i));
}
double[,] matrix = new double[3, 4];
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 4; j++)
{
matrix[i, j] = 0;
}
}
matrix[0, 0] = intervals;
for (int i = 1; i <= intervals; i++)
{
matrix[1, 0] += points[i].Item1;
matrix[2, 0] += points[i].Item1 * points[i].Item1;
matrix[2, 1] += points[i].Item1 * points[i].Item1 * points[i].Item1;
matrix[2, 2] += points[i].Item1 * points[i].Item1 * points[i].Item1 * points[i].Item1;
matrix[0, 3] += points[i].Item2;
matrix[1, 3] += points[i].Item2 * points[i].Item1;
matrix[2, 3] += points[i].Item1 * points[i].Item1 * points[i].Item2;
}
matrix[0, 1] = matrix[1, 0];
matrix[1, 1] = matrix[2, 0];
matrix[0, 2] = matrix[2, 0];
matrix[1, 2] = matrix[2, 1];
var result = KrammerCalc(matrix);
if (result.Item3 == 0)
{
break;
}
x_min = -1 * result.Item2 / (2 * result.Item3);
double A = result.Item3;
double B = result.Item2;
double C = result.Item1;
//F_min = A * x_min * x_min + B * x_min + C;
//F2 = A * x2 * x2 + B * x2 * C;
F_min = F(x_min);
F2 = F(x2);
line.Iteration_number = n.ToString();
line.X_prev = x2.ToString();
line.X_min = x_min.ToString();
line.Func_prev = F2.ToString();
line.Func_min = F_min.ToString();
line.a = x1.ToString();
line.b = x3.ToString();
Output.Add(line);
//F1 = F(a);
//F3 = F(b);
if (Math.Abs(x2 - x_min) < delta)
{
break;
}
else
{
if (x1 < x_min && x_min < x2)
{
if (F_min < F2)
{
x3 = x2;
F3 = F2;
x2 = x_min;
F2 = F_min;
}
else
{
x1 = x_min;
F1 = F_min;
}
}
else if (x2 < x_min && x_min < x3)
{
if (F_min < F2)
{
x1 = x2;
F1 = F2;
x2 = x_min;
F2 = F_min;
}
else
{
x3 = x_min;
F3 = F_min;
}
}
}
} while (n < 30);
//Print(n);
FileLine Down_header = new FileLine();
Down_header.X_prev = "x_min = ";
Down_header.X_min = x_min.ToString();
Down_header.Func_prev = "f(x_min) = ";
Down_header.Func_min = F_min.ToString();
Output.Add(Down_header);
SaveToCSV("X_polynom_approximation");
return(x_min);
}
/*public double CalcMin(double a, double b)
* {
* FileLine header = new FileLine();
* int n = 1;
* Console.WriteLine("f(x) = x ** 2");
* //Console.WriteLine("f(x) = cosh(x)");
* //header.X = "f(x) = cosh(x)";
* header.X = "f(x) = x ** 2";
* Output.Add(header);
* double x = (a + b) / 2;
* double d, x1, x2, f1, f2;
* double fn = F(a);
*
* while(Math.Abs(b - a) > delta)
* {
* FileLine line = new FileLine();
* Print(n);
* line.Iteration_number = n.ToString();
* x = (a + b) / 2;
* Print(x);
* line.X = x.ToString();
* d = delta / 10;
* //d = Math.Abs((b - a) / 100);
* x1 = x - d;
* Print(x1);
* line.X_left = x1.ToString();
* x2 = x + d;
* Print(x2);
* line.X_right = x2.ToString();
* f1 = F(x1);
* f2 = F(x2);
* fn = F(x);
* Print(f1);
* line.Func_left = f1.ToString();
* if (f1 < f2)
* {
* b = x2;
* Console.Write(" < |");
* line.Comp = "<";
* }
* else
* {
* Console.Write(" > |");
* a = x1;
* line.Comp = ">";
