def calculate_normalised_xsection(inputs,
bin_widths,
normalise_to_one=False,
covariance_matrix=None,
inputMC_covariance_matrix=None):
"""
Calculates normalised average x-section for each bin: 1/N *1/bin_width sigma_i
There are two ways to calculate this
1) N = sum(sigma_i)
2) N = sum(sigma_i/bin_width)
The latter one will normalise the total distribution to 1
@param inputs: list of value-error pairs
@param bin_widths: bin widths of the inputs
"""
values = [u.ufloat(i[0], i[1]) for i in inputs]
norm_cov_matrix = None
norm_corr_matrix = None
inputMC_norm_cov_matrix = None
if not covariance_matrix is None and not normalise_to_one:
values_correlated = u.correlated_values(
[v.nominal_value for v in values], covariance_matrix.tolist())
norm = sum(values_correlated)
norm_values_correlated = []
# Loop over unfolded number of events with correlated uncertainties
# And corresponding bin width
# Calculate normalised cross section, with correctly correlated uncertainty
for v, width in zip(values_correlated, bin_widths):
norm_values_correlated.append(v / width / norm)
# Get covariance and correlation matrix for normalised cross section
norm_cov_matrix = matrix(u.covariance_matrix(norm_values_correlated))
norm_corr_matrix = matrix(u.correlation_matrix(norm_values_correlated))
result = [(v.nominal_value, v.std_dev) for v in norm_values_correlated]
# Get Covariance Matrix for input MC
if not inputMC_covariance_matrix is None:
inputMC_values_correlated = u.correlated_values(
[v.nominal_value for v in values],
inputMC_covariance_matrix.tolist())
inputMC_norm = sum(inputMC_values_correlated)
inputMC_norm_values_correlated = []
for v, width in zip(inputMC_values_correlated, bin_widths):
inputMC_norm_values_correlated.append(v / width / inputMC_norm)
inputMC_norm_cov_matrix = matrix(
u.covariance_matrix(inputMC_norm_values_correlated))
else:
normalisation = 0
if normalise_to_one:
normalisation = sum([
value / bin_width
for value, bin_width in zip(values, bin_widths)
])
else:
normalisation = sum(values)
xsections = [(1 / bin_width) * value / normalisation
for value, bin_width in zip(values, bin_widths)]
result = [(xsection.nominal_value, xsection.std_dev)
for xsection in xsections]
return result, norm_cov_matrix, norm_corr_matrix, inputMC_norm_cov_matrix
def test_correlated_values():
"Correlated variables."
u = uncertainties.ufloat((1, 0.1))
cov = uncertainties.covariance_matrix([u])
# "1" is used instead of u.nominal_value because
# u.nominal_value might return a float. The idea is to force
# the new variable u2 to be defined through an integer nominal
# value:
u2, = uncertainties.correlated_values([1], cov)
expr = 2 * u2 # Calculations with u2 should be possible, like with u
####################
# Covariances between output and input variables:
x = ufloat((1, 0.1))
y = ufloat((2, 0.3))
z = -3 * x + y
covs = uncertainties.covariance_matrix([x, y, z])
# "Inversion" of the covariance matrix: creation of new
# variables:
(x_new, y_new, z_new) = uncertainties.correlated_values(
[x.nominal_value, y.nominal_value, z.nominal_value], covs, tags=["x", "y", "z"]
)
# Even the uncertainties should be correctly reconstructed:
assert matrices_close(numpy.array((x, y, z)), numpy.array((x_new, y_new, z_new)))
# ... and the covariances too:
assert matrices_close(numpy.array(covs), numpy.array(uncertainties.covariance_matrix([x_new, y_new, z_new])))
assert matrices_close(numpy.array([z_new]), numpy.array([-3 * x_new + y_new]))
####################
# ... as well as functional relations:
u = ufloat((1, 0.05))
v = ufloat((10, 0.1))
sum_value = u + 2 * v
# Covariance matrices:
cov_matrix = uncertainties.covariance_matrix([u, v, sum_value])
# Correlated variables can be constructed from a covariance matrix, if
# NumPy is available:
(u2, v2, sum2) = uncertainties.correlated_values([x.nominal_value for x in [u, v, sum_value]], cov_matrix)
# matrices_close() is used instead of _numbers_close() because
# it compares uncertainties too:
assert matrices_close(numpy.array([0]), numpy.array([sum2 - (u2 + 2 * v2)]))
def calculate_xsection(inputs,
bin_widths,
luminosity,
efficiency=1.,
covariance_matrix=None,
inputMC_covariance_matrix=None):
'''
BUG: this doesn't work unless the inputs are unfolded!
