02_sindy_multiscale.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.linalg as la\n",
    "from scipy.integrate import ode\n",
    "import scipy\n",
    "from scipy import signal\n",
    "import utils\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib import colors\n",
    "%matplotlib inline\n",
    "from IPython.display import set_matplotlib_formats\n",
    "set_matplotlib_formats('png', 'pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def find_boundary(coefficient_matrix, data, threshold):\n",
    "    boundary_data = np.zeros(coefficient_matrix.shape[0])\n",
    "    for i in range(boundary_data.size):\n",
    "        entries_above = np.where(coefficient_matrix[i] > threshold)\n",
    "        if entries_above[0].size==0:\n",
    "            index=0\n",
    "        else:\n",
    "            index = np.max(entries_above)+1\n",
    "        if index==coefficient_matrix.shape[1]:\n",
    "            boundary_data[i]=np.inf\n",
    "        else:\n",
    "            boundary_data[i]=data[index]\n",
    "    return boundary_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Two Van der Pol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "poly_order = 3\n",
    "coefficient_threshold = .001\n",
    "tol = 1e-10\n",
    "\n",
    "mu=5\n",
    "c1=0.005\n",
    "c2=1\n",
    "\n",
    "x0=[0.0,2.0,2.0,0.0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Uniform sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "num_periods_simulate = 1\n",
    "sampling_rate_simulate_exponent = 14\n",
    "sampling_rate_simulate = 2**sampling_rate_simulate_exponent\n",
    "\n",
    "frequency_multipliers = np.arange(10,110,10)\n",
    "test_durations = np.arange(.05,1.05,.05)\n",
    "\n",
    "sampling_rate_exponent = 12\n",
    "sampling_rate = 2**sampling_rate_exponent\n",
    "spacing = sampling_rate_simulate//sampling_rate\n",
    "\n",
    "total_samples = np.zeros((frequency_multipliers.size, test_durations.size))\n",
    "extra_coefficients = np.zeros((frequency_multipliers.size, test_durations.size))\n",
    "\n",
    "for idx,frequency_multiplier in enumerate(frequency_multipliers):\n",
    "    tau_fast = .2\n",
    "    tau_slow = tau_fast*frequency_multiplier\n",
    "\n",
    "    fast_period_length = 11.45015*tau_fast\n",
    "    slow_period_length = fast_period_length*frequency_multiplier\n",
    "\n",
    "    Xi_true = np.zeros((35,4))\n",
    "    Xi_true[2,0] = 1\n",
    "    Xi_true[3,0] = c1\n",
    "    Xi_true[1,1] = -1\n",
    "    Xi_true[2,1] = mu\n",
    "    Xi_true[16,1] = -mu\n",
    "    Xi_true[:,:2] /= tau_fast\n",
    "    Xi_true[1,2] = c2\n",
    "    Xi_true[4,2] = 1\n",
    "    Xi_true[3,3] = -1\n",
    "    Xi_true[4,3] = mu\n",
    "    Xi_true[32,3] = -mu\n",
    "    Xi_true[:,2:] /= tau_slow\n",
    "    \n",
    "    t_simulate = np.linspace(0, num_periods_simulate*slow_period_length,\n",
    "                    int(num_periods_simulate*sampling_rate_simulate*slow_period_length/fast_period_length))\n",
    "    dt_simulate = t_simulate[1]-t_simulate[0]\n",
    "    \n",
    "    initial_samples = int(5*sampling_rate_simulate)\n",
    "    vdp_simulation = utils.simulate_coupled_vdp(dt_simulate, t_simulate.size+initial_samples, x0=x0,\n",
    "                                              mu1=mu, mu2=mu, c1=c1, c2=c2,\n",
    "                                              tau1=tau_fast, tau2=tau_slow)[0][:,initial_samples:]\n",
    "    \n",
    "    for i,duration in enumerate(test_durations):\n",
    "        # get subsamples\n",
    "        t_max_idx = int(duration*frequency_multiplier*sampling_rate_simulate)+1\n",
