/// <summary>
/// n >= 1, r >= 1.
/// Common definition of sobolev function by integrals is used.
/// And to calc integrals rectangular formula is used .
/// </summary>
/// <param name="r"></param>
/// <param name="n"></param>
/// <returns></returns>
public static Func <double, double> MixedHaarByDef(int r, int n)
{
if (n <= r)
{
var fact = Factorial(n - 1);
return(x => Pow(x, n - 1) / fact);
}
var c = 1 / Factorial(r - 1);
var haarFunc = Haar(n - r);
return(x => c *Integrals.Rectangular(t => Pow(x - t, r - 1) *haarFunc(t), 0, x, 10000, Integrals.RectType.Center));
}
public static double[] Decomposition(Func <double, double> func, int n)
{
double[] result = new double[n];
var(k, j) = Common.Decompose(n);
double[] a = new double[1 << (k + 1)];
for (int i = 1; i <= a.Length / 2; i++)
{
double[] edge = new double[3];
double pow2k = Math.Pow(2, k);
double pow2k2 = Math.Pow(2, (k + 1) / 2.0);
edge[0] = (i - 1.0) / pow2k;
edge[1] = (2 * i - 1.0) / ((int)pow2k << 1);
edge[2] = i / pow2k;
a[2 * i - 2] = pow2k2 * Integrals.Rectangular(func, edge[0], edge[1], 2, Integrals.RectType.Center);
a[2 * i - 1] = pow2k2 * Integrals.Rectangular(func, edge[1], edge[2], 2, Integrals.RectType.Center);
}
double sqrt2 = Math.Sqrt(2);
for (int i = 1; i <= j; i++)
{
result[(int)Math.Pow(2, k) + i - 1] = (a[2 * i - 2] - a[2 * i - 1]) / sqrt2;
}
for (int i = 1; i <= Math.Pow(2, k); i++)
{
a[i - 1] = (a[2 * i - 2] + a[2 * i - 1]) / sqrt2;
}
for (int l = k - 1; l >= 0; l--)
{
int pow2l = (int)Math.Pow(2, l);
for (int i = 1; i <= pow2l; i++)
{
result[pow2l + i - 1] = (a[2 * i - 2] - a[2 * i - 1]) / sqrt2;
a[i - 1] = (a[2 * i - 2] + a[2 * i - 1]) / sqrt2;
}
}
result[0] = a[0];
return(result);
}
