def plot_L0_Pstar(self, axes=None, label=None, FIGSIZE=None):
if axes is None:
figure, axes = plt.subplots(1, figsize=FIGSIZE)
color = next(axes._get_lines.prop_cycler)['color']
axes.plot(np.arange(self.Nfreqs) + 1,
self.dct.logtau,
'.-',
c=color,
label=label)
axes.plot(np.arange(self.Nfreqs) + 1,
self.dct.logtau + self.dct.logtau_THEORY_std,
'--',
c=color)
axes.plot(np.arange(self.Nfreqs) + 1,
self.dct.logtau - self.dct.logtau_THEORY_std,
'--',
c=color)
axes.axvline(x=self.dct.aic_Kmin + 1, ls='--', c=color)
axes.set_xlim([0, 3 * self.dct.aic_Kmin])
max_y = np.amax((self.dct.logtau +
self.dct.logtau_THEORY_std)[self.dct.aic_Kmin:3 *
self.dct.aic_Kmin])
min_y = np.amin((self.dct.logtau -
self.dct.logtau_THEORY_std)[self.dct.aic_Kmin:3 *
self.dct.aic_Kmin])
axes.set_ylim([min_y * 0.8, max_y * 1.2])
axes.set_xlabel(r'$P^*$')
axes.set_ylabel(r'$L_0(P*)$')
return axes
def plot_kappa_Pstar(self, axes=None, label=None, FIGSIZE=None):
if axes is None:
figure, axes = plt.subplots(1, figsize=FIGSIZE)
color = next(axes._get_lines.prop_cycler)['color']
axes.plot(np.arange(self.Nfreqs) + 1,
self.dct.tau * self.kappa_scale * 0.5,
'.-',
c=color,
label=label)
axes.plot(np.arange(self.Nfreqs) + 1, (self.dct.tau + self.dct.tau_THEORY_std) * self.kappa_scale * 0.5,
'--', c=color) # yapf: disable
axes.plot(np.arange(self.Nfreqs) + 1, (self.dct.tau - self.dct.tau_THEORY_std) * self.kappa_scale * 0.5,
'--', c=color) # yapf: disable
axes.axvline(x=self.dct.aic_Kmin + 1, ls='--', c=color)
axes.axhline(y=self.kappa_Kmin, ls='--', c=color)
axes.set_xlim([0, 3 * self.dct.aic_Kmin])
max_y = np.amax(
self.kappa_scale * 0.5 *
(self.dct.tau + self.dct.tau_THEORY_std)[self.dct.aic_Kmin:3 *
self.dct.aic_Kmin])
min_y = np.amin(
self.kappa_scale * 0.5 *
(self.dct.tau - self.dct.tau_THEORY_std)[self.dct.aic_Kmin:3 *
self.dct.aic_Kmin])
axes.set_ylim([min_y * 0.8, max_y * 1.2])
axes.set_xlabel(r'$P^*$')
axes.set_ylabel(r'$\kappa(P^*)$ [W/(m*K)]')
return axes
def plot_ck(self, axes=None, label=None, FIGSIZE=None):
if axes is None:
figure, axes = plt.subplots(1, figsize=FIGSIZE)
color = next(axes._get_lines.prop_cycler)['color']
axes.plot(self.dct.logpsdK, 'o-', c=color, label=label)
axes.plot(self.dct.logpsdK + self.dct.logpsdK_THEORY_std,
'--',
c=color)
axes.plot(self.dct.logpsdK - self.dct.logpsdK_THEORY_std,
'--',
c=color)
axes.axvline(x=self.dct.aic_Kmin, ls='--', c=color)
axes.set_xlabel(r'$k$')
axes.set_ylabel(r'$c_k$')
return axes
def plot_cepstral_spectrum(self,
freq_units='thz',
freq_scale=1.0,
axes=None,
kappa_units=True,
FIGSIZE=None,
**plot_kwargs):
if axes is None:
figure, axes = plt.subplots(2, sharex=True, figsize=FIGSIZE)
plt.subplots_adjust(hspace=0.1)
if kappa_units:
psd_scale = 0.5 * self.kappa_scale
else:
psd_scale = 1.0
if (freq_units == 'thz') or (freq_units == 'THz'):
axes[0].plot(self.freqs_THz, self.dct.psd * psd_scale,
**plot_kwargs)
axes[1].plot(self.freqs_THz, self.dct.logpsd, **plot_kwargs)
axes[0].set_xlim([0., self.Nyquist_f_THz])
axes[1].set_xlim([0., self.Nyquist_f_THz])
elif (freq_units == 'red'):
axes[0].plot(self.freqs / freq_scale, self.dct.psd * psd_scale,
**plot_kwargs)
axes[1].plot(self.freqs / freq_scale, self.dct.logpsd,
**plot_kwargs)
axes[0].set_xlim([0., 0.5 / freq_scale])
axes[1].set_xlim([0., 0.5 / freq_scale])
else:
raise ValueError('Units not valid.')
