def test_derived_observables():
# Construct pseudo Obs with random shape
test_obs = pe.pseudo_Obs(2, 0.1 * (1 + np.random.rand()), 't',
int(1000 * (1 + np.random.rand())))
# Check if autograd and numgrad give the same result
d_Obs_ad = pe.derived_observable(
lambda x, **kwargs: x[0] * x[1] * np.sin(x[0] * x[1]),
[test_obs, test_obs])
d_Obs_ad.gamma_method()
d_Obs_fd = pe.derived_observable(
lambda x, **kwargs: x[0] * x[1] * np.sin(x[0] * x[1]),
[test_obs, test_obs],
num_grad=True)
d_Obs_fd.gamma_method()
assert d_Obs_ad.value == d_Obs_fd.value
assert np.abs(4.0 * np.sin(4.0) - d_Obs_ad.value) < 1000 * np.finfo(
np.float64).eps * np.abs(d_Obs_ad.value)
assert np.abs(d_Obs_ad.dvalue - d_Obs_fd.dvalue) < 1000 * np.finfo(
np.float64).eps * d_Obs_ad.dvalue
i_am_one = pe.derived_observable(lambda x, **kwargs: x[0] / x[1],
[d_Obs_ad, d_Obs_ad])
i_am_one.gamma_method()
assert i_am_one.value == 1.0
assert i_am_one.dvalue < 2 * np.finfo(np.float64).eps
assert i_am_one.e_dvalue['t'] <= 2 * np.finfo(np.float64).eps
assert i_am_one.e_ddvalue['t'] <= 2 * np.finfo(np.float64).eps
def test_function_overloading():
a = pe.pseudo_Obs(17, 2.9, 'e1')
b = pe.pseudo_Obs(4, 0.8, 'e1')
fs = [
lambda x: x[0] + x[1], lambda x: x[1] + x[0], lambda x: x[0] - x[1],
lambda x: x[1] - x[0], lambda x: x[0] * x[1], lambda x: x[1] * x[0],
lambda x: x[0] / x[1], lambda x: x[1] / x[0], lambda x: np.exp(x[0]),
lambda x: np.sin(x[0]), lambda x: np.cos(x[0]), lambda x: np.tan(x[0]),
lambda x: np.log(x[0]), lambda x: np.sqrt(np.abs(x[0])),
lambda x: np.sinh(x[0]), lambda x: np.cosh(x[0]),
lambda x: np.tanh(x[0])
]
for i, f in enumerate(fs):
t1 = f([a, b])
t2 = pe.derived_observable(f, [a, b])
c = t2 - t1
assert c.is_zero()
assert np.log(np.exp(b)) == b
assert np.exp(np.log(b)) == b
assert np.sqrt(b**2) == b
assert np.sqrt(b)**2 == b
np.arcsin(1 / b)
np.arccos(1 / b)
np.arctan(1 / b)
np.arctanh(1 / b)
np.sinc(1 / b)
def test_overloaded_functions():
funcs = [
np.exp, np.log, np.sin, np.cos, np.tan, np.sinh, np.cosh, np.arcsinh,
np.arccosh
]
deriv = [
np.exp, lambda x: 1 / x, np.cos, lambda x: -np.sin(x),
lambda x: 1 / np.cos(x)**2, np.cosh, np.sinh,
lambda x: 1 / np.sqrt(x**2 + 1), lambda x: 1 / np.sqrt(x**2 - 1)
]
val = 3 + 0.5 * np.random.rand()
dval = 0.3 + 0.4 * np.random.rand()
test_obs = pe.pseudo_Obs(val, dval, 't',
int(1000 * (1 + np.random.rand())))
for i, item in enumerate(funcs):
ad_obs = item(test_obs)
fd_obs = pe.derived_observable(lambda x, **kwargs: item(x[0]),
[test_obs],
num_grad=True)
ad_obs.gamma_method(S=0.01)
assert np.max((ad_obs.deltas['t'] - fd_obs.deltas['t']) /
ad_obs.deltas['t']) < 1e-8, item.__name__
assert np.abs(
(ad_obs.value - item(val)) / ad_obs.value) < 1e-10, item.__name__
assert np.abs(ad_obs.dvalue -
dval * np.abs(deriv[i](val))) < 1e-6, item.__name__
def test_man_grad():
a = pe.pseudo_Obs(17, 2.9, 'e1')
b = pe.pseudo_Obs(4, 0.8, 'e1')
fs = [
lambda x: x[0] + x[1], lambda x: x[1] + x[0], lambda x: x[0] - x[1],
lambda x: x[1] - x[0], lambda x: x[0] * x[1], lambda x: x[1] * x[0],
lambda x: x[0] / x[1], lambda x: x[1] / x[0], lambda x: np.exp(x[0]),
lambda x: np.sin(x[0]), lambda x: np.cos(x[0]), lambda x: np.tan(x[0]),
lambda x: np.log(x[0]), lambda x: np.sqrt(x[0]),
lambda x: np.sinh(x[0]), lambda x: np.cosh(x[0]),
lambda x: np.tanh(x[0])
]
for i, f in enumerate(fs):
t1 = f([a, b])
t2 = pe.derived_observable(f, [a, b])
