def xrf_resid(pars, peaks=None, mca=None, det=None, bgr=None,
sig=None, filters=None, flyield=None, use_bgr=False,
xray_en=30.0, emin=0.0, emax=30.0, **kws):
sig_o = pars.sig_o.value
sig_s = pars.sig_s.value
sig_q = pars.sig_q.value
model = mca.data * 0.0
if use_bgr:
model += mca.bgr
for use, pcen, psig, pamp in peaks:
amp = pamp.value
cen = pcen.value
sig = sig_o + cen * (sig_s + sig_q * cen)
psig.value = sig
if use: model += amp*gaussian(mca.energy, cen, sig)
mca.model = model
imin = index_of(mca.energy, emin)
imax = index_of(mca.energy, emax)
resid = (mca.data - model)
# if det['use']:
# resid = resid / np.maximum(1.e-29, (1.0 - mca.det_atten))
return resid[imin:imax]
def get_xranges(self, x):
opts = self.read_form()
dgroup = self.controller.get_group()
en_eps = min(np.diff(dgroup.energy)) / 5.
i1 = index_of(x, opts['emin'] + en_eps)
i2 = index_of(x, opts['emax'] + en_eps) + 1
return i1, i2
def get_xranges(self, x):
opts = self.read_form()
dgroup = self.controller.get_group()
en_eps = min(np.diff(dgroup.energy)) / 5.
i1 = index_of(x, opts['emin'] + en_eps)
i2 = index_of(x, opts['emax'] + en_eps) + 1
return i1, i2
def onPick2Timer(self, evt=None):
"""checks for 'Pick 2' events, and initiates 'Pick 2' guess
for a model from the selected data range
"""
try:
plotframe = self.controller.get_display(win=1)
curhist = plotframe.cursor_hist[:]
plotframe.Raise()
except:
return
if (time.time() - self.pick2_t0) > self.pick2_timeout:
msg = self.pick2_group.pick2_msg.SetLabel(" ")
plotframe.cursor_hist = []
self.pick2_timer.Stop()
return
if len(curhist) < 2:
self.pick2_group.pick2_msg.SetLabel("%i/2" % (len(curhist)))
return
self.pick2_group.pick2_msg.SetLabel("done.")
self.pick2_timer.Stop()
# guess param values
xcur = (curhist[0][0], curhist[1][0])
xmin, xmax = min(xcur), max(xcur)
dgroup = getattr(self.larch.symtable, self.controller.groupname)
x, y = dgroup.xdat, dgroup.ydat
i0 = index_of(dgroup.xdat, xmin)
i1 = index_of(dgroup.xdat, xmax)
x, y = dgroup.xdat[i0:i1+1], dgroup.ydat[i0:i1+1]
mod = self.pick2_group.mclass(prefix=self.pick2_group.prefix)
parwids = self.pick2_group.parwids
try:
guesses = mod.guess(y, x=x)
except:
return
for name, param in guesses.items():
if name in parwids:
parwids[name].value.SetValue(param.value)
dgroup._tmp = mod.eval(guesses, x=dgroup.xdat)
plotframe = self.controller.get_display(win=1)
plotframe.cursor_hist = []
plotframe.oplot(dgroup.xdat, dgroup._tmp)
self.pick2erase_panel = plotframe.panel
self.pick2erase_timer.Start(5000)
def onPick2Timer(self, evt=None):
"""checks for 'Pick 2' events, and initiates 'Pick 2' guess
for a model from the selected data range
"""
try:
plotframe = self.controller.get_display(stacked=False)
curhist = plotframe.cursor_hist[:]
plotframe.Raise()
except:
return
if (time.time() - self.pick2_t0) > self.pick2_timeout:
msg = self.pick2_group.pick2_msg.SetLabel(" ")
plotframe.cursor_hist = []
self.pick2_timer.Stop()
return
if len(curhist) < 2:
self.pick2_group.pick2_msg.SetLabel("%i/2" % (len(curhist)))
return
self.pick2_group.pick2_msg.SetLabel("done.")
self.pick2_timer.Stop()
# guess param values
xcur = (curhist[0][0], curhist[1][0])
xmin, xmax = min(xcur), max(xcur)
dgroup = getattr(self.larch.symtable, self.controller.groupname)
x, y = dgroup.x, dgroup.y
i0 = index_of(dgroup.x, xmin)
i1 = index_of(dgroup.x, xmax)
x, y = dgroup.x[i0:i1 + 1], dgroup.y[i0:i1 + 1]
mod = self.pick2_group.mclass(prefix=self.pick2_group.prefix)
parwids = self.pick2_group.parwids
try:
guesses = mod.guess(y, x=x)
except:
return
for name, param in guesses.items():
if name in parwids:
parwids[name].value.SetValue(param.value)
dgroup._tmp = mod.eval(guesses, x=dgroup.x)
plotframe = self.controller.get_display(stacked=False)
plotframe.cursor_hist = []
plotframe.oplot(dgroup.x, dgroup._tmp)
self.pick2erase_panel = plotframe.panel
self.pick2erase_timer.Start(5000)
def get_xranges(self, x):
xmin, xmax = min(x), max(x)
i1, i2 = 0, len(x)
_xmin = self.xmin.GetValue()
_xmax = self.xmax.GetValue()
if _xmin > min(x):
i1 = index_of(x, _xmin)
xmin = x[i1]
if _xmax < max(x):
i2 = index_of(x, _xmax) + 1
xmax = x[i2]
xv1 = max(min(x), xmin - (xmax - xmin) / 5.0)
xv2 = min(max(x), xmax + (xmax - xmin) / 5.0)
return i1, i2, xv1, xv2
def on_cursor(self, event=None, side='left'):
if event is None:
return
x, y = event.xdata, event.ydata
if len(self.panel.fig.properties()['axes']) > 1:
try:
x, y = self.panel.axes.transData.inverted().transform(
(event.x, event.y))
except:
pass
ix = x
if self.mca is not None:
ix = index_of(self.mca.energy, x)
if side == 'right':
self.xmarker_right = ix
elif side == 'left':
self.xmarker_left = ix
if self.xmarker_left is not None and self.xmarker_right is not None:
ix1, ix2 = self.xmarker_left, self.xmarker_right
self.xmarker_left = min(ix1, ix2)
self.xmarker_right = max(ix1, ix2)
if side == 'left':
self.energy_for_zoom = self.mca.energy[ix]
self.update_status()
self.draw()
def get_plot_arrays(self, dgroup):
form = self.read_form()
lab = plotlabels.norm
if dgroup is None:
return
dgroup.plot_y2label = None
dgroup.plot_xlabel = plotlabels.energy
dgroup.plot_yarrays = [('norm', PLOTOPTS_1, lab)]
if dgroup.datatype != 'xas':
pchoice = PlotOne_Choices_nonxas[
self.plotone_op.GetStringSelection()]
dgroup.plot_xlabel = 'x'
dgroup.plot_ylabel = 'y'
dgroup.plot_yarrays = [('ydat', PLOTOPTS_1, 'ydat')]
dgroup.dmude = np.gradient(dgroup.ydat) / np.gradient(dgroup.xdat)
if pchoice == 'dmude':
dgroup.plot_ylabel = 'dy/dx'
dgroup.plot_yarrays = [('dmude', PLOTOPTS_1, 'dy/dx')]
elif pchoice == 'norm+deriv':
lab = plotlabels.norm
dgroup.plot_y2label = 'dy/dx'
dgroup.plot_yarrays = [('ydat', PLOTOPTS_1, 'y'),
('dmude', PLOTOPTS_D, 'dy/dx')]
return
pchoice = PlotOne_Choices[self.plotone_op.GetStringSelection()]
if pchoice in ('mu', 'norm', 'flat', 'dmude'):
lab = getattr(plotlabels, pchoice)
dgroup.plot_yarrays = [(pchoice, PLOTOPTS_1, lab)]
elif pchoice == 'prelines':
dgroup.plot_yarrays = [('mu', PLOTOPTS_1, plotlabels.mu),
('pre_edge', PLOTOPTS_2, 'pre edge'),
('post_edge', PLOTOPTS_2, 'post edge')]
elif pchoice == 'preedge':
dgroup.pre_edge_sub = dgroup.norm * dgroup.edge_step
dgroup.plot_yarrays = [('pre_edge_sub', PLOTOPTS_1,
r'pre-edge subtracted $\mu$')]
lab = r'pre-edge subtracted $\mu$'
elif pchoice == 'norm+deriv':
lab = plotlabels.norm
lab2 = plotlabels.dmude
dgroup.plot_yarrays = [('norm', PLOTOPTS_1, lab),
('dmude', PLOTOPTS_D, lab2)]
dgroup.plot_y2label = lab2
dgroup.plot_ylabel = lab
y4e0 = dgroup.ydat = getattr(dgroup, dgroup.plot_yarrays[0][0],
dgroup.mu)
dgroup.plot_extras = []
if form['show_e0']:
ie0 = index_of(dgroup.energy, dgroup.e0)
dgroup.plot_extras.append(('marker', dgroup.e0, y4e0[ie0], {}))
def extend_plotrange(x, y, xmin=None, xmax=None, extend=0.05):
"""return plot limits to extend a plot range for x, y pairs"""
xeps = min(diff(x)) / 5.
if xmin is None:
xmin = min(x)
if xmax is None:
xmax = max(x)
i0 = index_of(x, xmin + xeps)
i1 = index_of(x, xmax + xeps) + 1
xspan = x[i0:i1]
xrange = max(xspan) - min(xspan)
yspan = y[i0:i1]
yrange = max(yspan) - min(yspan)
return (min(xspan) - extend * xrange,
max(xspan) + extend * xrange,
min(yspan) - extend * yrange,
max(yspan) + extend * yrange)
def fit_spectrum(self, energy, counts, energy_min=None,
energy_max=None):
work_energy = 1.0*energy
work_counts = 1.0*counts
floor = 1.e-12*np.percentile(counts, [99])[0]
work_counts[np.where(counts<floor)] = floor
if max(energy) < 250.0: # input energies are in keV
work_energy = 1000.0 * energy
self.set_fit_weight(work_energy, work_counts)
imin, imax = 0, len(counts)
if energy_min is None:
energy_min = self.energy_min
if energy_min is not None:
imin = index_of(work_energy, energy_min)
if energy_max is None:
energy_max = self.energy_max
if energy_max is not None:
imax = index_of(work_energy, energy_max)
self.fit_weight[:imin-1] = 0.0
self.fit_weight[imax+1:] = 0.0
self.fit_iter = 0
userkws = dict(data=work_counts,
index=np.arange(len(counts)))
kws = dict(method='leastsq', maxfev=4000, gtol=self.fit_toler,
ftol=self.fit_toler, xtol=self.fit_toler, epsfcn=1.e-5)
self.result = minimize(self.__resid, self.params, kws=userkws, **kws)
self.fit_report = fit_report(self.result, min_correl=0.5)
self.best_fit = self.calc_spectrum(energy, params=self.result.params)
# calculate transfer matrix for linear analysis using this model
tmat= []
for key, val in self.comps.items():
tmat.append(val / self.eigenvalues[key])
self.transfer_matrix = np.array(tmat)
def xrf_resid(pars,
peaks=None,
mca=None,
det=None,
bgr=None,
sig=None,
filters=None,
flyield=None,
use_bgr=False,
xray_en=30.0,
emin=0.0,
emax=30.0,
**kws):
sig_o = pars['sig_o'].value
sig_s = pars['sig_s'].value
sig_q = pars['sig_q'].value
model = mca.data * 0.0
if use_bgr:
model += mca.bgr
for use, pcen, psig, pamp in peaks:
amp = pars[pamp.name].value
cen = pars[pcen.name].value
sig = pars[psig.name].value
if use:
model += gaussian(mca.energy, amplitude=amp, center=cen, sigma=sig)
mca.model = model
imin = index_of(mca.energy, emin)
imax = index_of(mca.energy, emax)
resid = (mca.data - model)
# if det['use']:
# resid = resid / np.maximum(1.e-29, (1.0 - mca.det_atten))
return resid[imin:imax]
def plot_prepeaks_baseline(dgroup, subtract_baseline=False, show_fitrange=True,
show_peakrange=True, win=1, _larch=None, **kws):
"""Plot pre-edge peak baseline fit, as from `pre_edge_baseline` or XAS Viewer
dgroup must have a 'prepeaks' attribute
"""
if not hasattr(dgroup, 'prepeaks'):
raise ValueError('Group needs prepeaks')
#endif
ppeak = dgroup.prepeaks
px0, px1, py0, py1 = extend_plotrange(dgroup.xdat, dgroup.ydat,
xmin=ppeak.emin, xmax=ppeak.emax)
title = "pre_edge baesline\n %s" % dgroup.filename
popts = dict(xmin=px0, xmax=px1, ymin=py0, ymax=py1, title=title,
xlabel='Energy (eV)', ylabel='mu', delay_draw=True,
show_legend=True, style='solid', linewidth=3,
label='data', new=True,
marker='None', markersize=4, win=win, _larch=_larch)
popts.update(kws)
ydat = dgroup.ydat
xdat = dgroup.xdat
if subtract_baseline:
xdat = ppeak.energy
ydat = ppeak.baseline
popts['label'] = 'baseline subtracted peaks'
_plot(xdat, ydat, **popts)
else:
_plot(xdat, ydat, **popts)
popts['new'] = False
popts['label'] = 'baseline'
_oplot(ppeak.energy, ppeak.baseline, **popts)
popts = dict(win=win, _larch=_larch, delay_draw=True,
label='_nolegend_')
if show_fitrange:
for x in (ppeak.emin, ppeak.emax):
_plot_axvline(x, color='#DDDDCC', **popts)
_plot_axvline(ppeak.centroid, color='#EECCCC', **popts)
if show_peakrange:
for x in (ppeak.elo, ppeak.ehi):
y = ydat[index_of(xdat, x)]
_plot_marker(x, y, color='#222255', marker='o', size=8, **popts)
redraw(win=win, show_legend=True, _larch=_larch)
def guess_starting_values(self, y, x):
"""could probably improve this"""
ymax, ymin = max(y), min(y)
yex = ymax
self.set_initval(self.params.amplitude, 5.*(ymax-ymin))
if self.negative:
yex = ymin
self.params.amplitude.value = -(ymax - ymin)*5.0
iyex = index_nearest(y, yex)
self.set_initval(self.params.center, x[iyex])
halfy = yex /2.0
ihalfy = index_of(y, halfy)
sig0 = abs(x[iyex] - x[ihalfy])
sig1 = 0.15*(max(x) - min(x))
if sig1 < sig0 : sig0 = sig1
self.set_initval(self.params.sigma, sig0)
bkg0 = ymin
if self.negative: bkg0 = ymax
self.set_init_bkg(bkg0)
def mback_norm(energy, mu=None, group=None, z=None, edge='K', e0=None,
pre1=None, pre2=-50, norm1=100, norm2=None, nnorm=1, nvict=1,
_larch=None):
"""
simplified version of MBACK to Match mu(E) data for tabulated f''(E)
for normalization
Arguments:
energy, mu: arrays of energy and mu(E)
group: output group (and input group for e0)
z: Z number of absorber
e0: edge energy
pre1: low E range (relative to E0) for pre-edge fit
pre2: high E range (relative to E0) for pre-edge fit
norm1: low E range (relative to E0) for post-edge fit
norm2: high E range (relative to E0) for post-edge fit
nnorm: degree of polynomial (ie, nnorm+1 coefficients will be
found) for post-edge normalization curve fit to the
scaled f2. Default=1 (linear)
Returns:
group.norm_poly: normalized mu(E) from pre_edge()
group.norm: normalized mu(E) from this method
group.mback_mu: tabulated f2 scaled and pre_edge added to match mu(E)
group.mback_params: Group of parameters for the minimization
References:
* MBACK (Weng, Waldo, Penner-Hahn): http://dx.doi.org/10.1086/303711
* Chantler: http://dx.doi.org/10.1063/1.555974
