public TaylorSeriesCompute(int iterations, Expr symbol, Expr value, Expr function, Expr functionInput)
{
//initiliaze
DerivativeList = new List <TaylorSeriesIteration>();
//create the series
var series = Taylor(iterations, symbol, value, function);
//eval
var symbols = new Dictionary <string, FloatingPoint>();
symbols.Add("x", 1);
try {
var eval = Evaluate.Evaluate(symbols, functionInput);
//assign values
this.Aprox = eval;
} catch {
throw new ArgumentException("Invalid function input");
}
//assign to results
this.SeriesExpression = series;
this.InputFunction = function;
//var X = Expr.Symbol("x");
//var sample = Taylor(6, X, 0, Expr.Cos(X));
//string res = Infix.Format(sample);
//Console.WriteLine("taylor series: {0}", res);
}
public static void Main(string[] args)
{
//MoreLinq
Console.WriteLine(MoreEnumerable.Random().First());
//Newtonsoft
Console.WriteLine(JObject.Parse(@"{""foo"":42}"));
//Mathnet
var x = Expr.Symbol("x");
Console.WriteLine(Infix.Format(x + x));
//DynamicExpresso
Console.WriteLine(new Interpreter().Eval("2+2"));
//NDesk.Options
Console.WriteLine(new OptionSet {
{ "v", v => {} }
}.Parse(new[] { "-v", "foo" })[0]);
//System.Memory
Console.WriteLine(new Span <int>(new[] { 42 })[0]);
//System.Collections.Immutable
Console.WriteLine(new[] { 12 }.ToImmutableArray()[0]);
//Microsoft.Z3
try {
Console.WriteLine($"Z3: {Microsoft.Z3.Version.ToString()}");
} catch (DllNotFoundException) {
Console.WriteLine($"Warning, native Z3 library not detected");
}
}
/// <summary>
/// Initialize objects for symbolics calculations
/// </summary>
private void Initialize()
{
symbol = MathNet.Symbolics.Expression.Symbol("t");
symbols = new Dictionary <string, FloatingPoint> {
{ "t", 0 }
};
}
//create the function
Expr Taylor(int iterations, Expr symbol, Expr value, Expr function)
{
this.DerivativeList.Clear();
//counter for factorial
int factorial = 1;
//accumulates the results for each iteration (formula)
Expr accumulator = Expr.Zero;
//variable for holding the derivative of function for each iteration
Expr derivative = function;
for (int i = 0; i < iterations; i++)
{
//use for storing output
TaylorSeriesIteration OutputItem = new TaylorSeriesIteration();
//store the current iteration
OutputItem.Iteration = (i + 1).ToString();
//subs/replaces symbol with value from funct. Ex. symbol: x, func: x + 1, value: 1 result: 1 + 1
var subs = Structure.Substitute(symbol, value, derivative);
//get the derivative of derivative with respect to symbol
derivative = Calculus.Differentiate(symbol, derivative);
//output current derivative
OutputItem.Function = derivative;
//evaluate derivative, f(0)
var evalValue = new Dictionary <string, FloatingPoint> {
{ Infix.Format(symbol), 1 }
};
var eval = Evaluate.Evaluate(evalValue, Structure.Substitute(symbol, 0, derivative));
OutputItem.Evaluation = eval.ToString();
//create the formula and append to accumulator
accumulator = accumulator + subs / factorial * Expr.Pow(symbol - value, i);
//output current formula
OutputItem.Series = accumulator;
//current iteration + 1 as factorial (cause 0-based loop)
factorial *= (i + 1);
//append to list
this.DerivativeList.Add(OutputItem);
}
//return the formula/func in expanded form
return(Algebraic.Expand(accumulator));
}
public int GetProb(string raw, MathNet.Symbolics.Expression e)
{
sequence = MATH2.Utils.Sequences.ParseSequence(raw);
if (S.CalculateEqualizationDifNo(sequence) == 1)
{
return(100);
}
else
{
return(-100);
}
return(0);
}
private void Button_EvaluateExpression_Click(object sender, RoutedEventArgs e)
{
try {
Expr expression = Infix.ParseOrThrow(TextBox_ExpressionInput.Text);
string symbolstr = TextBox_InputSymbol.Text;
string x1 = TextBox_InputX1.Text;
string x2 = TextBox_InputX2.Text;
string ep = TextBox_InputEpsilon.Text;
var result = new SecantMethodDecimal()
{
Function = expression,
SymbolStr = symbolstr,
Epsillon = Decimal.Parse(ep)
};
result.ComputeSecantMethod(Decimal.Parse(x1), Decimal.Parse(x2));
this.ListView_Solution.ItemsSource = result.Results;
UIHelper.ResizeListViewColumnsToContent(this.ListView_Solution, null);
var lastResult = result.Results.Last();
