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|
import unittest
import numpy as np
from numpy import pi
from numpy.testing import (assert_, assert_allclose, assert_almost_equal,
assert_equal, dec)
import pytest
from scipy.version import version as scipy_version
from uncertainties import ufloat
from lmfit import Minimizer, Parameters, minimize
from lmfit.lineshapes import gaussian
from lmfit.minimizer import (HAS_EMCEE, SCALAR_METHODS, MinimizerResult,
_lnpost, _nan_policy)
def check(para, real_val, sig=3):
err = abs(para.value - real_val)
assert(err < sig * para.stderr)
def check_wo_stderr(para, real_val, sig=0.1):
err = abs(para.value - real_val)
assert(err < sig)
def check_paras(para_fit, para_real, sig=3):
for i in para_fit:
check(para_fit[i], para_real[i].value, sig=sig)
def test_simple():
# 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)
params.add('decay', value=0.1)
params.add('shift', value=0.0, min=-pi/2., max=pi/2)
params.add('omega', value=3.0)
# do fit, here with leastsq model
result = minimize(fcn2min, params, args=(x, data))
# assert that the real parameters are found
for para, val in zip(result.params.values(), [5, 0.025, -.1, 2]):
check(para, val)
def test_lbfgsb():
p_true = Parameters()
p_true.add('amp', value=14.0)
p_true.add('period', value=5.33)
p_true.add('shift', value=0.123)
p_true.add('decay', value=0.010)
def residual(pars, x, data=None):
amp = pars['amp']
per = pars['period']
shift = pars['shift']
decay = pars['decay']
if abs(shift) > pi/2:
shift = shift - np.sign(shift) * pi
model = amp * np.sin(shift + x / per) * np.exp(-x * x * decay * decay)
if data is None:
return model
return (model - data)
n = 2500
xmin = 0.
xmax = 250.0
noise = np.random.normal(scale=0.7215, size=n)
x = np.linspace(xmin, xmax, n)
data = residual(p_true, x) + noise
fit_params = Parameters()
fit_params.add('amp', value=11.0, min=5, max=20)
fit_params.add('period', value=5., min=1., max=7)
fit_params.add('shift', value=.10, min=0.0, max=0.2)
fit_params.add('decay', value=6.e-3, min=0, max=0.1)
out = minimize(residual, fit_params, method='lbfgsb', args=(x,),
kws={'data': data})
for para, true_para in zip(out.params.values(), p_true.values()):
check_wo_stderr(para, true_para.value)
def test_derive():
def func(pars, x, data=None):
model = pars['a'] * np.exp(-pars['b'] * x) + pars['c']
if data is None:
return model
return model - data
def dfunc(pars, x, data=None):
v = np.exp(-pars['b']*x)
return np.array([v, -pars['a']*x*v, np.ones(len(x))])
def f(var, x):
return var[0] * np.exp(-var[1] * x) + var[2]
params1 = Parameters()
params1.add('a', value=10)
params1.add('b', value=10)
params1.add('c', value=10)
params2 = Parameters()
params2.add('a', value=10)
params2.add('b', value=10)
params2.add('c', value=10)
a, b, c = 2.5, 1.3, 0.8
x = np.linspace(0, 4, 50)
y = f([a, b, c], x)
data = y + 0.15*np.random.normal(size=len(x))
# fit without analytic derivative
min1 = Minimizer(func, params1, fcn_args=(x,), fcn_kws={'data': data})
out1 = min1.leastsq()
# fit with analytic derivative
min2 = Minimizer(func, params2, fcn_args=(x,), fcn_kws={'data': data})
out2 = min2.leastsq(Dfun=dfunc, col_deriv=1)
check_wo_stderr(out1.params['a'], out2.params['a'].value, 0.00005)
check_wo_stderr(out1.params['b'], out2.params['b'].value, 0.00005)
check_wo_stderr(out1.params['c'], out2.params['c'].value, 0.00005)
def test_peakfit():
def residual(pars, x, data=None):
g1 = gaussian(x, pars['a1'], pars['c1'], pars['w1'])
g2 = gaussian(x, pars['a2'], pars['c2'], pars['w2'])
model = g1 + g2
if data is None:
return model
return (model - data)
n = 601
xmin = 0.