"""
### implement the First Argument Group convention
energy, mu, group = parse_group_args(energy, members=('energy', 'mu'),
defaults=(mu,), group=group,
fcn_name='mback')
if len(energy.shape) > 1:
energy = energy.squeeze()
if len(mu.shape) > 1:
mu = mu.squeeze()
group = set_xafsGroup(group, _larch=_larch)
group.norm_poly = group.norm*1.0
if z is not None: # need to run find_e0:
e0_nominal = xray_edge(z, edge)[0]
if e0 is None:
e0 = getattr(group, 'e0', None)
if e0 is None:
find_e0(energy, mu, group=group)
e0 = group.e0
atsym = None
if z is None or z < 2:
atsym, edge = guess_edge(group.e0, _larch=_larch)
z = atomic_number(atsym)
if atsym is None and z is not None:
atsym = atomic_symbol(z)
if getattr(group, 'pre_edge_details', None) is None: # pre_edge never run
preedge(energy, mu, pre1=pre1, pre2=pre2, nvict=nvict,
norm1=norm1, norm2=norm2, e0=e0, nnorm=nnorm)
mu_pre = mu - group.pre_edge
f2 = f2_chantler(z, energy)
weights = np.ones(len(energy))*1.0
if norm2 is None:
norm2 = max(energy) - e0
if norm2 < 0:
norm2 = max(energy) - e0 - norm2
# avoid l2 and higher edges
if edge.lower().startswith('l'):
if edge.lower() == 'l3':
e_l2 = xray_edge(z, 'L2').edge
norm2 = min(norm2, e_l2-e0)
elif edge.lower() == 'l2':
e_l2 = xray_edge(z, 'L1').edge
norm2 = min(norm2, e_l1-e0)
ipre2 = index_of(energy, e0+pre2)
inor1 = index_of(energy, e0+norm1)
inor2 = index_of(energy, e0+norm2) + 1
weights[ipre2:] = 0.0
weights[inor1:inor2] = np.linspace(0.1, 1.0, inor2-inor1)
params = Parameters()
params.add(name='slope', value=0.0, vary=True)
params.add(name='offset', value=-f2[0], vary=True)
params.add(name='scale', value=f2[-1], vary=True)
out = minimize(f2norm, params, method='leastsq',
gtol=1.e-5, ftol=1.e-5, xtol=1.e-5, epsfcn=1.e-5,
kws = dict(en=energy, mu=mu_pre, f2=f2, weights=weights))
p = out.params.valuesdict()
model = (p['offset'] + p['slope']*energy + f2) * p['scale']
group.mback_mu = model + group.pre_edge
pre_f2 = preedge(energy, model, nnorm=nnorm, nvict=nvict, e0=e0,
pre1=pre1, pre2=pre2, norm1=norm1, norm2=norm2)
step_new = pre_f2['edge_step']
group.edge_step_poly = group.edge_step
group.edge_step_mback = step_new
group.norm_mback = mu_pre / step_new
group.mback_params = Group(e0=e0, pre1=pre1, pre2=pre2, norm1=norm1,
norm2=norm2, nnorm=nnorm, fit_params=p,
fit_weights=weights, model=model, f2=f2,
pre_f2=pre_f2, atsym=atsym, edge=edge)
if (abs(step_new - group.edge_step)/(1.e-13+group.edge_step)) > 0.75:
print("Warning: mback edge step failed....")
else:
group.edge_step = step_new
group.norm = group.norm_mback
def plot_mu(dgroup,
show_norm=False,
show_deriv=False,
show_pre=False,
show_post=False,
show_e0=False,
with_deriv=False,
emin=None,
emax=None,
label='mu',
new=True,
title=None,
win=1,
_larch=None):
"""
plot_mu(dgroup, norm=False, deriv=False, show_pre=False, show_post=False,
show_e0=False, show_deriv=False, emin=None, emax=None, label=None,
new=True, win=1)
Plot mu(E) for an XAFS data group in various forms
Arguments
----------
dgroup group of XAFS data after pre_edge() results (see Note 1)
show_norm bool whether to show normalized data [False]
show_deriv bool whether to show derivative of XAFS data [False]
show_pre bool whether to show pre-edge curve [False]
show_post bool whether to show post-edge curve [False]
show_e0 bool whether to show E0 [False]
with_deriv bool whether to show deriv together with mu [False]
emin min energy to show, relative to E0 [None, start of data]
emax max energy to show, relative to E0 [None, end of data]
label string for label [None: 'mu', `dmu/dE', or 'mu norm']
title string for plot titlel [None, may use filename if available]
new bool whether to start a new plot [True]
win integer plot window to use [1]
Notes
-----
1. The input data group must have the following attributes:
energy, mu, norm, e0, pre_edge, edge_step
"""
if hasattr(dgroup, 'mu'):
mu = dgroup.mu
elif hasattr(dgroup, 'mutrans'):
mu = dgroup.mutrans
elif hasattr(dgroup, 'mufluor'):
mu = dgroup.mufluor
else:
raise ValueError("XAFS data group has no array for mu")
#endif
ylabel = plotlabels.mu
if label is None:
label = 'mu'
#endif
if show_deriv:
mu = gradient(mu) / gradient(dgroup.energy)
ylabel = plotlabels.dmude
dlabel = '%s (deriv)' % label
elif show_norm:
mu = dgroup.norm
ylabel = "%s (norm)" % ylabel
dlabel = "%s (norm)" % label
#endif
xmin, xmax = None, None
if emin is not None: xmin = dgroup.e0 + emin
if emax is not None: xmax = dgroup.e0 + emax
title = _get_title(dgroup, title=title)
opts = dict(win=win,
show_legend=True,
linewidth=3,
title=title,
xmin=xmin,
xmax=xmax,
_larch=_larch)
_plot(dgroup.energy,
mu,
xlabel=plotlabels.energy,
ylabel=ylabel,
label=label,
zorder=20,
new=new,
**opts)
if with_deriv:
dmu = gradient(mu) / gradient(dgroup.energy)
_plot(dgroup.energy,
dmu,
ylabel=plotlabels.dmude,
label='%s (deriv)' % label,
zorder=18,
side='right',
**opts)
#endif
if (not show_norm and not show_deriv):
if show_pre:
_plot(dgroup.energy,
dgroup.pre_edge,
label='pre_edge',
zorder=18,
**opts)
#endif
if show_post:
_plot(dgroup.energy,
dgroup.post_edge,
label='post_edge',
zorder=18,
**opts)
if show_pre:
i = index_of(dgroup.energy, dgroup.e0)
ypre = dgroup.pre_edge[i]
ypost = dgroup.post_edge[i]
_plot_arrow(dgroup.e0,
ypre,
dgroup.e0,
ypost,
color=plotlabels.e0color,
width=0.25,
head_width=0,
zorder=3,
win=win,
_larch=_larch)
#endif
#endif
#endif
if show_e0:
_plot_axvline(dgroup.e0,
zorder=2,
size=3,
label='E0',
color=plotlabels.e0color,
win=win,
_larch=_larch)
_getDisplay(win=win, _larch=_larch).panel.conf.draw_legend()
def process(self, gname, **kws):
""" handle process (pre-edge/normalize) XAS data from XAS form, overwriting
larch group 'x' and 'y' attributes to be plotted
"""
dgroup = self.controller.get_group(gname)
proc_opts = {}
proc_opts['xshift'] = self.xshift.GetValue()
proc_opts['yshift'] = self.yshift.GetValue()
proc_opts['xscale'] = self.xscale.GetValue()
proc_opts['yscale'] = self.yscale.GetValue()
proc_opts['smooth_op'] = self.smooth_op.GetStringSelection()
proc_opts['smooth_c0'] = int(self.smooth_c0.GetValue())
proc_opts['smooth_c1'] = int(self.smooth_c1.GetValue())
proc_opts['smooth_sig'] = float(self.smooth_sig.GetValue())
proc_opts['smooth_conv'] = self.smooth_conv.GetStringSelection()
self.xaspanel.Enable(dgroup.datatype.startswith('xas'))
if dgroup.datatype.startswith('xas'):
proc_opts['datatype'] = 'xas'
proc_opts['e0'] = self.xas_e0.GetValue()
proc_opts['edge_step'] = self.xas_step.GetValue()
proc_opts['pre1'] = self.xas_pre1.GetValue()
proc_opts['pre2'] = self.xas_pre2.GetValue()
proc_opts['norm1'] = self.xas_nor1.GetValue()
proc_opts['norm2'] = self.xas_nor2.GetValue()
proc_opts['nvict'] = self.xas_vict.GetSelection()
proc_opts['nnorm'] = self.xas_nnor.GetSelection()
proc_opts['auto_e0'] = self.xas_autoe0.IsChecked()
proc_opts['show_e0'] = self.xas_showe0.IsChecked()
proc_opts['auto_step'] = self.xas_autostep.IsChecked()
proc_opts['nnorm'] = int(self.xas_nnor.GetSelection())
proc_opts['nvict'] = int(self.xas_vict.GetSelection())
proc_opts['xas_op'] = self.xas_op.GetStringSelection()
self.controller.process(dgroup, proc_opts=proc_opts)
if dgroup.datatype.startswith('xas'):
if self.xas_autoe0.IsChecked():
self.xas_e0.SetValue(dgroup.proc_opts['e0'], act=False)
if self.xas_autostep.IsChecked():
self.xas_step.SetValue(dgroup.proc_opts['edge_step'], act=False)
self.xas_pre1.SetValue(dgroup.proc_opts['pre1'])
self.xas_pre2.SetValue(dgroup.proc_opts['pre2'])
self.xas_nor1.SetValue(dgroup.proc_opts['norm1'])
self.xas_nor2.SetValue(dgroup.proc_opts['norm2'])
dgroup.orig_ylabel = dgroup.plot_ylabel
dgroup.plot_ylabel = '$\mu$'
dgroup.plot_y2label = None
dgroup.plot_xlabel = '$E \,\mathrm{(eV)}$'
dgroup.plot_yarrays = [(dgroup.mu, PLOTOPTS_1, dgroup.plot_ylabel)]
y4e0 = dgroup.mu
out = self.xas_op.GetStringSelection().lower() # raw, pre, norm, flat
if out.startswith('raw data + pre'):
dgroup.plot_yarrays = [(dgroup.mu, PLOTOPTS_1, '$\mu$'),
(dgroup.pre_edge, PLOTOPTS_2, 'pre edge'),
(dgroup.post_edge, PLOTOPTS_2, 'post edge')]
elif out.startswith('pre'):
dgroup.pre_edge_sub = dgroup.norm * dgroup.edge_step
dgroup.plot_yarrays = [(dgroup.pre_edge_sub, PLOTOPTS_1,
'pre-edge subtracted $\mu$')]
y4e0 = dgroup.pre_edge_sub
dgroup.plot_ylabel = 'pre-edge subtracted $\mu$'
elif 'norm' in out and 'deriv' in out:
dgroup.plot_yarrays = [(dgroup.norm, PLOTOPTS_1, 'normalized $\mu$'),
(dgroup.dmude, PLOTOPTS_D, '$d\mu/dE$')]
y4e0 = dgroup.norm
dgroup.plot_ylabel = 'normalized $\mu$'
dgroup.plot_y2label = '$d\mu/dE$'
dgroup.y = dgroup.norm
elif out.startswith('norm'):
dgroup.plot_yarrays = [(dgroup.norm, PLOTOPTS_1, 'normalized $\mu$')]
y4e0 = dgroup.norm
dgroup.plot_ylabel = 'normalized $\mu$'
dgroup.y = dgroup.norm
elif out.startswith('deriv'):
dgroup.plot_yarrays = [(dgroup.dmude, PLOTOPTS_1, '$d\mu/dE$')]
y4e0 = dgroup.dmude
dgroup.plot_ylabel = '$d\mu/dE$'
dgroup.y = dgroup.dmude
dgroup.plot_ymarkers = []
if self.xas_showe0.IsChecked():
ie0 = index_of(dgroup.xdat, dgroup.e0)
dgroup.plot_ymarkers = [(dgroup.e0, y4e0[ie0], {'label': '_nolegend_'})]
def plot_mu(dgroup, show_norm=False, show_deriv=False,
show_pre=False, show_post=False, show_e0=False, with_deriv=False,
emin=None, emax=None, label='mu', new=True, delay_draw=False,
offset=0, title=None, win=1, _larch=None):
"""
plot_mu(dgroup, norm=False, deriv=False, show_pre=False, show_post=False,
show_e0=False, show_deriv=False, emin=None, emax=None, label=None,
new=True, win=1)
Plot mu(E) for an XAFS data group in various forms
Arguments
----------
dgroup group of XAFS data after pre_edge() results (see Note 1)
show_norm bool whether to show normalized data [False]
show_deriv bool whether to show derivative of XAFS data [False]
show_pre bool whether to show pre-edge curve [False]
show_post bool whether to show post-edge curve [False]
show_e0 bool whether to show E0 [False]
with_deriv bool whether to show deriv together with mu [False]
emin min energy to show, relative to E0 [None, start of data]
emax max energy to show, relative to E0 [None, end of data]
label string for label [None: 'mu', `dmu/dE', or 'mu norm']
title string for plot titlel [None, may use filename if available]
new bool whether to start a new plot [True]
delay_draw bool whether to delay draw until more traces are added [False]
offset vertical offset to use for y-array [0]
win integer plot window to use [1]
Notes
-----
1. The input data group must have the following attributes:
energy, mu, norm, e0, pre_edge, edge_step
"""
if hasattr(dgroup, 'mu'):
mu = dgroup.mu
elif hasattr(dgroup, 'mutrans'):
mu = dgroup.mutrans
elif hasattr(dgroup, 'mufluor'):
mu = dgroup.mufluor
else:
raise ValueError("XAFS data group has no array for mu")
#endif
ylabel = plotlabels.mu
if label is None:
label = 'mu'
#endif
if show_deriv:
mu = gradient(mu)/gradient(dgroup.energy)
ylabel = plotlabels.dmude
dlabel = '%s (deriv)' % label
elif show_norm:
mu = dgroup.norm
ylabel = "%s (norm)" % ylabel
dlabel = "%s (norm)" % label
#endif
xmin, xmax = None, None
if emin is not None: xmin = dgroup.e0 + emin
if emax is not None: xmax = dgroup.e0 + emax
title = _get_title(dgroup, title=title)
opts = dict(win=win, show_legend=True, linewidth=3,
title=title, xmin=xmin, xmax=xmax,
delay_draw=True, _larch=_larch)
_plot(dgroup.energy, mu+offset, xlabel=plotlabels.energy, ylabel=ylabel,
label=label, zorder=20, new=new, **opts)
if with_deriv:
dmu = gradient(mu)/gradient(dgroup.energy)
_plot(dgroup.energy, dmu+offset, ylabel=plotlabels.dmude,
label='%s (deriv)' % label, zorder=18, side='right', **opts)
#endif
if (not show_norm and not show_deriv):
if show_pre:
_plot(dgroup.energy, dgroup.pre_edge+offset, label='pre_edge',
zorder=18, **opts)
#endif
if show_post:
_plot(dgroup.energy, dgroup.post_edge+offset, label='post_edge',
zorder=18, **opts)
if show_pre:
i = index_of(dgroup.energy, dgroup.e0)
ypre = dgroup.pre_edge[i]
ypost = dgroup.post_edge[i]
_plot_arrow(dgroup.e0, ypre, dgroup.e0+offset, ypost,
color=plotlabels.e0color, width=0.25,
head_width=0, zorder=3, win=win, _larch=_larch)
#endif
#endif
#endif
if show_e0:
_plot_axvline(dgroup.e0, zorder=2, size=3,
label='E0', color=plotlabels.e0color, win=win,
_larch=_larch)
_getDisplay(win=win, _larch=_larch).panel.conf.draw_legend()
#endif
redraw(win=win, _larch=_larch)
def get_xlims(x, xmin, xmax):
xeps = min(np.diff(x))/ 5.
