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"""Tests for algebraic parameter constraints."""
import numpy as np
import pytest
from lmfit import Minimizer, Model, Parameters
from lmfit.lineshapes import gaussian, lorentzian
@pytest.fixture
def minimizer():
"""Return the Minimizer object."""
def residual(pars, x, sigma=None, data=None):
"""Define objective function."""
yg = gaussian(x, pars['amp_g'], pars['cen_g'], pars['wid_g'])
yl = lorentzian(x, pars['amp_l'], pars['cen_l'], pars['wid_l'])
model = yg + yl + pars['line_off'] + x * pars['line_slope']
if data is None:
return model
if sigma is None:
return model - data
return (model-data) / sigma
# generate synthetic data
n = 601
xmin = 0.
xmax = 20.0
x = np.linspace(xmin, xmax, n)
data = (gaussian(x, 21, 8.1, 1.2) + lorentzian(x, 10, 9.6, 2.4) +
np.random.normal(scale=0.23, size=n) + x*0.5)
# create initial Parameters
pars = Parameters()
pars.add(name='amp_g', value=10)
pars.add(name='cen_g', value=9)
pars.add(name='wid_g', value=1)
pars.add(name='amp_tot', value=20)
pars.add(name='amp_l', expr='amp_tot - amp_g')
pars.add(name='cen_l', expr='1.5+cen_g')
pars.add(name='wid_l', expr='2*wid_g')
pars.add(name='line_slope', value=0.0)
pars.add(name='line_off', value=0.0)
sigma = 0.021 # estimate of data error (for all data points)
mini = Minimizer(residual, pars, fcn_args=(x,), fcn_kws={'sigma': sigma,
'data': data})
return mini
def test_algebraic_constraints(minimizer):
"""Test algebraic constraints."""
result = minimizer.minimize(method='leastsq')
pfit = result.params
assert pfit['cen_l'].value == 1.5 + pfit['cen_g'].value
assert pfit['amp_l'].value == pfit['amp_tot'].value - pfit['amp_g'].value
assert pfit['wid_l'].value == 2.0 * pfit['wid_g'].value
def test_algebraic_constraints_function(minimizer):
"""Test constraints with a user-defined function added to symbol table."""
def width_func(wpar):
return 2.5*wpar
minimizer.params._asteval.symtable['wfun'] = width_func
minimizer.params.add(name='wid_l', expr='wfun(wid_g)')
result = minimizer.minimize(method='leastsq')
pfit = result.params
assert pfit['cen_l'].value == 1.5 + pfit['cen_g'].value
assert pfit['amp_l'].value == pfit['amp_tot'].value - pfit['amp_g'].value
assert pfit['wid_l'].value == 2.5 * pfit['wid_g'].value
def test_constraints_function_call():
"""Test a constraint with simple function call in Model class."""
x = np.array([1723, 1773, 1823, 1523, 1773, 1033.03078, 1042.98077,
1047.90937, 1053.95899, 1057.94906, 1063.13788, 1075.74218,
1086.03102])
y = np.array([0.79934, -0.31876, -0.46852, 0.05, -0.21, 11.1708, 10.31844,
9.73069, 9.21319, 9.12457, 9.05243, 8.66407, 8.29664])
def VFT(T, ninf=-3, A=5e3, T0=800):
return ninf + A/(T-T0)
vftModel = Model(VFT)
vftModel.set_param_hint('D', vary=False, expr=r'A*log(10)/T0')
result = vftModel.fit(y, T=x)
assert 2600.0 < result.params['A'].value < 2650.0
assert 7.0 < result.params['D'].value < 7.5
def test_constraints(minimizer):
"""Test changing of algebraic constraints."""
result = minimizer.minimize(method='leastsq')
pfit = result.params
assert pfit['cen_l'].value == 1.5 + pfit['cen_g'].value
assert pfit['amp_l'].value == pfit['amp_tot'].value - pfit['amp_g'].value
assert pfit['wid_l'].value == 2.0*pfit['wid_g'].value
# now, change fit slightly and re-run
minimizer.params['wid_l'].expr = '1.25*wid_g'
result = minimizer.minimize(method='leastsq')
pfit = result.params
assert pfit['cen_l'].value == 1.5 + pfit['cen_g'].value
assert pfit['amp_l'].value == pfit['amp_tot'].value - pfit['amp_g'].value
assert pfit['wid_l'].value == 1.25*pfit['wid_g'].value
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