/// <summary>
/// The internal method for calculating the auto-correlation.
/// </summary>
/// <param name="x">The data array to calculate auto-correlation for</param>
/// <param name="kLow">Min lag to calculate ACF for (0 = no shift with acf=1) must be zero or positive and smaller than x.Length</param>
/// <param name="kHigh">Max lag (EXCLUSIVE) to calculate ACF for must be positive and smaller than x.Length</param>
/// <returns>An array with the ACF as a function of the lags k.</returns>
private static double[] AutoCorrelationFft(double[] x, int kLow, int kHigh)
{
if (x == null)
{
throw new ArgumentNullException(nameof(x));
}
int N = x.Length; // Sample size
if (kLow < 0 || kLow >= N)
{
throw new ArgumentOutOfRangeException(nameof(kLow), "kMin must be zero or positive and smaller than x.Length");
}
if (kHigh < 0 || kHigh >= N)
{
throw new ArgumentOutOfRangeException(nameof(kHigh), "kMax must be positive and smaller than x.Length");
}
if (N < 1)
{
return(new double[0]);
}
int nFFT = Euclid.CeilingToPowerOfTwo(N) * 2;
Complex[] xFFT = new Complex[nFFT];
Complex[] xFFT2 = new Complex[nFFT];
double xDash = ArrayStatistics.Mean(x);
double xArrNow = 0.0d;
// copy values in range and substract mean - all the remaining parts are padded with zero.
for (int i = 0; i < x.Length; i++)
{
xFFT[i] = new Complex(x[i] - xDash, 0.0); // copy values in range and substract mean
}
Fourier.Forward(xFFT, FourierOptions.Matlab);
// maybe a Vector<Complex> implementation here would be faster
for (int i = 0; i < xFFT.Length; i++)
{
xFFT2[i] = Complex.Multiply(xFFT[i], Complex.Conjugate(xFFT[i]));
}
Fourier.Inverse(xFFT2, FourierOptions.Matlab);
double dc = xFFT2[0].Real;
double[] result = new double[kHigh - kLow + 1];
// normalize such that acf[0] would be 1.0
for (int i = 0; i < (kHigh - kLow + 1); i++)
{
result[i] = xFFT2[kLow + i].Real / dc;
}
return(result);
}