int decimalPlaces = UIHelper.CountDigitsAfterDecimal(TextBox_InputEpsilon.Text);
this.FC_Aproximation.Formula = result.GetAprox.ToString();
this.FC_AproximationRounded.Formula = result.GetRoundedOff.ToString();
this.FC_AproximationChopped.Formula = result.GetChoppedOff.ToString();
SnackBarNotif.MessageQueue.Enqueue(
UIHelper.NewSnackbarMessage(
PackIconKind.CheckAll,
"Success! Check solution and results!",
Colors.DarkGreen,
0.5
)
);
} catch {
//show error message
SnackBarNotif.MessageQueue.Enqueue(
UIHelper.NewSnackbarMessage(
PackIconKind.SignCaution,
"Error! Unable to compute aproximation!",
Colors.HotPink,
0.5
)
);
}
}
public Expr FindRoot(ExprLast variable, ExprLast expr)
{
ExprLast simple = Algebraic.Expand(Rational.Numerator(Rational.Simplify(variable, expr)));
ExprLast[] coeff = Polynomial.Coefficients(variable, simple);
switch (coeff.Length)
{
case 1: return(ExprLast.Zero.Equals(coeff[0]) ? variable : ExprLast.Undefined);
case 2: return(Rational.Simplify(variable, Algebraic.Expand(-coeff[0] / coeff[1])));
default: return(ExprLast.Undefined);
}
}
Expr SolveSimpleRoot(Expr variable, Expr expr)
{
// try to bring expression into polynomial form
Expr simple = Algebraic.Expand(Rational.Numerator(Rational.Simplify(variable, expr)));
// extract coefficients, solve known forms of order up to 1
Expr[] coeff = Polynomial.Coefficients(variable, simple);
switch (coeff.Length)
{
case 1: return(Expr.Zero.Equals(coeff[0]) ? variable : Expr.Undefined);
case 2: return(Rational.Simplify(variable, Algebraic.Expand(-coeff[0] / coeff[1])));
default: return(Expr.Undefined);
}
}
public static Func <int, int, double> ParseInput(string input)
{
var e = Expr.Symbol("edges");
var v = Expr.Symbol("vertices");
return((vertices, edges) =>
{
var symbols = new Dictionary <string, FloatingPoint>
{
{ "vertices", vertices },
{ "edges", edges }
};
return Evaluate.Evaluate(symbols, Infix.ParseOrUndefined(input)).RealValue;
});
}
private void Button_EvaluateExpression_Click(object sender, RoutedEventArgs e)
{
try {
Expr expression = Infix.ParseOrThrow(TextBox_ExpressionInput.Text);
Symbol symbol = Symbol.NewSymbol(TextBox_InputSymbol.Text);
var result = new BisectionResultRow(symbol, expression)
{
A = Double.Parse(TextBox_InputA.Text),
B = Double.Parse(TextBox_InputB.Text),
Epsillon = Double.Parse(TextBox_InputEpsilon.Text)
};
var results = BisectionResultRow.ComputeList(result);
this.ListView_Solution.ItemsSource = results;
UIHelper.ResizeListViewColumnsToContent(this.ListView_Solution, null);
var lastResult = results.Last();
int decimalPlaces = UIHelper.CountDigitsAfterDecimal(TextBox_InputEpsilon.Text);
this.FC_Aproximation.Formula = lastResult.B.ToString();
this.FC_AproximationRounded.Formula = Math.Round(lastResult.B, decimalPlaces).ToString();
this.FC_AproximationChopped.Formula = UIHelper.TruncateDecimal((decimal)lastResult.B, decimalPlaces).ToString();
SnackBarNotif.MessageQueue.Enqueue(
UIHelper.NewSnackbarMessage(
PackIconKind.KeyboardVariant,
"Success! Check solution and results!",
Colors.DarkGreen,
0.5
)
);
}
catch {
//show error message
SnackBarNotif.MessageQueue.Enqueue(
UIHelper.NewSnackbarMessage(
PackIconKind.KeyboardVariant,
"Invalid Input! Function Input (Value to Aprox.) syntax is invalid!",
Colors.HotPink,
0.5
)
);
}
}
public static void initFunctions(string a, string b, string f1In, string f2In)
{
try
{
x0 = double.Parse(a);
y0 = double.Parse(b);
x = Expr.Symbol("x");
y = Expr.Symbol("y");
//Functions should be declared before compilation
var parsedF1 = Infix.ParseOrThrow(f1In);
var parsedF2 = Infix.ParseOrThrow(f2In);
f1 = parsedF1;
f2 = parsedF2;
}
catch (Exception ex)
{
Console.ForegroundColor = ConsoleColor.Red;
Console.Error.WriteLine(ex.Message);
Console.ReadKey();
Environment.Exit(-1);
}
//But can be given from input
}
private void Algorithm()
{
_main.Header();
var result = "U(";
var p_values = "";
var xi = "";
for (int i = 1; i <= _main.CountParams; i++)
{
if (i == _main.CountParams)
{
xi += "x_" + i;
_alpha_ln_xi += _main.ConvertCommaToDot(_alpha[i - 1].ToString()) + "*\\ln(x_" + i + ")";
}
else
{
xi += "x_" + i + ",";
