def S_QCalculation(Q, I_Q, Ibkg_Q, scaleFactor, J_Q, Sinf, fe_Q, Ztot, density,
Iincoh_Q, minQ, QmaxIntegrate, maxQ, smoothFactor,
dampFactor):
"""Function for the S(Q) calculation.
"""
Isample_Q = MainFunctions.calc_IsampleQ(I_Q, scaleFactor, Ibkg_Q)
alpha = MainFunctions.calc_alpha(J_Q[Q <= QmaxIntegrate], Sinf,
Q[Q <= QmaxIntegrate],
Isample_Q[Q <= QmaxIntegrate],
fe_Q[Q <= QmaxIntegrate], Ztot, density)
Icoh_Q = MainFunctions.calc_Icoh(alpha, Isample_Q, Iincoh_Q)
S_Q = MainFunctions.calc_SQ(Icoh_Q, Ztot, fe_Q, Sinf, Q, minQ,
QmaxIntegrate, maxQ)
Ssmooth_Q = UtilityAnalysis.calc_SQsmoothing(Q, S_Q, Sinf, smoothFactor,
minQ, QmaxIntegrate, maxQ)
SsmoothDamp_Q = UtilityAnalysis.calc_SQdamp(Ssmooth_Q, Q, Sinf,
QmaxIntegrate, dampFactor)
return SsmoothDamp_Q
def Optimization(self):
"""Function to optimize and plot F(r)"""
#-------------------Intra-molecular components-----------------------------
# numAtoms, element, x, y, z = Utility.read_xyz_file(self.XYZFilePath)
numAtoms, element, x, y, z = Utility.read_xyz_file(
"/Users/ciccio/work/ID27/LASDiA/xyzFiles/Ar.xyz")
iintra_Q = Optimization.calc_iintra(self.Q, self.fe_Q, self.Ztot,
self.ui.QmaxIntegrate.value(),
self.ui.maxQ.value(),
self.elementList, element, x, y, z,
self.elementParameters)
iintradamp_Q = UtilityAnalysis.calc_iintradamp(iintra_Q,
self.dampingFunct)
Qiintradamp_Q = self.Q * iintradamp_Q
rintra, Fintra_r = MainFunctions.calc_Fr(
self.Q[self.Q <= self.ui.QmaxIntegrate.value()],
Qiintradamp_Q[self.Q <= self.ui.QmaxIntegrate.value()])
scaleFactor = self.ui.scaleFactorValue.value()
density0 = self.ui.densityValue.value()
# ----------------------First scale minimization---------------------------
scaleStep = 0.05
# sth = 0.008
# s0th = 0.006
sth = 0.0
s0th = 0.0
phi_matrix = 0.0
thickness_sampling = 0.0
scaleFactor = Minimization.OptimizeScale(
self.Q, self.I_Q, self.Ibkg_Q, self.J_Q, self.Iincoh_Q, self.fe_Q,
self.ui.maxQ.value(), self.ui.minQ.value(),
self.ui.QmaxIntegrate.value(), self.Ztot, density0,
scaleFactor, self.Sinf, self.ui.smoothingFactor.value(),
self.ui.rmin.value(), self.dampingFunct, Fintra_r,
self.ui.iterations.value(), scaleStep, sth, s0th,
thickness_sampling, phi_matrix, "n")
# ----------------------First density minimization-------------------------
densityStep = density0 / 50
densityStepEnd = density0 / 250
density = Minimization.OptimizeDensity(
self.Q, self.I_Q, self.Ibkg_Q, self.J_Q, self.Iincoh_Q, self.fe_Q,
self.ui.maxQ.value(), self.ui.minQ.value(),
self.ui.QmaxIntegrate.value(), self.Ztot, density0,
scaleFactor, self.Sinf, self.ui.smoothingFactor.value(),
self.ui.rmin.value(), self.dampingFunct, Fintra_r,
self.ui.iterations.value(), densityStep, densityStepEnd, sth, s0th,
thickness_sampling, phi_matrix, "n")
# print("density0, density", density0, density)
numLoopIteration = 0
while 1:
if np.abs(density - density0) > density / 25:
# print("First")
scaleStep = 0.006
densityStep = density / 10
WSamplestep = 0.0008
WRefstep = 0.0008
elif np.abs(density - density0) > density / 75:
# print("Second")
scaleStep = 0.0006
densityStep = density / 100
WSamplestep = 0.0002
WRefstep = 0.0002
else:
# print("Third")
scaleStep = 0.00006
densityStep = density / 1000
WSamplestep = 0.0001
WRefstep = 0.0001
scaleFactor = Minimization.OptimizeScale(
self.Q, self.I_Q, self.Ibkg_Q, self.J_Q, self.Iincoh_Q,
self.fe_Q, self.ui.maxQ.value(), self.ui.minQ.value(),
self.ui.QmaxIntegrate.value(), self.Ztot, density,
scaleFactor, self.Sinf, self.ui.smoothingFactor.value(),
