From 8bb1a910c613329c9015cf7fbddb913909497d05 Mon Sep 17 00:00:00 2001
From: Fabian Joswig <fabian.joswig@ed.ac.uk>
Date: Mon, 15 Nov 2021 14:57:58 +0000
Subject: [PATCH] docs: documentation of CObs extended

---
 pyerrors/__init__.py | 27 ++++++++++++++++++++++++---
 1 file changed, 24 insertions(+), 3 deletions(-)

diff --git a/pyerrors/__init__.py b/pyerrors/__init__.py
index a298f982..b7f8f1ed 100644
--- a/pyerrors/__init__.py
+++ b/pyerrors/__init__.py
@@ -22,8 +22,8 @@ print(my_new_obs)
 
 iamzero = my_new_obs - my_new_obs
 iamzero.gamma_method()
-print(iamzero)
-> 0.0
+print(iamzero == 0.0)
+> True
 ```
 
 # The `Obs` class
@@ -189,7 +189,28 @@ For the full API see `pyerrors.obs.Obs`
 For the full API see `pyerrors.correlators.Corr`
 
 # Complex observables
-`pyerrors.obs.CObs`
+
+`pyerrors` can handle complex valued observables via the class `pyerrors.obs.CObs`.
+`CObs` are initialized with a real and an imaginary part which both can be `Obs` valued.
+
+Example:
+```python
+my_real_part = pe.Obs([samples1], ['ensemble1'])
+my_imag_part = pe.Obs([samples2], ['ensemble1'])
+
+my_cobs = pe.CObs(my_real_part, my_imag_part)
+my_cobs.gamma_method()
+print(my_cobs)
+> (0.9959(91)+0.659(28)j)
+```
+
+Elementary mathematical operations are overloaded and samples are properly propagated as for the `Obs` class.
+```python
+my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)
+my_derived_cobs.gamma_method()
+print(my_derived_cobs)
+> (1.668(23)+0.0j)
+```
 
 # Optimization / fits / roots
 `pyerrors.fits`