/// <summary>
/// 逆FFTします。結果をcompensation倍します(compensationを指定しないとき1.0/N倍)
/// </summary>
/// <param name="aFrom">周波数ドメイン値X^m(q) 0≦m≦N</param>
/// <param name="compensation">倍率。指定しないとき1.0/Nとなる。</param>
/// <returns></returns>
public WWComplex[] InverseFft(WWComplex[] aFrom, double?compensation = null)
{
for (int i = 0; i < aFrom.Length; ++i)
{
aFrom[i] = new WWComplex(aFrom[i].real, -aFrom[i].imaginary);
}
var aTo = ForwardFft(aFrom);
double c = 1.0 / mNumPoints;
if (compensation != null)
{
c = (double)compensation;
}
for (int i = 0; i < aTo.Length; ++i)
{
aTo[i] = new WWComplex(aTo[i].real * c, -aTo[i].imaginary * c);
}
return(aTo);
}
/// <summary>
/// 1乗以上の項の係数項の表示。
/// </summary>
public static string FirstCoeffToString(WWComplex c, string variableString)
{
if (c.EqualValue(new WWComplex(1, 0)))
{
return(variableString); // 係数を表示せず、変数のみ表示する。
}
if (c.EqualValue(new WWComplex(-1, 0)))
{
return(string.Format("-{0}", variableString));
}
if (c.imaginary == 0)
{
// 実数。
return(string.Format("{0}{1}", c.real, variableString));
}
if (c.EqualValue(new WWComplex(0, 1)))
{
return(string.Format("{0}{1}", WWComplex.imaginaryUnit, variableString));
}
if (c.EqualValue(new WWComplex(0, -1)))
{
return(string.Format("-{0}{1}", WWComplex.imaginaryUnit, variableString));
}
if (c.real == 0)
{
// 純虚数。
return(string.Format("{0}{1}{2}", c.imaginary, WWComplex.imaginaryUnit, variableString));
}
// 純虚数ではない虚数。
return(string.Format("({0}){1}", c, variableString));
}
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);
}
/// <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)));
}
public static WWComplex Div(WWComplex lhs, double rhs)
{
var recip = 1.0 / rhs;
return(Mul(lhs, recip));
}
/// <summary>
/// create copy and copy := L / R, returns copy.
/// </summary>
public static WWComplex Div(WWComplex lhs, WWComplex rhs)
{
var recip = Reciprocal(rhs);
return(Mul(lhs, recip));
}
/// <summary>
/// returns reciprocal. this instance is not changed.
/// </summary>
public WWComplex Reciplocal()
{
return(WWComplex.Reciprocal(this));
}
/// <summary>
/// 1次元IDFT。compensationを出力値に乗算する。Dft1dとペアで使用すると値が元に戻る。
/// </summary>
/// <param name="from">入力</param>
/// <param name="compensation">出力に乗算する係数。省略時1</param>
/// <returns>出力IDFT結果</returns>
public static WWComplex[] Idft1d(WWComplex[] from, double?compensation = null)
{
/*
* W=e^(-j*2pi/N)
* Sk= seriesSum([ Gp * W^(-k*p) ], p, 0, N-1) (k=0,1,2,…,(N-1))
*
* from == Gp
* to == Sk
*/
// 要素数N
int N = from.Length;
var to = new WWComplex[N];
// Wのテーブル
var w = new WWComplex[N];
for (int i = 0; i < N; ++i)
{
double re = Math.Cos(i * 2.0 * Math.PI / N);
double im = Math.Sin(i * 2.0 * Math.PI / N);
w[i] = new WWComplex(re, im);
}
// IDFT実行。
for (int k = 0; k < N; ++k)
{
double sr = 0.0;
double si = 0.0;
for (int p = 0; p < N; ++p)
{
int posGr = p;
int posWr = (p * k) % N;
double gR = from[posGr].real;
double gI = from[posGr].imaginary;
double wR = w[posWr].real;
double wI = w[posWr].imaginary;
sr += gR * wR - gI * wI;
si += gR * wI + gI * wR;
}
to[k] = new WWComplex(sr, si);
}
double c = 1.0;
if (compensation != null)
{
c = (double)compensation;
}
if (c != 1.0)
{
var toC = new WWComplex[N];
for (int i = 0; i < N; ++i)
{
toC[i] = new WWComplex(to[i].real * c, to[i].imaginary * c);
}
return(toC);
}
else
{
return(to);
}
}
/// <summary>
/// create copy and copy := L - R, returns copy.