i1 = index_of(x, xmin + xeps)
i2 = index_of(x, xmax + xeps) + 1
return i1, i2
def mback(energy,
mu=None,
group=None,
order=3,
z=None,
edge='K',
e0=None,
emin=None,
emax=None,
whiteline=None,
leexiang=False,
tables='chantler',
fit_erfc=False,
return_f1=False,
_larch=None):
"""
Match mu(E) data for tabulated f''(E) using the MBACK algorithm and,
optionally, the Lee & Xiang extension
Arguments:
energy, mu: arrays of energy and mu(E)
order: order of polynomial [3]
group: output group (and input group for e0)
z: Z number of absorber
edge: absorption edge (K, L3)
e0: edge energy
emin: beginning energy for fit
emax: ending energy for fit
whiteline: exclusion zone around white lines
leexiang: flag to use the Lee & Xiang extension
tables: 'chantler' (default) or 'cl'
fit_erfc: True to float parameters of error function
return_f1: True to put the f1 array in the group
Returns:
group.f2: tabulated f2(E)
group.f1: tabulated f1(E) (if return_f1 is True)
group.fpp: matched data
group.mback_params: Group of parameters for the minimization
References:
* MBACK (Weng, Waldo, Penner-Hahn): http://dx.doi.org/10.1086/303711
* Lee and Xiang: http://dx.doi.org/10.1088/0004-637X/702/2/970
* Cromer-Liberman: http://dx.doi.org/10.1063/1.1674266
* Chantler: http://dx.doi.org/10.1063/1.555974
"""
order = int(order)
if order < 1: order = 1 # set order of polynomial
if order > MAXORDER: order = MAXORDER
### implement the First Argument Group convention
energy, mu, group = parse_group_args(energy,
members=('energy', 'mu'),
defaults=(mu, ),
group=group,
fcn_name='mback')
if len(energy.shape) > 1:
energy = energy.squeeze()
if len(mu.shape) > 1:
mu = mu.squeeze()
group = set_xafsGroup(group, _larch=_larch)
if e0 is None: # need to run find_e0:
e0 = xray_edge(z, edge, _larch=_larch)[0]
if e0 is None:
e0 = group.e0
if e0 is None:
find_e0(energy, mu, group=group)
### theta is an array used to exclude the regions <emin, >emax, and
### around white lines, theta=0.0 in excluded regions, theta=1.0 elsewhere
(i1, i2) = (0, len(energy) - 1)
if emin is not None: i1 = index_of(energy, emin)
if emax is not None: i2 = index_of(energy, emax)
theta = np.ones(len(energy)) # default: 1 throughout
theta[0:i1] = 0
theta[i2:-1] = 0
if whiteline:
pre = 1.0 * (energy < e0)
post = 1.0 * (energy > e0 + float(whiteline))
theta = theta * (pre + post)
if edge.lower().startswith('l'):
l2 = xray_edge(z, 'L2', _larch=_larch)[0]
l2_pre = 1.0 * (energy < l2)
l2_post = 1.0 * (energy > l2 + float(whiteline))
theta = theta * (l2_pre + l2_post)
## this is used to weight the pre- and post-edge differently as
## defined in the MBACK paper
weight1 = 1 * (energy < e0)
weight2 = 1 * (energy > e0)
weight = np.sqrt(sum(weight1)) * weight1 + np.sqrt(sum(weight2)) * weight2
## get the f'' function from CL or Chantler
if tables.lower() == 'chantler':
f1 = f1_chantler(z, energy, _larch=_larch)
f2 = f2_chantler(z, energy, _larch=_larch)
else:
(f1, f2) = f1f2(z, energy, edge=edge, _larch=_larch)
group.f2 = f2
if return_f1:
group.f1 = f1
em = xray_line(z, edge.upper(), _larch=_larch)[0] # erfc centroid
params = Parameters()
params.add(name='s', value=1, vary=True) # scale of data
params.add(name='xi', value=50, vary=fit_erfc, min=0) # width of erfc
params.add(name='a', value=0, vary=False) # amplitude of erfc
if fit_erfc:
params['a'].value = 1
params['a'].vary = True
for i in range(order): # polynomial coefficients
params.add(name='c%d' % i, value=0, vary=True)
out = minimize(match_f2,
params,
method='leastsq',
gtol=1.e-5,
ftol=1.e-5,
xtol=1.e-5,
epsfcn=1.e-5,
kws=dict(en=energy,
mu=mu,
f2=f2,
e0=e0,
em=em,
order=order,
weight=weight,
theta=theta,
leexiang=leexiang))
opars = out.params.valuesdict()
eoff = energy - e0
norm_function = opars['a'] * erfc(
(energy - em) / opars['xi']) + opars['c0']
for i in range(order):
j = i + 1
attr = 'c%d' % j
if attr in opars:
norm_function += opars[attr] * eoff**j
group.e0 = e0
group.fpp = opars['s'] * mu - norm_function
group.mback_params = opars
tmp = Group(energy=energy, mu=group.f2 - norm_function, e0=0)
# calculate edge step from f2 + norm_function: should be very smooth
pre_f2 = preedge(energy, group.f2 + norm_function, e0=e0, nnorm=2, nvict=0)
group.edge_step = pre_f2['edge_step'] / opars['s']
pre_fpp = preedge(energy, mu, e0=e0, nnorm=2, nvict=0)
group.norm = (mu - pre_fpp['pre_edge']) / group.edge_step
def onPlot(self, evt=None):
plot_choice = self.plot_choice.GetStringSelection()
opts = self.read_form()
dgroup = self.controller.get_group()
ppeaks = getattr(dgroup, 'prepeaks', None)
if ppeaks is None:
return
i1, i2 = self.get_xranges(dgroup.xdat)
# i2 = len(ppeaks.baseline) + i1
if len(dgroup.yfit) > len(ppeaks.baseline):
i2 = i1 + len(ppeaks.baseline)
# print(" Indexes: ", i1, i2, i2-i1, len(dgroup.yfit), len(ppeaks.baseline))
xdat = 1.0*dgroup.energy
ydat = 1.0*dgroup.ydat
yfit = 1.0*dgroup.ydat
baseline = 1.0*dgroup.ydat
yfit[i1:i2] = dgroup.yfit[:i2-i1]
baseline[i1:i2] = ppeaks.baseline[:i2-i1]
if opts['plot_sub_bline']:
ydat = ydat - baseline
if plot_choice in (PLOT_FIT, PLOT_RESID):
yfit = yfit - baseline
if plot_choice == PLOT_RESID:
resid = ydat - yfit
_xs = dgroup.energy[i1:i2]
xrange = max(_xs) - min(_xs)
pxmin = min(_xs) - 0.05 * xrange
pxmax = max(_xs) + 0.05 * xrange
jmin = index_of(dgroup.energy, pxmin)
jmax = index_of(dgroup.energy, pxmax) + 1
_ys = ydat[jmin:jmax]
yrange = max(_ys) - min(_ys)
pymin = min(_ys) - 0.05 * yrange
pymax = max(_ys) + 0.05 * yrange
title = ' pre-edge fit'
if plot_choice == PLOT_BASELINE:
title = ' pre-edge baseline'
if opts['plot_sub_bline']:
title = ' pre-edge peaks'
array_desc = self.array_choice.GetStringSelection()
plotopts = {'xmin': pxmin, 'xmax': pxmax,
'ymin': pymin, 'ymax': pymax,
'title': '%s: %s' % (opts['gname'], title),
'xlabel': 'Energy (eV)',
'ylabel': '%s $\mu$' % opts['array_desc'],
'label': '%s $\mu$' % opts['array_desc'],
'delay_draw': True,
'show_legend': True}
plot_extras = []
if opts['show_fitrange']:
popts = {'color': '#DDDDCC'}
emin = opts['emin']
emax = opts['emax']
imin = index_of(dgroup.energy, emin)
imax = index_of(dgroup.energy, emax)
plot_extras.append(('vline', emin, None, popts))
plot_extras.append(('vline', emax, None, popts))
if opts['show_peakrange']:
popts = {'marker': '+', 'markersize': 6}
elo = opts['elo']
ehi = opts['ehi']
ilo = index_of(dgroup.xdat, elo)
ihi = index_of(dgroup.xdat, ehi)
plot_extras.append(('marker', elo, ydat[ilo], popts))
plot_extras.append(('marker', ehi, ydat[ihi], popts))
if opts['show_centroid']:
popts = {'color': '#EECCCC'}
ecen = getattr(dgroup.prepeaks, 'centroid', -1)
if ecen > min(dgroup.energy):
plot_extras.append(('vline', ecen, None, popts))
pframe = self.controller.get_display(win=2,
stacked=(plot_choice==PLOT_RESID))
ppanel = pframe.panel
axes = ppanel.axes
plotopts.update(PLOTOPTS_1)
ppanel.plot(xdat, ydat, **plotopts)
if plot_choice == PLOT_BASELINE:
if not opts['plot_sub_bline']:
ppanel.oplot(dgroup.prepeaks.energy,
dgroup.prepeaks.baseline,
label='baseline', **PLOTOPTS_2)
elif plot_choice in (PLOT_FIT, PLOT_RESID):
ppanel.oplot(dgroup.energy, yfit,
label='fit', **PLOTOPTS_1)
if hasattr(dgroup, 'ycomps'):
ncomp = len(dgroup.ycomps)
icomp = 0
for label, ycomp in dgroup.ycomps.items():
icomp +=1
fcomp = self.fit_components[label]
# print("ycomp: ", plot_choice, label, len(ycomp), len(dgroup.xfit),
# fcomp.bkgbox.IsChecked(), opts['plot_sub_bline'], icomp, ncomp)
if not (fcomp.bkgbox.IsChecked() and opts['plot_sub_bline']):
ppanel.oplot(dgroup.xfit, ycomp, label=label,
delay_draw=(icomp!=ncomp), style='short dashed')
if plot_choice == PLOT_RESID:
_ys = resid
yrange = max(_ys) - min(_ys)
plotopts['ymin'] = min(_ys) - 0.05 * yrange
plotopts['ymax'] = max(_ys) + 0.05 * yrange
plotopts['delay_draw'] = False
plotopts['ylabel'] = 'data-fit'
plotopts['label'] = '_nolegend_'
pframe.plot(dgroup.energy, resid, panel='bot', **plotopts)
pframe.Show()
# print(" RESIDUAL PLOT margins: ")
# print(" top : ", pframe.panel.conf.margins)
# print(" bot : ", pframe.panel_bot.conf.margins)
for etype, x, y, opts in plot_extras:
if etype == 'marker':
popts = {'marker': 'o', 'markersize': 4,
'label': '_nolegend_',
'markerfacecolor': 'red',
'markeredgecolor': '#884444'}
popts.update(opts)
axes.plot([x], [y], **popts)
elif etype == 'vline':
popts = {'ymin': 0, 'ymax': 1.0, 'color': '#888888',
'label': '_nolegend_'}
popts.update(opts)
axes.axvline(x, **popts)
ppanel.canvas.draw()
def autobk(energy, mu=None, group=None, rbkg=1, nknots=None, e0=None,
edge_step=None, kmin=0, kmax=None, kweight=1, dk=0.1,
win='hanning', k_std=None, chi_std=None, nfft=2048, kstep=0.05,
pre_edge_kws=None, nclamp=4, clamp_lo=1, clamp_hi=1,
calc_uncertainties=True, err_sigma=1, _larch=None, **kws):
"""Use Autobk algorithm to remove XAFS background
Parameters:
-----------
energy: 1-d array of x-ray energies, in eV, or group
mu: 1-d array of mu(E)
group: output group (and input group for e0 and edge_step).
rbkg: distance (in Ang) for chi(R) above
which the signal is ignored. Default = 1.
e0: edge energy, in eV. If None, it will be determined.
edge_step: edge step. If None, it will be determined.
pre_edge_kws: keyword arguments to pass to pre_edge()
nknots: number of knots in spline. If None, it will be determined.
kmin: minimum k value [0]
kmax: maximum k value [full data range].
kweight: k weight for FFT. [1]
dk: FFT window window parameter. [0.1]
win: FFT window function name. ['hanning']
nfft: array size to use for FFT [2048]
kstep: k step size to use for FFT [0.05]
k_std: optional k array for standard chi(k).
chi_std: optional chi array for standard chi(k).
nclamp: number of energy end-points for clamp [2]
clamp_lo: weight of low-energy clamp [1]
clamp_hi: weight of high-energy clamp [1]
calc_uncertaintites: Flag to calculate uncertainties in
mu_0(E) and chi(k) [True]
err_sigma: sigma level for uncertainties in mu_0(E) and chi(k) [1]
Output arrays are written to the provided group.