* }
* Print(f2);
* line.Func_right = f2.ToString();
* Print(a);
* line.a = a.ToString();
* Print(b);
* line.b = b.ToString();
* x = (a + b) / 2;
* n++;
* Console.WriteLine();
* Output.Add(line);
* }
* FileLine Down_header = new FileLine();
* Down_header.X = "x_min = ";
* Down_header.X_left = x.ToString();
* Down_header.X_right = "f(x_min) = ";
* Down_header.Func_left = F(x).ToString();
* Output.Add(Down_header);
* //SaveToCSV("X_square_test");
* //sigma = 0;
* return Math.Abs(F(x) - 1);
* }
* public double GoldenCut_Simetria(double a, double b)
* {
* FileLine header = new FileLine();
* int n = 1;
* Console.WriteLine("f(x) = x ** 2");
* //Console.WriteLine("f(x) = cosh(x)");
* //header.X = "f(x) = cosh(x)";
* header.X = "f(x) = x ** 2";
* Output.Add(header);
* double tau = (1 + Math.Sqrt(5)) / 2;
* tau = Math.Round(tau, B);
* double x1 = b - (b - a) / tau;
* bool flipflag = false;
* double d, x2, f1, f2;
* x2 = a + b - x1;
* double fn = F(a);
* f1 = F(x1);
* f2 = F(x2);
* while (Math.Abs(b - a) > delta && a < 0)
* {
* FileLine line = new FileLine();
* Print(n);
* line.Iteration_number = n.ToString();
* if (flipflag)
* {
* x1 = a + b - x2;
* f1 = F(x1);
* }
* else
* {
* x2 = b - x1 + a;
* f2 = F(x2);
* }
* line.X_left = x1.ToString();
* line.X_right = x2.ToString();
* d = 0.00001;
* line.Func_left = f1.ToString();
* line.Func_right = f2.ToString();
*
* if(f1 < f2)
* {
* b = x2;
* x2 = x1;
* f2 = f1;
* flipflag = true;
* line.Comp = "<";
* }
* else
* {
* a = x1;
* x1 = x2;
* f1 = f2;
* flipflag = false;
* line.Comp = ">";
* }
* line.a = a.ToString();
* line.b = b.ToString();
* n++;
* Console.WriteLine();
* Output.Add(line);
* }
* double x = (b + a) / 2;
* FileLine Down_header = new FileLine();
* Down_header.X = "x_min = ";
* Down_header.X_left = x.ToString();
* Down_header.X_right = "f(x_min) = ";
* Down_header.Func_left = F(x).ToString();
* Output.Add(Down_header);
* //sigma = 0;
* //SaveToCSV("X_cosh_test_golden_simetrya");
* return Math.Abs(F(x) - 1);
* }
*
* public double Fibonachi_calculations(double a, double b)
* {
* FileLine header = new FileLine();
* int n = 1;
* Console.WriteLine("f(x) = x ** 2");
* //Console.WriteLine("f(x) = cosh(x)");
* header.X = "f(x) = cosh(x)";
* //header.X = "f(x) = x ** 2";
* Output.Add(header);
* CalcFibonachi(100);
* int expected_n = 10;
* while((Fibonachi[expected_n + 1] - Fibonachi[expected_n - 1]) * delta < (b - a))
* {
* expected_n++;
* }
* expected_n = expected_n - 1;
* a = b - (Fibonachi[expected_n + 1] - Fibonachi[expected_n - 1]) * delta;
* double tau = (1 + Math.Sqrt(5)) / 2;
* double l1 = b - a;
* double x1 = b - (Fibonachi[expected_n] - Fibonachi[expected_n - 2]) * delta;
* bool flipflag = false;
* double d, x2, f1, f2;
* x2 = a + b - x1;
* double fn = F(a);
* f1 = F(x1);
* f2 = F(x2);