    "\n",
    "        t_sample = t_simulate[:t_max_idx:spacing]\n",
    "        dt_sample = t_sample[1] - t_sample[0]\n",
    "        total_samples[idx,i] = t_sample.size\n",
    "\n",
    "        sampled_data = vdp_simulation[:,:t_max_idx:spacing]\n",
    "\n",
    "        sindy = utils.SINDy()\n",
    "        sindy.fit(sampled_data, poly_order, t=dt_sample, coefficient_threshold=coefficient_threshold)\n",
    "        extra_coefficients[idx,i] = np.where(((np.abs(Xi_true) < tol) & (np.abs(sindy.Xi) > tol))\\\n",
    "                                              | ((np.abs(Xi_true) > tol) & (np.abs(sindy.Xi) < tol)))[0].size\n",
    "\n",
    "vdp_data = [frequency_multipliers,\n",
    "            find_boundary(extra_coefficients, test_durations, 0)*frequency_multipliers*sampling_rate]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Burst sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(1)\n",
    "\n",
    "frequency_multipliers = np.arange(10,110,10)\n",
    "subsample_chunks_exponent = np.arange(2,12)\n",
    "\n",
    "subsample_chunk_size_exponent = 3\n",
    "subsample_chunk_size = 2**subsample_chunk_size_exponent\n",
    "\n",
    "extra_coefficients = np.zeros((frequency_multipliers.size, subsample_chunks_exponent.size))\n",
    "incorrect_trial_fraction = np.zeros((frequency_multipliers.size, subsample_chunks_exponent.size))\n",
    "total_samples = np.zeros((frequency_multipliers.size, subsample_chunks_exponent.size))\n",
    "\n",
    "subsample_duration = 2\n",
    "num_trials=100\n",
    "\n",
    "for idx,frequency_multiplier in enumerate(frequency_multipliers):\n",
    "    tau_fast = 0.2\n",
    "    tau_slow = tau_fast*frequency_multiplier\n",
    "\n",
    "    fast_period_length = 11.45015*tau_fast\n",
    "    slow_period_length = fast_period_length*frequency_multiplier\n",
    "\n",
    "    Xi_true = np.zeros((35,4))\n",
    "    Xi_true[2,0] = 1\n",
    "    Xi_true[3,0] = c1\n",
    "    Xi_true[1,1] = -1\n",
    "    Xi_true[2,1] = mu\n",
    "    Xi_true[16,1] = -mu\n",
    "    Xi_true[:,:2] /= tau_fast\n",
    "    Xi_true[1,2] = c2\n",
    "    Xi_true[4,2] = 1\n",
    "    Xi_true[3,3] = -1\n",
    "    Xi_true[4,3] = mu\n",
    "    Xi_true[32,3] = -mu\n",
    "    Xi_true[:,2:] /= tau_slow\n",
    "    \n",
    "    num_periods_simulate = 3\n",
    "    sampling_rate_simulate_exponent = 12\n",
    "    sampling_rate_simulate = 2**sampling_rate_simulate_exponent\n",
    "    t_simulate = np.linspace(0, num_periods_simulate*slow_period_length,\n",
    "                    int(num_periods_simulate*sampling_rate_simulate*frequency_multiplier))\n",
    "    dt_simulate = t_simulate[1]-t_simulate[0]\n",
    "\n",
    "    sampling_rate_base_exponent = 12\n",
    "    sampling_rate_base = 2**sampling_rate_base_exponent\n",
    "    spacing = 2**(sampling_rate_simulate_exponent - sampling_rate_base_exponent)\n",
    "    t_sample = t_simulate[::spacing]\n",
    "    dt_sample = t_sample[1] - t_sample[0]\n",
    "    \n",
    "    initial_samples = 5*sampling_rate_simulate\n",
    "    vdp_simulation = utils.simulate_coupled_vdp(dt_simulate, t_simulate.size+initial_samples, x0=[0,2,2,0],\n",
    "                                              mu1=mu, mu2=mu, c1=c1, c2=c2,\n",
    "                                              tau1=tau_fast, tau2=tau_slow)[0][:,initial_samples:]\n",
    "    vdp_solution = vdp_simulation[:,::spacing]\n",
    "        \n",
    "    for j,subsample_chunk_exponent in enumerate(subsample_chunks_exponent):\n",
    "        subsample_chunk = 2**subsample_chunk_exponent\n",
