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"""Tests of ModelResult.eval_uncertainty()"""
import os
import numpy as np
from numpy.testing import assert_allclose
from lmfit.lineshapes import gaussian
from lmfit.model import Model
from lmfit.models import ExponentialModel, GaussianModel, LinearModel
def get_linearmodel(slope=0.8, intercept=0.5, noise=1.5):
# create data to be fitted
np.random.seed(88)
x = np.linspace(0, 10, 101)
y = intercept + x*slope
y = y + np.random.normal(size=len(x), scale=noise)
model = LinearModel()
params = model.make_params(intercept=intercept, slope=slope)
return x, y, model, params
def get_gaussianmodel(amplitude=1.0, center=5.0, sigma=1.0, noise=0.1):
# create data to be fitted
np.random.seed(7392)
x = np.linspace(-20, 20, 201)
y = gaussian(x, amplitude, center=center, sigma=sigma)
y = y + np.random.normal(size=len(x), scale=noise)
model = GaussianModel()
params = model.make_params(amplitude=amplitude/5.0,
center=center-1.0,
sigma=sigma*2.0)
return x, y, model, params
def test_linear_constant_intercept():
x, y, model, params = get_linearmodel(slope=4, intercept=-10)
params['intercept'].vary = False
ret = model.fit(y, params, x=x)
dely = ret.eval_uncertainty(sigma=1)
slope_stderr = ret.params['slope'].stderr
assert_allclose(dely.min(), 0, rtol=1.e-2)
assert_allclose(dely.max(), slope_stderr*x.max(), rtol=1.e-2)
assert_allclose(dely.mean(), slope_stderr*x.mean(), rtol=1.e-2)
def test_linear_constant_slope():
x, y, model, params = get_linearmodel(slope=-4, intercept=2.3)
params['slope'].vary = False
ret = model.fit(y, params, x=x)
dely = ret.eval_uncertainty(sigma=1)
intercept_stderr = ret.params['intercept'].stderr
assert_allclose(dely.min(), intercept_stderr, rtol=1.e-2)
assert_allclose(dely.max(), intercept_stderr, rtol=1.e-2)
def test_gauss_sigmalevel():
"""Test that dely increases as sigma increases."""
x, y, model, params = get_gaussianmodel(amplitude=50.0, center=4.5,
sigma=0.78, noise=0.1)
ret = model.fit(y, params, x=x)
dely_sigma1 = ret.eval_uncertainty(sigma=1)
dely_sigma2 = ret.eval_uncertainty(sigma=2)
dely_sigma3 = ret.eval_uncertainty(sigma=3)
assert dely_sigma3.mean() > 1.5*dely_sigma2.mean()
assert dely_sigma2.mean() > 1.5*dely_sigma1.mean()
def test_gauss_noiselevel():
"""Test that dely increases as expected with changing noise level."""
lonoise = 0.05
hinoise = 10*lonoise
x, y, model, params = get_gaussianmodel(amplitude=20.0, center=2.1,
sigma=1.0, noise=lonoise)
ret1 = model.fit(y, params, x=x)
dely_lonoise = ret1.eval_uncertainty(sigma=1)
x, y, model, params = get_gaussianmodel(amplitude=20.0, center=2.1,
sigma=1.0, noise=hinoise)
ret2 = model.fit(y, params, x=x)
dely_hinoise = ret2.eval_uncertainty(sigma=1)
assert_allclose(dely_hinoise.mean(), 10*dely_lonoise.mean(), rtol=1.e-2)
def test_component_uncertainties():
"test dely_comps"
y, x = np.loadtxt(os.path.join(os.path.dirname(__file__), '..',
'examples', 'NIST_Gauss2.dat')).T
model = (GaussianModel(prefix='g1_') +
GaussianModel(prefix='g2_') +
ExponentialModel(prefix='bkg_'))
params = model.make_params(bkg_amplitude=100, bkg_decay=80,
g1_amplitude=3000,
g1_center=100,
g1_sigma=10,
g2_amplitude=3000,
g2_center=150,
g2_sigma=10)
result = model.fit(y, params, x=x)
comps = result.eval_components(x=x)
dely = result.eval_uncertainty(sigma=3)
assert 'g1_' in comps
assert 'g2_' in comps
assert 'bkg_' in comps
assert dely.mean() > 0.8
assert dely.mean() < 2.0
assert result.dely_comps['g1_'].mean() > 0.5
assert result.dely_comps['g1_'].mean() < 1.5
assert result.dely_comps['g2_'].mean() > 0.5
assert result.dely_comps['g2_'].mean() < 1.5
assert result.dely_comps['bkg_'].mean() > 0.5
assert result.dely_comps['bkg_'].mean() < 1.5
def test_scalar_independent_vars():
"""Github #951"""
mr = LinearModel().fit(data=[1, 2, 4], x=[1, 2, 3])
assert_allclose(mr.eval_uncertainty(x=1.2), np.array([0.60629034]))
assert_allclose(mr.eval_uncertainty(x=np.array(1.2j)), np.array([1.15903153+0.17475665j]))
def test_multidim_model():
"""test models that return a multi-dimension output"""
def fit(x, p=2):
return np.array([x, p*x])
model = Model(fit)
mr = model.fit(data=np.array([[1, 2, 3], [2, 3, 5]]), x=np.array([1, 2, 3]))
assert_allclose(mr.eval_uncertainty(x=np.array([3, 4])), np.array([[0, 0], [0.18432744, 0.24576991]]))
assert_allclose(mr.eval_uncertainty(x=np.array([3j, 4j])), np.array([[0, 0], [0.13033918+0.13033918j, 0.17378557+0.17378557j]]))
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