public static double CalculateExactRemainder(Expr func, FloatingPoint point, int order)
{
var pointVar = new Dictionary <string, FloatingPoint>
{
{ "x", point }
};
var taylorExpr1 = GetTaylorExpression(order + 1, Expr.Variable("x"), 0, func);
var trueValue = func.Evaluate(pointVar);
var taylorValue = taylorExpr1.Evaluate(pointVar);
return(trueValue.RealValue - taylorValue.RealValue);
}
public static double solve(Expr expr, string varName)
{
Expr v = Expr.Variable(varName);
expr = expr.RationalSimplify(v).Numerator().Expand();
Expr[] coeff = expr.Coefficients(v);
Console.WriteLine(coeff.Length);
switch (coeff.Length)
{
case 1: return(0.0); //Expr.Zero.Equals(coeff[0]) ? v : Expr.Undefined;
case 2: return((-coeff[0] / coeff[1]).Expand().RationalSimplify(v).RealNumberValue);
default: return(0.0); //Expr.Undefined.RealNumberValue;
}
}
static void Main(string[] args)
{
var x = Expr.Variable("x");
var y1 = Expr.Variable("y1");
var y2 = Expr.Variable("y2");
//Example 1
Dictionary <string, FloatingPoint> initialVal1 = new Dictionary <string, FloatingPoint>()
{
{ "x", 0 },
{ "y1", 3 },
{ "y2", 0 }
};
Expr func1 = (-2 * y1 + 4 * y2);
Expr func2 = (-y1 + 3 * y2);
var functions = new List <Expr>();
functions.Add(func1);
functions.Add(func2);
DifEquationSystem equation1 =
new DifEquationSystem(functions);
double[] section1 = new double[] { 0, 1 };
RungeKutta rungeKutta1 =
new RungeKutta(equation1, initialVal1, section1, 10);
Func <double, double> answer1 = (4 * (-x).Exp() - (2 * x).Exp()).Compile("x");
Func <double, double> answer2 = ((-x).Exp() - (2 * x).Exp()).Compile("x");
var answers = new List <Func <double, double> >();
answers.Add(answer1);
answers.Add(answer2);
rungeKutta1.Solve();
PrintRealAnswer(answers, initialVal1, section1, 10);
Console.ReadKey();
}
static void Main(string[] args)
{
var x = Expr.Variable("x");
var a = Expr.Variable("a");
string poly = "5x^2+3x+5";
int start;
int count;
int end;
int posOfx;
//int counting;
List <int> coeff = new List <int>();
end = poly.Length;
start = 0;
count = 0;
posOfx = 0;
//counting = 0;
while ((start <= end) && (posOfx > -1))
{
count = end - start;
posOfx = poly.IndexOf('x', start, count);
if (posOfx == -1)
{
break;
}
start = posOfx + 1;
coeff.Add(posOfx);
}
Console.WriteLine(coeff[0]);
foreach (int y in coeff)
{
Console.WriteLine(coeff[y]);
}
Console.ReadLine();
// menu();
}
public MainWindow()
{
InitializeComponent();
var a = Expr.Variable("a");
var b = Expr.Variable("b");
var diff = a.Differentiate(a);
// string latex = Expr.Parse("a_1_2_3^a^3^b/b_1^3").ToLaTeX();
var latex = Diff(a, a) + " = " + diff.ToLaTeX();
string fileName = @"formula.png";
var parser = new TexFormulaParser();
var formula = parser.Parse(latex);
//var renderer = formula.GetRenderer(TexStyle.Display, 20.0, "Arial");
//var bitmapSource = renderer.RenderToGeometry(0.0, 0.0);
var pngBytes = formula.RenderToPng(20.0, 0.0, 0.0, "Arial");
File.WriteAllBytes(fileName, pngBytes);
}
public static double CalculateLagrangeRemainder(Expr function, string variableName, int n, FloatingPoint x, FloatingPoint x0)
{
var results = new List <double>();
var length = GetLength(Math.Min(x.RealValue, x0.RealValue), Math.Max(x.RealValue, x0.RealValue));
var increment = length / 10;
double currentIncrement = Math.Min(x.RealValue, x0.RealValue);
var factorial = (FloatingPoint)SpecialFunctions.Factorial(n + 1);
while (currentIncrement < Math.Max(x.RealValue, x0.RealValue))
{
var variable = new Dictionary <string, FloatingPoint>
{
{ variableName, currentIncrement }
};
var derivativeResult = function.CalculateFunctionAtDerivative(variable, Expr.Variable(variableName), n + 1);
var result = derivativeResult.RealValue / factorial.RealValue * Math.Pow(Math.Abs(x.RealValue - x0.RealValue), n + 1);
results.Add(Math.Abs(result));
currentIncrement += increment;
}
var variableMax = new Dictionary <string, FloatingPoint>
{
{ variableName, Math.Max(x.RealValue, x0.RealValue) }
};
var derivativeResultMax = function.CalculateFunctionAtDerivative(variableMax, Expr.Variable(variableName), n + 1);
var resultMax = derivativeResultMax.RealValue / factorial.RealValue * Math.Pow(Math.Abs(x.RealValue - x0.RealValue), n + 1);
results.Add(Math.Abs(resultMax));
return(results.Max(x => x));
}
static void Main(string[] args)
{
//Используемые переменныые
var x1 = Expr.Variable("x1");
var x2 = Expr.Variable("x2");
var x3 = Expr.Variable("x3");
//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 Newton(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 Newton(system2, values2, 0.0001);
newton2.Solve();
Console.ReadLine();
}
public static Expr simplify(Expr expr, string varName)
{
return(expr.RationalSimplify(Expr.Variable(varName)));
}
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();
}