    "\n",
    "        expected_samples = subsample_chunk*subsample_chunk_size\n",
    "        t_max_idx = int(subsample_duration*frequency_multiplier*sampling_rate_base)+1\n",
    "\n",
    "        subsample_start_idxs = np.linspace(0, t_max_idx-subsample_chunk_size, subsample_chunk).astype(int)\n",
    "        sample_separation = subsample_start_idxs[1] - subsample_chunk_size\n",
    "        if (expected_samples/t_max_idx > .9) or (sample_separation <= 5):\n",
    "            total_samples[idx,j] = np.nan\n",
    "            extra_coefficients[idx,j] = np.nan\n",
    "            incorrect_trial_fraction[idx,j] = np.nan\n",
    "            continue\n",
    "\n",
    "        for trial in range(num_trials):    \n",
    "            subsample_start_idxs = np.linspace(0, t_max_idx-subsample_chunk_size, subsample_chunk).astype(int)\n",
    "            sample_separation = subsample_start_idxs[1] - subsample_chunk_size\n",
    "            subsample_offsets = np.random.randint(sample_separation-1, size=subsample_chunk-2)\\\n",
    "                                - (sample_separation-1)//2\n",
    "            subsample_start_idxs[1:-1] += subsample_offsets\n",
    "            subsample_idxs = np.unique(np.sort((subsample_start_idxs[:,np.newaxis] \\\n",
    "                                                + np.arange(subsample_chunk_size)).flatten()))\n",
    "\n",
    "            t_subsample = t_sample[subsample_idxs]\n",
    "\n",
    "            total_samples[idx,j] = t_subsample.size\n",
    "            subsampled_data = vdp_solution[:,subsample_idxs]\n",
    "            sindy = utils.SINDy()\n",
    "            sindy.fit(subsampled_data, poly_order, t_subsample, dt_max=1.5*dt_sample,\n",
    "                      coefficient_threshold=coefficient_threshold)\n",
    "            tmp = np.where(((np.abs(Xi_true) < tol) & (np.abs(sindy.Xi) > tol))\\\n",
    "                            | ((np.abs(Xi_true) > tol) & (np.abs(sindy.Xi) < tol)))[0].size\n",
    "            extra_coefficients[idx,j] += tmp\n",
    "            if tmp>0:\n",
    "                incorrect_trial_fraction[idx,j] += 1\n",
    "\n",
    "extra_coefficients /= num_trials\n",
    "incorrect_trial_fraction /= num_trials\n",
    "\n",
    "vdp_burst_data0 = [frequency_multipliers,\n",
    "                         (2**find_boundary(incorrect_trial_fraction,\n",
    "                                           subsample_chunks_exponent, 0))*(2**subsample_chunk_size_exponent)]\n",
    "vdp_burst_data05 = [frequency_multipliers,\n",
    "                         (2**find_boundary(incorrect_trial_fraction,\n",
    "                                           subsample_chunks_exponent, 0.05))*(2**subsample_chunk_size_exponent)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
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TDwAt4IEF4b4c//EXqMHXsIVyw3tkAmBK1G5AxkPRGUhZQRFh+5EV6KRQr2zh7yggV9Ss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\nMTQ2OSAwMDAwMCB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97j4ZmAyQkZERtfASkcMr21PJk/PymPpxAWZwy9d686Ov9qZFcmK0S5NjdNTQCPoWngey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\nSK0pNEREpNb+PwzahyGd2Tt4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7f9a602128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(vdp_data[0], vdp_data[1], '.-')\n",
    "plt.plot(vdp_burst_data0[0], vdp_burst_data0[1], '.-')\n",
    "plt.plot(vdp_burst_data05[0], vdp_burst_data05[1], '.-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Slow Van der Pol, fast Lorenz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "poly_order = 3\n",