Follows the 'First Argument Group' convention.
"""
msg = sys.stdout
if _larch is not None:
msg = _larch.writer.write
if 'kw' in kws:
kweight = kws.pop('kw')
if len(kws) > 0:
msg('Unrecognized a:rguments for autobk():\n')
msg(' %s\n' % (', '.join(kws.keys())))
return
energy, mu, group = parse_group_args(energy, members=('energy', 'mu'),
defaults=(mu,), group=group,
fcn_name='autobk')
if len(energy.shape) > 1:
energy = energy.squeeze()
if len(mu.shape) > 1:
mu = mu.squeeze()
energy = remove_dups(energy)
# if e0 or edge_step are not specified, get them, either from the
# passed-in group or from running pre_edge()
group = set_xafsGroup(group, _larch=_larch)
if edge_step is None and isgroup(group, 'edge_step'):
edge_step = group.edge_step
if e0 is None and isgroup(group, 'e0'):
e0 = group.e0
if e0 is None or edge_step is None:
# need to run pre_edge:
pre_kws = dict(nnorm=3, nvict=0, pre1=None,
pre2=-50., norm1=100., norm2=None)
if pre_edge_kws is not None:
pre_kws.update(pre_edge_kws)
pre_edge(energy, mu, group=group, _larch=_larch, **pre_kws)
if e0 is None:
e0 = group.e0
if edge_step is None:
edge_step = group.edge_step
if e0 is None or edge_step is None:
msg('autobk() could not determine e0 or edge_step!: trying running pre_edge first\n')
return
# get array indices for rkbg and e0: irbkg, ie0
ie0 = index_of(energy, e0)
rgrid = np.pi/(kstep*nfft)
if rbkg < 2*rgrid: rbkg = 2*rgrid
irbkg = int(1.01 + rbkg/rgrid)
# save ungridded k (kraw) and grided k (kout)
# and ftwin (*k-weighting) for FT in residual
enpe = energy[ie0:] - e0
kraw = np.sign(enpe)*np.sqrt(ETOK*abs(enpe))
if kmax is None:
kmax = max(kraw)
else:
kmax = max(0, min(max(kraw), kmax))
kout = kstep * np.arange(int(1.01+kmax/kstep), dtype='float64')
iemax = min(len(energy), 2+index_of(energy, e0+kmax*kmax/ETOK)) - 1
# interpolate provided chi(k) onto the kout grid
if chi_std is not None and k_std is not None:
chi_std = np.interp(kout, k_std, chi_std)
# pre-load FT window
ftwin = kout**kweight * ftwindow(kout, xmin=kmin, xmax=kmax,
window=win, dx=dk, dx2=dk)
# calc k-value and initial guess for y-values of spline params
nspl = max(5, min(64, int(2*rbkg*(kmax-kmin)/np.pi) + 2))
spl_y, spl_k, spl_e = np.zeros(nspl), np.zeros(nspl), np.zeros(nspl)
for i in range(nspl):
q = kmin + i*(kmax-kmin)/(nspl - 1)
ik = index_nearest(kraw, q)
i1 = min(len(kraw)-1, ik + 5)
i2 = max(0, ik - 5)
spl_k[i] = kraw[ik]
spl_e[i] = energy[ik+ie0]
spl_y[i] = (2*mu[ik+ie0] + mu[i1+ie0] + mu[i2+ie0] ) / 4.0
# get spline represention: knots, coefs, order=3
# coefs will be varied in fit.
knots, coefs, order = splrep(spl_k, spl_y)
# set fit parameters from initial coefficients
params = Parameters()
for i in range(len(coefs)):
params.add(name = FMT_COEF % i, value=coefs[i], vary=i<len(spl_y))
initbkg, initchi = spline_eval(kraw[:iemax-ie0+1], mu[ie0:iemax+1],
knots, coefs, order, kout)
# do fit
result = minimize(__resid, params, method='leastsq',
gtol=1.e-5, ftol=1.e-5, xtol=1.e-5, epsfcn=1.e-5,
kws = dict(ncoefs=len(coefs), chi_std=chi_std,
knots=knots, order=order,
kraw=kraw[:iemax-ie0+1],
mu=mu[ie0:iemax+1], irbkg=irbkg, kout=kout,
ftwin=ftwin, kweight=kweight,
nfft=nfft, nclamp=nclamp,
clamp_lo=clamp_lo, clamp_hi=clamp_hi))
# write final results
coefs = [result.params[FMT_COEF % i].value for i in range(len(coefs))]
bkg, chi = spline_eval(kraw[:iemax-ie0+1], mu[ie0:iemax+1],
knots, coefs, order, kout)
obkg = np.copy(mu)
obkg[ie0:ie0+len(bkg)] = bkg
# outputs to group
group = set_xafsGroup(group, _larch=_larch)
group.bkg = obkg
group.chie = (mu-obkg)/edge_step
group.k = kout
group.chi = chi/edge_step
group.e0 = e0
# now fill in 'autobk_details' group
details = Group(params=result.params)
details.init_bkg = np.copy(mu)
details.init_bkg[ie0:ie0+len(bkg)] = initbkg
details.init_chi = initchi/edge_step
details.knots_e = spl_e
details.knots_y = np.array([coefs[i] for i in range(nspl)])
details.init_knots_y = spl_y
details.nfev = result.nfev
details.kmin = kmin
details.kmax = kmax
group.autobk_details = details
# uncertainties in mu0 and chi: can be fairly slow.
if calc_uncertainties:
nchi = len(chi)
nmue = iemax-ie0 + 1
redchi = result.redchi
covar = result.covar / redchi
jac_chi = np.zeros(nchi*nspl).reshape((nspl, nchi))
jac_bkg = np.zeros(nmue*nspl).reshape((nspl, nmue))
cvals, cerrs = [], []
for i in range(len(coefs)):
par = result.params[FMT_COEF % i]
cvals.append(getattr(par, 'value', 0.0))
cdel = getattr(par, 'stderr', 0.0)
if cdel is None:
cdel = 0.0
cerrs.append(cdel/2.0)
cvals = np.array(cvals)
cerrs = np.array(cerrs)
# find derivatives by hand!
_k = kraw[:nmue]
_m = mu[ie0:iemax+1]
for i in range(nspl):
cval0 = cvals[i]
cvals[i] = cval0 + cerrs[i]
bkg1, chi1 = spline_eval(_k, _m, knots, cvals, order, kout)
cvals[i] = cval0 - cerrs[i]
bkg2, chi2 = spline_eval(_k, _m, knots, cvals, order, kout)
cvals[i] = cval0
jac_chi[i] = (chi1 - chi2) / (2*cerrs[i])
jac_bkg[i] = (bkg1 - bkg2) / (2*cerrs[i])
dfchi = np.zeros(nchi)
dfbkg = np.zeros(nmue)
for i in range(nspl):
for j in range(nspl):
dfchi += jac_chi[i]*jac_chi[j]*covar[i,j]
dfbkg += jac_bkg[i]*jac_bkg[j]*covar[i,j]
prob = 0.5*(1.0 + erf(err_sigma/np.sqrt(2.0)))
dchi = t.ppf(prob, nchi-nspl) * np.sqrt(dfchi*redchi)
dbkg = t.ppf(prob, nmue-nspl) * np.sqrt(dfbkg*redchi)
group.delta_chi = dchi
group.delta_bkg = 0.0*mu
group.delta_bkg[ie0:ie0+len(dbkg)] = dbkg
def mback(energy, mu=None, group=None, z=None, edge='K', e0=None, pre1=None, pre2=-50,
norm1=100, norm2=None, order=3, leexiang=False, tables='chantler', fit_erfc=False,
return_f1=False, _larch=None):
"""
Match mu(E) data for tabulated f''(E) using the MBACK algorithm and,
optionally, the Lee & Xiang extension
Arguments
----------
energy: array of x-ray energies, in eV.
mu: array of mu(E).
group: output group.
z: atomic number of the absorber.
edge: x-ray absorption edge (default 'K')
e0: edge energy, in eV. If None, it will be determined here.
pre1: low E range (relative to e0) for pre-edge region.
pre2: high E range (relative to e0) for pre-edge region.
norm1: low E range (relative to e0) for post-edge region.
norm2: high E range (relative to e0) for post-edge region.
order: order of the legendre polynomial for normalization.
(default=3, min=0, max=5).
leexiang: boolean (default False) to use the Lee & Xiang extension.
tables: tabulated scattering factors: 'chantler' (default) or 'cl' (cromer-liberman)
fit_erfc: boolean (default False) to fit parameters of error function.
return_f1: boolean (default False) to include the f1 array in the group.
Returns
-------
None
The following attributes will be written to the output group:
group.f2: tabulated f2(E).
group.f1: tabulated f1(E) (if 'return_f1' is True).
group.fpp: mback atched spectrum.
group.edge_step: edge step of spectrum.
group.norm: normalized spectrum.
group.mback_params: group of parameters for the minimization.
References:
* MBACK (Weng, Waldo, Penner-Hahn): http://dx.doi.org/10.1086/303711
* Lee and Xiang: http://dx.doi.org/10.1088/0004-637X/702/2/970
* Cromer-Liberman: http://dx.doi.org/10.1063/1.1674266
* Chantler: http://dx.doi.org/10.1063/1.555974
"""
order = max(min(order, MAXORDER), 0)
### implement the First Argument Group convention
energy, mu, group = parse_group_args(energy, members=('energy', 'mu'),
defaults=(mu,), group=group,
fcn_name='mback')
if len(energy.shape) > 1:
energy = energy.squeeze()
if len(mu.shape) > 1:
mu = mu.squeeze()
group = set_xafsGroup(group, _larch=_larch)
energy = remove_dups(energy)
if e0 is None or e0 < energy[1] or e0 > energy[-2]:
e0 = find_e0(energy, mu, group=group)
print(e0)
ie0 = index_nearest(energy, e0)
e0 = energy[ie0]
pre1_input = pre1
norm2_input = norm2
if pre1 is None: pre1 = min(energy) - e0
if norm2 is None: norm2 = max(energy) - e0
if norm2 < 0: norm2 = max(energy) - e0 - norm2
pre1 = max(pre1, (min(energy) - e0))
norm2 = min(norm2, (max(energy) - e0))
if pre1 > pre2:
pre1, pre2 = pre2, pre1
if norm1 > norm2:
norm1, norm2 = norm2, norm1
p1 = index_of(energy, pre1+e0)
p2 = index_nearest(energy, pre2+e0)
n1 = index_nearest(energy, norm1+e0)
n2 = index_of(energy, norm2+e0)
if p2 - p1 < 2:
p2 = min(len(energy), p1 + 2)
if n2 - n1 < 2:
p2 = min(len(energy), p1 + 2)
## theta is a boolean array indicating the
## energy values considered for the fit.
## theta=1 for included values, theta=0 for excluded values.
theta = np.zeros_like(energy, dtype='int')
theta[p1:(p2+1)] = 1
theta[n1:(n2+1)] = 1
## weights for the pre- and post-edge regions, as defined in the MBACK paper (?)
weight = np.ones_like(energy, dtype=float)
weight[p1:(p2+1)] = np.sqrt(np.sum(weight[p1:(p2+1)]))
weight[n1:(n2+1)] = np.sqrt(np.sum(weight[n1:(n2+1)]))
## get the f'' function from CL or Chantler
if tables.lower() == 'chantler':
f1 = f1_chantler(z, energy, _larch=_larch)
f2 = f2_chantler(z, energy, _larch=_larch)
else:
(f1, f2) = f1f2(z, energy, edge=edge, _larch=_larch)
group.f2 = f2
if return_f1:
group.f1 = f1
em = find_xray_line(z, edge)[0] # erfc centroid
params = Parameters()
params.add(name='s', value=1.0, vary=True) # scale of data
params.add(name='xi', value=50.0, vary=False, min=0) # width of erfc
params.add(name='a', value=0.0, vary=False) # amplitude of erfc
if fit_erfc:
params['a'].vary = True
params['a'].value = 0.5
params['xi'].vary = True
for i in range(order+1): # polynomial coefficients
params.add(name='c%d' % i, value=0, vary=True)
out = minimize(match_f2, params, method='leastsq',
gtol=1.e-5, ftol=1.e-5, xtol=1.e-5, epsfcn=1.e-5,
kws = dict(en=energy, mu=mu, f2=f2, e0=e0, em=em,
order=order, weight=weight, theta=theta, leexiang=leexiang))
opars = out.params.valuesdict()
eoff = energy - e0
norm_function = opars['a']*erfc((energy-em)/opars['xi']) + opars['c0']
for i in range(order):
attr = 'c%d' % (i + 1)
if attr in opars:
norm_function += opars[attr]* eoff**(i + 1)
group.e0 = e0
group.fpp = opars['s']*mu - norm_function
# calculate edge step and normalization from f2 + norm_function
pre_f2 = preedge(energy, group.f2+norm_function, e0=e0, pre1=pre1,
pre2=pre2, norm1=norm1, norm2=norm2, nnorm=2, nvict=0)
group.edge_step = pre_f2['edge_step'] / opars['s']
group.norm = (opars['s']*mu - pre_f2['pre_edge']) / pre_f2['edge_step']
group.mback_details = Group(params=opars, pre_f2=pre_f2,
f2_scaled=opars['s']*f2,
norm_function=norm_function)
def pre_edge_baseline(energy,
norm=None,
group=None,
form='lorentzian',
emin=None,
emax=None,
elo=None,
ehi=None,
with_line=True,
_larch=None):
"""remove baseline from main edge over pre edge peak region
This assumes that pre_edge() has been run successfully on the spectra
and that the spectra has decent pre-edge subtraction and normalization.
