/**************************************************************************/
public Tuple<double, int> methodCombined(MathExpression function, MathExpression derivative, MathExpression secondDerivative, double epsilon, double left, double right)
{
int counter = 0;
double x0;
if (GetValue(function, left) * GetValue(secondDerivative, left) > 0)
{
x0 = left;
}
else
{
x0 = right;
}
if (GetValue(derivative, x0) * GetValue(secondDerivative, x0) > 0)
{
while (!(Math.Abs(left - right) < epsilon))
{
left = left - (GetValue(function, left) * (right - left)) / (GetValue(function, right) - GetValue(function, left));
right = right - GetValue(function, right) / GetValue(derivative, right);
counter++;
}
}
else
{
while (!(Math.Abs(left - right) < epsilon))
{
left = left - GetValue(function, left) / GetValue(derivative, left);
right = right - (GetValue(function, right) * (right - left)) / (GetValue(function, right) - GetValue(function, left));
counter++;
}
}
return new Tuple<double, int>((left + right) / 2, counter);
}
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());
}
/***************************************************************/
public Tuple<double, int> methodChords(MathExpression function, MathExpression secondDerivative, double epsilon, double left, double right)
{
int counter = 0;
double x0, result, c;
if (GetValue(function, left) * GetValue(secondDerivative, left) > 0)
{
c = left;
result = right;
}
else
{
c = right;
result = left;
}
do
{
x0 = result;
result = x0 - ((x0 - c) * GetValue(function, x0)) / (GetValue(function, x0) - GetValue(function, c));
counter++;
} while (Math.Abs(result - x0) > epsilon);
return new Tuple<double, int>(result, counter);
}
public void MinusTest3()
{
expr = new MathExpression("sin(x)-2");
Assert.AreEqual(-1, expr.Calculate(Math.PI / 2));
}
public void DivisionTest2()
{
expr = new MathExpression("x/2");
Assert.AreEqual(5, expr.Calculate(10));
}
public void ComplexExpressionTest6()
{
expr = new MathExpression("sin(pi/3.8)*ln(100500)+arctg(2)");
Console.WriteLine(expr.Calculate().ToString());
Assert.AreEqual(9.58115, expr.Calculate(), 0.00001);
}
public void ComplexExpressionTest3()
{
expr = new MathExpression("abs(2-4)+tg(pi)");
Assert.AreEqual(2, expr.Calculate());
}
public void ComplexExpressionTest1()
{
expr = new MathExpression("x^2+2*x+1");
Assert.AreEqual(9, expr.Calculate(2));
}
public void SimpleTest3()
{
MathExpression expr = new MathExpression("x");
Assert.AreEqual(0.1, expr.Calculate(0.1));
}
private void buttonCalculate_Click(object sender, EventArgs e)
{
MathExpression expr = new MathExpression(textBoxInitialFunction.Text.ToString());
double a = Convert.ToDouble(textBoxA.Text.ToString());
double b = Convert.ToDouble(textBoxB.Text.ToString());
string inital = (expr.Calculate(b) - expr.Calculate(a)).ToString();
if (radioButtonLeftRectangle.Checked)
{
int iteration = 1;
N = 4;
double I1 = funcLeftRectangle();
N *= 2;
double I2 = funcLeftRectangle();
double EPS = Convert.ToDouble(textBoxE.Text.ToString());
while (Math.Abs(I1 - I2) > EPS)
{
iteration++;
I1 = I2;
N *= 2;
I2 = funcLeftRectangle();
}
textBoxIntegral.Text = I1.ToString();
textBoxInitial.Text = inital;
textBoxIterations.Text = iteration.ToString();
}
/***********************************************************************************/
if (radioButtonRightRectangle.Checked)
{
int iteration = 1;
N = 4;
double I1 = funcRightRectangle();
N *= 2;
double I2 = funcRightRectangle();
double EPS = Convert.ToDouble(textBoxE.Text.ToString());
while (Math.Abs(I1 - I2) > EPS)
{
iteration++;
I1 = I2;
N *= 2;
I2 = funcRightRectangle();
}
textBoxIntegral.Text = I1.ToString();
textBoxInitial.Text = inital;
textBoxIterations.Text = iteration.ToString();
}
/***********************************************************************************/