    "coefficient_threshold = .001\n",
    "tol = 1e-10\n",
    "\n",
    "mu=5\n",
    "sigma=10.\n",
    "rho=28.\n",
    "beta=8/3\n",
    "c1=0.01\n",
    "c2=10\n",
    "\n",
    "x0 = [0.0, 2.0, -8.0, 7.0, 27.0]\n",
    "\n",
    "lorenz_base_period_length = .759\n",
    "vdp_base_period_length = 11.45015"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Uniform sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "num_periods_simulate = 1.5\n",
    "sampling_rate_simulate_exponent = 14\n",
    "sampling_rate_simulate = 2**sampling_rate_simulate_exponent\n",
    "\n",
    "frequency_multipliers = np.arange(10,110,10)\n",
    "test_durations = np.arange(.05,1.05,.05)\n",
    "\n",
    "sampling_rate_exponent = 11\n",
    "sampling_rate = 2**sampling_rate_exponent\n",
    "spacing = sampling_rate_simulate//sampling_rate\n",
    "\n",
    "total_samples = np.zeros((frequency_multipliers.size, test_durations.size))\n",
    "extra_coefficients = np.zeros((frequency_multipliers.size, test_durations.size))\n",
    "\n",
    "for idx,frequency_multiplier in enumerate(frequency_multipliers):\n",
    "    tau_vdp = .05*frequency_multiplier\n",
    "    tau_lorenz = .05*vdp_base_period_length/lorenz_base_period_length\n",
    "\n",
    "    fast_period_length = tau_lorenz*lorenz_base_period_length\n",
    "    slow_period_length = tau_vdp*vdp_base_period_length\n",
    "\n",
    "    Xi_true = np.zeros((56,5))\n",
    "    Xi_true[2,0] = 1\n",
    "    Xi_true[3,0] = c1\n",
    "    Xi_true[1,1] = -1\n",
    "    Xi_true[2,1] = mu\n",
    "    Xi_true[22,1] = -mu\n",
    "    Xi_true[:,0:2] /= tau_vdp\n",
    "    Xi_true[1,2] = c2\n",
    "    Xi_true[3,2] = -sigma\n",
    "    Xi_true[4,2] = sigma\n",
    "    Xi_true[3,3] = rho\n",
    "    Xi_true[4,3] = -1\n",
    "    Xi_true[17,3] = -1\n",
    "    Xi_true[5,4] = -beta\n",
    "    Xi_true[16,4] = 1\n",
    "    Xi_true[:,2:] /= tau_lorenz\n",
    "    \n",
    "    t_simulate = np.linspace(0, num_periods_simulate*slow_period_length,\n",
    "                    int(num_periods_simulate*sampling_rate_simulate*slow_period_length/fast_period_length))\n",
    "    dt_simulate = t_simulate[1]-t_simulate[0]\n",
    "    \n",
    "    initial_samples = int(6*sampling_rate_simulate)\n",
    "    vdp_lorenz_simulation = utils.simulate_coupled_vdp_lorenz(dt_simulate, t_simulate.size+initial_samples, x0=x0,\n",
    "                                                 mu=mu, sigma=sigma, rho=rho, beta=beta, c1=c1, c2=c2,\n",
    "                                                 tau1=tau_vdp, tau2=tau_lorenz)[0][:,initial_samples:]\n",
    "    \n",
    "    for i,duration in enumerate(test_durations):\n",
    "        # get subsamples\n",
    "        t_max_idx = int(duration*frequency_multiplier*sampling_rate_simulate)+1\n",
    "\n",
    "        t_sample = t_simulate[:t_max_idx:spacing]\n",
    "        dt_sample = t_sample[1] - t_sample[0]\n",
    "        total_samples[idx,i] = t_sample.size\n",
    "\n",
    "        sampled_data = vdp_lorenz_simulation[:,:t_max_idx:spacing]\n",
    "\n",
    "        sindy = utils.SINDy()\n",
    "        sindy.fit(sampled_data, poly_order, t=dt_sample, coefficient_threshold=coefficient_threshold)\n",
    "        extra_coefficients[idx,i] = np.where(((np.abs(Xi_true) < tol) & (np.abs(sindy.Xi) > tol))\\\n",
    "                                              | ((np.abs(Xi_true) > tol) & (np.abs(sindy.Xi) < tol)))[0].size\n",
    "\n",
    "vdplorenz1_data = [frequency_multipliers,\n",
