def test_generatedfunction(self):
testhelpers.assertRaisesNothing(self, Gaussian, Height=7.5, Sigma=1.2, PeakCentre=10)
lb = LinearBackground()
g = Gaussian(Height=7.5, Sigma=1.2, PeakCentre=10)
s = lb + g
self.assertTrue( isinstance( s, CompositeFunctionWrapper) )
def test_attributes_passed_to_composite_functions(self):
cf = Gaussian() + LinearBackground()
self.assertEqual(cf.getAttributeValue('NumDeriv'), False)
cf = CompositeFunction(Gaussian(), LinearBackground(), NumDeriv=True)
self.assertEqual(cf.getAttributeValue('NumDeriv'), True)
def runTest(self):
from CrystalField import CrystalField, CrystalFieldFit, CrystalFieldMultiSite, Background, Function, ResolutionModel
cf = CrystalField('Ce', 'C2v')
cf = CrystalField('Ce', 'C2v', B20=0.37737, B22=3.9770)
cf['B40'] = -0.031
b = cf['B40']
# Calculate and return the Hamiltonian matrix as a 2D numpy array.
h = cf.getHamiltonian()
print(h)
# Calculate and return the eigenvalues of the Hamiltonian as a 1D numpy array.
e = cf.getEigenvalues()
print(e)
# Calculate and return the eigenvectors of the Hamiltonian as a 2D numpy array.
w = cf.getEigenvectors()
print(w)
# Using the keyword argument
cf = CrystalField('Ce', 'C2v', B20=0.37737, B22=3.9770, Temperature=44)
# Using the property
cf.Temperature = 44
print(cf.getPeakList())
#[[ 0.00000000e+00 2.44006198e+01 4.24977124e+01 1.80970926e+01 -2.44006198e+01]
# [ 2.16711565e+02 8.83098530e+01 5.04430056e+00 1.71153708e-01 1.41609425e-01]]
cf.ToleranceIntensity = 1
print(cf.getPeakList())
#[[ 0. 24.40061976 42.49771237]
# [ 216.71156467 88.30985303 5.04430056]]
cf.PeakShape = 'Gaussian'
cf.FWHM = 0.9
sp = cf.getSpectrum()
print(cf.function)
CrystalField_Ce = CreateWorkspace(*sp)
print(CrystalField_Ce)
# If the peak shape is Gaussian
cf.peaks.param[1]['Sigma'] = 2.0
cf.peaks.param[2]['Sigma'] = 0.01
# If the peak shape is Lorentzian
cf.PeakShape = 'Lorentzian'
cf.peaks.param[1]['FWHM'] = 2.0
cf.peaks.param[2]['FWHM'] = 0.01
cf = CrystalField('Ce',
'C2v',
B20=0.37737,
B22=3.9770,
B40=-0.031787,
B42=-0.11611,
B44=-0.12544,
Temperature=44.0,
FWHM=1.1)
cf.background = Background(peak=Function('Gaussian',
Height=10,
Sigma=1),
background=Function('LinearBackground',
A0=1.0,
A1=0.01))
h = cf.background.peak.param['Height']
a1 = cf.background.background.param['A1']
print(h)
print(a1)
cf.ties(B20=1.0, B40='B20/2')
cf.constraints('1 < B22 <= 2', 'B22 < 4')
print(cf.function[1].getTies())
print(cf.function[1].getConstraints())
cf.background.peak.ties(Height=10.1)
cf.background.peak.constraints('Sigma > 0')
cf.background.background.ties(A0=0.1)
cf.background.background.constraints('A1 > 0')
print(cf.function[0][0].getConstraints())
print(cf.function[0][1].getConstraints())
print(cf.function.getTies())
print(cf.function.getConstraints())
cf.peaks.ties({'f2.FWHM': '2*f1.FWHM', 'f3.FWHM': '2*f2.FWHM'})
cf.peaks.constraints('f0.FWHM < 2.2', 'f1.FWHM >= 0.1')
cf.PeakShape = 'Gaussian'
cf.peaks.tieAll('Sigma=0.1', 3)
cf.peaks.constrainAll('0 < Sigma < 0.1', 4)
cf.peaks.tieAll('Sigma=f0.Sigma', 1, 3)
cf.peaks.ties({
'f1.Sigma': 'f0.Sigma',
'f2.Sigma': 'f0.Sigma',
'f3.Sigma': 'f0.Sigma'
})
rm = ResolutionModel(([1, 2, 3, 100], [0.1, 0.3, 0.35, 2.1]))
cf = CrystalField('Ce',
