def test_merge_linked():
"Check that that merge works correctly for models with linked parameters"
submodel1 = dl.dd_gauss
submodel2 = dl.dd_gauss2
submodel2 = dl.link(submodel2,
mean=['mean1', 'mean2'],
width=['width1', 'width2'])
x = np.linspace(0, 10, 100)
ref1 = submodel1(x, 3, 0.2)
ref2 = submodel1(x, 4, 0.3)
# Create a global model
model = dl.merge(submodel1, submodel2, addweights=True)
response = model(x,
x,
mean_1=3,
width_1=0.2,
mean_2=4,
width_2=0.3,
amp1_2=1,
amp2_2=1,
scale_1=1,
weight_1=1,
weight_2=1)
assert all(
[np.allclose(response[n], ref) for n, ref in enumerate([ref1, ref2])])
def test_globalmodel():
"Check the profiling works with multiple datasets"
r = np.linspace(2, 6, 300)
sigma = 0.1
modelA = deepcopy(dd_gauss)
modelB = deepcopy(dd_gauss)
model = merge(modelA, modelB)
model = link(model,
mean=['mean_1', 'mean_2'],
width=['width_1', 'width_2'])
y = model(r, r, mean=3, width=0.2, scale_1=1, scale_2=1)
y[0] += whitegaussnoise(r, sigma, seed=1)
y[1] += whitegaussnoise(r, sigma, seed=1)
profuq = profile_analysis(model, y, r, r, samples=3, noiselvl=sigma)
x, pdf = profuq['mean'].pardist()
mean_mean = x[np.argmax(pdf)]
x, pdf = profuq['width'].pardist()
width_mean = x[np.argmax(pdf)]
assert np.allclose([mean_mean, width_mean], [3, 0.2], rtol=1e-2)
def dropletmodel(t):
#----------------------------------------------------------------------------------
# Dispersed-state component model
Vdis_model = dl.dipolarmodel(t,
r,
Pmodel=dl.dd_gauss,
Bmodel=dl.bg_exp,
npathways=2)
# Liquid-droplet-state component model
Vld_model = dl.dipolarmodel(t,
r,
Pmodel=dl.dd_gauss,
Bmodel=dl.bg_strexp,
npathways=2)
# Create a dipolar signal model that is a linear combination of both components
Vmodel = dl.lincombine(Vdis_model, Vld_model, addweights=True)
Vmodel = dl.link(Vmodel,
reftime1=['reftime1_1', 'reftime1_2'],
reftime2=['reftime2_1', 'reftime2_2'],
lam1=['lam1_1', 'lam1_2'],
lam2=['lam2_1', 'lam2_2'])
# Make the second weight dependent on the first one
Vmodel = dl.relate(Vmodel, weight_2=lambda weight_1: 1 - weight_1)
return Vmodel, Vdis_model, Vld_model
Vs = [Vexp1,Vexp2]
# Normalize the datasets
Vs = [V/np.max(V) for V in Vs]
# Distance vector
r = np.linspace(2,5,150) # nm
# Construct the dipolar models for the individual signals
V1model = dl.dipolarmodel(ts[0],r)
V2model = dl.dipolarmodel(ts[1],r)
# Make the global model by joining the individual models
globalmodel = dl.merge(V1model,V2model)
# Link the distance distribution into a global parameter
globalmodel = dl.link(globalmodel,P=['P_1','P_2'])
# Fit the model to the data
fit = dl.fit(globalmodel,Vs)
# %%
plt.figure(figsize=[10,7])
violet = '#4550e6'
for n in range(len(fit.model)):
# Extract fitted dipolar signal
Vfit = fit.model[n]
Vci = fit.modelUncert[n].ci(95)
# Extract fitted distance distribution
r = np.linspace(1.5, 6, 90)
# Construct a non-parametric distance distribution that is a
# linear combination of two non-parametric distributions
PAmodel = dl.freedist(r)
PBmodel = dl.freedist(r)
