public NewtonMethodSystem(EquationsSystem eq, Dictionary <string, FloatingPoint> values, double e)
{
Equations = eq;
Eps = e;
X = values;
Counter = 0;
//Все свойства якобиана вычисляются при создании объекта Newton
Jacobian = new Expr[Equations.Functions.GetLength(0), Equations.Functions.GetLength(1)];
for (int i = 0; i < Jacobian.GetLength(0); i++)
{
for (int j = 0; j < Jacobian.GetLength(1); j++)
{
//Взятие производной из каждой функции
if (Equations.Functions[i, j] != null)
{
Jacobian[i, j] = Equations.Functions[i, j].Differentiate($"x{j + 1}");
}
}
}
}
static void Main(string[] args)
{
//Используемые переменныые
var x1 = Expr.Variable("x1");
var x2 = Expr.Variable("x2");
var x3 = Expr.Variable("x3");
var x4 = Expr.Variable("x4");
var x5 = Expr.Variable("x5");
var x6 = Expr.Variable("x6");
var x7 = Expr.Variable("x7");
var x8 = Expr.Variable("x8");
var x9 = Expr.Variable("x9");
var x10 = Expr.Variable("x10");
//Пример 1
var values1 = new Dictionary <string, FloatingPoint>
{
{ "x1", 0.9 },
{ "x2", 0.5 }
};
var f1 = (x1 * x1);
var f2 = (x2 * x2 - 1);
var f3 = (x1 * x1 * x1);
var f4 = (-x2);
Expr[,] functions1 = new Expr[, ] {
{ f1, f2 }, { f3, f4 }
};
var system1 = new EquationsSystem(functions1);
system1.Print();
var newton1 = new NewtonMethodSystem(system1, values1, 0.0001);
newton1.Solve();
//Пример 2
var values2 = new Dictionary <string, FloatingPoint>
{
{ "x1", 0.5 },
{ "x2", 0.5 },
{ "x3", 0.5 }
};
f1 = (x1 * x1);
f2 = (x2 * x2);
f3 = (x3 * x3 - 1);
f4 = (2 * x1 * x1);
var f5 = f2;
var f6 = (-4 * x3);
var f7 = (3 * x1 * x1);
var f8 = (-4 * x2);
var f9 = (x3 * x3);
Expr[,] functions2 = new Expr[, ] {
{ f1, f2, f3 }, { f4, f5, f6 }, { f7, f8, f9 }
};
var system2 = new EquationsSystem(functions2);
system2.Print();
var newton2 = new NewtonMethodSystem(system2, values2, 0.0001);
newton2.Solve();
Console.WriteLine("Введите уравнения системы, =0 в конце вводить не нужно");
Console.WriteLine("По окончанию ввода введите 0");
List <string> equations = new List <string>();
while (true)
{
string temp = Console.ReadLine();
if (temp == "0")
{
break;
}
equations.Add(temp);
}
Expr[,] functions3 = new Expr[equations.Count, equations.Count];
int i = 0;
foreach (string equation in equations)
{
Expr temp = Expr.Parse(equation);
List <Expr> expression = new List <Expr>();
for (int j = 0; j < temp.NumberOfOperands; j++)
{
expression.Add(temp[j]);
}
if (temp.NumberOfOperands > equations.Count)
{
expression[0] = temp[0] + temp[1];
expression.RemoveAt(1);
}
for (int j = 0; j < equations.Count; j++)
{
functions3[i, j] = expression[j];
}
i++;
}
var system3 = new EquationsSystem(functions3);
Console.WriteLine("Введите изначальное приближение");
var values3 = new Dictionary <string, FloatingPoint>(equations.Count);
for (int j = 0; j < equations.Count; j++)
{
Console.Write($"x{j+1}=");
String[] temp = Console.ReadLine().Split('=');
FloatingPoint floatingPoint = float.Parse(temp[0]);
values3.Add($"x{j + 1}", floatingPoint);
}
var newton3 = new NewtonMethodSystem(system3, values3, 0.0001);
newton3.Solve();
Console.ReadLine();
}
