Additional GEVP method with errors (#195)

* Added the function error_gevp() to compute the gevp with statistical errors.

* Changed method name from error_gevp to error_GEVP and removed automatic gamma method

* added auto_gamma to error_GEVP

* Specified exceptions in Corr.error_GEVP

* Fixed a wrong path. It should be np.linalg.LinAlgError

* Added a test for error_GEVP

* The tests of error_gevp loads a test matrix

* Incorporated eigenvectors with uncertainties in GEVP routine

* Cleaned up GEVP routines

* Cleaned up breaking change from merge

* Released tolerance in test of GEVP

* Repaired broken GEVP test

---------

Co-authored-by: Simon Kuberski <simon.kuberski@uni-muenster.de>

tests/correlators_test.py

@@ -200,17 +200,17 @@ def test_padded_correlator():
 
 def test_corr_exceptions():
     obs_a = pe.Obs([np.random.normal(0.1, 0.1, 100)], ['test'])
-    obs_b= pe.Obs([np.random.normal(0.1, 0.1, 99)], ['test'])
+    obs_b = pe.Obs([np.random.normal(0.1, 0.1, 99)], ['test'])
     with pytest.raises(Exception):
         pe.Corr([obs_a, obs_b])
 
     obs_a = pe.Obs([np.random.normal(0.1, 0.1, 100)], ['test'])
-    obs_b= pe.Obs([np.random.normal(0.1, 0.1, 100)], ['test'], idl=[range(1, 200, 2)])
+    obs_b = pe.Obs([np.random.normal(0.1, 0.1, 100)], ['test'], idl=[range(1, 200, 2)])
     with pytest.raises(Exception):
         pe.Corr([obs_a, obs_b])
 
     obs_a = pe.Obs([np.random.normal(0.1, 0.1, 100)], ['test'])
-    obs_b= pe.Obs([np.random.normal(0.1, 0.1, 100)], ['test2'])
+    obs_b = pe.Obs([np.random.normal(0.1, 0.1, 100)], ['test2'])
     with pytest.raises(Exception):
         pe.Corr([obs_a, obs_b])
 
@@ -436,6 +436,7 @@ def test_GEVP_solver():
     sp_vecs = [v / np.sqrt((v.T @ mat2 @ v)) for v in sp_vecs]
 
     assert np.allclose(sp_vecs, pe.correlators._GEVP_solver(mat1, mat2), atol=1e-14)
+    assert np.allclose(np.abs(sp_vecs), np.abs(pe.correlators._GEVP_solver(mat1, mat2, method='cholesky')))
 
 
 def test_GEVP_none_entries():
@@ -552,7 +553,7 @@ def test_corr_no_filtering():
     li = [-pe.pseudo_Obs(.2, .1, 'a', samples=10) for i in range(96)]
     for i in range(len(li)):
         li[i].idl['a'] = range(1, 21, 2)
-    c= pe.Corr(li)
+    c = pe.Corr(li)
     b = pe.pseudo_Obs(1, 1e-11, 'a', samples=30)
     c *= b
     assert np.all([c[0].idl == o.idl for o in c])
@@ -572,6 +573,28 @@ def test_corr_symmetric():
         assert scorr[0] == corr[0]
 
 
+def test_error_GEVP():
+    corr = pe.input.json.load_json("tests/data/test_matrix_corr.json.gz")
+    t0, ts, state = 3, 6, 0
+    vec_regular = corr.GEVP(t0=t0)[state][ts]
+    vec_errors = corr.GEVP(t0=t0, vector_obs=True, auto_gamma=True)[state][ts]
+    vec_regular_chol = corr.GEVP(t0=t0, method='cholesky')[state][ts]
+    print(vec_errors)
+    print(type(vec_errors[0]))
+    assert(np.isclose(np.asarray([e.value for e in vec_errors]), vec_regular).all())
+    assert(all([e.dvalue > 0. for e in vec_errors]))
+
+    projected_regular = corr.projected(vec_regular).content[ts + 1][0]
+    projected_errors = corr.projected(vec_errors).content[ts + 1][0]
+    projected_regular.gamma_method()
+    projected_errors.gamma_method()
+    assert(projected_errors.dvalue > projected_regular.dvalue)
+    assert(corr.GEVP(t0, vector_obs=True)[state][42] is None)
+
+    assert(np.isclose(vec_regular_chol, vec_regular).all())
+    assert(np.isclose(corr.GEVP(t0=t0, state=state)[ts], vec_regular).all())
+
+
 def test_corr_array_ndim1_init():
     y = [pe.pseudo_Obs(2 + np.random.normal(0.0, 0.1), .1, 't') for i in np.arange(5)]
     cc1 = pe.Corr(y)
@@ -688,7 +711,6 @@ def test_matrix_trace():
     for el in corr.trace():
         assert el == 0
 
-
     with pytest.raises(ValueError):
         corr.item(0, 0).trace()