|
public static Interpolate ( double xs, double ys, int n, int offset, double x ) : |
||
| xs | double | |
| ys | double | |
| n | int | |
| offset | int | |
| x | double | |
| return | ||
/// <summary>
/// Romberg - adapted from "Numerical Recipes in C"
/// </summary>
/// <param name="min"></param>
/// <param name="max"></param>
/// <returns></returns>
public double Romberg(double min, double max)
{
int MAX = 20;
double TOLERANCE = 1e-7;
int K = 4;
double[] s = new double[MAX + 1];
double[] h = new double[MAX + 1];
ValueWithError result = new ValueWithError(0, 0);
h[0] = 1.0;
for (int j = 1; j <= MAX; j++)
{
s[j - 1] = Trapezoid(min, max, j);
if (j >= K)
{
result = Polynomial.Interpolate(h, s, K, j - K, 0.0);
if (Math.Abs(result.Error) < TOLERANCE * result.Value)
{
break;
}
}
s[j] = s[j - 1];
h[j] = 0.25 * h[j - 1];
}
return(result.Value);
}
/// <summary>
/// Integrate the polynomial function from <paramref name="min"/> to <paramref name="min"/> using the Romberg rule.
/// </summary>
/// <param name="min">The lower limit of the integrate range.</param>
/// <param name="max">The upper limit of the integrate range.</param>
/// <returns></returns>
/// <remarks>Romberg - adapted from "Numerical Recipes in C"</remarks>
public double Romberg(double min, double max)
{
int maxCount = 20;
int K = 4;
double[] s = new double[maxCount + 1];
double[] h = new double[maxCount + 1];
Tuple <double, double> result = Tuple.Create(0d, 0d);
h[0] = 1.0;
for (int j = 1; j <= maxCount; j++)
{
s[j - 1] = Trapezoid(min, max, j);
if (j >= K)
{
result = Polynomial.Interpolate(h, s, K, j - K, 0.0);
if (Math.Abs(result.Item2) < Tolerance * result.Item1)
{
break;
}
}
s[j] = s[j - 1];
h[j] = 0.25 * h[j - 1];
}
return(result.Item1);
}