def test_cb_integral():
obs = zfit.Space('x', limits=bounds)
mu_ = zfit.Parameter('mu_cb5', mu)
sigma_ = zfit.Parameter('sigma_cb5', sigma)
alphal_ = zfit.Parameter('alphal_cb5', alphal)
nl_ = zfit.Parameter('nl_cb5', nl)
cbl = CrystalBall(obs=obs, mu=mu_, sigma=sigma_, alpha=alphal_, n=nl_)
int_limits = (-1, 3)
integral_numeric = cbl.numeric_integrate(limits=int_limits,
norm_range=False)
integral = cbl.analytic_integrate(limits=int_limits, norm_range=False)
integral_numeric = zfit.run(integral_numeric)
integral = zfit.run(integral)
assert pytest.approx(integral_numeric, integral, 1e-5)
def test_cb_integral():
obs = zfit.Space("x", limits=bounds)
mu_ = zfit.Parameter("mu_cb5", mu)
sigma_ = zfit.Parameter("sigma_cb5", sigma)
alphal_ = zfit.Parameter("alphal_cb5", alphal)
nl_ = zfit.Parameter("nl_cb5", nl)
cbl = CrystalBall(obs=obs, mu=mu_, sigma=sigma_, alpha=alphal_, n=nl_)
int_limits = (-1, 3)
integral_numeric = cbl.numeric_integrate(limits=int_limits, norm=False)
integral = cbl.analytic_integrate(limits=int_limits, norm=False)
integral_numeric = zfit.run(integral_numeric)
integral = zfit.run(integral)
assert pytest.approx(integral_numeric, integral, 1e-5)
rnd_limits = sorted(np.random.uniform(*bounds, 13))
integrals = []
for low, up in zip(rnd_limits[:-1], rnd_limits[1:]):
integrals.append(cbl.integrate((low, up), norm=False))
integral = np.sum(integrals)
integral_full = zfit.run(cbl.integrate(bounds, norm=False))
assert pytest.approx(integral_full, integral)
def test_cb_dcb():
obs = zfit.Space('x', limits=bounds)
mu_ = zfit.Parameter('mu_cb5', mu)
sigma_ = zfit.Parameter('sigma_cb5', sigma)
alphal_ = zfit.Parameter('alphal_cb5', alphal)
nl_ = zfit.Parameter('nl_cb5', nl)
alphar_ = zfit.Parameter('alphar_cb5', alphar)
nr_ = zfit.Parameter('nr_cb5', nr)
cbl = CrystalBall(obs=obs, mu=mu_, sigma=sigma_, alpha=alphal_, n=nl_)
cbr = CrystalBall(obs=obs, mu=mu_, sigma=sigma_, alpha=-alphar_, n=nr_)
dcb = DoubleCB(obs=obs,
mu=mu_,
sigma=sigma_,
alphal=alphal_,
nl=nl_,
alphar=alphar_,
nr=nr_)
sample_testing(cbl)
sample_testing(cbr)
sample_testing(dcb)
x = np.random.normal(mu, sigma, size=10000)
probsl = eval_testing(cbl, x)
probsr = eval_testing(cbr, x)
assert not any(np.isnan(probsl))
assert not any(np.isnan(probsr))
probsl_scipy = crystalball.pdf(x, beta=alphal, m=nl, loc=mu, scale=sigma)
probsr_scipy = crystalball.pdf(-x, beta=alphar, m=nr, loc=mu, scale=sigma)
ratio_l = probsl_scipy / probsl
ratio_r = probsr_scipy / probsr
assert np.allclose(ratio_l, ratio_l[0])
assert np.allclose(ratio_r, ratio_r[0])
kwargs = dict(limits=(-5.0, mu), norm_range=lbounds)
intl = cbl.integrate(**kwargs) - dcb.integrate(**kwargs)
assert pytest.approx(intl.numpy()) == 0.
intl = cbr.integrate(**kwargs) - dcb.integrate(**kwargs)
assert pytest.approx(intl.numpy()) != 0
kwargs = dict(limits=(mu, 2.0), norm_range=rbounds)
intr = cbr.integrate(**kwargs) - dcb.integrate(**kwargs)
assert pytest.approx(intr.numpy()) == 0.
intr = cbl.integrate(**kwargs) - dcb.integrate(**kwargs)
assert pytest.approx(intr.numpy()) != 0.