Arguments
----------
energy: array of x-ray energies, in eV, or group (see note 1)
norm: array of normalized mu(E)
group: output group
elo: low energy of pre-edge peak region to not fit baseline [e0-20]
ehi: high energy of pre-edge peak region ot not fit baseline [e0-10]
emax max energy (eV) to use for baesline fit [e0-5]
emin: min energy (eV) to use for baesline fit [e0-40]
form: form used for baseline (see note 2) ['lorentzian']
with_line: whether to include linear component in baseline ['True']
Returns
-------
None
A group named 'prepeaks' will be created in the output group, with the following
attributes:
energy energy array for pre-edge peaks = energy[emin-eneg:emax+epos]
baseline fitted baseline array over pre-edge peak energies
mu baseline-subtraced spectrum over pre-edge peak energies
dmu estimated uncertainty in mu from fit
centroid estimated centroid of pre-edge peaks (see note 3)
peak_energies list of predicted peak energies (see note 4)
fit_details details of fit to extract pre-edge peaks.
(if the output group is None, _sys.xafsGroup will be written to)
Notes
-----
1 If the first argument is a Group, it must contain 'energy' and 'norm'.
See First Argrument Group in Documentation
2 A function will be fit to the input mu(E) data over the range between
[emin:elo] and [ehi:emax], ignorng the pre-edge peaks in the
region [elo:ehi]. The baseline function is specified with the `form`
keyword argument, which can be one of
'lorentzian', 'gaussian', or 'voigt',
with 'lorentzian' the default. In addition, the `with_line` keyword
argument can be used to add a line to this baseline function.
3 The value calculated for `prepeaks.centroid` will be found as
(prepeaks.energy*prepeaks.mu).sum() / prepeaks.mu.sum()
4 The values in the `peak_energies` list will be predicted energies
of the peaks in `prepeaks.mu` as found by peakutils.
"""
energy, norm, group = parse_group_args(energy,
members=('energy', 'norm'),
defaults=(norm, ),
group=group,
fcn_name='pre_edge_baseline')
if len(energy.shape) > 1:
energy = energy.squeeze()
if len(norm.shape) > 1:
norm = norm.squeeze()
dat_emin, dat_emax = min(energy), max(energy)
dat_e0 = getattr(group, 'e0', -1)
if dat_e0 > 0:
if emin is None:
emin = dat_e0 - 30.0
if emax is None:
emax = dat_e0 - 1.0
if elo is None:
elo = dat_e0 - 15.0
if ehi is None:
ehi = dat_e0 - 5.0
if emin < 0:
emin += dat_e0
if elo < 0:
elo += dat_e0
if emax < dat_emin:
emax += dat_e0
if ehi < dat_emin:
ehi += dat_e0
if emax is None or emin is None or elo is None or ehi is None:
raise ValueError("must provide emin and emax to pre_edge_baseline")
# get indices for input energies
if emin > emax:
emin, emax = emax, emin
if emin > elo:
elo, emin = emin, elo
if ehi > emax:
ehi, emax = emax, ehi
imin = index_of(energy, emin)
ilo = index_of(energy, elo)
ihi = index_of(energy, ehi)
imax = index_of(energy, emax)
# build xdat, ydat: dat to fit (skipping pre-edge peaks)
xdat = np.concatenate((energy[imin:ilo + 1], energy[ihi:imax + 1]))
ydat = np.concatenate((norm[imin:ilo + 1], norm[ihi:imax + 1]))
# build fitting model: note that we always include
# a LinearModel but may fix slope and intercept
form = form.lower()
if form.startswith('voig'):
model = VoigtModel()
elif form.startswith('gaus'):
model = GaussianModel()
else:
model = LorentzianModel()
model += LinearModel()
params = model.make_params(amplitude=1.0,
sigma=2.0,
center=emax,
intercept=0,
slope=0)
params['amplitude'].min = 0.0
params['sigma'].min = 0.25
params['sigma'].max = 50.0
params['center'].max = emax + 25.0
params['center'].min = emax - 25.0
if not with_line:
params['slope'].vary = False
params['intercept'].vary = False
# run fit
result = model.fit(ydat, params, x=xdat)
# energy including pre-edge peaks, for output
edat = energy[imin:imax + 1]
# get baseline and resulting mu over edat range
bline = result.eval(result.params, x=edat)
mu = norm[imin:imax + 1] - bline
# uncertainty in mu includes only uncertainties in baseline fit
dmu = result.eval_uncertainty(result.params, x=edat)
# estimate centroid and its uncertainty
cen = (edat * mu).sum() / mu.sum()
cen_plus = (edat * (mu + dmu)).sum() / (mu + dmu).sum()
cen_minus = (edat * (mu - dmu)).sum() / (mu - dmu).sum()
dcen = abs(cen_minus - cen_plus) / 2.0
# locate peak positions
peak_energies = []
if HAS_PEAKUTILS:
peak_ids = peakutils.peak.indexes(mu, thres=0.05, min_dist=2)
peak_energies = [edat[pid] for pid in peak_ids]
group = set_xafsGroup(group, _larch=_larch)
group.prepeaks = Group(energy=edat,
mu=mu,
delta_mu=dmu,
baseline=bline,
centroid=cen,
delta_centroid=dcen,
peak_energies=peak_energies,
fit_details=result,
emin=emin,
emax=emax,
elo=elo,
ehi=ehi,
form=form,
with_line=with_line)
return
def concentration_resid(pars,
lineData=None,
mca=None,
phiPrime=np.pi / 2.,
phiDblPrime=np.pi / 2.,
xray_energy=30000.,
larch=None):
cscPhiPrime = 1. / np.sin(phiPrime)
cscPhiDblPrime = 1. / np.sin(phiDblPrime)
energy = mca.get_energy() * 1000.
dE = energy[1] - energy[0]
probeSpectrum = np.zeros(len(energy))
ind = index_of(energy, xray_energy)
probeSpectrum[ind] = 1.0
C = np.array([pars[elem + '_con'].value for elem in lineData], ndmin=2).T
Cal = np.array([pars[elem + '_cal'].value for elem in lineData])
Intensity = np.array([lineData[elem][2] for elem in lineData])
mu = np.zeros((len(lineData) + 1, len(energy)))
for i, elem_i in enumerate(lineData):
mu[i, :] = mu_elam(elem_i, energy, kind='total', _larch=larch)
mu[-1, :] += C[i, 0] * mu[i, :]
beta = np.zeros((len(lineData), len(lineData), len(energy)))
delta = np.zeros((len(lineData), len(lineData), len(energy)))
for i, elem_i in enumerate(lineData):
line_en_i = lineData[elem_i][1]
edge_i = lineData[elem_i][0][len(elem_i)].title()
edge_en_i, _, r_i = xray_edge(elem_i, edge_i, _larch=larch)
for j, elem_j in enumerate(lineData):
line_en_j = lineData[elem_j][1]
edge_j = lineData[elem_j][0][len(elem_j)].title()
line_j = lineData[elem_j][0][len(elem_j):].title()
edge_en_j, _, r_j = xray_edge(elem_j, edge_j, _larch=larch)
yield_j, _, prob_j = fluo_yield(elem_j,
edge_j,
line_j,
np.max(energy),
_larch=larch)
k_j = prob_j * yield_j * (r_j - 1.) / r_j
mu_s_prime = mu[-1, :] * cscPhiPrime
mu_s_line_en_j = np.interp(line_en_j, energy, mu[-1, :])
mu_s_dblPrime_line_en_i = np.interp(line_en_i, energy,
mu[-1, :]) * cscPhiDblPrime
P_ij = np.log(1. + mu_s_prime / mu_s_line_en_j) / mu_s_prime + \
np.log(1. + mu_s_dblPrime_line_en_i / mu_s_line_en_j) / mu_s_dblPrime_line_en_i
beta[i,j,:] = mu[j,:] * cscPhiPrime + \
np.interp(line_en_i, energy, mu[j,:]) * cscPhiDblPrime
beta[i,j,:] /= mu[i,:] * cscPhiPrime + \
np.interp(line_en_i, energy, mu[i,:]) * cscPhiDblPrime
beta[i, j, :] -= 1.
delta[i, j, :] = np.where(energy >= edge_en_j, 0.5, 0.0)
if line_en_j <= edge_en_i: delta[i, j, :] *= 0.
delta[i, j, :] *= k_j
delta[i, j, :] *= mu[j, :] * cscPhiPrime
delta[i, j, :] *= np.interp(line_en_j, energy, mu[i, :])
delta[i,j,:] /= (mu[-1,:] * cscPhiPrime) + \
(np.interp(line_en_i, energy, mu[-1,:]) * cscPhiDblPrime)
delta[i, j, :] *= P_ij
W = np.zeros((1, len(lineData), len(energy)))
for i, elem in enumerate(lineData):
line_en_i = lineData[elem_i][1]
mu_i_star = mu[i,:] * cscPhiPrime +\
np.interp(line_en_i, energy, mu[i,:]) * cscPhiDblPrime
W[0, i, :] = mu[i, :] * probeSpectrum * dE
W[0, i, :] /= mu_i_star * (1 + np.sum(C * beta[i, :, :], axis=0))
alpha = np.sum(W * beta, axis=2) / np.sum(W, axis=2)
epsilon = np.sum(W * delta, axis=2) / np.sum(W, axis=2)
num = 1 + np.sum(C.T * epsilon, axis=1)
den = 1 + np.sum(C.T * alpha, axis=1)
C = np.reshape(C, (len(C)))
print(pars['cu_con'].value, pars['zn_con'].value, pars['mn_con'].value)
return Intensity - Cal * C * num / den
def autobk(energy, mu=None, group=None, rbkg=1, nknots=None, e0=None,
edge_step=None, kmin=0, kmax=None, kweight=1, dk=0,
win='hanning', k_std=None, chi_std=None, nfft=2048, kstep=0.05,
pre_edge_kws=None, nclamp=4, clamp_lo=1, clamp_hi=1,
calc_uncertainties=True, err_sigma=1, _larch=None, **kws):
"""Use Autobk algorithm to remove XAFS background
Parameters:
-----------
energy: 1-d array of x-ray energies, in eV, or group
mu: 1-d array of mu(E)
group: output group (and input group for e0 and edge_step).
rbkg: distance (in Ang) for chi(R) above
which the signal is ignored. Default = 1.
e0: edge energy, in eV. If None, it will be determined.
edge_step: edge step. If None, it will be determined.
pre_edge_kws: keyword arguments to pass to pre_edge()
nknots: number of knots in spline. If None, it will be determined.
kmin: minimum k value [0]
kmax: maximum k value [full data range].
kweight: k weight for FFT. [1]
dk: FFT window window parameter. [0]
win: FFT window function name. ['hanning']
nfft: array size to use for FFT [2048]
kstep: k step size to use for FFT [0.05]
k_std: optional k array for standard chi(k).
chi_std: optional chi array for standard chi(k).
nclamp: number of energy end-points for clamp [2]
clamp_lo: weight of low-energy clamp [1]
clamp_hi: weight of high-energy clamp [1]
calc_uncertaintites: Flag to calculate uncertainties in
mu_0(E) and chi(k) [True]
err_sigma: sigma level for uncertainties in mu_0(E) and chi(k) [1]
Output arrays are written to the provided group.
Follows the 'First Argument Group' convention.