* while (Math.Abs(b - a) > delta)
* {
* FileLine line = new FileLine();
* Print(n);
* line.Iteration_number = n.ToString();
* if (flipflag)
* {
* x1 = a + b - x2;
* f1 = F(x1);
* }
* else
* {
* x2 = b - x1 + a;
* f2 = F(x2);
* }
* line.X_left = x1.ToString();
* line.X_right = x2.ToString();
* d = 0.00001;
* line.Func_left = f1.ToString();
* line.Func_right = f2.ToString();
*
* if (f1 < f2)
* {
* b = x2;
* x2 = x1;
* f2 = f1;
* flipflag = true;
* line.Comp = "<";
* }
* else
* {
* a = x1;
* x1 = x2;
* f1 = f2;
* flipflag = false;
* line.Comp = ">";
* }
* line.a = a.ToString();
* line.b = b.ToString();
* n++;
* Console.WriteLine();
* Output.Add(line);
* }
* double x = (b + a) / 2;
* FileLine Down_header = new FileLine();
* Down_header.X = "x_min = ";
* Down_header.X_left = x.ToString();
* Down_header.X_right = "f(x_min) = ";
* Down_header.Func_left = F(x).ToString();
* Output.Add(Down_header);
* //sigma = 0;
* //SaveToCSV("X_cosh_test_Fibonachi");
* return x;
* }
* public double GoldenCut_Calculation(double a, double b)
* {
* FileLine header = new FileLine();
* int n = 1;
* Console.WriteLine("f(x) = x ** 2");
* //Console.WriteLine("f(x) = cosh(x)");
* header.X = "f(x) = cosh(x)";
* //header.X = "f(x) = x ** 2";
* Output.Add(header);
* double tau = (1 + Math.Sqrt(5)) / 2;
*
* tau = Math.Round(tau, B);
* double x1 = b - (b - a) / tau;
* bool flipflag = false;
* double d, x2, f1, f2;
* x2 = a + b - x1;
* double fn = F(a);
* f1 = F(x1);
* f2 = F(x2);
* while (Math.Abs(b - a) > delta)
* {
* FileLine line = new FileLine();
* Print(n);
* line.Iteration_number = n.ToString();
* if (flipflag)
* {
* x1 = b - (b - a) / tau;
* f1 = F(x1);
* }
* else
* {
* x2 = (b - a) / tau + a;
*
* f2 = F(x2);
* }
* line.X_left = x1.ToString();
* line.X_right = x2.ToString();
* d = 0.00001;
* line.Func_left = f1.ToString();
* line.Func_right = f2.ToString();
*
* if (f1 < f2)
* {
* b = x2;
* x2 = x1;
* f2 = f1;
* flipflag = true;
* line.Comp = "<";
* }
* else
* {
* a = x1;
* x1 = x2;
* f1 = f2;
* flipflag = false;
* line.Comp = ">";
* }
* line.a = a.ToString();
* line.b = b.ToString();
* n++;
* Console.WriteLine();
* Output.Add(line);
* }
* double x = (b + a) / 2;
* FileLine Down_header = new FileLine();
* Down_header.X = "x_min = ";
* Down_header.X_left = x.ToString();
* Down_header.X_right = "f(x_min) = ";
* Down_header.Func_left = F(x).ToString();
* Output.Add(Down_header);
* sigma = 0;
* //SaveToCSV("X_cosh_test_golden_calculation");
* return x;
* }*/
public double Golden_combinated(double a, double b, int N)
{
FileLine header = new FileLine();
int n = 1;
Console.WriteLine("f(x) = x ** 2");
//Console.WriteLine("f(x) = cosh(x)");
//header.X = "f(x) = cosh(x)";
//header.X = "f(x) = x ** 2";
Output.Add(header);
double tau = (1 + Math.Sqrt(5)) / 2;
tau = Math.Round(tau, B);
