def test_residuals(self):
# weighted, with and without transform
assert_almost_equal(self.objective.residuals(),
(self.data.y - self.mod) / self.data.y_err)
objective = Objective(self.model, self.data,
transform=Transform('lin'))
assert_almost_equal(objective.residuals(),
(self.data.y - self.mod) / self.data.y_err)
# unweighted, with and without transform
objective = Objective(self.model, self.data, use_weights=False)
assert_almost_equal(objective.residuals(),
self.data.y - self.mod)
objective = Objective(self.model, self.data, use_weights=False,
transform=Transform('lin'))
assert_almost_equal(objective.residuals(),
self.data.y - self.mod)
def test_multidimensionality(self):
# Check that ND data can be used with an objective/model/data
# (or at least it doesn't stand in the way)
rng = np.random.default_rng()
x = rng.uniform(size=100).reshape(50, 2)
desired = line_ND(x, self.p)
assert desired.shape == (50, 2)
data = Data1D((x, desired))
model = Model(self.p, fitfunc=line_ND)
y = model(x)
assert_allclose(y, desired)
objective = Objective(model, data)
assert_allclose(objective.chisqr(), 0)
assert_allclose(objective.generative(), desired)
assert_allclose(objective.residuals(), 0)
assert objective.residuals().shape == (50, 2)
objective.logl()
objective.logpost()
covar = objective.covar()
assert covar.shape == (2, 2)
def test_reflectivity_emcee(self):
model = self.model361
model.dq = 5.
objective = Objective(model,
(self.qvals361, self.rvals361, self.evals361),
transform=Transform('logY'))
fitter = CurveFitter(objective, nwalkers=100)
assert_(len(objective.generative().shape) == 1)
assert_(len(objective.residuals().shape) == 1)
res = fitter.fit('least_squares')
res_mcmc = fitter.sample(steps=5, nthin=10, random_state=1,
verbose=False)
mcmc_val = [mcmc_result.median for mcmc_result in res_mcmc]
assert_allclose(mcmc_val, res.x, rtol=0.05)
def test_multipledataset_corefinement(self):
# test corefinement of three datasets
data361 = ReflectDataset(os.path.join(self.pth, 'e361r.txt'))
data365 = ReflectDataset(os.path.join(self.pth, 'e365r.txt'))
data366 = ReflectDataset(os.path.join(self.pth, 'e366r.txt'))
si = SLD(2.07, name='Si')
sio2 = SLD(3.47, name='SiO2')
d2o = SLD(6.36, name='d2o')
h2o = SLD(-0.56, name='h2o')
cm3 = SLD(3.47, name='cm3')
polymer = SLD(1, name='polymer')
structure361 = si | sio2(10, 4) | polymer(200, 3) | d2o(0, 3)
structure365 = si | structure361[1] | structure361[2] | cm3(0, 3)
structure366 = si | structure361[1] | structure361[2] | h2o(0, 3)
structure365[-1].rough = structure361[-1].rough
structure366[-1].rough = structure361[-1].rough
structure361[1].thick.setp(vary=True, bounds=(0, 20))
structure361[2].thick.setp(value=200., bounds=(200., 250.), vary=True)
structure361[2].sld.real.setp(vary=True, bounds=(0, 2))
structure361[2].vfsolv.setp(value=5., bounds=(0., 100.), vary=True)
model361 = ReflectModel(structure361, bkg=2e-5)
model365 = ReflectModel(structure365, bkg=2e-5)
model366 = ReflectModel(structure366, bkg=2e-5)
model361.bkg.setp(vary=True, bounds=(1e-6, 5e-5))
model365.bkg.setp(vary=True, bounds=(1e-6, 5e-5))
model366.bkg.setp(vary=True, bounds=(1e-6, 5e-5))
objective361 = Objective(model361, data361)
objective365 = Objective(model365, data365)
objective366 = Objective(model366, data366)
global_objective = GlobalObjective(
[objective361, objective365, objective366])
# are the right numbers of parameters varying?
assert_equal(len(global_objective.varying_parameters()), 7)
# can we set the parameters?
global_objective.setp(np.array([1e-5, 10, 212, 1, 10, 1e-5, 1e-5]))
f = CurveFitter(global_objective)
f.fit()
indiv_chisqr = np.sum(
[objective.chisqr() for objective in global_objective.objectives])
# the overall chi2 should be sum of individual chi2
global_chisqr = global_objective.chisqr()
assert_almost_equal(global_chisqr, indiv_chisqr)