"""
msg = _larch.writer.write
if 'kw' in kws:
kweight = kws.pop('kw')
if len(kws) > 0:
msg('Unrecognized a:rguments for autobk():\n')
msg(' %s\n' % (', '.join(kws.keys())))
return
energy, mu, group = parse_group_args(energy, members=('energy', 'mu'),
defaults=(mu,), group=group,
fcn_name='autobk')
if len(energy.shape) > 1:
energy = energy.squeeze()
if len(mu.shape) > 1:
mu = mu.squeeze()
energy = remove_dups(energy)
# if e0 or edge_step are not specified, get them, either from the
# passed-in group or from running pre_edge()
group = set_xafsGroup(group, _larch=_larch)
if edge_step is None and isgroup(group, 'edge_step'):
edge_step = group.edge_step
if e0 is None and isgroup(group, 'e0'):
e0 = group.e0
if e0 is None or edge_step is None:
# need to run pre_edge:
pre_kws = dict(nnorm=3, nvict=0, pre1=None,
pre2=-50., norm1=100., norm2=None)
if pre_edge_kws is not None:
pre_kws.update(pre_edge_kws)
pre_edge(energy, mu, group=group, _larch=_larch, **pre_kws)
if e0 is None:
e0 = group.e0
if edge_step is None:
edge_step = group.edge_step
if e0 is None or edge_step is None:
msg('autobk() could not determine e0 or edge_step!: trying running pre_edge first\n')
return
# get array indices for rkbg and e0: irbkg, ie0
ie0 = index_of(energy, e0)
rgrid = np.pi/(kstep*nfft)
if rbkg < 2*rgrid: rbkg = 2*rgrid
irbkg = int(1.01 + rbkg/rgrid)
# save ungridded k (kraw) and grided k (kout)
# and ftwin (*k-weighting) for FT in residual
enpe = energy[ie0:] - e0
kraw = np.sign(enpe)*np.sqrt(ETOK*abs(enpe))
if kmax is None:
kmax = max(kraw)
else:
kmax = max(0, min(max(kraw), kmax))
kout = kstep * np.arange(int(1.01+kmax/kstep), dtype='float64')
iemax = min(len(energy), 2+index_of(energy, e0+kmax*kmax/ETOK)) - 1
# interpolate provided chi(k) onto the kout grid
if chi_std is not None and k_std is not None:
chi_std = np.interp(kout, k_std, chi_std)
# pre-load FT window
ftwin = kout**kweight * ftwindow(kout, xmin=kmin, xmax=kmax,
window=win, dx=dk)
# calc k-value and initial guess for y-values of spline params
nspl = max(4, min(128, 2*int(rbkg*(kmax-kmin)/np.pi) + 1))
spl_y, spl_k, spl_e = np.zeros(nspl), np.zeros(nspl), np.zeros(nspl)
for i in range(nspl):
q = kmin + i*(kmax-kmin)/(nspl - 1)
ik = index_nearest(kraw, q)
i1 = min(len(kraw)-1, ik + 5)
i2 = max(0, ik - 5)
spl_k[i] = kraw[ik]
spl_e[i] = energy[ik+ie0]
spl_y[i] = (2*mu[ik+ie0] + mu[i1+ie0] + mu[i2+ie0] ) / 4.0
# get spline represention: knots, coefs, order=3
# coefs will be varied in fit.
knots, coefs, order = splrep(spl_k, spl_y)
# set fit parameters from initial coefficients
params = Parameters()
for i in range(len(coefs)):
params.add(name = FMT_COEF % i, value=coefs[i], vary=i<len(spl_y))
initbkg, initchi = spline_eval(kraw[:iemax-ie0+1], mu[ie0:iemax+1],
knots, coefs, order, kout)
# do fit
result = minimize(__resid, params, method='leastsq',
gtol=1.e-5, ftol=1.e-5, xtol=1.e-5, epsfcn=1.e-5,
kws = dict(ncoefs=len(coefs), chi_std=chi_std,
knots=knots, order=order,
kraw=kraw[:iemax-ie0+1],
mu=mu[ie0:iemax+1], irbkg=irbkg, kout=kout,
ftwin=ftwin, kweight=kweight,
nfft=nfft, nclamp=nclamp,
clamp_lo=clamp_lo, clamp_hi=clamp_hi))
# write final results
coefs = [result.params[FMT_COEF % i].value for i in range(len(coefs))]
bkg, chi = spline_eval(kraw[:iemax-ie0+1], mu[ie0:iemax+1],
knots, coefs, order, kout)
obkg = np.copy(mu)
obkg[ie0:ie0+len(bkg)] = bkg
# outputs to group
group = set_xafsGroup(group, _larch=_larch)
group.bkg = obkg
group.chie = (mu-obkg)/edge_step
group.k = kout
group.chi = chi/edge_step
# now fill in 'autobk_details' group
details = Group(params=result.params)
details.init_bkg = np.copy(mu)
details.init_bkg[ie0:ie0+len(bkg)] = initbkg
details.init_chi = initchi/edge_step
details.knots_e = spl_e
details.knots_y = np.array([coefs[i] for i in range(nspl)])
details.init_knots_y = spl_y
details.nfev = result.nfev
details.kmin = kmin
details.kmax = kmax
group.autobk_details = details
# uncertainties in mu0 and chi: can be fairly slow.
if calc_uncertainties:
nchi = len(chi)
nmue = iemax-ie0 + 1
redchi = result.redchi
covar = result.covar / redchi
jac_chi = np.zeros(nchi*nspl).reshape((nspl, nchi))
jac_bkg = np.zeros(nmue*nspl).reshape((nspl, nmue))
cvals, cerrs = [], []
for i in range(len(coefs)):
par = result.params[FMT_COEF % i]
cvals.append(getattr(par, 'value', 0.0))
cdel = getattr(par, 'stderr', 0.0)
if cdel is None:
cdel = 0.0
cerrs.append(cdel/2.0)
cvals = np.array(cvals)
cerrs = np.array(cerrs)
# find derivatives by hand!
_k = kraw[:nmue]
_m = mu[ie0:iemax+1]
for i in range(nspl):
cval0 = cvals[i]
cvals[i] = cval0 + cerrs[i]
bkg1, chi1 = spline_eval(_k, _m, knots, cvals, order, kout)
cvals[i] = cval0 - cerrs[i]
bkg2, chi2 = spline_eval(_k, _m, knots, cvals, order, kout)
cvals[i] = cval0
jac_chi[i] = (chi1 - chi2) / (2*cerrs[i])
jac_bkg[i] = (bkg1 - bkg2) / (2*cerrs[i])
dfchi = np.zeros(nchi)
dfbkg = np.zeros(nmue)
for i in range(nspl):
for j in range(nspl):
dfchi += jac_chi[i]*jac_chi[j]*covar[i,j]
dfbkg += jac_bkg[i]*jac_bkg[j]*covar[i,j]
prob = 0.5*(1.0 + erf(err_sigma/np.sqrt(2.0)))
dchi = t.ppf(prob, nchi-nspl) * np.sqrt(dfchi*redchi)
dbkg = t.ppf(prob, nmue-nspl) * np.sqrt(dfbkg*redchi)
group.delta_chi = dchi
group.delta_bkg = 0.0*mu
group.delta_bkg[ie0:ie0+len(dbkg)] = dbkg
def pre_edge(energy, mu=None, group=None, e0=None, step=None,
nnorm=2, nvict=0, pre1=None, pre2=-50,
norm1=100, norm2=None, make_flat=True, _larch=None):
"""pre edge subtraction, normalization for XAFS
This performs a number of steps:
1. determine E0 (if not supplied) from max of deriv(mu)
2. fit a line of polymonial to the region below the edge
3. fit a polymonial to the region above the edge
4. extrapolae the two curves to E0 to determine the edge jump
Arguments
----------
energy: array of x-ray energies, in eV, or group (see note)
mu: array of mu(E)
group: output group
e0: edge energy, in eV. If None, it will be determined here.
step: edge jump. If None, it will be determined here.
pre1: low E range (relative to E0) for pre-edge fit
pre2: high E range (relative to E0) for pre-edge fit
nvict: energy exponent to use for pre-edg fit. See Note
norm1: low E range (relative to E0) for post-edge fit
norm2: high E range (relative to E0) for post-edge fit
nnorm: degree of polynomial (ie, nnorm+1 coefficients will be found) for
post-edge normalization curve. Default=2 (quadratic), max=5
make_flat: boolean (Default True) to calculate flattened output.
Returns
-------
None
The following attributes will be written to the output group:
e0 energy origin
edge_step edge step
norm normalized mu(E)
flat flattened, normalized mu(E)
pre_edge determined pre-edge curve
post_edge determined post-edge, normalization curve
dmude derivative of mu(E)
(if the output group is None, _sys.xafsGroup will be written to)
Notes
-----
1 nvict gives an exponent to the energy term for the fits to the pre-edge
and the post-edge region. For the pre-edge, a line (m * energy + b) is
fit to mu(energy)*energy**nvict over the pre-edge region,
energy=[e0+pre1, e0+pre2]. For the post-edge, a polynomial of order
nnorm will be fit to mu(energy)*energy**nvict of the post-edge region
energy=[e0+norm1, e0+norm2].
2 If the first argument is a Group, it must contain 'energy' and 'mu'.
If it exists, group.e0 will be used as e0.
See First Argrument Group in Documentation
"""
energy, mu, group = parse_group_args(energy, members=('energy', 'mu'),
defaults=(mu,), group=group,
fcn_name='pre_edge')
if len(energy.shape) > 1:
energy = energy.squeeze()
if len(mu.shape) > 1:
mu = mu.squeeze()
pre_dat = preedge(energy, mu, e0=e0, step=step, nnorm=nnorm,
nvict=nvict, pre1=pre1, pre2=pre2, norm1=norm1,
norm2=norm2)
group = set_xafsGroup(group, _larch=_larch)
e0 = pre_dat['e0']
norm = pre_dat['norm']
norm1 = pre_dat['norm1']
norm2 = pre_dat['norm2']
# generate flattened spectra, by fitting a quadratic to .norm
# and removing that.
flat = norm
ie0 = index_nearest(energy, e0)
p1 = index_of(energy, norm1+e0)
p2 = index_nearest(energy, norm2+e0)
if p2-p1 < 2:
p2 = min(len(energy), p1 + 2)
if make_flat and p2-p1 > 4:
enx, mux = remove_nans2(energy[p1:p2], norm[p1:p2])
# enx, mux = (energy[p1:p2], norm[p1:p2])
fpars = Parameters()
ncoefs = len(pre_dat['norm_coefs'])
fpars.add('c0', value=0, vary=True)
fpars.add('c1', value=0, vary=(ncoefs>1))
fpars.add('c2', value=0, vary=(ncoefs>2))
fit = Minimizer(flat_resid, fpars, fcn_args=(enx, mux))
result = fit.leastsq(xtol=1.e-6, ftol=1.e-6)
fc0 = result.params['c0'].value
fc1 = result.params['c1'].value
fc2 = result.params['c2'].value
flat_diff = fc0 + energy * (fc1 + energy * fc2)
flat = norm - (flat_diff - flat_diff[ie0])
flat[:ie0] = norm[:ie0]
group.e0 = e0
group.norm = norm
group.flat = flat
group.dmude = np.gradient(mu)/np.gradient(energy)
group.edge_step = pre_dat['edge_step']
group.pre_edge = pre_dat['pre_edge']
group.post_edge = pre_dat['post_edge']
group.pre_edge_details = Group()
group.pre_edge_details.pre1 = pre_dat['pre1']
group.pre_edge_details.pre2 = pre_dat['pre2']
group.pre_edge_details.nnorm = pre_dat['nnorm']
group.pre_edge_details.norm1 = pre_dat['norm1']
group.pre_edge_details.norm2 = pre_dat['norm2']
group.pre_edge_details.nvict = pre_dat['nvict']
group.pre_edge_details.pre1_input = pre_dat['pre1_input']
group.pre_edge_details.norm2_input = pre_dat['norm2_input']
group.pre_edge_details.pre_slope = pre_dat['precoefs'][0]
group.pre_edge_details.pre_offset = pre_dat['precoefs'][1]
for i in range(MAX_NNORM):
if hasattr(group, 'norm_c%i' % i):
delattr(group, 'norm_c%i' % i)
for i, c in enumerate(pre_dat['norm_coefs']):
setattr(group.pre_edge_details, 'norm_c%i' % i, c)
return
def rebin_xafs(energy, mu=None, group=None, e0=None, pre1=None, pre2=-30,
pre_step=2, xanes_step=None, exafs1=15, exafs2=None,
exafs_kstep=0.05, method='centroid', _larch=None):
"""rebin XAFS energy and mu to a 'standard 3 region XAFS scan'
Arguments
---------
energy input energy array
mu input mu array
group output group
e0 energy reference -- all energy values are relative to this
pre1 start of pre-edge region [1st energy point]
pre2 end of pre-edge region, start of XANES region [-30]
pre_step energy step for pre-edge region [2]
xanes_step energy step for XANES region [see note]
exafs1 end of XANES region, start of EXAFS region [15]
exafs2 end of EXAFS region [last energy point]
exafs_kstep k-step for EXAFS region [0.05]
method one of 'boxcar', 'centroid' ['centroid']
Returns
-------
None
A group named 'rebinned' will be created in the output group, with the
following attributes:
energy new energy array
mu mu for energy array
e0 e0 copied from current group
(if the output group is None, _sys.xafsGroup will be written to)
Notes
------
1 If the first argument is a Group, it must contain 'energy' and 'mu'.
See First Argrument Group in Documentation
2 If xanes_step is None, it will be found from the data. If it is
given, it may be increased to better fit the input energy array.
3 The EXAFS region will be spaced in k-space
4 The rebinned data is found by determining which segments of the
input energy correspond to each bin in the new energy array. That
is, each input energy is assigned to exactly one bin in the new
array. For each new energy bin, the new value is selected from the
data in the segment as either
a) linear interpolation if there are fewer than 3 points in the segment.
b) mean value ('boxcar')
c) centroid ('centroid')
"""
energy, mu, group = parse_group_args(energy, members=('energy', 'mu'),
defaults=(mu,), group=group,
fcn_name='rebin_xafs')
if e0 is None:
e0 = getattr(group, 'e0', None)
if e0 is None:
raise ValueError("need e0")
if pre1 is None:
pre1 = pre_step*int((min(energy) - e0)/pre_step)
if exafs2 is None:
exafs2 = max(energy) - e0
# determine xanes step size:
# find mean of energy difference, ignoring first/last 1% of energies
npts = len(energy)
n1 = max(2, int(npts/100.0))
de_mean = np.diff(energy[n1:-n1]).mean()
xanes_step_def = max(0.1, 0.05 * (1 + int(de_mean/0.05)))
if xanes_step is None:
xanes_step = xanes_step_def
else:
xanes_step = max(xanes_step, xanes_step_def)
# create new energy array from the 3 segments (pre, xanes, exafs)
en = []
for start, stop, step, isk in ((pre1, pre2, pre_step, False),
(pre2, exafs1, xanes_step, False),
(exafs1, exafs2, exafs_kstep, True)):
if isk:
start = etok(start)
stop = etok(stop)
reg = np.linspace(start+step, stop, int(0.1 + abs(stop-start)/step))
if isk:
reg = ktoe(reg)
en.extend(e0 + reg)
# find the segment boundaries of the old energy array
bounds = [index_of(energy, e) for e in en]
mu_out = []
err_out = []
j0 = 0
for i in range(len(en)):
if i == len(en) - 1:
j1 = len(energy) - 1
else:
j1 = int((bounds[i] + bounds[i+1] + 1)/2.0)
# if not enough points in segment, do interpolation
if (j1 - j0) < 3:
jx = j1 + 1
if (jx - j0) < 2:
jx += 1
val = interp1d(energy[j0:jx], mu[j0:jx], en[i])
err = mu[j0:j1].std()
else:
if method.startswith('box'):
val = mu[j0:j1].mean()
else:
val = (mu[j0:j1]*energy[j0:j1]).mean()/energy[j0:j1].mean()
mu_out.append(val)
err_out.append(mu[j0:j1].std())
j0 = j1
newname = group.__name__ + '_rebinned'
group.rebinned = Group(energy=np.array(en), mu=np.array(mu_out),
delta_mu=np.array(err_out), e0=e0,
__name__=newname)
return
def pre_edge_baseline(energy, norm=None, group=None, form='lorentzian',
emin=None, emax=None, elo=None, ehi=None,
with_line=True, _larch=None):
"""remove baseline from main edge over pre edge peak region
This assumes that pre_edge() has been run successfully on the spectra
and that the spectra has decent pre-edge subtraction and normalization.
