pyerrors/pyerrors/misc.py

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2020-10-13 16:53:00 +02:00
#!/usr/bin/env python
# coding: utf-8
import numpy as np
from .obs import Obs
2020-10-13 16:53:00 +02:00
def gen_correlated_data(means, cov, name, tau=0.5, samples=1000):
""" Generate observables with given covariance and autocorrelation times.
Arguments
-----------------
means -- list containing the mean value of each observable.
cov -- covariance matrix for the data to be geneated.
name -- ensemble name for the data to be geneated.
tau -- can either be a real number or a list with an entry for
every dataset.
samples -- number of samples to be generated for each observable.
"""
assert len(means) == cov.shape[-1]
tau = np.asarray(tau)
if np.min(tau) < 0.5:
raise Exception('All integrated autocorrelations have to be >= 0.5.')
a = (2 * tau - 1) / (2 * tau + 1)
rand = np.random.multivariate_normal(np.zeros_like(means), cov * samples, samples)
# Normalize samples such that sample variance matches input
norm = np.array([np.var(o, ddof=1) / samples for o in rand.T])
rand = rand @ np.diag(np.sqrt(np.diag(cov))) @ np.diag(1 / np.sqrt(norm))
data = [rand[0]]
for i in range(1, samples):
data.append(np.sqrt(1 - a ** 2) * rand[i] + a * data[-1])
corr_data = np.array(data) - np.mean(data, axis=0) + means
return [Obs([dat], [name]) for dat in corr_data.T]