/// <summary>
/// Создать источник по основным характеристикам
/// </summary>
/// <param name="center"></param>
/// <param name="normals"></param>
/// <param name="filter"></param>
/// <param name="fmas"></param>
/// <param name="type"></param>
/// <param name="radius"></param>
public Source(Point center, Normal2D[] normals, Func <Point, bool> filter, Complex[] fmas, Type type, double radius)
{
Center = center.dup;
Norms = normals; //new Normal2D[normals.Length];
//for (int i = 0; i < normals.Length; i++)
// Norms[i] = new Normal2D(normals[i]);
Filter = new Func <Point, bool>(filter);
Fmas = fmas.Dup();
this.radius = radius;
MeType = type;
}
private void button1_Click(object sender, EventArgs e)
{
Read();
double res = 0;
if (radioButton21.Checked)
{
MonteKarloEnum KK = MonteKarloEnum.Usual;
if (radioButton23.Checked)
{
KK = MonteKarloEnum.Geo;
}
МатКлассы.Point p = new МатКлассы.Point(a, b);
MultiFunc F = (double[] t) => f(t[0]);
h_Count = count;
n = count;
EPS = Double.NaN;
res = MonteKarlo(F, KK, p);
textBox7.Text = Math.Abs(res - DefIntegral(f, a, b, C, Criterion.StepCount, count, eps, seq)).ToString();
h_Count = count;
n = count;
EPS = Double.NaN;
//return;
}
else
{
Criterion K = Criterion.StepCount;
if (radioButton19.Checked)
{
K = Criterion.Accuracy;
}
if (radioButton20.Checked)
{
K = Criterion.SegmentCount;
}
if ((int)C < 3)
{
res = DefIntegral(f, a, b, C, K, count, eps, seq);
}
else
{
res = DefIntegral(f, a, b, C, K, nn, eps, seq);
}
}
textBox6.Text = res.ToString();
textBox3.Text = h_Count.ToString();
textBox4.Text = EPS.ToString();
}
/// <summary>
/// Двойной интеграл
/// </summary>
/// <param name="f"></param>
/// <param name="Curve"></param>
/// <returns></returns>
public static double Integral(Functional f, int Curve)
{
Func <double, double, double> func = (double x, double y) =>
{
Point t = new Point(x, y);
if (KursMethods.filters[Curve](t))
{
return(f(t));
}
return(0);
};
double a, b, c, d;
switch (Curve)
{
case 0:
a = -KursMethods.MAX_RADIUS;
b = KursMethods.MAX_RADIUS;
c = a;
d = b;
break;
case 1:
a = 0;
b = KursMethods.MIN_RADIUS;
c = a;
d = b * Math.Sqrt(3) / 2;
break;
case 3:
a = 0;
b = KursMethods.MIN_RADIUS;
c = a;
d = b;
break;
default:
a = 0;
b = KursMethods.MIN_RADIUS;
c = a;
d = b * Math.Sqrt(3) / 2;
break;
}
return(MathNet.Numerics.Integration.GaussLegendreRule.Integrate(func, a, b, c, d, n));
}
public static double g8(Point point)
{
double dx = MIN_RADIUS / 2;
double dy = MIN_RADIUS / 2 * Math.Sqrt(3);
double argument;
//C++ TO C# CONVERTER TODO TASK: The following line was determined to contain a copy constructor call - this should be verified and a copy constructor should be created:
//ORIGINAL LINE: Point d = point;
Point d = new Point(point); //d.x=-0.25;d.y=-0.25;
d.x -= dx;
d.y -= dy; //сдвиг к началу координат
if (d.x == 0)
{
argument = pi / 2 * Math.Sign((sbyte)d.y);
}
else
{
if (d.y == 0)
{
argument = pi * Math.Sign((sbyte)-1 + Math.Sign((sbyte)d.x));
}
else
{
argument = Math.Atan(d.y / d.x) + Math.Sign((sbyte)Math.Abs(d.x) - d.x) * Math.Sign((sbyte)d.y) * pi;
}
}
//return argument;
//cout+d.x+" "+d.y+" аргумент в доли: "+argument/pi+endl;
if ((-pi <= argument) && (argument < -2 * pi / 3))
{
return(-1.0 / 2);
}
if ((-2 * pi / 3 <= argument) && (argument <= -pi / 3))
{
return(0); //return 1; //единицы будут
}
if ((-pi / 3 < argument) && (argument <= pi / 2))
{
return(1.0 / 2); //return 1; //уже не будут
}
/*if ((pi / 2 < argument) && (argument <= pi))*/
return(-1.0 / 2);
}
public void DrawCurves()
{
SequenceFunc t = (double x, int kk) => Math.Log(0.01 + (x + 1 - 0.1 * kk).Sqr());//1.0/(1.0+kk*x*x);//FuncMethods.Monoms;
RealFunc[] f = new RealFunc[] { (double x) => Math.Exp(x / (x.Abs() + 1)), (double x) => Math.Sin(x + 2) * Math.Cos(2 * x), (double x) => x.Abs() * Math.Exp(Math.Cos(x)), (double x) => Math.Log(1 + x.Abs()) * Math.Sinh(x / 2), (double x) => Math.Sin(x) - 8.0 / (2 * x + 6), (double x) => x.Abs() + Math.Log(0.01 + x * x) };
Point[] b = new Point[] { new Point(0, 5), new Point(-4, 4), new Point(-2, 4), new Point(-2, 2), new Point(-1, 1), new Point(-1, 1) };