Arguments
----------
energy: array of x-ray energies, in eV, or group (see note 1)
norm: array of normalized mu(E)
group: output group
elo: low energy of pre-edge peak region to not fit baseline [e0-20]
ehi: high energy of pre-edge peak region ot not fit baseline [e0-10]
emax: max energy (eV) to use for baesline fit [e0-5]
emin: min energy (eV) to use for baesline fit [e0-40]
form: form used for baseline (see note 2) ['lorentzian']
with_line: whether to include linear component in baseline ['True']
Returns
-------
None
A group named 'prepeaks' will be created in the output group, with the following
attributes:
energy energy array for pre-edge peaks = energy[emin:emax]
baseline fitted baseline array over pre-edge peak energies
mu spectrum over pre-edge peak energies
peaks baseline-subtraced spectrum over pre-edge peak energies
dmu estimated uncertainty in peaks from fit
centroid estimated centroid of pre-edge peaks (see note 3)
peak_energies list of predicted peak energies (see note 4)
fit_details details of fit to extract pre-edge peaks.
(if the output group is None, _sys.xafsGroup will be written to)
Notes
-----
1 If the first argument is a Group, it must contain 'energy' and 'norm'.
See First Argrument Group in Documentation
2 A function will be fit to the input mu(E) data over the range between
[emin:elo] and [ehi:emax], ignorng the pre-edge peaks in the
region [elo:ehi]. The baseline function is specified with the `form`
keyword argument, which can be one of
'lorentzian', 'gaussian', or 'voigt',
with 'lorentzian' the default. In addition, the `with_line` keyword
argument can be used to add a line to this baseline function.
3 The value calculated for `prepeaks.centroid` will be found as
(prepeaks.energy*prepeaks.peaks).sum() / prepeaks.peaks.sum()
4 The values in the `peak_energies` list will be predicted energies
of the peaks in `prepeaks.peaks` as found by peakutils.
"""
energy, norm, group = parse_group_args(energy, members=('energy', 'norm'),
defaults=(norm,), group=group,
fcn_name='pre_edge_baseline')
if len(energy.shape) > 1:
energy = energy.squeeze()
if len(norm.shape) > 1:
norm = norm.squeeze()
dat_emin, dat_emax = min(energy), max(energy)
dat_e0 = getattr(group, 'e0', -1)
if dat_e0 > 0:
if emin is None:
emin = dat_e0 - 30.0
if emax is None:
emax = dat_e0 - 1.0
if elo is None:
elo = dat_e0 - 15.0
if ehi is None:
ehi = dat_e0 - 5.0
if emin < 0:
emin += dat_e0
if elo < 0:
elo += dat_e0
if emax < dat_emin:
emax += dat_e0
if ehi < dat_emin:
ehi += dat_e0
if emax is None or emin is None or elo is None or ehi is None:
raise ValueError("must provide emin and emax to pre_edge_baseline")
# get indices for input energies
if emin > emax:
emin, emax = emax, emin
if emin > elo:
elo, emin = emin, elo
if ehi > emax:
ehi, emax = emax, ehi
imin = index_of(energy, emin)
ilo = index_of(energy, elo)
ihi = index_of(energy, ehi)
imax = index_of(energy, emax)
# build xdat, ydat: dat to fit (skipping pre-edge peaks)
xdat = np.concatenate((energy[imin:ilo+1], energy[ihi:imax+1]))
ydat = np.concatenate((norm[imin:ilo+1], norm[ihi:imax+1]))
# build fitting model: note that we always include
# a LinearModel but may fix slope and intercept
form = form.lower()
if form.startswith('voig'):
model = VoigtModel()
elif form.startswith('gaus'):
model = GaussianModel()
else:
model = LorentzianModel()
model += LinearModel()
params = model.make_params(amplitude=1.0, sigma=2.0,
center=emax,
intercept=0, slope=0)
params['amplitude'].min = 0.0
params['sigma'].min = 0.25
params['sigma'].max = 50.0
params['center'].max = emax + 25.0
params['center'].min = emax - 25.0
if not with_line:
params['slope'].vary = False
params['intercept'].vary = False
# run fit
result = model.fit(ydat, params, x=xdat)
# energy including pre-edge peaks, for output
edat = energy[imin: imax+1]
# get baseline and resulting mu over edat range
bline = result.eval(result.params, x=edat)
mu = norm[imin:imax+1]
peaks = mu-bline
# estimate centroid
cen = (edat*peaks).sum() / peaks.sum()
# uncertainty in mu includes only uncertainties in baseline fit
# and uncertainty in centroid:
try:
dpeaks = result.eval_uncertainty(result.params, x=edat)
except:
dbpeaks = 0.0
cen_plus = (edat*(peaks+dpeaks)).sum()/ (peaks+dpeaks).sum()
cen_minus = (edat*(peaks-dpeaks)).sum()/ (peaks-dpeaks).sum()
dcen = abs(cen_minus - cen_plus) / 2.0
# locate peak positions
peak_energies = []
if HAS_PEAKUTILS:
peak_ids = peakutils.peak.indexes(peaks, thres=0.05, min_dist=2)
peak_energies = [edat[pid] for pid in peak_ids]
group = set_xafsGroup(group, _larch=_larch)
group.prepeaks = Group(energy=edat, mu=mu, baseline=bline,
peaks=peaks, delta_peaks=dpeaks,
centroid=cen, delta_centroid=dcen,
peak_energies=peak_energies,
fit_details=result,
emin=emin, emax=emax, elo=elo, ehi=ehi,
form=form, with_line=with_line)
return
def preedge(energy, mu, e0=None, step=None,
nnorm=2, nvict=0, pre1=None, pre2=-50,
norm1=100, norm2=None):
"""pre edge subtraction, normalization for XAFS (straight python)
This performs a number of steps:
1. determine E0 (if not supplied) from max of deriv(mu)
2. fit a line of polymonial to the region below the edge
3. fit a polymonial to the region above the edge
4. extrapolae the two curves to E0 to determine the edge jump
Arguments
----------
energy: array of x-ray energies, in eV
mu: array of mu(E)
e0: edge energy, in eV. If None, it will be determined here.
step: edge jump. If None, it will be determined here.
pre1: low E range (relative to E0) for pre-edge fit
pre2: high E range (relative to E0) for pre-edge fit
nvict: energy exponent to use for pre-edg fit. See Note
norm1: low E range (relative to E0) for post-edge fit
norm2: high E range (relative to E0) for post-edge fit
nnorm: degree of polynomial (ie, nnorm+1 coefficients will be found) for
post-edge normalization curve. Default=2 (quadratic), max=5
Returns
-------
dictionary with elements (among others)
e0 energy origin in eV
edge_step edge step
norm normalized mu(E)
pre_edge determined pre-edge curve
post_edge determined post-edge, normalization curve
Notes
-----
1 nvict gives an exponent to the energy term for the fits to the pre-edge
and the post-edge region. For the pre-edge, a line (m * energy + b) is
fit to mu(energy)*energy**nvict over the pre-edge region,
energy=[e0+pre1, e0+pre2]. For the post-edge, a polynomial of order
nnorm will be fit to mu(energy)*energy**nvict of the post-edge region
energy=[e0+norm1, e0+norm2].
"""
energy = remove_dups(energy)
if e0 is None or e0 < energy[1] or e0 > energy[-2]:
e0 = _finde0(energy, mu)
nnorm = max(min(nnorm, MAX_NNORM), 0)
ie0 = index_nearest(energy, e0)
e0 = energy[ie0]
pre1_input = pre1
norm2_input = norm2
if pre1 is None: pre1 = min(energy) - e0
if norm2 is None: norm2 = max(energy) - e0
if norm2 < 0: norm2 = max(energy) - e0 - norm2
pre1 = max(pre1, (min(energy) - e0))
norm2 = min(norm2, (max(energy) - e0))
if pre1 > pre2:
pre1, pre2 = pre2, pre1
if norm1 > norm2:
norm1, norm2 = norm2, norm1
p1 = index_of(energy, pre1+e0)
p2 = index_nearest(energy, pre2+e0)
if p2-p1 < 2:
p2 = min(len(energy), p1 + 2)
omu = mu*energy**nvict
ex, mx = remove_nans2(energy[p1:p2], omu[p1:p2])
precoefs = polyfit(ex, mx, 1)
pre_edge = (precoefs[0] * energy + precoefs[1]) * energy**(-nvict)
# normalization
p1 = index_of(energy, norm1+e0)
p2 = index_nearest(energy, norm2+e0)
if p2-p1 < 2:
p2 = min(len(energy), p1 + 2)
# reduce dimension to linear if less than 75 eV given
if abs(norm2-norm1) < 75.0:
nnorm = min(nnorm, 1)
coefs = polyfit(energy[p1:p2], omu[p1:p2], nnorm)
post_edge = 0
norm_coefs = []
for n, c in enumerate(reversed(list(coefs))):
post_edge += c * energy**(n-nvict)
norm_coefs.append(c)
edge_step = step
if edge_step is None:
edge_step = post_edge[ie0] - pre_edge[ie0]
norm = (mu - pre_edge)/edge_step
return {'e0': e0, 'edge_step': edge_step, 'norm': norm,
'pre_edge': pre_edge, 'post_edge': post_edge,
'norm_coefs': norm_coefs, 'nvict': nvict,
'nnorm': nnorm, 'norm1': norm1, 'norm2': norm2,
'pre1': pre1, 'pre2': pre2, 'precoefs': precoefs,
'norm2_input': norm2_input, 'pre1_input': pre1_input}
def pre_edge(energy,
mu=None,
group=None,
e0=None,
step=None,
nnorm=3,
nvict=0,
pre1=None,
pre2=-50,
norm1=100,
norm2=None,
make_flat=True,
_larch=None):
"""pre edge subtraction, normalization for XAFS
This performs a number of steps:
1. determine E0 (if not supplied) from max of deriv(mu)
2. fit a line of polymonial to the region below the edge
3. fit a polymonial to the region above the edge
4. extrapolae the two curves to E0 to determine the edge jump
Arguments
----------
energy: array of x-ray energies, in eV, or group (see note)
mu: array of mu(E)
group: output group
e0: edge energy, in eV. If None, it will be determined here.
step: edge jump. If None, it will be determined here.
pre1: low E range (relative to E0) for pre-edge fit
pre2: high E range (relative to E0) for pre-edge fit
nvict: energy exponent to use for pre-edg fit. See Note
norm1: low E range (relative to E0) for post-edge fit
norm2: high E range (relative to E0) for post-edge fit
nnorm: degree of polynomial (ie, nnorm+1 coefficients will be found) for
post-edge normalization curve. Default=3 (quadratic), max=5
make_flat: boolean (Default True) to calculate flattened output.
Returns
-------
None
The following attributes will be written to the output group:
e0 energy origin
edge_step edge step
norm normalized mu(E)
flat flattened, normalized mu(E)
pre_edge determined pre-edge curve
post_edge determined post-edge, normalization curve
dmude derivative of mu(E)
(if the output group is None, _sys.xafsGroup will be written to)
Notes
-----
1 nvict gives an exponent to the energy term for the fits to the pre-edge
and the post-edge region. For the pre-edge, a line (m * energy + b) is
fit to mu(energy)*energy**nvict over the pre-edge region,
energy=[e0+pre1, e0+pre2]. For the post-edge, a polynomial of order
nnorm will be fit to mu(energy)*energy**nvict of the post-edge region
energy=[e0+norm1, e0+norm2].
2 If the first argument is a Group, it must contain 'energy' and 'mu'.
If it exists, group.e0 will be used as e0.
See First Argrument Group in Documentation
"""
energy, mu, group = parse_group_args(energy,
members=('energy', 'mu'),
defaults=(mu, ),
group=group,
fcn_name='pre_edge')
if len(energy.shape) > 1:
energy = energy.squeeze()
if len(mu.shape) > 1:
mu = mu.squeeze()
pre_dat = preedge(energy,
mu,
e0=e0,
step=step,
nnorm=nnorm,
nvict=nvict,
pre1=pre1,
pre2=pre2,
norm1=norm1,
norm2=norm2)
group = set_xafsGroup(group, _larch=_larch)
e0 = pre_dat['e0']
norm = pre_dat['norm']
norm1 = pre_dat['norm1']
norm2 = pre_dat['norm2']
