def pseudovoigtfit(xdata, ydata, x0=None):
[m, b, CoD, yD, err, mErr,
bErr] = dm.linReg(np.concatenate((xdata[0:5], xdata[-5:])),
np.concatenate((ydata[0:5], ydata[-5:])))
[yMax, i] = bf.max(ydata - (m * xdata + b))
if x0 is None:
yLeft = m * xdata[0] + b
yRight = m * xdata[-1] + b
ySum = np.sum(ydata * np.abs(np.gradient(xdata))) - (0.5 * np.abs(
(xdata[-1] - xdata[0]) * (yRight - yLeft)) + np.abs(
bf.min(yLeft, yRight)[0] *
(xdata[-1] - xdata[0]))) # estimated area of peak
xMax = xdata[i] # find belonging x value
sigma = ySum / (yMax * np.pi) # estimate width of peak
x0 = [ySum, sigma, xMax, m, b, 0.5] # start values Pseudo-Voigt
x_par = op.leastsq(pseudovoigtopt, x0, (xdata, ydata))
x = x_par[0]
yFit = pseudovoigtfunction(x, xdata)
# check quality of peak
meanNoise = (yLeft + yRight) / 2
peakQuality = (yMax + meanNoise) / (meanNoise + 3 * meanNoise**0.5)
err = 0
# adapt dimensions of x if x0 has different dimensions
if bf.size(x0) != bf.size(x):
x = np.transpose(x)
return x, x0, yMax, yFit, peakQuality, err, meanNoise
def pearson7fit(xdata, ydata, x0=None):
[m, b, CoD, yD, err, mErr,
bErr] = dm.linReg(np.concatenate((xdata[0:5], xdata[-5:])),
np.concatenate((ydata[0:5], ydata[-5:])))
[yMax, i] = bf.max(ydata - (m * xdata + b))
if x0 is None:
yLeft = m * xdata[1] + b
yRight = m * xdata[-1] + b
ySum = np.sum(ydata * np.abs(np.gradient(xdata))) - (0.5 * np.abs(
(xdata[-1] - xdata[0]) * (yRight - yLeft)) + np.abs(
bf.min(yLeft, yRight)[0] *
(xdata[-1] - xdata[0]))) # estimated area of peak
xMax = xdata[i] # find belonging x value
sigma = ySum / (yMax * (2 * np.pi)**0.5) # estimate width of peak
x0 = [ySum, sigma, xMax, m, b, 2.0] # start values Pearson7
else:
x0 = [x0[0], x0[1], x0[2], x0[3], x0[4], 1] # start values Pearson7
x_par = op.leastsq(pearson7opt, x0, (xdata, ydata))
x = x_par[0]
yFit = pearson7function(x, xdata)
# adapt x to fit peak description
x = [x[0], x[1] / (2 * x[5] - 3)**0.5, x[2], x[3], x[4], x[5]]
# check quality of peak
meanNoise = (yLeft + yRight) / 2
peakQuality = (yMax + meanNoise) / (meanNoise + 3 * meanNoise**0.5)
err = 0
# adapt dimensions of x if x0 has different dimensions
if bf.size(x0) != bf.size(x):
x = np.transpose(x)
return x, x0, yMax, yFit, peakQuality, err, meanNoise
def sin2PsiAnalysis(data, maxPsi=None):
