def sub_ctr(self):
# the used keys
key_list = ['absorption', 'roughness', 'scale']
# input substrate ubr and substrate index
subr, sindex = tc.initialize_contral_vars(self.ubr_index,
['substrate'], key_list)
substrate_ctr = structure.substrate_ctr(self.var_list, self.iq, subr,
sindex, self.absorption,
self.h, self.h, self.scale,
key_list)
# roughness
cr = roughness(self.iq)
r = cr.robinson_roughness(self.roughness)
return np.multiply(self.intensity * substrate_ctr, np.mat(r).T)
def slab_ctr(self):
# used keys
key_list = ['lattice_abc', 'dw']
# input slab ubr and slab index
slab_ubr, slab_index = tc.initialize_contral_vars(
self.ubr_index,
np.unique(self.var_table['slab_list']).tolist(), key_list)
fctr = structure.film_ctr(self.var_list, self.var_table, slab_ubr,
slab_index, self.iq, self.h, self.k,
key_list)
# roughness
cr = roughness(self.iq)
r = cr.robinson_roughness(self.roughness)
# interface roughness
ir = cr.interface_roughness(self.iroughness)
return np.multiply(np.multiply(self.intensity * fctr,
np.mat(r).T),
np.mat(ir).T)
def pos_refine(self):
# the used keys
sub_key_list = ['absorption', 'roughness', 'scale']
# input substrate ubr and substrate index
sub_ubr, sub_index = tc.initialize_contral_vars(
self.ubr_index, ['substrate'], sub_key_list)
substrate_ctr = structure.substrate_ctr(self.var_list, self.iq,
sub_ubr, sub_index,
self.absorption, self.h,
self.h, self.scale,
sub_key_list)
# roughness
cr = roughness(self.iq)
r = cr.robinson_roughness(self.roughness)
s = np.multiply(self.intensity * substrate_ctr, np.mat(r).T)
subr0 = self.var_table['posz_list']
slab_index = 'posz'
key_list = ['pos']
mask = tc.bragg_mask(self.iq, 3, 1, mode='yin', limit=24)
# fig, ax = plt.subplots()
def varience(subr):
fctr = structure.film_ctr(self.var_list, self.var_table, subr,
slab_index, self.iq, self.h, self.k,
key_list)
# roughness
cr = roughness(self.iq)
# interface roughness
ir = cr.interface_roughness(self.iroughness)
f = np.multiply(np.multiply(self.intensity * fctr,
np.mat(r).T),
np.mat(ir).T)
a = s + f
e = np.sqrt(self.i)
# plt.cla()
# plt.plot(np.log10(e))
# plt.plot(np.log10(abs(a)))
v = np.sum(
abs(mask * (np.log10(abs(a) + 1e-6) - np.log10(e + 1e-6))))
print(v)
return v
re = so.minimize(varience,
subr0,
method='Nelder-Mead',
options={'maxiter': 50})
subr1 = re.x
fctr1 = structure.film_ctr(self.var_list, self.var_table, subr1,
slab_index, self.iq, self.h, self.k,
key_list)
# roughness
cr = roughness(self.iq)
# interface roughness
ir = cr.interface_roughness(self.iroughness)
return np.multiply(np.multiply(self.intensity * fctr1,
np.mat(r).T),
np.mat(ir).T)
def dw_refine(self, p_mask=13, n_mask=3, weight=1, key_list=['dw']):
# Prepare the data mask
# yin mask to mask the bragg peaks
bn_mask = np.mat(tc.bragg_mask(self.iq, n_mask, 1, mode='yin'))
# yang mask to refine the signal around bragg peaks only
bp_mask = np.mat(tc.bragg_mask(self.iq, p_mask, 1, mode='yang'))
bgm = np.asarray(np.multiply(bn_mask, bp_mask).T).reshape(-1) * weight
# calculate ss tot.For only seveal signal points are calculate
# mean value is np.sum(abs(i)*bgm)/np.sum(bgm)
ss_tot = np.sum(
(abs(self.i) * bgm - np.sum(abs(self.i) * bgm) / np.sum(bgm))**2)
# initialize the variable about the lattice
slab_list = np.unique(self.var_table['slab_list']).tolist()
ubr_index = tc.contral_vars(self.var_list)
subr, sindex = tc.initialize_contral_vars(ubr_index, slab_list, ['dw'])
# roughness
cr = roughness(self.iq)
r = cr.robinson_roughness(self.roughness)
# substrate ctr
# the used keys
key_list = ['absorption', 'roughness', 'scale']
# input substrate ubr and substrate index
sub_ubr, sub_index = tc.initialize_contral_vars(
self.ubr_index, ['substrate'], key_list)
substrate_ctr = structure.substrate_ctr(self.var_list, self.iq,
sub_ubr, sub_index,
self.absorption, self.h,
self.h, self.scale, key_list)
