private double[][] GenerateAMatrix(int N, MathExpression tFunc, MathExpression bFunc, MathExpression sigmaFunc)
{
double h = 1.0 / N;
double[][] res = new double[N][];
for (int i = 0; i < N; i++)
{
res[i] = new double[N];
for (int j = 0; j < N; j++)
{
if (i != N - 1)
{
if (i == j)
{
res[i][j] = (1.0 / h) * (tFunc.Calculate(h * (i + 1) - (h / 2.0)) + tFunc.Calculate(h * (i + 1) + (h / 2.0))) +
(h / 3.0) *
(sigmaFunc.Calculate(h * (i + 1) - (h / 2.0)) + sigmaFunc.Calculate(h * (i + 1) + (h / 2.0))) +
(1.0 / 2.0) * (bFunc.Calculate(h * (i + 1) - (h / 2.0)) - bFunc.Calculate(h * (i + 1) + (h / 2.0)));
}
else if (j == i + 1)
{
res[i][j] = -(1.0 / h) * tFunc.Calculate(h * (i + 1) + (h / 2.0)) +
(1.0 / 2.0) * bFunc.Calculate(h * (i + 1) + (h / 2.0)) +
(h / 6.0) * sigmaFunc.Calculate(h * (i + 1) + (h / 2.0));
}
else if (j == i - 1)
{
res[i][j] = -(1.0 / h) * tFunc.Calculate(h * (i + 1) - (h / 2.0)) -
(1.0 / 2.0) * bFunc.Calculate(h * (i + 1) - (h / 2.0)) +
(h / 6.0) * sigmaFunc.Calculate(h * (i + 1) - (h / 2.0));
}
else
{
res[i][j] = 0;
}
}
else
{
if (j < N - 2)
{
res[i][j] = 0;
}
else if (j == N - 2)
{
res[i][j] = -(1.0 / h) * tFunc.Calculate(h * (i + 1) - (h / 2.0)) -
(1.0 / 2.0) * bFunc.Calculate(h * (i + 1) - (h / 2.0)) +
(h / 6.0) * sigmaFunc.Calculate(h * (i + 1) - (h / 2.0));
}
else if (j == N - 1)
{
res[i][j] = (1.0 / h) * tFunc.Calculate(h * (i + 1) - (h / 2.0)) +
(1.0 / 2.0) * bFunc.Calculate(h * (i + 1) - (h / 2.0)) +
(h / 3.0) * sigmaFunc.Calculate(h * (i + 1) - (h / 2.0));
}
}
}
}
return(res);
}
public double[] GenerateFVector(int N, MathExpression fFunc)
{
double h = 1.0 / N;
double[] res = new double[N];
for (int i = 0; i < N - 1; i++)
{
res[i] = (h / 2.0) * (fFunc.Calculate(h * (i + 1) - (h / 2.0)) + fFunc.Calculate(h * (i + 1) + (h / 2.0)));
}
res[N - 1] = (h / 2.0) * (fFunc.Calculate(h * N - (h / 2.0))) /*- q*/;
return(res);
}
private double[] GenerateFVector()
{
MathExpression fFunc = new MathExpression(fFunction);
double h = 1.0 / n;
double[] res = new double[n];
for (int i = 0; i < n - 1; i++)
{
res[i] = (h / 2.0) * (fFunc.Calculate(h * (i + 1) - (h / 2.0)) + fFunc.Calculate(h * (i + 1) + (h / 2.0)));
}
res[n - 1] = (h / 2.0) * (fFunc.Calculate(h * n - (h / 2.0))) - q;
return(res);
}
public static double Calculate(double a, double b, int amountOfPartitions, MathExpression function, params Var[] variables)
{
List <double> Xk = new List <double>()
{
-0.8611363, -0.3399810, 0.3399810, 0.8611363
};
List <double> Ck = new List <double>()
{
0.3478548, 0.6521452, 0.6521452, 0.3478548
};
double result = 0;
double step = (b - a) / amountOfPartitions;
for (int i = 0; i < amountOfPartitions; i++)
{
double a_new = a + step * i;
double b_new = a + step * (i + 1);
double sum = 0;
for (int j = 0; j < Xk.Count; j++)
{
variables[0].Value = (a_new + b_new) / 2.0 + (b_new - a_new) / 2.0 * Xk[j];
sum += Ck[j] * function.Calculate(variables);
}
result += sum * (b_new - a_new) / 2.0;
}
return(result);
}
private double GetENormSquared(double q1, double q2, double h, double x1)
{
double midPoint = x1 + h / 2.0;
MathExpression muFunc = new MathExpression(muFunction);
MathExpression betaFunc = new MathExpression(betaFunction);
MathExpression sigmaFunc = new MathExpression(sigmaFunction);
MathExpression fFunc = new MathExpression(fFunction);