double x1 = b - (b - a) / tau;
bool flipflag = false;
double d, x2, f1, f2;
x2 = a + b - x1;
//double fn = F(a);
f1 = F(x1);
f2 = F(x2);
for (int i = 0; i < N; i++)
{
FileLine line = new FileLine();
Print(n);
line.Iteration_number = n.ToString();
if (flipflag)
{
x1 = b - (b - a) / tau;
f1 = F(x1);
}
else
{
x2 = (b - a) / tau + a;
f2 = F(x2);
}
//line.X_left = x1.ToString();
//line.X_right = x2.ToString();
d = 0.00001;
//line.Func_left = f1.ToString();
//line.Func_right = f2.ToString();
if (f1 < f2)
{
b = x2;
x2 = x1;
f2 = f1;
flipflag = true;
//line.Comp = "<";
}
else
{
a = x1;
x1 = x2;
f1 = f2;
flipflag = false;
//line.Comp = ">";
}
line.a = a.ToString();
line.b = b.ToString();
n++;
Console.WriteLine();
//Output.Add(line);
}
Console.WriteLine(A);
/*double x = (b + a) / 2;
* FileLine Down_header = new FileLine();
* Down_header.X = "x_min = ";
* Down_header.X_left = x.ToString();
* Down_header.X_right = "f(x_min) = ";
* Down_header.Func_left = F(x).ToString();
* Output.Add(Down_header);
* sigma = 0;
* //SaveToCSV("X_cosh_test_golden_calculation");
* return x;*/
//int n = 0;
double F1, F2, F3;
if (flipflag)
{
x2 = x1;
F2 = f1;
}
else
{
F2 = f2;
}
x1 = a;
double x3 = b;
//x2 = (b + a) / 2;
F1 = F(x1);
//F2 = F(x2);
F3 = F(x3);
do
{
n++;
Print(n - N - 1);
Console.WriteLine();
double[,] matrix = new double[3, 4];
matrix[0, 0] = x1 * x1;
matrix[1, 0] = x2 * x2;
matrix[2, 0] = x3 * x3;
matrix[0, 1] = x1;
matrix[1, 1] = x2;
matrix[2, 1] = x3;
matrix[0, 2] = 1;
matrix[1, 2] = 1;
matrix[2, 2] = 1;
matrix[0, 3] = F1;
matrix[1, 3] = F2;
matrix[2, 3] = F3;
var res = KrammerCalc(matrix);
double c2 = res.Item1;
double c1 = res.Item2;
double x_min = -c1 / (2 * c2);
double F_min = F(x_min);
if (Math.Abs(x2 - x_min) < delta)
{
Console.WriteLine(A);
return(x_min);
}
else
{
if (x1 < x_min && x_min < x2)
{
if (F_min < F2)
{
x3 = x2;
F3 = F2;
x2 = x_min;
F2 = F_min;
}
else
{
x1 = x_min;
F1 = F_min;
}
}
else if (x2 < x_min && x_min < x3)
{
if (F_min < F2)
{
x1 = x2;
F1 = F2;
x2 = x_min;
F2 = F_min;
}
else
{
x3 = x_min;
F3 = F_min;
}
}
//x2 = x_min;
}
} while (true);
}
public double SquareInterpolation(double a, double b)
{
FileLine header = new FileLine();
header.X_prev = "y = 5x^3 - 3x^5";
Output.Add(header);
int n = 0;
double x1 = a;
double x3 = b;
double x2 = (b + a) / 2;
double x_min, F_min;
double F1, F2, F3;
F1 = F(x1);
F2 = F(x2);
F3 = F(x3);
do
{
FileLine line = new FileLine();
n++;
double[,] matrix = new double[3, 4];
matrix[0, 0] = x1 * x1;
matrix[1, 0] = x2 * x2;
matrix[2, 0] = x3 * x3;
matrix[0, 1] = x1;
matrix[1, 1] = x2;
matrix[2, 1] = x3;
matrix[0, 2] = 1;
matrix[1, 2] = 1;
matrix[2, 2] = 1;
matrix[0, 3] = F1;
matrix[1, 3] = F2;
matrix[2, 3] = F3;
var res = KrammerCalc(matrix);
double c2 = res.Item1;
double c1 = res.Item2;