_alpha_ln_xi += _main.ConvertCommaToDot(_alpha[i - 1].ToString()) + "*\\ln(x_" + i + ") + ";
}
p_values += "p_" + i + " = " + _main.ConvertCommaToDot(_main.PValuesParams[i - 1]);
_pi += "p_" + i;
if (i < _main.CountParams)
{
_pi += "," + _main.SetText(" ");
p_values += ",";
}
}
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(result + xi + ")=" + _alpha_ln_xi), Align = HorizontalAlignment.Center });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(p_values), Align = HorizontalAlignment.Center });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Решение:", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("1. Решим задачу оптимального поведения потребителя, если цены благ соответственно равны ", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(p_values + _main.SetText(" и доход равен ") + "M = " + _main.MParam + ".") });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Найдем функции спроса потребителя:", true)) });
for (int i = 1; i <= _main.CountParams; i++)
{
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula("x_" + i + " = f_" + i + "(" + _pi + ",M);"), Align = HorizontalAlignment.Center });
}
result = _main.SetText("где ");
var blag = "";
for (int i = 1; i <= _main.CountParams; i++)
{
_xi += "x_" + i;
blag += i + "-го";
if (i < _main.CountParams)
{
_xi += ", ";
}
if (i < _main.CountParams - 1)
{
blag += ", ";
}
else if (i == _main.CountParams - 1)
{
blag += " и ";
}
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(result + _xi + _main.SetText(" - количество приобретаемого блага " + blag + " вида.")) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Для этого решим следующую задачу оптимального поведения потребителя.", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Математическая модель задачи имеет вид:")) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(@"\alpha_j > 0, x_j > 0, j = \overline{1, " + _main.CountParams +"}" + _main.SetText(" (1)")), Align = HorizontalAlignment.Center });
for (int i = 1; i <= _main.CountParams; i++)
{
_pi_xi += "x_" + i + "*p_" + i;
_minus_pi_xi += "- x_" + i + "*p_" + i;
if (i < _main.CountParams)
{
_pi_xi += " + ";
_minus_pi_xi += " ";
}
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_pi_xi + " = M" + _main.SetText(" (2)")), Align = HorizontalAlignment.Center });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula("U = " + _alpha_ln_xi + " \\rightarrow max" + _main.SetText(" (3)")), Align = HorizontalAlignment.Center });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Левая часть условия (2) – стоимость приобретаемых благ, а условие (3) означает, что полезность этих", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("благ должна быть максимальной.")) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Решим задачу методом множителей Лагранжа. Функция Лагранжа:", true)) });
result = "L(" + _xi + ",\\lambda) = U(" + _xi + ") + \\lambda(M " + _minus_pi_xi + ").";
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + result) });
result = "L(" + _xi + ",\\lambda) = " + _alpha_ln_xi + " + \\lambda(M " + _minus_pi_xi + ").";
_L = _alpha_ln_xi + "+" + _lambda + "*(" + _M + _minus_pi_xi + ")";
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + result) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Найдем частные производные функции Лагранжа и приравняем их к нулю:", true)) });
for (int i = 0; i < _main.CountParams; i++)
{
_lst.Add(_main.Diff(_L.Replace("\\", ""), _variables[i]));
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + @"\frac{\partial L}{\partial x_" + (i + 1) + "} = " + (_lst[i] as Expr).ToLaTeX().Replace(_lambda, @"\lambda") + " = 0") });
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + @"\frac{\partial L}{\partial \lambda } = " + _M + _minus_pi_xi + " = 0") });
_main.ResultCollection.Add(_main.RedLine);
for (int i = 0; i < _lst.Count; i++)
{
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + (_lst[i] as Expr).Substitute(Expr.Parse("p_" + (i + 1)), Expr.Parse("0")).ToLaTeX() + " = " + @"\lambda*p_" + (i + 1)) });
}
_main.ResultCollection.Add(_main.RedLine);
for (int i = 0; i < _lst.Count; i++)
{
