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feat: positive semi-definite estimator for the covariance implemented,

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fits.covariance matrix deprecated, covariance can now handle lists of
observables.
This commit is contained in:
Fabian Joswig 2022-03-01 09:45:25 +00:00
parent 8e3e34bbea
commit 82419b7a88
5 changed files with 65 additions and 79 deletions
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32
pyerrors/fits.py
View file

@ -239,7 +239,7 @@ def total_least_squares(x, y, func, silent=False, **kwargs):
if kwargs.get('covariance') is not None:
cov = kwargs.get('covariance')
else:
cov = covariance_matrix(np.concatenate((y, x.ravel())))
cov = covariance(np.concatenate((y, x.ravel())))
number_of_x_parameters = int(m / x_f.shape[-1])
@ -455,7 +455,7 @@ def _standard_fit(x, y, func, silent=False, **kwargs):
x0 = [0.1] * n_parms
if kwargs.get('correlated_fit') is True:
cov = covariance_matrix(y)
cov = covariance(y)
covdiag = np.diag(1. / np.sqrt(np.diag(cov)))
corr = np.copy(cov)
for i in range(len(y)):
@ -527,7 +527,7 @@ def _standard_fit(x, y, func, silent=False, **kwargs):
if kwargs.get('expected_chisquare') is True:
if kwargs.get('correlated_fit') is not True:
W = np.diag(1 / np.asarray(dy_f))
cov = covariance_matrix(y)
cov = covariance(y)
A = W @ jacobian(func)(fit_result.x, x)
P_phi = A @ np.linalg.inv(A.T @ A) @ A.T
expected_chisquare = np.trace((np.identity(x.shape[-1]) - P_phi) @ W @ cov @ W)
@ -651,33 +651,9 @@ def residual_plot(x, y, func, fit_res):
plt.draw()
def covariance_matrix(y):
"""Returns the covariance matrix of y.
Parameters
----------
y : list or numpy.ndarray
List or one dimensional array of Obs
"""
length = len(y)
cov = np.zeros((length, length))
for i, item in enumerate(y):
for j, jtem in enumerate(y[:i + 1]):
if i == j:
cov[i, j] = item.dvalue ** 2
else:
cov[i, j] = covariance(item, jtem)
cov = cov + cov.T - np.diag(np.diag(cov))
eigenvalues = np.linalg.eigh(cov)[0]
if not np.all(eigenvalues >= 0):
warnings.warn("Covariance matrix is not positive semi-definite", RuntimeWarning)
print("Eigenvalues of the covariance matrix:", eigenvalues)
return cov
def error_band(x, func, beta):
"""Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta."""
cov = covariance_matrix(beta)
cov = covariance(beta)
if np.any(np.abs(cov - cov.T) > 1000 * np.finfo(np.float64).eps):
warnings.warn("Covariance matrix is not symmetric within floating point precision", RuntimeWarning)