int k = 64;
int[] mas = new int[k];
for (int i = 0; i < k; i++)
{
mas[i] = i + 1;
}
Parallel.For(0, f.Length, (int i) =>
{
var c = FuncMethods.UltraVsNormal(f[i], t, SequenceFuncKind.Other, k, b[i].x, b[i].y);
StreamWriter fs = new StreamWriter($"Monoms {i + 1}.txt");
fs.WriteLine($"count normal ultra");
for (int j = 0; j < k; j++)
{
fs.WriteLine($"{mas[j]} {c.Item1[j]} {c.Item2[j]}");
}
fs.Close();
});
//k = 75;
//mas = new int[k];
//for (int i = 0; i < k; i++)
// mas[i] = i + 1;
//Parallel.For(0, f.Length, (int i) =>
//{
// t = FuncMethods.TrigSystem(b[i].x, b[i].y);
// var c = FuncMethods.UltraVsNormal(f[i], t, SequenceFuncKind.Orthogonal, k, b[i].x, b[i].y);
// StreamWriter fs = new StreamWriter($"Trig {i + 1}.txt");
// fs.WriteLine($"count normal ultra");
// for (int j = 0; j < k; j++)
// fs.WriteLine($"{mas[j]} {c.Item1[j]} {c.Item2[j]}");
// fs.Close();
//});
}
private void MakeArrow(Point beg, Point Normal, Color col, DCircle circle)
{
chart1.Series.Add(counter++.ToString());
chart1.Series.Last().IsVisibleInLegend = false;
chart1.Series.Last().ChartType = System.Windows.Forms.DataVisualization.Charting.SeriesChartType.FastLine;
chart1.Series.Last().BorderWidth = 2;
chart1.Series.Last().Color = col;
double r = Normal.Abs, s = r / 4;
double cor = Math.Acos((Normal.x) / r) * Math.Sign(Normal.y);
Point p1 = new Point(s * Math.Cos(-Math.PI - corner), s * Math.Sin(-Math.PI - corner)).Turn(Point.Zero, cor);
Point p2 = new Point(s * Math.Cos(-Math.PI + corner), s * Math.Sin(-Math.PI + corner)).Turn(Point.Zero, cor);
chart1.Series.Last().Points.AddXY(beg.x, beg.y);
chart1.Series.Last().Points.AddXY(beg.x + Normal.x, beg.y + Normal.y);
chart1.Series.Last().Points.AddXY(beg.x + Normal.x + p1.x, beg.y + Normal.y + p1.y);
chart1.Series.Last().Points.AddXY(beg.x + Normal.x, beg.y + Normal.y);
chart1.Series.Last().Points.AddXY(beg.x + Normal.x + p2.x, beg.y + Normal.y + p2.y);
}
public void Test()
{
Read();
double res = 0;
Criterion K = Criterion.StepCount;
if (radioButton19.Checked)
{
K = Criterion.Accuracy;
}
if (radioButton20.Checked)
{
K = Criterion.SegmentCount;
}
for (C = 0; (int)C <= 2; C++)
{
res = DefIntegral(f, a, b, C, K, count, eps, seq);
Program.PER.listView1.Items[(int)C].SubItems[1].Text = res.ToString();
}
C += 2;
res = DefIntegral(f, a, b, (Method)3, K, nn, eps, seq);
Program.PER.listView1.Items[(int)C].SubItems[1].Text = res.ToString();
C++;
res = DefIntegral(f, a, b, (Method)4, K, nn, eps, seq);
Program.PER.listView1.Items[(int)C].SubItems[1].Text = res.ToString();
C++;
res = DefIntegral(f, a, b, (Method)5, K, nn, eps, seq);
Program.PER.listView1.Items[(int)C].SubItems[1].Text = res.ToString();
for (MonteKarloEnum KK = 0; (int)KK < 2; KK++)
{
МатКлассы.Point p = new МатКлассы.Point(a, b);
MultiFunc F = (double[] t) => f(t[0]);
h_Count = count;
n = count;
EPS = Double.NaN;
res = MonteKarlo(F, KK, p);
Program.PER.listView1.Items[(int)KK + 3].SubItems[1].Text = res.ToString();
}
}
public MostSimpleGrafic(Func <double, double> f, Point[] mas, string name, bool parallel = true)
{
InitializeComponent();
chart1.Series[0].IsVisibleInLegend = false;
chart1.Series.Add(name);
chart1.Series[1].BorderWidth = 3;
chart1.Series[1].ChartType = System.Windows.Forms.DataVisualization.Charting.SeriesChartType.Line;
Point[] p = new Point[mas.Length];
Parallel.For(0, p.Length, (int i) => p[i] = new Point(mas[i].x, f(mas[i].x)));
for (int i = 0; i < p.Length; i++)
{
chart1.Series[0].Points.AddXY(mas[i].x, mas[i].y);
chart1.Series[1].Points.AddXY(p[i].x, p[i].y);
}
Библиотека_графики.ForChart.SetToolTips(ref chart1);
}
public void DrawCurves2()
{
SequenceFunc t = (double x, int k) => Math.Exp(k * x);//FuncMethods.Monoms;
int[] count = new int[] { 9, 16, 34 };
RealFunc[] f = new RealFunc[count.Length];
Point[] b = new Point[] { new Point(-1, 5), new Point(-4, 4), new Point(-2, 4), new Point(-2, 2), new Point(-1, 1), new Point(-1, 1) };
RealFunc f1 = (double x) => Math.Cos(2 * x) * (Math.Exp((x / 3).Abs()) - 4 * Math.Log(1 + x.Abs()));//Math.Sin(5 * x) / Math.Exp(x.Abs() / 3);
