/// <summary>
/// Differentiation of a one dimensional function after <c>f.Parameters[n]</c>.
/// </summary>
public static double dfdp(IParametricFunction2D f, double x, double y, int n, out double abserr)
{
// adapted from gsl_diff_central
/* Construct a divided difference table with a fairly large step
* size to get a very rough estimate of f'''. Use this to estimate
* the step size which will minimize the error in calculating f'. */
IList <double> p = f.Parameters;
int i, k;
double h = GSL_SQRT_DBL_EPSILON, a3, temp, pn = p[n], f0, f1;
double[] a = new double[4], d = new double[4];
/* Algorithm based on description on pg. 204 of Conte and de Boor
* (CdB) - coefficients of Newton form of polynomial of degree 3. */
for (i = 0; i < 4; i++)
{
a[i] = pn + (i - 2) * h;
p[n] = a[i];
d[i] = f.f(x, y);
p[n] = pn;
}
for (k = 1; k < 5; k++)
{
for (i = 0; i < 4 - k; i++)
{
d[i] = (d[i + 1] - d[i]) / (a[i + k] - a[i]);
}
}
/* Adapt procedure described on pg. 282 of CdB to find best
* value of step size. */
a3 = Math.Abs(d[0] + d[1] + d[2] + d[3]);
if (a3 < 100 * GSL_SQRT_DBL_EPSILON)
{
a3 = 100 * GSL_SQRT_DBL_EPSILON;
}
h = Math.Pow(GSL_SQRT_DBL_EPSILON / (2 * a3), 1.0 / 3.0);
if (h > 100 * GSL_SQRT_DBL_EPSILON)
{
h = 100 * GSL_SQRT_DBL_EPSILON;
}
abserr = Math.Abs(100.0 * a3 * h * h);
temp = pn + h;
GetH(pn, ref h, temp);
p[n] = pn + h;
f0 = f.f(x, y);
p[n] = pn - h;
f1 = f.f(x, y);
return((f0 - f1) / (2 * h));
}
/// <summary>
/// An alias for the routine dfdp.
/// </summary>
public static double diffp(IParametricFunction2D f, double x, double y, int n, out double abserr)
{
return(dfdp(f, x, y, n, out abserr));
}