axes[0].xaxis.set_ticks_position('top')
axes[0].set_ylabel(r'PSD')
if kappa_units:
axes[0].set_ylabel(r'PSD [W/mK]')
else:
axes[0].set_ylabel(r'PSD')
axes[0].grid()
axes[1].xaxis.set_ticks_position('bottom')
axes[1].set_xlabel(r'$f$ [THz]')
axes[1].set_ylabel(r'log(PSD)')
axes[1].grid()
return axes
def fstar_analysis(x, TSKIP_LIST, aic_type='aic', Kmin_corrfactor=1.0, plot=True, axes=None, FIGSIZE=None,
verbose=False, **plot_kwargs): # yapf: disable
"""
Perform cepstral analysis on a set of resampled time series, to study the effect of f*.
For each TSKIP in TSKIP_LIST, the HeatCurrent x is filtered & resampled, and then cesptral-analysed.
Parameters
----------
TSKIP_LIST = list of sampling times [steps]
aic_type = the Akaike Information Criterion function used to choose the cutoff ('aic', 'aicc')
Kmin_corrfactor = correction factor multiplied by the AIC cutoff (cutoff = Kmin_corrfactor * aic_Kmin)
plot = plot the PSD (True/False)
axes = matplotlib.axes.Axes object (if None, create one)
FIGSIZE = plot figure size
verbose = verbose output (default: False)
**plot_kwargs = other parameters passed to plot function
Returns
-------
xf : array_like
an array of HeatCurrents, corresponding the values of TSKIP_LIST
ax : array_like, optional (if plot=True)
array of plot axes
fig : figure, optional (if axes=None)
plot figure
"""
if not isinstance(x, HeatCurrent):
raise ValueError('x must be a HeatCurrent object.')
xf = []
for TSKIP in TSKIP_LIST:
log.write_log('TSKIP = {:d}'.format(TSKIP))
xff = resample_current(x, TSKIP, plot=False, verbose=verbose)
xff.cepstral_analysis(aic_type, Kmin_corrfactor)
xf.append(xff)
FSTAR_THZ_LIST = [xff.Nyquist_f_THz for xff in xf]
if plot:
if axes is None:
figure, ax = plt.subplots(2, sharex=True, figsize=FIGSIZE)
else:
ax = axes
ax[0].errorbar(FSTAR_THZ_LIST, [xff.kappa_Kmin for xff in xf],
yerr=[xff.kappa_Kmin_std for xff in xf],
**plot_kwargs)
ax[1].errorbar(FSTAR_THZ_LIST, [xff.dct.logtau_Kmin for xff in xf],
yerr=[xff.dct.logtau_std_Kmin for xff in xf],
**plot_kwargs)
# ax[0].plot(x.freqs_THz, x.fpsd, **plot_kwargs)
# ax[1].plot(x.freqs_THz, x.flogpsd, **plot_kwargs)
ax[0].xaxis.set_ticks_position('top')
ax[0].set_ylabel(r'PSD')
ax[0].grid()
ax[1].xaxis.set_ticks_position('bottom')
ax[1].set_xlabel(r'$f$ [THz]')
ax[1].set_ylabel(r'log(PSD)')
ax[1].grid()
if axes is None:
ax2 = [ax[0].twinx(), ax[1].twinx()]
color = next(ax[0]._get_lines.prop_cycler)['color']
color = next(ax[1]._get_lines.prop_cycler)['color']
x.plot_periodogram(axes=ax2, c=color)
ax[0].set_ylabel(r'$\kappa$ [W/(m*K)]')
ax[1].set_ylabel(r'$\kappa$ [W/(m*K)]')
return xf, ax, figure
else:
return xf, ax
else:
return xf
def resample_current(x, TSKIP=None, fstar_THz=None, FILTER_W=None, plot=True, PSD_FILTER_W=None, freq_units='thz',
FIGSIZE=None, verbose=True): # yapf: disable
"""
Simulate the resampling of x.