# now check that the parameters were held in common correctly.
slabs361 = structure361.slabs()
slabs365 = structure365.slabs()
slabs366 = structure366.slabs()
assert_equal(slabs365[0:2, 0:5], slabs361[0:2, 0:5])
assert_equal(slabs366[0:2, 0:5], slabs361[0:2, 0:5])
assert_equal(slabs365[-1, 3], slabs361[-1, 3])
assert_equal(slabs366[-1, 3], slabs361[-1, 3])
# check that the residuals are the correct lengths
res361 = objective361.residuals()
res365 = objective365.residuals()
res366 = objective366.residuals()
res_global = global_objective.residuals()
assert_allclose(res_global[0:len(res361)], res361, rtol=1e-5)
assert_allclose(res_global[len(res361):len(res361) + len(res365)],
res365,
rtol=1e-5)
assert_allclose(res_global[len(res361) + len(res365):],
res366,
rtol=1e-5)
repr(global_objective)
class TestFitterGauss(object):
# Test CurveFitter with a noisy gaussian, weighted and unweighted, to see
# if the parameters and uncertainties come out correct
@pytest.fixture(autouse=True)
def setup_method(self, tmpdir):
self.path = os.path.dirname(os.path.abspath(__file__))
self.tmpdir = tmpdir.strpath
theoretical = np.loadtxt(os.path.join(self.path, "gauss_data.txt"))
xvals, yvals, evals = np.hsplit(theoretical, 3)
xvals = xvals.flatten()
yvals = yvals.flatten()
evals = evals.flatten()
# these best weighted values and uncertainties obtained with Igor
self.best_weighted = [-0.00246095, 19.5299, -8.28446e-2, 1.24692]
self.best_weighted_errors = [
0.0220313708486,
1.12879436221,
0.0447659158681,
0.0412022938883,
]
self.best_weighted_chisqr = 77.6040960351
self.best_unweighted = [
-0.10584111872702096,
19.240347049328989,
0.0092623066070940396,
1.501362314145845,
]
self.best_unweighted_errors = [
0.34246565477,
0.689820935208,
0.0411243173041,
0.0693429375282,
]
self.best_unweighted_chisqr = 497.102084956
self.p0 = np.array([0.1, 20.0, 0.1, 0.1])
self.names = ["bkg", "A", "x0", "width"]
self.bounds = [(-1, 1), (0, 30), (-5.0, 5.0), (0.001, 2)]
self.params = Parameters(name="gauss_params")
for p, name, bound in zip(self.p0, self.names, self.bounds):
param = Parameter(p, name=name)
param.range(*bound)
param.vary = True
self.params.append(param)
self.model = Model(self.params, fitfunc=gauss)
self.data = Data1D((xvals, yvals, evals))
self.objective = Objective(self.model, self.data)
return 0
def test_pickle(self):
# tests if a CurveFitter can be pickled/unpickled.
f = CurveFitter(self.objective)
pkl = pickle.dumps(f)
g = pickle.loads(pkl)
g._check_vars_unchanged()
def test_best_weighted(self):
assert_equal(len(self.objective.varying_parameters()), 4)
self.objective.setp(self.p0)
f = CurveFitter(self.objective, nwalkers=100)
res = f.fit("least_squares", jac="3-point")
output = res.x
assert_almost_equal(output, self.best_weighted, 3)
assert_almost_equal(self.objective.chisqr(), self.best_weighted_chisqr,
5)
# compare the residuals
res = (self.data.y - self.model(self.data.x)) / self.data.y_err
assert_equal(self.objective.residuals(), res)
# compare objective.covar to the best_weighted_errors
uncertainties = [param.stderr for param in self.params]
assert_allclose(uncertainties, self.best_weighted_errors, rtol=0.005)
# we're also going to try the checkpointing here.
checkpoint = os.path.join(self.tmpdir, "checkpoint.txt")
# compare samples to best_weighted_errors
np.random.seed(1)
f.sample(steps=201, random_state=1, verbose=False, f=checkpoint)
process_chain(self.objective, f.chain, nburn=50, nthin=10)
uncertainties = [param.stderr for param in self.params]
assert_allclose(uncertainties, self.best_weighted_errors, rtol=0.07)
# test that the checkpoint worked
check_array = np.loadtxt(checkpoint)
check_array = check_array.reshape(201, f._nwalkers, f.nvary)
assert_allclose(check_array, f.chain)
# test loading the checkpoint
chain = load_chain(checkpoint)
assert_allclose(chain, f.chain)
f.initialise("jitter")
f.sample(steps=2, nthin=4, f=checkpoint, verbose=False)
assert_equal(f.chain.shape[0], 2)
# we should be able to produce 2 * 100 steps from the generator
g = self.objective.pgen(ngen=20000000000)
s = [i for i, a in enumerate(g)]
assert_equal(np.max(s), 200 - 1)
g = self.objective.pgen(ngen=200)
pvec = next(g)
assert_equal(pvec.size, len(self.objective.parameters.flattened()))
# check that all the parameters are returned via pgen, not only those
# being varied.
self.params[0].vary = False
f = CurveFitter(self.objective, nwalkers=100)
f.initialise("jitter")
f.sample(steps=2, nthin=4, f=checkpoint, verbose=False)
g = self.objective.pgen(ngen=100)
pvec = next(g)
assert_equal(pvec.size, len(self.objective.parameters.flattened()))
# the following test won't work because of emcee/gh226.
# chain = load_chain(checkpoint)
# assert_(chain.shape == f.chain.shape)
# assert_allclose(chain, f.chain)
# try reproducing best fit with parallel tempering
self.params[0].vary = True
f = CurveFitter(self.objective, nwalkers=100, ntemps=10)
f.fit("differential_evolution", seed=1)
f.sample(steps=201, random_state=1, verbose=False)
process_chain(self.objective, f.chain, nburn=50, nthin=15)
print(self.params[0].chain.shape, self.params[0].chain)
uncertainties = [param.stderr for param in self.params]
assert_allclose(uncertainties, self.best_weighted_errors, rtol=0.07)
def test_best_unweighted(self):
self.objective.weighted = False
f = CurveFitter(self.objective, nwalkers=100)
res = f.fit()
output = res.x
assert_almost_equal(self.objective.chisqr(),
self.best_unweighted_chisqr)
assert_almost_equal(output, self.best_unweighted, 5)
# compare the residuals
res = self.data.y - self.model(self.data.x)
assert_equal(self.objective.residuals(), res)
# compare objective._covar to the best_unweighted_errors
uncertainties = np.array([param.stderr for param in self.params])
assert_almost_equal(uncertainties, self.best_unweighted_errors, 3)