self.ui.rmin.value(), self.dampingFunct, Fintra_r,
self.ui.iterations.value(), scaleStep, sth, s0th,
thickness_sampling, phi_matrix, "n")
density0 = density
density = Minimization.OptimizeDensity(
self.Q, self.I_Q, self.Ibkg_Q, self.J_Q, self.Iincoh_Q,
self.fe_Q, self.ui.maxQ.value(), self.ui.minQ.value(),
self.ui.QmaxIntegrate.value(), self.Ztot, density0,
scaleFactor, self.Sinf, self.ui.smoothingFactor.value(),
self.ui.rmin.value(), self.dampingFunct, Fintra_r,
self.ui.iterations.value(), densityStep, density / 250, sth,
s0th, thickness_sampling, phi_matrix, "n")
numLoopIteration += 1
# print("numLoopIteration", numLoopIteration, scaleFactor, density)
if (np.abs(density - density0) > np.abs(
density / 2500)) and (numLoopIteration <= 30):
continue
else:
break
# print("final scale", scaleFactor, "final density", density)
self.ui.scaleFactorValue.setValue(scaleFactor)
self.ui.densityValue.setValue(density)
Isample_Q = MainFunctions.calc_IsampleQ(self.I_Q, scaleFactor,
self.Ibkg_Q)
alpha = MainFunctions.calc_alpha(
self.J_Q[self.Q <= self.ui.QmaxIntegrate.value()], self.Sinf,
self.Q[self.Q <= self.ui.QmaxIntegrate.value()],
Isample_Q[self.Q <= self.ui.QmaxIntegrate.value()],
self.fe_Q[self.Q <= self.ui.QmaxIntegrate.value()], self.Ztot,
density)
Icoh_Q = MainFunctions.calc_Icoh(alpha, Isample_Q, self.Iincoh_Q)
S_Q = MainFunctions.calc_SQ(Icoh_Q, self.Ztot, self.fe_Q, self.Sinf,
self.Q, self.ui.minQ.value(),
self.ui.QmaxIntegrate.value(),
self.ui.maxQ.value())
Ssmooth_Q = UtilityAnalysis.calc_SQsmoothing(
self.Q, S_Q, self.Sinf, self.ui.smoothingFactor.value(),
self.ui.minQ.value(), self.ui.QmaxIntegrate.value(),
self.ui.maxQ.value())
SsmoothDamp_Q = UtilityAnalysis.calc_SQdamp(Ssmooth_Q, self.Sinf,
self.dampingFunct)
i_Q = MainFunctions.calc_iQ(SsmoothDamp_Q, self.Sinf)
Qi_Q = self.Q * i_Q
r, F_r = MainFunctions.calc_Fr(
self.Q[self.Q <= self.ui.QmaxIntegrate.value()],
Qi_Q[self.Q <= self.ui.QmaxIntegrate.value()])
Fopt_r, deltaFopt_r = Optimization.calc_optimize_Fr(
self.ui.iterations.value(), F_r, Fintra_r, density,
i_Q[self.Q <= self.ui.QmaxIntegrate.value()],
self.Q[self.Q <= self.ui.QmaxIntegrate.value()], self.Sinf,
self.J_Q[self.Q <= self.ui.QmaxIntegrate.value()], r,
self.ui.rmin.value(), "n")
Scorr_Q = MainFunctions.calc_SQCorr(Fopt_r, r, self.Q, self.Sinf)
self.ui.distfuncPlot.canvas.ax.plot(r,
Fopt_r,
"g",
label=r"$F_{opt}(r)$")
self.ui.distfuncPlot.canvas.ax.legend()
self.ui.distfuncPlot.canvas.draw()
self.ui.factorPlot.canvas.ax.plot(self.Q,
Scorr_Q,
"g",
label=r"$S_{opt}(Q)$")
self.ui.factorPlot.canvas.ax.legend()
self.ui.factorPlot.canvas.draw()
def SQ(self):
"""Function to calculate and plot the structure factor S(Q)"""
self.elementList = Utility.molToElemList(self.molecule)
# self.elementList = Utility.molToElemList("Ar")
self.elementParameters = Utility.read_parameters(
self.elementList, "./elementParameters.txt")
# print(elementList)
# print(elementParameters)
self.Q, self.I_Q, self.Qbkg, self.Ibkg_Q = UtilityAnalysis.check_data_length(
self.Q, self.I_Q, self.Qbkg, self.Ibkg_Q, self.ui.minQ.value(),
self.ui.maxQ.value())
two_theta = UtilityAnalysis.Qto2theta(self.Q)
absCorrFactor = Geometry.calcAbsCorrection(
self.ui.absLength.value(), two_theta, self.ui.dacThickness.value(),
self.ui.dacAngle.value())
self.I_Q = self.I_Q / absCorrFactor
self.Ibkg_Q = self.Ibkg_Q / absCorrFactor
self.fe_Q, self.Ztot = MainFunctions.calc_eeff(self.elementList,
self.Q,
self.elementParameters)
self.Iincoh_Q = MainFunctions.calc_Iincoh(self.elementList, self.Q,
