Merge pull request #102 from fjosw/feature/covariance_idl2

Feature/covariance idl2

pyerrors/obs.py

@@ -1,5 +1,7 @@
 import warnings
 import pickle
+from math import gcd
+from functools import reduce
 import numpy as np
 import autograd.numpy as anp  # Thinly-wrapped numpy
 from autograd import jacobian
@@ -981,6 +983,39 @@ def _merge_idx(idl):
     return sorted(set().union(*idl))
 
 
+def _intersection_idx(idl):
+    """Returns the intersection of all lists in idl as sorted list
+
+    Parameters
+    ----------
+    idl : list
+        List of lists or ranges.
+    """
+
+    def _lcm(*args):
+        """Returns the lowest common multiple of args.
+
+        From python 3.9 onwards the math library contains an lcm function."""
+        return reduce(lambda a, b: a * b // gcd(a, b), args)
+
+    # Use groupby to efficiently check whether all elements of idl are identical
+    try:
+        g = groupby(idl)
+        if next(g, True) and not next(g, False):
+            return idl[0]
+    except Exception:
+        pass
+
+    if np.all([type(idx) is range for idx in idl]):
+        if len(set([idx[0] for idx in idl])) == 1:
+            idstart = max([idx.start for idx in idl])
+            idstop = min([idx.stop for idx in idl])
+            idstep = _lcm(*[idx.step for idx in idl])
+            return range(idstart, idstop, idstep)
+
+    return sorted(set.intersection(*[set(o) for o in idl]))
+
+
 def _expand_deltas_for_merge(deltas, idx, shape, new_idx):
     """Expand deltas defined on idx to the list of configs that is defined by new_idx.
        New, empty entries are filled by 0. If idx and new_idx are of type range, the smallest
@@ -1008,6 +1043,34 @@ def _expand_deltas_for_merge(deltas, idx, shape, new_idx):
     return np.array([ret[new_idx[i] - new_idx[0]] for i in range(len(new_idx))])
 
 
+def _collapse_deltas_for_merge(deltas, idx, shape, new_idx):
+    """Collapse deltas defined on idx to the list of configs that is defined by new_idx.
+       If idx and new_idx are of type range, the smallest
+       common divisor of the step sizes is used as new step size.
+
+    Parameters
+    ----------
+    deltas : list
+        List of fluctuations
+    idx : list
+        List or range of configs on which the deltas are defined.
+        Has to be a subset of new_idx and has to be sorted in ascending order.
+    shape : list
+        Number of configs in idx.
+    new_idx : list
+        List of configs that defines the new range, has to be sorted in ascending order.
+    """
+
+    if type(idx) is range and type(new_idx) is range:
+        if idx == new_idx:
+            return deltas
+    ret = np.zeros(new_idx[-1] - new_idx[0] + 1)
+    for i in range(shape):
+        if idx[i] in new_idx:
+            ret[idx[i] - new_idx[0]] = deltas[i]
+    return np.array([ret[new_idx[i] - new_idx[0]] for i in range(len(new_idx))])
+
+
 def _filter_zeroes(deltas, idx, eps=Obs.filter_eps):
     """Filter out all configurations with vanishing fluctuation such that they do not
        contribute to the error estimate anymore. Returns the new deltas and
@@ -1429,8 +1492,8 @@ def _covariance_element(obs1, obs2):
     """Estimates the covariance of two Obs objects, neglecting autocorrelations."""
 
     def calc_gamma(deltas1, deltas2, idx1, idx2, new_idx):
-        deltas1 = _expand_deltas_for_merge(deltas1, idx1, len(idx1), new_idx)
+        deltas1 = _collapse_deltas_for_merge(deltas1, idx1, len(idx1), new_idx)
-        deltas2 = _expand_deltas_for_merge(deltas2, idx2, len(idx2), new_idx)
+        deltas2 = _collapse_deltas_for_merge(deltas2, idx2, len(idx2), new_idx)
         return np.sum(deltas1 * deltas2)
 
     if set(obs1.names).isdisjoint(set(obs2.names)):
@@ -1450,29 +1513,30 @@ def _covariance_element(obs1, obs2):
         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]])
+            idl_d[r_name] = _intersection_idx([obs1.idl[r_name], obs2.idl[r_name]])
 
         gamma = 0.0
 
         for r_name in obs1.e_content[e_name]:
             if r_name not in obs2.e_content[e_name]:
                 continue
+            if len(idl_d[r_name]) == 0:
+                continue
             gamma += calc_gamma(obs1.deltas[r_name], obs2.deltas[r_name], obs1.idl[r_name], obs2.idl[r_name], idl_d[r_name])
 