var root = _main.FindRoot(ExprLast.Symbol("x_" + (i + 1)), Infix.ParseOrThrow((_lst[i] as Expr).ToString()));
_lst.RemoveAt(i);
_lst.Insert(i, root);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + "x_" + (i + 1) + " = " + (_lst[i] as Expr).ToLaTeX().Replace(_lambda, @"\" + _lambda)) });
}
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + _pi_xi + " = " + _M + _main.SetText(" (4)")) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Подставим найденные значения ", true) + _xi + _main.SetText(" в (4) и выразим ") + @"\" + _lambda) });
result = _pi_xi;
for (int i = 0; i < _lst.Count; i++)
{
var expr = Expr.Parse(result).Substitute(Expr.Parse("x_" + (i + 1)), _lst[i] as Expr);
result = _main.ConvertExprLastToExpr(Rational.Simplify(ExprLast.Symbol("x_" + (i + 1)), _main.ConvertExprToExprLast(expr))).ToString();
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + Expr.Parse(result).ToLaTeX().Replace(_lambda, @"\" + _lambda) + " = " + _M) });
result += "-" + _M;
var lam_star = _main.FindRoot(ExprLast.Symbol(_lambda), Infix.ParseOrThrow(result));
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + @"\lambda^* = " + lam_star.ToLaTeX() + " = " + lam_star.Substitute("M", _main.MParam).ToLaTeX()) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + _main.SetText(@"Найдем оптимальный набор благ потребителя.")) });
result = @"X^* = (";
for (int i = 0; i < _main.CountParams; i++)
{
result += "x_" + (i + 1) + "^*";
if (i < _main.CountParams - 1)
{
result += ",";
}
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + result + ")" + _main.SetText(@" при заданных ценах на блага и доходе:")) });
_main.ResultCollection.Add(_main.RedLine);
for (int i = 0; i < _main.CountParams; i++)
{
var res = (_lst[i] as Expr).Substitute(Expr.Parse(_lambda), lam_star);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + "x_" + (i + 1) + "^* = " + res.ToLaTeX()) });
_lst[i] = res;
}
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + p_values + ", M = " + _main.ConvertCommaToDot(_main.MParam)) });
_main.ResultCollection.Add(_main.RedLine);
for (int i = 0; i < _main.CountParams; i++)
{
var res = (_lst[i] as Expr).Substitute(Expr.Parse(_M), Expr.Parse(_main.ConvertCommaToDot(_main.MParam))).Substitute(Expr.Parse("p_" + (i + 1)), Expr.Parse(_main.ConvertCommaToDot(_main.PValuesParams[i])));
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + "x_" + (i + 1) + "^* = " + res.ToLaTeX()) });
_x_star[i] = double.Parse(_main.ConvertDotToComma(res.RealNumberValue.ToString()));
}
result = @"X^* = (";
for (int i = 0; i < _main.CountParams; i++)
{
result += "x_" + (i + 1) + "^*";
if (i < _main.CountParams - 1)
{
result += ",";
}
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Проверим, выполняется ли для найденного оптимального решения ", true) + result + _main.SetText(") бюджетное ограничение:")) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_pi_xi + " = M"), Align = HorizontalAlignment.Center });
result = "";
for (int i = 0; i < _main.CountParams; i++)
{
result += _main.ConvertCommaToDot(_main.PValuesParams[i]) + "*" + _main.ConvertCommaToDot(_x_star[i]);
if (i < _main.CountParams - 1)
{
result += "+";
}
}
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(result + " = " + _main.ConvertCommaToDot(_main.MParam)), Align = HorizontalAlignment.Center });
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(Expr.Parse(result).ToLaTeX() + " = " + _main.ConvertCommaToDot(_main.MParam)), Align = HorizontalAlignment.Center });
result = @"\overline{ X}^ * = (" + _x_star.Aggregate("", (b, n) => b + (!string.IsNullOrEmpty(b) ? ";" : "") + Math.Truncate(n).ToString()) + ")";
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Если речь идет о неделимых благах, то оптимальный выбор потребителя составит ", true) + result + ",") });
result = _main.SetText(" т.е. ему необходимо приобрести ");
for (int i = 0; i < _main.CountParams; i++)
{
result += (i + 1) + _main.SetText("-го блага - ") + _main.ConvertCommaToDot(Math.Truncate(_x_star[i]));
if (i < _main.CountParams - 2)
{
result += ", ";
}
if (i < _main.CountParams - 1)
{
result += _main.SetText(" и ");
