/// <summary>
/// Вычисление криволинейного интеграла первого рода по этой кривой от функции f методом трапеции
/// </summary>
/// <param name="f"></param>
/// <returns></returns>
public double FirstkindTr(Functional f)//(в программе не используется)
{
Get_h(ITER_INTEG);
double value = 0;
for (int k = 0; k <= M - 1; k++)
{
value += f(Transfer((a + (k + 1) * _h + a + (k) * _h) / 2)) * Point.Eudistance(Transfer(a + (k + 1) * _h), Transfer(a + (k) * _h));
}
return(value);
}
/// <summary> /// Создержит ли круг точку (взято с запасом) /// </summary> /// <param name="p"></param> /// <param name="RadiusCoef">Коэффициент определяющий, сколько радиусов от центра круга считаются собственностью окружности</param> /// <returns></returns> public bool ContainPoint(Point p, double RadiusCoef = 2.0) => Point.Eudistance(p, this.center) < this.radius * RadiusCoef;
public void UpVal()
{
double rr = 1;
Curve c = new Curve(0, 2 * Math.PI, (double t, double r) => r * Math.Cos(t), (double t, double r) => r * Math.Sin(t), rr);
c.S = (double tx, double ty, double r) => tx * ty * r; c.End = (double r) => 2 * Math.PI;
//Functional mp = (Point g) => 1;
//DoubleIntegral(mp, c, c.S, parallel: true, cy: 300, M: Method.GaussKronrod61).Show();
Func <Point, int, double> ro = (Point p, int k) => {
var cc = new Complex(p.x, p.y);
return(Math.Pow(cc.Abs, k) * Math.Cos(k * cc.Arg));
};
Func <Point, Point, double> E = (Point x, Point y) => Math.Log(Point.Eudistance(x, y));
int xc = 100, yc = 100;
double x0 = -8, X = 8, y0 = -8, Y = 8;
double hx = (X - x0) / (xc - 1), hy = (Y - y0) / (yc - 1);
double[] xa = new double[xc], ya = new double[yc];
for (int i = 0; i < xc; i++)
{
xa[i] = x0 + hx * i;
}
for (int i = 0; i < yc; i++)
{
ya[i] = y0 + hy * i;
}
int[] kk = new int[] { 3, 5, 25, 50, 200, 500 };
double[][,] val = new double[kk.Length][, ];
for (int i = 0; i < kk.Length; i++)
{
val[i] = new double[xc, yc];
Functional fl = (Point x) =>
{
Functional tmp = (Point y) => ro(y, kk[i]) * E(x, y);
return(DoubleIntegral(tmp, c, c.S, parallel: true, cy: 200, M: Method.GaussKronrod61));
};
Functional fl2 = (Point x) =>
{
Complex z = new Complex(x.x, x.y);
Functional tmp = (Point y) => {
Complex w = new Complex(y.x, y.y);
return(Math.Pow(w.Abs, kk[i]) * Math.Cos(kk[i] * (w.Arg)) * Math.Log(z.Abs.Sqr() + w.Abs.Sqr() - 2 * z.Abs * w.Abs * Math.Cos(w.Arg)));
};
return(DoubleIntegral(tmp, c, c.S, parallel: true, cy: 200, M: Method.GaussKronrod61) / 2 * Math.Cos(kk[i] * z.Arg));
};
Functional fr = (Point x) =>
{
Complex z = new Complex(x.x, x.y);
return(Math.PI * Math.Cos(kk[i] * z.Arg) / (kk[i] + 2) * Math.Max(Math.Log((z.Abs - 1).Sqr()).Abs(), Math.Log((z.Abs + 1).Sqr()).Abs()));
};
for (int ix = 0; ix < xc; ix++)
{
for (int iy = 0; iy < yc; iy++)
{
Point t = new Point(xa[ix], ya[iy]), o = new Point(0);
double rad = Point.Eudistance(t, o);
// $"t = {t} fr = {fr(t)} fl = {fl(t)}".Show();
//$"{fl(t)} {fl2(t)}".Show();
//Assert.IsTrue((fl(t) - fl2(t)).Abs() < 1e-7);
if (rad > 1.0)
{
val[i][ix, iy] = fr(t).Abs() - fl(t).Abs();
}
else
{
val[i][ix, iy] = Double.NaN;
}
}
}
}
StreamWriter args = new StreamWriter("arg.txt");
StreamWriter vals = new StreamWriter("vals.txt");
for (int i = 0; i < xc; i++)
{
args.WriteLine($"{xa[i]} {ya[i]}");
}
for (int i = 0; i < xc; i++)
{
for (int j = 0; j < yc; j++)
{
string st = "";
for (int s = 0; s < kk.Length; s++)
{
st += (val[s][i, j] + " ");
}
vals.WriteLine(st.Replace("NaN", "NA"));
}
}
args.Close();
vals.Close();
}