# data: dVals, errVals, tauVals, phiVals, psiVals, hklVal, s1Val, hs2Val, ibVals???
# extract needed data
dVals = data['dVals']
dErrVals = data['dErr']
tauVals = data['tauVals']
phiVals = data['phiVals']
psiVals = data['psiVals']
ibVals = data['ibVals']
hklVal = data['hklVal']
s1Val = data['s1Val']
hs2Val = data['hs2Val']
a0Val = bf.getDictValOrDef(data, 'a0Val')
# define derived values
phiUni = np.sort(np.unique(phiVals))
sinpsi2 = bc.sind(psiVals)**2
sinpsi2Distr = np.arange(0, 1.001, 0.01)
psiUni = np.unique(psiVals)
psiUniWithoutZero = psiUni[psiUni != 0]
psiSign = np.sign(psiUniWithoutZero[-1]) # sign of last psi value
psiUni = psiUni[(np.sign(psiUni) == psiSign) |
(psiUni == 0)] # only negative or positive values
if maxPsi is not None:
psiUni = psiUni[(psiUni <= maxPsi) & (
psiUni >=
-maxPsi)] # take only values smaller than or equal to |maxPsi°|
maxUsedPsi = np.max(np.abs(psiUni))
sinpsi2Uni = bc.sind(psiUni)**2
sin2psiUni = bc.sind(np.abs(2 * psiUni))
# define global regression values
mVals = np.zeros(6)
bVals = np.zeros(6)
errVals = np.zeros(6)
errValsStar = 0
# perform linear regressions for one peak
sinpsi2StarSingle = s1Val / hs2Val
sinpsi2Star = -2 * s1Val / hs2Val
sinpsi2Plus = 1 + s1Val / hs2Val
dValsValid = (dVals > 0) & (np.isnan(dVals) == False)
tauValsValid = (tauVals >= 0) & (tauVals < 1e6)
ibValsValid = (ibVals > 0) & (ibVals < 1000)
if maxPsi is None:
tauMean = np.sum(tauVals[tauValsValid]) / len(tauVals[tauValsValid])
# tauMean = (max(tauVals[tauValsValid]) + min(tauVals[tauValsValid])) / 2
else:
# take only values smaller than or equal to | maxPsi° |
curTau = tauVals[(psiVals <= maxPsi) & (psiVals >= -maxPsi)
& tauValsValid]
tauMean = np.sum(curTau) / len(curTau)
# tauMean = (max(curTau) + min(curTau)) / 2
# determine mean values of IB
valuesIb = np.zeros(len(phiUni))
for j in range(len(phiUni)):
if maxPsi is None:
valuesIb[j] = np.mean(ibVals[phiVals == phiUni[j] & ibValsValid])
else:
valuesIb[j] = np.mean(
ibVals[(phiVals == phiUni[j]) & (psiVals <= maxPsi) &
(psiVals >= -maxPsi) & ibValsValid])
# perform linear regression of all phi values
valsAll = np.zeros((len(psiUni), 2))
vals45 = np.zeros((len(psiUni), 2))
vals0_180 = np.zeros((len(psiUni), 3))
vals90_270 = np.zeros((len(psiUni), 3))
for i in range(len(psiUni)):
if bf.max(bf.containsItems(psiVals, psiUni[i])[0])[0] and bf.max(
bf.containsItems(psiVals, -psiUni[i])[0])[0]:
# positive and negative psi values
val0 = np.array([
dVals[(psiVals == psiUni[i]) & (phiVals == 0) & dValsValid],
dErrVals[(psiVals == psiUni[i]) & (phiVals == 0) & dValsValid]
])
val90 = np.array([
dVals[(psiVals == psiUni[i]) & (phiVals == 90) & dValsValid],
dErrVals[(psiVals == psiUni[i]) & (phiVals == 90) & dValsValid]
])
val180 = np.array([
dVals[(psiVals == -psiUni[i]) & (phiVals == 0) & dValsValid],
dErrVals[(psiVals == -psiUni[i]) & (phiVals == 0) & dValsValid]
])
val270 = np.array([
dVals[(psiVals == -psiUni[i]) & (phiVals == 90) & dValsValid],
dErrVals[(psiVals == -psiUni[i]) & (phiVals == 90)
& dValsValid]
])
else:
val0 = np.array([
dVals[(psiVals == psiUni[i]) & (phiVals == 0) & dValsValid],
dErrVals[(psiVals == psiUni[i]) & (phiVals == 0) & dValsValid]
])
val90 = np.array([
dVals[(psiVals == psiUni[i]) & (phiVals == 90) & dValsValid],
dErrVals[(psiVals == psiUni[i]) & (phiVals == 90) & dValsValid]
])
val180 = np.array([
dVals[(psiVals == psiUni[i]) & (phiVals == 180) & dValsValid],
dErrVals[(psiVals == psiUni[i]) & (phiVals == 180)
& dValsValid]
])
val270 = np.array([
