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import os
import numpy as np
from numpy import pi
from numpy.testing import assert_allclose, assert_almost_equal
import pytest
from lmfit import Parameters, minimize
from lmfit.lineshapes import exponential
from lmfit.models import ExponentialModel, LinearModel, VoigtModel
def check(para, real_val, sig=3):
err = abs(para.value - real_val)
assert err < sig * para.stderr
def test_bounded_parameters():
return
# create data to be fitted
np.random.seed(1)
x = np.linspace(0, 15, 301)
data = (5. * np.sin(2 * x - 0.1) * np.exp(-x*x*0.025) +
np.random.normal(size=len(x), scale=0.2))
# define objective function: returns the array to be minimized
def fcn2min(params, x, data):
""" model decaying sine wave, subtract data"""
amp = params['amp']
shift = params['shift']
omega = params['omega']
decay = params['decay']
model = amp * np.sin(x * omega + shift) * np.exp(-x*x*decay)
return model - data
# create a set of Parameters
params = Parameters()
params.add('amp', value=10, min=0, max=50)
params.add('decay', value=0.1, min=0, max=10)
params.add('shift', value=0.0, min=-pi/2., max=pi/2.)
params.add('omega', value=3.0, min=0, max=np.inf)
# do fit, here with leastsq model
result = minimize(fcn2min, params, args=(x, data),
epsfcn=1.e-14)
# assert that the real parameters are found
for para, val in zip(result.params.values(), [5, 0.025, -.1, 2]):
check(para, val)
# assert that the covariance matrix is correct [cf. lmfit v0.9.10]
cov_x = np.array([
[1.42428250e-03, 9.45395985e-06, -4.33997922e-05, 1.07362106e-05],
[9.45395985e-06, 1.84110424e-07, -2.90588963e-07, 7.19107184e-08],
[-4.33997922e-05, -2.90588963e-07, 9.53427031e-05, -2.37750362e-05],
[1.07362106e-05, 7.19107184e-08, -2.37750362e-05, 9.60952336e-06]])
assert_allclose(result.covar, cov_x, rtol=1.e-3, atol=1.e-6)
# assert that stderr and correlations are correct [cf. lmfit v0.9.10]
assert_almost_equal(result.params['amp'].stderr, 0.03773967, decimal=4)
assert_almost_equal(result.params['decay'].stderr, 4.2908e-04, decimal=4)
assert_almost_equal(result.params['shift'].stderr, 0.00976436, decimal=4)
assert_almost_equal(result.params['omega'].stderr, 0.00309992, decimal=4)
assert_almost_equal(result.params['amp'].correl['decay'],
0.5838166760743324, decimal=4)
assert_almost_equal(result.params['amp'].correl['shift'],
-0.11777303073961824, decimal=4)
assert_almost_equal(result.params['amp'].correl['omega'],
0.09177027400788784, decimal=4)
assert_almost_equal(result.params['decay'].correl['shift'],
-0.0693579417651835, decimal=4)
assert_almost_equal(result.params['decay'].correl['omega'],
0.05406342001021014, decimal=4)
assert_almost_equal(result.params['shift'].correl['omega'],
-0.7854644476455469, decimal=4)
def test_bounds_expression():
# load data to be fitted
data = np.loadtxt(os.path.join(os.path.dirname(__file__), '..', 'examples',
'test_peak.dat'))
x = data[:, 0]
y = data[:, 1]
# define the model and initialize parameters
mod = VoigtModel()
params = mod.guess(y, x=x)
params['amplitude'].set(min=0, max=100)
params['center'].set(min=5, max=10)
# do fit, here with leastsq model
result = mod.fit(y, params, x=x, fit_kws={'epsfcn': 1.e-14})
# assert that stderr and correlations are correct [cf. lmfit v0.9.10]
assert_almost_equal(result.params['sigma'].stderr, 0.00368468, decimal=4)
assert_almost_equal(result.params['center'].stderr, 0.00505496, decimal=4)
assert_almost_equal(result.params['amplitude'].stderr, 0.13861506,
decimal=4)
assert_almost_equal(result.params['gamma'].stderr, 0.00368468, decimal=4)
assert_almost_equal(result.params['fwhm'].stderr, 0.01326862028, decimal=4)
assert_almost_equal(result.params['height'].stderr, 0.0395990, decimal=4)
assert_almost_equal(result.params['sigma'].correl['center'],
-4.6623973788006615e-05, decimal=4)
assert_almost_equal(result.params['sigma'].correl['amplitude'],
0.651304091954038, decimal=4)
assert_almost_equal(result.params['center'].correl['amplitude'],
-4.390334984618851e-05, decimal=4)
@pytest.mark.parametrize("fit_method", ['nelder', 'lbfgs'])
def test_numdifftools_no_bounds(fit_method):
pytest.importorskip("numdifftools")
np.random.seed(7)
x = np.linspace(0, 100, num=50)
noise = np.random.normal(scale=0.25, size=x.size)
y = exponential(x, amplitude=5, decay=15) + noise
mod = ExponentialModel()
params = mod.guess(y, x=x)
# do fit, here with leastsq model
result = mod.fit(y, params, x=x, method='leastsq')