if (radioButtonMidleRectangle.Checked)
{
int iteration = 1;
N = 4;
double I1 = funcMidleRectangle();
N *= 2;
double I2 = funcMidleRectangle();
double EPS = Convert.ToDouble(textBoxE.Text.ToString());
while (Math.Abs(I1 - I2) > EPS)
{
iteration++;
I1 = I2;
N *= 2;
I2 = funcMidleRectangle();
}
textBoxIntegral.Text = I1.ToString();
textBoxInitial.Text = inital;
textBoxIterations.Text = iteration.ToString();
}
/***********************************************************************************/
if (radioButtonTrapeze.Checked)
{
int iteration = 1;
N = 4;
double I1 = funcTrapeze();
N *= 2;
double I2 = funcTrapeze();
double EPS = Convert.ToDouble(textBoxE.Text.ToString());
while (Math.Abs(I1 - I2) > EPS)
{
iteration++;
I1 = I2;
N *= 2;
I2 = funcTrapeze();
}
textBoxIntegral.Text = I1.ToString();
textBoxInitial.Text = inital;
textBoxIterations.Text = iteration.ToString();
}
/***********************************************************************************/
if (radioButtonSimpson.Checked)
{
int iteration = 1;
N = 4;
double I1 = funcSimpson();
N *= 2;
double I2 = funcSimpson();
double EPS = Convert.ToDouble(textBoxE.Text.ToString());
while (Math.Abs(I1 - I2) > EPS)
{
iteration++;
I1 = I2;
N *= 2;
I2 = funcSimpson();
}
textBoxIntegral.Text = I1.ToString();
textBoxInitial.Text = inital;
textBoxIterations.Text = iteration.ToString();
}
/***********************************************************************************/
if (radioButtonThreeEighths.Checked)
{
int iteration = 1;
N = 4;
double I1 = funcThreeEighths();
N *= 2;
double I2 = funcThreeEighths();
double EPS = Convert.ToDouble(textBoxE.Text.ToString());
while (Math.Abs(I1 - I2) > EPS)
{
iteration++;
I1 = I2;
N *= 2;
I2 = funcThreeEighths();
}
textBoxIntegral.Text = I1.ToString();
textBoxInitial.Text = inital;
textBoxIterations.Text = iteration.ToString();
}
/***********************************************************************************/
if (radioButtonGaus.Checked)
{
int iteration = 1;
N = 4;
double I1 = funcGaus();
N *= 2;
double I2 = funcGaus();
double EPS = Convert.ToDouble(textBoxE.Text.ToString());
while (Math.Abs(I1 - I2) > EPS)
{
iteration++;
I1 = I2;
N *= 2;
I2 = funcGaus();
}
textBoxIntegral.Text = I1.ToString();
textBoxInitial.Text = inital;
textBoxIterations.Text = iteration.ToString();
}
/***********************************************************************************/
if (radioButtonChebyshev.Checked)
{
int iteration = 1;
N = 4;
double I1 = funcChebyshev();
N *= 2;
double I2 = funcChebyshev();
double EPS = Convert.ToDouble(textBoxE.Text.ToString());
while (Math.Abs(I1 - I2) > EPS)
{
iteration++;
I1 = I2;
N *= 2;
I2 = funcChebyshev();
}
textBoxIntegral.Text = I1.ToString();
textBoxInitial.Text = inital;
textBoxIterations.Text = iteration.ToString();
}
}
private double funcThreeEighths()
{
double a = Convert.ToDouble(textBoxA.Text.ToString());
double b = Convert.ToDouble(textBoxB.Text.ToString());
double h = (b - a) / (3 * N);
MathExpression expr = new MathExpression(textBoxFunction.Text.ToString());
double resault = expr.Calculate(a) + expr.Calculate(b);
for (int i = 1; i < 3 * N; i++)
{
a += h;
if (i % 3 == 0)
{
resault += 2 * expr.Calculate(a);
}
else
{
resault += 3 * expr.Calculate(a);
}
}
return resault * h * 3.0 / 8.0;
}
private double funcSimpson()
{
double a = Convert.ToDouble(textBoxA.Text.ToString());
double b = Convert.ToDouble(textBoxB.Text.ToString());
double h = (b - a) / N;
MathExpression expr = new MathExpression(textBoxFunction.Text.ToString());
double resault = expr.Calculate(a) + expr.Calculate(b);
for (int i = 0; i < N - 1; i++)
{
a += h;
if (i % 2 == 0)
{
resault += 4 * expr.Calculate(a);
}
else
{
resault += 2 * expr.Calculate(a);
}
}
return resault * h / 3.0;
}
private double funcRightRectangle()
{
double a = Convert.ToDouble(textBoxA.Text.ToString());
