diff --git a/__pycache__/analysis.cpython-37.pyc b/__pycache__/analysis.cpython-37.pyc
index 121d58ba..2b29feb5 100644
Binary files a/__pycache__/analysis.cpython-37.pyc and b/__pycache__/analysis.cpython-37.pyc differ
diff --git a/analysis.py b/analysis.py
index f39a67d8..c61550ee 100644
--- a/analysis.py
+++ b/analysis.py
@@ -45,6 +45,15 @@ import scipy
 import matplotlib
 from sklearn import *
 
+import collections
+import numbers
+
+from fractions import Fraction
+from decimal import Decimal
+from itertools import groupby
+from bisect import bisect_left, bisect_right
+
+
 def _init_device (setting, arg): #initiates computation device for ANNs
     if setting == "cuda":
         temp = setting + ":" + arg