self.elementParameters)
self.J_Q = MainFunctions.calc_JQ(self.Iincoh_Q, self.Ztot, self.fe_Q)
self.Sinf = MainFunctions.calc_Sinf(self.elementList, self.fe_Q,
self.Q, self.Ztot,
self.elementParameters)
self.dampingFunct = UtilityAnalysis.calc_dampingFunction(
self.Q,
self.ui.dampingFactor.value(), self.ui.QmaxIntegrate.value(),
self.ui.dampingFunction.currentText())
Isample_Q = MainFunctions.calc_IsampleQ(
self.I_Q, self.ui.scaleFactorValue.value(), self.Ibkg_Q)
alpha = MainFunctions.calc_alpha(
self.J_Q[self.Q <= self.ui.QmaxIntegrate.value()], self.Sinf,
self.Q[self.Q <= self.ui.QmaxIntegrate.value()],
Isample_Q[self.Q <= self.ui.QmaxIntegrate.value()],
self.fe_Q[self.Q <= self.ui.QmaxIntegrate.value()], self.Ztot,
self.ui.densityValue.value())
Icoh_Q = MainFunctions.calc_Icoh(alpha, Isample_Q, self.Iincoh_Q)
S_Q = MainFunctions.calc_SQ(Icoh_Q, self.Ztot, self.fe_Q, self.Sinf,
self.Q, self.ui.minQ.value(),
self.ui.QmaxIntegrate.value(),
self.ui.maxQ.value())
Ssmooth_Q = UtilityAnalysis.calc_SQsmoothing(
self.Q, S_Q, self.Sinf, self.ui.smoothingFactor.value(),
self.ui.minQ.value(), self.ui.QmaxIntegrate.value(),
self.ui.maxQ.value())
self.SsmoothDamp_Q = UtilityAnalysis.calc_SQdamp(
Ssmooth_Q, self.Sinf, self.dampingFunct)
# self.ui.factorPlot.canvas.ax.plot(self.Q, self.SsmoothDamp_Q, "b", label=r"$S(Q)$")
# self.ui.factorPlot.canvas.ax.legend()
# self.ui.factorPlot.canvas.draw()
return self.SsmoothDamp_Q
def Kaplow_method(Q, I_Q, Ibkg_Q, J_Q, fe_Q, Iincoh_Q, Sinf, Ztot, scaleFactor,
density, Fintra_r, r, minQ, QmaxIntegrate, maxQ,
smoothFactor, dampFactor, iteration, rmin):
"""Function to apply the Kaplow method.
Parameters
----------
variables : module
input variables setted by the user
Q : numpy array
momentum transfer (nm^-1)
I_Q : numpy array
measured scattering intensity
Ibkg_Q : numpy array
background scattering intensity
J_Q : numpy array
J(Q)
fe_Q : numpy array
effective electric form factor
Iincoh_Q : numpy array
incoherent scattering intensity
Sinf : float
value of S(Q) for Q->inf
Ztot : int
total Z number
scaleFactor : float
scale factor
density : float
average atomic density
Fintra_r : numpy array
intramolecular contribution of F(r)
r : numpy array
atomic distance (nm)
Returns
-------
chi2 : float
chi2 value
SsmoothDamp_Q : numpy array
smoothed and damped structure factor
Fopt_r : numpy array
optimized F(r)
"""
Isample_Q = MainFunctions.calc_IsampleQ(I_Q, scaleFactor, Ibkg_Q)
alpha = MainFunctions.calc_alpha(J_Q[Q <= QmaxIntegrate], Sinf,
Q[Q <= QmaxIntegrate],
Isample_Q[Q <= QmaxIntegrate],
fe_Q[Q <= QmaxIntegrate], Ztot, density)
Icoh_Q = MainFunctions.calc_Icoh(alpha, Isample_Q, Iincoh_Q)
S_Q = MainFunctions.calc_SQ(Icoh_Q, Ztot, fe_Q, Sinf, Q, minQ,
QmaxIntegrate, maxQ)
Ssmooth_Q = UtilityAnalysis.calc_SQsmoothing(Q, S_Q, Sinf, smoothFactor,
minQ, QmaxIntegrate, maxQ)
SsmoothDamp_Q = UtilityAnalysis.calc_SQdamp(Ssmooth_Q, Q, Sinf,
QmaxIntegrate, dampFactor)
i_Q = MainFunctions.calc_iQ(SsmoothDamp_Q, Sinf)
F_r = MainFunctions.calc_Fr(r, Q[Q <= QmaxIntegrate],
i_Q[Q <= QmaxIntegrate])
Fopt_r, deltaFopt_r = Optimization.calc_optimize_Fr(
iteration, F_r, Fintra_r, density, i_Q[Q <= QmaxIntegrate],
Q[Q <= QmaxIntegrate], Sinf, J_Q[Q <= QmaxIntegrate], r, rmin, "n")
chi2 = simps(deltaFopt_r[r < rmin]**2, r[r < rmin])
return (chi2, SsmoothDamp_Q, F_r, Fopt_r)
def Kaplow_methodFZ(numAtoms, variables, Q, I_Q, Ibkg_Q, aff_squared_mean,
aff_mean_squared, Iincoh_Q, sf, rho0, Fintra_r, r):
"""Function to apply the Kaplow method with Waseda FZ formalism.