65
pyerrors/obs.py
View file

@ -1332,20 +1332,50 @@ def correlate(obs_a, obs_b):
return o
def covariance(obs1, obs2, correlation=False, **kwargs):
"""Calculates the covariance of two observables.
def covariance(obs, window=min, correlation=False, **kwargs):
"""Calculates the covariance matrix of a set of observables.
covariance(obs, obs) is equal to obs.dvalue ** 2
covariance([obs, obs])[0,1] is equal to obs.dvalue ** 2
The gamma method has to be applied first to both observables.
If abs(covariance(obs1, obs2)) > obs1.dvalue * obs2.dvalue, the covariance
is constrained to the maximum value.
Parameters
----------
obs : list or numpy.ndarray
List or one dimensional array of Obs
window: function or dict
Function which selects the window for each ensemble, examples 'min', 'max', 'np.mean', 'np.median'
Alternatively a dictionary with an entry for every ensemble can be manually specified.
correlation : bool
if true the correlation instead of the covariance is returned (default False)
"""
if isinstance(window, dict):
window_dict = window
else:
window_dict = {}
names = sorted(set([item for sublist in [o.mc_names for o in obs] for item in sublist]))
for name in names:
window_list = []
for ob in obs:
if ob.e_windowsize.get(name) is not None:
window_list.append(ob.e_windowsize[name])
window_dict[name] = int(window(window_list))
length = len(obs)
cov = np.zeros((length, length))
for i, item in enumerate(obs):
for j, jtem in enumerate(obs[:i + 1]):
cov[i, j] = _covariance_element(item, jtem, window_dict)
cov = cov + cov.T - np.diag(np.diag(cov))
eigenvalues = np.linalg.eigh(cov)[0]
if not np.all(eigenvalues >= 0):
warnings.warn("Covariance matrix is not positive semi-definite", RuntimeWarning)
print("Eigenvalues of the covariance matrix:", eigenvalues)
return cov
def _covariance_element(obs1, obs2, window_dict, correlation=False, **kwargs):
"""TODO
"""
def expand_deltas(deltas, idx, shape, new_idx):
"""Expand deltas defined on idx to a contiguous range [new_idx[0], new_idx[-1]].
@ -1398,21 +1428,16 @@ def covariance(obs1, obs2, correlation=False, **kwargs):
if e_name not in obs2.mc_names:
continue
window = window_dict[e_name]
idl_d = {}
r_length = []
for r_name in obs1.e_content[e_name]:
if r_name not in obs2.e_content[e_name]:
continue
idl_d[r_name] = _merge_idx([obs1.idl[r_name], obs2.idl[r_name]])
if isinstance(idl_d[r_name], range):
r_length.append(len(idl_d[r_name]))
else:
r_length.append((idl_d[r_name][-1] - idl_d[r_name][0] + 1))
# TODO: Is a check needed if the length of an ensemble is zero?
if not r_length:
return 0.
w_max = max(r_length) // 2
w_max = window + 1
e_gamma[e_name] = np.zeros(w_max)
for r_name in obs1.e_content[e_name]:
@ -1438,11 +1463,10 @@ def covariance(obs1, obs2, correlation=False, **kwargs):
e_rho[e_name] = e_gamma[e_name][:w_max] / e_gamma[e_name][0]
e_n_tauint[e_name] = np.cumsum(np.concatenate(([0.5], e_rho[e_name][1:])))
# Make sure no entry of tauint is smaller than 0.5
e_n_tauint[e_name][e_n_tauint[e_name] < 0.5] = 0.500000000001
e_n_tauint[e_name][e_n_tauint[e_name] < 0.5] = 0.5 + np.finfo(np.float64).eps
window = min(obs1.e_windowsize[e_name], obs2.e_windowsize[e_name])
# Bias correction hep-lat/0306017 eq. (49)
e_dvalue[e_name] = 2 * (e_n_tauint[e_name][window] + obs1.tau_exp[e_name] * np.abs(e_rho[e_name][window + 1])) * (1 + (2 * window + 1) / e_N) * e_gamma[e_name][0] / e_N
e_dvalue[e_name] = 2 * (e_n_tauint[e_name][window]) * (1 + (2 * window + 1) / e_N) * e_gamma[e_name][0] / e_N
dvalue += e_dvalue[e_name]
@ -1453,8 +1477,9 @@ def covariance(obs1, obs2, correlation=False, **kwargs):
dvalue += float(np.dot(np.transpose(obs1.covobs[e_name].grad), np.dot(obs1.covobs[e_name].cov, obs2.covobs[e_name].grad)))
if np.abs(dvalue / obs1.dvalue / obs2.dvalue) > 1.0:
dvalue = np.sign(dvalue) * obs1.dvalue * obs2.dvalue
# TODO: Check if this is needed.
# if np.abs(dvalue / obs1.dvalue / obs2.dvalue) > 1.0:
# dvalue = np.sign(dvalue) * obs1.dvalue * obs2.dvalue
if correlation:
dvalue = dvalue / obs1.dvalue / obs2.dvalue

6
tests/covobs_test.py
View file

@ -39,8 +39,8 @@ def test_covobs():
assert(np.isclose(oc.value, op.value, rtol=1e-14, atol=1e-14))
[o.gamma_method() for o in cl]
assert(pe.covariance(cl[0], cl[1]) == cov[0][1])
assert(pe.covariance(cl[0], cl[1]) == cov[1][0])
assert(pe.covariance([cl[0], cl[1]])[0, 1] == cov[0][1])
assert(pe.covariance([cl[0], cl[1]])[0, 1] == cov[1][0])
do = cl[0] * cl[1]
assert(np.array_equal(do.covobs['rAP'].grad, np.transpose([pi[1], pi[0]]).reshape(2, 1)))
@ -89,7 +89,7 @@ def test_covobs_covariance():
x = [a + b, a - b]
[o.gamma_method() for o in x]
covariance = pe.fits.covariance_matrix(x)
covariance = pe.covariance(x)
assert covariance[0, 0] == covariance[1, 1]
assert covariance[0, 1] == a.dvalue ** 2 - b.dvalue ** 2