RealFunc fl;
Parallel.For(0, f.Length, (int i) =>
{
f[i] = FuncMethods.Approx(f1, t, SequenceFuncKind.Other, count[i], b[0].x, b[0].y, true);
});
fl = FuncMethods.Approx(f1, t, SequenceFuncKind.Other, count[count.Length - 1], b[0].x, b[0].y);
int c = 280;
double h = (b[0].y - b[0].x) / (c - 1);
StreamWriter fs = new StreamWriter($"Monoms vs.txt");
//fs.WriteLine($"count normal ultra");
for (int j = 0; j < c; j++)
{
double arg = b[0].x + j * h;
fs.Write($"{arg} {f1(arg)} {fl(arg)}");
for (int i = 0; i < count.Length; i++)
{
fs.Write($" {f[i](arg)}");
}
fs.WriteLine();
}
fs.Close();
}
private void RandArrows(DCircle circle, int count = 100)
{
if (count == 0)
{
return;
}
chart1.Series.Add(counter++.ToString());
chart1.Series.Last().IsVisibleInLegend = false;
chart1.Series.Last().ChartType = System.Windows.Forms.DataVisualization.Charting.SeriesChartType.Point;
chart1.Series.Last().MarkerStyle = System.Windows.Forms.DataVisualization.Charting.MarkerStyle.Star5;
chart1.Series.Last().MarkerSize = 8;
chart1.Series.Last().BorderWidth = 8;
chart1.Series.Last().Color = Color.Green;
int n = chart1.Series.Count - 1;
double cof = GetWindowsCoef();
int c = 0;
Random r = new Random();
double x, y, q = circle.Radius * cof;
Point f, p;
while (c < count)
{
x = -q + r.NextDouble() * q * 2 + circle.Center.x;
y = -q + r.NextDouble() * q * 2 + circle.Center.y;
p = new Point(x, y);
if (!circle.ContainPoint(p, 1.05))
{
chart1.Series[n].Points.AddXY(x, y);
f = circle.GetNormal(p, 0.1 * q);
MakeArrow(new Point(p.x - f.x, p.y - f.y), f, Color.Blue, circle);
c++;
}
}
}
public static double g5(Point point) => masPoints[0].PotentialF(point);
public static double g4(Point point) => CONSTANT;
public static double g3(Point point) => 3 * point.x + 6 * point.y + Math.Sqrt(point.x.Sqr() + point.y.Sqr()) + 0.5 * point.y.Sqr();
public static double g10(Point p) => Math.Exp(p.x) * (Math.Cos(p.y) + 3 * Math.Sin(p.y));
private void button1_Click(object sender, EventArgs e)
{
for (int i = 0; i < 9; i++)
{
Program.FORM.chart1.Series[i].Points.Clear();
}
for (int i = 0; i < chart1.Series.Count; i++)
{
chart1.Series[i].IsVisibleInLegend = false;
}
for (int i = 9; i < Program.FORM.chart1.Series.Count; i++)
{
Program.FORM.chart1.Series.RemoveAt(i); i--;
}
Func <double, double> f = Math.Sin;
FuncMethods.NetFunc net = new FuncMethods.NetFunc();
Func <double, double> g1, g2, g3, g4, g5, g6, g7;
//SequenceFunc Monom, Leg, Cheb, Lager, Her, Trig, Har;
g1 = g2 = g3 = g4 = g5 = g6 = g7 = null;
//определить действительную функцию
if (radioButton5.Checked)
{
f = (double x) => (Math.Cos(x) - 1);
}
if (radioButton6.Checked)
{
f = (double x) => (Math.Abs(x - 1));
}
if (radioButton7.Checked)
{
f = (double x) => (Math.Exp(x - x * x));
}
if (radioButton8.Checked)
{
f = (double x) => (Math.Exp(x) / (Math.Abs(x) + 1));
}
if (radioButton9.Checked)
{
f = (double x) => (x * Math.Sin(x) / (Math.Abs(x) + 2));
}
if (radioButton10.Checked)
{
f = (double x) => (x / (1 + x * x));
}
if (radioButton11.Checked)
{
f = (double x) => (x * Math.Cos(x));
}
if (radioButton12.Checked)
{
f = (double x) => (Math.Log(1 + Math.Abs(x)));
}
if (radioButton13.Checked)
{
f = (double x) => (x * x * x + x - 4);
}
if (radioButton14.Checked)
{
f = (double x) => (3);
}
if (radioButton15.Checked)
{
f = (double x) => (2 * x - Math.Exp(-x));
}
if (radioButton16.Checked)
{
string s = textBox7.Text;
try
{
f = Parser.GetDelegate(s);
textBox7.Text = Parser.FORMULA;
}
catch
{
f = (double x) => 0;
}
}
chart1.Series[0].IsVisibleInLegend = true;
FileStream fs = new FileStream("Данные об аппроксимации.txt", FileMode.Create);
TextWriter tmp = Console.Out;
StreamWriter sw = new StreamWriter(fs);
Console.SetOut(sw);
const string message = "Все доступные поля должны быть заполнены действительными числами. Число шагов и число отрезков - натуральными числами. При записи действительных чисел используются запятые, а не точки. Количество заверенных точек должно быть не больше количества действительно заданных точек.";
const string caption = "Неверные входные данные!";
try
{