}
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(result + ".") });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Но т.к. мы условились, что речь будет идти о делимых благах, то оптимальный выбор потребителя будет:", true)) });
result = @"\overline{ X}^ * = (" + _x_star.Aggregate("", (b, n) => b + (!string.IsNullOrEmpty(b) ? ";" : "") + _main.ConvertCommaToDot(n.ToString())) + ")";
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + result + _main.SetText(", т.е. следует приобрести: ")) });
for (int i = 0; i < _main.CountParams; i++)
{
result = _main.SetText("блага ", true) + (i + 1) + _main.SetText("-го вида - ") + _main.ConvertCommaToDot(_x_star[i]);
if (i < _main.CountParams - 1)
{
result += ", ";
}
if (i == _main.CountParams - 1)
{
result += ".";
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(result) });
}
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Решение 2:", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Функции спроса потребителя найдены в пункте 1.", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Вычислим реакции потребителя при изменении дохода М и цен ", true) + _pi + _main.SetText(" в точке оптимума ") + @"\overline{ X}^ *.") });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Реакции потребителя при изменении дохода М:", true)) });
var minBlag = -1.0;
var maxBlag = -1.0;
var indMinBlag = -1;
var indMaxBlag = -1;
for (int i = 0; i < _main.CountParams; i++)
{
var res = _main.Diff((_lst[i] as Expr).ToString(), "M");
var p = Expr.Parse(_main.ConvertCommaToDot(_main.PValuesParams[i].ToString()));
var val = double.Parse(_main.ConvertDotToComma(res.Substitute(Expr.Parse("p_" + (i + 1)), p).RealNumberValue.ToString()));
if (i == 0)
{
minBlag = maxBlag = val;
indMinBlag = indMaxBlag = i;
}
if (val < minBlag)
{
minBlag = val;
indMinBlag = i;
}
if (val > maxBlag)
{
maxBlag = val;
indMaxBlag = i;
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + @"\frac{\partial x_" + (i + 1) + @"}{\partial M } = " + res.ToLaTeX() + @"\approx" + _main.ConvertCommaToDot(val.ToString())) });
if (i == 0)
{
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Поскольку при увеличении дохода спрос на 1-благо возрастает, то это благо ценное.", true)) });
_main.ResultCollection.Add(_main.RedLine);
}
}
if (_main.CountParams == 2)
{
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Оставшееся благо также является ценным для потребителя. При этом наиболее ценным является " + (indMaxBlag + 1) + "-е благо, а наименее ценным – " + (indMinBlag + 1) + "-е.", true)) });
}
else
{
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Остальные блага также являются ценными для потребителя. При этом наиболее ценным является " + (indMaxBlag + 1) + "-е благо, а наименее ценным – " + (indMinBlag + 1) + "-е.", true)) });
}
for (int i = 0; i < _main.CountParams; i++)
{
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Определим реакции потребителя при изменении цены на " + (i + 1) + "-е благо:", true)) });
for (int j = 0; j < _main.CountParams; j++)
{
_main.ResultCollection.Add(_main.RedLine);
var res = _main.Diff((_lst[i] as Expr).ToString(), "p_" + (i + 1));
var m = Expr.Parse(_main.ConvertCommaToDot(_main.MParam.ToString()));
var p = Expr.Parse(_main.ConvertCommaToDot(_main.PValuesParams[j].ToString()));
var val = double.Parse(_main.ConvertDotToComma(res.Substitute(Expr.Parse("M"), m).Substitute(Expr.Parse("p_" + (i + 1)), p).RealNumberValue.ToString()));
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + @"\frac{\partial x_" + (j + 1) + @"}{\partial p_" + (i + 1) + " } = " + res.ToLaTeX() + (val == 0 ? "=" : @"\approx") + _main.ConvertCommaToDot(val.ToString()) + (val != 0 ? " (" + (val >= 0 ? ">" : "<") + "0)" : "")) });
if (i == j && val < 0)
{
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("С увеличением цены на " + (i + 1) + "-е благо спрос на него уменьшается, значит, "+ (j+1)+"-е благо нормальное.", true)) });
}
else if (i == j && val > 0)
{
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("С увеличением цены на " + (i + 1) + "-е благо спрос на него уменьшается, значит, " + (j + 1) + "-е благо ненормальное.", true)) });
