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import numpy as np
import lmfit
from lmfit.lineshapes import gaussian
from lmfit.models import GaussianModel, SplineModel
def _isclose(name, expected_value, fit_value, atol, rtol):
"""isclose with error message"""
assert np.isclose(expected_value, fit_value, atol=atol, rtol=rtol), \
f"bad value for {name}: expected {expected_value}, got {fit_value}."
def check_fit(model, params, x, y, test_values, noise_scale=1.e-3, atol=0.1, rtol=0.05):
"""Checks that a model fits noisy data well
Parameters
-----------
model: model to use
par: parameters to use
x: x data
y: y data
test_values: dict of 'true values'
noise_scale: float, optional
The standard deviation of noise that is added to the test data.
atol: float, optional
Absolute tolerance for considering fit parameters close to the
parameters test data was generated with.
rtol: float, optional
Relative tolerance for considering fit parameters close to the
parameters test data was generated with.
Returns
-------
fit result
Raises
-------
AssertionError
Any fit parameter that is not close to the parameter used to
generate the test data raises this error.
"""
y += np.random.normal(scale=noise_scale, size=len(y))
result = model.fit(y, params, x=x)
fit_values = result.best_values
for name, test_val in test_values.items():
_isclose(name, test_val, fit_values[name], atol, rtol)
return result
def testLinear():
mod = lmfit.models.LinearModel()
x = np.linspace(-1, 1, 201)
y = 10*x + 2
params = mod.make_params(intercept=1, slope=2)
check_fit(mod, params, x, y, dict(intercept=2, slope=10))
def testQuadratic():
mod = lmfit.models.QuadraticModel()
x = np.linspace(-1, 1, 201)
y = 0.3*x*x + 10*x + 2
params = mod.make_params(a=0, b=5, c=1)
check_fit(mod, params, x, y, dict(a=0.3, b=10, c=2))
def testSine_partialperiod():
mod = lmfit.models.SineModel()
x = np.linspace(-1, 1, 201)
pars = dict(amplitude=1.5, frequency=0.9, shift=0.4)
y = pars['amplitude']*np.sin(x*pars['frequency'] + pars['shift'])
params = mod.make_params(amplitude=1, frequency=1, shift=-0.2)
check_fit(mod, params, x, y, pars)
def testSineWithLine():
mod = lmfit.models.SineModel() + lmfit.models.LinearModel()
x = np.linspace(-5, 5, 501)
pars = dict(amplitude=5.3, frequency=3.8, shift=0.1, intercept=8.2, slope=0.2)
y = pars['amplitude']*np.sin(x*pars['frequency'] + pars['shift'])
y += pars['intercept'] + x * pars['slope']
params = mod.make_params(amplitude=10, frequency=4.5, shift=0.1,
intercept=10, slope=0)
check_fit(mod, params, x, y, pars, noise_scale=0.02)
def testSineManyShifts():
mod = lmfit.models.SineModel() + lmfit.models.LinearModel()
x = np.linspace(-5, 5, 501)
pars = dict(amplitude=5.3, frequency=3.8, intercept=8.2, slope=0.2)
for shift in (0.1, 0.5, 1.0, 1.5):
pars['shift'] = shift
y = pars['amplitude']*np.sin(x*pars['frequency'] + pars['shift'])
y += pars['intercept'] + x*pars['slope']
params = mod.make_params(amplitude=10, frequency=4.5, shift=0.8,
intercept=10, slope=0)
check_fit(mod, params, x, y, pars, noise_scale=0.02)
def testSineModel_guess():
mod = lmfit.models.SineModel()
x = np.linspace(-10, 10, 201)
pars = dict(amplitude=1.5, frequency=0.5, shift=0.4)
y = pars['amplitude']*np.sin(x*pars['frequency'] + pars['shift'])
params = mod.guess(y, x=x)
assert params['amplitude'] > 0.5
assert params['amplitude'] < 5.0
assert params['frequency'] > 0.1
assert params['frequency'] < 1.5
assert params['shift'] > 0.0
assert params['shift'] < 1.0
def testSineModel_make_params():
mod = lmfit.models.SineModel()
pars = mod.make_params(amplitude=1.5, frequency=0.5,
shift=dict(value=0.4, min=-10, max=10))
assert pars['amplitude'].value > 1.4
assert pars['amplitude'].value < 1.6
assert pars['amplitude'].min == 0
assert pars['amplitude'].max > 1e99
assert pars['shift'].value > 0.35
assert pars['shift'].value < 0.45
assert pars['shift'].min < -9.5
assert pars['shift'].max > 9.5
def testSplineModel():
x = np.linspace(0, 25, 501)
y = gaussian(x, amplitude=10, center=16.2, sigma=0.8) + 3 + 0.03*x + np.sin(x/4)
model = GaussianModel(prefix='peak_')
params = model.make_params(amplitude=8, center=16, sigma=1)
knot_xvals = np.array([1, 3, 5, 7, 9, 11, 13, 19, 21, 23, 25])
bkg = SplineModel(prefix='bkg_', xknots=knot_xvals)
params.update(bkg.guess(y, x))
model = model + bkg
pars = dict(peak_amplitude=10, peak_center=16.2, peak_sigma=0.8)
check_fit(model, params, x, y, pars, noise_scale=0.05)
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