xmax = 15.0
noise = np.random.normal(scale=.65, size=n)
x = np.linspace(xmin, xmax, n)
org_params = Parameters()
org_params.add_many(('a1', 12.0, True, None, None, None),
('c1', 5.3, True, None, None, None),
('w1', 1.0, True, None, None, None),
('a2', 9.1, True, None, None, None),
('c2', 8.1, True, None, None, None),
('w2', 2.5, True, None, None, None))
data = residual(org_params, x) + noise
fit_params = Parameters()
fit_params.add_many(('a1', 8.0, True, None, 14., None),
('c1', 5.0, True, None, None, None),
('w1', 0.7, True, None, None, None),
('a2', 3.1, True, None, None, None),
('c2', 8.8, True, None, None, None))
fit_params.add('w2', expr='2.5*w1')
myfit = Minimizer(residual, fit_params, fcn_args=(x,),
fcn_kws={'data': data})
myfit.prepare_fit()
out = myfit.leastsq()
check_paras(out.params, org_params)
def test_scalar_minimize_has_no_uncertainties():
# scalar_minimize doesn't calculate uncertainties.
# when a scalar_minimize is run the stderr and correl for each parameter
# should be None. (stderr and correl are set to None when a Parameter is
# initialised).
# This requires a reset after a leastsq fit has been done.
# Only when scalar_minimize calculates stderr and correl can this test
# be removed.
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)
params.add('decay', value=0.1)
params.add('shift', value=0.0, min=-pi/2., max=pi/2)
params.add('omega', value=3.0)
mini = Minimizer(fcn2min, params, fcn_args=(x, data))
out = mini.minimize()
assert_(np.isfinite(out.params['amp'].stderr))
assert out.errorbars
out2 = mini.minimize(method='nelder-mead')
assert_(out2.params['amp'].stderr is None)
assert_(out2.params['decay'].stderr is None)
assert_(out2.params['shift'].stderr is None)
assert_(out2.params['omega'].stderr is None)
assert_(out2.params['amp'].correl is None)
assert_(out2.params['decay'].correl is None)
assert_(out2.params['shift'].correl is None)
assert_(out2.params['omega'].correl is None)
assert not out2.errorbars
def test_scalar_minimize_reduce_fcn():
# test that the reduce_fcn option for scalar_minimize
# gives different and improved results with outliers
np.random.seed(2)
x = np.linspace(0, 10, 101)
yo = 1.0 + 2.0*np.sin(4*x) * np.exp(-x / 5)
y = yo + np.random.normal(size=len(yo), scale=0.250)
outliers = np.random.randint(int(len(x)/3.0), len(x), int(len(x)/12))
y[outliers] += 5*np.random.random(len(outliers))
# define objective function: returns the array to be minimized
def objfunc(pars, x, data):
decay = pars['decay']
offset = pars['offset']
omega = pars['omega']
amp = pars['amp']
model = offset + amp * np.sin(x*omega) * np.exp(-x/decay)
return model - data
# create a set of Parameters
params = Parameters()
params.add('offset', 2.0)
params.add('omega', 3.3)
params.add('amp', 2.5)
params.add('decay', 1.0)
method = 'L-BFGS-B'
out1 = minimize(objfunc, params, args=(x, y), method=method)
out2 = minimize(objfunc, params, args=(x, y), method=method,
reduce_fcn='neglogcauchy')
assert_allclose(out1.params['omega'].value, 4.0, rtol=0.01)
assert_allclose(out1.params['decay'].value, 7.6, rtol=0.01)
assert_allclose(out2.params['omega'].value, 4.0, rtol=0.01)
assert_allclose(out2.params['decay'].value, 5.8, rtol=0.01)
def test_multidimensional_fit_GH205():
# test that you don't need to flatten the output from the objective
# function. Tests regression for GH205.
pos = np.linspace(0, 99, 100)
xv, yv = np.meshgrid(pos, pos)
f = lambda xv, yv, lambda1, lambda2: (np.sin(xv * lambda1) +
np.cos(yv * lambda2))
data = f(xv, yv, 0.3, 3)
assert_(data.ndim, 2)
def fcn2min(params, xv, yv, data):
"""model decaying sine wave, subtract data"""
model = f(xv, yv, params['lambda1'], params['lambda2'])
return model - data
# create a set of Parameters
params = Parameters()
params.add('lambda1', value=0.4)
params.add('lambda2', value=3.2)
mini = Minimizer(fcn2min, params, fcn_args=(xv, yv, data))
mini.minimize()
def test_ufloat():
"""Test of ufloat from uncertainties."""