# generate flattened spectra, by fitting a quadratic to .norm
# and removing that.
flat = norm
ie0 = index_nearest(energy, e0)
p1 = index_of(energy, norm1 + e0)
p2 = index_nearest(energy, norm2 + e0)
if p2 - p1 < 2:
p2 = min(len(energy), p1 + 2)
if make_flat and p2 - p1 > 4:
enx, mux = remove_nans2(energy[p1:p2], norm[p1:p2])
# enx, mux = (energy[p1:p2], norm[p1:p2])
fpars = Parameters()
fpars.add('c0', value=0, vary=True)
fpars.add('c1', value=0, vary=True)
fpars.add('c2', value=0, vary=True)
fit = Minimizer(flat_resid, fpars, fcn_args=(enx, mux))
result = fit.leastsq(xtol=1.e-6, ftol=1.e-6)
fc0 = result.params['c0'].value
fc1 = result.params['c1'].value
fc2 = result.params['c2'].value
flat_diff = fc0 + energy * (fc1 + energy * fc2)
flat = norm - flat_diff + flat_diff[ie0]
flat[:ie0] = norm[:ie0]
group.e0 = e0
group.norm = norm
group.flat = flat
group.dmude = np.gradient(mu) / np.gradient(energy)
group.edge_step = pre_dat['edge_step']
group.pre_edge = pre_dat['pre_edge']
group.post_edge = pre_dat['post_edge']
group.pre_edge_details = Group()
group.pre_edge_details.pre1 = pre_dat['pre1']
group.pre_edge_details.pre2 = pre_dat['pre2']
group.pre_edge_details.nnorm = pre_dat['nnorm']
group.pre_edge_details.norm1 = pre_dat['norm1']
group.pre_edge_details.norm2 = pre_dat['norm2']
group.pre_edge_details.pre1_input = pre_dat['pre1_input']
group.pre_edge_details.norm2_input = pre_dat['norm2_input']
group.pre_edge_details.pre_slope = pre_dat['precoefs'][0]
group.pre_edge_details.pre_offset = pre_dat['precoefs'][1]
for i in range(MAX_NNORM):
if hasattr(group, 'norm_c%i' % i):
delattr(group, 'norm_c%i' % i)
for i, c in enumerate(pre_dat['norm_coefs']):
setattr(group.pre_edge_details, 'norm_c%i' % i, c)
return
def mback(energy,
mu,
group=None,
order=3,
z=None,
edge='K',
e0=None,
emin=None,
emax=None,
whiteline=None,
leexiang=False,
tables='chantler',
fit_erfc=False,
return_f1=False,
_larch=None):
"""
Match mu(E) data for tabulated f''(E) using the MBACK algorithm and,
optionally, the Lee & Xiang extension
Arguments:
energy, mu: arrays of energy and mu(E)
order: order of polynomial [3]
group: output group (and input group for e0)
z: Z number of absorber
edge: absorption edge (K, L3)
e0: edge energy
emin: beginning energy for fit
emax: ending energy for fit
whiteline: exclusion zone around white lines
leexiang: flag to use the Lee & Xiang extension
tables: 'chantler' (default) or 'cl'
fit_erfc: True to float parameters of error function
return_f1: True to put the f1 array in the group
Returns:
group.f2: tabulated f2(E)
group.f1: tabulated f1(E) (if return_f1 is True)
group.fpp: matched data
group.mback_params: Group of parameters for the minimization
References:
* MBACK (Weng, Waldo, Penner-Hahn): http://dx.doi.org/10.1086/303711
* Lee and Xiang: http://dx.doi.org/10.1088/0004-637X/702/2/970
* Cromer-Liberman: http://dx.doi.org/10.1063/1.1674266
* Chantler: http://dx.doi.org/10.1063/1.555974
"""
order = int(order)
if order < 1: order = 1 # set order of polynomial
if order > MAXORDER: order = MAXORDER
### implement the First Argument Group convention
energy, mu, group = parse_group_args(energy,
members=('energy', 'mu'),
defaults=(mu, ),
group=group,
fcn_name='mback')
if len(energy.shape) > 1:
energy = energy.squeeze()
if len(mu.shape) > 1:
mu = mu.squeeze()
group = set_xafsGroup(group, _larch=_larch)
if e0 is None: # need to run find_e0:
e0 = xray_edge(z, edge, _larch=_larch)[0]
if e0 is None:
e0 = group.e0
if e0 is None:
find_e0(energy, mu, group=group)
### theta is an array used to exclude the regions <emin, >emax, and
### around white lines, theta=0.0 in excluded regions, theta=1.0 elsewhere
(i1, i2) = (0, len(energy) - 1)
if emin is not None: i1 = index_of(energy, emin)
if emax is not None: i2 = index_of(energy, emax)
theta = np.ones(len(energy)) # default: 1 throughout
theta[0:i1] = 0
theta[i2:-1] = 0
if whiteline:
pre = 1.0 * (energy < e0)
post = 1.0 * (energy > e0 + float(whiteline))
theta = theta * (pre + post)
if edge.lower().startswith('l'):
l2 = xray_edge(z, 'L2', _larch=_larch)[0]
l2_pre = 1.0 * (energy < l2)
l2_post = 1.0 * (energy > l2 + float(whiteline))
theta = theta * (l2_pre + l2_post)
## this is used to weight the pre- and post-edge differently as
## defined in the MBACK paper
weight1 = 1 * (energy < e0)
weight2 = 1 * (energy > e0)
weight = np.sqrt(sum(weight1)) * weight1 + np.sqrt(sum(weight2)) * weight2
## get the f'' function from CL or Chantler
if tables.lower() == 'chantler':
f1 = f1_chantler(z, energy, _larch=_larch)
f2 = f2_chantler(z, energy, _larch=_larch)
else:
(f1, f2) = f1f2(z, energy, edge=edge, _larch=_larch)
group.f2 = f2
if return_f1: group.f1 = f1
n = edge
if edge.lower().startswith('l'): n = 'L'
params = Group(
s=Parameter(1, vary=True, _larch=_larch), # scale of data
xi=Parameter(50, vary=fit_erfc, min=0, _larch=_larch), # width of erfc
em=Parameter(xray_line(z, n, _larch=_larch)[0],
vary=False,
_larch=_larch), # erfc centroid
e0=Parameter(e0, vary=False, _larch=_larch), # abs. edge energy
## various arrays need by the objective function
en=energy,
mu=mu,
f2=group.f2,
weight=weight,
theta=theta,
leexiang=leexiang,
_larch=_larch)
if fit_erfc:
params.a = Parameter(1, vary=True, _larch=_larch) # amplitude of erfc
else:
params.a = Parameter(0, vary=False, _larch=_larch) # amplitude of erfc
for i in range(order): # polynomial coefficients
setattr(params, 'c%d' % i, Parameter(0, vary=True, _larch=_larch))
fit = Minimizer(match_f2, params, _larch=_larch, toler=1.e-5)
fit.leastsq()
eoff = energy - params.e0.value
normalization_function = params.a.value * erfc(
(energy - params.em.value) / params.xi.value) + params.c0.value
for i in range(MAXORDER):
j = i + 1
attr = 'c%d' % j
if hasattr(params, attr):
normalization_function = normalization_function + getattr(
getattr(params, attr), 'value') * eoff**j
group.fpp = params.s * mu - normalization_function
group.mback_params = params
def preedge(energy,
mu,
e0=None,
step=None,
nnorm=2,
nvict=0,
pre1=None,
pre2=-50,
norm1=100,
norm2=None):
"""pre edge subtraction, normalization for XAFS (straight python)
This performs a number of steps:
1. determine E0 (if not supplied) from max of deriv(mu)
2. fit a line of polymonial to the region below the edge
3. fit a polymonial to the region above the edge
4. extrapolae the two curves to E0 to determine the edge jump
Arguments
----------
energy: array of x-ray energies, in eV
mu: array of mu(E)
e0: edge energy, in eV. If None, it will be determined here.
step: edge jump. If None, it will be determined here.
pre1: low E range (relative to E0) for pre-edge fit
pre2: high E range (relative to E0) for pre-edge fit
nvict: energy exponent to use for pre-edg fit. See Note
norm1: low E range (relative to E0) for post-edge fit
norm2: high E range (relative to E0) for post-edge fit
nnorm: degree of polynomial (ie, nnorm+1 coefficients will be found) for
post-edge normalization curve. Default=2 (quadratic), max=5
Returns
-------
dictionary with elements (among others)
e0 energy origin in eV
edge_step edge step
norm normalized mu(E)
pre_edge determined pre-edge curve
post_edge determined post-edge, normalization curve
Notes
-----
1 nvict gives an exponent to the energy term for the fits to the pre-edge
and the post-edge region. For the pre-edge, a line (m * energy + b) is
fit to mu(energy)*energy**nvict over the pre-edge region,
energy=[e0+pre1, e0+pre2]. For the post-edge, a polynomial of order
nnorm will be fit to mu(energy)*energy**nvict of the post-edge region
energy=[e0+norm1, e0+norm2].
"""
energy = remove_dups(energy)
if e0 is None or e0 < energy[0] or e0 > energy[-1]:
energy = remove_dups(energy)
dmu = np.gradient(mu) / np.gradient(energy)
# find points of high derivative
high_deriv_pts = np.where(dmu > max(dmu) * 0.05)[0]
idmu_max, dmu_max = 0, 0
for i in high_deriv_pts:
if (dmu[i] > dmu_max and (i + 1 in high_deriv_pts)
and (i - 1 in high_deriv_pts)):
idmu_max, dmu_max = i, dmu[i]
e0 = energy[idmu_max]
nnorm = max(min(nnorm, MAX_NNORM), 0)
ie0 = index_nearest(energy, e0)
e0 = energy[ie0]
pre1_input = pre1
norm2_input = norm2
if pre1 is None: pre1 = min(energy) - e0
if norm2 is None: norm2 = max(energy) - e0
if norm2 < 0: norm2 = max(energy) - e0 - norm2
pre1 = max(pre1, (min(energy) - e0))
norm2 = min(norm2, (max(energy) - e0))
if pre1 > pre2:
pre1, pre2 = pre2, pre1
if norm1 > norm2:
norm1, norm2 = norm2, norm1
p1 = index_of(energy, pre1 + e0)
p2 = index_nearest(energy, pre2 + e0)
if p2 - p1 < 2:
p2 = min(len(energy), p1 + 2)
omu = mu * energy**nvict
ex, mx = remove_nans2(energy[p1:p2], omu[p1:p2])
precoefs = polyfit(ex, mx, 1)
pre_edge = (precoefs[0] * energy + precoefs[1]) * energy**(-nvict)
# normalization
p1 = index_of(energy, norm1 + e0)
p2 = index_nearest(energy, norm2 + e0)
if p2 - p1 < 2:
p2 = min(len(energy), p1 + 2)
# reduce dimension to linear if less than 75 eV given
if abs(norm2 - norm1) < 75.0:
nnorm = min(nnorm, 1)
coefs = polyfit(energy[p1:p2], omu[p1:p2], nnorm)
post_edge = 0
norm_coefs = []
for n, c in enumerate(reversed(list(coefs))):
post_edge += c * energy**(n - nvict)
norm_coefs.append(c)
edge_step = step
if edge_step is None:
edge_step = post_edge[ie0] - pre_edge[ie0]
norm = (mu - pre_edge) / edge_step
return {
'e0': e0,
'edge_step': edge_step,
'norm': norm,
'pre_edge': pre_edge,
'post_edge': post_edge,
'norm_coefs': norm_coefs,
'nvict': nvict,
'nnorm': nnorm,
'norm1': norm1,
'norm2': norm2,
'pre1': pre1,
'pre2': pre2,
'precoefs': precoefs,
'norm2_input': norm2_input,
'pre1_input': pre1_input
}
def estimate_noise(k, chi=None, group=None, rmin=15.0, rmax=30.0,
kweight=1, kmin=0, kmax=20, dk=4, dk2=None, kstep=0.05,
kwindow='kaiser', nfft=2048, _larch=None, **kws):
"""
estimate noise levels in EXAFS spectrum and estimate highest k
where data is above the noise level
Parameters:
-----------
k: 1-d array of photo-electron wavenumber in Ang^-1 (or group)
chi: 1-d array of chi
group: output Group [see Note below]
rmin: minimum R value for high-R region of chi(R)
rmax: maximum R value for high-R region of chi(R)
kweight: exponent for weighting spectra by k**kweight [1]
kmin: starting k for FT Window [0]
kmax: ending k for FT Window [20]
dk: tapering parameter for FT Window [4]
dk2: second tapering parameter for FT Window [None]
kstep: value to use for delta_k ( Ang^-1) [0.05]
window: name of window type ['kaiser']
nfft: value to use for N_fft [2048].
Returns:
---------
None -- outputs are written to supplied group. Values (scalars) written
to output group:
epsilon_k estimated noise in chi(k)
epsilon_r estimated noise in chi(R)
kmax_suggest highest estimated k value where |chi(k)| > epsilon_k
Notes:
-------
1. This method uses the high-R portion of chi(R) as a measure of the noise
level in the chi(R) data and uses Parseval's theorem to convert this noise
level to that in chi(k). This method implicitly assumes that there is no
signal in the high-R portion of the spectrum, and that the noise in the
spectrum s "white" (independent of R) . Each of these assumptions can be
questioned.
2. The estimate for 'kmax_suggest' has a tendency to be fair but pessimistic
in how far out the chi(k) data goes before being dominated by noise.
3. Follows the 'First Argument Group' convention, so that you can either
specifiy all of (an array for 'k', an array for 'chi', option output Group)
OR pass a group with 'k' and 'chi' as the first argument
"""
k, chi, group = parse_group_args(k, members=('k', 'chi'),
defaults=(chi,), group=group,
fcn_name='esitmate_noise')
# save _sys.xafsGroup -- we want to NOT write to it here!
savgroup = set_xafsGroup(None, _larch=_larch)
tmpgroup = Group()
rmax_out = min(10*pi, rmax+2)
xftf(k, chi, kmin=kmin, kmax=kmax, rmax_out=rmax_out,
kweight=kweight, dk=dk, dk2=dk2, kwindow=kwindow,
nfft=nfft, kstep=kstep, group=tmpgroup, _larch=_larch)
chir = tmpgroup.chir
rstep = tmpgroup.r[1] - tmpgroup.r[0]
irmin = int(0.01 + rmin/rstep)
irmax = min(nfft/2, int(1.01 + rmax/rstep))
highr = realimag(chir[irmin:irmax])
# get average of window function value, scale eps_r scale by this
# this is imperfect, but improves the result.
kwin_ave = tmpgroup.kwin.sum()*kstep/(kmax-kmin)
eps_r = sqrt((highr*highr).sum() / len(highr)) / kwin_ave
# use Parseval's theorem to convert epsilon_r to epsilon_k,
# compensating for kweight
w = 2 * kweight + 1
scale = sqrt((2*pi*w)/(kstep*(kmax**w - kmin**w)))
eps_k = scale*eps_r
# do reverse FT to get chiq array
xftr(tmpgroup.r, tmpgroup.chir, group=tmpgroup, rmin=0.5, rmax=9.5,
dr=1.0, window='parzen', nfft=nfft, kstep=kstep, _larch=_larch)
# sets kmax_suggest to the largest k value for which
# | chi(q) / k**kweight| > epsilon_k
iq0 = index_of(tmpgroup.q, (kmax+kmin)/2.0)
tst = tmpgroup.chiq_mag[iq0:] / ( tmpgroup.q[iq0:])**kweight
kmax_suggest = tmpgroup.q[iq0 + where(tst < eps_k)[0][0]]
# restore original _sys.xafsGroup, set output variables
_larch.symtable._sys.xafsGroup = savgroup
group = set_xafsGroup(group, _larch=_larch)
group.epsilon_k = eps_k
group.epsilon_r = eps_r
group.kmax_suggest = kmax_suggest
