add spike-distance, PWL function (probably buggy)

3 files changed, 129 insertions, 7 deletions

diff --git a/pyspike/__init__.py b/pyspike/__init__.py
index 6895bd8..a5f146a 100644
--- a/pyspike/__init__.py
+++ b/pyspike/__init__.py
@@ -1,5 +1,5 @@
 __all__ = ["function", "distances", "spikes"]
 
-from function import PieceWiseConstFunc
-from distances import isi_distance
+from function import PieceWiseConstFunc, PieceWiseLinFunc
+from distances import isi_distance, spike_distance
 from spikes import spike_train_from_string, merge_spike_trains
diff --git a/pyspike/distances.py b/pyspike/distances.py
index f4989c8..2ea80e7 100644
--- a/pyspike/distances.py
+++ b/pyspike/distances.py
@@ -7,11 +7,11 @@ Copyright 2014, Mario Mulansky <mario.mulansky@gmx.net>
 
 import numpy as np
 
-from pyspike import PieceWiseConstFunc
+from pyspike import PieceWiseConstFunc, PieceWiseLinFunc
 
 def isi_distance(spikes1, spikes2, T_end, T_start=0.0):
-    """ Computes the instantaneous isi-distance S_isi (t) of the two given spike
-    trains. 
+    """ Computes the instantaneous isi-distance S_isi (t) of the two given 
+    spike trains. 
     Args:
     - spikes1, spikes2: ordered arrays of spike times.
     - T_end: end time of the observation interval.
@@ -50,6 +50,7 @@ def isi_distance(spikes1, spikes2, T_end, T_start=0.0):
         # check which spike is next - from s1 or s2
         if s1[index1+1] <= s2[index2+1]:
             index1 += 1
+            # break condition relies on existence of spikes at T_end
             if index1 >= len(nu1):
                 break
             spike_events[index] = s1[index1]
@@ -63,3 +64,95 @@ def isi_distance(spikes1, spikes2, T_end, T_start=0.0):
                             max(nu1[index1], nu2[index2])
         index += 1
     return PieceWiseConstFunc(spike_events, isi_values)
+
+
+def get_min_dist(spike_time, spike_train, start_index=0):
+    """ Returns the minimal distance |spike_time - spike_train[i]| 
+    with i>=start_index
+    """
+    d = abs(spike_time - spike_train[start_index])
+    start_index += 1
+    while start_index < len(spike_train):
+        d_temp = abs(spike_time - spike_train[start_index])
+        if d_temp > d:
+            break
+        else:
+            d = d_temp
+        start_index += 1
+    return d
+
+
+def spike_distance(spikes1, spikes2, T_end, T_start=0.0):
+    """ Computes the instantaneous spike-distance S_spike (t) of the two given
+    spike trains.
+    Args:
+    - spikes1, spikes2: ordered arrays of spike times.
+    - T_end: end time of the observation interval.
+    - T_start: begin of the observation interval (default=0.0).
+    Returns:
+    - PieceWiseLinFunc describing the spike-distance.
+    """
+    # add spikes at the beginning and end of the interval
+    t1 = np.empty(len(spikes1)+2)
+    t1[0] = T_start
+    t1[-1] = T_end
+    t1[1:-1] = spikes1
+    t2 = np.empty(len(spikes2)+2)
+    t2[0] = T_start
+    t2[-1] = T_end
+    t2[1:-1] = spikes2
+
+    spike_events = np.empty(len(t1)+len(t2)-2)
+    spike_events[0] = T_start
+    spike_events[-1] = T_end
+    y_starts = np.empty(len(spike_events)-1)
+    y_starts[0] = 0.0
+    y_ends = np.empty(len(spike_events)-1)
+
+    index1 = 0
+    index2 = 0
+    index = 1
+    dt_p1 = 0.0
+    dt_f1 = get_min_dist(t1[1], t2, 0)
+    dt_p2 = 0.0
+    dt_f2 = get_min_dist(t2[1], t1, 0)
+    isi1 = t1[1]-t1[0]
+    isi2 = t2[1]-t2[0]
