Initial public release

pyerrors/misc.py

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+#!/usr/bin/env python
+# coding: utf-8
+
+import gc
+import numpy as np
+import scipy.stats
+import matplotlib.pyplot as plt
+from .pyerrors import Obs
+
+
+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]
+
+
+def ks_test(obs=None):
+    """Performs a Kolmogorov–Smirnov test for the Q-values of a list of Obs.
+
+    If no list is given all Obs in memory are used.
+
+    Disclaimer: The determination of the individual Q-values as well as this function have not been tested yet.
+    """
+
+    if obs is None:
+        obs_list = []
+        for obj in gc.get_objects():
+            if isinstance(obj, Obs):
+                obs_list.append(obj)
+    else:
+        obs_list = obs
+
+    Qs = []
+    for obs_i in obs_list:
+        for ens in obs_i.e_names:
+            if obs_i.e_Q[ens] is not None:
+                Qs.append(obs_i.e_Q[ens])
+
+    bins = len(Qs)
+    x = np.arange(0, 1.001, 0.001)
+    plt.plot(x, x, 'k', zorder=1)
+    plt.xlim(0, 1)
+    plt.ylim(0, 1)
+    plt.xlabel('Q value')
+    plt.ylabel('Cumulative probability')
+    plt.title(str(bins) + ' Q values')
+
+    n = np.arange(1, bins + 1) / np.float(bins)
+    Xs = np.sort(Qs)
+    plt.step(Xs, n)
+    diffs = n - Xs
+    loc_max_diff = np.argmax(np.abs(diffs))
+    loc = Xs[loc_max_diff]
+    plt.annotate(s='', xy=(loc, loc), xytext=(loc, loc + diffs[loc_max_diff]), arrowprops=dict(arrowstyle='<->', shrinkA=0, shrinkB=0))
+    plt.show()
+
+    print(scipy.stats.kstest(Qs, 'uniform'))
+