Init(
double a,
double b,
IList <double> x
)
{
if (null == x)
{
throw new ArgumentNullException("x");
}
if (x.Count < 1)
{
throw new ArgumentOutOfRangeException("x");
}
if (b <= a)
{
throw new ArgumentOutOfRangeException("b");
}
_transformSummand = -0.5 * (a + b);
_transformFactor = 2.0 / (b - a);
// trigonometric recurrence
double a0 = 0.0;
double delta = Math.PI / (x.Count - 1);
double alpha = Math.Sin(delta / 2);
alpha = 2 * alpha * alpha;
double beta = Math.Sin(delta);
double ca = Math.Cos(a0);
double sa = Math.Sin(a0);
double sign = 1.0;
// construct chebyshev points and barycentric weights
double[] t = new double[x.Count];
double[] w = new double[x.Count];
t[0] = ca;
w[0] = 0.5;
for (int i = 1; i < t.Length; i++)
{
double temps = sa - (alpha * sa - beta * ca);
double tempc = ca - (alpha * ca + beta * sa);
sa = temps;
ca = tempc;
sign = -sign;
t[i] = ca;
w[i] = sign;
}
w[w.Length - 1] *= 0.5;
_barycentric.Init(t, x, w);
}
Init(
double a,
double b,
IList <double> x
)
{
if (null == x)
{
throw new ArgumentNullException("x");
}
if (x.Count < 1)
{
throw new ArgumentOutOfRangeException("x");
}
if (b <= a)
{
throw new ArgumentOutOfRangeException("b");
}
// construct equidistant points
double[] t = new double[x.Count];
t[0] = a;
double step = (b - a) / (t.Length - 1);
for (int i = 1; i < t.Length; i++)
{
t[i] = t[i - 1] + step;
}
// construct barycentric weights
double[] w = new double[x.Count];
w[0] = 1.0;
for (int i = 1; i < w.Length; i++)
{
w[i] = -(w[i - 1] * (w.Length - i)) / i;
}
_barycentric.Init(t, x, w);
}
Init(
IList <double> t,
IList <double> x,
int order
)
{
if (null == t)
{
throw new ArgumentNullException("t");
}
if (null == x)
{
throw new ArgumentNullException("x");
}
if (t.Count < 1)
{
throw new ArgumentOutOfRangeException("t");
}
if (t.Count != x.Count)
{
throw new ArgumentException(Properties.Resources.ArgumentVectorsSameLengths);
}
if (0 > order || t.Count < order)
{
throw new ArgumentOutOfRangeException("order");
}
double[] ww = new double[x.Count];
double[] tt = new double[t.Count];
t.CopyTo(tt, 0);
// order: odd -> negative, even -> positive
double sign = ((order & 0x1) == 0x1) ? -1.0 : 1.0;
// init permutation vector
int[] perm = new int[ww.Length];
for (int i = 0; i < perm.Length; i++)
{
perm[i] = i;
}
// sort and update permutation vector
for (int i = 0; i < perm.Length - 1; i++)
{
for (int j = i + 1; j < perm.Length; j++)
{
if (tt[j] < tt[i])
{
double s = tt[i];
tt[i] = tt[j];
tt[j] = s;
int k = perm[i];
perm[i] = perm[j];
perm[j] = k;
}
}
}
// compute barycentric weights
for (int k = 0; k < ww.Length; k++)
{
// Wk
double s = 0;
for (int i = Math.Max(k - order, 0); i <= Math.Min(k, ww.Length - 1 - order); i++)
{
double v = 1;
for (int j = i; j <= i + order; j++)
{
if (j != k)
{
v = v / Math.Abs(tt[k] - tt[j]);
}
}
s = s + v;
}
ww[k] = sign * s;
sign = -sign;
}
// reorder back to original order, based on the permutation vector.
double[] w = new double[ww.Length];
for (int i = 0; i < w.Length; i++)
{
w[perm[i]] = ww[i];
}
_barycentric.Init(t, x, w);
}
