// cos(x/2) ^ 2
// (1/2)*(x+sin(x))
//
//
private void integrate()
{
double a = double.Parse(intervalA.Text);
double b = double.Parse(intervalB.Text);
double eps = double.Parse(epsilon.Text);
if (eps >= 1 || eps < 0)
{
throw new Exception("Epsilon must me between 0 and 1");
}
double exactValue = MyParser.calculate(original.Text, b) - MyParser.calculate(original.Text, a);
_dummyCollection.Clear();
foreach (NumericalIntegration method in methods)
{
KeyValuePair <double, int> res = method.CalculateIntegral(a, b, eps, function.Text);
double error = Math.Abs(res.Key - exactValue);
_dummyCollection.Add(new IntegrateResult {
Method = method.ToString(), Value = res.Key, Intervals = res.Value, Error = string.Format("{0:0.########}", error)
});
}
_dummyCollection.Add(new IntegrateResult {
Method = "Exact value", Value = exactValue
});
dataGrid1.ItemsSource = _dummyCollection;
}
protected override double Calculate(double a, double b, int n, string integral)
{
double res = 0;
double A = (b - a) / 2;
double B = (b + a) / 2;
double[] x = GaussLegendre.arr[25].x;
double[] w = GaussLegendre.arr[25].w;
for (int i = 0; i < GaussLegendre.arr.Length; i++)
{
if (GaussLegendre.arr[i].n == n)
{
x = GaussLegendre.arr[i].x;
w = GaussLegendre.arr[i].w;
}
}
if (n % 2 == 1)
{
res = w[0] * MyParser.calculate(integral, B);
for (int i = 1; i < x.Length; i++)
{
res += w[i] * (MyParser.calculate(integral, B + A * x[i]) + MyParser.calculate(integral, B - A * x[i]));
}
}
else
{
for (int i = 0; i < x.Length; i++)
{
res += w[i] * (MyParser.calculate(integral, B + A * x[i]) + MyParser.calculate(integral, B - A * x[i]));
}
}
return(A * res);
}
protected override double Calculate(double a, double b, int n, string integral)
{
double res = 0;
double h = (b - a) / n;
for (int i = 1; i <= n; ++i)
{
res += MyParser.calculate(integral, (a + i * h));
}
res *= h;
return(res);
}
protected override double Calculate(double a, double b, int n, string integral)
{
double res = 0;
double h = (b - a) / n;
bool even = false;
for (int i = 1; i < n; ++i)
{
res += (even ? 2 : 4) * MyParser.calculate(integral, (a + i * h));
even = !even;
}
res += MyParser.calculate(integral, a) + MyParser.calculate(integral, b);
res *= h / 3;
return(res);
}
//public override KeyValuePair<double, int> CalculateIntegral(double a, double b, double eps, string integral)
//{
// int n = 3;
// double i1 = Calculate(a, b, n, integral);
// double i2 = 0;
// int k = 2;
// do
// {
// i2 = 0;
// for (int i = 0; i < k; i++)
// {
// i2 += Calculate(a + i * (b - a) / k, a + (i + 1) * (b - a) / k, n, integral);
// }
// double tmp = i2;
// i2 = i1;
// i1 = tmp;
// k++;
// } while (Math.Abs(i1 - i2) >= eps);
// return new KeyValuePair<double, int>(i1, k);
//}
protected override double Calculate(double a, double b, int n, string integral)
{
if (n == 8 || n > 9)
{
n = 9;
}
double res = 0;
double A = (b - a) / 2;
double B = (b + a) / 2;
double[] x = ChebyshevCoefs.arr[7].x;
for (int i = 0; i < ChebyshevCoefs.arr.Length; i++)
{
if (ChebyshevCoefs.arr[i].n == n)
{
x = ChebyshevCoefs.arr[i].x;
}
}
for (int i = 0; i < x.Length; i++)
{
res += MyParser.calculate(integral, A * x[i] + B);
}
return(2 * res * A / n);
}