}
else if (val < 0)
{
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("С увеличением цены на " + (i + 1) + "-е благо спрос на " + (j + 1) + "-е благо увеличивается, эти блага взаимодополняемые.", true)) });
}
else if (val > 0)
{
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("С увеличением цены на " + (i + 1) + "-е благо спрос на " + (j + 1) + "-е благо увеличивается, эти блага взаимозаменяемые.", true)) });
}
}
}
result = @"\overline{ X}^ * = (";
for (int i = 0; i < _main.CountParams; i++)
{
result += "x_" + (i + 1) + "^*";
if (i < _main.CountParams - 1)
{
result += ",";
}
}
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Решение3:", true)) });
_main.ResultCollection.Add(new Result()
{
ItemResult = _main.RenderFormula(_main.SetText("Вычислим предельные полезности благ в точке экстремума ", true) + result + ")" +
_main.SetText(". Это значения частных производных "))
});
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("функции полезности ") + "U = (" + _xi + ")" + _main.SetText(" по соответствующим аргументам в точке ") + @"\overline{ X}^*.") });
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(@"\overline{ X}^ * = (" + _x_star.Aggregate("", (b, n) => b + (!string.IsNullOrEmpty(b) ? ";" : "") + _main.ConvertCommaToDot(n.ToString())) + ")") });
var dU_x_star = new double[_main.CountParams];
for (int i = 0; i < _main.CountParams; i++)
{
_main.ResultCollection.Add(_main.RedLine);
var res = _main.Diff(_alpha_ln_xi.Replace("\\", ""), "x_" + (i + 1));
var x = Expr.Parse(_main.ConvertCommaToDot(_x_star[i].ToString()));
var val = double.Parse(_main.ConvertDotToComma(res.Substitute(Expr.Parse("x_" + (i + 1)), x).RealNumberValue.ToString()));
dU_x_star[i] = val;
_main.ResultCollection.Add(new Result()
{
ItemResult = _main.RenderFormula(_main.SetText("", true) + @"\frac{\partial U}{\partial x_" + (i + 1) + " } = " + res.ToLaTeX() + _main.SetText("; ") +
@"\frac{\partial U}{\partial x_" + (i + 1) + " }(\\overline{ X})^* = " + res.ToLaTeX() + _main.SetText(" = ") + _main.ConvertCommaToDot(val.ToString()))
});
}
_main.ResultCollection.Add(_main.RedLine);
for (int i = 0; i < _main.CountParams; i++)
{
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("На 1 дополнительную единицу " + (i + 1) + "-го блага приходится ", true) + dU_x_star[i] + _main.SetText(" единиц дополнительной полезности.")) });
}
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Решение4:", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Вычислим нормы замещения благ в точке оптимума ", true) + "\\overline{X}^*.") });
for (int i = 0; i < _main.CountParams; i++)
{
for (int j = 0; j < _main.CountParams; j++)
{
if (i == j)
continue;
var dudx = dU_x_star[i] / dU_x_star[j];
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Норма замены " + (i + 1) + "-го блага " + (j + 1) + "-м:", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + @"n_{" + (j + 1) + "," + (i + 1) + @"} = -\frac{\partial U}{\partial x_" + (i + 1) + @"} : \frac{\partial U}{\partial x_" + (j + 1) + "} = " + _main.ConvertCommaToDot((-dudx).ToString())) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Для замещения 1 единицы " + (i + 1) + "-го блага необходимо дополнительно приобрести ", true) + _main.ConvertCommaToDot((dudx).ToString())) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText(" единиц " + (j + 1) + "-го блага, чтобы удовлетворенность осталась на прежнем уровне.")) });
}
}
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Решение5:", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Вычислим коэффициенты эластичности по доходу и ценам при заданных ценах и доходе: ", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(p_values + ", M = " + _main.ConvertCommaToDot(_main.MParam.ToString()) + ".") });
var empSum = 0.0;
for (int i = 0; i < _main.CountParams; i++)
{
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Для блага " + (i + 1) + ":", true)) });
var res = _main.Diff((_lst[i] as Expr).ToString(), "M").Divide("x_" + (i + 1) + "/M");
