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 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 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 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
10067.28 120488.7 89110.0998902 0.30168329
10073.72 118833.7 88265.1000656 0.29738025
10080.18 118434.7 88372.1004302 0.29280544
10086.66 117995.7 88449.0998063 0.28822094
10093.17 118435.7 89180.0997098 0.28371228
10099.69 117303.7 88720.0998253 0.27927983
10106.22 117929.7 89581.1003571 0.27494432
10112.78 116857.7 89144.1003332 0.27070279
10119.36 115791.7 88718.1000129 0.26632896
10125.96 111467.7 85797.099695 0.26174966
10132.57 110079.7 85128.099834 0.25704747
10139.21 104190.7 80953.0999403 0.2523529
10145.86 93726.7 73074.0996945 0.24890911'''
raw_data_lines = raw_data.split('\n')
raw_data_table = []
for line in raw_data_lines:
raw_data_table.append(list(map(lambda x: float(x), line.strip().split())))
table = np.array(raw_data_table)
group.energy = table[:, 0]
group.mu = table[:, 3]
e0 = find_e0(group, _larch=mylarch)
pre_edge(group, _larch=mylarch)
autobk(group, _larch=mylarch)
xftf(group, _larch=mylarch)
xftr(group, _larch=mylarch)
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 deglitch(energy, mu, group, e_window='xas', sg_window_length=9, sg_polyorder=3,
alpha=.025, max_glitches='Default', max_glitch_length=4, plot_res=False):
"""Routine to deglitch a XAS spectrum.
This function deglitches points in XAS data through two-step
fitting with Savitzky-Golay filter and outlier identification
with generalized extreme student deviate test.
This code requires the data group to have at least an energy
and normalized absorption channel.
Parameters
----------
energy : array
Array of the energies of the XAS scan
mu : array
Array of the absorption coefficient data
group : Larch Group
Larch Group to be modified by deglitching procedure
e_window : {'xas', 'xanes', 'exafs', (float, float)}
'xas' scans the full spectrum.
'xanes' looks from the beginning up to the edge + 150eV.
'exafs' looks at the edge + 150eV to the end.
(float, float) provides start and end energies in eV for analysis
sg_window_length : odd int, default: 7
Window length to build Savitzky-Golay filter from normalized data
sg_polyorder : int, default: 3
Polynomial order to build Savitzky-Golay filter from normalized data
alpha : float, default: .001
Alpha value for generalized ESD test for outliers.
max_glitches : int, default: len(data)//10
Maximum number of outliers to remove.
plot_res : bool, default: False
Command to plot the final normalized residuals and a histogram of their distribution.
Returns
-------
None
"""
import numpy as np
from scipy.interpolate import interp1d
from scipy.signal import savgol_filter
from larch_plugins.utils import group2dict
from larch_plugins.xafs import find_e0
from larch import Interpreter
from copy import deepcopy
session = Interpreter(with_plugins=False)
# computing the energy window to perform the deglitch:
e_val = 150 # energy limit to separate xanes from exafs [eV]
e_windows = ['xas', 'xanes', 'exafs']
if e_window in e_windows:
if e_window =='xas':
e_window = [energy[0], energy[-1]]
else:
if 'e0' not in dir(group):
e0 = find_e0(energy, mu=mu, group=group, _larch=session)
else:
e0 = getattr(group, 'e0')
if e_window =='xanes':
e_window = [energy[0], e0+e_val]
else:
e_window = [e0+e_val, energy[-1]]
index = np.where((energy >= e_window[0]) & (energy <= e_window[1]))
index = index[0]
# creating copies of original data
mu_copy = np.copy(mu) # interpolated values for posterior analysis will be inserted in this
ener = np.copy(energy) # copy of energy to create interp1d function without the potential glitches
# not limited to start:end to ensure data at edges gets best possible fit
sg_init = savgol_filter(mu, sg_window_length, sg_polyorder)
# computing the difference between normalized spectrum and the savitsky-golay filter
res1 = mu - sg_init
roll_mad1 = roll_med(abs(res1), window = 2*(sg_window_length+(max_glitch_length-1))+1, edgemethod='calc')
