mirror of
https://github.com/fjosw/pyerrors.git
synced 2025-03-15 06:40:24 +01:00
feat: covariance is now estimated from the uncorrelated correlation
matrix rescaled by the full (correlated) errors.
This commit is contained in:
parent
82419b7a88
commit
74b0f77c2d
1 changed files with 18 additions and 34 deletions
|
@ -1332,50 +1332,40 @@ def correlate(obs_a, obs_b):
|
|||
return o
|
||||
|
||||
|
||||
def covariance(obs, window=min, correlation=False, **kwargs):
|
||||
def covariance(obs, correlation=False, **kwargs):
|
||||
"""Calculates the covariance matrix of a set of observables.
|
||||
|
||||
covariance([obs, obs])[0,1] is equal to obs.dvalue ** 2
|
||||
The gamma method has to be applied first to both observables.
|
||||
The gamma method has to be applied first to all observables.
|
||||
|
||||
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)
|
||||
for i in range(length):
|
||||
for j in range(i, length):
|
||||
cov[i, j] = _covariance_element(obs[i], obs[j])
|
||||
cov = cov + cov.T - np.diag(np.diag(cov))
|
||||
|
||||
corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov)))
|
||||
|
||||
errors = [o.dvalue for o in obs]
|
||||
cov = np.sqrt(np.diag(errors)) @ corr @ np.sqrt(np.diag(errors))
|
||||
|
||||
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)
|
||||
warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning)
|
||||
return cov
|
||||
|
||||
|
||||
def _covariance_element(obs1, obs2, window_dict, correlation=False, **kwargs):
|
||||
"""TODO
|
||||
"""
|
||||
def _covariance_element(obs1, obs2):
|
||||
"""Estimates the covariance of two Obs objects based on fixed window sizes passed to the function."""
|
||||
|
||||
def expand_deltas(deltas, idx, shape, new_idx):
|
||||
"""Expand deltas defined on idx to a contiguous range [new_idx[0], new_idx[-1]].
|
||||
|
@ -1407,7 +1397,9 @@ def _covariance_element(obs1, obs2, window_dict, correlation=False, **kwargs):
|
|||
max_gamma = min(new_shape, w_max)
|
||||
# The padding for the fft has to be even
|
||||
padding = new_shape + max_gamma + (new_shape + max_gamma) % 2
|
||||
gamma[:max_gamma] += (np.fft.irfft(np.fft.rfft(deltas1, padding) * np.conjugate(np.fft.rfft(deltas2, padding)))[:max_gamma] + np.fft.irfft(np.fft.rfft(deltas2, padding) * np.conjugate(np.fft.rfft(deltas1, padding)))[:max_gamma]) / 2.0
|
||||
rfft1 = np.fft.rfft(deltas1, padding)
|
||||
rfft2 = np.fft.rfft(deltas2, padding)
|
||||
gamma[:max_gamma] += (np.fft.irfft(rfft1 * np.conjugate(rfft2))[:max_gamma] + np.fft.irfft(rfft2 * np.conjugate(rfft1))[:max_gamma]) / 2.0
|
||||
|
||||
return gamma
|
||||
|
||||
|
@ -1428,14 +1420,13 @@ def _covariance_element(obs1, obs2, window_dict, correlation=False, **kwargs):
|
|||
if e_name not in obs2.mc_names:
|
||||
continue
|
||||
|
||||
window = window_dict[e_name]
|
||||
window = 0
|
||||
|
||||
idl_d = {}
|
||||
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]])
|
||||
# TODO: Is a check needed if the length of an ensemble is zero?
|
||||
|
||||
w_max = window + 1
|
||||
e_gamma[e_name] = np.zeros(w_max)
|
||||
|
@ -1477,13 +1468,6 @@ def _covariance_element(obs1, obs2, window_dict, 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)))
|
||||
|
||||
# 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
|
||||
|
||||
return dvalue
|
||||
|
||||
|
||||
|
|
Loading…
Add table
Reference in a new issue