sharpness = 5000 # with ideally dense sampled data, this should converge to infinity; reduce it to avoid ringing
return -1j * np.sum(y * np.arctan(1/(new_x_grid - old_x_grid)/sharpness)*sharpness, axis=1) / len(x) / (2*pi)
if test_kramers_kronig:
## Test the Kramers-Kronig relations - in f
new_f = np.linspace(-maxplotf, maxplotf, 1000)
conv = naive_hilbert_transform(f, yf, new_f)
#conv = naive_hilbert_transform(freq, yf2, new_f) ## FIXME - using these data, the KK amplitude goes wrong
plot_complex(new_f, conv, c='b', alpha=.6, lw=.5, label='KKR in $f$')
## Spectrum 4: use the Filter-Diagonalisation Method, implemented in Harminv, to find discrete oscillators
if harmonic_inversion:
import harminv_wrapper
tscale = 1.0 ## harminv output may have to be tuned by changing this value
x = x[int(len(x)*FDMtrunc[0]):int(len(x)*FDMtrunc[1])]*tscale
y = y[int(len(y)*FDMtrunc[0]):int(len(y)*FDMtrunc[1])]
hi = harminv_wrapper.harminv(x, y, amplitude_prescaling=None)
hi['frequency'] *= tscale
hi['decay'] *= tscale
oscillator_count = len(hi['frequency'])
freq_fine = np.linspace(-maxplotf, maxplotf, 2000)
sumosc = np.zeros_like(freq_fine)*1j
for osc in range(oscillator_count):
osc_y = lorentz(omega=freq_fine*2*pi,
omega0=hi['frequency'][osc]*2*pi,
gamma=hi['decay'][osc]*2*pi,
ampli=hi['amplitude'][osc] * np.abs(hi['frequency'][osc])*2*pi)
sumosc += osc_y
plot_complex(freq_fine, sumosc, color='g', alpha=.6, lw=2, label=u"Harminv modes sum") # (optional) plot amplitude
Wh = np.trapz(y=np.abs(sumosc)**2, x=freq_fine); print 'Plancherel theorem test: Energy in Harminv f :', Wh, '(i.e. %.5g of timedomain)' % (Wh/Wt)
#print 'All harminv oscillators (frequency, decay and amplitude):\n', np.vstack([hi['frequency'], hi['decay'], hi['amplitude']])
for line in datafile:
if line[0:1] in "0123456789": break # end of file header
value = line.replace(",", " ").split()[-1] # the value of the parameter will be separated by space or comma
if not Kz and ("Kz" in line): Kz = float(value)
if not cellsize and ("cellsize" in line): cellsize = float(value)
Kz = Kz*cellsize/2/np.pi
(t, E) = np.loadtxt(filename, usecols=list(range(2)), unpack=True, )
if plot_FDM:
import harminv_wrapper
tscale = 3e9 ## TODO check again that this prescaling is needed
t1 = t[len(t)*FDMtrunc[0]:len(t)*FDMtrunc[1]]*tscale
t1 -= np.min(t1)
E1 = E[len(t)*FDMtrunc[0]:len(t)*FDMtrunc[1]]
try:
hi = harminv_wrapper.harminv(t1, E1, d=.1, f=15)
hi['frequency'] *= tscale /frequnit
hi['amplitude'] /= np.max(hi['amplitude'])
hi['error'] /= np.max(hi['amplitude'])
FDM_freqs = np.append(FDM_freqs, hi['frequency'])
FDM_amplis= np.append(FDM_amplis, hi['amplitude'])
FDM_phases= np.append(FDM_phases, hi['phase'])
FDM_Kzs = np.append(FDM_Kzs, Kz*np.ones_like(hi['frequency']))
except:
print "Error: Harminv did not find any oscillator in %s" % filename
if plot_FFT:
for field in (E,):
field[t>max(t)*FFTcutoff] = field[t>max(t)*FFTcutoff]*(.5 + .5*np.cos(np.pi * (t[t>max(t)*FFTcutoff]/max(t)-FFTcutoff)/(1-FFTcutoff)))
## 1D FFT with cropping for useful frequencies
if test_kramers_kronig:
## Test the Kramers-Kronig relations - in f
new_f = np.linspace(-maxplotf, maxplotf, 1000)
conv = naive_hilbert_transform(f, yf, new_f)
#conv = naive_hilbert_transform(freq, yf2, new_f) ## FIXME - using these data, the KK amplitude goes wrong
plot_complex(new_f, conv, c='b', alpha=.6, lw=.5, label='KKR in $f$')
## Spectrum 4: use the Filter-Diagonalisation Method, implemented in Harminv, to find discrete oscillators
if harmonic_inversion:
import harminv_wrapper
tscale = 1.0 ## harminv output may have to be tuned by changing this value
x = x[int(len(x) * FDMtrunc[0]):int(len(x) * FDMtrunc[1])] * tscale
y = y[int(len(y) * FDMtrunc[0]):int(len(y) * FDMtrunc[1])]
hi = harminv_wrapper.harminv(x, y, amplitude_prescaling=None)
hi['frequency'] *= tscale
hi['decay'] *= tscale
oscillator_count = len(hi['frequency'])
freq_fine = np.linspace(-maxplotf, maxplotf, 2000)
sumosc = np.zeros_like(freq_fine) * 1j
for osc in range(oscillator_count):
osc_y = lorentz(omega=freq_fine * 2 * pi,
omega0=hi['frequency'][osc] * 2 * pi,
gamma=hi['decay'][osc] * 2 * pi,
ampli=hi['amplitude'][osc] *
np.abs(hi['frequency'][osc]) * 2 * pi)
sumosc += osc_y
plot_complex(freq_fine,
sumosc,