inputs = list of value-error pairs
luminosity = integrated luminosity of the measurement
'''
abs_cov_matrix = None
abs_corr_matrix = None
inputMC_abs_cov_matrix = None
result = []
add_result = result.append
values = [u.ufloat(i[0], i[1]) for i in inputs]
if not covariance_matrix is None:
values_correlated = u.correlated_values(
[v.nominal_value for v in values], covariance_matrix.tolist())
abs_values_correlated = []
# Loop over unfolded number of events with correlated uncertainties
# And corresponding bin width
# Calculate absolute cross section, with correctly correlated uncertainty
for v, width in zip(values_correlated, bin_widths):
abs_values_correlated.append(v / width / luminosity / efficiency)
# Get covariance and correlation matrix for absolute cross section
abs_cov_matrix = matrix(u.covariance_matrix(abs_values_correlated))
abs_corr_matrix = matrix(u.correlation_matrix(abs_values_correlated))
result = [(v.nominal_value, v.std_dev) for v in abs_values_correlated]
# Get Covariance Matrix for input MC
if not inputMC_covariance_matrix is None:
inputMC_values_correlated = u.correlated_values(
[v.nominal_value for v in values],
inputMC_covariance_matrix.tolist())
inputMC_abs_values_correlated = []
for v, width in zip(inputMC_values_correlated, bin_widths):
inputMC_abs_values_correlated.append(v / width / luminosity /
efficiency)
inputMC_abs_cov_matrix = matrix(
u.covariance_matrix(inputMC_abs_values_correlated))
else:
for valueAndErrors, binWidth in zip(inputs, bin_widths):
value = valueAndErrors[0]
error = valueAndErrors[1]
xsection = value / (luminosity * efficiency * binWidth)
xsection_error = error / (luminosity * efficiency * binWidth)
add_result((xsection, xsection_error))
return result, abs_cov_matrix, abs_corr_matrix, inputMC_abs_cov_matrix
def test_copy():
"Standard copy module integration"
import gc
x = ufloat((3, 0.1))
assert x == x
y = copy.copy(x)
assert x != y
assert not (x == y)
assert y in list(
y.derivatives.keys()) # y must not copy the dependence on x
z = copy.deepcopy(x)
assert x != z
# Copy tests on expressions:
t = x + 2 * z
# t depends on x:
assert x in t.derivatives
# The relationship between the copy of an expression and the
# original variables should be preserved:
t_copy = copy.copy(t)
# Shallow copy: the variables on which t depends are not copied:
assert x in t_copy.derivatives
assert (uncertainties.covariance_matrix(
[t, z]) == uncertainties.covariance_matrix([t_copy, z]))
# However, the relationship between a deep copy and the original
# variables should be broken, since the deep copy created new,
# independent variables:
t_deepcopy = copy.deepcopy(t)
assert x not in t_deepcopy.derivatives
assert (uncertainties.covariance_matrix([t, z]) !=
uncertainties.covariance_matrix([t_deepcopy, z]))
# Test of implementations with weak references:
# Weak references: destroying a variable should never destroy the
# integrity of its copies (which would happen if the copy keeps a
# weak reference to the original, in its derivatives member: the
# weak reference to the original would become invalid):
del x
gc.collect()
assert y in list(y.derivatives.keys())
def calculation_Q_conventional(K, a):
if kontrola_rozmeru(K, a)==False:
return False, False, False
Q = -np.dot(K, a)
Q_covarianceMatrix = covariance_matrix(Q)
Q_correlationMatrix = correlation_matrix(Q)
return Q, Q_covarianceMatrix, Q_correlationMatrix
def test_correlated_values_correlation_mat():
'''
Tests the input of correlated value.
Test through their correlation matrix (instead of the
covariance matrix).
'''
x = ufloat((1, 0.1))
y = ufloat((2, 0.3))
z = -3 * x + y
cov_mat = uncertainties.covariance_matrix([x, y, z])
std_devs = numpy.sqrt(numpy.array(cov_mat).diagonal())
corr_mat = cov_mat / std_devs / std_devs[numpy.newaxis].T
# We make sure that the correlation matrix is indeed diagonal:
assert (corr_mat - corr_mat.T).max() <= 1e-15
# We make sure that there are indeed ones on the diagonal:
assert (corr_mat.diagonal() - 1).max() <= 1e-15
# We try to recover the correlated variables through the
# correlation matrix (not through the covariance matrix):
nominal_values = [v.nominal_value for v in (x, y, z)]
std_devs = [v.std_dev() for v in (x, y, z)]
x2, y2, z2 = uncertainties.correlated_values_norm(
list(zip(nominal_values, std_devs)), corr_mat)
# matrices_close() is used instead of _numbers_close() because
# it compares uncertainties too:
# Test of individual variables:
assert matrices_close(numpy.array([x]), numpy.array([x2]))
assert matrices_close(numpy.array([y]), numpy.array([y2]))
assert matrices_close(numpy.array([z]), numpy.array([z2]))
# Partial correlation test:
assert matrices_close(numpy.array([0]),
numpy.array([z2 - (-3 * x2 + y2)]))
# Test of the full covariance matrix:
assert matrices_close(
numpy.array(cov_mat),
numpy.array(uncertainties.covariance_matrix([x2, y2, z2])))
def test_copy():
"Standard copy module integration"
import gc
x = ufloat((3, 0.1))
assert x == x
y = copy.copy(x)
assert x != y
assert not(x == y)
assert y in y.derivatives.keys() # y must not copy the dependence on x
z = copy.deepcopy(x)
assert x != z
# Copy tests on expressions:
t = x + 2*z
# t depends on x:
assert x in t.derivatives
# The relationship between the copy of an expression and the
# original variables should be preserved:
t_copy = copy.copy(t)
# Shallow copy: the variables on which t depends are not copied:
assert x in t_copy.derivatives
assert (uncertainties.covariance_matrix([t, z]) ==
uncertainties.covariance_matrix([t_copy, z]))
# However, the relationship between a deep copy and the original
# variables should be broken, since the deep copy created new,
# independent variables:
t_deepcopy = copy.deepcopy(t)
assert x not in t_deepcopy.derivatives
assert (uncertainties.covariance_matrix([t, z]) !=
uncertainties.covariance_matrix([t_deepcopy, z]))
# Test of implementations with weak references:
# Weak references: destroying a variable should never destroy the
# integrity of its copies (which would happen if the copy keeps a
# weak reference to the original, in its derivatives member: the
# weak reference to the original would become invalid):
del x
gc.collect()
assert y in y.derivatives.keys()
def test_correlated_values_correlation_mat():
'''
Tests the input of correlated value.
Test through their correlation matrix (instead of the
covariance matrix).