    "                   find_boundary(extra_coefficients, test_durations, 0)*frequency_multipliers*sampling_rate]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Burst sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(2)\n",
    "\n",
    "frequency_multipliers = np.arange(10,110,10)\n",
    "subsample_chunks_exponent = np.arange(2,13)\n",
    "\n",
    "subsample_chunk_size_exponent = 3\n",
    "subsample_chunk_size = 2**subsample_chunk_size_exponent\n",
    "\n",
    "extra_coefficients = np.zeros((frequency_multipliers.size, subsample_chunks_exponent.size))\n",
    "incorrect_trial_fraction = np.zeros((frequency_multipliers.size, subsample_chunks_exponent.size))\n",
    "total_samples = np.zeros((frequency_multipliers.size, subsample_chunks_exponent.size))\n",
    "\n",
    "subsample_duration = 2\n",
    "num_trials=100\n",
    "\n",
    "for idx,frequency_multiplier in enumerate(frequency_multipliers):\n",
    "    tau_vdp = .05*frequency_multiplier\n",
    "    tau_lorenz = .05*vdp_base_period_length/lorenz_base_period_length\n",
    "\n",
    "    fast_period_length = tau_lorenz*lorenz_base_period_length\n",
    "    slow_period_length = tau_vdp*vdp_base_period_length\n",
    "\n",
    "    Xi_true = np.zeros((56,5))\n",
    "    Xi_true[2,0] = 1\n",
    "    Xi_true[3,0] = c1\n",
    "    Xi_true[1,1] = -1\n",
    "    Xi_true[2,1] = mu\n",
    "    Xi_true[22,1] = -mu\n",
    "    Xi_true[:,0:2] /= tau_vdp\n",
    "    Xi_true[1,2] = c2\n",
    "    Xi_true[3,2] = -sigma\n",
    "    Xi_true[4,2] = sigma\n",
    "    Xi_true[3,3] = rho\n",
    "    Xi_true[4,3] = -1\n",
    "    Xi_true[17,3] = -1\n",
    "    Xi_true[5,4] = -beta\n",
    "    Xi_true[16,4] = 1\n",
    "    Xi_true[:,2:] /= tau_lorenz\n",
    "    \n",
    "    num_periods_simulate = 2.5\n",
    "    sampling_rate_simulate_exponent = 12\n",
    "    sampling_rate_simulate = 2**sampling_rate_simulate_exponent\n",
    "    t_simulate = np.linspace(0, num_periods_simulate*slow_period_length,\n",
    "                    int(num_periods_simulate*sampling_rate_simulate*frequency_multiplier))\n",
    "    dt_simulate = t_simulate[1]-t_simulate[0]\n",
    "\n",
    "    sampling_rate_base_exponent = 11\n",
    "    sampling_rate_base = 2**sampling_rate_base_exponent\n",
    "    spacing = 2**(sampling_rate_simulate_exponent - sampling_rate_base_exponent)\n",
    "    t_sample = t_simulate[::spacing]\n",
    "    dt_sample = t_sample[1] - t_sample[0]\n",
    "    \n",
    "    initial_samples = 6*sampling_rate_simulate\n",
    "    vdp_lorenz_simulation = utils.simulate_coupled_vdp_lorenz(dt_simulate, t_simulate.size+initial_samples, x0=x0,\n",
    "                                                 mu=mu, sigma=sigma, rho=rho, beta=beta, c1=c1, c2=c2,\n",
    "                                                 tau1=tau_vdp, tau2=tau_lorenz)[0][:,initial_samples:]\n",
    "    vdp_lorenz_solution = vdp_lorenz_simulation[:,::spacing]\n",
    "        \n",
    "    for j,subsample_chunk_exponent in enumerate(subsample_chunks_exponent):\n",
    "        subsample_chunk = 2**subsample_chunk_exponent\n",
    "\n",
    "        expected_samples = subsample_chunk*subsample_chunk_size\n",
    "        t_max_idx = int(subsample_duration*frequency_multiplier*sampling_rate_base)+1\n",
    "\n",
    "        subsample_start_idxs = np.linspace(0, t_max_idx-subsample_chunk_size, subsample_chunk).astype(int)\n",
    "        sample_separation = subsample_start_idxs[1] - subsample_chunk_size\n",
    "        if (expected_samples/t_max_idx > .9) or (sample_separation <= 5):\n",
    "            total_samples[idx,j] = np.nan\n",