Parameters
----------
numAtoms : int
number of atoms in the molecule
variables : module
input variables setted by the user
Q : numpy array
momentum transfer (nm^-1)
I_Q : numpy array
measured scattering intensity
Ibkg_Q : numpy array
background scattering intensity
aff_squared_mean : numpy array
mean of the squared form factor: <f^2>
aff_mean_squared : numpy array
squared of the mean form factor: <f>^2
Iincoh_Q : numpy array
incoherent scattering intensity
sf : float
scale factor
rho0 : float
average atomic density
Fintra_r : numpy array
intramolecular contribution of F(r)
r : numpy array
atomic distance (nm)
Returns
-------
chi2 : float
chi2 value
"""
Isample_Q = MainFunctions.calc_IsampleQ(I_Q, sf, Ibkg_Q)
alpha = Formalism.calc_alphaFZ(Q, Isample_Q, Iincoh_Q, rho0,
aff_squared_mean, aff_mean_squared)
Icoh_Q = MainFunctions.calc_Icoh(alpha, Isample_Q, Iincoh_Q)
S_Q = Formalism.calc_SFZ_Q(Q, Icoh_Q, aff_squared_mean, aff_mean_squared, variables.minQ, \
variables.QmaxIntegrate, variables.maxQ)
S_Qsmoothed = UtilityAnalysis.calc_SQsmoothing(Q, S_Q, 1, variables.smooth_factor, \
variables.minQ, variables.QmaxIntegrate, variables.maxQ)
S_QsmoothedDamp = UtilityAnalysis.calc_SQdamp(S_Qsmoothed, Q, 1, \
variables.QmaxIntegrate, variables.damping_factor)
i_Q = MainFunctions.calc_iQ(S_QsmoothedDamp, 1)
F_r = MainFunctions.calc_Fr(r, Q[Q<=variables.QmaxIntegrate], \
i_Q[Q<=variables.QmaxIntegrate])
# J_Q = Iincoh_Q/aff_mean_squared
F_rIt, deltaF_rIt = Formalism.calc_optimize_FrFZ(variables.iteration, F_r, \
Fintra_r, rho0, i_Q[Q<=variables.QmaxIntegrate], Q[Q<=variables.QmaxIntegrate], \
Iincoh_Q[Q<=variables.QmaxIntegrate], r, variables.rmin)
chi2 = simps(deltaF_rIt[r < variables.rmin]**2, r[r < variables.rmin])
return (chi2, S_QsmoothedDamp, F_rIt)
def OptimizeDensityGofRCorr(Q, I_Q, Ibkg_Q, J_Q, fe_Q, maxQ, minQ,
QmaxIntegrate, Ztot, density, scaleFactor, Sinf, smoothingFactor, rmin, NumPoints,
dampingFunction, Fintra_r, iterations, densityStep, densityStepEnd):
"""Function for the density optimization.
"""
Flag = 0
NoPeak = 0
# densityStep = density/50
# densityStepEnd = density/250
numSample = 23
density = density-densityStep*11
Qorg = Q
while ((10*densityStep>densityStepEnd) and (NoPeak<5)): # Loop for the range shifting
densityArray = make_array_loop(density, densityStep, numSample)
chi2Array = np.zeros(numSample)
for i in range(len(densityArray)):
# ------------------Kaplow method for scale--------------------
Q = Qorg
Subt = calc_Subt(I_Q, Ibkg_Q, scaleFactor)
alpha = calc_alpha(J_Q[Q<=QmaxIntegrate], Sinf,
Q[Q<=QmaxIntegrate], Subt[Q<=QmaxIntegrate],
fe_Q[Q<=QmaxIntegrate], Ztot, densityArray[i])
S_Q = calc_SQ(Q, Subt, alpha, fe_Q, J_Q, Ztot, Sinf,
QmaxIntegrate)
Ssmooth_Q = UtilityAnalysis.calc_SQsmoothing(Q, S_Q, Sinf,
smoothingFactor,
minQ, QmaxIntegrate, maxQ)
Q, Ssmooth_Q = UtilityAnalysis.rebinning(Q, Ssmooth_Q, 0.0,
maxQ, NumPoints)
SsmoothDamp_Q = UtilityAnalysis.calc_SQdamp(Ssmooth_Q, Sinf,
dampingFunction)
chi2Array[i] = FitRemoveGofRPeaks(Q, SsmoothDamp_Q, Sinf,
QmaxIntegrate, Fintra_r, iterations,
rmin, densityArray[i], J_Q, Ztot)
# --------------------Range shifting selection --------------------
density = densityArray[np.argmin(chi2Array)] - densityStep*1.1
nearIdx, nearEl = UtilityAnalysis.find_nearest(densityArray, density)
if nearIdx == 0:
print("out3")
density -= densityStep*10
densityStep *= 10
NoPeak += 1
if nearIdx >= numSample-2:
print("out4")
density += densityStep*10
densityStep *= 10
NoPeak += 1
densityStep /= 10
Flag += 1
print(Flag)
plt.scatter(densityArray, chi2Array)
plt.grid(True)
# plt.show
# if ((10*densityStep<=densityStepEnd) and (NoPeak>=5)):
# break
# ------------------------chi2 curve fit for scale-------------------------
xFit, yFit, density, chi2Min = chi2Fit(density, densityArray, chi2Array)
print("final density", density)
return density
def OptimizeScaleGofRCorr(Q, I_Q, Ibkg_Q, J_Q, fe_Q, maxQ, minQ,
QmaxIntegrate, Ztot, density, scaleFactor, Sinf, smoothingFactor, rmin, NumPoints,
dampingFunction, Fintra_r, iterations, scaleStep):
"""Function for the scale factor optimization.