'''
x = ufloat((1, 0.1))
y = ufloat((2, 0.3))
z = -3*x+y
cov_mat = uncertainties.covariance_matrix([x, y, z])
std_devs = numpy.sqrt(numpy.array(cov_mat).diagonal())
corr_mat = cov_mat/std_devs/std_devs[numpy.newaxis].T
# We make sure that the correlation matrix is indeed diagonal:
assert (corr_mat-corr_mat.T).max() <= 1e-15
# We make sure that there are indeed ones on the diagonal:
assert (corr_mat.diagonal()-1).max() <= 1e-15
# We try to recover the correlated variables through the
# correlation matrix (not through the covariance matrix):
nominal_values = [v.nominal_value for v in (x, y, z)]
std_devs = [v.std_dev() for v in (x, y, z)]
x2, y2, z2 = uncertainties.correlated_values_norm(
list(zip(nominal_values, std_devs)), corr_mat)
# matrices_close() is used instead of _numbers_close() because
# it compares uncertainties too:
# Test of individual variables:
assert matrices_close(numpy.array([x]), numpy.array([x2]))
assert matrices_close(numpy.array([y]), numpy.array([y2]))
assert matrices_close(numpy.array([z]), numpy.array([z2]))
# Partial correlation test:
assert matrices_close(numpy.array([0]), numpy.array([z2-(-3*x2+y2)]))
# Test of the full covariance matrix:
assert matrices_close(
numpy.array(cov_mat),
numpy.array(uncertainties.covariance_matrix([x2, y2, z2])))
def calculation_Q_conventional(K, a_out, a):
#pridani vnejsi koncentrace do vektoru koncentraci
a = np.append(a, ufloat(a_out, 0.05 * a_out))
if kontrola_rozmeru(K, a) == False:
return False, False, False
Q = -np.dot(K, a)
Q_covarianceMatrix = covariance_matrix(Q)
Q_correlationMatrix = correlation_matrix(Q)
return Q, Q_covarianceMatrix, Q_correlationMatrix
def calculation_Q_conventional():
K, a = prepare_for_calculation()
# breakpoint()
if np.isscalar(K):
print('Nelze provest vypocet.')
Q = -np.dot(K, a)
Q_covarianceMatrix = covariance_matrix(Q)
Q_correlationMatrix = correlation_matrix(Q)
return Q, Q_covarianceMatrix, Q_correlationMatrix
def linleastsquares(functions, x_values, y_values):
y = unp.nominal_values(y_values)
Z = np.linalg.inv(unc.covariance_matrix(y_values))
A = np.column_stack([f(x_values) for f in functions])
invATA = np.linalg.inv(A.T @ Z @ A)
params = invATA @ A.T @ Z @ y
cov = invATA
return unc.correlated_values(params.flat, cov)
def test_covariances():
"Covariance matrix"
x = ufloat((1, 0.1))
y = -2 * x + 10
z = -3 * x
covs = uncertainties.covariance_matrix([x, y, z])
# Diagonal elements are simple:
assert _numbers_close(covs[0][0], 0.01)
assert _numbers_close(covs[1][1], 0.04)
assert _numbers_close(covs[2][2], 0.09)
# Non-diagonal elements:
assert _numbers_close(covs[0][1], -0.02)
def test_covariances():
"Covariance matrix"
x = ufloat((1, 0.1))
y = -2*x+10
z = -3*x
covs = uncertainties.covariance_matrix([x, y, z])
# Diagonal elements are simple:
assert _numbers_close(covs[0][0], 0.01)
assert _numbers_close(covs[1][1], 0.04)
assert _numbers_close(covs[2][2], 0.09)
# Non-diagonal elements:
assert _numbers_close(covs[0][1], -0.02)
def linleastsquares(functionlist, x_values, y_values):
y = np.matrix(unp.nominal_values(y_values)).T
Z = np.matrix(unc.covariance_matrix(y_values)).I
# N rows vor every value, p columns for every function
dim = (len(x_values), len(functionlist))
A = np.matrix(np.zeros(dim))
for i, func in enumerate(functionlist):
A[:, i] = func(x_values)[:, np.newaxis]
invATA = (A.T * Z * A).I
params = invATA * A.T * Z * y
cov = invATA
return (np.array(unc.correlated_values(params.flat, np.array(cov))))
def linleastsquares(functionlist, x_values, y_values):
y = np.matrix(unp.nominal_values(y_values)).T
Z = np.matrix(unc.covariance_matrix(y_values)).I
# N rows vor every value, p columns for every function
dim = (len(x_values), len(functionlist))
A = np.matrix(np.zeros(dim))
for i, func in enumerate(functionlist):
A[:, i] = func(x_values)[:, np.newaxis]
invATA = (A.T * Z * A).I
params = invATA * A.T * Z * y
cov = invATA
return (np.array(unc.correlated_values(params.flat, np.array(cov))))
def calibration(detector_name, mu, s_mu):
"""
does a linear fit fit three points !!!
"""
def lin_func(x, a, b):
return(a*x + b)
fit_, cov_fit_ = curve_fit(lin_func, Es, mu, p0=None, sigma=s_mu)
fit_corr_ = uc.correlated_values(fit_, cov_fit_)
fit_corr = np.array([1 / fit_corr_[0], - fit_corr_[1] / fit_corr_[0]])
fit = un.nominal_values(fit_corr)
cov_fit = uc.covariance_matrix(fit_corr)
s_fit = un.std_devs(fit_corr)
fit_r, s_fit_r = err_round(fit, cov_fit)
fit_both = np.array([fit_r, s_fit_r])
fit_both = np.reshape(fit_both.T, np.size(fit_both))
fig1, ax1 = plt.subplots(1, 1)
if not save_fig:
fig1.suptitle("Calibration: " + detector_name)
#plot1, = ax1.plot(mu, Es, '.', alpha=0.9)
mu_grid = np.linspace(0, 700, 100)
plot_fit, = ax1.plot(mu_grid, lin_func(mu_grid, *fit), alpha=0.5)
ax1.errorbar(mu, Es, xerr=s_mu, fmt='.', alpha=0.99, c=plot_fit.get_color()) # errors of t are not changed!