xl = x[x <= mu]
xr = x[x > mu]
probs_dcb_l = eval_testing(dcb, xl)
probs_dcb_r = eval_testing(dcb, xr)
probsl_scipy = crystalball.pdf(xl, beta=alphal, m=nl, loc=mu, scale=sigma)
probsr_scipy = crystalball.pdf(-xr, beta=alphar, m=nr, loc=mu, scale=sigma)
ratio_l = probsl_scipy / probs_dcb_l
ratio_r = probsr_scipy / probs_dcb_r
assert np.allclose(ratio_l, ratio_l[0])
assert np.allclose(ratio_r, ratio_r[0])
def test_cb_dcb():
obs = zfit.Space("x", limits=bounds)
mu_ = zfit.Parameter("mu_cb5", mu)
sigma_ = zfit.Parameter("sigma_cb5", sigma)
alphal_ = zfit.Parameter("alphal_cb5", alphal)
nl_ = zfit.Parameter("nl_cb5", nl)
alphar_ = zfit.Parameter("alphar_cb5", alphar)
nr_ = zfit.Parameter("nr_cb5", nr)
cbl = CrystalBall(obs=obs, mu=mu_, sigma=sigma_, alpha=alphal_, n=nl_)
cbr = CrystalBall(obs=obs, mu=mu_, sigma=sigma_, alpha=-alphar_, n=nr_)
dcb = DoubleCB(obs=obs,
mu=mu_,
sigma=sigma_,
alphal=alphal_,
nl=nl_,
alphar=alphar_,
nr=nr_)
sample_testing(cbl)
sample_testing(cbr)
sample_testing(dcb)
x = np.random.normal(mu, sigma, size=10000)
probsl = eval_testing(cbl, x)
probsr = eval_testing(cbr, x)
assert not any(np.isnan(probsl))
assert not any(np.isnan(probsr))
probsl_scipy = crystalball.pdf(x, beta=alphal, m=nl, loc=mu, scale=sigma)
probsr_scipy = crystalball.pdf(-x + 2 * mu,
beta=alphar,
m=nr,
loc=mu,
scale=sigma)
# We take the ration as the normalization is not fixed
ratio_l = probsl_scipy / probsl
ratio_r = probsr_scipy / probsr
assert np.allclose(ratio_l, ratio_l[0])
assert np.allclose(ratio_r, ratio_r[0])
kwargs = dict(limits=(-5.0, mu), norm_range=lbounds)
intl = cbl.integrate(**kwargs) - dcb.integrate(**kwargs)
assert pytest.approx(intl.numpy(), abs=1e-3) == 0.0
intl = cbr.integrate(**kwargs) - dcb.integrate(**kwargs)
assert pytest.approx(intl.numpy(), abs=1e-3) != 0
# TODO: update test to fixed DCB integral
kwargs = dict(limits=(mu, 2.0), norm_range=rbounds)
dcb_integr1 = dcb.integrate(**kwargs)
intr = cbr.integrate(**kwargs) - dcb_integr1
assert pytest.approx(intr.numpy(), abs=1e-3) == 0.0
intr = cbl.integrate(**kwargs) - dcb.integrate(**kwargs)
assert pytest.approx(intr.numpy(), abs=1e-3) != 0.0
xl = x[x <= mu]
xr = x[x > mu]
probs_dcb_l = eval_testing(dcb, xl)
probs_dcb_r = eval_testing(dcb, xr)
probsl_scipy = crystalball.pdf(xl, beta=alphal, m=nl, loc=mu, scale=sigma)
probsr_scipy = crystalball.pdf(-xr + 2 * mu,
beta=alphar,
m=nr,
loc=mu,
scale=sigma)
ratio_l = probsl_scipy / probs_dcb_l
ratio_r = probsr_scipy / probs_dcb_r
assert np.allclose(ratio_l, ratio_l[0])
assert np.allclose(ratio_r, ratio_r[0])
rnd_limits = sorted(np.random.uniform(*bounds, 130))
integrals = []
for low, up in zip(rnd_limits[:-1], rnd_limits[1:]):
integrals.append(dcb.integrate((low, up), norm=False))
integral = np.sum(integrals)
integral_full = zfit.run(dcb.integrate((bounds[0], up), norm=False))
assert pytest.approx(integral_full, integral)