/// </summary>
public static WWComplex Sub(WWComplex lhs, WWComplex rhs)
{
return(new WWComplex(lhs.real - rhs.real, lhs.imaginary - rhs.imaginary));
}
/// <summary>
/// create copy and copy := L + R, returns copy.
/// </summary>
public static WWComplex Add(WWComplex lhs, WWComplex rhs)
{
return(new WWComplex(lhs.real + rhs.real, lhs.imaginary + rhs.imaginary));
}
public static double Distance(WWComplex a, WWComplex b)
{
var s = WWComplex.Sub(a, b);
return(s.Magnitude());
}
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());
}
}
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 void Print(string x)
{
if (0 < coeffList.Length)
{
bool bFirst = true;
for (int i = coeffList.Length - 1; 0 <= i; --i)
{
if (coeffList[i].AlmostZero())
{
continue;
}
if (bFirst)
{
bFirst = false;
}
else
{
Console.Write(" + ");
}
if (i == 0)
{
Console.Write("{0}", coeffList[i]);
}
else if (i == 1)
{
Console.Write("{0}*{1}", coeffList[i], x);
}
else
{
Console.Write("{0}*({1}^{2})", coeffList[i], x, i);
}
}
if (!bFirst)
{
Console.Write(" + ");
}
}
Console.Write(" { ");
{
bool bFirst = true;
for (int i = numerCoeffList.Length - 1; 0 <= i; --i)
{
if (numerCoeffList[i].AlmostZero())
{
continue;
}
if (bFirst)
{
bFirst = false;
}
else
{
Console.Write(" + ");
}
if (i == 0)
{
Console.Write("{0}", numerCoeffList[i]);
}
else if (i == 1)
{
Console.Write("{0}*{1}", numerCoeffList[i], x);
}
else
{
Console.Write("{0}*({1}^{2})", numerCoeffList[i], x, i);
}
}
}
Console.Write(" } / { ");
{
for (int i = 0; i < denomRootList.Length; ++i)
{
if (denomRootList[i].AlmostZero())
{
Console.WriteLine(" {0} ", x);
continue;
}
Console.Write("({0}+({1}))", x, WWComplex.Minus(denomRootList[i]));
}
}
Console.WriteLine(" }");
}
/// <summary>
/// 窓関数をかけた周波数ドメイン値X^m(q)を戻す。
/// 同様の処理をWWGoertzel (Stable Goertzel algorithm)で行うこともできるだろう。
/// </summary>
public WWComplex[] FilterWithWindow(double x, WWWindowFunc.WindowType wt)
{
var r = Filter(x);
var rW = new WWComplex[r.Length];
var w = WWWindowFunc.FreqDomainWindowCoeffs(wt);
switch (w.Length)
{
case 2:
for (int i = 0; i < mN; ++i)
{
int il = i - 1;
if (il < 0)
{
il = mN - 1;
}
int ir = i + 1;
if (mN <= ir)
{
ir = 0;
}
rW[i] = WWComplex.Add(
WWComplex.Mul(r[il], w[1] * 0.5),
WWComplex.Mul(r[i], w[0]),
WWComplex.Mul(r[ir], w[1] * 0.5));
}
return(rW);
case 3:
for (int i = 0; i < mN; ++i)
{
var pos = new int[5];