int n1 = Convert.ToInt32(numericUpDown1.Value), n2 = Convert.ToInt32(numericUpDown2.Value);
double[,] MAS = new double[chart1.Series.Count, n2 + 1];
//определить сеточную функцию
if (!radioButton1.Checked)
{
double a = Convert.ToDouble(textBox1.Text), b = Convert.ToDouble(textBox2.Text);
int n = Convert.ToInt16(textBox6.Text), ccount = Convert.ToInt32(numericUpDown3.Value);
double h = (b - a) / (ccount - 1);
Point[] mas1, mas2, mas3 = new Point[ccount];
for (int i = 0; i < ccount; i++)
{
mas3[i] = new Point(a + i * h, f(a + i * h));
}
//чтение набора узлов
int m = Convert.ToInt32(textBox4.Text);
mas2 = new МатКлассы.Point[m];
string s;
string[] st;
for (int k = 0; k < m; k++)
{
s = textBox5.Lines[k];
st = s.Split(' ');//в аргументах указывается массив символов, которым разделяются числа
mas2[k] = new МатКлассы.Point(Convert.ToDouble(st[0]), Convert.ToDouble(st[1]));
}
//чтение массива абцисс
s = textBox3.Lines[0];
st = s.Split(' ');//в аргументах указывается массив символов, которым разделяются числа;
m = st.Length;
mas1 = new МатКлассы.Point[m];
for (int k = 0; k < m; k++)
{
double v = Convert.ToDouble(st[k]);
mas1[k] = new МатКлассы.Point(v, f(v));
}
if (radioButton2.Checked)
{
net = new FuncMethods.NetFunc(mas1);
}
else
{
net = new FuncMethods.NetFunc(mas2);
}
if (checkBox10.Checked)
{
net = new FuncMethods.NetFunc(mas3);
}
a = net.MinArg;
b = net.MaxArg;
if (checkBox9.Checked)
{
for (n = n1; n <= n2; n++)
{
Matrix O = new Matrix(MAS);
O.PrintMatrix(); "".Show();
if (checkBox1.Checked)
{
SequenceFunc t = FuncMethods.Monoms;
Func <double, double> g = FuncMethods.Approx(net, t, SequenceFuncKind.Other, n);
if (radioButton2.Checked)
{
MAS[1, n] = FuncMethods.RealFuncMethods.NormDistance(f, g, a, b);
}
else
{
MAS[1, n] = FuncMethods.NetFunc.Distance(net, g);
}
chart1.Series[1].Points.AddXY(n, Math.Log10(MAS[1, n])); chart1.Series[1].IsVisibleInLegend = true;
}
if (checkBox2.Checked)
{
SequenceFunc t = FuncMethods.Lezhandrs(a, b);
Func <double, double> g = FuncMethods.Approx(net, t, SequenceFuncKind.Orthogonal, n);
if (radioButton2.Checked)
{
MAS[2, n] = FuncMethods.RealFuncMethods.NormDistance(f, g, a, b);
}
else
{
MAS[2, n] = FuncMethods.NetFunc.Distance(net, g);
}
chart1.Series[2].Points.AddXY(n, Math.Log10(MAS[2, n])); chart1.Series[2].IsVisibleInLegend = true;
}
if (checkBox6.Checked)
{
SequenceFunc t = FuncMethods.TrigSystem(a, b);
Func <double, double> g = FuncMethods.Approx(net, t, SequenceFuncKind.Orthonormal, n);
if (radioButton2.Checked)
{
MAS[6, n] = FuncMethods.RealFuncMethods.NormDistance(f, g, a, b);
}
else
{
MAS[6, n] = FuncMethods.NetFunc.Distance(net, g);
}
chart1.Series[6].Points.AddXY(n, Math.Log10(MAS[6, n])); chart1.Series[6].IsVisibleInLegend = true;
}
if (checkBox7.Checked)
{
SequenceFunc t = FuncMethods.HaarSystem(a, b);
Func <double, double> g = FuncMethods.Approx(net, t, SequenceFuncKind.Orthogonal, n);
if (radioButton2.Checked)
{
MAS[7, n] = FuncMethods.RealFuncMethods.NormDistance(f, g, a, b);
}
else
{
MAS[7, n] = FuncMethods.NetFunc.Distance(net, g);
}
chart1.Series[7].Points.AddXY(n, Math.Log10(MAS[7, n])); chart1.Series[7].IsVisibleInLegend = true;
}
if (checkBox8.Checked)
{
SequenceFunc t = (double x, int k) => Math.Exp(k * x);
Func <double, double> g = FuncMethods.Approx(net, t, SequenceFuncKind.Other, n);
if (radioButton2.Checked)
{
MAS[8, n] = FuncMethods.RealFuncMethods.NormDistance(f, g, a, b);
}
else
{
MAS[8, n] = FuncMethods.NetFunc.Distance(net, g);
}
chart1.Series[8].Points.AddXY(n, Math.Log10(MAS[8, n])); chart1.Series[8].IsVisibleInLegend = true;
}
}
}
else//если рисуется не график зависимости от числа функций
{
if (radioButton2.Checked)
{
net = new FuncMethods.NetFunc(mas1); Draw_mas(mas1, Color.Blue);
}
else
{
net = new FuncMethods.NetFunc(mas2); Draw_mas(mas2, Color.Blue);
}
if (checkBox10.Checked)
{
net = new FuncMethods.NetFunc(mas3); Draw_mas(mas3, Color.Blue);
}
a = net.MinArg;
b = net.MaxArg;
//ShowPoints(net);//показать точки на графике
if (checkBox1.Checked)
{
SequenceFunc t = FuncMethods.Monoms;
//SequencePol t = FuncMethods.Monom;