# the samples won't compare to the covariance matrix...
# f.sample(nsteps=150, nburn=20, nthin=30, random_state=1)
# uncertainties = [param.stderr for param in self.params]
# assert_allclose(uncertainties, self.best_unweighted_errors,
# rtol=0.15)
def test_all_minimisers(self):
"""test minimisers against the Gaussian fit"""
f = CurveFitter(self.objective)
methods = ["differential_evolution", "L-BFGS-B", "least_squares"]
if hasattr(sciopt, "shgo"):
methods.append("shgo")
if hasattr(sciopt, "dual_annealing"):
methods.append("dual_annealing")
for method in methods:
self.objective.setp(self.p0)
res = f.fit(method=method)
assert_almost_equal(res.x, self.best_weighted, 3)
# smoke test to check that we can use nlpost
self.objective.setp(self.p0)
logp0 = self.objective.logp()
# check that probabilities are calculated correctly
assert_allclose(
self.objective.logpost(),
self.objective.logp() + self.objective.logl(),
)
assert_allclose(self.objective.nlpost(), -self.objective.logpost())
assert_allclose(self.objective.nlpost(self.p0),
-self.objective.logpost(self.p0))
# if the priors are all uniform then the only difference between
# logpost and logl is a constant. A minimiser should converge on the
# same answer. The following tests examine that.
# The test works for dual_annealing, but not for differential
# evolution, not sure why that is.
self.objective.setp(self.p0)
res1 = f.fit(method="dual_annealing", seed=1)
assert_almost_equal(res1.x, self.best_weighted, 3)
nll1 = self.objective.nll()
nlpost1 = self.objective.nlpost()
self.objective.setp(self.p0)
res2 = f.fit(method="dual_annealing", target="nlpost", seed=1)
assert_almost_equal(res2.x, self.best_weighted, 3)
nll2 = self.objective.nll()
nlpost2 = self.objective.nlpost()
assert_allclose(nlpost1, nlpost2, atol=0.001)
assert_allclose(nll1, nll2, atol=0.001)
# these two priors are calculated for different parameter values
# (before and after the fit) they should be the same because all
# the parameters have uniform priors.
assert_almost_equal(self.objective.logp(), logp0)
def test_pymc3_sample(self):
# test sampling with pymc3
try:
import pymc3 as pm
from refnx.analysis import pymc3_model
except (ModuleNotFoundError, ImportError, AttributeError):
# can't run test if pymc3/theano not installed
return
with pymc3_model(self.objective):
s = pm.NUTS()
pm.sample(
200,
tune=100,
step=s,
discard_tuned_samples=True,
compute_convergence_checks=False,
random_seed=1,
)
class TestObjective(object):
def setup_method(self):
# Choose the "true" parameters.
# Reproducible results!
np.random.seed(123)
self.m_true = -0.9594
self.b_true = 4.294
self.f_true = 0.534
self.m_ls = -1.1040757010910947
self.b_ls = 5.4405552502319505
# Generate some synthetic data from the model.
N = 50
x = np.sort(10 * np.random.rand(N))
y_err = 0.1 + 0.5 * np.random.rand(N)
y = self.m_true * x + self.b_true
y += np.abs(self.f_true * y) * np.random.randn(N)
y += y_err * np.random.randn(N)
self.data = Data1D(data=(x, y, y_err))
self.p = Parameter(self.b_ls, 'b') | Parameter(self.m_ls, 'm')
self.model = Model(self.p, fitfunc=line)
self.objective = Objective(self.model, self.data)
# want b and m
self.p[0].vary = True
self.p[1].vary = True
mod = np.array([
4.78166609, 4.42364699, 4.16404064, 3.50343504, 3.4257084,
2.93594347, 2.92035638, 2.67533842, 2.28136038, 2.19772983,
1.99295496, 1.93748334, 1.87484436, 1.65161016, 1.44613461,
1.11128101, 1.04584535, 0.86055984, 0.76913963, 0.73906649,
0.73331407, 0.68350418, 0.65216599, 0.59838566, 0.13070299,
0.10749131, -0.01010195, -0.10010155, -0.29495372, -0.42817431,
-0.43122391, -0.64637715, -1.30560686, -1.32626428, -1.44835768,
-1.52589881, -1.56371158, -2.12048349, -2.24899179, -2.50292682,
-2.53576659, -2.55797996, -2.60870542, -2.7074727, -3.93781479,
-4.12415366, -4.42313742, -4.98368609, -5.38782395, -5.44077086
])
self.mod = mod
def test_model(self):
# test that the line data produced by our model is the same as the
# test data
assert_almost_equal(self.model(self.data.x), self.mod)
def test_synthetic_data(self):
# test that we create the correct synthetic data by performing a least
# squares fit on it
assert_(self.data.y_err is not None)
x, y, y_err, _ = self.data.data
A = np.vstack((np.ones_like(x), x)).T
C = np.diag(y_err * y_err)
cov = np.linalg.inv(np.dot(A.T, np.linalg.solve(C, A)))
b_ls, m_ls = np.dot(cov, np.dot(A.T, np.linalg.solve(C, y)))
assert_almost_equal(b_ls, self.b_ls)
assert_almost_equal(m_ls, self.m_ls)
def test_setp(self):
# check that we can set parameters
self.p[0].vary = False
assert_(len(self.objective.varying_parameters()) == 1)
self.objective.setp(np.array([1.23]))
assert_equal(self.p[1].value, 1.23)
self.objective.setp(np.array([1.234, 1.23]))
assert_equal(np.array(self.p), [1.234, 1.23])
def test_pvals(self):
assert_equal(self.objective.parameters.pvals, [self.b_ls, self.m_ls])
self.objective.parameters.pvals = [1, 2]
assert_equal(self.objective.parameters.pvals, [1, 2.])