c = t2 - t1
assert c.value == 0.0, str(i)
assert np.all(np.abs(c.deltas['e1']) < 1e-14), str(i)
def test_overloading(n):
# Construct pseudo Obs with random shape
obs_list = []
for i in range(5):
value = np.abs(np.random.normal(5, 2)) + 2.0
dvalue = np.abs(np.random.normal(0, 0.1)) + 1e-5
obs_list.append(pe.pseudo_Obs(value, dvalue, 't', 2000))
# Test if the error is processed correctly
def f(x):
return x[0] * x[1] + np.sin(x[2]) * np.exp(
x[3] / x[1] / x[0]) - np.sqrt(2) / np.cosh(x[4] / x[0])
o_obs = f(obs_list)
d_obs = pe.derived_observable(f, obs_list)
assert np.max(
np.abs((o_obs.deltas['t'] - d_obs.deltas['t']) /
o_obs.deltas['t'])) < 1e-7, str(obs_list)
assert np.abs((o_obs.value - d_obs.value) / o_obs.value) < 1e-10
def fit_general(x, y, func, silent=False, **kwargs):
"""Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
Plausibility of the results should be checked. To control the numerical differentiation
the kwargs of numdifftools.step_generators.MaxStepGenerator can be used.
func has to be of the form
def func(a, x):
y = a[0] + a[1] * x + a[2] * np.sinh(x)
return y
y has to be a list of Obs, the dvalues of the Obs are used as yerror for the fit.
x can either be a list of floats in which case no xerror is assumed, or
a list of Obs, where the dvalues of the Obs are used as xerror for the fit.
Keyword arguments
-----------------
silent -- If true all output to the console is omitted (default False).
initial_guess -- can provide an initial guess for the input parameters. Relevant for non-linear fits
with many parameters.
"""
if not callable(func):
raise TypeError('func has to be a function.')
for i in range(10):
try:
func(np.arange(i), 0)
except:
pass
else:
break
n_parms = i
if not silent:
print('Fit with', n_parms, 'parameters')
global print_output, beta0
print_output = 1
if 'initial_guess' in kwargs:
beta0 = kwargs.get('initial_guess')
if len(beta0) != n_parms:
raise Exception('Initial guess does not have the correct length.')
else:
beta0 = np.arange(n_parms)
if len(x) != len(y):
raise Exception('x and y have to have the same length')
if all(isinstance(n, pe.Obs) for n in x):
obs = x + y
x_constants = None
xerr = [o.dvalue for o in x]
yerr = [o.dvalue for o in y]
elif all(isinstance(n, float) or isinstance(n, int)
for n in x) or isinstance(x, np.ndarray):
obs = y
x_constants = x
xerr = None
yerr = [o.dvalue for o in y]
else:
raise Exception('Unsupported types for x')
def do_the_fit(obs, **kwargs):
global print_output, beta0
func = kwargs.get('function')
yerr = kwargs.get('yerr')
length = len(yerr)
xerr = kwargs.get('xerr')
if length == len(obs):
assert 'x_constants' in kwargs
data = RealData(kwargs.get('x_constants'), obs, sy=yerr)
fit_type = 2
elif length == len(obs) // 2:
data = RealData(obs[:length], obs[length:], sx=xerr, sy=yerr)
fit_type = 0
else:
raise Exception('x and y do not fit together.')
model = Model(func)
odr = ODR(data, model, beta0, partol=np.finfo(np.float64).eps)
odr.set_job(fit_type=fit_type, deriv=1)
output = odr.run()
if print_output and not silent:
print(*output.stopreason)
print('chisquare/d.o.f.:', output.res_var)
print_output = 0
beta0 = output.beta
return output.beta[kwargs.get('n')]
res = []
for n in range(n_parms):
res.append(
pe.derived_observable(do_the_fit,
obs,
function=func,
xerr=xerr,
yerr=yerr,
x_constants=x_constants,
num_grad=True,
n=n,
**kwargs))
return res