Parameters
----------
TSKIP = sampling time [steps]
fstar_THz = target cutoff frequency [THz]
FILTER_W = pre-sampling filter window width [steps]
plot = plot the PSD (True/False)
PSD_FILTER_W = PSD filtering window width [chosen frequency units]
freq_units = 'thz' THz
'red' omega*DT/(2*pi)
FIGSIZE = plot figure size
Returns
-------
xf : HeatCurrent object
a filtered & resampled HeatCurrent
ax : array_like, optional (if plot=True)
an array of plot axes
"""
if not isinstance(x, HeatCurrent):
raise ValueError('x must be a HeatCurrent object.')
if (TSKIP is not None) and (fstar_THz is not None):
raise ValueError('Please specify either TSKIP or fstar_THz.')
if TSKIP is None:
if fstar_THz is None:
raise ValueError('Please specify either TSKIP or fstar_THz.')
else:
TSKIP = int(round(x.Nyquist_f_THz / fstar_THz))
if plot:
figure, axes = plt.subplots(2, sharex=True, figsize=FIGSIZE)
axes = x.plot_periodogram(
PSD_FILTER_W, freq_units, 1.0,
axes=axes) # this also updates x.FILTER_WINDOW_WIDTH
fstar_THz = x.Nyquist_f_THz / TSKIP
fstar_idx = np.argmin(x.freqs_THz < fstar_THz)
# filter and sample
if FILTER_W is None:
FILTER_W = TSKIP
trajf = md.tools.filter_and_sample(x.traj, FILTER_W, TSKIP, 'rectangular')
#TODO: document the units of frequency used everywere in the library and use a consistent scheme.
# resample filtering window width in order to use the same filtering frequency window in the plot
# if PSD_FILTER_W was specified, then x.FILTER_WINDOW_WIDTH was updated by the previous plot function
#if x.FILTER_WINDOW_WIDTH is not None:
# PSD_FILTER_W = x.FILTER_WINDOW_WIDTH * TSKIP
# define new HeatCurrent
if not x.many_currents:
xf = HeatCurrent(trajf, x.units, x.DT_FS * TSKIP, x.TEMPERATURE,
x.VOLUME, PSD_FILTER_W, freq_units)
else:
if x.otherMD is None:
raise RuntimeError(
'x.otherMD cannot be none (wrong/missing initialization?)')
# filter_and_sample also other trajectories
yf = []
yf.append(trajf)
for y in x.otherMD:
tmp = md.tools.filter_and_sample(y.traj, FILTER_W, TSKIP,
'rectangular')
yf.append(tmp)
xf = HeatCurrent(yf, x.units, x.DT_FS * TSKIP, x.TEMPERATURE, x.VOLUME,
PSD_FILTER_W, freq_units)
if plot:
if (freq_units == 'thz') or (freq_units == 'THz'):
xf.plot_periodogram(x.FILTER_WINDOW_WIDTH * 1000. / x.DT_FS,
'thz',
TSKIP,
axes=axes)
elif (freq_units == 'red'):
log.write_log(PSD_FILTER_W)
log.write_log(x.FILTER_WINDOW_WIDTH)
xf.plot_periodogram(x.FILTER_WINDOW_WIDTH * TSKIP,
'red',
TSKIP,
axes=axes)
# write log
xf.resample_log = \
'-----------------------------------------------------\n' +\
' RESAMPLE TIME SERIES\n' +\
'-----------------------------------------------------\n' +\
' Original Nyquist freq f_Ny = {:12.5f} THz\n'.format(x.Nyquist_f_THz) +\
' Resampling freq f* = {:12.5f} THz\n'.format(fstar_THz) +\
' Sampling time TSKIP = {:12d} steps\n'.format(TSKIP) +\
' = {:12.3f} fs\n'.format(TSKIP * x.DT_FS) +\
' Original n. of frequencies = {:12d}\n'.format(x.Nfreqs) +\
' Resampled n. of frequencies = {:12d}\n'.format(xf.Nfreqs)
if x.fpsd is not None and xf.fpsd is not None:
xf.resample_log += \
' PSD @cutoff (pre-filter) = {:12.5f}\n'.format(x.fpsd[fstar_idx]) +\
' (post-filter) = {:12.5f}\n'.format(xf.fpsd[-1]) +\
' log(PSD) @cutoff (pre-filter) = {:12.5f}\n'.format(x.flogpsd[fstar_idx]) +\
' (post-filter) = {:12.5f}\n'.format(xf.flogpsd[-1]) +\
' min(PSD) (pre-filter) = {:12.5f}\n'.format(x.psd_min) +\
' min(PSD) (post-filter) = {:12.5f}\n'.format(xf.psd_min) +\
' % of original PSD Power f<f* (pre-filter) = {:5f}\n'.format(np.trapz(x.psd[:fstar_idx+1]) / x.psd_power * 100.)
