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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Discrete Principle 3\n",
    "\n",
    "This notebook demonstrates the superior accuracy obtained by using the discretized version of Principle 3 that takes into account the simulation timestep."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%pylab inline\n",
    "import pylab\n",
    "try:\n",
    "    import seaborn as sns  # optional; prettier graphs\n",
    "except ImportError:\n",
    "    pass\n",
    "\n",
    "import numpy as np\n",
    "import nengo\n",
    "import nengolib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def go(sys=nengolib.synapses.Bandpass(20, 5), T=1.0, dt=0.001, n_neurons=200,\n",
    "       synapse=0.02, seed=0, discretized=True, neuron_type=nengo.LIF()):\n",
    "\n",
    "    with nengolib.Network(seed=seed) as model:\n",
    "        stim = nengo.Node(output=nengo.processes.WhiteSignal(T, high=50, rms=0.1, y0=0))\n",
    "        subnet = nengolib.networks.LinearNetwork(\n",
    "            sys, n_neurons_per_ensemble=n_neurons, synapse=synapse,\n",
    "            radii=1.0, dt=dt if discretized else None, output_synapse=synapse,\n",
    "            neuron_type=neuron_type)\n",
    "        nengo.Connection(stim, subnet.input, synapse=None)\n",
    "\n",
    "        p = nengo.Probe(subnet.output)\n",
    "        p_stim = nengo.Probe(stim)\n",
    "\n",
    "    with nengo.Simulator(model, dt=dt, seed=seed) as sim:\n",
    "        sim.run(T)\n",
    "\n",
    "    return sim.trange(), sim.data[p], sim.data[p_stim]\n",
    "\n",
    "t, disc_actual, expected = go(neuron_type=nengo.LIFRate())\n",
    "t, cont_actual, expected = go(discretized=False, neuron_type=nengo.LIFRate())\n",
    "t, ideal, expected = go(neuron_type=nengo.Direct())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pylab.figure(figsize=(16, 6))\n",
    "pylab.title(\"Comparison of Synapse Mapping Methods on a Bandpass Filter\")\n",
    "pylab.plot(t, disc_actual, linewidth=2, label=\"Discretized\")\n",
    "pylab.plot(t, cont_actual, linewidth=2, label=\"Principle 3\")\n",
    "pylab.plot(t, ideal, linestyle='--', linewidth=2, label=\"Target\")\n",
    "pylab.legend()\n",
    "pylab.xlabel(\"Time (s)\")\n",
    "pylab.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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