         if gamma == 0.0:
             continue
 
         gamma_div = 0.0
-        e_N = 0
         for r_name in obs1.e_content[e_name]:
             if r_name not in obs2.e_content[e_name]:
                 continue
-            gamma_div += calc_gamma(np.ones(obs1.shape[r_name]), np.ones(obs2.shape[r_name]), obs1.idl[r_name], obs2.idl[r_name], idl_d[r_name])
+            if len(idl_d[r_name]) == 0:
-            e_N += len(idl_d[r_name])
+                continue
-        gamma /= max(gamma_div, 1.0)
+            gamma_div += np.sqrt(calc_gamma(obs1.deltas[r_name], obs1.deltas[r_name], obs1.idl[r_name], obs1.idl[r_name], idl_d[r_name]) * calc_gamma(obs2.deltas[r_name], obs2.deltas[r_name], obs2.idl[r_name], obs2.idl[r_name], idl_d[r_name]))
+        gamma /= gamma_div
 
-        # Bias correction hep-lat/0306017 eq. (49)
+        dvalue += gamma
-        dvalue += (1 + 1 / e_N) * gamma / e_N
 
     for e_name in obs1.cov_names:
 

tests/obs_test.py

@@ -515,6 +515,35 @@ def test_merge_idx():
     assert pe.obs._merge_idx([range(500, 6050, 50), range(500, 6250, 250)]) == range(500, 6250, 50)
 
 
+def test_intersection_idx():
+    assert pe.obs._intersection_idx([range(1, 100), range(1, 100), range(1, 100)]) == range(1, 100)
+    assert pe.obs._intersection_idx([range(1, 100, 10), range(1, 100, 2)]) == range(1, 100, 10)
+    assert pe.obs._intersection_idx([range(10, 1010, 10), range(10, 1010, 50)]) == range(10, 1010, 50)
+    assert pe.obs._intersection_idx([range(500, 6050, 50), range(500, 6250, 250)]) == range(500, 6050, 250)
+
+    for ids in [[list(range(1, 80, 3)), list(range(1, 100, 2))], [range(1, 80, 3), range(1, 100, 2), range(1, 100, 7)]]:
+        assert list(pe.obs._intersection_idx(ids)) == pe.obs._intersection_idx([list(o) for o in ids])
+
+def test_merge_intersection():
+    for idl_list in [[range(1, 100), range(1, 100), range(1, 100)],
+                     [range(4, 80, 6), range(4, 80, 6)],
+                     [[0, 2, 8, 19, 205], [0, 2, 8, 19, 205]]]:
+        assert pe.obs._merge_idx(idl_list) == pe.obs._intersection_idx(idl_list)
+
+
+def test_intersection_collapse():
+    range1 = range(1, 2000, 2)
+    range2 = range(2, 2001, 8)
+
+    obs1 = pe.Obs([np.random.normal(1.0, 0.1, len(range1))], ["ens"], idl=[range1])
+    obs_merge = obs1 + pe.Obs([np.random.normal(1.0, 0.1, len(range2))], ["ens"], idl=[range2])
+
+    intersection = pe.obs._intersection_idx([o.idl["ens"] for o in [obs1, obs_merge]])
+    coll = pe.obs._collapse_deltas_for_merge(obs_merge.deltas["ens"], obs_merge.idl["ens"], len(obs_merge.idl["ens"]), range1)
+
+    assert np.all(coll == obs1.deltas["ens"])
+
+
 def test_irregular_error_propagation():
     obs_list = [pe.Obs([np.random.rand(100)], ['t']),
                 pe.Obs([np.random.rand(50)], ['t'], idl=[range(1, 100, 2)]),
@@ -619,6 +648,26 @@ def test_covariance_is_variance():
     assert np.isclose(test_obs.dvalue ** 2, pe.covariance([test_obs, test_obs])[0, 1])
 
 
+def test_covariance_vs_numpy():
+    N = 1078
+    data1 = np.random.normal(2.5, 0.2, N)
+    data2 = np.random.normal(0.5, 0.08, N)
+    data3 = np.random.normal(-178, 5, N)
+    uncorr = np.row_stack([data1, data2, data3])
+    corr = np.random.multivariate_normal([0.0, 17, -0.0487], [[1.0, 0.6, -0.22], [0.6, 0.8, 0.01], [-0.22, 0.01, 1.9]], N).T
+
+    for X in [uncorr, corr]:
+        obs1 = pe.Obs([X[0]], ["ens1"])
+        obs2 = pe.Obs([X[1]], ["ens1"])
+        obs3 = pe.Obs([X[2]], ["ens1"])
+        obs1.gamma_method(S=0.0)
+        obs2.gamma_method(S=0.0)
+        obs3.gamma_method(S=0.0)
+        pe_cov = pe.covariance([obs1, obs2, obs3])
+        np_cov = np.cov(X) / N
+        assert np.allclose(pe_cov, np_cov, atol=1e-14)
+
+
 def test_covariance_symmetry():
     value1 = np.random.normal(5, 10)
     dvalue1 = np.abs(np.random.normal(0, 1))
@@ -729,6 +778,86 @@ def test_covariance_idl():
     pe.covariance([obs1, obs2])
 