    "            extra_coefficients[idx,j] = np.nan\n",
    "            incorrect_trial_fraction[idx,j] = np.nan\n",
    "            continue\n",
    "\n",
    "        for trial in range(num_trials):    \n",
    "            subsample_start_idxs = np.linspace(0, t_max_idx-subsample_chunk_size, subsample_chunk).astype(int)\n",
    "            sample_separation = subsample_start_idxs[1] - subsample_chunk_size\n",
    "            subsample_offsets = np.random.randint(sample_separation-1, size=subsample_chunk-2)\\\n",
    "                                - (sample_separation-1)//2\n",
    "            subsample_start_idxs[1:-1] += subsample_offsets\n",
    "            subsample_idxs = np.unique(np.sort((subsample_start_idxs[:,np.newaxis] \\\n",
    "                                                + np.arange(subsample_chunk_size)).flatten()))\n",
    "\n",
    "            t_subsample = t_sample[subsample_idxs]\n",
    "\n",
    "            total_samples[idx,j] = t_subsample.size\n",
    "            subsampled_data = vdp_lorenz_solution[:,subsample_idxs]\n",
    "            sindy = utils.SINDy()\n",
    "            sindy.fit(subsampled_data, poly_order, t_subsample, dt_max=1.5*dt_sample,\n",
    "                      coefficient_threshold=coefficient_threshold)\n",
    "            tmp = np.where(((np.abs(Xi_true) < tol) & (np.abs(sindy.Xi) > tol))\\\n",
    "                            | ((np.abs(Xi_true) > tol) & (np.abs(sindy.Xi) < tol)))[0].size\n",
    "            extra_coefficients[idx,j] += tmp\n",
    "            if tmp>0:\n",
    "                incorrect_trial_fraction[idx,j] += 1\n",
    "\n",
    "extra_coefficients /= num_trials\n",
    "incorrect_trial_fraction /= num_trials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/kpchamp/anaconda/envs/py3/lib/python3.6/site-packages/ipykernel_launcher.py:4: RuntimeWarning: invalid value encountered in greater\n",
      "  after removing the cwd from sys.path.\n"
     ]
    }
   ],
   "source": [
    "vdplorenz1_burst_data0 = [frequency_multipliers,\n",
    "                         (2**find_boundary(incorrect_trial_fraction,\n",
    "                                           subsample_chunks_exponent, 0))*(2**subsample_chunk_size_exponent)]\n",
    "vdplorenz1_burst_data05 = [frequency_multipliers,\n",
    "                         (2**find_boundary(incorrect_trial_fraction,\n",
    "                                           subsample_chunks_exponent, 0.05))*(2**subsample_chunk_size_exponent)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f7f7e365b70>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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hbnMgL0ZsYWdzIDMyCi9Gb250QkJveCBbIC0xMDIxIC00NjMgMTc5NCAxMjMzIF0gL0Fz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\nMCBSID4+CnN0YXJ0eHJlZgo2MTU1CiUlRU9GCg==\n",
      "image/png": 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BJ3dBQSY8tBYCjBmncSz/GI9veBxPF08WDV+Er5vvJe0/ufdkTpWcYkncEnxc\nfRjTbUwtRSqMIslB2Kw/Ek/w0e9HeDCsFUM6NYBR0GXFsPJ+yNoHo74wrDtkdmE24zeMx6RNLB2+\nlOaNml/yMZRSvDjgRU6VnGJ29Gx83Xy5rd1ttRCtMIokB2GTThWW8syq3bRt2ogXbmoAa0GbyuGr\nRyH5D7hrCXQYZkgYeSV5TPhlAjnFOSy9cSltvdte9rEcHRyZec1MCkoLmP7HdLxcvBjcYnDNBSsM\nJQ3SwuZorXlpTTwnTpcw997e9X8UtNbw7RRI+B7+9jb0uNuQMIrKi5i8aTJH844yd8hcuje58snj\nXBxdmDtkLl38uvDslmeJzpSxRw2FJAdhc9bGpvPdngymDutAjxBvo8O5chumQ+wncN00GDDekBDK\nzGU88+szxGbFMvOamQwMGlhjx/Zw9mD+sPkEeQYxedNkEnISauzYwjiSHIRNSc0t5OU18YS28uWJ\nwe2NDufK/TEXIj6AfuNg8DRDQjBrM9P/mM7WtK28FPYSN7S+ocbP4evmy6Lhi/B08WTChgmk5KfU\n+DlE3ZLkIGyGyboWtFlbRkE7OtTzbqsxKyx3Dd3+bqlOMqAbrtaad3a8w3dJ3zG592RGdhpZa+dq\n3qg5C