x_min = -c1 / (2 * c2);
F_min = F(x_min);
line.Iteration_number = n.ToString();
line.X_prev = x2.ToString();
line.X_min = x_min.ToString();
line.Func_prev = F2.ToString();
line.Func_min = F_min.ToString();
line.a = x1.ToString();
line.b = x3.ToString();
Output.Add(line);
if (Math.Abs(x2 - x_min) < delta)
{
break;
//return x_min;
}
else
{
if (x1 < x_min && x_min < x2)
{
if (F_min < F2)
{
x3 = x2;
F3 = F2;
x2 = x_min;
F2 = F_min;
}
else
{
x1 = x_min;
F1 = F_min;
}
}
else if (x2 < x_min && x_min < x3)
{
if (F_min < F2)
{
x1 = x2;
F1 = F2;
x2 = x_min;
F2 = F_min;
}
else
{
x3 = x_min;
F3 = F_min;
}
}
//x2 = x_min;
}
} while (true);
FileLine Down_header = new FileLine();
Down_header.X_prev = "x_min = ";
Down_header.X_min = x_min.ToString();
Down_header.Func_prev = "f(x_min) = ";
Down_header.Func_min = F_min.ToString();
Output.Add(Down_header);
SaveToCSV("X_polynom_interpolation");
return(x_min);
}
public void CountChanges()
{
List <FileLine> Output1 = new List <FileLine>();
//sigma = 0;
for (int i = 1; i < 20; i++)
{
A = 0;
//sigma = 0.1 * i + 0.1;
FileLine line = new FileLine();
//line.X = i.ToString();
/*double n = Math.Abs(SquareInterpolation(-2, 1) + 1);
* double n1 = Math.Abs(SquareApproximation(-2, 1) + 1);
* if(n1 == Double.NaN)
* {
* n1 = 0;
* }
* for (int j = 0; j < 20; j++)
* {
* n += Math.Abs(SquareInterpolation(-2, 1) + 1);
* var temp = Math.Abs(SquareApproximation(-2, 1) + 1);
* if(temp == Double.NaN)
* {
* temp = 0;
* }
* n1 += temp;
* }
* n = n / 21;
* n1 = n1 / 21;
* //delta = delta / 10;
* line.X_right = n1.ToString();
* line.X_left = n.ToString();
* line.X = sigma.ToString();*/
var n = Golden_combinated(-2, 1, i);
line.X_prev = i.ToString();
line.X_min = A.ToString();
Output1.Add(line);
}
/*var x_interpol = SquareInterpolation(-2, 1);
* var x_approx = SquareApproximation(-2, 1);
* var x_comb = Golden_combinated(-2, 1, 5);
* FileLine line_interp = new FileLine();
* FileLine line_approx = new FileLine();
* FileLine line_comb = new FileLine();
* line_interp.X_left = x_interpol.ToString();
* line_interp.X_right = F(x_interpol).ToString();
* line_interp.Iteration_number = "Interpolation";
* line_approx.Iteration_number = "Approximation";
* line_approx.X_left = x_approx.ToString();
* line_approx.X_right = F(x_approx).ToString();
* line_comb.Iteration_number = "Combinated";
* line_comb.X_left = x_comb.ToString();
* line_comb.X_right = F(x_comb).ToString();
* Output1.Add(line_interp);
* Output1.Add(line_approx);
* Output1.Add(line_comb);*/
string filename = "X_polynom_combinated";
using (StreamWriter writer = new StreamWriter(filename + ".csv"))
{
using (CsvWriter csvWriter = new CsvWriter(writer, System.Globalization.CultureInfo.CurrentCulture))
{
csvWriter.Configuration.Delimiter = ";";
csvWriter.WriteRecords(Output1);
}
}
Output1.Clear();
}