def test_lnprior(self):
self.p[0].range(0, 10)
assert_almost_equal(self.objective.lnprior(), np.log(0.1))
# lnprior should set parameters
self.objective.lnprior([8, 2])
assert_equal(np.array(self.objective.parameters), [8, 2])
# if we supply a value outside the range it should return -inf
assert_equal(self.objective.lnprior([-1, 2]), -np.inf)
def test_lnprob(self):
# http://dan.iel.fm/emcee/current/user/line/
assert_almost_equal(self.objective.lnprior(), 0)
# the uncertainties are underestimated in this example...
assert_almost_equal(self.objective.lnlike(), -559.01078135444595)
assert_almost_equal(self.objective.lnprob(), -559.01078135444595)
def test_chisqr(self):
assert_almost_equal(self.objective.chisqr(), 1231.1096772954229)
def test_residuals(self):
# weighted, with and without transform
assert_almost_equal(self.objective.residuals(),
(self.data.y - self.mod) / self.data.y_err)
objective = Objective(self.model,
self.data,
transform=Transform('lin'))
assert_almost_equal(objective.residuals(),
(self.data.y - self.mod) / self.data.y_err)
# unweighted, with and without transform
objective = Objective(self.model, self.data, use_weights=False)
assert_almost_equal(objective.residuals(), self.data.y - self.mod)
objective = Objective(self.model,
self.data,
use_weights=False,
transform=Transform('lin'))
assert_almost_equal(objective.residuals(), self.data.y - self.mod)
def test_lnprob_extra(self):
self.objective.lnprob_extra = lnprob_extra
# repeat lnprior test
self.p[0].range(0, 10)
assert_almost_equal(self.objective.lnprior(), np.log(0.1) + 1)
def test_objective_pickle(self):
# can you pickle the objective function?
pkl = pickle.dumps(self.objective)
pickle.loads(pkl)
# check the ForkingPickler as well.
if hasattr(ForkingPickler, 'dumps'):
pkl = ForkingPickler.dumps(self.objective)
pickle.loads(pkl)
# can you pickle with an extra function present?
self.objective.lnprob_extra = lnprob_extra
pkl = pickle.dumps(self.objective)
pickle.loads(pkl)
# check the ForkingPickler as well.
if hasattr(ForkingPickler, 'dumps'):
pkl = ForkingPickler.dumps(self.objective)
pickle.loads(pkl)
def test_transform_pickle(self):
# can you pickle the Transform object?
pkl = pickle.dumps(Transform('logY'))
pickle.loads(pkl)
def test_transform(self):
pth = os.path.dirname(os.path.abspath(__file__))
fname = os.path.join(pth, 'c_PLP0011859_q.txt')
data = ReflectDataset(fname)
t = Transform('logY')
yt, et = t(data.x, data.y, y_err=data.y_err)
assert_equal(yt, np.log10(data.y))
yt, _ = t(data.x, data.y, y_err=None)
assert_equal(yt, np.log10(data.y))
EPy, EPe = EP.EPlog10(data.y, data.y_err)
assert_equal(yt, EPy)
assert_equal(et, EPe)
def test_lnsigma(self):
# check that lnsigma works correctly
def lnprior(theta, x, y, yerr):
m, b, lnf = theta
if -5.0 < m < 0.5 and 0.0 < b < 10.0 and -10.0 < lnf < 1.0:
return 0.0
return -np.inf
def lnlike(theta, x, y, yerr):
m, b, lnf = theta
model = m * x + b
inv_sigma2 = 1.0 / (yerr**2 + model**2 * np.exp(2 * lnf))
print(inv_sigma2)
return -0.5 * (np.sum((y - model)**2 * inv_sigma2 -
np.log(inv_sigma2)))
x, y, yerr, _ = self.data.data
theta = [self.m_true, self.b_true, np.log(self.f_true)]
bo = BaseObjective(theta,
lnlike,
lnprior=lnprior,
fcn_args=(x, y, yerr))
lnsigma = Parameter(np.log(self.f_true),
'lnsigma',
bounds=(-10, 1),
vary=True)
self.objective.setp(np.array([self.b_true, self.m_true]))
self.objective.lnsigma = lnsigma
assert_allclose(self.objective.lnlike(), bo.lnlike())
def test_base_emcee(self):
# check that the base objective works against the emcee example.
def lnprior(theta, x, y, yerr):
m, b, lnf = theta
if -5.0 < m < 0.5 and 0.0 < b < 10.0 and -10.0 < lnf < 1.0:
return 0.0
return -np.inf
def lnlike(theta, x, y, yerr):
m, b, lnf = theta
model = m * x + b
inv_sigma2 = 1.0 / (yerr**2 + model**2 * np.exp(2 * lnf))
return -0.5 * (np.sum((y - model)**2 * inv_sigma2 -
np.log(inv_sigma2)))
x, y, yerr, _ = self.data.data
theta = [self.m_true, self.b_true, np.log(self.f_true)]
bo = BaseObjective(theta,
lnlike,
lnprior=lnprior,
fcn_args=(x, y, yerr))
# test that the wrapper gives the same lnlike as the direct function
assert_almost_equal(bo.lnlike(theta), lnlike(theta, x, y, yerr))
assert_almost_equal(bo.lnlike(theta), -bo.nll(theta))
assert_almost_equal(bo.nll(theta), 12.8885352412)