4cvxKRNjNswjuzC7Fo7l6h9khyEzViyNYmoIzm8els3WvhVr8+9zdr/HXz7FLS7Hu5cCA7G\nvNUWxy3mk/2fMLrLaMb1GFfr52vr3ZYFwxaQU5zDhF8mkFeSV+vnFLVDkoOwCV/tTGHWTwcY0MaP\nu/vW81HQR7ZaeiYF9YF7PwEnY8ZnrEpYxbxd87il7S38s98/62wAYfcm3Zk7ZC5H844yedNkisqL\n6uS8omZJchCGMJk1iVkFrI5JZeKnO3n2yz2YNcSmnCLm2Cmjw7t86bGwchT4tYEHvgQXY+aBWn90\nPW9EvsG1Idfy+qDXcVB1+1YfGDSQmdfMJDYrlme3PEuZuaxOzy+unIxzELVOa03yyUJ2p54iLjWP\nPWl57E3L40ypZeI2Z8f/faMtN5mJTDpJ31aXNmLXJpw8bBn97O4Do1eDRx2ve2AVkR7BtK3T6NWs\nF7Ovm42zg7MhcdzQ+gZeKnmJGZEzmP7HdN68+s06T1Li8klyEDVKa03aqSLiUvPYnZpHXJolIeQX\nlwPg4uRAtyAv7u4bQo8QH3qGeJNXVMaDH0VRVm7G2cmBsLb+Br+Ky5CfDv+9w/L4wTXgHWxIGHHZ\ncUzdPJWkJCNyAAAZv0lEQVQ23m34v6H/h7uTuyFxnDWy00hOlZxi3q55+Lj68K9+/2oY82PZAUkO\n4ooczy9mT2oee1JPsSc1j7i0PHLOWBaid3ZUdG7uxS1XBdEz2JseId50DGiM85+sxfDp2DAik04S\n1ta//t01FObAir9DUS48/C00MaYLbtKpJCZunIifmx8Lhy3Ey8WYKcDPN67HOHKLc/lk/yf4ufkx\nrmftN4yLKyfJQVTbidMlxKXlsSfFckewJzWPrALLoi8OCjoGNGZYl2aWO4Jgbzo1b4ybc/VGN/dt\n5Vv/kgJA6Rn47F7IOWxZkyGotyFhZJzOYPyG8TgqRxYPX0xTj6aGxPFnlFL8s98/OVVyig92fYC3\nq3etdqkVNUOSg/hTeYVlxKXlVbQTxKXlkXbK0utEKWjX1JOr2zehR4g3PUO86RroXf+nubhU5aWw\n6iFIi4aR/4U21xoSRk5xDuM3jKewrJBlI5bRwquFIXH8FQflwOuDXie/NJ83It/Ax9WnVgbjiZoj\nycHO7UzO5beDWfh7ulJcZqqoGko+WVixTSt/D/q08uXh8Nb0CPGmW5AXjd2MaeS0GWYzrHkCEn+B\nWz+ALrcaEsaZsjNM/GUiGWcyWDh8IZ38OhkSR3U4Ozgz+7rZPL7hcZ7b+hyNXRrX6DQeomap+rqS\nU2hoqI6Olkm+rsTqmFSe/XI35kr/BYJ93OkZYmkf6BnsQ49gb7w97DwRnE9r+PFfsH0RDHsVrn7a\nkDBKTaVM3DiR6Mxo5gyZU29mRM0vzefhnx4mtSCVpTcurZEJAEX1KaV2aq1Dq9quyn5lSqkWSqnN\nSql9Sqm9Sqkp1nI/pdQGpdQh62/fSvs8r5RKVEolKKVurFTeVykVZ33uA2XttqCUclVKfWEtj1JK\ntb6cFy2q53RJOTO+28czlRKDg4Inh7Tjj2nXs2B0XyYObs/VHZpIYvgzW962JIaBk2DQVENCMJlN\nTNs6jaiMKF4f9Hq9SQwAXi5eLBy2ED83P5745QmS8pKMDkn8iep0Oi4HntFadwXCgCeVUl2BacBG\nrXUHYKP1b6zP3Qd0A0YA85VSZyujFwDjgA7WnxHW8seAXK11e+B9YFYNvDZxHq01P8RlMOzdLSz9\n4wjDugTg6uSAo7J0Mb2+c4DRIdq+HUvg17eg1wNwwxuGzZf0RtQbbEjewLOhz9bLRXaaejRl8fDF\nOCpHxv88nswzmUaHJM5TZXLQWmdorWOsjwuA/UAwcDuw3LrZcsDayZvbgc+11iVa6yNAItBfKRUI\neGmtI7WlLuu/5+1z9lhfAUPP3lWImnH0xBnGLNvBxE9j8Gvkwuonwln8UCifjQvjHzd04tOxYfWz\nt1Bdiv8avn8WOt1kaWcw6L/ovF3z+OrgV4ztMbZeL8/ZwqsFC4cvpLCskPEbxpNbnGt0SKKSSxqu\naK3u6Q1EAQFa6wzrU5nA2a+dwUDl+XpTrWXB1sfnl5+zj9a6HMgDLhgJpZQar5SKVkpFZ2fLjI/V\nUVxmYs4vB7lhzm/EJOfyyq1dWTdpEL1bWhJB31a+PDmkvSSGqiRuhNUToFU43L0UHI3py7Fi3woW\nxy3mrg538VTvpwyJoSZ18uvEvKHzSD+dzsRfJnKm7IzRIQmraicHpZQn8DUwVWudX/k5651Arbds\na60Xaa1DtdahTZvaTj9uW7X1UDYj5vzGnF8OcWO35mx65joeGdQGpz8ZhCb+QsoO+GI0NOsMo1aC\nszGjjr89/C1v73ibYS2H8XLYyw1mpHHfgL7Mvm42+3P2M3XzVEpNpUaHJKhmclBKOWNJDJ9qrVdb\ni49bq4qw/s6ylqcBlTtah1jL0qyPzy8/Zx+llBPgDZy81BcjLI7nF/PkZzE8+NF2lFKseKw/80b1\nppmXm9Gh1T9ZB+Cze6Bxc8t8SW7GrEy3JWULL//xMgOaD2DmtTNxdGhYY0oGtxjM64NeJzIjkue3\nPo/JbDI6JLtX5b2xte7/I2C/1vq9Sk+tA8YAM62/11Yq/0wp9R4QhKXhebvW2qSUyldKhWGplnoI\nmHfesbYBdwObdH3tY2ugcpOZ5duSeX/DQUpNZv4xvCMTrmuLq1PD+iCpM6eOwYo7wdEVHvwGPJsZ\nEkbM8Rie2fIMnfw6Mff6ubg6uhoSR227rd1t5BbnMjt6Nt5R3g3q7qg+qk7F6SDgQSBOKRVrLXsB\nS1JYpZR6DEgGRgJorfcqpVYB+7D0dHpSa332a8BE4GPAHfjR+gOW5LNCKZUI5GDp7SQuQcyxXF76\nJp59GfkM7tSU127rRit/Y6aLbhDOnLAkhrIz8MiP4NvakDASchKYtHESgY0CWTBsAY2cG/a/6Zhu\nYzhVcoolcUvwdfNlcu/JRodkt6pMDlrr34GLpe+hF9nnTeDNPymPBi4Y8aK1LgbuqSoWcaFThaXM\n+ukAK7en0NzLjQUP9GFE9+byjetKlBRYpt7OS4OH1kBAN0PCSClI4fFfHsfd2Z1Fwxfh52bMFOB1\n7aneT5FbnMuiPYvwdfVldNfRRodkl2T6jHrKbNZ8FZPKzB8PkFdUxrhr2jBlWEc8XS/xnzRlOxzd\nCq2vgRb9ayfY+hTHka2wbhKcSoFRn0PLsDoPITYrli2pW1ibuJYycxnLRywn0DOwzuMwilKKl8Ne\nJq8kj1k7ZpFXkoerkyuhAaH0atbLsLhis2KJPh5teBx1RZJDPZSQWcBLa+LYcTSX0Fa+vHFndzo3\nv4zpmY9FwfJbwFQGDk4wYIIx1Se5RyFqIZjLjY8jcj5oMzg6WxbtqWOxWbGM/XksJSbLbLevDnyV\ndj7t6jwOozk6ODLz2pk89MND/GfPf1AoHB0ceaDzA4Q0rvtlZFMLUvn0wKeYzWZcHF1YfMPiBp8g\nJDnUI2dKypm78RAf/X4ELzcn3r67J3