+    while True:
+        print(index, index1, index2)
+        if t1[index1+1] < t2[index2+1]:
+            index1 += 1
+            # break condition relies on existence of spikes at T_end
+            if index1+1 >= len(t1):
+                break
+            spike_events[index] = t1[index1]
+            # first calculate the previous interval end value
+            dt_p1 = dt_f1 # the previous time now was the following time before
+            s1 = dt_p1
+            s2 = (dt_p2*(t2[index2+1]-t1[index1]) + dt_f2*(t1[index1]-t2[index2])) / isi2
+            y_ends[index-1] = (s1*isi2 + s2*isi1) / ((isi1+isi2)**2/2)
+            # now the next interval start value
+            dt_f1 = get_min_dist(t1[index1+1], t2, index2)
+            s1 = dt_f1
+            isi1 = t1[index1+1]-t1[index1]
+            # s2 is the same as above, thus we can compute y2 immediately
+            y_starts[index] = (s1*isi2 + s2*isi1) / ((isi1+isi2)**2/2)
+        else:
+            index2 += 1
+            if index2+1 >= len(t2):
+                break
+            spike_events[index] = t2[index2]
+            # first calculate the previous interval end value
+            dt_p2 = dt_f2 # the previous time now was the following time before
+            s1 = (dt_p1*(t1[index1+1]-t2[index2]) + dt_f1*(t2[index2]-t1[index1])) / isi1
+            s2 = dt_p2
+            y_ends[index-1] = (s1*isi2 + s2*isi1) / ((isi1+isi2)**2/2)
+            # now the next interval start value
+            dt_f2 = get_min_dist(t2[index2+1], t1, index1)
+            s2 = dt_f2
+            isi2 = t2[index2+1]-t2[index2]
+            # s2 is the same as above, thus we can compute y2 immediately
+            y_starts[index] = (s1*isi2 + s2*isi1) / ((isi1+isi2)**2/2)
+        index += 1
+
+    return PieceWiseLinFunc(spike_events, y_starts, y_ends)
diff --git a/pyspike/function.py b/pyspike/function.py
index c1de9cb..adf4dbb 100644
--- a/pyspike/function.py
+++ b/pyspike/function.py
@@ -44,8 +44,6 @@ class PieceWiseConstFunc:
         Returns:
         - the average a. 
         """
-        print(self.x)
-        print(self.y)
         return np.sum((self.x[1:]-self.x[:-1]) * self.y) / \
             (self.x[-1]-self.x[0])
 
@@ -58,3 +56,34 @@ class PieceWiseConstFunc:
         """
         return np.sum((self.x[1:]-self.x[:-1]) * np.abs(self.y)) / \
             (self.x[-1]-self.x[0])
+
+
+class PieceWiseLinFunc:
+    """ A class representing a piece-wise linear function. """
+    
+    def __init__(self, x, y1, y2):
+        """ Constructs the piece-wise linear function.
+        Params:
+        - x: array of length N+1 defining the edges of the intervals of the pwc
+        function.
+        - y1: array of length N defining the function values at the left of the 
+        intervals.
+        - y2: array of length N defining the function values at the right of the 
+        intervals.
+        """
+        self.x = x
+        self.y1 = y1
+        self.y2 = y2
+
+    def get_plottable_data(self):
+        """ Returns two arrays containing x- and y-coordinates for immeditate
+        plotting of the piece-wise function.
+        """
+        x_plot = np.empty(2*len(self.x)-2)
+        x_plot[0] = self.x[0]
+        x_plot[1::2] = self.x[1:]
+        x_plot[2::2] = self.x[1:-1]
+        y_plot = np.empty_like(x_plot)
+        y_plot[0::2] = self.y1
+        y_plot[1::2] = self.y2
+        return x_plot, y_plot