public static double[] RealFastFourierTransform(Complex[] src, double amplitude = 1.0)
{
int n4 = 1 << (Mt.Log2Int(src.Length) - 1);
int n = n4 * 4, n2 = n4 * 2, n3 = n4 * 3;
int n2mask = n2 - 1;
Complex[] Data = new Complex[n2];
TriangularTable Triangle = TriangularTable.Get(n);
for (int i = n4; i >= 0; --i)
{
int j = n2 - i;
Complex g1 = src[i];
Complex g2 = Complex.Conjugate(src[j]);
Complex h1 = (g1 + g2);
Complex h2 = (g1 - g2) * Triangle.Complex(n4 + i);
Data[i] = (h1 + h2);
Data[j & n2mask] = Complex.Conjugate(h1 - h2);
}
Data = FastFourierTransform_(Data, false);
LetMul(Data, amplitude / n);
double[] Dst = New.Array(n, i => (i & 1) == 0 ? Data[i / 2].Real : Data[i / 2].Imaginary);
return(Dst);
}
//---------------------------------------------------------------------------
#region Numerical optimization functions
public static double[] ArgminSimplex(double[] arguments, double[] delta, Func <double[], double> func, double tolerance)
{
int EstimationCountMax = 5000;
int EstimationCount = 0;
int D = arguments.Length, D1 = D + 1;
double[][] Args = New.Array(D + 1, j => New.Array(D, i => arguments[i] + (i == j ? delta[i] : 0.0)));
double[] ArgSum = New.Array(D, i => Ex.Range(D + 1).Sum(j => Args[j][i]));
double[] ArgTry = new double[D];
double[] Values = Args.Select(arg => func(arg)).ToArray();
Func <int, double, double> tryfunc = (int i, double fac) =>
{
double[] arg = Args[i];
double fac1 = (1 - fac) / D;
double fac2 = fac1 - fac;
for (int j = D; --j >= 0;)
{
ArgTry[j] = ArgSum[j] * fac1 - arg[j] * fac2;
}
double y = func(ArgTry);
if (Values[i] > y)
{
Values[i] = y;
for (int j = D; --j >= 0;)
{
ArgSum[j] += ArgTry[j] - arg[j];
arg[j] = ArgTry[j];
}
}
return(y);
};
while (true)
{
int iMin = 0;
int iMax = Values[0] > Values[1] ? 0 : 1;
int iMax2 = 1 - iMax;
for (int i = 0; i < D1; i++)
{
double v = Values[i];
if (v <= Values[iMin])
{
iMin = i;
}
if (v > Values[iMax])
{
iMax2 = iMax; iMax = i;
}
else if (v > Values[iMax2] && i != iMax)
{
iMax2 = i;
}
}
double d = 2.0 * Math.Abs(Values[iMax] - Values[iMin])
/ (Math.Abs(Values[iMax]) + Math.Abs(Values[iMin]) + Mt.DoubleEps);
if (d < tolerance)
{
break;
}
if (EstimationCount >= EstimationCountMax)
{
ThrowException.WriteLine("ArgminSimplex: too many function estimations.");
break;
}
EstimationCount += 2;
double vTry = tryfunc(iMax, -1);
if (vTry <= Values[iMin])
{
tryfunc(iMax, 2); continue;
}
if (vTry < Values[iMax2])
{
EstimationCount--; continue;
}
double vTryPrev = Values[iMax];
vTry = tryfunc(iMax, 0.5);
if (vTry < vTryPrev)
{
continue;
}
EstimationCount += D;
for (int i = 0; i < D1; i++)
{
if (i == iMin)
{
continue;
}
for (int j = 0; j < D; j++)
{
Args[i][j] = (Args[i][j] + Args[iMin][j]) / 2;
}
Values[i] = func(Args[i]);
}
for (int i = D; --i >= 0;)
{
ArgSum[i] = Ex.Range(D + 1).Sum(j => Args[j][i]);
}
}
return(New.Array(D, i => Ex.Range(D1).Average(j => Args[j][i])));
}