double qPrime = (q2 - q1) / h;
double qMiddle = (q2 + q1) / 2.0;
double Pe = h * betaFunc.Calculate(midPoint) / muFunc.Calculate(midPoint);
double sh = h * h * sigmaFunc.Calculate(midPoint) / muFunc.Calculate(midPoint);
double result = (5.0 / 6.0) * Math.Pow(h, 3.0) * Math.Pow(fFunc.Calculate(midPoint) - qPrime * betaFunc.Calculate(midPoint) - sigmaFunc.Calculate(midPoint) * qMiddle, 2.0)
/ (muFunc.Calculate(midPoint) * (10 + Pe * sh));
return(result);
}
public static double Integrate(MathExpression function, double lowerBound, double higherBound)
{
double h = (higherBound - lowerBound) / percision;
double result = 0;
for (double i = lowerBound; i <= higherBound; i += h)
{
double a = function.Calculate(i);
double b = function.Calculate(i + h);
double S = ((a + b) / 2) * h;
result += S;
}
return(result);
}
private double[] GenerateFVector(double[] mesh)
{
MathExpression fFunc = new MathExpression(fFunction);
double[] res = new double[mesh.Length - 1];
double h = 0.0;
for (int i = 1; i < res.Length; i++)
{
h = Math.Abs(mesh[i] - mesh[i - 1]);
double hNext = Math.Abs(mesh[i + 1] - mesh[i]);
res[i - 1] = (h / 2.0) * fFunc.Calculate(mesh[i] - (h / 2.0)) + (hNext / 2.0) * fFunc.Calculate(mesh[i] + (hNext / 2.0));
}
h = mesh[mesh.Length - 1] - mesh[mesh.Length - 2];
res[res.Length - 1] = (h / 2.0) * (fFunc.Calculate(mesh[mesh.Length - 1] - (h / 2.0)));
return(res);
}
private double GetValueOnElement(double x1, double x2, double q1, double q2)
{
double h = Math.Abs(x1 - x2) / 2.0;
double midPoint = x1 + h / 2.0;
MathExpression muFunc = new MathExpression(muFunction);
MathExpression betaFunc = new MathExpression(betaFunction);
MathExpression sigmaFunc = new MathExpression(sigmaFunction);
MathExpression fFunc = new MathExpression(fFunction);
double mu = muFunc.Calculate(midPoint);
double beta = betaFunc.Calculate(midPoint);
double sigma = sigmaFunc.Calculate(midPoint);
double f = fFunc.Calculate(midPoint);
double pe = h * beta / mu;
double sh = h * h * sigma / mu;
double qPrime = Math.Abs(q2 - q1) / h;
double qVal = (q2 + q1) / 2.0;
return((Math.Pow(h, 3.0) * Math.Pow((fFunc.Calculate(midPoint) - beta * qPrime - sigma * qVal), 2.0)) / (mu * (10 + pe * sh)));
}
public List <double> Generate(double[] mesh)
{
MathExpression fFunc = new MathExpression(_presizeFunction);
List <double> results = new List <double>();
for (int i = 0; i < mesh.Length; i++)
{
results.Add(fFunc.Calculate(mesh[i]));
}
return(results);
}
public static List <double> Calculate_Fj(string func, List <double> points)
{
List <double> result = new List <double>();
MathExpression function = new MathExpression(func);
for (int i = 0; i < points.Count; i++)
{
result.Add(function.Calculate(points[i]));
}
return(result);
}
private void buttonCalculateExpr_Click(object sender, RoutedEventArgs e)
{
listBoxTokens.Items.Clear();
textBoxReversePolishNotation.Clear();
textBoxResult.Clear();
string input = textBoxInput.Text;
MathExpression expr = new MathExpression(input);
foreach (Token t in expr.Tokens)
{
listBoxTokens.Items.Add(t);
}
foreach (Token t in expr.ReversePolishNotation)
{
textBoxReversePolishNotation.Text += t.Lexeme;
}
double result = 0;
if (textBoxVar.Text != "")
{
double var = double.Parse(textBoxVar.Text);
result = expr.Calculate(var);