dVals[(psiVals == psiUni[i]) & (phiVals == 270) & dValsValid],
dErrVals[(psiVals == psiUni[i]) & (phiVals == 270)
& dValsValid]
])
val45 = np.array([
dVals[(psiVals == psiUni[i]) & (phiVals == 45) & dValsValid],
dErrVals[(psiVals == psiUni[i]) & (phiVals == 45) & dValsValid]
])
if val45.size > 0:
vals45[i, :] = val45
if val0.size > 0 and val180.size > 0:
vals0_180[i, 0] = 0.5 * (val0[0] + val180[0])
vals0_180[i, 1] = 0.5 * (val0[0] - val180[0])
vals0_180[i, 2] = 0.5 * (val0[1] + val180[1])
elif val0.size > 0:
vals0_180[i, 0] = val0[0]
vals0_180[i, 1] = 0
vals0_180[i, 2] = val0[1]
elif val180.size > 0:
vals0_180[i, 0] = val180[0]
vals0_180[i, 1] = 0
vals0_180[i, 2] = val180[1]
if val90.size > 0 and val270.size > 0:
vals90_270[i, 0] = 0.5 * (val90[0] + val270[0])
vals90_270[i, 1] = 0.5 * (val90[0] - val270[0])
vals90_270[i, 2] = 0.5 * (val90[1] + val270[1])
elif val90.size > 0:
vals90_270[i, 0] = val90[0]
vals90_270[i, 1] = 0
vals90_270[i, 2] = val90[1]
elif val270.size > 0:
vals90_270[i, 0] = val270[0]
vals90_270[i, 1] = 0
vals90_270[i, 2] = val270[1]
if vals0_180[i, 0] != 0 and vals90_270[i, 0] != 0:
valsAll[i, :] = 0.5 * (vals0_180[i, [0, 2]] +
vals90_270[i, [0, 2]])
# check for validity
# perform linear regression for all phi values
usedIndex = np.array(range(len(psiUni)))
used = usedIndex[valsAll[:, 0] != 0]
if len(used) > 0:
if np.all(valsAll[used, 1] != 0):
[m, b, CoD, yD, err, err33,
bErr] = dm.linRegWeighted(sinpsi2Uni[used], valsAll[used, 0],
1 / valsAll[used, 1])
else:
[m, b, CoD, yD, err, err33,
bErr] = dm.linReg(sinpsi2Uni[used], valsAll[used, 0])
mVals[5] = m
bVals[5] = b
errVals[5] = err33
errValsStar = bErr
# perform linear regression of phi values with phi = 45° (if exist)
used12 = usedIndex[vals45[:, 0] != 0]
if len(used12) > 0:
if len(used) > 0:
if np.all(vals45[used12, 1] != 0):
[m12, b12, CoD12, yD12, err, err12,
bErr] = dm.linRegWeighted(sinpsi2Uni[used12], vals45[used12,
0],
1 / vals45[used12, 1], 'b', b)
else:
[m12, b12, CoD12, yD12, err, err12,
bErr] = dm.linReg(sinpsi2Uni[used12], vals45[used12, 0], 'b',
b)
else:
if np.all(vals45[used12, 1] != 0):
[m12, b12, CoD12, yD12, err, err12,
bErr] = dm.linRegWeighted(sinpsi2Uni[used12], vals45[used12,
0],
1 / vals45[used12, 1])
else:
[m12, b12, CoD12, yD12, err, err12,
bErr] = dm.linReg(sinpsi2Uni[used12], vals45[used12, 0])
mVals[5] = m12
bVals[5] = b12
mVals[4] = m12
bVals[4] = b12
errVals[4] = err12
# perform linear regression of phi values with phi = 0°/180°
used1 = usedIndex[vals0_180[:, 0] != 0]
if len(used1) > 0:
if len(used) > 0:
if np.all(vals0_180[used1, 2] != 0):
[m1, b1, CoD1, yD1, err, err1,
bErr] = dm.linRegWeighted(sinpsi2Uni[used1], vals0_180[used1,
0],
1 / vals0_180[used1, 2], 'b', b)
else:
[m1, b1, CoD1, yD1, err, err1,
bErr] = dm.linReg(sinpsi2Uni[used1], vals0_180[used1, 0], 'b',
b)
else:
if np.all(vals0_180[used1, 2] != 0):
[m1, b1, CoD1, yD1, err, err1,
bErr] = dm.linRegWeighted(sinpsi2Uni[used1], vals0_180[used1,
0],
1 / vals0_180[used1, 2])
else:
[m1, b1, CoD1, yD1, err, err1,
bErr] = dm.linReg(sinpsi2Uni[used1], vals0_180[used1, 0])
mVals[5] = m1
bVals[5] = b1
# [m1f, err1f] = lsqcurvefit(linM,m1,sinpsi2Uni(used1),vals0_180(used1,1));
mVals[0] = m1
bVals[0] = b1
errVals[0] = err1
if np.all(vals0_180[used1, 2] != 0):
[m13, b13, CoD13, yD13, err, err13,
bErr] = dm.linRegWeighted(sin2psiUni[used1], vals0_180[used1, 1],
1 / vals0_180[used1, 2], 'b', 0)
else:
[m13, b13, CoD13, yD13, err, err13,
bErr] = dm.linReg(sin2psiUni[used1], vals0_180[used1, 1], 'b', 0)