else:
xf.resample_log += ' fPSD not calculated before resampling!\n '
xf.resample_log += '-----------------------------------------------------\n'
if verbose:
log.write_log(xf.resample_log)
if plot:
if (freq_units == 'thz') or (freq_units == 'THz'):
axes[0].axvline(x=fstar_THz, ls='--', c='k')
axes[1].axvline(x=fstar_THz, ls='--', c='k')
axes[0].set_xlim([0., x.Nyquist_f_THz])
axes[1].set_xlim([0., x.Nyquist_f_THz])
elif (freq_units == 'red'):
axes[0].axvline(x=0.5 / TSKIP, ls='--', c='k')
axes[1].axvline(x=0.5 / TSKIP, ls='--', c='k')
axes[0].set_xlim([0., 0.5 / TSKIP])
axes[1].set_xlim([0., 0.5 / TSKIP])
return xf, axes
else:
return xf
def plot_periodogram(self, PSD_FILTER_W=None, freq_units='thz', freq_scale=1.0, axes=None, kappa_units=False,
FIGSIZE=None, **plot_kwargs): # yapf: disable
"""
Plot the periodogram.
PSD_FILTER_W = width of the filtering window
freq_units = 'thz' THz
'red' omega*DT/(2*pi)
freq_scale = rescale red frequencies by this factor (e.g. 2 --> freq = [0, 0.25])
axes = matplotlib.axes.Axes object (if None, create one)
FIGSIZE = size of the plot
Returns a matplotlib.axes.Axes object.
"""
# recompute PSD if needed
if self.psd is None:
if not self.many_currents:
self.compute_psd()
else:
if self.otherMD is None:
raise ValueError(
'self.otherMD cannot be None (missing initialization?)'
)
self.compute_kappa_multi(others=self.otherMD)
if PSD_FILTER_W is None:
if self.FILTER_WINDOW_WIDTH is None:
self.filter_psd(0.)
else:
if (freq_units == 'thz') or (freq_units == 'THz'):
self.filter_psd(freq_THz_to_red(PSD_FILTER_W, self.DT_FS))
elif (freq_units == 'red'):
self.filter_psd(PSD_FILTER_W)
else:
raise ValueError('Units not valid.')
if kappa_units:
# plot psd in units of kappa - the log(psd) is not converted
psd_scale = 0.5 * self.kappa_scale
else:
psd_scale = 1.0
if axes is None:
figure, axes = plt.subplots(2, sharex=True, figsize=FIGSIZE)
plt.subplots_adjust(hspace=0.1)
if (freq_units == 'thz') or (freq_units == 'THz'):
axes[0].plot(self.freqs_THz, psd_scale * self.fpsd, **plot_kwargs)
axes[1].plot(self.freqs_THz, self.flogpsd, **plot_kwargs)
axes[0].set_xlim([0., self.Nyquist_f_THz])
axes[1].set_xlim([0., self.Nyquist_f_THz])
elif (freq_units == 'red'):
axes[0].plot(self.freqs / freq_scale, psd_scale * self.fpsd,
**plot_kwargs)
axes[1].plot(self.freqs / freq_scale, self.flogpsd, **plot_kwargs)
axes[0].set_xlim([0., 0.5 / freq_scale])
axes[1].set_xlim([0., 0.5 / freq_scale])
else:
raise ValueError('Units not valid.')