var resReplace = res.Substitute("M", _main.ConvertCommaToDot(_main.MParam.ToString())).Substitute("x_" + (i + 1), _main.ConvertCommaToDot(_x_star[i].ToString())).Substitute("p_" + (i + 1), _main.ConvertCommaToDot(_main.PValuesParams[i].ToString())).ToString();
empSum = double.Parse(_main.ConvertDotToComma(resReplace));
var resRound = Math.Round(empSum);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + @"E_" + (i + 1) + @"^M = \frac{\partial x_" + (i + 1) + @"}{\partial M } : " + @"\frac{ x_" + (i + 1) + "}{ M } = " + res.ToLaTeX() + " = " + resRound) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("При увеличении дохода на 1 % спрос на " + (i + 1) + "-e благо возрастает на 1 %.", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Коэффициенты эластичности по ценам:", true)) });
result = "E_" + (i + 1) + "^M + ";
for (int j = 0; j < _main.CountParams; j++)
{
result += "E_{ " + (i + 1) + "" + (j + 1) + "}^p";
if (j < _main.CountParams - 1)
{
result += " + ";
}
res = _main.Diff((_lst[i] as Expr).ToString(), "p_" + (j + 1)).Divide("x_" + (i + 1) + "/p_" + (j + 1));
resReplace = res.Substitute("M", _main.ConvertCommaToDot(_main.MParam.ToString())).Substitute("x_" + (i + 1), _main.ConvertCommaToDot(_x_star[i].ToString())).Substitute("p_" + (j + 1), _main.ConvertCommaToDot(_main.PValuesParams[i].ToString())).ToString();
var epi = double.Parse(_main.ConvertDotToComma(resReplace));
empSum += epi;
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + @"E_{" + (i + 1) + "" + (j + 1) + @"}^p = \frac{\partial x_" + (i + 1) + @"}{\partial p_" + (j + 1) + " } : " + @"\frac{ x_" + (i + 1) + "}{ p_" + (j + 1) + " } = " + resReplace) });
var output = "При росте цены на " + (j + 1) + "-е благо на 1 %";
if (epi != 0)
{
if (epi < 0)
{
output += " спрос на него уменьшается на ";
}
else
{
output += "спрос на него увеличивается на ";
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText(output, true) + _main.ConvertCommaToDot(Math.Abs(epi).ToString()) + _main.SetText("%.")) });
}
else
{
output += " оно является независимым.";
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText(output, true)) });
}
_main.ResultCollection.Add(_main.RedLine);
}
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Проверка:", true)) });
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("", true) + result + " = " + _main.ConvertCommaToDot(empSum.ToString())) });
}
_main.ResultCollection.Add(_main.RedLine);
_main.ResultCollection.Add(new Result() { ItemResult = _main.RenderFormula(_main.SetText("Все расчеты произведены достаточно точно и правильно.", true)) });
}
/// <summary>
/// Create trajectory from given parametrization
/// </summary>
private void CreateTrajectory()
{
// Try to parse parametrizations' strings
try
{
xExpression = Infix.ParseOrThrow(XParametrizationTextBox.Text);
yExpression = Infix.ParseOrThrow(YParametrizationTextBox.Text);
}
catch (Exception exception)
{
TrajectoryLoaded = false;
MessageBox.Show("Wrong format of parametrization.\n" + exception.Message);
return;
}
// Try to parse parameters
try
{
minParameterValue = double.Parse(MinParameterValueTextBox.Text);
maxParameterValue = double.Parse(MaxParameterValueTextBox.Text);
pointsCount = double.Parse(PointsCountTextBox.Text);
if (minParameterValue >= maxParameterValue || pointsCount < 2)
{
throw new Exception();
}
}
catch (Exception)
{
TrajectoryLoaded = false;
MessageBox.Show("Parameters are invalid.");
return;
}
TrajectoryPoints = new List <Point3D>();
var flag = true;
// Try to calculate curve's trajectory
try
{
var parameterStep = (maxParameterValue - minParameterValue) / (pointsCount - 1);
for (double t = minParameterValue; t < maxParameterValue + parameterStep / 2; t += parameterStep)
{
symbols["t"] = t;
double xResult = Evaluate.Evaluate(symbols, xExpression).RealValue;
double yResult = Evaluate.Evaluate(symbols, yExpression).RealValue;
TrajectoryPoints.Add(new Point3D(xResult, yResult, 0.0));
if (flag)
{
flag = false;
}
}
}
catch (Exception exception)
{
TrajectoryLoaded = false;
TrajectoryPoints.Clear();
if (exception.HResult == HResultWrongParam)
{
MessageBox.Show("Given parametrization is not based on [t] variable.\n");
}