Func <double, double> g = FuncMethods.Approx(net, t, SequenceFuncKind.Other, n);
chart1.Series[1].Points.DataBindXY(МатКлассы.Point.PointsX(g, 100, a, b), МатКлассы.Point.PointsY(g, 100, a, b)); chart1.Series[1].IsVisibleInLegend = true;
Console.WriteLine("--------Для системы мономов---------");
if (radioButton2.Checked)
{
FuncMethods.ShowApprox(f, net.Arguments, t, SequenceFuncKind.Other, n);
}
else
{
FuncMethods.ShowApprox(net, t, SequenceFuncKind.Other, n);
}
}
//Наименьшие перпендикуляры
if (n == 2)
{
double a0 = 0, a1 = 0;
double dist = 0, distold = 0;;
SLAU S = new SLAU(2);
for (int i = 0; i < net.CountKnots; i++)
{
S.A[0, 0] += net.Arg(i);
S.A[1, 0] += net.Arg(i) * net[i];
S.A[1, 1] += net[i];
S.b[1] -= net[i] * net[i];
}
S.A[0, 1] = net.CountKnots;
S.b[0] = -S.A[1, 1];
//S.Show();
S.GaussSelection();
a1 = S.x[0]; a0 = S.x[1];
Func <double, double> pol = new Polynom(new double[] { -a0, -a1 }).Value;
SLAU T = new SLAU(FuncMethods.Monoms, net, n);
T.Gauss();//T.Show();
for (int i = 0; i < net.CountKnots; i++)
{
dist += Math.Pow(a1 * net.Arg(i) + net[i] + a0, 2);
distold += Math.Pow(T.x[1] * net.Arg(i) + net[i] + T.x[0], 2);
}
dist /= net.CountKnots;
distold /= net.CountKnots;
dist = Math.Sqrt(dist);
distold = Math.Sqrt(distold);
Console.WriteLine("\t(в среднеквадратичной норме перпендикуляров) равна {0}", distold);
Program.FORM.chart1.Series.Add("Прямая с наилучшими перпендикулярами");
int count = Program.FORM.chart1.Series.Count - 1;
Program.FORM.chart1.Series[count].Color = Color.Black;
Program.FORM.chart1.Series[count].ChartType = System.Windows.Forms.DataVisualization.Charting.SeriesChartType.Line;
//Program.FORM.chart1.Series[count].IsVisibleInLegend = false;
Program.FORM.chart1.Series[count].BorderWidth = 2;
chart1.Series[count].Points.DataBindXY(МатКлассы.Point.PointsX(pol, 100, a, b), МатКлассы.Point.PointsY(pol, 100, a, b));
Console.WriteLine("--------Для наименьших перпендикуляров---------");
Console.WriteLine("Аппроксимация сеточной функции полученной функцией");
Console.WriteLine("\t(в дискретной среднеквадратичной норме) равна {0}", FuncMethods.NetFunc.Distance(net, pol));
Console.WriteLine("\t(в среднеквадратичной норме перпендикуляров) равна {0}", dist);
}
if (checkBox2.Checked)
{
SequenceFunc t = FuncMethods.Lezhandrs(a, b);
//SequencePol t = FuncMethods.Lezhandr(a, b);
Func <double, double> g = FuncMethods.Approx(net, t, SequenceFuncKind.Orthogonal, n);
chart1.Series[2].Points.DataBindXY(МатКлассы.Point.PointsX(g, 100, a, b), МатКлассы.Point.PointsY(g, 100, a, b)); chart1.Series[2].IsVisibleInLegend = true;
Console.WriteLine("--------Для системы полиномов Лежандра---------");
if (radioButton2.Checked)
{
FuncMethods.ShowApprox(f, net.Arguments, t, SequenceFuncKind.Orthogonal, n);
}
else
{
FuncMethods.ShowApprox(net, t, SequenceFuncKind.Orthogonal, n);
}
}
if (checkBox6.Checked)
{
SequenceFunc t = FuncMethods.TrigSystem(a, b);
Func <double, double> g = FuncMethods.Approx(net, t, SequenceFuncKind.Orthonormal, n);
chart1.Series[6].Points.DataBindXY(МатКлассы.Point.PointsX(g, 100, a, b), МатКлассы.Point.PointsY(g, 100, a, b)); chart1.Series[6].IsVisibleInLegend = true;
Console.WriteLine("--------Для ортонормированной системы тригонометрических полиномов---------");
if (radioButton2.Checked)
{
FuncMethods.ShowApprox(f, net.Arguments, t, SequenceFuncKind.Orthonormal, n);
}
else
{
FuncMethods.ShowApprox(net, t, SequenceFuncKind.Orthonormal, n);
}
}
if (checkBox7.Checked)
{
SequenceFunc t = FuncMethods.HaarSystem(a, b);
Func <double, double> g = FuncMethods.Approx(net, t, SequenceFuncKind.Orthogonal, n);
chart1.Series[7].Points.DataBindXY(МатКлассы.Point.PointsX(g, 100, a, b), МатКлассы.Point.PointsY(g, 100, a, b)); chart1.Series[7].IsVisibleInLegend = true;
Console.WriteLine("--------Для системы Хаара---------");
if (radioButton2.Checked)
{
FuncMethods.ShowApprox(f, net.Arguments, t, SequenceFuncKind.Orthogonal, n);
}
else
{
FuncMethods.ShowApprox(net, t, SequenceFuncKind.Orthogonal, n);
}
}
if (checkBox8.Checked)
{
SequenceFunc t = (double x, int k) => Math.Exp(k * x);