 
+def test_correlation_intersection_of_idls():
+    range1 = range(1, 2000, 2)
+    range2 = range(2, 2001, 2)
+
+    obs1 = pe.Obs([np.random.normal(1.0, 0.1, len(range1))], ["ens"], idl=[range1])
+    obs2_a = 0.4 * pe.Obs([np.random.normal(1.0, 0.1, len(range1))], ["ens"], idl=[range1]) + 0.6 * obs1
+    obs1.gamma_method()
+    obs2_a.gamma_method()
+
+    cov1 = pe.covariance([obs1, obs2_a])
+    corr1 = pe.covariance([obs1, obs2_a], correlation=True)
+
+    obs2_b = obs2_a + pe.Obs([np.random.normal(1.0, 0.1, len(range2))], ["ens"], idl=[range2])
+    obs2_b.gamma_method()
+
+    cov2 = pe.covariance([obs1, obs2_b])
+    corr2 = pe.covariance([obs1, obs2_b], correlation=True)
+
+    assert np.isclose(corr1[0, 1], corr2[0, 1], atol=1e-14)
+    assert cov1[0, 1] > cov2[0, 1]
+
+    obs2_c = pe.Obs([np.random.normal(1.0, 0.1, len(range2))], ["ens"], idl=[range2])
+    obs2_c.gamma_method()
+    assert np.isclose(0, pe.covariance([obs1, obs2_c])[0, 1], atol=1e-14)
+
+
+def test_covariance_non_identical_objects():
+    obs1 = pe.Obs([np.random.normal(1.0, 0.1, 1000), np.random.normal(1.0, 0.1, 1000), np.random.normal(1.0, 0.1, 732)], ["ens|r1", "ens|r2", "ens2"])
+    obs1.gamma_method()
+    obs2 = obs1 + 1e-18
+    obs2.gamma_method()
+    assert obs1 == obs2
+    assert obs1 is not obs2
+    assert np.allclose(np.ones((2, 2)), pe.covariance([obs1, obs2], correlation=True), atol=1e-14)
+
+
+def test_covariance_additional_non_overlapping_data():
+    range1 = range(1, 20, 2)
+
+    data2 = np.random.normal(0.0, 0.1, len(range1))
+
+    obs1 = pe.Obs([np.random.normal(1.0, 0.1, len(range1))], ["ens"], idl=[range1])
+    obs2_a = pe.Obs([data2], ["ens"], idl=[range1])
+    obs1.gamma_method()
+    obs2_a.gamma_method()
+
+    corr1 = pe.covariance([obs1, obs2_a], correlation=True)
+
+    added_data = np.random.normal(0.0, 0.1, len(range1))
+    added_data -= np.mean(added_data) - np.mean(data2)
+    data2_extended = np.ravel([data2, added_data], 'F')
+
+    obs2_b = pe.Obs([data2_extended], ["ens"])
+    obs2_b.gamma_method()
+
+    corr2 = pe.covariance([obs1, obs2_b], correlation=True)
+
+    assert np.isclose(corr1[0, 1], corr2[0, 1], atol=1e-14)
+
+
+def test_coavariance_reorder_non_overlapping_data():
+    range1 = range(1, 20, 2)
+    range2 = range(1, 41, 2)
+
+    obs1 = pe.Obs([np.random.normal(1.0, 0.1, len(range1))], ["ens"], idl=[range1])
+    obs2_b = pe.Obs([np.random.normal(1.0, 0.1, len(range2))], ["ens"], idl=[range2])
+    obs1.gamma_method()
+    obs2_b.gamma_method()
+
+    corr1 = pe.covariance([obs1, obs2_b], correlation=True)
+
+    deltas = list(obs2_b.deltas['ens'][:len(range1)]) + sorted(obs2_b.deltas['ens'][len(range1):])
+    obs2_a = pe.Obs([obs2_b.value + np.array(deltas)], ["ens"], idl=[range2])
+    obs2_a.gamma_method()
+
+    corr2 = pe.covariance([obs1, obs2_a], correlation=True)
+
+    assert np.isclose(corr1[0, 1], corr2[0, 1], atol=1e-14)
+
+
 def test_empty_obs():
     o = pe.Obs([np.random.rand(100)], ['test'])
     q = o + pe.Obs([], [], means=[])