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@lotka
Created March 31, 2016 09:38
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{
"cells": [
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x7f5b556970d0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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dZx11Vp+eo7a2ltra2j7H4sS8pycB54nI2VhzFpWIyKPGmH8N3Sg0EbhF785i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\nESilVJbTRKCUUlnu/wMRhkFONwiaWQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f5b522bbd50>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x7f5b5213f550>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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wtP2h2UMEvvc9uOcea32lDUG+zW24DS0MZsH0JTQrcRa7j+7myOkjTodim4am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\nRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f5b520df1d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"class spike_rate_test():\n",
" def __init__(self,spike_train,dt):\n",
" self.dt = dt\n",
" self.spikes = np.array(spike_train)\n",
" self.noSpikes = len(self.spikes)\n",
" self.times = []\n",
" for i in xrange(self.noSpikes):\n",
" self.times.append(i*dt)\n",
" self.times = np.array(self.times)\n",
"\n",
" def plot_spikes(self):\n",
" plt.figure()\n",
" plt.scatter(np.array(self.times)[self.spikes > 0],np.array(self.spikes)[self.spikes > 0],color='red',s=50)\n",
" plt.xlim(0,self.noSpikes*self.dt)\n",
" def calculate_spiking_rate(self):\n",
"\n",
" spike_times, = np.where(self.spikes)\n",
"\n",
" fr = []\n",
" for i in xrange(len(spike_times)-1) :\n",
" t0 = spike_times[i] * self.dt\n",
" t1 = spike_times[i+1] * self.dt\n",
" s = t1 - t0\n",
" if s == 0:\n",
" print \"Divide Zero\"\n",
" return False\n",
" else :\n",
" fr.append(1.0/s)\n",
"\n",
" spike_times[-1]\n",
" plt.plot(self.dt*spike_times[:len(fr)],np.array(fr),label='subtract')\n",
" \n",
" def calculate_spiking_rate2(self):\n",
" \n",
" sum = self.spikes.sum()\n",
" window_size_s = float(len(self.spikes))/(float(sum)*2)\n",
" step = int(np.ceil(window_size_s))\n",
" t = []\n",
" fr = []\n",
" for i in xrange(0,len(self.spikes),step):\n",
" t.append(i*self.dt)\n",
" fr.append(self.spikes[i:i+step].sum()/(self.dt*step))\n",
" t = np.array(t)\n",
" fr = np.array(fr)\n",
" plt.plot(t,fr,label='window')\n",
" \n",
" def compareMethods(self):\n",
" a.plot_spikes()\n",
" plt.figure()\n",
" a.calculate_spiking_rate()\n",
" a.calculate_spiking_rate2()\n",
" plt.xlabel('time (s)')\n",
" plt.ylabel('spike rate 1/s')\n",
" plt.legend()\n",
" plt.show()\n",
"\n",
"a = spike_rate_test([1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1],0.1)\n",
"a.compareMethods()\n",
"a = spike_rate_test([1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1],0.1)\n",
"a.compareMethods()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.10"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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