public static CubicSplain CreateCubicSpline(List <double> x_s,
List <double> y_s)
{
List <double> h = new List <double>();
List <double> b = new List <double>();
List <double> v = new List <double>();
List <double> u = new List <double>();
for (int i = 0; i < x_s.Count - 1; ++i)
{
h.Add(x_s[i + 1] - x_s[i]);
b.Add((y_s[i + 1] - y_s[i]) / h.Last());
}
for (int i = 1; i < x_s.Count - 1; ++i)
{
v.Add(2.0 * (h[i - 1] + h[i]));
u.Add(6.0 * (b[i] - b[i - 1]));
}
//выбрать только внутренние значения, игнорим первую и последнюю
List <double> sliced_h =
h.Skip(1).Take(h.Count - 2).ToList();
var result = SolveTridiagonal(sliced_h, v, sliced_h, u);
//первая производная точки равны 0
List <double> z = new List <double>();
z.Add(0.0);
z = z.Concat(result).ToList();
z.Add(0.0);
List <CubicSection> sections = new List <CubicSection>();
for (int i = 0; i < z.Count - 1; ++i)
{
double cBegin = z[i + 1] / (6.0 * h[i]);
double cEnd = z[i] / (6.0 * h[i]);
double lBegin = y_s[i + 1] / h[i] - z[i + 1] * h[i] / 6.0;
double lEnd = y_s[i] / h[i] - h[i] * z[i] / 6.0;
double tBegin = x_s[i];
double tEnd = x_s[i + 1];
sections.Add(new CubicSection(cBegin,
cEnd,
lBegin,
lEnd,
tBegin,
tEnd));
}
CubicSplain cubicSplain = new CubicSplain(x_s,
sections);
return(cubicSplain);
}
public static CubicSplain CreateCubicSplineSecond(List <double> x_s,
List <double> y_s)
{
int n = x_s.Count;
List <double> h = new List <double>();
List <double> b = new List <double>();
List <double> v = new List <double>();
List <double> u = new List <double>();
for (int i = 0; i < n - 1; ++i)
{
h.Add(x_s[i + 1] - x_s[i]);
b.Add((y_s[i + 1] - y_s[i]) / h.Last());
}
for (int i = 1; i < n - 1; ++i)
{
v.Add(2.0 * (h[i - 1] + h[i]));
u.Add(6.0 * (b[i] - b[i - 1]));
}
v[0] = 1.5 * h[0] + 2.0 * h[1];
v[v.Count - 1] = 1.5 * h[h.Count() - 2] + 2.0 * h[h.Count() - 1];
u[0] = u[0] - 3.0 * b[0];
u[u.Count - 1] = u[u.Count() - 1] + 3.0 * b.Last();
List <double> sliced_h = h.Skip(1).Take(h.Count() - 2).ToList();
List <double> res = SolveTridiagonal(sliced_h, v, sliced_h, u);
List <double> z = new List <double>();
z.Add(0.5 * (6.0 * b.First() / h.First() - res.First()));
z = z.Concat(res).ToList();
z.Add(-0.5 * (6.0 * b.Last() / h.Last() + res.Last()));
List <CubicSection> sections = new List <CubicSection>();
for (int i = 0; i < z.Count() - 1; ++i)
{
double cBegin = z[i + 1] / (6.0 * h[i]);
double cEnd = z[i] / (6.0 * h[i]);
double lBegin = y_s[i + 1] / h[i] - z[i + 1] * h[i] / 6.0;
double lEnd = y_s[i] / h[i] - h[i] * z[i] / 6.0;
double tBegin = x_s[i];
double tEnd = x_s[i + 1];
CubicSection cubicSection = new CubicSection(cBegin,
cEnd,
lBegin,
lEnd,
tBegin,
tEnd);
sections.Add(cubicSection);
}
CubicSplain cubicSplain = new CubicSplain(x_s,
sections);
return(cubicSplain);
}