ax1.set_xlabel("channel")
ax1.set_ylabel("Energy / keV")
textstr = 'Results of linear fit for %s'%detector_name + ":\n"
textstr += '\\begin{eqnarray*}\
E(\mu)&=& a \mu + E_0 \\\\ \
a &=& (%.4f \pm %.4f)\, \mathrm{keV / ch} \\\\ \
E_0 &=& (%.1f \pm %.1f)\, \mathrm{keV} \\\\ \
\end{eqnarray*}'%tuple(fit_both)
ax1.text(0.1, 0.95, textstr, transform=ax1.transAxes, va='top', bbox=props)
if show_fig:
fig1.show()
if save_fig:
file_name = "detector_calibration_" + detector_name
fig1.savefig(fig_dir + file_name + ".pdf")
fig1.savefig(fig_dir + file_name + ".png")
return fit_corr[0]
def ucurve_fit(f, xdata, ydata, **kwargs):
"""
Wrapper for curve_fit that allows use of uncertainties both in model and data.
It returns a tuple o ufloat for parametres, correlated.
"""
x, ux = unpack_unarray(xdata)
y, uy = unpack_unarray(ydata)
uy = unc.covariance_matrix(
ydata
) # I use the covariance matrix as sigma, to fit correlated values
@wraps(f
) # need for pass the number of parametres. Without curve_fit fails
def model(x, *pars):
# if you give to nominal_values a standard numpy.array it returns it
return unumpy.nominal_values(f(x, *pars))
p, cov = curve_fit(f=model, xdata=x, ydata=y, sigma=uy, **kwargs)
return unc.correlated_values(p, cov)
def weighted_mean(y, covy=None):
"""
Weighted mean (with covariance matrix).
Parameters
----------
y : array of numbers or ufloats
covy : None or matrix
If covy is None, y must be an array of ufloats.
Returns
-------
a : ufloat
Weighted mean of y.
Q : float
Chisquare (the value of the minimized quadratic form at the minimum).
"""
# get covariance matrix
if covy is None:
covy = un.covariance_matrix(y)
else:
y = un.correlated_values(y, covy)
# compute weighted average
inv_covy = np.linalg.inv(covy)
vara = 1 / np.sum(inv_covy)
a = vara * np.sum(np.dot(inv_covy, y))
# check computation of uncertainties module against direct computation
assert np.allclose(vara, a.s ** 2)
# compute chisquare
res = unp.nominal_values(y) - a.n
Q = float(res.reshape(1,-1) @ inv_covy @ res.reshape(-1,1))
return a, Q
def formatcov(x, cov=None, labels=None, corrfmt='.0f'):
"""
Format an estimate with a covariance matrix as an upper triangular matrix
with values on the diagonal (with uncertainties) and correlations
off-diagonal.
Parameters
----------
x : M-length array
Values to be written on the diagonal.
cov : (M, M) matrix or None
Covariance matrix from which uncertainties and correlations are
computed. If None, a covariance matrix is extracted from x with
uncertainties.covariance_matrix(x).
labels : list of strings
Labels for the header of the matrix. If there are less than M labels,
only the first elements are given labels.
corrfmt : str
Format for the correlations.
Returns
-------
matrix : TextMatrix
A TextMatrix instance. Can be converted to a string with str(). Has a
method latex() to format as a LaTeX table.
See also
--------
TextMatrix
Examples
--------
>>> popt, pcov = scipy.optimize.curve_fit(f, x, y, ...)
>>> print(formatcov(popt, pcov))
>>> print(formatcov(popt, pcov).latex()) # LaTeX table
"""
if cov is None:
cov = uncertainties.covariance_matrix(x)
x = unumpy.nominal_values(x)
if isinstance(x, dict) and isinstance(cov, dict):
keys = list(x.keys())
x = [x[key] for key in keys]
cov = [[float(cov[keyi, keyj]) for keyj in keys] for keyi in keys]
if labels is None:
labels = keys
pars = _uformat_vect(x, np.sqrt(np.diag(cov)))
corr = normcov(cov) * 100
matrix = []
if not (labels is None):
if len(labels) < len(x):
labels = list(labels) + [''] * (len(x) - len(labels))
elif len(labels) > len(x):
labels = labels[:len(x)]
matrix.append(labels)
for i in range(len(corr)):
matrix.append([pars[i]])
for j in range(i + 1, len(corr)):
c = corr[i, j]
cs = ('{:' + corrfmt +
'} %').format(c) if math.isfinite(c) else str(c)
matrix[-1].append(cs)
return TextMatrix(matrix, fill_side='left')
def calculate(self, dataframe, ibin):
# >>> acceptance selection
var0 = [True,]*len(dataframe)
if self.delR:
var0 = var0 & (dataframe['delR'] > self.delR)
if self.delDxy:
var0 = var0 & (dataframe['delDxy'] < self.delDxy)
if self.delDz:
var0 = var0 & (dataframe['delDz'] < self.delDz)
if all(var0):
df = dataframe.copy()
else:
