Merge branch 'develop' into documentation

pyerrors/correlators.py

@@ -457,25 +457,16 @@ class Corr:
 
         return (self + T_partner) / 2
 
-    def deriv(self, symmetric=True):
+    def deriv(self, variant="symmetric"):
         """Return the first derivative of the correlator with respect to x0.
 
         Parameters
         ----------
-        symmetric : bool
+        variant : str
-            decides whether symmetric of simple finite differences are used. Default: True
+            decides which definition of the finite differences derivative is used.
+            Available choice: symmetric, forward, backward, improved, default: symmetric
         """
-        if not symmetric:
+        if variant == "symmetric":
-            newcontent = []
-            for t in range(self.T - 1):
-                if (self.content[t] is None) or (self.content[t + 1] is None):
-                    newcontent.append(None)
-                else:
-                    newcontent.append(self.content[t + 1] - self.content[t])
-            if(all([x is None for x in newcontent])):
-                raise Exception("Derivative is undefined at all timeslices")
-            return Corr(newcontent, padding=[0, 1])
-        if symmetric:
             newcontent = []
             for t in range(1, self.T - 1):
                 if (self.content[t - 1] is None) or (self.content[t + 1] is None):
@@ -485,9 +476,49 @@ class Corr:
             if(all([x is None for x in newcontent])):
                 raise Exception('Derivative is undefined at all timeslices')
             return Corr(newcontent, padding=[1, 1])
+        elif variant == "forward":
+            newcontent = []
+            for t in range(self.T - 1):
+                if (self.content[t] is None) or (self.content[t + 1] is None):
+                    newcontent.append(None)
+                else:
+                    newcontent.append(self.content[t + 1] - self.content[t])
+            if(all([x is None for x in newcontent])):
+                raise Exception("Derivative is undefined at all timeslices")
+            return Corr(newcontent, padding=[0, 1])
+        elif variant == "backward":
+            newcontent = []
+            for t in range(1, self.T):
+                if (self.content[t - 1] is None) or (self.content[t] is None):
+                    newcontent.append(None)
+                else:
+                    newcontent.append(self.content[t] - self.content[t - 1])
+            if(all([x is None for x in newcontent])):
+                raise Exception("Derivative is undefined at all timeslices")
+            return Corr(newcontent, padding=[1, 0])
+        elif variant == "improved":
+            newcontent = []
+            for t in range(2, self.T - 2):
+                if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None):
+                    newcontent.append(None)
+                else:
+                    newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2]))
+            if(all([x is None for x in newcontent])):
+                raise Exception('Derivative is undefined at all timeslices')
+            return Corr(newcontent, padding=[2, 2])
+        else:
+            raise Exception("Unknown variant.")
 
-    def second_deriv(self):
+    def second_deriv(self, variant="symmetric"):
-        """Return the second derivative of the correlator with respect to x0."""
+        """Return the second derivative of the correlator with respect to x0.
+
+        Parameters
+        ----------
+        variant : str
+            decides which definition of the finite differences derivative is used.
+            Available choice: symmetric, improved, default: symmetric
+        """
+        if variant == "symmetric":
             newcontent = []
             for t in range(1, self.T - 1):
                 if (self.content[t - 1] is None) or (self.content[t + 1] is None):
@@ -497,6 +528,18 @@ class Corr:
             if(all([x is None for x in newcontent])):
                 raise Exception("Derivative is undefined at all timeslices")
             return Corr(newcontent, padding=[1, 1])
+        elif variant == "improved":
+            newcontent = []
+            for t in range(2, self.T - 2):
+                if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None):
+                    newcontent.append(None)
+                else:
+                    newcontent.append((1 / 12) * (-self.content[t + 2] + 16 * self.content[t + 1] - 30 * self.content[t] + 16 * self.content[t - 1] - self.content[t - 2]))
+            if(all([x is None for x in newcontent])):
+                raise Exception("Derivative is undefined at all timeslices")
+            return Corr(newcontent, padding=[2, 2])
+        else:
+            raise Exception("Unknown variant.")
 
     def m_eff(self, variant='log', guess=1.0):
         """Returns the effective mass of the correlator as correlator object

tests/correlators_test.py

@@ -45,7 +45,7 @@ def test_modify_correlator():
         exponent = np.random.normal(3, 5)
         corr_content.append(pe.pseudo_Obs(2 + 10 ** exponent, 10 ** (exponent - 1), 't'))
 
-    corr = pe.correlators.Corr(corr_content)
+    corr = pe.Corr(corr_content)
 
     with pytest.warns(RuntimeWarning):
         corr.symmetric()
@@ -53,14 +53,40 @@ def test_modify_correlator():
         corr.anti_symmetric()
 
     for pad in [0, 2]:
-        corr = pe.correlators.Corr(corr_content, padding=[pad, pad])
+        corr = pe.Corr(corr_content, padding=[pad, pad])
         corr.roll(np.random.randint(100))
-        corr.deriv(symmetric=True)
+        corr.deriv(variant="forward")
-        corr.deriv(symmetric=False)
+        corr.deriv(variant="symmetric")
+        corr.deriv(variant="improved")
         corr.deriv().deriv()
-        corr.second_deriv()
+        corr.second_deriv(variant="symmetric")
+        corr.second_deriv(variant="improved")
         corr.second_deriv().second_deriv()
 
+    for i, e in enumerate(corr.content):
+        corr.content[i] = None
+
+    for func in [pe.Corr.deriv, pe.Corr.second_deriv]:
+        for variant in ["symmetric", "improved", "forward", "gibberish", None]:
+            with pytest.raises(Exception):
+                func(corr, variant=variant)
+
+
+def test_deriv():
+    corr_content = []
+    for t in range(24):
+        exponent = 1.2
+        corr_content.append(pe.pseudo_Obs(2 + t ** exponent, 0.2, 't'))
+
+    corr = pe.Corr(corr_content)
+
+    forward = corr.deriv(variant="forward")
+    backward = corr.deriv(variant="backward")
+    sym = corr.deriv(variant="symmetric")
+    assert np.all([o == 0 for o in (0.5 * (forward + backward) - sym)[1:-1]])
+    assert np.all([o == 0 for o in (corr.deriv('forward').deriv('backward') - corr.second_deriv())[1:-1]])
+    assert np.all([o == 0 for o in (corr.deriv('backward').deriv('forward') - corr.second_deriv())[1:-1]])
+
 
 def test_m_eff():
     for padding in [0, 4]: