/// <summary>
/// output string represents "c1x + c0"
/// </summary>
public static string PolynomialToString(WWComplex c1, WWComplex c0, string variableSymbol)
{
if (c1.Magnitude() == 0)
{
return(string.Format("{0}", c0));
}
return(string.Format("{0}{1}", FirstCoeffToString(c1, variableSymbol), ZeroOrderCoeffToString(c0)));
}
/// <summary>
/// rational poly
/// n1x + n0
/// ----------
/// d1x + d0
/// </summary>
/// <param name="n1">numerator first orderPlus1 coefficient</param>
/// <param name="n0">numerator zero orderPlus1 coefficient</param>
/// <param name="d1">denominator first orderPlus1 coefficient</param>
/// <param name="d0">denominator zero orderPlus1 coefficient</param>
public FirstOrderComplexRationalPolynomial(WWComplex n1, WWComplex n0, WWComplex d1, WWComplex d0)
{
if (d1.Magnitude() == 0 && d0.Magnitude() == 0)
{
throw new DivideByZeroException();
}
numer[1] = n1;
numer[0] = n0;
denom[1] = d1;
denom[0] = d0;
}
/// <summary>
/// 1乗以上の項が存在するときに、そのあとにつなげて書くときの定数項の値表示。
/// </summary>
public static string ZeroOrderCoeffToString(WWComplex c)
{
if (c.Magnitude() == 0)
{
return("");
}
if (c.imaginary == 0)
{
if (c.real < 0)
{
return(string.Format(" {0}", c.real));
}
else
{
return(string.Format(" +{0}", c.real));
}
}
if (c.real == 0)
{
if (c.imaginary == 1)
{
return(string.Format(" {0}", WWComplex.imaginaryUnit));
}
if (c.imaginary == -1)
{
return(string.Format(" -{0}", WWComplex.imaginaryUnit));
}
if (c.imaginary < 0)
{
return(string.Format(" {0}{1}", c.imaginary, WWComplex.imaginaryUnit));
}
else
{
return(string.Format(" +{0}{1}", c.imaginary, WWComplex.imaginaryUnit));
}
}
if (c.real < 0)
{
return(c.ToString());
}
else
{
return(string.Format(" +{0}", c));
}
}
/// <summary>
/// output string represents "c2x^2 + c1x + c0"
/// </summary>
public static string PolynomialToString(WWComplex c2, WWComplex c1, WWComplex c0, string variableSymbol)
{
if (c2.Magnitude() == 0)
{
// 1乗以下の項のみ。
return(PolynomialToString(c1, c0, variableSymbol));
}
if (c1.Magnitude() == 0 && c0.Magnitude() == 0)
{
// 2乗の項のみ。
return(FirstCoeffToString(c2, string.Format("{0}^2", variableSymbol)));
}
if (c0.Magnitude() == 0)
{
// 2乗の項と1乗の項。
return(string.Format("{0}{1}",
FirstCoeffToString(c2, string.Format("{0}^2", variableSymbol)),
ContinuedCoeffToString(c1, variableSymbol)));
}
if (c1.Magnitude() == 0)
{
// 2乗の項と定数項。
return(string.Format("{0}{1}",
FirstCoeffToString(c2, string.Format("{0}^2", variableSymbol)),
ZeroOrderCoeffToString(c0)));
}
// 2乗＋1乗＋定数
return(string.Format("{0}{1}{2}",
FirstCoeffToString(c2, string.Format("{0}^2", variableSymbol)),
ContinuedCoeffToString(c1, variableSymbol),
ZeroOrderCoeffToString(c0)));
}
private void FindRootCubic(double[] coeffs)
{
// 3次多項式 cubic poly equation
// https://en.wikipedia.org/wiki/Cubic_function#Algebraic_solution
System.Diagnostics.Debug.Assert(4 == coeffs.Length);
double a = coeffs[3];
double b = coeffs[2];
double c = coeffs[1];
double d = coeffs[0];
double Δ =
18 * a * b * c * d
- 4 * b * b * b * d
+ 1 * b * b * c * c
- 4 * a * c * c * c
- 27 * a * a * d * d;
double Δ0 = b * b - 3 * a * c;
// ↓ 雑な0かどうかの判定処理。
if (AlmostZero(Δ))
{
if (AlmostZero(Δ0))
{
// triple root
double root = -b / (3 * a);
mRoots.Add(new WWComplex(root, 0));
mRoots.Add(new WWComplex(root, 0));
mRoots.Add(new WWComplex(root, 0));
return;
}
// double root and a simple root
double root2 = (9 * a * d - b * c) / (2 * Δ0);
double root1 = (4 * a * b * c - 9 * a * a * d - b * b * b);
mRoots.Add(new WWComplex(root2, 0));
mRoots.Add(new WWComplex(root2, 0));
mRoots.Add(new WWComplex(root1, 0));
return;
}
{
double Δ1 =
+2 * b * b * b
- 9 * a * b * c
+ 27 * a * a * d;
WWComplex C;
{
WWComplex c1 = new WWComplex(Δ1 / 2, 0);
double c2Sqrt = Math.Sqrt(Math.Abs(-27 * a * a * Δ) / 4);
WWComplex c2;
if (Δ < 0)
{
//C2 is real number
c2 = new WWComplex(c2Sqrt, 0);
}
else
{
//C2 is imaginary number
c2 = new WWComplex(0, c2Sqrt);
}
WWComplex c1c2;
WWComplex c1Pc2 = WWComplex.Add(c1, c2);
WWComplex c1Mc2 = WWComplex.Sub(c1, c2);
if (c1Mc2.Magnitude() <= c1Pc2.Magnitude())
{
c1c2 = c1Pc2;
}
else
{
c1c2 = c1Mc2;
}
// 3乗根 = 大きさが3分の1乗で角度が3分の1．
double magnitude = c1c2.Magnitude();
double phase = c1c2.Phase();
double cMag = Math.Pow(magnitude, 1.0 / 3.0);
double cPhase = phase / 3;
C = new WWComplex(cMag * Math.Cos(cPhase), cMag * Math.Sin(cPhase));
}
var ζ = new WWComplex(-1.0 / 2.0, 1.0 / 2.0 * Math.Sqrt(3.0));
var ζ2 = new WWComplex(-1.0 / 2.0, -1.0 / 2.0 * Math.Sqrt(3.0));
var r3a = new WWComplex(-1.0 / 3.0 / a, 0);
WWComplex root0 = WWComplex.Mul(r3a, WWComplex.Add(
WWComplex.Add(new WWComplex(b, 0), C),
WWComplex.Div(new WWComplex(Δ0, 0), C)));
WWComplex root1 = WWComplex.Mul(r3a, WWComplex.Add(
WWComplex.Add(new WWComplex(b, 0), WWComplex.Mul(ζ, C)),
WWComplex.Div(new WWComplex(Δ0, 0), WWComplex.Mul(ζ, C))));
WWComplex root2 = WWComplex.Mul(r3a, WWComplex.Add(
WWComplex.Add(new WWComplex(b, 0), WWComplex.Mul(ζ2, C)),
WWComplex.Div(new WWComplex(Δ0, 0), WWComplex.Mul(ζ2, C))));
mRoots.Add(root0);
mRoots.Add(root1);
mRoots.Add(root2);
return;
}
}