df = dataframe.loc[var0].copy()
# <<< acceptance selection
# >>> columns for tnp efficiency
df['pass_muon'] = df['muon_ID'] >= self.ID
df['pass_antiMuon'] = df['antiMuon_ID'] >= self.ID
if self.pfIso:
df['pass_muon'] = df['pass_muon'] & (df['muon_pfIso'] < self.pfIso)
df['pass_antiMuon'] = df['pass_antiMuon'] & (df['antiMuon_pfIso'] < self.pfIso)
if self.tkIso:
df['pass_muon'] = df['pass_muon'] & (df['muon_tkIso'] < self.tkIso)
df['pass_antiMuon'] = df['pass_antiMuon'] & (df['antiMuon_tkIso'] < self.tkIso)
df['pass_muon_antiMuon'] = df['pass_muon'] & df['pass_antiMuon']
nMinus = df['pass_muon'].sum()
nPlus = df['pass_antiMuon'].sum()
nPlusMinus = df['pass_muon_antiMuon'].sum()
if self.HLT:
df['pass_muon_HLT'] = df['pass_muon_antiMuon'] & df['muon_hlt_{0}'.format(self.HLT)]
df['pass_antiMuon_HLT'] = df['pass_muon_antiMuon'] & df['antiMuon_hlt_{0}'.format(self.HLT)]
df['pass_muon_antiMuon_HLT'] = df['pass_muon_HLT'] & df['pass_antiMuon_HLT']
nMinus_HLT = df['pass_muon_HLT'].sum()
nPlus_HLT = df['pass_antiMuon_HLT'].sum()
nPlusMinus_HLT = df['pass_muon_antiMuon_HLT'].sum()
# <<< columns for tnp efficiency
# >>> columns for true efficiency
if self.HLT:
df['reco'] = df['pass_muon_antiMuon'] & (df['pass_muon_HLT'] | df['pass_antiMuon_HLT'])
else:
df['reco'] = df['pass_muon_antiMuon']
df['not_reco'] = ~df['reco']
nZReco = df['reco'].sum()
nZNotReco = df['not_reco'].sum()
# <<< columns for true efficiency
# >>> construct full covariance matrix
if self.HLT:
corr_matrix = df[['reco','not_reco','pass_muon_antiMuon','pass_muon','pass_antiMuon','pass_muon_antiMuon_HLT','pass_muon_HLT','pass_antiMuon_HLT']].corr()
nZReco, nZNotReco, nPlusMinus, nMinus, nPlus, nPlusMinus_HLT, nMinus_HLT, nPlus_HLT = unc.correlated_values_norm(
[(nZReco, np.sqrt(nZReco)), (nZNotReco, np.sqrt(nZNotReco)),
(nPlusMinus, np.sqrt(nPlusMinus)), (nMinus, np.sqrt(nMinus)), (nPlus, np.sqrt(nPlus)),
(nPlusMinus_HLT, np.sqrt(nPlusMinus_HLT)), (nMinus_HLT, np.sqrt(nMinus_HLT)), (nPlus_HLT, np.sqrt(nPlus_HLT))],
corr_matrix)
else:
corr_matrix = df[['reco','not_reco','pass_muon_antiMuon','pass_muon','pass_antiMuon']].corr()
nZReco, nZNotReco, nPlusMinus, nMinus, nPlus = unc.correlated_values_norm(
[(nZReco, np.sqrt(nZReco)), (nZNotReco, np.sqrt(nZNotReco)),
(nPlusMinus, np.sqrt(nPlusMinus)), (nMinus, np.sqrt(nMinus)), (nPlus, np.sqrt(nPlus))],
corr_matrix)
# <<< construct full covariance matrix
# >>> compute true and tnp efficiency
eff_true = nZReco / (nZNotReco + nZReco)
MuPlusEff = nPlusMinus/nMinus
MuMinusEff = nPlusMinus/nPlus
eff_tnp = MuPlusEff * MuMinusEff
if self.HLT:
MuPlusEff_HLT = nPlusMinus_HLT/nMinus_HLT
MuMinusEff_HLT = nPlusMinus_HLT/nPlus_HLT
eff_tnpZ = (1 - (1 - MuPlusEff_HLT) * (1 - MuMinusEff_HLT) ) * eff_tnp
# <<< compute true and tnp efficiency
else:
eff_tnpZ = eff_tnp
# >>> store
self.eff_corr.append(unc.covariance_matrix([eff_tnpZ, eff_true]))
self.eff_tnp.append(eff_tnp)
self.eff_tnpZ.append(eff_tnpZ)
self.eff_true.append(eff_true)
#(3.1415+/-0)e+10
#>>> print ufloat(3.1415, 0.0005)
#3.1415+/-0.0005
#>>> print '{:.2f}'.format(ufloat(3.14, 0.001))
#3.14+/-0.00
#>>> print '{:.2f}'.format(ufloat(3.14, 0.00))
#3.14+/-0
u = ufloat(1, 0.1, "u variable") # Tag
v = ufloat(10, 0.1, "v variable")
sum_value = u+2*v
print(sum_value)
cov_matrix = covariance_matrix([u, v, sum_value])
print(cov_matrix)
(u2, v2, sum2) = uncertainties.correlated_values([1, 10, 21], cov_matrix)
print(sum2)
for (var, error) in sum_value.error_components().items():
print("{}: {}".format(var.tag, error))
output = subprocess.check_output(["echo", "Hello World!"])
print(subprocess.getoutput('ls /bin/ls'))
print(subprocess.getoutput('echo %s' %"Hello World!"))
print(b'hi'.decode('ascii'))
print(output)
def __init__(self,
dir_x,
dir_y,
dir_z,
unc_x,
unc_y,
unc_z,
num_samples=1000000,
random_seed=42,
weighted_normalization=True,
fix_delta=True):
"""Initialize DNN LLH object.
Parameters
----------
dir_x : float
The best fit direction vector x component.
This is the output of the DNN reco for the x-component.
dir_y : float
The best fit direction vector y component.
This is the output of the DNN reco for the y-component.
dir_z : float
The best fit direction vector z component.
This is the output of the DNN reco for the z-component.
unc_x : float
The estimated uncertainty for the direction vector x component.
This is the output of the DNN reco for the estimated uncertainty.
unc_y : float
The estimated uncertainty for the direction vector y component.
This is the output of the DNN reco for the estimated uncertainty.
unc_z : float
The estimated uncertainty for the direction vector z component.
This is the output of the DNN reco for the estimated uncertainty.
num_samples : int, optional
Number of samples to sample for internal calculations.
The more samples, the more accurate, but also slower.
random_seed : int, optional
Random seed for sampling.
weighted_normalization : bool, optional
If True the normalization vectors get normalized according to the
uncertainty on each of its components.
If False, the vectors get scaled by their norm to obtain unit
vectors.
fix_delta : bool, optional
If True, the sampled direction vectors will sampled in a way such
that the deltas of the angles: abs(azimuth - sampled_azimuth) and
abs(zenith - sampled_zenith) follow the expected distribution.
"""
self.weighted_normalization = weighted_normalization
u_dir_x = ufloat(dir_x, unc_x)
u_dir_y = ufloat(dir_y, unc_y)
u_dir_z = ufloat(dir_z, unc_z)
u_dir_x, u_dir_y, u_dir_z = self.u_normalize_dir(
u_dir_x, u_dir_y, u_dir_z)
# Assign values with propagated and normalized vector
u_zenith, u_azimuth = self.u_get_zenith_azimuth(
u_dir_x, u_dir_y, u_dir_z)
self.dir_x = u_dir_x.nominal_value
self.dir_y = u_dir_y.nominal_value
self.dir_z = u_dir_z.nominal_value
self.zenith = unumpy.nominal_values(u_zenith)
self.azimuth = unumpy.nominal_values(u_azimuth)
self.unc_zenith = unumpy.std_devs(u_zenith)
self.unc_azimuth = unumpy.std_devs(u_azimuth)
cov = np.array(covariance_matrix([u_zenith, u_azimuth]))
DNN_LLH_Base_Elliptical.__init__(self, self.zenith, self.azimuth, cov,
num_samples, random_seed,
weighted_normalization, fix_delta)
def __init__(self,
dir_x,
dir_y,
dir_z,
unc_x,
unc_y,
unc_z,
propagate_errors=False,
num_samples=1000000,
random_seed=42,
scale_unc=True,
weighted_normalization=True,
fix_delta=True):
"""Initialize DNN LLH object.
Parameters
----------
dir_x : float
The best fit direction vector x component.
This is the output of the DNN reco for the x-component.
dir_y : float
The best fit direction vector y component.
This is the output of the DNN reco for the y-component.
dir_z : float
The best fit direction vector z component.
This is the output of the DNN reco for the z-component.
unc_x : float
The estimated uncertainty for the direction vector x component.
This is the output of the DNN reco for the estimated uncertainty.
unc_y : float
The estimated uncertainty for the direction vector y component.
This is the output of the DNN reco for the estimated uncertainty.
unc_z : float
The estimated uncertainty for the direction vector z component.
This is the output of the DNN reco for the estimated uncertainty.
propagate_errors : bool, optional
Propagate errors and account for correlations.
num_samples : int, optional
Number of samples to sample for internal calculations.
The more samples, the more accurate, but also slower.
random_seed : int, optional
Random seed for sampling.
scale_unc : bool, optional
Due to the normalization of the direction vectors, the components
of the vector are correlated, hence the actual spread in sampled
direction vectors shrinks. The nn model predicts the Gaussian
Likelihood of the normalized vectors (if normalization is included)
in network model. In this case, the uncertainties of the
direction vector components can be scaled to account for this
correlation.
If set to True, the uncertainties will be scaled.
weighted_normalization : bool, optional
If True the normalization vectors get normalized according to the
uncertainty on each of its components.
If False, the vectors get scaled by their norm to obtain unit
vectors.
fix_delta : bool, optional
If True, the sampled direction vectors will sampled in a way such
that the deltas: abs(dir_i - sampled_dir_i) follows the expected
distribution.
"""
# call init from base class
DNN_LLH_Base.__init__(self, dir_x, dir_y, dir_z, unc_x, unc_y, unc_z,
random_seed, weighted_normalization)
self._num_samples = num_samples
self.propagate_errors = propagate_errors
self._fix_delta = fix_delta
if self.propagate_errors:
# propagate errors
u_dir_x = unumpy.uarray(dir_x, unc_x)
u_dir_y = unumpy.uarray(dir_y, unc_y)
u_dir_z = unumpy.uarray(dir_z, unc_z)
u_dir_x, u_dir_y, u_dir_z = self.u_normalize_dir(
u_dir_x, u_dir_y, u_dir_z)
# Assign values with propagated and normalized vector
self.unc_x = u_dir_x.std_dev
self.unc_y = u_dir_y.std_dev
self.unc_z = u_dir_z.std_dev
self.dir_x = u_dir_x.nominal_value
self.dir_y = u_dir_y.nominal_value
self.dir_z = u_dir_z.nominal_value
self.cov_matrix = np.array(
uncertainties.covariance_matrix([u_dir_x, u_dir_y, u_dir_z]))
self.dist = multivariate_normal(mean=(self.dir_x, self.dir_y,
self.dir_z),
cov=self.cov_matrix,
allow_singular=True)
else:
self.unc_x = unc_x
self.unc_y = unc_y
self.unc_z = unc_z
self.dir_x, self.dir_y, self.dir_z = \
self.normalize_dir(dir_x, dir_y, dir_z)
# -------------------------
# scale up unc if necessary
# -------------------------
self.scale_unc = scale_unc
if self.scale_unc:
def _scale():
dir_x_s, dir_y_s, dir_z_s = self.sample_dir(
min(self._num_samples, 1000))
# print('scaling x by:', self.unc_x / np.std(dir_x_s))
# print('scaling y by:', self.unc_y / np.std(dir_y_s))
# print('scaling z by:', self.unc_z / np.std(dir_z_s))
self.unc_x *= self.unc_x / np.std(dir_x_s)
self.unc_y *= self.unc_y / np.std(dir_y_s)
self.unc_z *= self.unc_z / np.std(dir_z_s)
_scale()
# -------------------------
self.zenith, self.azimuth = self.get_zenith_azimuth(
self.dir_x, self.dir_y, self.dir_z)
# sample contours
self.dir_x_s, self.dir_y_s, self.dir_z_s = \
self.sample_dir(self._num_samples)
self.neg_llh_values = -self.log_prob_dir(self.dir_x_s, self.dir_y_s,
self.dir_z_s)
# sort sampled points according to neg llh
sorted_indices = np.argsort(self.neg_llh_values)
self.dir_x_s = self.dir_x_s[sorted_indices]
self.dir_y_s = self.dir_y_s[sorted_indices]
self.dir_z_s = self.dir_z_s[sorted_indices]
self.neg_llh_values = self.neg_llh_values[sorted_indices]
# get sampled zenith and azimuth
self.zenith_s, self.azimuth_s = self.get_zenith_azimuth(
self.dir_x_s, self.dir_y_s, self.dir_z_s)
def test_correlated_values():
"""
Correlated variables.
Test through the input of the (full) covariance matrix.
"""
u = uncertainties.ufloat((1, 0.1))
cov = uncertainties.covariance_matrix([u])
# "1" is used instead of u.nominal_value because
# u.nominal_value might return a float. The idea is to force
# the new variable u2 to be defined through an integer nominal
# value:
u2, = uncertainties.correlated_values([1], cov)
expr = 2 * u2 # Calculations with u2 should be possible, like with u
####################
# Covariances between output and input variables:
x = ufloat((1, 0.1))
y = ufloat((2, 0.3))
z = -3 * x + y
covs = uncertainties.covariance_matrix([x, y, z])
# Test of the diagonal covariance elements:
assert matrices_close(numpy.array([v.std_dev()**2 for v in (x, y, z)]),
numpy.array(covs).diagonal())
# "Inversion" of the covariance matrix: creation of new
# variables:
(x_new, y_new, z_new) = uncertainties.correlated_values(
[x.nominal_value, y.nominal_value, z.nominal_value],
covs,
tags=['x', 'y', 'z'])
# Even the uncertainties should be correctly reconstructed:
assert matrices_close(numpy.array((x, y, z)),
numpy.array((x_new, y_new, z_new)))
# ... and the covariances too:
assert matrices_close(
numpy.array(covs),
numpy.array(uncertainties.covariance_matrix([x_new, y_new,
z_new])))
assert matrices_close(numpy.array([z_new]),
numpy.array([-3 * x_new + y_new]))
####################
# ... as well as functional relations:
u = ufloat((1, 0.05))
v = ufloat((10, 0.1))
sum_value = u + 2 * v
# Covariance matrices:
cov_matrix = uncertainties.covariance_matrix([u, v, sum_value])
# Correlated variables can be constructed from a covariance
# matrix, if NumPy is available:
(u2, v2, sum2) = uncertainties.correlated_values(
[x.nominal_value for x in [u, v, sum_value]], cov_matrix)
# matrices_close() is used instead of _numbers_close() because
# it compares uncertainties too:
assert matrices_close(numpy.array([u]), numpy.array([u2]))
assert matrices_close(numpy.array([v]), numpy.array([v2]))
assert matrices_close(numpy.array([sum_value]), numpy.array([sum2]))
assert matrices_close(numpy.array([0]),
numpy.array([sum2 - (u2 + 2 * v2)]))
def __init__(self, values, cov=None, stds=None, info=None, labels=None):
"""
Store parameters and associated uncertainties.
Parameters
----------
values : array_like, dict or uncertainties object
Either the nominal values of the parameters, a dictionary
containing `values` and `stds` or `cov` used to create
a parameter object, or values with associated uncertainties
created by the `uncertainties` package.
cov : array_like
The covariance matrix for the specified parameters used for
propagating errors. Only used if `values` is array_like, in
which case i should be an array of shape (len(values), len(values)).
stds : array_like
Standard deviations of the values. This does not account for
correllated uncertainties - use `cov` for that. Only used if
`values` is array_like, in which case `stds` should be the
same length as `values`.
info : str
A description of the parameteters, to be stored alongside the
values.
labels : array_like
Parameter names.
"""
if isinstance(values, dict):
vd = values.copy()
values = vd['values']
if 'stds' in vd:
stds = vd['stds']
if 'cov' in vd:
cov = vd['cov']
if 'info' in vd:
info = vd['info']
if 'labels' in vd:
labels = vd['labels']
if info is None:
info = 'No information given.'
self.info = info
self.labels = labels
self.param_name = ''
if ucheck(values):
self.values = values
else:
if cov is not None:
self.values = un.correlated_values(values, cov)
elif stds is not None:
self.values = unp.uarray(values, stds)
else:
self.values = values
if ucheck(self.values):
self.nom_values = unp.nominal_values(self.values)
self.stds = unp.std_devs(self.values)
self.cov = un.covariance_matrix(self.values)
else:
self.nom_values = np.asanyarray(self.values)
self.stds = np.full(len(self.values), np.nan)
self.stds = np.full((len(self.values),len(self.values)), np.nan)
self.wrap = TextWrapper(linewidth).wrap
def test_monte_carlo_comparison():
"""
Full comparison to a Monte-Carlo calculation.
Both the nominal values and the covariances are compared between
the direct calculation performed in this module and a Monte-Carlo
simulation.
"""
try:
import numpy
import numpy.random
except ImportError:
import warnings
warnings.warn("Test not performed because NumPy is not available")
return
# Works on numpy.arrays of Variable objects (whereas umath.sin()
# does not):
sin_uarrayncert = numpy.vectorize(umath.sin, otypes=[object])
# Example expression (with correlations, and multiple variables combined
# in a non-linear way):
def function(x, y):
"""
Function that takes two NumPy arrays of the same size.
"""
# The uncertainty due to x is about equal to the uncertainty
# due to y:
return 10 * x**2 - x * sin_uarrayncert(y**3)
x = uncertainties.ufloat((0.2, 0.01))
y = uncertainties.ufloat((10, 0.001))
function_result_this_module = function(x, y)
nominal_value_this_module = function_result_this_module.nominal_value
# Covariances "f*f", "f*x", "f*y":
covariances_this_module = numpy.array(uncertainties.covariance_matrix(
(x, y, function_result_this_module)))
def monte_carlo_calc(n_samples):
"""
Calculate function(x, y) on n_samples samples and returns the
median, and the covariances between (x, y, function(x, y)).
"""
# Result of a Monte-Carlo simulation:
x_samples = numpy.random.normal(x.nominal_value, x.std_dev(),
n_samples)
y_samples = numpy.random.normal(y.nominal_value, y.std_dev(),
n_samples)
function_samples = function(x_samples, y_samples)
cov_mat = numpy.cov([x_samples, y_samples], function_samples)
return (numpy.median(function_samples), cov_mat)
(nominal_value_samples, covariances_samples) = monte_carlo_calc(1000000)
## Comparison between both results:
# The covariance matrices must be close:
# We rely on the fact that covariances_samples very rarely has
# null elements:
assert numpy.vectorize(test_uncertainties._numbers_close)(
covariances_this_module,
covariances_samples,
0.05).all(), (
"The covariance matrices do not coincide between"
" the Monte-Carlo simulation and the direct calculation:\n"
"* Monte-Carlo:\n%s\n* Direct calculation:\n%s"
% (covariances_samples, covariances_this_module)
)
# The nominal values must be close:
assert test_uncertainties._numbers_close(
nominal_value_this_module,
nominal_value_samples,
# The scale of the comparison depends on the standard
# deviation: the nominal values can differ by a fraction of
# the standard deviation:
math.sqrt(covariances_samples[2, 2])
/ abs(nominal_value_samples) * 0.5), (
"The nominal value (%f) does not coincide with that of"
" the Monte-Carlo simulation (%f), for a standard deviation of %f."
% (nominal_value_this_module,
nominal_value_samples,
math.sqrt(covariances_samples[2, 2]))
)
def test_monte_carlo_comparison():
"""
Full comparison to a Monte-Carlo calculation.
Both the nominal values and the covariances are compared between
the direct calculation performed in this module and a Monte-Carlo
simulation.
"""
try:
import numpy
import numpy.random
except ImportError:
import warnings
warnings.warn("Test not performed because NumPy is not available")
return
# Works on numpy.arrays of Variable objects (whereas umath.sin()
# does not):
sin_uarray_uncert = numpy.vectorize(umath.sin, otypes=[object])
# Example expression (with correlations, and multiple variables combined
# in a non-linear way):
def function(x, y):
"""
Function that takes two NumPy arrays of the same size.
"""
# The uncertainty due to x is about equal to the uncertainty
# due to y:
return 10 * x**2 - x * sin_uarray_uncert(y**3)
x = ufloat(0.2, 0.01)
y = ufloat(10, 0.001)
function_result_this_module = function(x, y)
nominal_value_this_module = function_result_this_module.nominal_value
# Covariances "f*f", "f*x", "f*y":
covariances_this_module = numpy.array(
uncertainties.covariance_matrix((x, y, function_result_this_module)))
def monte_carlo_calc(n_samples):
"""
Calculate function(x, y) on n_samples samples and returns the
median, and the covariances between (x, y, function(x, y)).
"""
# Result of a Monte-Carlo simulation:
x_samples = numpy.random.normal(x.nominal_value, x.std_dev, n_samples)
y_samples = numpy.random.normal(y.nominal_value, y.std_dev, n_samples)
# !!! astype() is a temporary fix for NumPy 1.8:
function_samples = function(x_samples, y_samples).astype(float)
cov_mat = numpy.cov([x_samples, y_samples], function_samples)
return (numpy.median(function_samples), cov_mat)
(nominal_value_samples, covariances_samples) = monte_carlo_calc(1000000)
## Comparison between both results:
# The covariance matrices must be close:
# We rely on the fact that covariances_samples very rarely has
# null elements:
assert numpy.vectorize(test_uncertainties.numbers_close)(
covariances_this_module, covariances_samples, 0.05).all(), (
"The covariance matrices do not coincide between"
" the Monte-Carlo simulation and the direct calculation:\n"
"* Monte-Carlo:\n%s\n* Direct calculation:\n%s" %
(covariances_samples, covariances_this_module))
# The nominal values must be close:
assert test_uncertainties.numbers_close(
nominal_value_this_module,
nominal_value_samples,
# The scale of the comparison depends on the standard
# deviation: the nominal values can differ by a fraction of
# the standard deviation:
math.sqrt(covariances_samples[2, 2]) / abs(nominal_value_samples) *
0.5), (
"The nominal value (%f) does not coincide with that of"
" the Monte-Carlo simulation (%f), for a standard deviation of %f."
% (nominal_value_this_module, nominal_value_samples,
math.sqrt(covariances_samples[2, 2])))
