PartialFractionDecomposition(
WWComplex [] nCoeffs, WWComplex [] dRoots)
{
var result = new List <FirstOrderComplexRationalPolynomial>();
if (dRoots.Length == 1 && nCoeffs.Length == 1)
{
result.Add(new FirstOrderComplexRationalPolynomial(WWComplex.Zero(),
nCoeffs[0], WWComplex.Unity(), WWComplex.Minus(dRoots[0])));
return(result);
}
if (dRoots.Length < 2)
{
throw new ArgumentException("denomR");
}
if (dRoots.Length < nCoeffs.Length)
{
throw new ArgumentException("nCoeffs");
}
for (int k = 0; k < dRoots.Length; ++k)
{
// cn = ... + nCoeffs[2]s^2 + nCoeffs[1]s + nCoeffs[0]
// 係数c[0]は、s==denomR[0]としたときの、cn/(s-denomR[1])(s-denomR[2])(s-denomR[3])…(s-denomR[p-1])
// 係数c[1]は、s==denomR[1]としたときの、cn/(s-denomR[0])(s-denomR[2])(s-denomR[3])…(s-denomR[p-1])
// 係数c[2]は、s==denomR[2]としたときの、cn/(s-denomR[0])(s-denomR[1])(s-denomR[3])…(s-denomR[p-1])
// 分子の値c。
var c = WWComplex.Zero();
var s = WWComplex.Unity();
for (int j = 0; j < nCoeffs.Length; ++j)
{
c = WWComplex.Add(c, WWComplex.Mul(nCoeffs[j], s));
s = WWComplex.Mul(s, dRoots[k]);
}
for (int i = 0; i < dRoots.Length; ++i)
{
if (i == k)
{
continue;
}
c = WWComplex.Div(c, WWComplex.Sub(dRoots[k], dRoots[i]));
}
result.Add(new FirstOrderComplexRationalPolynomial(
WWComplex.Zero(), c,
WWComplex.Unity(), WWComplex.Minus(dRoots[k])));
}
return(result);
}
public static double Distance(WWComplex a, WWComplex b)
{
var s = WWComplex.Sub(a, b);
return(s.Magnitude());
}
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;
}
}
