From a729def9374fd54831e93f7c9fd052c61e850b2c Mon Sep 17 00:00:00 2001
From: Fabian Joswig <fabian.joswig@ed.ac.uk>
Date: Mon, 31 Jan 2022 12:10:38 +0000
Subject: [PATCH] feat: backward derivative implemented, additional tests for
 deriv

---
 pyerrors/correlators.py   | 12 +++++++++++-
 tests/correlators_test.py | 14 ++++++++++++++
 2 files changed, 25 insertions(+), 1 deletion(-)

diff --git a/pyerrors/correlators.py b/pyerrors/correlators.py
index 1594b14d..49388330 100644
--- a/pyerrors/correlators.py
+++ b/pyerrors/correlators.py
@@ -467,7 +467,7 @@ class Corr:
         ----------
         variant : str
             decides which definition of the finite differences derivative is used.
-            Available choice: symmetric, forward, improved, default: symmetric
+            Available choice: symmetric, forward, backward, improved, default: symmetric
         """
         if variant == "symmetric":
             newcontent = []
@@ -489,6 +489,16 @@ class Corr:
             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):
diff --git a/tests/correlators_test.py b/tests/correlators_test.py
index ce58e370..f83dc3f4 100644
--- a/tests/correlators_test.py
+++ b/tests/correlators_test.py
@@ -72,6 +72,20 @@ def test_modify_correlator():
                 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():