double b = Convert.ToDouble(textBoxB.Text.ToString());
double h = (b - a) / N;
MathExpression expr = new MathExpression(textBoxFunction.Text.ToString());
double resault = expr.Calculate(b);
for (int i = 0; i < N - 1; i++)
{
b -= h;
resault += expr.Calculate(b);
}
return resault * h;
}
private double funcGaus()
{
double a = Convert.ToDouble(textBoxA.Text.ToString());
double b = Convert.ToDouble(textBoxB.Text.ToString());
double h = (b - a) / N;
double[] coefs = new double[] { 0.478629, 0.236927, 0.568889, 0.236927, 0.478629 };
double[] points = new double[] { -0.9061800, -0.538469, 0, 0.538469, 0.9061800 };
MathExpression expr = new MathExpression(textBoxFunction.Text.ToString());
double resault = 0.0;
double left = a;
double right = a + h;
for (int i = 0; i < N; i++)
{
for(int j = 0; j < points.Length; j++)
{
resault += coefs[j] * expr.Calculate((left + right) / 2.0 + (right - left) / 2.0 * points[j]);
}
left = right;
right += h;
}
return resault * h / 2.0;
}
private double funcChebyshev()
{
double a = Convert.ToDouble(textBoxA.Text.ToString());
double b = Convert.ToDouble(textBoxB.Text.ToString());
double h = (b - a) / N;
double[] points = new double[] { 0.832498, 0.374541, 0, -0.374541, -0.832498 };
double coef = 2.0 / points.Length;
MathExpression expr = new MathExpression(textBoxFunction.Text.ToString());
double resault = 0.0;
double left = a;
double right = a + h;
for (int i = 0; i < N; i++)
{
for (int j = 0; j < points.Length; j++)
{
resault += (right - left) / points.Length * expr.Calculate((left + right) / 2.0 + (right - left) / 2.0 * points[j]);
}
left = right;
right += h;
}
return resault;
}
public void SeveralVariablesTest5()
{
MathExpression expr = new MathExpression("x*y+y*z+z*x");
Assert.AreEqual(11, expr.Calculate(1, 2, 3));
}
public void SimpleTest2()
{
MathExpression expr = new MathExpression("x");
Assert.AreEqual(2, expr.Calculate(2));
}
private double funcTrapeze()
{
double a = Convert.ToDouble(textBoxA.Text.ToString());
double b = Convert.ToDouble(textBoxB.Text.ToString());
double h = (b - a) / N;
MathExpression expr = new MathExpression(textBoxFunction.Text.ToString());
double resault = expr.Calculate(a) + expr.Calculate(b);
for (int i = 0; i < N - 1; i++ )
{
a += h;
resault += 2 * expr.Calculate(a);
}
return resault * h / 2.0;
}
public void UnaryMinusTest1()
{
expr = new MathExpression("-2+3");
Console.WriteLine(expr.ToString());
Assert.AreEqual(1, expr.Calculate());
}
public void MultiplicationTest2()
{
expr = new MathExpression("x*2");
Assert.AreEqual(6, expr.Calculate(3));
}
public void ComplexExpressionTest2()
{
expr = new MathExpression("sin(pi/2)+(x+2)*5");
Assert.AreEqual(21, expr.Calculate(2));
}
public void PlusTest2()
{
expr = new MathExpression("x+2");
Assert.AreEqual(5, expr.Calculate(3));
}
public void ComplexExpressionTest5()
{
expr = new MathExpression("x^ 2 + 2.5");
Assert.AreEqual(6.5, expr.Calculate(2));
}
public void SeveralVariablesTest1()
{
MathExpression expr = new MathExpression("x+y");
Assert.AreEqual(5, expr.Calculate(new Var("x", 2), new Var("y", 3)));
}
public void DerivativeTest()
{
MathExpression expr = new MathExpression("e^x+sin(x)");
Assert.AreEqual(2, expr.Derivative(0), 0.000001);
}
public void SeveralVariablesTest2()
{
MathExpression expr = new MathExpression("1/(x*y)");
Assert.AreEqual(0.1, expr.Calculate(new Var("x", 2), new Var("y", 5)));
}
public void MinusTest2()
{
expr = new MathExpression("x-2");
Assert.AreEqual(1, expr.Calculate(3));
}
public void SeveralVariablesTest3()
{
MathExpression expr = new MathExpression("x+y");
Assert.AreEqual(5, expr.Calculate(2, 3));
}
public void SeveralVariablesTest4()
{
MathExpression expr = new MathExpression("1/(x*y)");
Assert.AreEqual(0.1, expr.Calculate(2, 5));
}
public double GetValue(MathExpression function, double x)
{
return function.Calculate(x);
}