res_norm = res1 / roll_mad1
#If the max is not set to an int, the max will be set to the default of the length of the analyzed data//10
if type(max_glitches) != int:
max_glitches = len(res1)//10
out1 = genesd(res_norm[index], max_glitches, alpha) #finds outliers in residuals between data and Savitzky-Golay filter
if index[0] != 0: #compensates for nonzero starting index
out1 = out1 + index[0]
if len(out1) == 0: #deglitching ends here if no outliers are found in this first round of analysis
return
e2 = np.delete(ener, out1) #removes points that are poorly fitted by the S-G filter
n2 = np.delete(mu_copy, out1)
f = interp1d(e2, n2, kind='cubic')
interp_pts = f(energy[out1]) #interpolates for normalized mu at the removed energies
for i, point in enumerate(out1):
mu_copy[point] = interp_pts[i] #inserts interpolated points into normalized data
sg_final = savgol_filter(mu_copy, sg_window_length, sg_polyorder) #fits the normalized absorption with the interpolated points
res2 = mu - sg_final
roll_mad2 = roll_med(abs(res2), window = (2*max_glitch_length)+1, edgemethod='calc')
res_norm2 = res2 / roll_mad2
if plot_res:
import matplotlib.pyplot as plt
fig, axes = plt.subplots(ncols=2, figsize=(8,2.5), gridspec_kw={'width_ratios':[2, 1]})
axes[0].plot(res_norm, color='tab:orange')
axes[0].set_ylabel('Residuals (μ(E))')
axes[0].set_xlabel('Point Index')
#plotting the normalized residuals on a point-index basis
critval = find_critval(res_norm2, alpha)
axes[1].hist(res_norm, bins=len(ener)//20, range=(-1*critval, critval), color='tab:orange') #plots histogram for normalized residuals
axes[1].set_ylabel('Number of Points')
axes[1].set_xlabel('Norm. Resid. Value')
#Will not plot large outliers, since the limits are set at the initial critical values for the genesd
plt.show()
glitches_init = genesd(res_norm2[index], max_glitches, alpha)#by normalizing the standard deviation to the same window as our S-G calculation,
#we can tackle the full spectrum, accounting for the noise we expect in the data;
#as a bonus, with the S-G filter, we ideally have a near-normal distribution of residuals
#(which makes the generalized ESD a robust method for finding the outliers)
if index[0] != 0:
glitches_init = glitches_init + index[0]
glitches = np.array([])
for glitch in glitches_init:
if True in np.where(abs(glitch-out1)<(sg_window_length//2)+1, True, False):
glitches = np.append(glitches, glitch)
glitches[::-1].sort()
glitches = glitches.astype(int)
data_filt = deepcopy(group) #non-destructive copy for comparison
group_dict = group2dict(data_filt) #transfers data copy to a dictionary (easier to work with)
if len(glitches) == 0:
glitches = None
else:
glitch_dict = {energy[glitch] : {} for glitch in glitches}
for number in glitches:
targetLength = len(energy) #everything that is of the same length as the energy array will have the indices
#corresponding to glitches removed
for key in dir(group):
if type(getattr(group, key)) == np.ndarray or type(getattr(group, key)) == list:
if len(getattr(group, key)) == targetLength and key!='energy': #deletes the energy last
glitch_dict[getattr(group, 'energy')[number]].update({key : group_dict[key][number]})
group_dict[key] = np.delete(group_dict[key], number) #replaces the array with one that removes glitch points
#numpy arrays require extra steps to delete an element (which is why this takes this structure)
#removed indices is reversed to avoid changing the length ahead of the removal of points
group_dict['energy'] = np.delete(group_dict['energy'], number)
glitch_dict[energy[number]].update({'params' : {'e_window':e_window, 'sg_window_length':sg_window_length,
'sg_polyorder':sg_polyorder, 'alpha':alpha,
'max_glitches':max_glitches, 'max_glitch_length':max_glitch_length}})
if glitches is not None:
if hasattr(group,'glitches'):
group_dict['glitches'].update(glitch_dict)
else:
setattr(group,'glitches', glitch_dict)
dataKeys = list(group_dict.keys())
for item in dataKeys:
setattr(group, item, group_dict[item])
return