add some util functions

util.py

@@ -0,0 +1,36 @@
+import numpy as np
+
+def gaussKernel(sigma, dt):
+    """ Creates a Gaussian kernel with a given standard deviation and an integral of 1.
+
+    Args:
+        sigma (float): The standard deviation of the kernel.
+        dt (float): The temporal resolution of the kernel, given in seconds.
+
+    Returns:
+        numpy.ndarray : the kernel in the range -4 to +4 sigma
+    """
+    x = np.arange(-4. * sigma, 4. * sigma, dt)
+    y = np.exp(-0.5 * (x / sigma) ** 2) / np.sqrt(2. * np.pi) / sigma
+    return y
+
+
+def firing_rate(spikes, duration, sigma=0.005, dt=1./20000.):
+    """Convert spike times to a firing rate using the kernel convolution with a Gaussian kernel
+
+    Args:
+        spikes (iterable): list of spike times, times should be in seconds
+        duration (float): duration of the trial in seconds
+        sigma (float, optional): standard deviation of the Gaussian kernel. Defaults to 0.005s.
+        dt (float, optional): The stepsize of the trace. Defaults to 1./20000.s.
+
+    Returns:
+        np.ndarray: the firing rate
+    """
+    binary = np.zeros(int(np.round(duration/dt)))
+    indices = np.asarray(np.round(spikes / dt), dtype=np.int)
+    binary[indices[indices < len(binary)]] = 1
+    kernel = gaussKernel(sigma, dt)
+
+    rate = np.convolve(kernel, binary, mode="same")
+    return rate