def d_refine(d_var):
fctr = structure.film_ctr(self.var_list, self.var_table, d_var,
sindex, self.iq, self.h, self.k, ['dw'])
ss = np.multiply(np.mat(fctr) + substrate_ctr,
np.mat(r).T) * self.intensity
# calculate r square
sa = np.asarray(ss).reshape(-1)
ss_res = np.sum((abs(self.i) * bgm - abs(sa) * bgm)**2)
varience = ss_res / ss_tot
print(int(varience * 1e4) / 1e4)
return varience
d0 = subr
re = so.minimize(d_refine, d0, method='Nelder-Mead', tol=1)
self.ubr_index = tc.refresh_index(self.ubr_index, re.x, sindex)
# plot the refined result
fctr = structure.film_ctr(self.var_list, self.var_table, re.x, sindex,
self.iq, self.h, self.k, ['dw'])
ss = np.multiply(np.mat(fctr) + substrate_ctr, np.mat(r).T)
plt.plot(self.iq, np.log(abs(ss * self.intensity)))
plt.plot(self.iq, np.log(np.sqrt(self.i)))
def lattice_refine(self, p_mask=13, n_mask=3, weight=1):
# Prepare the data mask
# yin mask to mask the bragg peaks
bn_mask = np.mat(tc.bragg_mask(self.iq, n_mask, 1, mode='yin'))
# yang mask to refine the signal around bragg peaks only
bp_mask = np.mat(tc.bragg_mask(self.iq, p_mask, 1, mode='yang'))
bgm = np.asarray(np.multiply(bn_mask, bp_mask).T).reshape(-1) * weight
# calculate ss tot.For only seveal signal points are calculate
# mean value is np.sum(abs(i)*bgm)/np.sum(bgm)
ss_tot = np.sum((abs(self.i)*bgm - \
np.sum(abs(self.i)*bgm)/np.sum(bgm))**2)
# initialize the variable about the lattice
slab_list = np.unique(self.var_table['slab_list']).tolist()
subr, sindex = tc.initialize_contral_vars(self.ubr_index, slab_list,
['lattice_abc'])
# substrate ctr
# the used keys
key_list = ['absorption', 'roughness', 'scale']
# input substrate ubr and substrate index
sub_ubr, sub_index = tc.initialize_contral_vars(
self.ubr_index, ['substrate'], key_list)
substrate_ctr = structure.substrate_ctr(self.var_list, self.iq,
sub_ubr, sub_index,
self.absorption, self.h,
self.h, self.scale, key_list)
# roughness
cr = roughness(self.iq)
r = cr.robinson_roughness(self.roughness)
def c_refine(c_var):
# input lattice c variable into subr
if len(slab_list) == 1:
subr[2] = c_var
elif len(slab_list) >= 2:
for slabi in range(len(slab_list)):
subr[slabi * 3 - 1] = c_var[slabi]
fctr = structure.film_ctr(self.var_list, self.var_table, subr,
sindex, self.iq, self.h, self.k,
['lattice_abc'])
ss = np.multiply(np.mat(fctr) + substrate_ctr,
np.mat(r).T) * self.intensity
# calculate r square
sa = np.asarray(ss).reshape(-1)
ss_res = np.sum((abs(self.i) * bgm - abs(sa) * bgm)**2)
varience = ss_res / ss_tot
print(int(varience * 1e4) / 1e4)
return varience
# select properity optimized method for lattice_c optimize
# if there are only one or two variables, step_brute method is a direct method
if len(slab_list) == 1:
print('lattice c optimising....\nOPT_STEP_BRUTE method is used')
rec = tt.opt_step_brute(c_refine, [[0.8, 1.2]], grid_size=20)
elif len(slab_list) == 2:
print('lattice c optimising....\nOPT_STEP_BRUTE method is used')
rec = tt.opt_step_brute(c_refine, [[0.8, 1.2], [0.8, 1.2]],
grid_size=10)
# for larger variable number, Nelder-Mead method is more comparable
elif len(slab_list) >= 3:
print('lattice c optimising....\nNELDER_MEAD method is used')
c0 = np.ones(len(slab_list)).tolist()
resc = so.minimize(c_refine, c0, method='Nelder-Mead', tol=10)
rec = resc.x
# update subr
if len(slab_list) == 1:
subr[2] = rec
elif len(slab_list) >= 2:
for slabi in range(len(slab_list)):
subr[slabi * 3 - 1] = rec[0][slabi]
# update ubr_index
self.ubr_index = tc.refresh_index(self.ubr_index, subr, sindex)
# plot the refined result
fctr = structure.film_ctr(self.var_list, self.var_table, subr, sindex,
self.iq, self.h, self.k, ['lattice_abc'])
ss = np.multiply(np.mat(fctr) + substrate_ctr, np.mat(r).T)
plt.plot(self.iq, np.log(abs(ss * self.intensity)))
plt.plot(self.iq, np.log(np.sqrt(self.i)))