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 WWComplex Next()
{
if (mFirst)
{
mFirst = false;
return(WWComplex.Unity());
}
double gn = 3.0 / 2.0 - 0.5 * ((mYi * mYi) + (mYq * mYq));
double yi = gn * (mYi * mCosθ - mYq * mSinθ);
double yq = gn * (mYq * mCosθ + mYi * mSinθ);
mYi = yi;
mYq = yq;
return(new WWComplex(yi, yq));
}
RootListToCoeffList(WWComplex [] b, WWComplex c)
{
var coeff = new List <WWComplex>();
if (b.Length == 0)
{
// 定数項のみ。(?)
coeff.Add(c);
return(coeff.ToArray());
}
var b2 = new List <WWComplex>();
foreach (var i in b)
{
b2.Add(i);
}
// (p-b[0])
coeff.Add(WWComplex.Mul(b2[0], -1));
coeff.Add(WWComplex.Unity());
b2.RemoveAt(0);
WWComplex[] coeffArray = coeff.ToArray();
while (0 < b2.Count)
{
// 多項式に(p-b[k])を掛ける。
var s1 = ComplexPolynomial.MultiplyX(new ComplexPolynomial(coeffArray));
var s0 = ComplexPolynomial.MultiplyC(new ComplexPolynomial(coeffArray),
WWComplex.Mul(b2[0], -1));
coeffArray = ComplexPolynomial.Add(s1, s0).ToArray();
b2.RemoveAt(0);
}
return(ComplexPolynomial.MultiplyC(new ComplexPolynomial(coeffArray), c).ToArray());
}
public WWComplex Next()
{
if (mFt == 0)
{
return(WWComplex.Unity());
}
// mFt != 0の場合。
++mCounter;
if (mCounter == mLcm)
{
mLcm = 0;
// 位相を0にリセットします。
double gn = 3.0 / 2.0 - 0.5 * ((mYi * mYi) + (mYq * mYq));
double yi = gn;
double yq = 0;
mYi = yi;
mYq = yq;
return(new WWComplex(yi, yq));
}
else
{
double gn = 3.0 / 2.0 - 0.5 * ((mYi * mYi) + (mYq * mYq));
double yi = gn * (mYi * mCosθ - mYq * mSinθ);
double yq = gn * (mYq * mCosθ + mYi * mSinθ);
mYi = yi;
mYq = yq;
return(new WWComplex(yi, yq));
}
}
public WWComplex Evaluate(WWComplex x)
{
WWComplex n = WWComplex.Zero();
WWComplex xN = WWComplex.Unity();
for (int i = 0; i < numer.Length; ++i)
{
n = WWComplex.Add(n, WWComplex.Mul(xN, numer[i]));
xN = WWComplex.Mul(xN, x);
}
WWComplex d = WWComplex.Zero();
xN = WWComplex.Unity();
for (int i = 0; i < denom.Length; ++i)
{
d = WWComplex.Add(d, WWComplex.Mul(xN, denom[i]));
xN = WWComplex.Mul(xN, x);
}
WWComplex y = WWComplex.Div(n, d);
return(y);
}
public static void Test()
{
{
/*
* 部分分数分解のテスト。
* s + 3
* X(s) = -------------
* (s+1)s(s-2)
*
* 部分分数分解すると
*
* 2/3 -3/2 5/6
* X(s) = ------- + ------ + -------
* s + 1 s s - 2
*/
var numerCoeffs = new WWComplex [] {
new WWComplex(3, 0),
new WWComplex(1, 0)
};
var dRoots = new WWComplex [] {
new WWComplex(-1, 0),
WWComplex.Zero(),
new WWComplex(2, 0)
};
var p = WWPolynomial.PartialFractionDecomposition(numerCoeffs, dRoots);
for (int i = 0; i < p.Count; ++i)
{
Console.WriteLine(p[i].ToString("s"));
if (i != p.Count - 1)
{
Console.WriteLine(" + ");
}
}
Console.WriteLine("");
}
{
// 約分のテスト
// p-1 (p+1) -(p+1) + (p-1) -2
// ───── ⇒ ────────────────────── ⇒ 1 + ─────
// p+1 p+1 p+1
var numerC = new List <WWComplex>();
numerC.Add(new WWComplex(-1, 0)); // 定数項。
numerC.Add(WWComplex.Unity()); // 1乗の項。
var denomR = new List <WWComplex>();
denomR.Add(new WWComplex(-1, 0));
var r = Reduction(numerC.ToArray(), denomR.ToArray());
r.Print("p");
}
{
// 約分のテスト
// p^2+3x+2 (p^2+3x+2) -(p^2+7x+12) -4x-10
// ──────────── ⇒ 1+ ───────────────────────── ⇒ 1 + ────────────
// (p+3)(p+4) p^2+7x+12 (p+3)(p+4)
var numerC = new WWComplex [] {
new WWComplex(2, 0), // 定数項。
new WWComplex(3, 0), // 1乗の項。
WWComplex.Unity()
}; // 2乗の項。
var denomR = new WWComplex [] {
new WWComplex(-3, 0),
new WWComplex(-4, 0)
};
var r = Reduction(numerC, denomR);
r.Print("p");
}
{
// 部分分数分解。
// -4x-10 2 -6
// ──────────── ⇒ ───── + ─────
// (p+3)(p+4) p+3 p+4
var numerC = new WWComplex [] {
new WWComplex(-10, 0),
new WWComplex(-4, 0)
};
var denomR = new WWComplex [] {
new WWComplex(-3, 0),
new WWComplex(-4, 0)
};
var p = WWPolynomial.PartialFractionDecomposition(numerC, denomR);
for (int i = 0; i < p.Count; ++i)
{
Console.WriteLine(p[i].ToString("s"));
if (i != p.Count - 1)
{
Console.WriteLine(" + ");
}
}
Console.WriteLine("");
}
{
var deriv = new RealPolynomial(new double[] { 1, 1, 1, 1 }).Derivative();
Console.WriteLine("derivative of p^3+p^2+p+1={0}",
deriv.ToString("p"));
}
{
var r2 = AlgebraicLongDivision(new RealPolynomial(new double[] { 6, 3, 1 }),
new RealPolynomial(new double[] { 1, 1 }));
Console.WriteLine("(p^2+3x+6)/(p+1) = {0} r {1}",
r2.quotient.ToString(), r2.remainder.ToString());
}
}
/// <summary>
/// 1次多項式を作る。
/// mCoeffs[0] + p * mCoeffs[1]
/// </summary>
public static List <FirstOrderComplexRationalPolynomial> CreateFromCoeffList(WWComplex [] coeffList)
{
var p = new List <FirstOrderComplexRationalPolynomial>();
if (coeffList.Length == 0)
{
return(p);
}
if (coeffList.Length == 1)
{
// 定数を追加。
p.Add(new FirstOrderComplexRationalPolynomial(WWComplex.Zero(), coeffList[0], WWComplex.Zero(), WWComplex.Unity()));
}
if (coeffList.Length == 2)
{
// 1次式を追加。
p.Add(new FirstOrderComplexRationalPolynomial(coeffList[1], coeffList[0], WWComplex.Zero(), WWComplex.Unity()));
}
return(p);
}