x = ufloat(1, 0.1)
assert_allclose(x.nominal_value, 1.0, rtol=1.e-7)
assert_allclose(x.std_dev, 0.1, rtol=1.e-7)
y = x*x
assert_allclose(y.nominal_value, 1.0, rtol=1.e-7)
assert_allclose(y.std_dev, 0.2, rtol=1.e-7)
y = x - x
assert_allclose(y.nominal_value, 0.0, rtol=1.e-7)
assert_allclose(y.std_dev, 0.0, rtol=1.e-7)
class CommonMinimizerTest(unittest.TestCase):
def setUp(self):
"""
test scale minimizers except newton-cg (needs jacobian) and
anneal (doesn't work out of the box).
"""
p_true = Parameters()
p_true.add('amp', value=14.0)
p_true.add('period', value=5.33)
p_true.add('shift', value=0.123)
p_true.add('decay', value=0.010)
self.p_true = p_true
n = 2500
xmin = 0.
xmax = 250.0
noise = np.random.normal(scale=0.7215, size=n)
self.x = np.linspace(xmin, xmax, n)
self.data = self.residual(p_true, self.x) + noise
fit_params = Parameters()
fit_params.add('amp', value=11.0, min=5, max=20)
fit_params.add('period', value=5., min=1., max=7)
fit_params.add('shift', value=.10, min=0.0, max=0.2)
fit_params.add('decay', value=6.e-3, min=0, max=0.1)
self.fit_params = fit_params
self.mini = Minimizer(self.residual, fit_params, [self.x, self.data])
def residual(self, pars, x, data=None):
amp = pars['amp']
per = pars['period']
shift = pars['shift']
decay = pars['decay']
if abs(shift) > pi/2:
shift = shift - np.sign(shift) * pi
model = amp*np.sin(shift + x/per) * np.exp(-x*x*decay*decay)
if data is None:
return model
return model - data
def test_diffev_bounds_check(self):
# You need finite (min, max) for each parameter if you're using
# differential_evolution.
self.fit_params['decay'].min = -np.inf
self.fit_params['decay'].vary = True
self.minimizer = 'differential_evolution'
pytest.raises(ValueError, self.scalar_minimizer)
# but only if a parameter is not fixed
self.fit_params['decay'].vary = False
self.mini.scalar_minimize(method='differential_evolution', maxiter=1)
def test_scalar_minimizers(self):
# test all the scalar minimizers
for method in SCALAR_METHODS:
if method in ['newton', 'dogleg', 'trust-ncg', 'cg', 'trust-exact',
'trust-krylov', 'trust-constr']:
continue
self.minimizer = SCALAR_METHODS[method]
if method == 'Nelder-Mead':
sig = 0.2
else:
sig = 0.15
self.scalar_minimizer(sig=sig)
def scalar_minimizer(self, sig=0.15):
out = self.mini.scalar_minimize(method=self.minimizer)
self.residual(out.params, self.x)
for para, true_para in zip(out.params.values(), self.p_true.values()):
check_wo_stderr(para, true_para.value, sig=sig)
def test_nan_policy(self):
# check that an error is raised if there are nan in
# the data returned by userfcn
self.data[0] = np.nan
major, minor, _micro = scipy_version.split('.', 2)
for method in SCALAR_METHODS:
if (method == 'differential_evolution' and int(major) > 0 and
int(minor) >= 2):
pytest.raises(RuntimeError, self.mini.scalar_minimize,
SCALAR_METHODS[method])
else:
pytest.raises(ValueError, self.mini.scalar_minimize,
SCALAR_METHODS[method])
pytest.raises(ValueError, self.mini.minimize)
# now check that the fit proceeds if nan_policy is 'omit'
self.mini.nan_policy = 'omit'
res = self.mini.minimize()
assert_equal(res.ndata, np.size(self.data, 0) - 1)
for para, true_para in zip(res.params.values(), self.p_true.values()):
check_wo_stderr(para, true_para.value, sig=0.15)
def test_nan_policy_function(self):
a = np.array([0, 1, 2, 3, np.nan])
pytest.raises(ValueError, _nan_policy, a)