}
else
{
result = expr.Calculate();
}
textBoxResult.Text = result.ToString();
MathExpression expr2 = new MathExpression("1/(x*y)");
MessageBox.Show(expr2.Calculate(new Var("x", 2), new Var("y", 5)).ToString());
}
private void buttonCalculate_Click(object sender, RoutedEventArgs e)
{
var x = 2;
var formula1 = new MathExpression("40");
var formula2 = new MathExpression("40*x");
var formula3 = new MathExpression("40 * x");
var formula4 = new MathExpression("3*x^2");
var res1 = formula1.Calculate(x);
var res2 = formula2.Calculate(x);
var res3 = formula3.Calculate(x);
var res4 = formula4.Calculate(x);
try
{
var N = int.Parse(textBoxN.Text);
var miu = new MathExpression(fixMinus(textBoxMuFunction.Text));
var beta = new MathExpression(fixMinus(textBoxBetaFunction.Text));
var sigma = new MathExpression(fixMinus(textBoxSigmaFunction.Text));
var f = new MathExpression(fixMinus(textBoxFFunction.Text));
var calculator = new Calculator_MSE(miu, beta, sigma, f, -1.0, 1.0, 0.0, 0.0);
var result = calculator.CalculateApproximation(N);
var points = new List <Point>();
for (int i = 0; i < result.XValues.Length; i++)
{
points.Add(new Point(result.XValues[i], result.UValues[i]));
}
drawGraphic(points, "u(x)");
}
catch (Exception exc)
{
MessageBox.Show(exc.Message);
}
buttonClear.IsEnabled = true;
}
public void ComplexExpressionTest2()
{
expr = new MathExpression("sin(pi/2)+(x+2)*5");
Assert.AreEqual(21, expr.Calculate(2));
}
public void SeveralVariablesTest4()
{
MathExpression expr = new MathExpression("1/(x*y)");
Assert.AreEqual(0.1, expr.Calculate(2, 5));
}
private CalculationResult CalculateApproximation(int N, double[] discret_x)
{
double[] L = new double[N];
double[][] A = new double[N][];
for (int i = 0; i < N; i++)
{
A[i] = new double[N];
if (i > 0)
{
Func <double, double> a__i_minus_1__i = new Func <double, double>((x) =>
{
double phi_i = kurant_function(i, x);
double phi_i_minus_1 = kurant_function(i - 1, x);
double derivative_phi_i = derivative_kurant_function(i, x);
double derivative_phi_i_minus_1 = derivative_kurant_function(i - 1, x);
return(_miu.Calculate(x) * derivative_phi_i_minus_1 * derivative_phi_i +
_beta.Calculate(x) * derivative_phi_i_minus_1 * phi_i +
_sigma.Calculate(x) * phi_i_minus_1 * phi_i);
});
A[i][i - 1] = IntegralCalculator.Integrate(a__i_minus_1__i, discret_x[i - 1], discret_x[i]);
}
Func <double, double> a__i__i = new Func <double, double>((x) =>
{
double phi_i = kurant_function(i, x);
double derivative_phi_i = derivative_kurant_function(i, x);
return(_miu.Calculate(x) * derivative_phi_i * derivative_phi_i +
_beta.Calculate(x) * derivative_phi_i * phi_i +
_sigma.Calculate(x) * phi_i * phi_i);
});
A[i][i] = IntegralCalculator.Integrate(a__i__i, i > 0 ? discret_x[i - 1] : _a, (i < N - 1) ? discret_x[i + 1] : _b);
if (i < N - 1)
{
Func <double, double> a__i__i_plus_1 = new Func <double, double>((x) =>
{
double phi_i = kurant_function(i, x);
double phi_i_plus_1 = kurant_function(i + 1, x);
double derivative_phi_i = derivative_kurant_function(i, x);
double derivative_phi_i_plus_1 = derivative_kurant_function(i + 1, x);
return(_miu.Calculate(x) * derivative_phi_i * derivative_phi_i_plus_1 +
_beta.Calculate(x) * derivative_phi_i * phi_i_plus_1 +
_sigma.Calculate(x) * phi_i * phi_i_plus_1);
});