10
tests/fits_test.py
View file

@ -60,7 +60,7 @@ def test_least_squares():
beta[i].gamma_method(S=1.0)
assert math.isclose(beta[i].value, popt[i], abs_tol=1e-5)
assert math.isclose(pcov[i, i], beta[i].dvalue ** 2, abs_tol=1e-3)
assert math.isclose(pe.covariance(beta[0], beta[1]), pcov[0, 1], abs_tol=1e-3)
assert math.isclose(pe.covariance([beta[0], beta[1]])[0, 1], pcov[0, 1], abs_tol=1e-3)
chi2_pyerrors = np.sum(((f(x, *[o.value for o in beta]) - y) / yerr) ** 2) / (len(x) - 2)
chi2_scipy = np.sum(((f(x, *popt) - y) / yerr) ** 2) / (len(x) - 2)
@ -81,7 +81,7 @@ def test_least_squares():
betac[i].gamma_method(S=1.0)
assert math.isclose(betac[i].value, popt[i], abs_tol=1e-5)
assert math.isclose(pcov[i, i], betac[i].dvalue ** 2, abs_tol=1e-3)
assert math.isclose(pe.covariance(betac[0], betac[1]), pcov[0, 1], abs_tol=1e-3)
assert math.isclose(pe.covariance([betac[0], betac[1]])[0, 1], pcov[0, 1], abs_tol=1e-3)
def test_alternative_solvers():
@ -195,7 +195,7 @@ def test_total_least_squares():
beta[i].gamma_method(S=1.0)
assert math.isclose(beta[i].value, output.beta[i], rel_tol=1e-5)
assert math.isclose(output.cov_beta[i, i], beta[i].dvalue ** 2, rel_tol=2.5e-1), str(output.cov_beta[i, i]) + ' ' + str(beta[i].dvalue ** 2)
assert math.isclose(pe.covariance(beta[0], beta[1]), output.cov_beta[0, 1], rel_tol=2.5e-1)
assert math.isclose(pe.covariance([beta[0], beta[1]])[0, 1], output.cov_beta[0, 1], rel_tol=2.5e-1)
out = pe.total_least_squares(ox, oy, func, const_par=[beta[1]])
@ -218,7 +218,7 @@ def test_total_least_squares():
betac[i].gamma_method(S=1.0)
assert math.isclose(betac[i].value, output.beta[i], rel_tol=1e-3)
assert math.isclose(output.cov_beta[i, i], betac[i].dvalue ** 2, rel_tol=2.5e-1), str(output.cov_beta[i, i]) + ' ' + str(betac[i].dvalue ** 2)
assert math.isclose(pe.covariance(betac[0], betac[1]), output.cov_beta[0, 1], rel_tol=2.5e-1)
assert math.isclose(pe.covariance([betac[0], betac[1]])[0, 1], output.cov_beta[0, 1], rel_tol=2.5e-1)
outc = pe.total_least_squares(oxc, oyc, func, const_par=[betac[1]])
@ -233,7 +233,7 @@ def test_total_least_squares():
betac[i].gamma_method(S=1.0)
assert math.isclose(betac[i].value, output.beta[i], rel_tol=1e-3)
assert math.isclose(output.cov_beta[i, i], betac[i].dvalue ** 2, rel_tol=2.5e-1), str(output.cov_beta[i, i]) + ' ' + str(betac[i].dvalue ** 2)
assert math.isclose(pe.covariance(betac[0], betac[1]), output.cov_beta[0, 1], rel_tol=2.5e-1)
assert math.isclose(pe.covariance([betac[0], betac[1]])[0, 1], output.cov_beta[0, 1], rel_tol=2.5e-1)
outc = pe.total_least_squares(oxc, oy, func, const_par=[betac[1]])