"""
Flag = 0
NoPeak = 0
# scaleStep = 0.05
scaleStepEnd = 0.00006
numSample = 23
scaleFactor = scaleFactor-scaleStep*11
Qorg = Q
# Loop for the range shifting
while ((10*scaleStep>scaleStepEnd) and (NoPeak<5) and ((Flag==1) or (scaleFactor+scaleStep*1.1>=0))):
# print("scale loop")
scaleArray = make_array_loop(scaleFactor, scaleStep, numSample)
chi2Array = np.zeros(numSample)
for i in range(len(scaleArray)):
# ------------------Kaplow method for scale--------------------
Q = Qorg
Subt = calc_Subt(I_Q, Ibkg_Q, scaleArray[i])
alpha = calc_alpha(J_Q[Q<=QmaxIntegrate], Sinf,
Q[Q<=QmaxIntegrate], Subt[Q<=QmaxIntegrate],
fe_Q[Q<=QmaxIntegrate], Ztot, density)
S_Q = calc_SQ(Q, Subt, alpha, fe_Q, J_Q, Ztot, Sinf,
QmaxIntegrate)
Ssmooth_Q = UtilityAnalysis.calc_SQsmoothing(Q, S_Q, Sinf,
smoothingFactor,
minQ, QmaxIntegrate, maxQ)
Q, Ssmooth_Q = UtilityAnalysis.rebinning(Q, Ssmooth_Q, 0.0,
maxQ, NumPoints)
SsmoothDamp_Q = UtilityAnalysis.calc_SQdamp(Ssmooth_Q, Sinf,
dampingFunction)
chi2Array[i] = FitRemoveGofRPeaks(Q, SsmoothDamp_Q, Sinf,
QmaxIntegrate, Fintra_r, iterations,
rmin, density, J_Q, Ztot)
# --------------------Range shifting selection --------------------
if np.amax(chi2Array) > 10**8:
scaleFactor = scaleArray[np.argmin(chi2Array[0:np.argmax(chi2Array)])] - scaleStep*1.1
else:
scaleFactor = scaleArray[np.argmin(chi2Array)] - scaleStep*1.1
nearIdx, nearEl = UtilityAnalysis.find_nearest(scaleArray, scaleFactor)
if nearIdx == 0:
print("out1")
scaleFactor -= scaleStep*10
scaleStep *= 10
NoPeak += 1
if nearIdx >= numSample-2:
print("out2")
scaleFactor += scaleStep*10
scaleStep *= 10
NoPeak += 1
scaleStep /= 10
Flag += 1
print(Flag)
# ------------------------chi2 curve fit for scale-------------------------
xFit, yFit, scaleFactor, chi2Min = chi2Fit(scaleFactor, scaleArray, chi2Array)
# plt.plot(xFit, yFit)
# plt.grid(True)
print("final scale factor", scaleFactor)
# plt.show()
return scaleFactor
alpha = MainFunctions.calc_alpha(J_Q[Q <= variables.QmaxIntegrate], Sinf,
Q[Q <= variables.QmaxIntegrate],
Isample_Q[Q <= variables.QmaxIntegrate],
fe_Q[Q <= variables.QmaxIntegrate], Ztot,
density)
Icoh_Q = MainFunctions.calc_Icoh(alpha, Isample_Q, Iincoh_Q)
S_Q = MainFunctions.calc_SQ(Icoh_Q, Ztot, fe_Q, Sinf, Q, variables.minQ,
variables.QmaxIntegrate, variables.maxQ)
Ssmooth_Q = UtilityAnalysis.calc_SQsmoothing(Q, S_Q, Sinf, smoothingFactor,
variables.minQ,
variables.QmaxIntegrate,
variables.maxQ)
SsmoothDamp_Q = UtilityAnalysis.calc_SQdamp(Ssmooth_Q, Sinf,
dampingFunction)
i_Q = MainFunctions.calc_iQ(SsmoothDamp_Q, Sinf)
Qi_Q = Q * i_Q
r, F_r = MainFunctions.calc_Fr(Q[Q <= variables.QmaxIntegrate],
Qi_Q[Q <= variables.QmaxIntegrate])
Fopt_r, deltaFopt_r = Optimization.calc_optimize_Fr(
variables.iterations, F_r, Fintra_r, density,
i_Q[Q <= variables.QmaxIntegrate], Q[Q <= variables.QmaxIntegrate],
Sinf, J_Q[Q <= variables.QmaxIntegrate], r, variables.rmin, "n")
deltaFopt_r[np.where(r >= variables.rmin)] = 0.0
chi2 = np.mean(deltaFopt_r**2)
def OptimizeScale(Q, I_Q, Ibkg_Q, J_Q, Iincoh_Q, fe_Q, minQ, QmaxIntegrate,
maxQ, Ztot, density, scaleFactor, Sinf, smoothingFactor,
rmin, dampingFunction, Fintra_r, iterations, scaleStep, sth,
s0th, mccFlag, thickness_sampling, phi_matrix):
"""Function for the scale factor optimization.
