public static Polynomial Lagrange(DomainType[] x, DomainType[] y)
{
if (x.Length != y.Length)
{
throw new System.ArgumentException("x と y の次数は等しくなければいけません。");
}
int len = x.Length;
Polynomial p = (Polynomial)(CoefType)0.0;
Polynomial X = Polynomial.X(1);
for (int i = 0; i < len; ++i)
{
Polynomial q = (Polynomial)(CoefType)y[i];
for (int j = 0; j < len; ++j)
{
if (i == j)
{
continue;
}
Polynomial temp = (X - (CoefType)x[j]);
temp /= (x[i] - x[j]);
q *= (X - (CoefType)x[j]) / (x[i] - (CoefType)x[j]);
}
p += q;
}
return(p);
}
/// <summary>
/// チェビシェフ多項式を計算する。
/// </summary>
/// <param name="n">次数</param>
/// <returns>次数 n のチェビシェフ多項式</returns>
public static Polynomial Chebyshev(int n)
{
if (n == 0)
{
return(Polynomial.X(0, 1));
}
else if (n == 1)
{
return(Polynomial.X(1, 1));
}
return(Polynomial.X(1, 2) * Polynomial.Chebyshev(n - 1) - Polynomial.Chebyshev(n - 2));
}
/// <summary>
/// チェビシェフ有理式(elliptic rational)を計算する。
/// </summary>
/// <param name="n">次数</param>
/// <param name="l">x > 1 における極小値</param>
/// <returns>次数 n のチェビシェフ有理式</returns>
public static Rational Elliptic(int n, double l)
{
double m1 = 1 / (l * l);
double m1p = 1 - m1;
double Kk1 = Ellip.K(m1);
double Kk1p = Ellip.K(m1p);
double m = Ellip.InverseQ(Math.Exp(-Math.PI * Kk1p / (n * Kk1)));
double Kk = Ellip.K(m);
Polynomial num = Polynomial.X(0, 1);
Polynomial denom = Polynomial.X(0, 1);
Rational r = new Rational(Polynomial.X(0, 1), Polynomial.X(0, 1));
double g = 1;
for (int i = n - 1; i > 0; i -= 2)
{
double u = Kk * (double)i / n;
double sn = Ellip.Sn(u, m);
double w = sn * sn;
g *= (m * w - 1) / (1 / w - 1);
num *= Polynomial.X(2, 1 / w) - 1;
denom *= Polynomial.X(2, m * w) - 1;
}
if ((n & 1) == 1)
{
num *= Polynomial.X(1);
}
num *= g;
return(new Rational(num, denom));
}
/// <summary>
/// x の n 乗を返す。
/// </summary>
/// <param name="n">指数</param>
/// <returns>x の n 乗</returns>
public static Polynomial X(int n)
{
return(Polynomial.X(n, 1));
}
