def calc_IFFT_Fr(r, F_r):
"""Function to calculate the FFT following the IGOR procedure.
I do not agree with this procedure, but I follow it to compare my results
with Igor Pro's ones.
Parameters
----------
r : numpy array
atomic distance (nm)
F_r : numpy array
F(r)
Returns
-------
Q : numpy array
momentum transfer (nm^-1)
Qi_Q : numpy array
Qi(Q)
"""
NumPoints = 2**math.ceil(math.log(len(F_r)-1)/math.log(2))
F_r = Utility.resize_zero(F_r, NumPoints)
Q = np.linspace(0.0, 109, 550)
DelQ = 2*np.pi/(np.mean(np.diff(r))*NumPoints)
meanDeltar = np.mean(np.diff(r))
Q1 = fftpack.fftfreq(r.size, meanDeltar)
Qi_Q = fftpack.fft(F_r)
Qi_Q = Qi_Q[np.where(Q1>=0.0)]
Qi_Q = -np.imag(Qi_Q)*meanDeltar
Q1 = np.arange(0.0, 0.0+DelQ*len(Qi_Q), DelQ)
idxArray = np.zeros(550, dtype=np.int)
for i in range(len(Q)):
idxArray[i], _ = UtilityAnalysis.find_nearest(Q1, Q[i])
Qi_Q = Qi_Q[idxArray]
return (Q, Qi_Q)
def calc_FFT_QiQ(Q, Qi_Q, QmaxIntegrate):
"""Function to calculate the FFT following the Igor Pro procedure.
I do not agree with this procedure, but I follow it to compare my results
with Igor Pro's ones.
Parameters
----------
Q : numpy array
momentum transfer (nm^-1)
Qi_Q : numpy array
Q*i(Q)
QmaxIntegrate : float
maximum Q value for the integrations
Returns
-------
r : numpy array
atomic distance (nm)
F_r : numpy array
F(r)
"""
pMax, elem = UtilityAnalysis.find_nearest(Q, QmaxIntegrate)
NumPoints = 2*2*2**math.ceil(math.log(5*(pMax+1))/math.log(2))
DelR = 2*np.pi/(np.mean(np.diff(Q))*NumPoints)
Qi_Q = Utility.resize_zero(Qi_Q[Q<=QmaxIntegrate], NumPoints)
Qi_Q[pMax+1:] = 0.0
Q = np.arange(np.amin(Q), np.amin(Q)+np.mean(np.diff(Q))*NumPoints, np.mean(np.diff(Q)))
r = MainFunctions.calc_r(Q)
F_r = fftpack.fft(Qi_Q)
F_r = F_r[np.where(r>=0.0)]
F_r = -np.imag(F_r)*np.mean(np.diff(Q))*2/np.pi
r = np.arange(0.0, 0.0+DelR*len(F_r), DelR)
return (r, F_r)