Q : numpy array
momentum transfer (nm^-1)
I_Q : numpy array
measured scattering intensity
Ibkg_Q : numpy array
background scattering intensity
J_Q : numpy array
J(Q)
Iincoh_Q : numpy array
incoherent scattering intensity
fe_Q : numpy array
effective electric form factor
minQ : float
minimum Q value
QmaxIntegrate : float
maximum Q value for the intagrations
maxQ : float
maximum Q value
Ztot : int
total Z number
density : float
average atomic density
scaleFactor : float
scale factor
Sinf : float
value of S(Q) for Q->inf
smoothingFactor : float
smoothing factor
rmin : float
r cut-off value (nm)
dampingFunction : numpy array
damping function
Fintra_r : numpy array
intramolecular contribution of F(r)
iterations : int
number of iterations
scaleStep
sth
s0th
MCC_flag
"""
numSample = 23
if mccFlag.lower() == "y":
T_MCC_sth, T_MCC_corr_factor_bkg = Geometry.MCC_correction(
sth, s0th, thickness_sampling, phi_matrix)
# print(thickness_sampling)
# plt.contour(phi_matrix)
# plt.show()
# x = np.linspace(0, len(T_MCC_sth), len(T_MCC_sth), endpoint=True)
# _, T_MCC_sth = UtilityAnalysis.rebinning(x, T_MCC_sth, np.amin(T_MCC_sth),
# np.amax(T_MCC_sth), len(I_Q))
# plt.plot(T_MCC_sth)
# plt.show()
I_Q = I_Q / T_MCC_sth
Ibkg_Q = Ibkg_Q * T_MCC_corr_factor_bkg / (T_MCC_sth)
flag = 0
# Loop for the range shifting
while 1:
# print(type(scaleFactor))
# print(type(scaleStep))
scaleArray = UtilityAnalysis.makeArrayLoop(scaleFactor, scaleStep)
chi2Array = np.zeros(numSample)
flag += 1
print("iter flag ", flag)
for i in range(numSample):
print("sample ", i, scaleArray[i])
# ------------------Kaplow method for scale--------------------
Isample_Q = MainFunctions.calc_IsampleQ(I_Q, scaleArray[i], Ibkg_Q)
alpha = MainFunctions.calc_alpha(J_Q[Q <= QmaxIntegrate], Sinf,
Q[Q <= QmaxIntegrate],
Isample_Q[Q <= QmaxIntegrate],
fe_Q[Q <= QmaxIntegrate], Ztot,
density)
Icoh_Q = MainFunctions.calc_Icoh(alpha, Isample_Q, Iincoh_Q)
S_Q = MainFunctions.calc_SQ(Icoh_Q, Ztot, fe_Q, Sinf, Q, minQ,
QmaxIntegrate, maxQ)
Ssmooth_Q = UtilityAnalysis.calc_SQsmoothing(
Q, S_Q, Sinf, smoothingFactor, minQ, QmaxIntegrate, maxQ)
SsmoothDamp_Q = UtilityAnalysis.calc_SQdamp(
Ssmooth_Q, Sinf, dampingFunction)
i_Q = MainFunctions.calc_iQ(SsmoothDamp_Q, Sinf)
Qi_Q = Q * i_Q
r, F_r = MainFunctions.calc_Fr(Q[Q <= QmaxIntegrate],
Qi_Q[Q <= QmaxIntegrate])
Fopt_r, deltaFopt_r = Optimization.calc_optimize_Fr(
iterations, F_r, Fintra_r, density, i_Q[Q <= QmaxIntegrate],
Q[Q <= QmaxIntegrate], Sinf, J_Q[Q <= QmaxIntegrate], r, rmin,
"n")
deltaFopt_r[np.where(r >= rmin)] = 0.0 # Igor version
chi2Array[i] = np.mean(deltaFopt_r**2) # Igor version
# Fth_r = Fintra_r - 4*np.pi*r*density
# plt.plot(r, Fth_r)
# plt.show()
# print(Fth_r)
# print(Fintra_r)
# chi2Array[i] = simps(deltaFopt_r[np.where((r>0)&(r<rmin))]**2)
# --------------------Range shifting selection --------------------
plt.scatter(scaleArray, chi2Array)
plt.grid(True)
plt.show()
maxLimit = 10**5
if np.amax(chi2Array) >= maxLimit:
scaleArray = scaleArray[0:np.argmax(chi2Array >= maxLimit)]
chi2Array = chi2Array[0:np.argmax(chi2Array >= maxLimit)]
if np.argmin(chi2Array) < 6:
scaleFactor -= scaleStep * 10
if np.argmin(chi2Array) > 16:
scaleFactor += scaleStep * 10
if (np.argmin(chi2Array) >= 6 and np.argmin(chi2Array) <= 16):
break
else:
continue
# ------------------------chi2 curve fit for scale-------------------------
# plt.ioff()
xFit, yFit, scaleFactor, chi2 = IgorFunctions.chi2Fit(
scaleFactor, scaleArray, chi2Array)
print("final scale factor", scaleFactor)
plt.scatter(scaleArray, chi2Array)
plt.plot(xFit, yFit)
plt.grid(True)
plt.show()
return scaleFactor
def OptimizeThicknessRef(Q, I_Q, Ibkg_Q, J_Q, Iincoh_Q, fe_Q, maxQ, minQ,
QmaxIntegrate, Ztot, density, scaleFactor, sth, s0th,
Sinf, smoothingFactor, rmin, dampingFunction,
Fintra_r, iterations, s0thStep, ws1, ws2, r1, r2, d,
phi_matrix_flag):
"""Function for the thickness optimization.