for (int offs = -2; offs <= 2; ++offs)
{
int p = i + offs;
if (p < 0)
{
p += mN;
}
if (mN <= p)
{
p -= mN;
}
pos[offs + 2] = p;
}
rW[i] = WWComplex.Add(
WWComplex.Mul(r[pos[0]], w[2] * 0.5),
WWComplex.Mul(r[pos[1]], w[1] * 0.5),
WWComplex.Mul(r[pos[2]], w[0]),
WWComplex.Mul(r[pos[3]], w[1] * 0.5),
WWComplex.Mul(r[pos[4]], w[2] * 0.5));
}
return(rW);
default:
System.Diagnostics.Debug.Assert(false);
return(null);
}
}
Add(HighOrderComplexRationalPolynomial lhs, FirstOrderComplexRationalPolynomial rhs)
{
/* nL nR
* p^2+2x+2 p+4
* ───────── + ────
* p^2+ p+1 p+3
* dL dR
*
* dL dR
* 分母 = (p^2+p+1) (p+3)
* 分母の次数 = degree(dL) + degree(dR) + 1
*
* nL dR nR dL
* 分子 = (p^2+2x+2)(p+3) + (p+4)(p^2+p+1)
* 分子の次数 = degree(nL) + degree(dR) + 1 か degree(nR) * degree(dL) + 1の大きいほう
*/
ComplexPolynomial denomL;
{
var d = new WWComplex[lhs.DenomDegree() + 1];
for (int i = 0; i <= lhs.DenomDegree(); ++i)
{
d[i] = lhs.D(i);
}
denomL = new ComplexPolynomial(d);
}
ComplexPolynomial numerL;
{
var n = new WWComplex[lhs.NumerDegree() + 1];
for (int i = 0; i <= lhs.NumerDegree(); ++i)
{
n[i] = lhs.N(i);
}
numerL = new ComplexPolynomial(n);
}
// 分母の項
ComplexPolynomial denomResult;
{
var denomX = new ComplexPolynomial(new WWComplex[0]);
if (1 == rhs.DenomDegree())
{
denomX = ComplexPolynomial.MultiplyC(ComplexPolynomial.MultiplyX(denomL), rhs.D(1));
}
var denomC = ComplexPolynomial.MultiplyC(denomL, rhs.D(0));
denomResult = ComplexPolynomial.Add(denomX, denomC);
}
// 分子の項
ComplexPolynomial numerResult;
{
ComplexPolynomial numer0;
{
var numerX0 = new ComplexPolynomial(new WWComplex[0]);
if (1 == rhs.DenomDegree())
{
numerX0 = ComplexPolynomial.MultiplyC(ComplexPolynomial.MultiplyX(numerL), rhs.D(1));
}
var numerC0 = ComplexPolynomial.MultiplyC(numerL, rhs.D(0));
numer0 = ComplexPolynomial.Add(numerX0, numerC0);
}
ComplexPolynomial numer1;
{
var numerX1 = new ComplexPolynomial(new WWComplex[0]);
if (1 == rhs.NumerDegree())
{
numerX1 = ComplexPolynomial.MultiplyC(ComplexPolynomial.MultiplyX(denomL), rhs.N(1));
}
var numerC1 = ComplexPolynomial.MultiplyC(denomL, rhs.N(0));
numer1 = ComplexPolynomial.Add(numerX1, numerC1);
}
numerResult = ComplexPolynomial.Add(numer0, numer1);
}
return(new HighOrderComplexRationalPolynomial(numerResult.ToArray(), denomResult.ToArray()));
}
/// <summary>
/// create copy and copy := -uni, returns copy.
/// argument value is not changed.