assert_(np.isnan(_nan_policy(a, nan_policy='propagate')[-1]))
assert_equal(_nan_policy(a, nan_policy='omit'), [0, 1, 2, 3])
a[-1] = np.inf
pytest.raises(ValueError, _nan_policy, a)
assert_(np.isposinf(_nan_policy(a, nan_policy='propagate')[-1]))
assert_equal(_nan_policy(a, nan_policy='omit'), [0, 1, 2, 3])
assert_equal(_nan_policy(a, handle_inf=False), a)
@dec.slow
def test_emcee(self):
# test emcee
if not HAS_EMCEE:
return True
np.random.seed(123456)
out = self.mini.emcee(nwalkers=100, steps=200, burn=50, thin=10)
check_paras(out.params, self.p_true, sig=3)
@dec.slow
def test_emcee_method_kwarg(self):
# test with emcee as method keyword argument
if not HAS_EMCEE:
return True
np.random.seed(123456)
out = self.mini.minimize(method='emcee', nwalkers=100, steps=200,
burn=50, thin=10)
assert out.method == 'emcee'
assert out.nfev == 100*200
check_paras(out.params, self.p_true, sig=3)
out_unweighted = self.mini.minimize(method='emcee', is_weighted=False)
assert out_unweighted.method == 'emcee'
@dec.slow
def test_emcee_PT(self):
# test emcee with parallel tempering
if not HAS_EMCEE:
return True
np.random.seed(123456)
self.mini.userfcn = residual_for_multiprocessing
out = self.mini.emcee(ntemps=4, nwalkers=50, steps=200,
burn=100, thin=10, workers=2)
check_paras(out.params, self.p_true, sig=3)
@dec.slow
def test_emcee_multiprocessing(self):
# test multiprocessing runs
if not HAS_EMCEE:
return True
np.random.seed(123456)
self.mini.userfcn = residual_for_multiprocessing
self.mini.emcee(steps=10, workers=4)
def test_emcee_bounds_length(self):
# the log-probability functions check if the parameters are
# inside the bounds. Check that the bounds and parameters
# are the right lengths for comparison. This can be done
# if nvarys != nparams
if not HAS_EMCEE:
return True
self.mini.params['amp'].vary = False
self.mini.params['period'].vary = False
self.mini.params['shift'].vary = False
self.mini.emcee(steps=10)
@dec.slow
def test_emcee_partial_bounds(self):
# mcmc with partial bounds
if not HAS_EMCEE:
return True
np.random.seed(123456)
# test mcmc output vs lm, some parameters not bounded
self.fit_params['amp'].max = np.inf
# self.fit_params['amp'].min = -np.inf
out = self.mini.emcee(nwalkers=100, steps=300, burn=100, thin=10)
check_paras(out.params, self.p_true, sig=3)
def test_emcee_init_with_chain(self):
# can you initialise with a previous chain
if not HAS_EMCEE:
return True
out = self.mini.emcee(nwalkers=100, steps=5)
# can initialise with a chain
self.mini.emcee(nwalkers=100, steps=1, pos=out.chain)
# can initialise with a correct subset of a chain
self.mini.emcee(nwalkers=100, steps=1, pos=out.chain[..., -1, :])
# but you can't initialise if the shape is wrong.
pytest.raises(ValueError,
self.mini.emcee,
nwalkers=100,
steps=1,
pos=out.chain[..., -1, :-1])
def test_emcee_reuse_sampler(self):
if not HAS_EMCEE:
return True
self.mini.emcee(nwalkers=100, steps=5)
# if you've run the sampler the Minimizer object should have a _lastpos
# attribute
assert_(hasattr(self.mini, '_lastpos'))
# now try and re-use sampler
out2 = self.mini.emcee(steps=10, reuse_sampler=True)
assert_(out2.chain.shape[1] == 15)
# you shouldn't be able to reuse the sampler if nvarys has changed.
self.mini.params['amp'].vary = False
pytest.raises(ValueError, self.mini.emcee, reuse_sampler=True)
def test_emcee_lnpost(self):