axes[0].xaxis.set_ticks_position('top')
if kappa_units:
axes[0].set_ylabel(r'PSD [W/mK]')
else:
axes[0].set_ylabel(r'PSD')
axes[0].grid()
axes[1].xaxis.set_ticks_position('bottom')
axes[1].set_xlabel(r'$f$ [THz]')
axes[1].set_ylabel(r'log(PSD)')
axes[1].grid()
return axes
def fstar_analysis(x,
TSKIP_LIST,
aic_type='aic',
Kmin_corrfactor=1.0,
plot=True,
axes=None,
FIGSIZE=None,
**plot_kwargs):
"""
Simulate the resampling of x.
TSKIP = sampling time [steps]
fstar_THz = target cutoff frequency [THz]
FILTER_W = pre-sampling filter window width [steps]
plot = plot the PSD (True/False)
PSD_FILTER_W = PSD filtering window width [chosen frequency units]
freq_units = 'thz' THz
'red' omega*DT/(2*pi)
FIGSIZE = plot figure size
"""
if not isinstance(x, HeatCurrent):
raise ValueError('x must be a HeatCurrent object.')
xf = []
for TSKIP in TSKIP_LIST:
print 'TSKIP = {:d}'.format(TSKIP)
xff = resample_current(x, TSKIP, plot=False)
xff.cepstral_analysis(aic_type, Kmin_corrfactor)
xf.append(xff)
FSTAR_THZ_LIST = [xff.Nyquist_f_THz for xff in xf]
if plot:
if axes is None:
figure, ax = plt.subplots(2, sharex=True, figsize=FIGSIZE)
else:
ax = axes
ax[0].errorbar(FSTAR_THZ_LIST, [xff.kappa_Kmin for xff in xf],
yerr=[xff.kappa_Kmin_std for xff in xf],
**plot_kwargs)
ax[1].errorbar(FSTAR_THZ_LIST, [xff.dct.logtau_Kmin for xff in xf],
yerr=[xff.dct.logtau_std_Kmin for xff in xf],
**plot_kwargs)
#ax[0].plot(x.freqs_THz, x.fpsd, **plot_kwargs)
#ax[1].plot(x.freqs_THz, x.flogpsd, **plot_kwargs)
ax[0].xaxis.set_ticks_position('top')
ax[0].set_ylabel(r'PSD')
ax[0].grid()
ax[1].xaxis.set_ticks_position('bottom')
ax[1].set_xlabel(r'$f$ [THz]')
ax[1].set_ylabel(r'log(PSD)')
ax[1].grid()
if axes is None:
ax2 = [ax[0].twinx(), ax[1].twinx()]
color = next(ax[0]._get_lines.prop_cycler)['color']
color = next(ax[1]._get_lines.prop_cycler)['color']
x.plot_periodogram(axes=ax2, c=color)
ax[0].set_ylabel(r'$\kappa$ [W/(m*K)]')
ax[1].set_ylabel(r'$\kappa$ [W/(m*K)]')
return xf, ax, figure
else:
return xf, ax
else:
return xf
def resample_current(x,
TSKIP=None,
fstar_THz=None,
FILTER_W=None,
plot=True,
PSD_FILTER_W=None,
freq_units='thz',
FIGSIZE=None):
"""
Simulate the resampling of x.
TSKIP = sampling time [steps]
fstar_THz = target cutoff frequency [THz]
FILTER_W = pre-sampling filter window width [steps]
plot = plot the PSD (True/False)
PSD_FILTER_W = PSD filtering window width [chosen frequency units]
freq_units = 'thz' THz
'red' omega*DT/(2*pi)
FIGSIZE = plot figure size
"""
if not isinstance(x, HeatCurrent):
raise ValueError('x must be a HeatCurrent object.')
if (TSKIP is not None) and (fstar_THz is not None):
raise ValueError('Please specify either TSKIP or fstar_THz.')
if TSKIP is None:
if fstar_THz is None:
raise ValueError('Please specify either TSKIP or fstar_THz.')