"""
Flag = 0
NoPeak = 0
s0th = max(s0th - s0thStep * 11, 0.0)
s0thStepEnd = 0.0006
numSample = 23
# Loop for the range shifting
while 1:
s0thArray = IgorFunctions.makeArrayLoop(s0th, s0thStep)
chi2Array = np.zeros(numSample)
for i in range(numSample):
# ------------------Kaplow method for scale--------------------
T_MCC_sth, T_MCC_corr_factor_bkg = Geometry.MCCCorrection(
sth, s0thArray[i], thickness_sampling, phi_matrix)
I_Q = I_Q / T_MCC_sth
Ibkg_Q = Ibkg_Q * T_MCC_corr_factor_bkg / (T_MCC_sth)
Isample_Q = MainFunctions.calc_IsampleQ(I_Q, scaleFactor, Ibkg_Q)
alpha = MainFunctions.calc_alpha(J_Q[Q <= QmaxIntegrate], Sinf,
Q[Q <= QmaxIntegrate],
Isample_Q[Q <= QmaxIntegrate],
fe_Q[Q <= QmaxIntegrate], Ztot,
density)
Icoh_Q = MainFunctions.calc_Icoh(alpha, Isample_Q, Iincoh_Q)
S_Q = MainFunctions.calc_SQ(Icoh_Q, Ztot, fe_Q, Sinf, Q, minQ,
QmaxIntegrate, maxQ)
Ssmooth_Q = UtilityAnalysis.calc_SQsmoothing(
Q, S_Q, Sinf, smoothingFactor, minQ, QmaxIntegrate, maxQ)
SsmoothDamp_Q = UtilityAnalysis.calc_SQdamp(
Ssmooth_Q, Sinf, dampingFunction)
i_Q = MainFunctions.calc_iQ(SsmoothDamp_Q, Sinf)
Qi_Q = Q * i_Q
r, F_r = MainFunctions.calc_Fr(Q[Q <= QmaxIntegrate],
Qi_Q[Q <= QmaxIntegrate])
Fopt_r, deltaFopt_r = Optimization.calc_optimize_Fr(
iterations, F_r, Fintra_r, density, i_Q[Q <= QmaxIntegrate],
Q[Q <= QmaxIntegrate], Sinf, J_Q[Q <= QmaxIntegrate], r, rmin,
"n")
deltaFopt_r[np.where(r >= rmin)] = 0.0
chi2Array[i] = np.mean(deltaFopt_r**2)
# --------------------Range shifting selection --------------------
if np.amax(chi2Array) > 10**8:
s0thIdx = np.argmin(chi2Array[0:np.argmax(chi2Array)])
else:
s0thIdx = np.argmin(chi2Array)
s0th = s0thArray[s0thIdx] - s0thStep * 1.1
nearIdx, nearEl = UtilityAnalysis.find_nearest(s0thArray, s0th)
if nearIdx == 0:
print("out1")
s0th -= s0thStep * 10
s0thStep *= 10
NoPeak += 1
if nearIdx >= numSample - 2:
print("out2")
s0th += s0thStep * 10
s0thStep *= 10
NoPeak += 1
s0thStep /= 10
Flag += 1
if ((10 * s0thStep > s0thStepEnd) and (NoPeak < 5)):
continue
else:
break
# ------------------------chi2 curve fit for scale-------------------------
xFit, yFit, sth, chi2 = IgorFunctions.chi2Fit(s0th, s0thArray, chi2Array)
print("final sample thickness ref", s0th)
return s0th
def OptimizeDensity(Q, I_Q, Ibkg_Q, J_Q, Iincoh_Q, fe_Q, minQ, QmaxIntegrate,
maxQ, Ztot, density, scaleFactor, Sinf, smoothingFactor,
rmin, dampingFunction, Fintra_r, iterations, densityStep,
sth, s0th, mccFlag, thickness_sampling, phi_matrix):
"""Function for the density optimization.