'C2v',
B20=0.37737,
B22=3.9770,
Temperature=44.0,
ResolutionModel=rm)
rm = ResolutionModel(self.my_func,
xstart=0.0,
xend=24.0,
accuracy=0.01)
cf = CrystalField('Ce',
'C2v',
B20=0.37737,
B22=3.9770,
Temperature=44.0,
ResolutionModel=rm)
marires = PyChop2('MARI')
marires.setChopper('S')
marires.setFrequency(250)
marires.setEi(30)
rm = ResolutionModel(marires.getResolution,
xstart=0.0,
xend=29.0,
accuracy=0.01)
cf = CrystalField('Ce',
'C2v',
B20=0.37737,
B22=3.9770,
Temperature=44.0,
ResolutionModel=rm)
cf = CrystalField('Ce',
'C2v',
B20=0.37737,
B22=3.9770,
Temperature=44.0,
ResolutionModel=rm,
FWHMVariation=0.1)
# ---------------------------
cf = CrystalField('Ce',
'C2v',
B20=0.37737,
B22=3.9770,
B40=-0.031787,
B42=-0.11611,
B44=-0.12544,
Temperature=[44.0, 50],
FWHM=[1.1, 0.9])
cf.PeakShape = 'Lorentzian'
cf.peaks[0].param[0]['FWHM'] = 1.11
cf.peaks[1].param[1]['FWHM'] = 1.12
cf.background = Background(peak=Function('Gaussian',
Height=10,
Sigma=0.3),
background=Function('FlatBackground',
A0=1.0))
cf.background[1].peak.param['Sigma'] = 0.8
cf.background[1].background.param['A0'] = 1.1
# The B parameters are common for all spectra - syntax doesn't change
cf.ties(B20=1.0, B40='B20/2')
cf.constraints('1 < B22 <= 2', 'B22 < 4')
# Backgrounds and peaks are different for different spectra - must be indexed
cf.background[0].peak.ties(Height=10.1)
cf.background[0].peak.constraints('Sigma > 0.1')
cf.background[1].peak.ties(Height=20.2)
cf.background[1].peak.constraints('Sigma > 0.2')
cf.peaks[1].tieAll('FWHM=2*f1.FWHM', 2, 5)
cf.peaks[0].constrainAll('FWHM < 2.2', 1, 4)
rm = ResolutionModel([self.my_func, marires.getResolution],
0,
100,
accuracy=0.01)
cf.ResolutionModel = rm
# Calculate second spectrum, use the generated x-values
sp = cf.getSpectrum(1)
# Calculate second spectrum, use the first spectrum of a workspace
sp = cf.getSpectrum(1, 'CrystalField_Ce')
# Calculate first spectrum, use the i-th spectrum of a workspace
i = 0
sp = cf.getSpectrum(0, 'CrystalField_Ce', i)
print(cf.function)
cf.Temperature = [5, 50, 150]
print()
print(cf.function)
ws = 'CrystalField_Ce'
ws1 = 'CrystalField_Ce'
ws2 = 'CrystalField_Ce'
cf = CrystalField('Ce',
'C2v',
B20=0.37737,
B22=3.9770,
B40=-0.031787,
B42=-0.11611,
B44=-0.12544,
Temperature=5)
# In case of a single spectrum (ws is a workspace)
fit = CrystalFieldFit(Model=cf, InputWorkspace=ws)
# Or for multiple spectra
fit = CrystalFieldFit(Model=cf, InputWorkspace=[ws1, ws2])
cf.Temperature = [5, 50]
fit.fit()
params = {
'B20': 0.377,
'B22': 3.9,
'B40': -0.03,
'B42': -0.116,
'B44': -0.125,
'Temperature': [44.0, 50],
'FWHM': [1.1, 0.9]
}
cf1 = CrystalField('Ce', 'C2v', **params)
cf2 = CrystalField('Pr', 'C2v', **params)
cfms = cf1 + cf2
cf = 2 * cf1 + cf2
cfms = CrystalFieldMultiSite(Ions=['Ce', 'Pr'],
Symmetries=['C2v', 'C2v'],
Temperatures=[44.0],
FWHMs=[1.1])
cfms['ion0.B40'] = -0.031
cfms['ion1.B20'] = 0.37737
b = cfms['ion0.B22']
print(b)
print(cfms.function)
cfms = CrystalFieldMultiSite(Ions=['Ce', 'Pr'],
Symmetries=['C2v', 'C2v'],
Temperatures=[44.0],
FWHMs=[1.1],
parameters={
'ion0.B20': 0.37737,
'ion0.B22': 3.9770,
'ion1.B40': -0.031787,
'ion1.B42': -0.11611,
'ion1.B44': -0.12544
})
cfms = CrystalFieldMultiSite(