else:
TSKIP = int(round(x.Nyquist_f_THz / fstar_THz))
if plot:
figure, axes = plt.subplots(2, sharex=True, figsize=FIGSIZE)
axes = x.plot_periodogram(PSD_FILTER_W, freq_units, 1.0, axes=axes)
fstar_THz = x.Nyquist_f_THz / TSKIP
fstar_idx = np.argmin(x.freqs_THz < fstar_THz)
# filter and sample
if FILTER_W is None:
FILTER_W = TSKIP
trajf = md.tools.filter_and_sample(x.traj, FILTER_W, TSKIP, 'rectangular')
if not x.multicomponent:
xf = HeatCurrent(trajf, x.units, x.DT_FS * TSKIP, x.TEMPERATURE,
x.VOLUME, x.FILTER_WINDOW_WIDTH * TSKIP)
else:
if x.otherMD is None:
raise ValueError(
'x.otherMD cannot be none (wrong/missing initialization?)')
# filter_and_sample also other trajectories
yf = []
yf.append(trajf)
for y in x.otherMD:
tmp = md.tools.filter_and_sample(y.traj, FILTER_W, TSKIP,
'rectangular')
yf.append(tmp)
xf = HeatCurrent(yf, x.units, x.DT_FS * TSKIP, x.TEMPERATURE, x.VOLUME,
x.FILTER_WINDOW_WIDTH * TSKIP)
if plot:
if (freq_units == 'thz') or (freq_units == 'THz'):
xf.plot_periodogram(x.FILTER_WINDOW_WIDTH * 1000. / x.DT_FS,
'thz',
TSKIP,
axes=axes)
elif (freq_units == 'red'):
print PSD_FILTER_W
print x.FILTER_WINDOW_WIDTH
xf.plot_periodogram(x.FILTER_WINDOW_WIDTH * TSKIP,
'red',
TSKIP,
axes=axes)
xf.resample_log = '-----------------------------------------------------\n' +\
' RESAMPLE TIME SERIES\n' +\
'-----------------------------------------------------\n' +\
' Original Nyquist freq f_Ny = {:12.5f} THz\n'.format(x.Nyquist_f_THz) +\
' Resampling freq f* = {:12.5f} THz\n'.format(fstar_THz) +\
' Sampling time TSKIP = {:12d} steps\n'.format(TSKIP) +\
' = {:12.3f} fs\n'.format(TSKIP * x.DT_FS) +\
' Original n. of frequencies = {:12d}\n'.format(x.Nfreqs) +\
' Resampled n. of frequencies = {:12d}\n'.format(xf.Nfreqs) +\
' PSD @cutoff (pre-filter) = {:12.5f}\n'.format(x.fpsd[fstar_idx]) +\
' (post-filter) = {:12.5f}\n'.format(xf.fpsd[-1]) +\
' log(PSD) @cutoff (pre-filter) = {:12.5f}\n'.format(x.flogpsd[fstar_idx]) +\
' (post-filter) = {:12.5f}\n'.format(xf.flogpsd[-1]) +\
' min(PSD) (pre-filter) = {:12.5f}\n'.format(x.psd_min) +\
' min(PSD) (post-filter) = {:12.5f}\n'.format(xf.psd_min) +\
' % of original PSD Power f<f* (pre-filter) = {:5f}\n'.format(np.trapz(x.psd[:fstar_idx+1]) / x.psd_power * 100.) +\
'-----------------------------------------------------\n'
print xf.resample_log
if plot:
if (freq_units == 'thz') or (freq_units == 'THz'):
axes[0].axvline(x=fstar_THz, ls='--', c='k')
axes[1].axvline(x=fstar_THz, ls='--', c='k')
axes[0].set_xlim([0., x.Nyquist_f_THz])
axes[1].set_xlim([0., x.Nyquist_f_THz])
elif (freq_units == 'red'):
axes[0].axvline(x=0.5 / TSKIP, ls='--', c='k')
axes[1].axvline(x=0.5 / TSKIP, ls='--', c='k')
axes[0].set_xlim([0., 0.5 / TSKIP])
axes[1].set_xlim([0., 0.5 / TSKIP])
return xf, axes
else:
return xf