/// </summary>
public static WWComplex Minus(WWComplex uni)
{
return(new WWComplex(-uni.real, -uni.imaginary));
}
/// <summary>
/// 連続FFT オーバーラップアド法でLinear convolution x ** hする。
/// </summary>
/// <param name="h">コンボリューションカーネル。左右反転される。</param>
/// <param name="x">入力数列。</param>
/// <param name="fragmentSz">個々のFFTに入力するxの断片サイズ。</param>
public WWComplex[] ConvolutionContinuousFft(WWComplex[] h, WWComplex[] x, int fragmentSz)
{
System.Diagnostics.Debug.Assert(2 <= fragmentSz);
if (x.Length < h.Length)
{
// swap x and h
var tmp = h;
h = x;
x = tmp;
}
// h.Len <= x.Len
int fullConvLen = h.Length + x.Length - 1;
var r = new WWComplex[fullConvLen];
for (int i = 0; i < r.Length; ++i)
{
r[i] = WWComplex.Zero();
}
// hをFFTしてHを得る。
int fragConvLen = h.Length + fragmentSz - 1;
int fftSize = Functions.NextPowerOf2(fragConvLen);
var h2 = new WWComplex[fftSize];
Array.Copy(h, 0, h2, 0, h.Length);
for (int i = h.Length; i < h2.Length; ++i)
{
h2[i] = WWComplex.Zero();
}
var fft = new WWRadix2Fft(fftSize);
var H = fft.ForwardFft(h2);
for (int offs = 0; offs < x.Length; offs += fragmentSz)
{
// xFをFFTしてXを得る。
var xF = WWComplex.ZeroArray(fftSize);
for (int i = 0; i < fragmentSz; ++i)
{
if (i + offs < x.Length)
{
xF[i] = x[offs + i];
}
else
{
break;
}
}
var X = fft.ForwardFft(xF);
var Y = WWComplex.Mul(H, X);
var y = fft.InverseFft(Y);
// オーバーラップアド法。FFT結果を足し合わせる。
for (int i = 0; i < fragConvLen; ++i)
{
r[offs + i] = WWComplex.Add(r[offs + i], y[i]);
}
}
return(r);
}
/// <summary>
/// create copy and copy := complex conjugate of uni, returns copy.
/// </summary>
public static WWComplex ComplexConjugate(WWComplex uni)
{
return(new WWComplex(uni.real, -uni.imaginary));
}
private void FftStageN(int stageNr, WWComplex[] x, WWComplex[] y)
{
/*
* stage0: 2つの入力データにバタフライ演算 (length=8の時) 4回 (nRepeat=4, nSubRepeat=2)
* y[0] = x[0] + w_n^(0*4) * x[1]
* y[1] = x[0] + w_n^(1*4) * x[1]
*
* y[2] = x[2] + w_n^(0*4) * x[3]
* y[3] = x[2] + w_n^(1*4) * x[3]
*
* y[4] = x[4] + w_n^(0*4) * x[5]
* y[5] = x[4] + w_n^(1*4) * x[5]
*
* y[6] = x[6] + w_n^(0*4) * x[7]
* y[7] = x[6] + w_n^(1*4) * x[7]
*/
/*
* stage1: 4つの入力データにバタフライ演算 (length=8の時) 2回 (nRepeat=2, nSubRepeat=4)
* y[0] = x[0] + w_n^(0*2) * x[2]
* y[1] = x[1] + w_n^(1*2) * x[3]
* y[2] = x[0] + w_n^(2*2) * x[2]
* y[3] = x[1] + w_n^(3*2) * x[3]
*
* y[4] = x[4] + w_n^(0*2) * x[6]
* y[5] = x[5] + w_n^(1*2) * x[7]
* y[6] = x[4] + w_n^(2*2) * x[6]
* y[7] = x[5] + w_n^(3*2) * x[7]
*/
/*
* stage2: 8つの入力データにバタフライ演算 (length=8の時) 1回 (nRepeat=1, nSubRepeat=8)
* y[0] = x[0] + w_n^(0*1) * x[4]