Func <double, double> g = FuncMethods.Approx(net, t, SequenceFuncKind.Other, n);
chart1.Series[8].Points.DataBindXY(МатКлассы.Point.PointsX(g, 100, a, b), МатКлассы.Point.PointsY(g, 100, a, b)); chart1.Series[8].IsVisibleInLegend = true;
Console.WriteLine("--------Для системы экспонент---------");
if (radioButton2.Checked)
{
FuncMethods.ShowApprox(f, net.Arguments, t, SequenceFuncKind.Other, n);
}
else
{
FuncMethods.ShowApprox(net, t, SequenceFuncKind.Other, n);
}
}
}
}
else
{
double a = Convert.ToDouble(textBox1.Text), b = Convert.ToDouble(textBox2.Text);
int n = Convert.ToInt16(textBox6.Text);
if (checkBox9.Checked)
{
chart1.Series[0].Name = "Функция по системе Хаара, выраженная без учёта ортогональности этой системы";
chart1.Series[0].IsVisibleInLegend = true;
for (n = n1; n <= n2; n++)
{
if (checkBox1.Checked)
{
//SequenceFunc t = FuncMethods.Monoms;
SequencePol t = FuncMethods.Monom;
Func <double, double> g = FuncMethods.Approx(f, t, SequenceFuncKind.Other, n, a, b);
MAS[1, n] = FuncMethods.RealFuncMethods.NormDistance(f, g, a, b);
chart1.Series[1].Points.AddXY(n, Math.Log10(MAS[1, n])); chart1.Series[1].IsVisibleInLegend = true;
chart1.Series[1].Name = "Мономы с применением ультра-гибрида";
//g = FuncMethods.Approx(f, t, SequenceFuncKind.Other, n, a, b, false);
//MAS[0, n] = FuncMethods.RealFuncMethods.NormDistance(f, g, a, b);
//chart1.Series[0].Points.AddXY(n, Math.Log10(MAS[0, n]));
//chart1.Series[0].IsVisibleInLegend = true;
}
if (checkBox2.Checked)
{
//SequenceFunc t = FuncMethods.Lezhandrs(a,b);
SequencePol t = FuncMethods.Lezhandr(a, b);
Polynom s = new Polynom(new double[] { -2 * a / (b - a) - 1, 2.0 / (b - a) });
Func <double, double>[] MyMas = new Func <double, double> [n];
for (int i = 0; i < n; i++)
{
MyMas[i] = /*Polynom.Lezh(i).Value;*/ Polynom.Lezh(i).Value(s).Value;
}
//Func<double,double> g = FuncMethods.ApproxForLezhandr(f, MyMas, a, b);
Func <double, double> g = FuncMethods.Approx(f, t, SequenceFuncKind.Orthogonal, n, a, b);
MAS[2, n] = FuncMethods.RealFuncMethods.NormDistance(f, g, a, b);
chart1.Series[2].Points.AddXY(n, Math.Log10(MAS[2, n])); chart1.Series[2].IsVisibleInLegend = true;
}
if (checkBox6.Checked)
{
SequenceFunc t = FuncMethods.TrigSystem(a, b);
Func <double, double> g = FuncMethods.Approx(f, t, SequenceFuncKind.Orthonormal, n, a, b);
MAS[6, n] = FuncMethods.RealFuncMethods.NormDistance(f, g, a, b);
chart1.Series[6].Points.AddXY(n, Math.Log10(MAS[6, n])); chart1.Series[6].IsVisibleInLegend = true;
chart1.Series[6].Name = "Тригонометрическая система с применением ультра-гибрида";
//g = FuncMethods.Approx(f, t, SequenceFuncKind.Orthonormal, n, a, b, false);
//MAS[0, n] = FuncMethods.RealFuncMethods.NormDistance(f, g, a, b);
//chart1.Series[0].Points.AddXY(n, Math.Log10(MAS[0, n]));
//chart1.Series[0].IsVisibleInLegend = true;
}
if (checkBox7.Checked)
{
SequenceFunc t = FuncMethods.HaarSystem(a, b);
Func <double, double> g = FuncMethods.Approx(f, t, SequenceFuncKind.Orthogonal, n, a, b);
MAS[7, n] = FuncMethods.RealFuncMethods.NormDistance(f, g, a, b);
chart1.Series[7].Points.AddXY(n, Math.Log10(MAS[7, n])); chart1.Series[7].IsVisibleInLegend = true;
chart1.Series[7].Name = "Система Хаара как ортогональная система";
//g = FuncMethods.Approx(f, t, SequenceFuncKind.Other, n, a, b, false);
//MAS[0, n] = FuncMethods.RealFuncMethods.NormDistance(f, g, a, b);
//chart1.Series[0].Points.AddXY(n, Math.Log10(MAS[0, n]));
//chart1.Series[0].IsVisibleInLegend = true;
}
if (checkBox8.Checked)
{
SequenceFunc t = (double x, int k) => Math.Exp(k * x);
Func <double, double> g = FuncMethods.Approx(f, t, SequenceFuncKind.Other, n, a, b);
MAS[8, n] = FuncMethods.RealFuncMethods.NormDistance(f, g, a, b);
chart1.Series[8].Points.AddXY(n, Math.Log10(MAS[8, n])); chart1.Series[8].IsVisibleInLegend = true;
chart1.Series[8].Name = "Экспоненты с применением ультра-гибрида";
//g = FuncMethods.Approx(f, t, SequenceFuncKind.Other, n, a, b, false);
//MAS[0, n] = FuncMethods.RealFuncMethods.NormDistance(f, g, a, b);
//chart1.Series[0].Points.AddXY(n, Math.Log10(MAS[0, n]));
//chart1.Series[0].IsVisibleInLegend = true;
