/// <summary>
/// ニュートン法により、正の平方根を求める。虚数単位に対応。
/// </summary>
/// <param name="a">正の平方根を求めたい実数</param>
/// <returns></returns>
public static double[] Sqrt(double a)
{
double[] sqrt = new double[2];
double[] buf = new double[2] {
1, 1
};
double temp = 0;
if (a > 0)
{
while (temp != buf[0])
{
temp = buf[0];
buf[0] = (BinomialTheorem.RealExpo(buf[0], 2) + a) / (2 * buf[0]);
}
sqrt[0] = buf[0];
}
else if (a == 0)
{
return(sqrt);
}
else
{
a = (-1) * a;
while (temp != buf[1])
{
temp = buf[1];
buf[1] = (BinomialTheorem.RealExpo(buf[1], 2) + a) / (2 * buf[1]);
}
sqrt[1] = buf[1];
}
return(sqrt);
}
/// <summary>
/// ラジアンを入力すると正弦の値を返す。0 <= rad < 2PI
/// </summary>
/// <param name="rad">ラジアン</param>
/// <returns></returns>
public static double RadSine(double rad)
{
double Sine = 0;
double buf = 0;
if (rad == PI / 2)
{
return(1);
}
if (rad == PI / 6)
{
return(0.5);
}
if (rad == 0)
{
return(0);
}
if (Math.Floor(rad % PI) == rad % PI)
{
return(0);
}
for (int ic = 0; ic < 100; ic++)
{
buf += BinomialTheorem.RealExpo(-1, ic) * BinomialTheorem.RealExpo(rad, 2 * ic + 1) / BinomialTheorem.DoubleFactorial(2 * ic + 1);
}
Sine = buf;
return(Sine);
}
private double[] CreateSine()
{
Sine = new double[ComplexCount];
for (int ic = 0; ic < ComplexCount; ic++)
{
Sine[ic] = RealPrt[ic] / Math.Sqrt(BinomialTheorem.RealExpo(RealPrt[ic], 2) + BinomialTheorem.RealExpo(ImaginPrt[ic], 2));
}
return(Sine);
}
/// <summary>
/// 正弦の引数倍角の値を計算する。引数が2だったら2倍角、3だったら3倍角。
/// チェビシェフの公式を使用
/// </summary>
/// <param name="Num"></param>
private void NtimesAngleSine(int Num)
{
for (int select = 0; select < SelectedComplexes.Length; select++)
{
for (int ic = 0; ic <= Math.Floor((double)(Num - 1) / 2); ic++)
{
NtimesAngledSine[select] += BinomialTheorem.RealExpo(-1, ic) * BinomialTheorem.Combination(Num - ic - 1, ic) * BinomialTheorem.RealExpo(2 * Cosine[select - 1], Num - 2 * ic - 1);
}
}
}
/// <summary>
/// 自然対数の底の指数関数。マクローリン展開の収束半径が∞であることを利用。
/// </summary>
/// <param name="val">指数</param>
/// <returns></returns>
public double CreateNapierFunc(double val)
{
double Val = 0;
double buf = 0;
for (int ic = 0; ic < 1000; ic++)
{
buf += BinomialTheorem.RealExpo(val, ic) / BinomialTheorem.DoubleFactorial(ic);
}
Val = buf;
return(Val);
}
/// <summary>
/// 逆正接 連分数展開により求める。
/// </summary>
/// <param name="val"></param>
/// <returns></returns>
public static double Arctan(double val)
{
double arctan;
double buf = val;
double random = double.MaxValue;
for (int ic = 10000; ic >= 1; ic--)
{
buf = 2 * ic - 1 + (BinomialTheorem.RealExpo(ic, 2) * BinomialTheorem.RealExpo(val, 2)) / random;
random = buf;
}
arctan = val / buf;
return(arctan);
}
protected static void TellAbsandArg()
{
AbsandArg = new double[ComplexCount, 2];
for (int ic = 0; ic < ComplexCount; ic++)
{
double[] sqrtbuf = Sqrt(BinomialTheorem.RealExpo(ComplexNumber[ic, 0], 2) + BinomialTheorem.RealExpo(ComplexNumber[ic, 1], 2));
AbsandArg[ic, 0] = sqrtbuf[0];
if (ComplexNumber[ic, 0] > 0 && ComplexNumber[ic, 1] > 0)
{
AbsandArg[ic, 1] = Arctan(ComplexNumber[ic, 1] / ComplexNumber[ic, 0]);
}
else if (ComplexNumber[ic, 0] < 0 && ComplexNumber[ic, 1] > 0)
{
AbsandArg[ic, 1] = PI - Arctan((-1) * ComplexNumber[ic, 1] / ComplexNumber[ic, 0]);
}
else if (ComplexNumber[ic, 0] < 0 && ComplexNumber[ic, 1] < 0)
{
AbsandArg[ic, 1] = PI + Arctan(ComplexNumber[ic, 1] / ComplexNumber[ic, 0]);
}
else if (ComplexNumber[ic, 0] > 0 && ComplexNumber[ic, 1] < 0)
{
AbsandArg[ic, 1] = 2 * PI - Arctan((-1) * ComplexNumber[ic, 1] / ComplexNumber[ic, 0]);
}
else if (ComplexNumber[ic, 0] > 0 && ComplexNumber[ic, 1] == 0)
{
AbsandArg[ic, 1] = 0;
}
else if (ComplexNumber[ic, 0] < 0 && ComplexNumber[ic, 1] == 0)
{
AbsandArg[ic, 1] = PI;
}
else if (ComplexNumber[ic, 0] == 0 && ComplexNumber[ic, 1] > 0)
{
AbsandArg[ic, 1] = PI / 2;
}
else if (ComplexNumber[ic, 0] == 0 && ComplexNumber[ic, 1] < 0)
{
AbsandArg[ic, 1] = 3 * PI / 2;
}
else if (ComplexNumber[ic, 0] == 0 && ComplexNumber[ic, 1] == 0)
{
AbsandArg[ic, 1] = 0;
}
sqrtbuf = null;
}
}
/// <summary>
/// 円周率を求める。
/// ラマヌジャンの公式を使用
/// </summary>
protected static void CreatePI()
{
double buf1 = 0;
double buf2 = 1;
int ic = 0;
while (buf1 != buf2)
{
buf2 = buf1;
buf1 += (BinomialTheorem.RealExpo(-1, ic) * BinomialTheorem.DoubleFactorial(4 * ic) * (1123 + 21460 * ic))
/ (BinomialTheorem.RealExpo(882, 2 * ic + 1) * BinomialTheorem.RealExpo(BinomialTheorem.RealExpo(4, ic) * BinomialTheorem.DoubleFactorial(ic), 4));
ic += 1;
}
PI = 4 / buf1;
}
/// <summary>
/// ラジアンを入力すると余弦の値を返す。0 <= rad < 2PI
/// </summary>
/// <param name="rad"></param>
/// <returns></returns>
public static double RadCosine(double rad)
{
double Cos = 0;
double buf = 0;
if (rad == PI / 2)
{
return(0);
}
if (rad == PI / 3)
{
return(0.5);
}
if (rad == 0)
{
return(1);
}
for (int ic = 0; ic < 100; ic++)
{
buf += BinomialTheorem.RealExpo(-1, ic) * BinomialTheorem.RealExpo(rad, 2 * ic) / BinomialTheorem.DoubleFactorial(2 * ic);
}
Cos = buf;
return(Cos);
}