// inverts the Fourier transform of the Cooley-Tukey algorhitm via conjugating before and after the transform
/// <summary>
/// Calculates the inverse Fourier transformation using the CT algorithm.
/// The inversion is accounted by complex conjugation of the whole array before and after the transformation with the CT algorithm.
/// </summary>
/// <returns>Inverse Fourier transformed array</returns>
/// <param name="f">Array to be inverse Fourier transformed</param>
public static ComplexNumber[] ICT(ComplexNumber[] f)
{
// Complex conjugation of the whole array
for (int i = 0; i < f.Length; i++)
{
f[i] = f[i].Conjugate();
}
f = FFT.CT(f);
// Complex conjugation of the whole array again and resizing the parameters
for (int i = 0; i < f.Length; i++)
{
f[i] = f[i].Conjugate();
f[i] = f[i] / f.Length;
}
return(f);
}
/// <summary>
/// Simulates on timestep of the time evolution by performing the splitstep fourier method only once.
/// </summary>
/// <param name="FT">Algorithm which will be used for the Fouriertransformation</param>
public void splitStepFourier(string FT)
{
int size = this.psi.Length;
// psi=psi.*exp(-0.5*1i*dt*(V+(g1d/hbar)*abs(psi).ˆ2));
for (int i = 0; i < size; i++)
{
psi[i] = psi[i] * ComplexNumber.Exp(-0.5 * ComplexNumber.ImaginaryOne * deltaT
* (V[i] + g1D / PhysConst.hbar
* Math.Pow(psi[i].Norm(), 2)));
}
// decides which algorithm will be used for the FT
switch (FT)
{
case "DFT":
psi = FFT.DFT(psi);
break;
case "CT":
psi = FFT.CT(psi);
break;
case "BR":
psi = FFT.BR(psi, reversedBits);
break;
default:
break;
}
psi = FFT.Shift(psi); // shift the lower half with the upper one to restore normal order
for (int i = 0; i < size; i++)
{
psi[i] = psi[i] / size;
}
// psi_k=psi_k*exp(-0.5*dt*1i*(hbar/m)*kˆ2)
for (int i = 0; i < size; i++)
{
psi[i] = psi[i] * ComplexNumber.Exp(-0.5 * ComplexNumber.ImaginaryOne * deltaT * PhysConst.hbar / mass * Math.Pow(K[i], 2));
}
psi = FFT.Shift(psi); // shifts again, so that the result of the IFT will be normal orderd
// decides which algorithm will be used for the IFT
switch (FT)
{
case "DFT":
psi = FFT.IDFT(psi);
break;
case "CT":
psi = FFT.ICT(psi);
break;
case "BR":
psi = FFT.IBR(psi, reversedBits);
break;
default:
break;
}
for (int i = 0; i < size; i++)
{
psi[i] = psi[i] * size;
}
//psi = psi.* exp(-0.5 * 1i * dt * (V + (g1d / hbar) * abs(psi).ˆ2));
for (int i = 0; i < size; i++)
{
psi[i] = psi[i] * ComplexNumber.Exp(-0.5 * ComplexNumber.ImaginaryOne * deltaT
* (V[i] + g1D / PhysConst.hbar
* Math.Pow(psi[i].Norm(), 2)));
}
}