# Find the maximum likelihood value.
result = minimize(bo.nll, theta)
# for repeatable sampling
np.random.seed(1)
ndim, nwalkers = 3, 100
pos = [
result["x"] + 1e-4 * np.random.randn(ndim) for i in range(nwalkers)
]
sampler = emcee.EnsembleSampler(nwalkers, ndim, bo.lnprob)
sampler.run_mcmc(pos, 800, rstate0=np.random.get_state())
burnin = 200
samples = sampler.chain[:, burnin:, :].reshape((-1, ndim))
samples[:, 2] = np.exp(samples[:, 2])
m_mc, b_mc, f_mc = map(
lambda v: (v[1], v[2] - v[1], v[1] - v[0]),
zip(*np.percentile(samples, [16, 50, 84], axis=0)))
assert_allclose(m_mc, (-1.0071664, 0.0809444, 0.0784894), rtol=0.04)
assert_allclose(b_mc, (4.5428107, 0.3549174, 0.3673304), rtol=0.04)
assert_allclose(f_mc, (0.4610898, 0.0823304, 0.0640812), rtol=0.06)
# # smoke test for covariance matrix
bo.parameters = np.array(result['x'])
covar1 = bo.covar()
uncertainties = np.sqrt(np.diag(covar1))
# covariance from objective._covar should be almost equal to
# the covariance matrix from sampling
covar2 = np.cov(samples.T)
assert_almost_equal(np.sqrt(np.diag(covar2))[:2], uncertainties[:2], 2)
# check covariance of self.objective
# TODO
var_arr = result['x'][:]
var_arr[0], var_arr[1], var_arr[2] = var_arr[2], var_arr[1], var_arr[0]
# assert_(self.objective.data.weighted)
# self.objective.parameters.pvals = var_arr
# covar3 = self.objective.covar()
# uncertainties3 = np.sqrt(np.diag(covar3))
# assert_almost_equal(uncertainties3, uncertainties)
# assert(False)
def test_covar(self):
# checks objective.covar against optimize.least_squares covariance.
path = os.path.dirname(os.path.abspath(__file__))
theoretical = np.loadtxt(os.path.join(path, 'gauss_data.txt'))
xvals, yvals, evals = np.hsplit(theoretical, 3)
xvals = xvals.flatten()
yvals = yvals.flatten()
evals = evals.flatten()
p0 = np.array([0.1, 20., 0.1, 0.1])
names = ['bkg', 'A', 'x0', 'width']
bounds = [(-1, 1), (0, 30), (-5., 5.), (0.001, 2)]
params = Parameters(name="gauss_params")
for p, name, bound in zip(p0, names, bounds):
param = Parameter(p, name=name)
param.range(*bound)
param.vary = True
params.append(param)
model = Model(params, fitfunc=gauss)
data = Data1D((xvals, yvals, evals))
objective = Objective(model, data)
# first calculate least_squares jac/hess/covariance matrices
res = least_squares(objective.residuals,
np.array(params),
jac='3-point')
hess_least_squares = np.matmul(res.jac.T, res.jac)
covar_least_squares = np.linalg.inv(hess_least_squares)
# now calculate corresponding matrices by hand, to see if the approach
# concurs with least_squares
objective.setp(res.x)
_pvals = np.array(res.x)
def residuals_scaler(vals):
return np.squeeze(objective.residuals(_pvals * vals))
jac = approx_derivative(residuals_scaler, np.ones_like(_pvals))
hess = np.matmul(jac.T, jac)
covar = np.linalg.inv(hess)
covar = covar * np.atleast_2d(_pvals) * np.atleast_2d(_pvals).T
assert_allclose(covar, covar_least_squares)
# check that objective.covar corresponds to the least_squares
# covariance matrix
objective.setp(res.x)
_pvals = np.array(res.x)
covar_objective = objective.covar()
assert_allclose(covar_objective, covar_least_squares)
# now see what happens with a parameter that has no effect on residuals
param = Parameter(1.234, name='dummy')
param.vary = True
params.append(param)
from pytest import raises
with raises(LinAlgError):
objective.covar()
class TestFitterGauss(object):
# Test CurveFitter with a noisy gaussian, weighted and unweighted, to see
# if the parameters and uncertainties come out correct
@pytest.fixture(autouse=True)
def setup_method(self, tmpdir):
self.path = os.path.dirname(os.path.abspath(__file__))
self.tmpdir = tmpdir.strpath
theoretical = np.loadtxt(os.path.join(self.path, 'gauss_data.txt'))
xvals, yvals, evals = np.hsplit(theoretical, 3)
xvals = xvals.flatten()
yvals = yvals.flatten()
evals = evals.flatten()
# these best weighted values and uncertainties obtained with Igor
self.best_weighted = [-0.00246095, 19.5299, -8.28446e-2, 1.24692]
self.best_weighted_errors = [0.0220313708486, 1.12879436221,
0.0447659158681, 0.0412022938883]
self.best_weighted_chisqr = 77.6040960351
self.best_unweighted = [-0.10584111872702096, 19.240347049328989,
0.0092623066070940396, 1.501362314145845]
self.best_unweighted_errors = [0.34246565477, 0.689820935208,
0.0411243173041, 0.0693429375282]
self.best_unweighted_chisqr = 497.102084956
self.p0 = np.array([0.1, 20., 0.1, 0.1])
self.names = ['bkg', 'A', 'x0', 'width']
self.bounds = [(-1, 1), (0, 30), (-5., 5.), (0.001, 2)]
self.params = Parameters(name="gauss_params")
for p, name, bound in zip(self.p0, self.names, self.bounds):
param = Parameter(p, name=name)
param.range(*bound)
param.vary = True
self.params.append(param)
self.model = Model(self.params, fitfunc=gauss)
self.data = Data1D((xvals, yvals, evals))
self.objective = Objective(self.model, self.data)
return 0
def test_best_weighted(self):
assert_equal(len(self.objective.varying_parameters()), 4)
self.objective.setp(self.p0)
f = CurveFitter(self.objective, nwalkers=100)
res = f.fit('least_squares', jac='3-point')
output = res.x
assert_almost_equal(output, self.best_weighted, 3)
assert_almost_equal(self.objective.chisqr(),
self.best_weighted_chisqr, 5)
# compare the residuals
res = (self.data.y - self.model(self.data.x)) / self.data.y_err
assert_equal(self.objective.residuals(), res)
# compare objective.covar to the best_weighted_errors
uncertainties = [param.stderr for param in self.params]
assert_allclose(uncertainties, self.best_weighted_errors, rtol=0.005)