result_ndt = mod.fit(y, params, x=x, method=fit_method)
# assert that fit converged to the same result
vals = [result.params[p].value for p in result.params.valuesdict()]
vals_ndt = [result_ndt.params[p].value for p in result_ndt.params.valuesdict()]
assert_allclose(vals_ndt, vals, rtol=0.1)
assert_allclose(result_ndt.chisqr, result.chisqr, rtol=1e-5)
# assert that parameter uncertainties from leastsq and calculated from
# the covariance matrix using numdifftools are very similar
stderr = [result.params[p].stderr for p in result.params.valuesdict()]
stderr_ndt = [result_ndt.params[p].stderr for p in result_ndt.params.valuesdict()]
perr = np.array(stderr) / np.array(vals)
perr_ndt = np.array(stderr_ndt) / np.array(vals_ndt)
assert_almost_equal(perr_ndt, perr, decimal=3)
# assert that parameter correlatations from leastsq and calculated from
# the covariance matrix using numdifftools are very similar
for par1 in result.var_names:
cor = [result.params[par1].correl[par2] for par2 in
result.params[par1].correl.keys()]
cor_ndt = [result_ndt.params[par1].correl[par2] for par2 in
result_ndt.params[par1].correl.keys()]
assert_almost_equal(cor_ndt, cor, decimal=2)
@pytest.mark.parametrize("fit_method", ['nelder', 'basinhopping', 'ampgo',
'shgo', 'dual_annealing'])
def test_numdifftools_with_bounds(fit_method):
pytest.importorskip("numdifftools")
# load data to be fitted
data = np.loadtxt(os.path.join(os.path.dirname(__file__), '..', 'examples',
'test_peak.dat'))
x = data[:, 0]
y = data[:, 1]
# define the model and initialize parameters
mod = VoigtModel()
params = mod.guess(y, x=x)
params['amplitude'].set(min=25, max=70)
params['sigma'].set(max=1)
params['center'].set(min=5, max=15)
# do fit, here with leastsq model
result = mod.fit(y, params, x=x, method='leastsq')
result_ndt = mod.fit(y, params, x=x, method=fit_method)
# assert that fit converged to the same result
vals = [result.params[p].value for p in result.params.valuesdict()]
vals_ndt = [result_ndt.params[p].value for p in result_ndt.params.valuesdict()]
assert_allclose(vals_ndt, vals, rtol=0.1)
assert_allclose(result_ndt.chisqr, result.chisqr, rtol=1e-5)
# assert that parameter uncertainties from leastsq and calculated from
# the covariance matrix using numdifftools are very similar
stderr = [result.params[p].stderr for p in result.params.valuesdict()]
stderr_ndt = [result_ndt.params[p].stderr for p in result_ndt.params.valuesdict()]
perr = np.array(stderr) / np.array(vals)
perr_ndt = np.array(stderr_ndt) / np.array(vals_ndt)
assert_almost_equal(perr_ndt, perr, decimal=3)
# assert that parameter correlatations from leastsq and calculated from
# the covariance matrix using numdifftools are very similar
for par1 in result.var_names:
cor = [result.params[par1].correl[par2] for par2 in
result.params[par1].correl.keys()]
cor_ndt = [result_ndt.params[par1].correl[par2] for par2 in
result_ndt.params[par1].correl.keys()]
assert_almost_equal(cor_ndt, cor, decimal=2)
def test_numdifftools_calc_covar_false():
pytest.importorskip("numdifftools")
# load data to be fitted
data = np.loadtxt(os.path.join(os.path.dirname(__file__), '..', 'examples',
'test_peak.dat'))
x = data[:, 0]
y = data[:, 1]
# define the model and initialize parameters
mod = VoigtModel()
params = mod.guess(y, x=x)
params['sigma'].set(min=-np.inf)
# do fit, with leastsq and nelder
result = mod.fit(y, params, x=x, method='leastsq')
result_ndt = mod.fit(y, params, x=x, method='nelder', calc_covar=False)
# assert that fit converged to the same result
vals = [result.params[p].value for p in result.params.valuesdict()]
vals_ndt = [result_ndt.params[p].value for p in result_ndt.params.valuesdict()]
assert_allclose(vals_ndt, vals, rtol=5e-3)
assert_allclose(result_ndt.chisqr, result.chisqr)
assert result_ndt.covar is None
assert result_ndt.errorbars is False
def test_final_parameter_values():
model = LinearModel()
params = model.make_params()
params['intercept'].set(value=-1, min=-20, max=0)
params['slope'].set(value=1, min=-100, max=400)
np.random.seed(78281)
x = np.linspace(0, 9, 10)
y = x * 1.34 - 4.5 + np.random.normal(scale=0.05, size=x.size)
result = model.fit(y, x=x, method='nelder', params=params)
assert_almost_equal(result.chisqr, 0.014625543, decimal=6)
assert_almost_equal(result.params['intercept'].value, -4.511087126, decimal=6)
assert_almost_equal(result.params['slope'].value, 1.339685514, decimal=6)
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