31
tests/obs_test.py
View file

@ -251,10 +251,10 @@ def test_covariance_is_variance():
dvalue = np.abs(np.random.normal(0, 1))
test_obs = pe.pseudo_Obs(value, dvalue, 't')
test_obs.gamma_method()
assert np.abs(test_obs.dvalue ** 2 - pe.covariance(test_obs, test_obs)) <= 10 * np.finfo(np.float64).eps
assert np.abs(test_obs.dvalue ** 2 - pe.covariance([test_obs, test_obs])[0, 1]) <= 10 * np.finfo(np.float64).eps
test_obs = test_obs + pe.pseudo_Obs(value, dvalue, 'q', 200)
test_obs.gamma_method()
assert np.abs(test_obs.dvalue ** 2 - pe.covariance(test_obs, test_obs)) <= 10 * np.finfo(np.float64).eps
assert np.abs(test_obs.dvalue ** 2 - pe.covariance([test_obs, test_obs])[0, 1]) <= 10 * np.finfo(np.float64).eps
def test_fft():
@ -268,21 +268,6 @@ def test_fft():
assert np.abs(test_obs1.dvalue - test_obs2.dvalue) <= 10 * max(test_obs1.dvalue, test_obs2.dvalue) * np.finfo(np.float64).eps
def test_covariance_symmetry():
value1 = np.random.normal(5, 10)
dvalue1 = np.abs(np.random.normal(0, 1))
test_obs1 = pe.pseudo_Obs(value1, dvalue1, 't')
test_obs1.gamma_method()
value2 = np.random.normal(5, 10)
dvalue2 = np.abs(np.random.normal(0, 1))
test_obs2 = pe.pseudo_Obs(value2, dvalue2, 't')
test_obs2.gamma_method()
cov_ab = pe.covariance(test_obs1, test_obs2)
cov_ba = pe.covariance(test_obs2, test_obs1)
assert np.abs(cov_ab - cov_ba) <= 10 * np.finfo(np.float64).eps
assert np.abs(cov_ab) < test_obs1.dvalue * test_obs2.dvalue * (1 + 10 * np.finfo(np.float64).eps)
def test_gamma_method_uncorrelated():
# Construct pseudo Obs with random shape
value = np.random.normal(5, 10)
@ -629,8 +614,8 @@ def test_covariance_symmetry():
dvalue2 = np.abs(np.random.normal(0, 1))
test_obs2 = pe.pseudo_Obs(value2, dvalue2, 't')
test_obs2.gamma_method()
cov_ab = pe.covariance(test_obs1, test_obs2)
cov_ba = pe.covariance(test_obs2, test_obs1)
cov_ab = pe.covariance([test_obs1, test_obs2])[0, 1]
cov_ba = pe.covariance([test_obs2, test_obs1])[0, 1]
assert np.abs(cov_ab - cov_ba) <= 10 * np.finfo(np.float64).eps
assert np.abs(cov_ab) < test_obs1.dvalue * test_obs2.dvalue * (1 + 10 * np.finfo(np.float64).eps)
@ -643,10 +628,10 @@ def test_covariance_symmetry():
idx = [i + 1 for i in range(len(configs)) if configs[i] == 1]
a = pe.Obs([zero_arr], ['t'], idl=[idx])
a.gamma_method()
assert np.isclose(a.dvalue**2, pe.covariance(a, a), atol=100, rtol=1e-4)
assert np.isclose(a.dvalue ** 2, pe.covariance([a, a])[0, 1], atol=100, rtol=1e-4)
cov_ab = pe.covariance(test_obs1, a)
cov_ba = pe.covariance(a, test_obs1)
cov_ab = pe.covariance([test_obs1, a])[0, 1]
cov_ba = pe.covariance([a, test_obs1])[0, 1]
assert np.abs(cov_ab - cov_ba) <= 10 * np.finfo(np.float64).eps
assert np.abs(cov_ab) < test_obs1.dvalue * a.dvalue * (1 + 10 * np.finfo(np.float64).eps)
@ -704,4 +689,4 @@ def test_merge_idx():
new_idx = pe.obs._merge_idx(idl)
assert(new_idx[-1] > new_idx[0])
for i in range(1, len(new_idx)):
assert(new_idx[i - 1] < new_idx[i])
assert(new_idx[i - 1] < new_idx[i])