# we're also going to try the checkpointing here.
checkpoint = os.path.join(self.tmpdir, 'checkpoint.txt')
# compare samples to best_weighted_errors
np.random.seed(1)
f.sample(steps=101, random_state=1, verbose=False, f=checkpoint)
process_chain(self.objective, f.chain, nburn=50, nthin=10)
uncertainties = [param.stderr for param in self.params]
assert_allclose(uncertainties, self.best_weighted_errors, rtol=0.07)
# test that the checkpoint worked
check_array = np.loadtxt(checkpoint)
check_array = check_array.reshape(101, f._nwalkers, f.nvary)
assert_allclose(check_array, f.chain)
# test loading the checkpoint
chain = load_chain(checkpoint)
assert_allclose(chain, f.chain)
f.initialise('jitter')
f.sample(steps=2, nthin=4, f=checkpoint, verbose=False)
assert_equal(f.chain.shape[0], 2)
# the following test won't work because of emcee/gh226.
# chain = load_chain(checkpoint)
# assert_(chain.shape == f.chain.shape)
# assert_allclose(chain, f.chain)
def test_best_unweighted(self):
self.objective.weighted = False
f = CurveFitter(self.objective, nwalkers=100)
res = f.fit()
output = res.x
assert_almost_equal(self.objective.chisqr(),
self.best_unweighted_chisqr)
assert_almost_equal(output, self.best_unweighted, 5)
# compare the residuals
res = self.data.y - self.model(self.data.x)
assert_equal(self.objective.residuals(), res)
# compare objective._covar to the best_unweighted_errors
uncertainties = np.array([param.stderr for param in self.params])
assert_almost_equal(uncertainties, self.best_unweighted_errors, 3)
class TestObjective(object):
def setup_method(self):
# Choose the "true" parameters.
# Reproducible results!
np.random.seed(123)
self.m_true = -0.9594
self.b_true = 4.294
self.f_true = 0.534
self.m_ls = -1.1040757010910947
self.b_ls = 5.4405552502319505
# Generate some synthetic data from the model.
N = 50
x = np.sort(10 * np.random.rand(N))
y_err = 0.1 + 0.5 * np.random.rand(N)
y = self.m_true * x + self.b_true
y += np.abs(self.f_true * y) * np.random.randn(N)
y += y_err * np.random.randn(N)
self.data = Data1D(data=(x, y, y_err))
self.p = Parameter(self.b_ls, "b") | Parameter(self.m_ls, "m")
self.model = Model(self.p, fitfunc=line)
self.objective = Objective(self.model, self.data)
# want b and m
self.p[0].vary = True
self.p[1].vary = True
mod = np.array([
4.78166609,
4.42364699,
4.16404064,
3.50343504,
3.4257084,
2.93594347,
2.92035638,
2.67533842,
2.28136038,
2.19772983,
1.99295496,
1.93748334,
1.87484436,
1.65161016,
1.44613461,
1.11128101,
1.04584535,
0.86055984,
0.76913963,
0.73906649,
0.73331407,
0.68350418,
0.65216599,
0.59838566,
0.13070299,
0.10749131,
-0.01010195,
-0.10010155,
-0.29495372,
-0.42817431,
-0.43122391,
-0.64637715,
-1.30560686,
-1.32626428,
-1.44835768,
-1.52589881,
-1.56371158,
-2.12048349,
-2.24899179,
-2.50292682,
-2.53576659,
-2.55797996,
-2.60870542,
-2.7074727,
-3.93781479,
-4.12415366,
-4.42313742,
-4.98368609,
-5.38782395,
-5.44077086,
])
self.mod = mod
def test_model(self):
# test that the line data produced by our model is the same as the
# test data
assert_almost_equal(self.model(self.data.x), self.mod)
def test_synthetic_data(self):
# test that we create the correct synthetic data by performing a least
# squares fit on it
assert_(self.data.y_err is not None)
x, y, y_err, _ = self.data.data
A = np.vstack((np.ones_like(x), x)).T
C = np.diag(y_err * y_err)
cov = np.linalg.inv(np.dot(A.T, np.linalg.solve(C, A)))
b_ls, m_ls = np.dot(cov, np.dot(A.T, np.linalg.solve(C, y)))
assert_almost_equal(b_ls, self.b_ls)
assert_almost_equal(m_ls, self.m_ls)
def test_setp(self):
# check that we can set parameters
self.p[0].vary = False
assert_(len(self.objective.varying_parameters()) == 1)
self.objective.setp(np.array([1.23]))
assert_equal(self.p[1].value, 1.23)
self.objective.setp(np.array([1.234, 1.23]))
assert_equal(np.array(self.p), [1.234, 1.23])
def test_pvals(self):
assert_equal(self.objective.parameters.pvals, [self.b_ls, self.m_ls])
self.objective.parameters.pvals = [1, 2]
assert_equal(self.objective.parameters.pvals, [1, 2.0])
def test_logp(self):
self.p[0].range(0, 10)
assert_almost_equal(self.objective.logp(), np.log(0.1))
# logp should set parameters
self.objective.logp([8, 2])
assert_equal(np.array(self.objective.parameters), [8, 2])
# if we supply a value outside the range it should return -inf
assert_equal(self.objective.logp([-1, 2]), -np.inf)
def test_logpost(self):
# http://dan.iel.fm/emcee/current/user/line/
assert_almost_equal(self.objective.logp(), 0)
assert_almost_equal(self.objective.nlpost(), -self.objective.logpost())