}
}
Analys(MAS, n1, n2);
}
else
{
chart1.Series[0].Points.DataBindXY(МатКлассы.Point.PointsX(f, 100, a, b), МатКлассы.Point.PointsY(f, 100, a, b));
if (checkBox1.Checked)
{
//SequenceFunc t = FuncMethods.Monoms;
SequencePol t = FuncMethods.Monom;
Func <double, double> g = FuncMethods.Approx(f, t, SequenceFuncKind.Other, n, a, b);
chart1.Series[1].Points.DataBindXY(МатКлассы.Point.PointsX(g, 100, a, b), МатКлассы.Point.PointsY(g, 100, a, b)); chart1.Series[1].IsVisibleInLegend = true;
Console.WriteLine("--------Для системы мономов---------");
FuncMethods.ShowApprox(f, t, SequenceFuncKind.Other, n, a, b);
}
if (checkBox2.Checked)
{
//SequenceFunc t = FuncMethods.Lezhandrs(a,b);
SequencePol t = FuncMethods.Lezhandr(a, b);
Polynom s = new Polynom(new double[] { -2 * a / (b - a) - 1, 2.0 / (b - a) });
Func <double, double>[] MyMas = new Func <double, double> [n];
for (int i = 0; i < n; i++)
{
MyMas[i] = /*Polynom.Lezh(i).Value;*/ Polynom.Lezh(i).Value(s).Value;
}
Func <double, double> g = FuncMethods.ApproxForLezhandr(f, MyMas, a, b);
chart1.Series[2].Points.DataBindXY(МатКлассы.Point.PointsX(g, 100, a, b), МатКлассы.Point.PointsY(g, 100, a, b)); chart1.Series[2].IsVisibleInLegend = true;
Console.WriteLine("--------Для системы полиномов Лежандра---------");
FuncMethods.ShowApprox(f, t, SequenceFuncKind.Orthogonal, n, a, b);
}
if (checkBox3.Checked)
{
//SequencePol t = FuncMethods.Cheb(a,b);
SequenceFunc t = FuncMethods.Chebs(a, b);
Func <double, double> g = FuncMethods.Approx(f, t, SequenceFuncKind.Other, n, a, b);
chart1.Series[3].Points.DataBindXY(МатКлассы.Point.PointsX(g, 100, a, b), МатКлассы.Point.PointsY(g, 100, a, b)); chart1.Series[3].IsVisibleInLegend = true;
}
if (checkBox4.Checked)
{
SequenceFunc t = FuncMethods.Lagerrs(a, b);
Func <double, double> g = FuncMethods.Approx(f, t, SequenceFuncKind.Other, n, a, b);
chart1.Series[4].Points.DataBindXY(МатКлассы.Point.PointsX(g, 100, a, b), МатКлассы.Point.PointsY(g, 100, a, b)); chart1.Series[4].IsVisibleInLegend = true;
}
if (checkBox5.Checked)
{
SequenceFunc t = FuncMethods.Hermits(a, b);
Func <double, double> g = FuncMethods.Approx(f, t, SequenceFuncKind.Other, n, a, b);
chart1.Series[5].Points.DataBindXY(МатКлассы.Point.PointsX(g, 100, a, b), МатКлассы.Point.PointsY(g, 100, a, b)); chart1.Series[5].IsVisibleInLegend = true;
}
if (checkBox6.Checked)
{
SequenceFunc t = FuncMethods.TrigSystem(a, b);
Func <double, double> g = FuncMethods.Approx(f, t, SequenceFuncKind.Orthonormal, n, a, b);
chart1.Series[6].Points.DataBindXY(МатКлассы.Point.PointsX(g, 100, a, b), МатКлассы.Point.PointsY(g, 100, a, b)); chart1.Series[6].IsVisibleInLegend = true;
Console.WriteLine("--------Для ортонормированной системы тригонометрических полиномов---------");
FuncMethods.ShowApprox(f, t, SequenceFuncKind.Orthonormal, n, a, b);
}
if (checkBox7.Checked)
{
SequenceFunc t = FuncMethods.HaarSystem(a, b);
Func <double, double> g = FuncMethods.Approx(f, t, SequenceFuncKind.Orthogonal, n, a, b);
chart1.Series[7].Points.DataBindXY(МатКлассы.Point.PointsX(g, 100, a, b), МатКлассы.Point.PointsY(g, 100, a, b)); chart1.Series[7].IsVisibleInLegend = true;
Console.WriteLine("--------Для системы Хаара---------");
FuncMethods.ShowApprox(f, t, SequenceFuncKind.Orthogonal, n, a, b);
}
if (checkBox8.Checked)
{
SequenceFunc t = (double x, int k) => Math.Exp(k * x);
Func <double, double> g = FuncMethods.Approx(f, t, SequenceFuncKind.Other, n, a, b);
chart1.Series[8].Points.DataBindXY(МатКлассы.Point.PointsX(g, 100, a, b), МатКлассы.Point.PointsY(g, 100, a, b)); chart1.Series[8].IsVisibleInLegend = true;
Console.WriteLine("--------Для системы экспонент---------");
FuncMethods.ShowApprox(f, t, SequenceFuncKind.Other, n, a, b);
}
}
}
}
catch
{
var MBSave = MessageBox.Show(message, caption, MessageBoxButtons.OK, MessageBoxIcon.Error);
return;
}
finally
{
sw.Close();
Console.SetOut(tmp);
Console.WriteLine("Запись завершена!");
Program.DATA.textBox1.Text = "";
StreamReader sr = new StreamReader("Данные об аппроксимации.txt");
string ss = "";
while (ss != null)
{
