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();
}
}