# the uncertainties are underestimated in this example...
# amendment factor because dfm emcee example does not include 2pi
amend = 0.5 * self.objective.npoints * np.log(2 * np.pi)
assert_almost_equal(self.objective.logl() + amend, -559.01078135444595)
assert_almost_equal(self.objective.logpost() + amend,
-559.01078135444595)
def test_prior_transform(self):
self.p[0].bounds = PDF(stats.uniform(-10, 20))
self.p[1].bounds = PDF(stats.norm(loc=5, scale=10))
x = self.objective.prior_transform([0.1, 0.9])
assert_allclose(
x,
stats.uniform.ppf(0.1, -10, 20),
stats.norm.ppf(0.9, loc=5, scale=10),
)
def test_chisqr(self):
assert_almost_equal(self.objective.chisqr(), 1231.1096772954229)
def test_residuals(self):
# weighted, with and without transform
assert_almost_equal(
self.objective.residuals(),
(self.data.y - self.mod) / self.data.y_err,
)
objective = Objective(self.model,
self.data,
transform=Transform("lin"))
assert_almost_equal(objective.residuals(),
(self.data.y - self.mod) / self.data.y_err)
# unweighted, with and without transform
objective = Objective(self.model, self.data, use_weights=False)
assert_almost_equal(objective.residuals(), self.data.y - self.mod)
objective = Objective(
self.model,
self.data,
use_weights=False,
transform=Transform("lin"),
)
assert_almost_equal(objective.residuals(), self.data.y - self.mod)
def test_masked_dataset(self):
residuals = self.objective.residuals()
mask = np.full_like(self.objective.data.y, True, bool)
mask[1] = False
self.objective.data.mask = mask
assert_equal(self.objective.residuals().size, residuals.size - 1)
def test_logp_extra(self):
original_logl = self.objective.logl()
self.objective.logp_extra = logp_extra
assert_almost_equal(self.objective.logl(), original_logl + 1)
def test_objective_pickle(self):
# can you pickle the objective function?
pkl = pickle.dumps(self.objective)
pickle.loads(pkl)
# check the ForkingPickler as well.
if hasattr(ForkingPickler, "dumps"):
pkl = ForkingPickler.dumps(self.objective)
pickle.loads(pkl)
# can you pickle with an extra function present?
self.objective.logp_extra = logp_extra
pkl = pickle.dumps(self.objective)
pickle.loads(pkl)
# check the ForkingPickler as well.
if hasattr(ForkingPickler, "dumps"):
pkl = ForkingPickler.dumps(self.objective)
pickle.loads(pkl)
def test_transform_pickle(self):
# can you pickle the Transform object?
pkl = pickle.dumps(Transform("logY"))
pickle.loads(pkl)
def test_transform(self):
pth = os.path.dirname(os.path.abspath(__file__))
fname = os.path.join(pth, "c_PLP0011859_q.txt")
data = ReflectDataset(fname)
t = Transform("logY")
yt, et = t(data.x, data.y, y_err=data.y_err)
assert_equal(yt, np.log10(data.y))
yt, _ = t(data.x, data.y, y_err=None)
assert_equal(yt, np.log10(data.y))
EPy, EPe = EP.EPlog10(data.y, data.y_err)
assert_equal(yt, EPy)
assert_equal(et, EPe)
def test_repr_transform(self):
p = Transform(None)
q = eval(repr(p))
assert p.form == q.form
p = Transform("logY")
q = eval(repr(p))
assert p.form == q.form
def test_lnsigma(self):
# check that lnsigma works correctly, by using the emcee line fit
# example
def logp(theta, x, y, yerr):
m, b, lnf = theta
if -5.0 < m < 0.5 and 0.0 < b < 10.0 and -10.0 < lnf < 1.0:
return 0.0
return -np.inf
def logl(theta, x, y, yerr):
m, b, lnf = theta
model = m * x + b
inv_sigma2 = 1.0 / (yerr**2 + model**2 * np.exp(2 * lnf))
print(inv_sigma2)
return -0.5 * (np.sum((y - model)**2 * inv_sigma2 -
np.log(inv_sigma2)))
x, y, yerr, _ = self.data.data
theta = [self.m_true, self.b_true, np.log(self.f_true)]
bo = BaseObjective(theta, logl, logp=logp, fcn_args=(x, y, yerr))
lnsigma = Parameter(np.log(self.f_true),
"lnsigma",
bounds=(-10, 1),
vary=True)
self.objective.setp(np.array([self.b_true, self.m_true]))
self.objective.lnsigma = lnsigma
# amendment factor because dfm emcee example does not include 2pi
amend = 0.5 * self.objective.npoints * np.log(2 * np.pi)
assert_allclose(self.objective.logl() + amend, bo.logl())
def test_base_emcee(self):
# check that the base objective works against the emcee example.
def logp(theta, x, y, yerr):
m, b, lnf = theta
if -5.0 < m < 0.5 and 0.0 < b < 10.0 and -10.0 < lnf < 1.0:
return 0.0
return -np.inf
def logl(theta, x, y, yerr):
m, b, lnf = theta
model = m * x + b
inv_sigma2 = 1.0 / (yerr**2 + model**2 * np.exp(2 * lnf))
return -0.5 * (np.sum((y - model)**2 * inv_sigma2 -
np.log(inv_sigma2)))
x, y, yerr, _ = self.data.data
theta = [self.m_true, self.b_true, np.log(self.f_true)]
bo = BaseObjective(theta, logl, logp=logp, fcn_args=(x, y, yerr))
# test that the wrapper gives the same logl as the direct function
assert_almost_equal(bo.logl(theta), logl(theta, x, y, yerr))
assert_almost_equal(bo.logl(theta), -bo.nll(theta))
assert_almost_equal(bo.nll(theta), 12.8885352412)