Program.DATA.textBox1.Text += ss + Environment.NewLine;
ss = sr.ReadLine();
}
sr.Close();
}
}
public static double g6(Point point) => point.x * point.x - point.y * point.y;
public static double g7(Point point) => g1(point) * Math.Exp(point.x - point.y);
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();
}
public static double g9(Point point) => g8(point) + g3(point);
private async void button2_Click(object sender, EventArgs e)
{
DateTime time = DateTime.Now;
//Func<double,double> f = t => Math.Sin(t*9) / Math.Exp(t * t / 3) * Math.Sign(Math.Max(0, (2*Math.PI- t.Abs())));
Func <double, double> f = t => Math.Cos(t * 9) * t / Math.Exp(t * t / 3) * Math.Sign(Math.Max(0, (Math.PI / 2 - t.Abs())));
//Func<double,double> f = t => Math.Sin(20*Math.PI*t)* Math.Sign(Math.Max(0, (1 - t.Abs())));
Func <double, double, Complex>[] f1 = new Func <double, double, Complex> [7];
Func <double, double>[] f2 = new Func <double, double> [7];
Wavelet[] w = new Wavelet[7];
//await Task.Run(() =>
//{
// for (int i = 0; i < 7; i++)
// {
// w[i] = new Wavelet((Wavelet.Wavelets)i);
// f1[i] = w[i].GetAnalys(f);
// f2[i] = w[i].GetSyntesis(f1[i]);
// }
//}
//);
w[3] = new Wavelet((Wavelet.Wavelets) 3);
f1[3] = w[3].GetAnalys(f);
f2[3] = w[3].GetSyntesis(/*f1[3]*/);
//Wavelet w = new Wavelet();
//var f1 = w.GetAnalys(f);
//var f2 = w.GetSyntesis(f1);
//ИнтеграцияСДругимиПрограммами.CreatTableInExcel((double a, double b) => f1[3](a, b).Re, 0.01, 5, 100, 0.01, 7, 100);
var p = OptimizationDCompFunc.GetMaxOnRectangle((double a, double b) => f1[3](a, b).Abs, 0.01, 5, 0.01, 10, eps: 1e-14, ogr: 5, nodescount: 15);
new nzy3d_winformsDemo.Form1("", 0.01, 5, 70, 0.01, 10, 70, (double a, double b) => f1[3](a, b).Abs).Show();
// ИнтеграцияСДругимиПрограммами.CreatTableInExcel(f1[3], 0.01, 3, 100, 0.01, 3, 100);
//ИнтеграцияСДругимиПрограммами.CreatTableInExcel(w[3].Dic,"Test Page",Number.Complex.ComplMode.Abs);
//c1Chart3D1.ChartGroups.Group0.ChartType = Chart3DTypeEnum.Surface;
//double[,] z = new double[100, 100];
//for (int s = 0; s < 31; s++)
// for (int n = 0; n < 21; n++)
// {
// z[s, n] = f1[3](0.01 + 0.01 * s, 0.01 + 0.01 * n).Re;
// }
// create dataset and put it to the chart
//Chart3DDataSetGrid gridset = new Chart3DDataSetGrid(0, 0, 1, 1, z);
//c1Chart3D1.ChartGroups[0].ChartData.Set = gridset;
//var o = w[3].Dic;
//МатКлассы.Point[] u = o.Keys.ToArray();
//var c = o.Values.ToArray();
//Chart3DPoint[] points1 = new Chart3DPoint[o.Count];
//for (int i = 0; i < o.Count; i++)
// points1[i] = new Chart3DPoint(u[i].x, u[i].y, 7/*(double)c[i].Value*/);
//Chart3DDataSetPoint pointset = new Chart3DDataSetPoint();
//pointset.AddSeries(points1);
//c1Chart3D1.ChartGroups[0].ChartData.Set = pointset;
List <double> tm = new List <double>(), m = new List <double>();
for (double i = beg; i < end; i += step)
{
double tmp0 = f(i);//,tmp2=f2(i);$"f = {tmp0} \tWf-1 = {tmp2} \teps = {(tmp2-tmp0)} \t f/f0 = {tmp0/tmp2}".Show();
double[] mas = new double[7];
await Task.Run(() =>
{
//for (int j = 0; j < 7; j++)
// mas[j] = f2[j](i);
mas[3] = f2[3](i);
});
(new Vectors(mas) - tmp0).Show();
chart1.Series[0].Points.AddXY(i, tmp0);
for (int j = 0; j < 7; j++)
{
chart1.Series[j + 1].Points.AddXY(i, mas[j]);
}
progressBar1.Value = (int)((i - beg) / (end - beg) * 100);
m.Add(mas[3]);
tm.Add(tmp0);
}
label1.Text = "Время работы (минуты полторы ушло на Excel): " + (DateTime.Now - time).ToString();
label2.Text = "Точность в евклидовой норме: " + (new Vectors(m.ToArray()) - new Vectors(tm.ToArray())).Sort.EuqlidNorm.ToString();
var s = new МатКлассы.Point(p.Item1, p.Item2);
label3.Text = "Точка максимума: " + s.ToString();
label4.Text = "Максимальное по модулю значение: " + f1[3](p.Item1, p.Item2).ToString();
}
public static double g11(Point p) => g1(p) + g2(p) + g3(p) + g4(p) + g4(p);
public static double g1(Point point) => point.x + point.y;
private Tuple <Point, Point> GetSourceRect() => Point.GetBigRect(sourcesArray.Select(s => s.Center).ToArray());
public static double g2(Point point) => Math.Sin(point.y) * (Math.Exp(point.x) + Math.Exp(-point.x));