else if (exception.HResult == HResultCannotCalculate)
{
MessageBox.Show("Cannot calculate curve for given set.\n");
}
else
{
MessageBox.Show("Cannot calculate curve for given set.\n" + exception.Message);
}
return;
}
TrajectoryLoaded = true;
}
public BisectionResultRow(Symbol symbol, Expr functionExpression)
{
this.FunctionExpression = functionExpression;
this.Symbol = symbol;
}
public Coordinates GetXYbyCircunsferencesIntersection(Circumference circumference1, Circumference
circumference2, Circumference circumference3)
{
var response = new Coordinates()
{
X = 0, Y = 0
};
var circumferenceVariables = new List <Variables>()
{
new Variables()
{
Name = "CircumferenceEquation"
, V_2_X_CoordX = ((-1) * circumference1.Coordinates.X) * 2
, L_CoordX_CoordX = circumference1.Coordinates.X * circumference1.Coordinates.X
, V_2_Y_CoordY = ((-1) * circumference1.Coordinates.Y) * 2
, L_CoordY_CoordY = circumference1.Coordinates.Y * circumference1.Coordinates.Y
, Radio = circumference1.Radio * circumference1.Radio
, ReductionFactor = 1
},
new Variables()
{
Name = "CircumferenceEquation"
, V_2_X_CoordX = ((-1) * circumference2.Coordinates.X) * 2
, L_CoordX_CoordX = (circumference2.Coordinates.X * circumference2.Coordinates.X)
, V_2_Y_CoordY = ((-1) * circumference2.Coordinates.Y) * 2
, L_CoordY_CoordY = (circumference2.Coordinates.Y * circumference2.Coordinates.Y)
, Radio = (circumference2.Radio * circumference2.Radio)
, ReductionFactor = -1
}
};
//Get First Equation to substitution on the last step
var equationForFinalSubstitution = string.Format("x^2+y^2{0}*x{1}{2}*y{3}{4}", (circumferenceVariables[0].V_2_X_CoordX > 0 ? "+" : "") + circumferenceVariables[0].V_2_X_CoordX
, (circumferenceVariables[0].L_CoordX_CoordX > 0 ? "+" : "") + circumferenceVariables[0].L_CoordX_CoordX
, (circumferenceVariables[0].V_2_Y_CoordY > 0 ? "+" : "") + circumferenceVariables[0].V_2_Y_CoordY
, (circumferenceVariables[0].L_CoordY_CoordY > 0 ? "+" : "") + circumferenceVariables[0].L_CoordY_CoordY
, ((-1) * circumferenceVariables[0].Radio) > 0 ? "+" : "") + ((-1) * circumferenceVariables[0].Radio);
//Apply factor for reduction
circumferenceVariables[1].V_2_X_CoordX *= circumferenceVariables[1].ReductionFactor;
circumferenceVariables[1].L_CoordX_CoordX *= circumferenceVariables[1].ReductionFactor;
circumferenceVariables[1].V_2_Y_CoordY *= circumferenceVariables[1].ReductionFactor;
circumferenceVariables[1].L_CoordY_CoordY *= circumferenceVariables[1].ReductionFactor;
circumferenceVariables[1].Radio *= circumferenceVariables[1].ReductionFactor;
//Apply Reduction
var reducedEquationSum =
from item in circumferenceVariables
group item by item.Name into reducedEquationGroup
select new
{
Name = reducedEquationGroup.Key,
V_2_X_CoordX = reducedEquationGroup.Sum(x => x.V_2_X_CoordX),
L_CoordX_CoordX = reducedEquationGroup.Sum(x => x.L_CoordX_CoordX),
V_2_Y_CoordY = reducedEquationGroup.Sum(x => x.V_2_Y_CoordY),
L_CoordY_CoordY = reducedEquationGroup.Sum(x => x.L_CoordY_CoordY),
Radio = reducedEquationGroup.Sum(x => x.Radio)
};
var reducedEquation = reducedEquationSum.ToList();
var GCDInValues = new int[3] {
Math.Abs((int)reducedEquation[0].V_2_X_CoordX),
Math.Abs((int)reducedEquation[0].V_2_Y_CoordY),
Math.Abs((int)reducedEquation[0].L_CoordX_CoordX + (int)reducedEquation[0].L_CoordY_CoordY)
};
string generalExpression = string.Format("{0}*x{1}{2}*y{3}{4}", reducedEquation[0].V_2_X_CoordX
, (reducedEquation[0].L_CoordX_CoordX > 0 ? "+": "") + reducedEquation[0].L_CoordX_CoordX
, (reducedEquation[0].V_2_Y_CoordY > 0 ? "+" : "") + reducedEquation[0].V_2_Y_CoordY
, (reducedEquation[0].L_CoordY_CoordY > 0 ? "+" : "") + reducedEquation[0].L_CoordY_CoordY
, (((-1) * reducedEquation[0].Radio) > 0 ? "+" : "") + (-1) * reducedEquation[0].Radio);
var x = Expr.Symbol("x");
var y = Expr.Symbol("y");
Expr aleft = Infix.ParseOrThrow(generalExpression);
Expr aright = Infix.ParseOrThrow("0");
//Resolve "x" from general expression
Expr xFromGeneralExpression = SolveSimpleRoot(x, aleft - aright);
//TODO Substitution and final result
return(response);
}
public Expr ConvertExprLastToExpr(ExprLast eq)
{
return(eq);
}