Pmodel = dl.lincombine(PAmodel, PBmodel, addweights=True)
# Construct the dipolar models of the individual signals
Vmodels = [dl.dipolarmodel(t, r, Pmodel) for t in ts]
# Create the global model
titrmodel = dl.merge(*Vmodels)
# Make the two components of the distance distriution global
titrmodel = dl.link(titrmodel,
PA=['P_1_1', 'P_1_2', 'P_1_3', 'P_1_4', 'P_1_5'],
PB=['P_2_1', 'P_2_2', 'P_2_3', 'P_2_4', 'P_2_5'])
# Functionalize the chemical equilibrium model
titrmodel.addnonlinear('Kdis',
lb=3,
ub=7,
par0=5,
description='Dissociation constant')
titrmodel = dl.relate(titrmodel,
weight_2_1=lambda weight_1_1: 1 - weight_1_1,
weight_1_1=lambda Kdis: chemicalequilibrium(Kdis, L[0]),
weight_2_2=lambda weight_1_2: 1 - weight_1_2,
weight_1_2=lambda Kdis: chemicalequilibrium(Kdis, L[1]),
weight_2_3=lambda weight_1_3: 1 - weight_1_3,
#----------------------------------------------------------------------------------
# Generate the models
Vmodel1, Vdismodel1, Vldmodel1 = dropletmodel(ts[0])
Vmodel2, Vdismodel2, Vldmodel2 = dropletmodel(ts[1])
# Create the global model
globalModel = dl.merge(Vmodel1, Vmodel2)
# Link global parameters toghether with new names
globalModel = dl.link(globalModel,
eta=['weight_1_1', 'weight_1_2'],
kdis=['decay_1_1', 'decay_1_2'],
kld=['decay_2_1', 'decay_2_2'],
Dld=['stretch_2_1', 'stretch_2_2'],
rmean_dis=['mean_1_1', 'mean_1_2'],
rmean_ld=['mean_2_1', 'mean_2_2'],
width_dis=['width_1_1', 'width_1_2'],
width_ld=['width_2_1', 'width_2_2'],
lam1=['lam1_1', 'lam1_2'],
lam2=['lam2_1', 'lam2_2'],
reftime1=['reftime1_1', 'reftime1_2'])
# Specify parameter boundaries and initial conditions
globalModel.eta.set(lb=0.468, ub=0.57, par0=0.520)
globalModel.kdis.set(lb=0.0, ub=0.09, par0=0.01)
globalModel.kld.set(lb=0.0, ub=1, par0=0.12)
globalModel.Dld.set(lb=2, ub=4, par0=2.5)
globalModel.rmean_dis.set(lb=3, ub=6.35, par0=3.7)
globalModel.rmean_ld.set(lb=1, ub=8, par0=2.6)
globalModel.width_dis.set(lb=0.25, ub=0.74, par0=0.44)
globalModel.width_ld.set(lb=0.2, ub=2, par0=0.7)
Pmodel.widthB.set(lb=0.05, ub=0.8, par0=0.1)
Pmodel.fracA.set(lb=0, ub=1, par0=0.5)
# Generate the individual dipolar signal models
Nsignals = len(Vexps)
Vmodels = [[]] * Nsignals
for n in range(Nsignals):
Vmodels[n] = dl.dipolarmodel(ts[n], r, Pmodel)
Vmodels[n].reftime.set(lb=0, ub=0.5, par0=0.2)
# Combine the individual signal models into a single global models
globalmodel = dl.merge(*Vmodels)
# Link the global parameters toghether
globalmodel = dl.link(globalmodel,
meanA=['meanA_1', 'meanA_2', 'meanA_3'],
meanB=['meanB_1', 'meanB_2', 'meanB_3'],
widthA=['widthA_1', 'widthA_2', 'widthA_3'],
widthB=['widthB_1', 'widthB_2', 'widthB_3'])
# Fit the datasets to the model globally
fit = dl.fit(globalmodel, Vexps)
# Extract the fitted fractions
fracAfit = [fit.fracA_1, fit.fracA_2, fit.fracA_3]
fracBfit = [1 - fit.fracA_1, 1 - fit.fracA_2, 1 - fit.fracA_3]
plt.figure(figsize=(10, 8))
for i in range(Nsignals):
# Get the fitted signals and confidence bands
Vfit = fit.model[i]