# Find the maximum likelihood value.
result = minimize(bo.nll, theta)
# for repeatable sampling
np.random.seed(1)
ndim, nwalkers = 3, 100
pos = [
result["x"] + 1e-4 * np.random.randn(ndim) for i in range(nwalkers)
]
sampler = emcee.EnsembleSampler(nwalkers, ndim, bo.logpost)
state = emcee.State(pos, random_state=np.random.get_state())
sampler.run_mcmc(state, 800)
burnin = 200
samples = sampler.get_chain()[burnin:, :, :].reshape((-1, ndim))
samples[:, 2] = np.exp(samples[:, 2])
m_mc, b_mc, f_mc = map(
lambda v: (v[1], v[2] - v[1], v[1] - v[0]),
zip(*np.percentile(samples, [16, 50, 84], axis=0)),
)
assert_allclose(m_mc, (-1.0071664, 0.0809444, 0.0784894), rtol=0.04)
assert_allclose(b_mc, (4.5428107, 0.3549174, 0.3673304), rtol=0.04)
assert_allclose(f_mc, (0.4610898, 0.0823304, 0.0640812), rtol=0.06)
# # smoke test for covariance matrix
bo.parameters = np.array(result["x"])
covar1 = bo.covar()
uncertainties = np.sqrt(np.diag(covar1))
# covariance from objective._covar should be almost equal to
# the covariance matrix from sampling
covar2 = np.cov(samples.T)
assert_almost_equal(np.sqrt(np.diag(covar2))[:2], uncertainties[:2], 2)
# check covariance of self.objective
# TODO
var_arr = result["x"][:]
var_arr[0], var_arr[1], var_arr[2] = var_arr[2], var_arr[1], var_arr[0]
# assert_(self.objective.data.weighted)
# self.objective.parameters.pvals = var_arr
# covar3 = self.objective.covar()
# uncertainties3 = np.sqrt(np.diag(covar3))
# assert_almost_equal(uncertainties3, uncertainties)
# assert(False)
def test_covar(self):
# checks objective.covar against optimize.least_squares covariance.
path = os.path.dirname(os.path.abspath(__file__))
theoretical = np.loadtxt(os.path.join(path, "gauss_data.txt"))
xvals, yvals, evals = np.hsplit(theoretical, 3)
xvals = xvals.flatten()
yvals = yvals.flatten()
evals = evals.flatten()
p0 = np.array([0.1, 20.0, 0.1, 0.1])
names = ["bkg", "A", "x0", "width"]
bounds = [(-1, 1), (0, 30), (-5.0, 5.0), (0.001, 2)]
params = Parameters(name="gauss_params")
for p, name, bound in zip(p0, names, bounds):
param = Parameter(p, name=name)
param.range(*bound)
param.vary = True
params.append(param)
model = Model(params, fitfunc=gauss)
data = Data1D((xvals, yvals, evals))
objective = Objective(model, data)
# first calculate least_squares jac/hess/covariance matrices
res = least_squares(objective.residuals,
np.array(params),
jac="3-point")
hess_least_squares = np.matmul(res.jac.T, res.jac)
covar_least_squares = np.linalg.inv(hess_least_squares)
# now calculate corresponding matrices by hand, to see if the approach
# concurs with least_squares
objective.setp(res.x)
_pvals = np.array(res.x)
def residuals_scaler(vals):
return np.squeeze(objective.residuals(_pvals * vals))
jac = approx_derivative(residuals_scaler, np.ones_like(_pvals))
hess = np.matmul(jac.T, jac)
covar = np.linalg.inv(hess)
covar = covar * np.atleast_2d(_pvals) * np.atleast_2d(_pvals).T
assert_allclose(covar, covar_least_squares)
# check that objective.covar corresponds to the least_squares
# covariance matrix, J.T x J
objective.setp(res.x)
covar_objective = objective.covar()
assert_allclose(covar_objective, covar_least_squares)
# sometimes the residuals method may not be usable, see if
# objective.covar calculated from a scalar works
objective.setp(res.x)
covar_objective = objective.covar("nll")
assert_allclose(
np.sqrt(np.diag(covar_objective)),
np.sqrt(np.diag(covar_least_squares)),
rtol=0.08,
)
# now see what happens with a parameter that has no effect on residuals
param = Parameter(1.234, name="dummy")
param.vary = True
params.append(param)
from pytest import raises
with raises(LinAlgError):
objective.covar()
@pytest.mark.xfail
def test_pymc3(self):
# test objective logl against pymc3
# don't run this test if pymc3 is not installed
try:
import pymc3 as pm
except ImportError:
return
logl = self.objective.logl()
from refnx.analysis import pymc3_model
from refnx.analysis.objective import _to_pymc3_distribution
mod = pymc3_model(self.objective)
with mod:
pymc_logl = mod.logp({
"p0": self.p[0].value,
"p1": self.p[1].value
})
assert_allclose(logl, pymc_logl)
# now check some of the distributions
with pm.Model():
p = Parameter(1, bounds=(1, 10))
d = _to_pymc3_distribution("a", p)
assert_almost_equal(d.distribution.logp(2).eval(), p.logp(2))
assert_(np.isneginf(d.distribution.logp(-1).eval()))
q = Parameter(1, bounds=PDF(stats.uniform(1, 9)))
d = _to_pymc3_distribution("b", q)
assert_almost_equal(d.distribution.logp(2).eval(), q.logp(2))
assert_(np.isneginf(d.distribution.logp(-1).eval()))
p = Parameter(1, bounds=PDF(stats.uniform))
d = _to_pymc3_distribution("c", p)
assert_almost_equal(d.distribution.logp(0.5).eval(), p.logp(0.5))
p = Parameter(1, bounds=PDF(stats.norm))
d = _to_pymc3_distribution("d", p)
assert_almost_equal(d.distribution.logp(2).eval(), p.logp(2))
p = Parameter(1, bounds=PDF(stats.norm(1, 10)))
d = _to_pymc3_distribution("e", p)
assert_almost_equal(d.distribution.logp(2).eval(), p.logp(2))