A[i][i + 1] = IntegralCalculator.Integrate(a__i__i_plus_1, discret_x[i], discret_x[i + 1]);
}
Func <double, double> l_func = new Func <double, double>((x) => _f.Calculate(x) * kurant_function(i, x));
L[i] = IntegralCalculator.Integrate(l_func, _a, _b) /*+ _ua * _miu.Calculate(1) * kurant_function(i, 1)*/;
}
//A = GenerateAMatrix(N, _miu, _beta, _sigma);
//L = GenerateFVector(N, _f);
double[] q = MatrixCalculation.ProhoncaCalculation(A, L);
var res = new Func <double, double>(x =>
{
var sum = 0.0;
for (int i = 0; i < N; i++)
{
sum += (q[i] * kurant_function(i, x));
}
return(_ua + sum);
});
var resVec = new double[N];
for (int i = 0; i < N; i++)
{
if (i == N - 1)
{
resVec[i] = 0.0;
}
else
{
resVec[i] = res(discret_x[i]);
}
}
return(new CalculationResult(discret_x, resVec));
double kurant_function(int i, double x)
{
if (i == 0)
{
return(0);
}
if (i == N - 1)
{
return(0);
}
if (x >= _a && x <= discret_x[i - 1])
{
return(0);
}
else if (x > discret_x[i - 1] && x <= discret_x[i])
{
return((x - discret_x[i + 1]) / (discret_x[i + 1] - discret_x[i]));
//return ((x - discret_x[i - 1]) / (discret_x[i + 1] - discret_x[i]));
}
else if (x > discret_x[i] && x <= discret_x[i + 1])
{
return(1 - ((x - discret_x[i + 1]) / (discret_x[i + 1] - discret_x[i])));
//return ((discret_x[i + 1] - x) / (discret_x[i + 1] - discret_x[i]));
}
else
{
return(0);
}
}
double derivative_kurant_function(int i, double x)
{
if (i == 0)
{
return(0);
}
else if (i == N - 1)
{
return(0);
}
else if (x >= _a && x <= discret_x[i - 1])
{
return(0);
}
else if (x > discret_x[i - 1] && x <= discret_x[i])
{
return(1 / (discret_x[i + 1] - discret_x[i]));
}
else if (x > discret_x[i] && x <= discret_x[i + 1])
{
return(-(1 / (discret_x[i + 1] - discret_x[i])));
}
else
{
return(0);
}
}
}
public void SimpleTest2()
{
MathExpression expr = new MathExpression("x");
Assert.AreEqual(2, expr.Calculate(2));
}
public void SeveralVariablesTest5()
{
MathExpression expr = new MathExpression("x*y+y*z+z*x");
Assert.AreEqual(11, expr.Calculate(1, 2, 3));
}
public void SimpleTest3()
{
MathExpression expr = new MathExpression("x");
Assert.AreEqual(0.1, expr.Calculate(0.1));
}
public void PlusTest2()
{
expr = new MathExpression("x+2");
Assert.AreEqual(5, expr.Calculate(3));
}
public void MinusTest3()
{
expr = new MathExpression("sin(x)-2");
Assert.AreEqual(-1, expr.Calculate(Math.PI / 2));
}
public void MinusTest2()
{
expr = new MathExpression("x-2");
Assert.AreEqual(1, expr.Calculate(3));
}
public void MultiplicationTest2()
{
expr = new MathExpression("x*2");
Assert.AreEqual(6, expr.Calculate(3));
}
public double Sigma(double x)
{
return(_sigma.Calculate(x));
}
public double Mu(double x)
{
return(_mu.Calculate(x));
}
public void ComplexExpressionTest1()
{
expr = new MathExpression("x^2+2*x+1");
Assert.AreEqual(9, expr.Calculate(2));
}
public void DivisionTest2()
{
expr = new MathExpression("x/2");
Assert.AreEqual(5, expr.Calculate(10));
}
public double Beta(double x)
{
return(_beta.Calculate(x));
}
public void ComplexExpressionTest3()
{
expr = new MathExpression("abs(2-4)+tg(pi)");
Assert.AreEqual(2, expr.Calculate());
}
public double F(double x)
{
return(_f.Calculate(x));
}
public void ComplexExpressionTest4()
{
expr = new MathExpression("x^2 + 2,5");
Assert.AreEqual(6.5, expr.Calculate(2));
}