* y[1] = x[1] + w_n^(1*1) * x[5]
* y[2] = x[2] + w_n^(2*1) * x[6]
* y[3] = x[3] + w_n^(3*1) * x[7]
* y[4] = x[0] + w_n^(4*1) * x[4]
* y[5] = x[1] + w_n^(5*1) * x[5]
* y[6] = x[2] + w_n^(6*1) * x[6]
* y[7] = x[3] + w_n^(7*1) * x[7]
*/
/*
* stageN:
*/
int nRepeat = Pow2(mNumStage - stageNr - 1);
int nSubRepeat = mNumPoints / nRepeat;
var t = WWComplex.Zero();
for (int i = 0; i < nRepeat; ++i)
{
int offsBase = i * nSubRepeat;
bool allZero = true;
for (int j = 0; j < nSubRepeat / 2; ++j)
{
int offs = offsBase + (j % (nSubRepeat / 2));
if (Double.Epsilon < x[offs].Magnitude())
{
allZero = false;
break;
}
if (Double.Epsilon < x[offs + nSubRepeat / 2].Magnitude())
{
allZero = false;
break;
}
}
if (allZero)
{
for (int j = 0; j < nSubRepeat; ++j)
{
y[j + offsBase] = WWComplex.Zero();
}
}
else
{
for (int j = 0; j < nSubRepeat; ++j)
{
int offs = offsBase + (j % (nSubRepeat / 2));
var v1 = x[offs];
var v2 = WWComplex.Mul(mWn[j * nRepeat], x[offs + nSubRepeat / 2]);
y[j + offsBase] = WWComplex.Add(v1, v2);
}
}
}
}
/// <summary>
/// 内容が全く同じときtrue
/// </summary>
public bool EqualValue(WWComplex rhs)
{
return(real == rhs.real && imaginary == rhs.imaginary);
}
public WWComplex[] DenomCoeffs()
{
WWComplex[] d = new WWComplex[denom.Length];
Array.Copy(denom, d, d.Length);
return(d);
}
public static WWComplex Add(WWComplex a, WWComplex b, WWComplex c, WWComplex d, WWComplex e)
{
return(new WWComplex(
a.real + b.real + c.real + d.real + e.real,
a.imaginary + b.imaginary + c.imaginary + d.imaginary + e.imaginary));
}
public static WWComplex Mul(WWComplex lhs, double v)
{
return(new WWComplex(lhs.real * v, lhs.imaginary * v));
}
static WWComplex Get(WWComplex[] v, int pos) {
if (pos < 0 || v.Length <= pos) {
return WWComplex.Zero();
}
return v[pos];
}
/// <summary>
/// 1次元DFT。要素数N。compensationを出力値に乗算する。省略時1/N。Idft1dとペアで使用すると値が元に戻る。
/// </summary>
/// <param name="from">入力。</param>
/// <param name="compensation">出力に乗算する係数。省略時1/N</param>
/// <returns>出力DFT結果</returns>
public static WWComplex[] Dft1d(WWComplex[] from, double?compensation = null)
{
/*
* W=e^(j*2pi/N)
* Gp = (1/N) * seriesSum(Sk * W^(k*p), k, 0, N-1) (p=0,1,2,…,(N-1))
*
* from == Sk
* to == Gp
*/
// 要素数N
int N = from.Length;
var to = new WWComplex[N];
// Wのテーブル
var w = new WWComplex[N];
for (int i = 0; i < N; ++i)
{
double re = Math.Cos(-i * 2.0 * Math.PI / N);
double im = Math.Sin(-i * 2.0 * Math.PI / N);
w[i] = new WWComplex(re, im);
}
for (int p = 0; p < N; ++p)
{
double gr = 0.0;
double gi = 0.0;
for (int k = 0; k < N; ++k)
{
int posSr = k;