Ions='Ce',
Symmetries='C2v',
Temperatures=[20],
FWHMs=[1.0],
Background=
'name=Gaussian,Height=0,PeakCentre=1,Sigma=0;name=LinearBackground,A0=0,A1=0'
)
cfms = CrystalFieldMultiSite(Ions=['Ce'],
Symmetries=['C2v'],
Temperatures=[50],
FWHMs=[0.9],
Background=LinearBackground(A0=1.0),
BackgroundPeak=Gaussian(Height=10,
Sigma=0.3))
cfms = CrystalFieldMultiSite(Ions='Ce',
Symmetries='C2v',
Temperatures=[20],
FWHMs=[1.0],
Background=Gaussian(PeakCentre=1) +
LinearBackground())
cfms = CrystalFieldMultiSite(Ions=['Ce', 'Pr'],
Symmetries=['C2v', 'C2v'],
Temperatures=[44, 50],
FWHMs=[1.1, 0.9],
Background=FlatBackground(),
BackgroundPeak=Gaussian(Height=10,
Sigma=0.3),
parameters={
'ion0.B20': 0.37737,
'ion0.B22': 3.9770,
'ion1.B40': -0.031787,
'ion1.B42': -0.11611,
'ion1.B44': -0.12544
})
cfms.ties({'sp0.bg.f0.Height': 10.1})
cfms.constraints('sp0.bg.f0.Sigma > 0.1')
cfms.constraints('ion0.sp0.pk1.FWHM < 2.2')
cfms.ties({
'ion0.sp1.pk2.FWHM': '2*ion0.sp1.pk1.FWHM',
'ion1.sp1.pk3.FWHM': '2*ion1.sp1.pk2.FWHM'
})
# --------------------------
params = {
'ion0.B20': 0.37737,
'ion0.B22': 3.9770,
'ion1.B40': -0.031787,
'ion1.B42': -0.11611,
'ion1.B44': -0.12544
}
cf = CrystalFieldMultiSite(Ions=['Ce', 'Pr'],
Symmetries=['C2v', 'C2v'],
Temperatures=[44.0, 50.0],
FWHMs=[1.0, 1.0],
ToleranceIntensity=6.0,
ToleranceEnergy=1.0,
FixAllPeaks=True,
parameters=params)
cf.fix('ion0.BmolX', 'ion0.BmolY', 'ion0.BmolZ', 'ion0.BextX',
'ion0.BextY', 'ion0.BextZ', 'ion0.B40', 'ion0.B42', 'ion0.B44',
'ion0.B60', 'ion0.B62', 'ion0.B64', 'ion0.B66',
'ion0.IntensityScaling', 'ion1.BmolX', 'ion1.BmolY',
'ion1.BmolZ', 'ion1.BextX', 'ion1.BextY', 'ion1.BextZ',
'ion1.B40', 'ion1.B42', 'ion1.B44', 'ion1.B60', 'ion1.B62',
'ion1.B64', 'ion1.B66', 'ion1.IntensityScaling',
'sp0.IntensityScaling', 'sp1.IntensityScaling')
chi2 = CalculateChiSquared(str(cf.function),
InputWorkspace=ws1,
InputWorkspace_1=ws2)[1]
fit = CrystalFieldFit(Model=cf,
InputWorkspace=[ws1, ws2],
MaxIterations=10)
fit.fit()
print(chi2)
cfms = CrystalFieldMultiSite(Ions='Ce',
Symmetries='C2',
Temperatures=[25],
FWHMs=[1.0],
PeakShape='Gaussian',
BmolX=1.0,
B40=-0.02)
print(str(cfms.function).split(',')[0])
# --------------------------
# Create some crystal field data
origin = CrystalField('Ce',
'C2v',
B20=0.37737,
B22=3.9770,
B40=-0.031787,
B42=-0.11611,
B44=-0.12544,
Temperature=44.0,
FWHM=1.1)
x, y = origin.getSpectrum()
ws = makeWorkspace(x, y)
# Define a CrystalField object with parameters slightly shifted.
cf = CrystalField('Ce',
'C2v',
B20=0,
B22=0,
B40=0,
B42=0,
B44=0,
Temperature=44.0,
FWHM=1.0,
ResolutionModel=([0, 100], [1, 1]),
FWHMVariation=0)
# Set any ties on the field parameters.
cf.ties(B20=0.37737)
# Create a fit object
fit = CrystalFieldFit(cf, InputWorkspace=ws)
# Find initial values for the field parameters.
# You need to define the energy splitting and names of parameters to estimate.
# Optionally additional constraints can be set on tied parameters (eg, peak centres).
fit.estimate_parameters(
EnergySplitting=50,
Parameters=['B22', 'B40', 'B42', 'B44'],
Constraints='20<f1.PeakCentre<45,20<f2.PeakCentre<45',
NSamples=1000)
print('Returned', fit.get_number_estimates(), 'sets of parameters.')