# check ln likelihood is calculated correctly. It should be
# -0.5 * chi**2.
result = self.mini.minimize()
# obtain the numeric values
# note - in this example all the parameters are varied
fvars = np.array([par.value for par in result.params.values()])
# calculate the cost function with scaled values (parameters all have
# lower and upper bounds.
scaled_fvars = []
for par, fvar in zip(result.params.values(), fvars):
par.value = fvar
scaled_fvars.append(par.setup_bounds())
val = self.mini.penalty(np.array(scaled_fvars))
# calculate the log-likelihood value
bounds = np.array([(par.min, par.max)
for par in result.params.values()])
val2 = _lnpost(fvars,
self.residual,
result.params,
result.var_names,
bounds,
userargs=(self.x, self.data))
assert_almost_equal(-0.5 * val, val2)
def test_emcee_output(self):
# test mcmc output
if not HAS_EMCEE:
return True
try:
from pandas import DataFrame
except ImportError:
return True
out = self.mini.emcee(nwalkers=10, steps=20, burn=5, thin=2)
assert_(isinstance(out, MinimizerResult))
assert_(isinstance(out.flatchain, DataFrame))
# check that we can access the chains via parameter name
assert_(out.flatchain['amp'].shape[0] == 80)
assert out.errorbars
assert_(np.isfinite(out.params['amp'].correl['period']))
# the lnprob array should be the same as the chain size
assert_(np.size(out.chain)//out.nvarys == np.size(out.lnprob))
# test chain output shapes
assert_(out.lnprob.shape == (10, (20-5+1)/2))
assert_(out.chain.shape == (10, (20-5+1)/2, out.nvarys))
assert_(out.flatchain.shape == (10*(20-5+1)/2, out.nvarys))
def test_emcee_PT_output(self):
# test mcmc output when using parallel tempering
if not HAS_EMCEE:
return True
try:
from pandas import DataFrame
except ImportError:
return True
out = self.mini.emcee(ntemps=6, nwalkers=10, steps=20, burn=5, thin=2)
assert_(isinstance(out, MinimizerResult))
assert_(isinstance(out.flatchain, DataFrame))
# check that we can access the chains via parameter name
assert_(out.flatchain['amp'].shape[0] == 80)
assert out.errorbars
assert_(np.isfinite(out.params['amp'].correl['period']))
# the lnprob array should be the same as the chain size
assert_(np.size(out.chain)//out.nvarys == np.size(out.lnprob))
# test chain output shapes
assert_(out.lnprob.shape == (6, 10, (20-5+1)/2))
assert_(out.chain.shape == (6, 10, (20-5+1)/2, out.nvarys))
# Only the 0th temperature is returned
assert_(out.flatchain.shape == (10*(20-5+1)/2, out.nvarys))
@dec.slow
def test_emcee_float(self):
# test that it works if the residuals returns a float, not a vector
if not HAS_EMCEE:
return True
def resid(pars, x, data=None):
return -0.5 * np.sum(self.residual(pars, x, data=data)**2)
# just return chi2
def resid2(pars, x, data=None):
return np.sum(self.residual(pars, x, data=data)**2)
self.mini.userfcn = resid
np.random.seed(123456)
out = self.mini.emcee(nwalkers=100, steps=200, burn=50, thin=10)
check_paras(out.params, self.p_true, sig=3)
self.mini.userfcn = resid2
np.random.seed(123456)
out = self.mini.emcee(nwalkers=100, steps=200,
burn=50, thin=10, float_behavior='chi2')
check_paras(out.params, self.p_true, sig=3)
@dec.slow
def test_emcee_seed(self):
# test emcee seeding can reproduce a sampling run
if not HAS_EMCEE:
return True
out = self.mini.emcee(params=self.fit_params,
nwalkers=100,
steps=1, seed=1)
out2 = self.mini.emcee(params=self.fit_params,
nwalkers=100,
steps=1, seed=1)
assert_almost_equal(out.chain, out2.chain)
def residual_for_multiprocessing(pars, x, data=None):
# a residual function defined in the top level is needed for
# multiprocessing. bound methods don't work.
amp = pars['amp']
per = pars['period']
shift = pars['shift']
decay = pars['decay']
if abs(shift) > pi/2:
shift = shift - np.sign(shift) * pi
model = amp*np.sin(shift + x/per) * np.exp(-x*x*decay*decay)
if data is None:
return model
return (model - data)
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