| public static Phi ( double u, double m ) : double | ||
| u | double | 引数 u |
| m | double | 率 k の2乗 |
| return | double | |
/// <summary>
/// Jacobi の楕円関数 cn u を求める。
/// </summary>
/// <param name="u">引数 u</param>
/// <param name="m">率 k の2乗</param>
/// <returns>cn(u, k)</returns>
public static double Cn(double u, double m)
{
if (m < 0.0 || m > 1.0)
{
return(double.NaN);
}
return(Math.Cos(Elliptic.Phi(u, m)));
}
/// <summary>
/// Jacobi の楕円関数(引数 u と率 k から振幅φおよび sn, cn, dn)を求める。
/// </summary>
/// <param name="u">引数 u</param>
/// <param name="m">率 k の2乗</param>
/// <param name="phi">振幅φ</param>
/// <param name="sn">sn(u, k)</param>
/// <param name="cn">cn(u, k)</param>
/// <param name="dn">dn(u, k)</param>
public static void Jacobi(double u, double m, out double phi, out double sn, out double cn, out double dn)
{
if (m < 0.0 || m > 1.0)
{
phi = double.NaN;
sn = double.NaN;
cn = double.NaN;
dn = double.NaN;
return;
}
if (m < EPSILON)
{
double t = Math.Sin(u);
double b = Math.Cos(u);
double ai = 0.25 * m * (u - t * b);
phi = u - ai;
sn = t - ai * b;
cn = b + ai * t;
dn = 1.0 - 0.5 * m * t * t;
return;
}
if (m >= 1 - EPSILON)
{
double ai = 0.25 * (1.0 - m);
double b = Math.Cosh(u);
double t = Math.Tanh(u);
double binv = 1.0 / b;
double twon = b * Math.Sinh(u);
phi = 2.0 * Math.Atan(Math.Exp(u)) - Constant.PI2 + ai * (twon - u) / b;
sn = t + ai * (twon - u) / (b * b);
ai *= t * phi;
cn = binv - ai * (twon - u);
dn = binv + ai * (twon + u);
return;
}
phi = Elliptic.Phi(u, m);
Elliptic.Jacobi(phi, m, out sn, out cn, out dn);
}