# The first set (the smallest chi squared) is selected by default.
# Select a different parameter set if required
fit.select_estimated_parameters(3)
print(cf['B22'], cf['B40'], cf['B42'], cf['B44'])
# Run fit
fit.fit()
# --------------------------
from CrystalField import PointCharge
axial_pc_model = PointCharge([[-2, 0, 0, -4], [-2, 0, 0, 4]], 'Nd')
axial_blm = axial_pc_model.calculate()
print(axial_blm)
from CrystalField import PointCharge
from mantid.geometry import CrystalStructure
perovskite_structure = CrystalStructure(
'4 4 4 90 90 90', 'P m -3 m',
'Ce 0 0 0 1 0; Al 0.5 0.5 0.5 1 0; O 0.5 0.5 0 1 0')
cubic_pc_model = PointCharge(perovskite_structure,
'Ce',
Charges={
'Ce': 3,
'Al': 3,
'O': -2
},
MaxDistance=7.5)
cubic_pc_model = PointCharge(perovskite_structure,
'Ce',
Charges={
'Ce': 3,
'Al': 3,
'O': -2
},
Neighbour=2)
print(cubic_pc_model)
cif_pc_model = PointCharge('Sm2O3.cif')
print(cif_pc_model.getIons())
cif_pc_model.Charges = {
'O1': -2,
'O2': -2,
'Sm1': 3,
'Sm2': 3,
'Sm3': 3
}
cif_pc_model.IonLabel = 'Sm2'
cif_pc_model.Neighbour = 1
cif_blm = cif_pc_model.calculate()
print(cif_blm)
bad_pc_model = PointCharge('Sm2O3.cif', MaxDistance=7.5, Neighbour=2)
print(bad_pc_model.Neighbour)
print(bad_pc_model.MaxDistance)
cif_pc_model.Charges = {'O': -2, 'Sm': 3}
cif_blm = cif_pc_model.calculate()
print(cif_blm)
cf = CrystalField('Sm',
'C2',
Temperature=5,
FWHM=10,
**cif_pc_model.calculate())
fit = CrystalFieldFit(cf, InputWorkspace=ws)
fit = CrystalFieldFit(cf, InputWorkspace=ws)
fit.fit()
# --------------------------
cf = CrystalField('Ce',
'C2v',
B20=0.37737,
B22=3.9770,
Temperature=44.0)
Cv = cf.getHeatCapacity(
) # Calculates Cv(T) for 1<T<300K in 1K steps (default)
T = np.arange(1, 900, 5)
Cv = cf.getHeatCapacity(
T
) # Calculates Cv(T) for specified values of T (1 to 900K in 5K steps here)
# Temperatures from a single spectrum workspace
ws = CreateWorkspace(T, T, T)
Cv = cf.getHeatCapacity(
ws) # Use the x-values of a workspace as the temperatures
ws_cp = CreateWorkspace(*Cv)
# Temperatures from a multi-spectrum workspace
ws = CreateWorkspace(T, T, T, NSpec=2)
Cv = cf.getHeatCapacity(
ws,
1) # Uses the second spectrum's x-values for T (e.g. 450<T<900)
chi_v = cf.getSusceptibility(T, Hdir=[1, 1, 1])
chi_v_powder = cf.getSusceptibility(T, Hdir='powder')
chi_v_cgs = cf.getSusceptibility(T, Hdir=[1, 1, 0], Unit='SI')
chi_v_bohr = cf.getSusceptibility(T, Unit='bohr')
print(type([chi_v, chi_v_powder, chi_v_cgs, chi_v_bohr]))
moment_t = cf.getMagneticMoment(
Temperature=T, Hdir=[1, 1, 1],
Hmag=0.1) # Calcs M(T) with at 0.1T field||[111]
H = np.linspace(0, 30, 121)
moment_h = cf.getMagneticMoment(
Hmag=H, Hdir='powder',
Temperature=10) # Calcs M(H) at 10K for powder sample
moment_SI = cf.getMagneticMoment(
H, [1, 1, 1], Unit='SI') # M(H) in Am^2/mol at 1K for H||[111]
moment_cgs = cf.getMagneticMoment(
100, Temperature=T,
Unit='cgs') # M(T) in emu/mol in a field of 100G || [001]
print(type([moment_t, moment_h, moment_SI, moment_cgs]))