Q : numpy array
momentum transfer (nm^-1)
I_Q : numpy array
measured scattering intensity
Ibkg_Q : numpy array
background scattering intensity
J_Q : numpy array
J(Q)
Iincoh_Q : numpy array
incoherent scattering intensity
fe_Q : numpy array
effective electric form factor
minQ : float
minimum Q value
QmaxIntegrate : float
maximum Q value for the intagrations
maxQ : float
maximum Q value
Ztot : int
total Z number
density : float
average atomic density
scaleFactor : float
scale factor
Sinf : float
value of S(Q) for Q->inf
smoothingFactor : float
smoothing factor
rmin : float
r cut-off value (nm)
dampingFunction : numpy array
damping function
Fintra_r : numpy array
intramolecular contribution of F(r)
iterations : int
number of iterations
scaleStep
sth
s0th
thickness_sampling : float
phi_matrix
MCC_flag
"""
numSample = 23
if mccFlag.lower() == "y":
T_MCC_sth, T_MCC_corr_factor_bkg = Geometry.MCC_correction(
sth, s0th, thickness_sampling, phi_matrix)
I_Q = I_Q / T_MCC_sth
Ibkg_Q = Ibkg_Q * T_MCC_corr_factor_bkg / (T_MCC_sth)
flag = 0
# Loop for the range shifting
while 1:
flag += 1
print("iter flag ", flag)
densityArray = UtilityAnalysis.makeArrayLoop(density, densityStep)
chi2Array = np.zeros(numSample)
for i in range(numSample):
print("sample ", i, densityArray[i])
# ------------------Kaplow method for scale--------------------
Isample_Q = MainFunctions.calc_IsampleQ(I_Q, scaleFactor, Ibkg_Q)
alpha = MainFunctions.calc_alpha(J_Q[Q <= QmaxIntegrate], Sinf,
Q[Q <= QmaxIntegrate],
Isample_Q[Q <= QmaxIntegrate],
fe_Q[Q <= QmaxIntegrate], Ztot,
densityArray[i])
Icoh_Q = MainFunctions.calc_Icoh(alpha, Isample_Q, Iincoh_Q)
S_Q = MainFunctions.calc_SQ(Icoh_Q, Ztot, fe_Q, Sinf, Q, minQ,
QmaxIntegrate, maxQ)
Ssmooth_Q = UtilityAnalysis.calc_SQsmoothing(
Q, S_Q, Sinf, smoothingFactor, minQ, QmaxIntegrate, maxQ)
SsmoothDamp_Q = UtilityAnalysis.calc_SQdamp(
Ssmooth_Q, Sinf, dampingFunction)
i_Q = MainFunctions.calc_iQ(SsmoothDamp_Q, Sinf)
Qi_Q = Q * i_Q
r, F_r = MainFunctions.calc_Fr(Q[Q <= QmaxIntegrate],
Qi_Q[Q <= QmaxIntegrate])
# r, F_r = MainFunctions.calc_Fr(Q[Q<=QmaxIntegrate],
# Qi_Q[Q<=QmaxIntegrate])
Fopt_r, deltaFopt_r = Optimization.calc_optimize_Fr(
iterations, F_r, Fintra_r, densityArray[i],
i_Q[Q <= QmaxIntegrate], Q[Q <= QmaxIntegrate], Sinf,
J_Q[Q <= QmaxIntegrate], r, rmin, "n")
deltaFopt_r[np.where(r >= rmin)] = 0.0
chi2Array[i] = np.mean(deltaFopt_r**2)
# --------------------Range shifting selection --------------------
# densityIdx = np.argmin(chi2Array)
# density = densityArray[densityIdx] - densityStep*1.1
# nearIdx, nearEl = UtilityAnalysis.find_nearest(densityArray, density)
plt.scatter(densityArray, chi2Array)
plt.grid(True)
plt.show()
maxLimit = 10**5
if np.amax(chi2Array) >= maxLimit:
densityArray = densityArray[0:np.argmax(chi2Array >= maxLimit)]
chi2Array = chi2Array[0:np.argmax(chi2Array >= maxLimit)]
# print(np.argmin(chi2Array))
if np.argmin(chi2Array) < 6:
# print("bug")
density -= densityStep * 10
if np.argmin(chi2Array) > 16:
density += densityStep * 10
if (np.argmin(chi2Array) >= 6 and np.argmin(chi2Array) <= 16):
break
else:
continue
# ------------------------chi2 curve fit for scale-------------------------
#xFit, yFit, density, chi2Min = chi2Fit(densityArray, chi2Array)
xFit, yFit, density, chi2 = IgorFunctions.chi2Fit(density, densityArray,
chi2Array)
print("final density", density)
plt.scatter(densityArray, chi2Array)
plt.plot(xFit, yFit)
plt.grid(True)
plt.show()
return density