int posWr = ((p * k) % N);
double sR = from[posSr].real;
double sI = from[posSr].imaginary;
double wR = w[posWr].real;
double wI = w[posWr].imaginary;
gr += sR * wR - sI * wI;
gi += sR * wI + sI * wR;
}
to[p] = new WWComplex(gr, gi);
}
double c = 1.0 / N;
if (compensation != null)
{
c = (double)compensation;
}
if (c != 1.0)
{
var toC = new WWComplex[N];
for (int i = 0; i < N; ++i)
{
toC[i] = new WWComplex(to[i].real * c, to[i].imaginary * c);
}
return(toC);
}
else
{
return(to);
}
}
private void FftStageN(int stageNr, LargeArray <WWComplex> x, LargeArray <WWComplex> y)
{
/*
* stage0: 2つの入力データにバタフライ演算 (length=8の時) 4回 (nRepeat=4, nSubRepeat=2)
* y[0] = x[0] + w_n^(0*4) * x[1]
* y[1] = x[0] + w_n^(1*4) * x[1]
*
* y[2] = x[2] + w_n^(0*4) * x[3]
* y[3] = x[2] + w_n^(1*4) * x[3]
*
* y[4] = x[4] + w_n^(0*4) * x[5]
* y[5] = x[4] + w_n^(1*4) * x[5]
*
* y[6] = x[6] + w_n^(0*4) * x[7]
* y[7] = x[6] + w_n^(1*4) * x[7]
*/
/*
* stage1: 4つの入力データにバタフライ演算 (length=8の時) 2回 (nRepeat=2, nSubRepeat=4)
* y[0] = x[0] + w_n^(0*2) * x[2]
* y[1] = x[1] + w_n^(1*2) * x[3]
* y[2] = x[0] + w_n^(2*2) * x[2]
* y[3] = x[1] + w_n^(3*2) * x[3]
*
* y[4] = x[4] + w_n^(0*2) * x[6]
* y[5] = x[5] + w_n^(1*2) * x[7]
* y[6] = x[4] + w_n^(2*2) * x[6]
* y[7] = x[5] + w_n^(3*2) * x[7]
*/
/*
* stage2: 8つの入力データにバタフライ演算 (length=8の時) 1回 (nRepeat=1, nSubRepeat=8)
* y[0] = x[0] + w_n^(0*1) * x[4]
* y[1] = x[1] + w_n^(1*1) * x[5]
* y[2] = x[2] + w_n^(2*1) * x[6]
* y[3] = x[3] + w_n^(3*1) * x[7]
* y[4] = x[0] + w_n^(4*1) * x[4]
* y[5] = x[1] + w_n^(5*1) * x[5]
* y[6] = x[2] + w_n^(6*1) * x[6]
* y[7] = x[3] + w_n^(7*1) * x[7]
*/
/*
* stageN:
*/
long nRepeat = Pow2(mNumStage - stageNr - 1);
long nSubRepeat = mNumPoints / nRepeat;
for (long i = 0; i < nRepeat; ++i)
{
long offsBase = i * nSubRepeat;
bool allZero = true;
for (long j = 0; j < nSubRepeat / 2; ++j)
{
long offs = offsBase + (j % (nSubRepeat / 2));
if (Double.Epsilon < x.At(offs).Magnitude())
{
allZero = false;
break;
}
if (Double.Epsilon < x.At(offs + nSubRepeat / 2).Magnitude())
{
allZero = false;
break;
}
}
if (allZero)
{
for (long j = 0; j < nSubRepeat; ++j)
{
y.Set(j + offsBase, WWComplex.Zero());
}
}
else
{
for (long j = 0; j < nSubRepeat; ++j)
{
long offs = offsBase + (j % (nSubRepeat / 2));
var t = x.At(offs);
var t2 = WWComplex.Mul(mWn.At(j * nRepeat), x.At(offs + nSubRepeat / 2));
var t3 = WWComplex.Add(t, t2);
y.Set(j + offsBase, t3);
}
}
}
}
public WWComplex[] NumerCoeffs()
{
WWComplex[] n = new WWComplex[numer.Length];
Array.Copy(numer, n, n.Length);
return(n);
}