From 11f05d9dac3711d89db37a043db3d9437958c6f3 Mon Sep 17 00:00:00 2001
From: Mario Mulansky <mario.mulansky@gmx.net>
Date: Wed, 22 Oct 2014 22:17:27 +0200
Subject: avrg functions now take intervals

---
 pyspike/function.py   | 51 ++++++++++++++++++++++++++++++++++++++++++++-------
 test/test_function.py | 19 ++++++++++++++++++-
 2 files changed, 62 insertions(+), 8 deletions(-)

diff --git a/pyspike/function.py b/pyspike/function.py
index 14ad7bd..e340096 100644
--- a/pyspike/function.py
+++ b/pyspike/function.py
@@ -83,20 +83,24 @@ class PieceWiseConstFunc(object):
         """
         if interval is None:
             # no interval given, average over the whole spike train
-            return np.sum((self.x[1:]-self.x[:-1]) * self.y) / \
+            a = np.sum((self.x[1:]-self.x[:-1]) * self.y) / \
                 (self.x[-1]-self.x[0])
         else:
+            # find the indices corresponding to the interval
             start_ind = np.searchsorted(self.x, interval[0], side='right')
             end_ind = np.searchsorted(self.x, interval[1], side='left')-1
-            print(start_ind, end_ind)
             assert start_ind > 0 and end_ind < len(self.x), \
                 "Invalid averaging interval"
-            a = np.sum((self.x[start_ind+1:end_ind] -
-                        self.x[start_ind:end_ind-1]) *
+            # first the contribution from between the indices
+            a = np.sum((self.x[start_ind+1:end_ind+1] -
+                        self.x[start_ind:end_ind]) *
                        self.y[start_ind:end_ind])
-            a += (self.x[start_ind]-interval[0]) * self.y[start_ind]
+            # correction from start to first index
+            a += (self.x[start_ind]-interval[0]) * self.y[start_ind-1]
+            # correction from last index to end
             a += (interval[1]-self.x[end_ind]) * self.y[end_ind]
-            return a / (interval[1]-interval[0])
+            a /= (interval[1]-interval[0])
+        return a
 
     def add(self, f):
         """ Adds another PieceWiseConst function to this function.
@@ -202,10 +206,43 @@ class PieceWiseLinFunc:
         :returns: the average a.
         :rtype: double
         """
+
+        def intermediate_value(x0, x1, y0, y1, x):
+            """ computes the intermediate value of a linear function """
+            return y0 + (y1-y0)*(x-x0)/(x1-x0)
+
         if interval is None:
             # no interval given, average over the whole spike train
-            return np.sum((self.x[1:]-self.x[:-1]) * 0.5*(self.y1+self.y2)) / \
+            a = np.sum((self.x[1:]-self.x[:-1]) * 0.5*(self.y1+self.y2)) / \
                 (self.x[-1]-self.x[0])
+        else:
+            # find the indices corresponding to the interval
+            start_ind = np.searchsorted(self.x, interval[0], side='right')
+            end_ind = np.searchsorted(self.x, interval[1], side='left')-1
+            assert start_ind > 0 and end_ind < len(self.x), \
+                "Invalid averaging interval"
+            # first the contribution from between the indices
+            a = np.sum((self.x[start_ind+1:end_ind+1] -
+                        self.x[start_ind:end_ind]) *
+                       0.5*(self.y1[start_ind:end_ind] +
+                            self.y2[start_ind:end_ind]))
+            # correction from start to first index
+            a += (self.x[start_ind]-interval[0]) * 0.5 * \
+                 (self.y2[start_ind-1] +
+                  intermediate_value(self.x[start_ind-1], self.x[start_ind],
+                                     self.y1[start_ind-1],
+                                     self.y2[start_ind-1],
+                                     interval[0]
+                                     ))
+            # correction from last index to end
+            a += (interval[1]-self.x[end_ind]) * 0.5 * \
+                 (self.y1[end_ind] +
+                  intermediate_value(self.x[end_ind], self.x[end_ind+1],
+                                     self.y1[end_ind], self.y2[end_ind],
+                                     interval[1]
+                                     ))
+            a /= (interval[1]-interval[0])
+        return a
 
     def add(self, f):
         """ Adds another PieceWiseLin function to this function.
diff --git a/test/test_function.py b/test/test_function.py
index cabcf44..ed0b2ed 100644
--- a/test/test_function.py
+++ b/test/test_function.py
@@ -31,8 +31,13 @@ def test_pwc():
 
     # interval averaging
     a = f.avrg([0.5, 3.5])
-    print(a)
     assert_almost_equal(a, (0.5-0.5+0.5*1.5+1.0*0.75)/3.0, decimal=16)
+    a = f.avrg([1.5, 3.5])
+    assert_almost_equal(a, (-0.5*0.5+0.5*1.5+1.0*0.75)/2.0, decimal=16)
+    a = f.avrg([1.0, 3.5])
+    assert_almost_equal(a, (-0.5*1.0+0.5*1.5+1.0*0.75)/2.5, decimal=16)
+    a = f.avrg([1.0, 4.0])
+    assert_almost_equal(a, (-0.5*1.0+0.5*1.5+1.5*0.75)/3.0, decimal=16)
 
 
 def test_pwc_add():
@@ -105,6 +110,18 @@ def test_pwl():
     avrg_expected = (1.25 - 0.45 + 0.75 + 1.5*0.5) / 4.0
     assert_almost_equal(f.avrg(), avrg_expected, decimal=16)
 
+    # interval averaging
+    a = f.avrg([0.5, 2.5])
+    assert_almost_equal(a, (1.375*0.5 - 0.45 + 0.75)/2.0, decimal=16)
+    a = f.avrg([1.5, 3.5])
+    assert_almost_equal(a, (-0.425*0.5 + 0.75 + (0.75+0.75-0.5/1.5)/2) / 2.0,
+                        decimal=16)
+    a = f.avrg([1.0, 3.5])
+    assert_almost_equal(a, (-0.45 + 0.75 + (0.75+0.75-0.5/1.5)/2) / 2.5,
+                        decimal=16)
+    a = f.avrg([1.0, 4.0])
+    assert_almost_equal(a, (-0.45 + 0.75 + 1.5*0.5) / 3.0, decimal=16)
+
 
 def test_pwl_add():
     x = [0.0, 1.0, 2.0, 2.5, 4.0]
-- 
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