# [m1f, err1f] = lsqcurvefit(linBase,m1,sin2psiUni(used1),vals0_180(used1,2));
mVals[2] = m13
bVals[2] = b13
errVals[2] = err13
# perform linear regression of phi values with phi = 90°/270°
used2 = usedIndex[vals90_270[:, 0] != 0]
if len(used2) > 0:
if len(used) > 0:
if np.all(vals90_270[used2, 2] != 0):
[m2, b2, CoD2, yD2, err, err2,
bErr] = dm.linRegWeighted(sinpsi2Uni[used2], vals90_270[used2,
0],
1 / vals90_270[used2, 2], 'b', b)
else:
[m2, b2, CoD2, yD2, err, err2,
bErr] = dm.linReg(sinpsi2Uni[used2], vals90_270[used2, 0],
'b', b)
else:
if np.all(vals90_270[used2, 2] != 0):
[m2, b2, CoD2, yD2, err, err2,
bErr] = dm.linRegWeighted(sinpsi2Uni[used2], vals90_270[used2,
0],
1 / vals90_270[used2, 2])
else:
[m2, b2, CoD2, yD2, err, err2,
bErr] = dm.linReg(sinpsi2Uni[used2], vals90_270[used2, 0])
mVals[5] = m2
bVals[5] = b2
# [m2f, err2f] = lsqcurvefit(linM,m2,sinpsi2Uni(used2),vals90_270(used2,1));
mVals[1] = m2
bVals[1] = b2
errVals[1] = err2
if np.all(vals90_270[used2, 2] != 0):
[m23, b23, CoD23, yD23, err, err23,
bErr] = dm.linRegWeighted(sin2psiUni[used2], vals90_270[used2, 1],
1 / vals90_270[used2, 2], 'b', 0)
else:
[m23, b23, CoD23, yD23, err, err23,
bErr] = dm.linReg(sin2psiUni[used2], vals90_270[used2, 1], 'b', 0)
# [m2f, err2f] = lsqcurvefit(linBase,m2,sin2psiUni(used2),vals90_270(used2,2));
mVals[3] = m23
bVals[3] = b23
errVals[3] = err23
# determine stresses
dStarVal0 = mVals[0] * sinpsi2StarSingle + bVals[0]
dStarVal90 = mVals[1] * sinpsi2StarSingle + bVals[1]
dStarVal = mVals[5] * sinpsi2Star + bVals[5]
dPlusVal = mVals[5] * sinpsi2Plus + bVals[5]
dComVal = mVals[5] * 2 / 3 + bVals[5]
s11_s33 = mVals[0] / (hs2Val * dStarVal)
ds11 = 2 * errVals[0]**0.5 / (hs2Val * dStarVal)
s22_s33 = mVals[1] / (hs2Val * dStarVal)
ds22 = 2 * errVals[1]**0.5 / (hs2Val * dStarVal)
s13 = mVals[2] / (hs2Val * dStarVal)
ds13 = 2 * errVals[2]**0.5 / (hs2Val * dStarVal)
s23 = mVals[3] / (hs2Val * dStarVal)
ds23 = 2 * errVals[3]**0.5 / (hs2Val * dStarVal)
if np.any((phiVals == 45) | (phiVals == -45) | (phiVals == 225)):
s12 = mVals[4] / (hs2Val * dStarVal) - 0.5 * (s11_s33 + s22_s33)
else:
s12 = mVals[4] / (hs2Val * dStarVal)
ds12 = 2 * errVals[4]**0.5 / (hs2Val * dStarVal)
aStarVal = conv.latticeDists2aVals2(dStarVal, hklVal)
if a0Val is None or a0Val == 0:
s33 = 0
ds33 = 0
else:
s33 = calcSigma33(aStarVal, a0Val, s1Val, hs2Val)
ds33 = 2 * errVals[5]**0.5 / (hs2Val * dStarVal)
# d0_1 = regVals(:,2) ./ (dekList(:,2) .* (s11_s33 + s22_s33) + s33 .* f33 + 1);
# [sMain, d0, quality] = stressesWithS33(dekList, dStarVals, [s11_s33 s22_s33 s12 s13 s23], ...
# [data(:,1) dVals error data(:,[7 8])], plotData);
# combine results
stresses = np.array([s11_s33, s22_s33, s13, s23, s12, s33])
accuracy = np.array([ds11, ds22, ds13, ds23, ds12, ds33])
# resData: tauMean, dStar, stresses, accuracy, mVals???, bVals???
resData = {
'tauMean': tauMean,
'dStar100': aStarVal,
'dStar100Err': 2 * errValsStar**0.5,
'stresses': stresses,
'accuracy': accuracy,
'meanIB': valuesIb
}
plotData = {
'dVals': data['dVals'],
'dErr': data['dErr'],
'phiVals': data['phiVals'],
'psiVals': data['psiVals'],
'hklVal': hklVal,
'mVals': mVals,
'bVals': bVals,
'errVals': errVals,
'sinpsi2Star': sinpsi2Star,
'meanVals': valsAll[used, :]
}
if len(used) > 0:
plotData['xMean'] = sinpsi2Uni[used]
plotData['yMean'] = yD
if len(used12) > 0:
plotData['x12'] = sinpsi2Uni[used12]
plotData['y12'] = yD12
if len(used1) > 0:
plotData['x1'] = sinpsi2Uni[used1]
plotData['y1'] = yD1
if len(used2) > 0:
plotData['x2'] = sinpsi2Uni[used2]
plotData['y2'] = yD2
return resData, plotData