private static void ParseFunction()
{
while (true)
{
InputFunction();
try
{
_parsedFunction = Expr.Parse(_function);
break;
}
catch
{
Console.WriteLine("Neteisingai įvesta funkcija, bandykite įvesti iš naujo.");
Console.WriteLine();
}
}
Console.WriteLine("Sėkmingai pasirinkta funkcija: " + _parsedFunction.ToString());
Console.WriteLine();
}
static void Main(string[] args)
{
//объявление переменных
var x = Expr.Variable("x");
var y1 = Expr.Variable("y1");
var y2 = Expr.Variable("y2");
#region Zadanie 1
//Метод последовательных приближений для решения системы
//Объявление системы
Expr expr_dy1 = (x + y1 * y2);
Expr expr_dy2 = (x * x - y1 * y1);
Func <double, double, double, double> dy1 = (expr_dy1).Compile("x", "y1", "y2");
Func <double, double, double, double> dy2 = (expr_dy2).Compile("x", "y1", "y2");
//Первое приближение
Expr expr_y1_1 = (1 + x * x / 2);
Expr expr_y2_1 = (-x + x * x * x / 3);
Func <double, double> y1_1 = expr_y1_1.Compile("x");
Func <double, double> y2_1 = expr_y2_1.Compile("x");
//Второе приближение
Expr expr_y1_2 = (1 - (x.Pow(4)) / 24 + (x.Pow(6)) / 36);
Expr expr_y2_2 = (-x - x.Pow(5) / 20);
Func <double, double> y1_2 = expr_y1_2.Compile("x");
Func <double, double> y2_2 = expr_y2_2.Compile("x");
//диапозон значений x
double[] section_x = new double[2] {
0, 1
};
//Количество делений
int divisions = 10;
//Определение величны шага
double h = (section_x[1] - section_x[0]) / divisions;
double[] x_val = new double[divisions + 1];
x_val[0] = section_x[0];
for (int i = 1; i <= divisions; i++)
{
x_val[i] = x_val[i - 1] + h;
}
//массивы для хранения значений y1 и y2
double[] y1_val = new double[divisions + 1];
double[] y2_val = new double[divisions + 1];
y1_val[0] = 1;
y2_val[0] = 0;
//Печать начальных условий
Console.WriteLine($"y1' = {expr_dy1.ToString()}");
Console.WriteLine($"y2' = {expr_dy2.ToString()}");
Console.WriteLine("Начальные условия: ");
Console.WriteLine("y1(0) = 1; y2(0) = 0;");
//Печать приближений
Console.WriteLine("Исходя из формулы y_n = y0 + integrate (f(x, y_(n-1)))dx from 0 to x , получаем:\n");
Console.WriteLine($"y1_1 = 1 + integrate (x + 0)dx from 0 to x = {expr_y1_1.ToString()}");
Console.WriteLine($"y2_1 = 1 + integrate (x^2 - 1)dx from 0 to x = {expr_y2_1.ToString()}\n");
Console.WriteLine($"y1_2 = 1 + integrate (x + (1 + x^2/2)*(-x + x^3/3))dx from 0 to x = {expr_y1_2.ToString()}");
Console.WriteLine($"y2_2 = 1 + integrate (x^2 + (1 + x^2 + x^4/4))dx from 0 to x = {expr_y2_2.ToString()}\n");
//Результат
Console.WriteLine($"x\ty1_1\ty2_1\ty1_2\ty2_2");
for (int i = 0; i <= divisions; i++)
{
Console.Write($"{x_val[i]:0.00}\t");
Console.Write($"{y1_1(x_val[i]):0.0000}\t");
Console.Write($"{y2_1(x_val[i]):0.0000}\t");
Console.Write($"{y1_2(x_val[i]):0.0000}\t");
Console.WriteLine($"{y2_2(x_val[i]):0.0000}\t");
}
Console.WriteLine();
#endregion
Expr expr_f1 = -2 * y1 + 4 * y2;
Func <double, double, double, double> f1 = (expr_f1).Compile("x", "y1", "y2");
Expr expr_f2 = -y1 + 3 * y2;
Func <double, double, double, double> f2 = (expr_f2).Compile("x", "y1", "y2");
Console.WriteLine($"Уравнение:\ny1' = {expr_f1.ToString()}\ny2' = {expr_f2.ToString()}\n");
Console.WriteLine("Начальные условия: ");
Console.WriteLine("y1(0) = 3; y2(0) = 0;\n");
#region Zadanie 2
Miln(f1, f2, 10, 0, 1, 3, 0);
#endregion
#region Zadanie 3
Adams(f1, f2, 10, 0, 1, 3, 0);
#endregion
}
private void AssertParse(ASTNode node, Expr expected) => this.AssertParse(node, expected.ToString());
public static void GetAllFactors(MathNet.Symbolics.SymbolicExpression sym, List <string> list)
{
if (sym.Factors().Count() == 1)
{
try { var tmp = sym.RealNumberValue; }
catch
{
if (sym.Expression.IsPower)
{
var hh = sym.Expression as MathNet.Symbolics.Expression.Power;
if (hh.Item1.IsIdentifier)
{
if (!list.Contains((hh.Item1 as MathNet.Symbolics.Expression.Identifier).Item.Item.ToString()))
{
list.Add((hh.Item1 as MathNet.Symbolics.Expression.Identifier).Item.Item.ToString());
}
}
else
{
var sym1 = new MathNet.Symbolics.SymbolicExpression(hh.Item1);
GetAllFactors(sym1, list);
}
if (hh.Item2.IsIdentifier)
{
if (!list.Contains((hh.Item2 as MathNet.Symbolics.Expression.Identifier).Item.Item.ToString()))
{
list.Add((hh.Item2 as MathNet.Symbolics.Expression.Identifier).Item.Item.ToString());
}
}
else
{
var sym1 = new MathNet.Symbolics.SymbolicExpression(hh.Item2);
GetAllFactors(sym1, list);
}
}
else if (sym.Expression.IsFunction)
{
var hh = sym.Expression as MathNet.Symbolics.Expression.Function;
if (hh.Item2.IsIdentifier)
{
if (!list.Contains((hh.Item2 as MathNet.Symbolics.Expression.Identifier).Item.Item.ToString()))
{
list.Add((hh.Item2 as MathNet.Symbolics.Expression.Identifier).Item.Item.ToString());
}
}
else
{
var sym1 = new MathNet.Symbolics.SymbolicExpression(hh.Item2);
GetAllFactors(sym1, list);
}
}
else if (!list.Contains(sym.ToString()))
{
list.Add(sym.ToString());
}
}
}
else
{
foreach (var item in sym.Factors())
{
GetAllFactors(item, list);
}
}
}