# --------------------------
from CrystalField import CrystalField, CrystalFieldFit, PhysicalProperties
# Fits a heat capacity dataset - you must have subtracted the phonon contribution by some method already
# and the data must be in J/mol/K.
cf = CrystalField('Ce',
'C2v',
B20=0.37737,
B22=3.9770,
B40=-0.031787,
B42=-0.11611,
B44=-0.12544,
PhysicalProperty=PhysicalProperties('Cv'))
fitcv = CrystalFieldFit(Model=cf, InputWorkspace=ws)
fitcv.fit()
params = {
'B20': 0.37737,
'B22': 3.9770,
'B40': -0.031787,
'B42': -0.11611,
'B44': -0.12544
}
cf = CrystalField('Ce', 'C2v', **params)
cf.PhysicalProperty = PhysicalProperties('Cv')
fitcv = CrystalFieldFit(Model=cf, InputWorkspace=ws)
fitcv.fit()
# Fits a susceptibility dataset. Data is the volume susceptibility in SI units
cf = CrystalField('Ce', 'C2v', **params)
cf.PhysicalProperty = PhysicalProperties('susc',
Hdir='powder',
Unit='SI')
fit_chi = CrystalFieldFit(Model=cf, InputWorkspace=ws)
fit_chi.fit()
# Fits a magnetisation dataset. Data is in emu/mol, and was measured at 5K with the field || [111].
cf = CrystalField('Ce', 'C2v', **params)
cf.PhysicalProperty = PhysicalProperties('M(H)',
Temperature=5,
Hdir=[1, 1, 1],
Unit='cgs')
fit_mag = CrystalFieldFit(Model=cf, InputWorkspace=ws)
fit_mag.fit()
# Fits a magnetisation vs temperature dataset. Data is in Am^2/mol, measured with a 0.1T field || [110]
cf = CrystalField('Ce', 'C2v', **params)
cf.PhysicalProperty = PhysicalProperties('M(T)',
Hmag=0.1,
Hdir=[1, 1, 0],
Unit='SI')
fit_moment = CrystalFieldFit(Model=cf, InputWorkspace=ws)
fit_moment.fit()
# --------------------------
# Pregenerate the required workspaces
for tt in [10, 44, 50]:
cf = CrystalField('Ce',
'C2v',
B20=0.37737,
B22=3.9770,
B40=-0.031787,
B42=-0.11611,
B44=-0.12544,
Temperature=tt,
FWHM=0.5)
x, y = cf.getSpectrum()
self.my_create_ws('ws_ins_' + str(tt) + 'K', x, y)
ws_ins_10K = mtd['ws_ins_10K']
ws_ins_44K = mtd['ws_ins_44K']
ws_ins_50K = mtd['ws_ins_50K']
ws_cp = self.my_create_ws('ws_cp', *cf.getHeatCapacity())
ws_chi = self.my_create_ws(
'ws_chi',
*cf.getSusceptibility(np.linspace(1, 300, 100),
Hdir='powder',
Unit='cgs'))
ws_mag = self.my_create_ws(
'ws_mag',
*cf.getMagneticMoment(Hmag=np.linspace(0, 30, 100),
Hdir=[1, 1, 1],
Unit='bohr',
Temperature=5))
# --------------------------
# Fits an INS spectrum (at 10K) and the heat capacity simultaneously
cf = CrystalField('Ce',
'C2v',
B20=0.37737,
B22=3.9770,
B40=-0.031787,
B42=-0.11611,
B44=-0.12544)
cf.Temperature = 10
cf.FWHM = 1.5
cf.PhysicalProperty = PhysicalProperties('Cv')
fit = CrystalFieldFit(Model=cf, InputWorkspace=[ws_ins_10K, ws_cp])
fit.fit()
# Fits two INS spectra (at 44K and 50K) and the heat capacity, susceptibility and magnetisation simultaneously.
PPCv = PhysicalProperties('Cv')
PPchi = PhysicalProperties('susc', 'powder', Unit='cgs')
PPMag = PhysicalProperties('M(H)', [1, 1, 1], 5, 'bohr')
cf = CrystalField('Ce',
'C2v',
B20=0.37737,
B22=3.9770,
B40=-0.031787,
B42=-0.11611,
B44=-0.12544,
Temperature=[44.0, 50],
FWHM=[1.1, 0.9],
PhysicalProperty=[PPCv, PPchi, PPMag])
fit = CrystalFieldFit(
Model=cf,
InputWorkspace=[ws_ins_44K, ws_ins_50K, ws_cp, ws_chi, ws_mag])
fit.fit()