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 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);
}