f3CcHB4TKqkNJ2wurxcLbboLkMtv1fzQZ8OWwmDrPlTqaO\n72J+PvpzRWJwwIHcEvsdGObq6Mp1La5jX84+NJpycznL9y2vesdaVmwqZnPKZkkOwnhaa9bvzeS1\nb/eRkVfMff1a8NyIzvg2uoyF63OSYOPrsPcbcPUGB+f/fVMe+V8I6lPzL6Aq6TGWqa9NZTYUh4ul\niqsObUnZwpcHvwQsicHF0YXQgCrnR2vQwoPCWRq/lDJzGc4Ozrx33Xt0a1L3bUB7T+zlH1v+Qamp\nFI1mxb4VADzW4zGbWVSppsmsrDbu2MlCXlkXz+aEbLoEevHGHd0vbzTz6Wz47W2IXmr54Bs4CcIn\nQ/YB26jrt5U2BwPi0FqzJG4J83bNo7NfZyb0nMCR/CN2U7ddFVup6z8bRyuvVmw6tonvk77Hy9WL\n8T3Gc1/n+3BxvIwvawao7qyskhxsVEm5iUVbkvi/zYk4OSieHt6Rh8NbX/ro5tIzsG0+/DEXygqh\nz4Mw+HnLoC5huKLyIqb/MZ2fjv7E31r/jdcGvWb4us+ieg7kHOD9ne8TkR5BsGcwk3pP4qY2N+Gg\nbHsGAkkO9dgfiSd4eU08SSfOcHOPQF6+pSvNvS9xdLOpHGI/gc3/htOZ0PkWGPoKNO1YO0GLS5Zx\nOoMpm6dwIOcAT/V5ise6PyZdkOuhiPQI5uycw/6c/XTx68LUvlMJDwo3OqyLkuRwETuTc212Ifus\n/GLe+H4/63an08rfg9dv7851HS9xDimtIeEH+OVVOHEQQvrDDTMM6ZIpLi7meAxP//o0paZSZl07\ni2tDjFliVNQMszbzw5EfmBczj/Qz6YQHhfN036fp7NfZ6NAuIMnhT+xMzmXUokjKTGYcHRQTrmvL\nVSE++Hi44O3ujLe7Mz4ezrg51+10EyazZsW2o7z780FKTGYmDm7H49e1u/Q4UrbDzy9DSiT4d4Bh\nr1juGOTbqE356uBXvBn1JsGewXww5APa+rQ1OiRRQ0pNpaw8sJLFcYvJL8nn5rY3M7n3ZII8g4wO\nrYIkhz/x4eZEZq9PqHL6WBcnB3wqJQtvd2e83J3xcXc5p8z77G93Z3ys2zhfYptAbMopXvwmjr3p\n+VzToQmv396dNk0ucYqEE4dg42uw/1vwDIDB06D3Q4ZNKy3+XJm5jLe3v83nCZ8zKGgQs66dhber\nMRP5idqVX5rPR3Ef8en+TzFrM6M6j2J8z/E28e8tyeFP7EzO5YElkZSVm3FydGDOvb0I8fUgr6iM\nvKIyThWVWh4XWv+2/q78c7qk/C/P4enqVCmZOF80mWTlF7M2Np3dqXkEeLky/ZZu3NTjEqe9KDgO\nW2bCzuWWaaQHTYGwieDqeUnXRdS+3OJcntnyDDsyd/Bwt4eZ2mdqg5tZVVwo80wmH8Z+yNrEtXi6\neDK2x1ju73w/bk7GzZAsyeEirrTNocxkJr8imZT9RTIpPafsVFEZpeXmC47n6KD4+JF+XNPhEtoW\nSgogYh5E/B+YSqDvI3Ddc+Apa1zYooScBKZsnkJ2YTavhr/Kre1uNTokUccO5R5iTswcfkv9jQCP\nACb1nsStbW815AuCJAcbVFxmIq+ojP/8epjl245i1uCo4B83dOLJIe2rPoCpDHZ+DFtmwZls6HoH\nDJ0O/vY3vUJ98UvyL7zw+ws0dm7MnCFz6NG0h9EhCQPtyNzBe9HvEX8yng6+HZjaZyrXBF9Tp73U\nqpscbLtDbgPj5uxIgJcbt1wVhIuTA44KnJ0cCGt7wYqo59Ia9q6BDwfAD89Ck44wdiOMXC6JwUaZ\ntZn5sfN5+ten6eDTgZW3rJTEIOjXvB+f3fwZ71z3DsXlxTy58Uke+/kx4k/EGx3aBeTOwSDVrt46\n+gdsmA5p0dC0Cwx7FTreKD2QbFhhWSEv/P4CG49t5LZ2tzF94PQGu0CPuHxlpjK+PPglC/csJKc4\nhxGtR/BU76do4dWi6p2vgFQr1XdZByxjFQ7+CI2DYMgL0Ot+kEZMm5ZSkMJTm54iKS+JZ0OfZXSX\n0TKwTfyl06WnWbZ3GSv2raDMXMbIjiOZcNWEWlu/Q5JDfZWfDpvfgthPwcUTrp4KA54AFw+jIxNV\niMqI4pktz6C15p3r3rHpUbLC9mQXZjN/93y+OfQNbk5uPNr9UUZ3GY2Hc82+9yU51DfFefD7HIhc\nYFnXoP84uOZZaFRFe4QwnNaalQdW8vaOt2nl1Yp518+jpVdLo8MS9VRSXhJzd85lU8ommro3ZWKv\nidzR/g6cHGpm3JIkh/qivMQyU+qWt6EoB3rcA9e/ZNiaxeLSlJpKeTPqTVYfWs3gkMH8+5p/4+ki\n40zElduVtYt3o99ld/Zu2nq3ZUqfKQxpMeSKqyklOVxE1K6lxCRvZGCbG+nV7d5aiKyaUrZbkkJy\nhGVivDbXwfDXIKh3nYaxK2sXURlRhAaE0rNpzzo9d2V7svcQmx1r+LTMl+JE0Qme3vw0sdmxjOsx\njkm9J9n8jJyiftFas+nYJubEzOFo/lH6NOvDLW1vIa8077LfK5Ic/kRs/Gc8Ev0W5Vj68I4sKOCu\ngjN0LC0zsE+vghvftIxsrqOGy7TTaWxL38YPR35gR+aOOjlndTkqRyb3nsy9ne616W/ge0/uZcqm\nKeSV5DHj6hmMaD3C6JBEA1ZuLmf1odV8EPMBeaV5KBSujq6XtVxpdZODXU2+E520HjOAUpi15nMv\nLz738sLP0Y2B7kEVP82carnx9+jvcHgzoEE5QHlxrSaG06Wn2Z65nYj0CCIzIknOTwbA0/l/H74K\nxcCggfRr3q/W4riYHZk72Ja+DY3GpE3MiZnDvF3z6Nm0JwODBhIeFE43/241Vud6pX5I+oHpEdPx\nc/NjxU0rbHLmTdGwODk4MbLTSE4UneA/u/+DRlNmLiP6eHSt3WnbxrutjoS2vRGXkzspQ+Os4e2e\nk8j3ak5EegTbMiL5PjsJgPY+7Ss+lPoG9K35xVdaXwPJ2yzrN9fCcpTl5nL2ntxreV3p29iTvQeT\nNuHu5E6/5v0Y1XkUAwMHkl+az7ifx1UswfjEVU8YUqUTGhBKzPEYysxlODk48UzoM2QXZrMtfRsL\nYhcwP3Y+jZ0bMyBwAAODBjIwaCAtGtduX/A/YzKbmLdrHh/Ff0SfZn14b/B7+LtLhwFRd8KDwlkW\nv6ziPVuby8jaVbUSWKqWopPWE9r2Rnp1v7+i3KzNHMw9WPGBGnM8hlJzKc4OzvRp1qfiQ6mzX+ea\nqVeu4eUoUwpS2Ja+jW3p24jKiKKgrACFopt/t4rYezXthbOj8zn72doSjOfHcar4FJGZkUSmRxKR\nHkHGmQwAQjxDCA8KJzwonH6B/Wp9Hd+C0gKmbZ3Gb6m/cXfHu3mh/wsXXEsh6sKVvmelzeEKFZUX\nsev4LiLSI4jIiOBQ7iEAfF19CQsMq/jAbd7ImOU280vz2ZGxwxJfegSpp1MBCGwUSHhQOGFBYYQ1\nD8PHzceQ+GqD1pqj+UcrkuD2zO0UlhfioBzo0aRHxd1e9ybdcXaouQ/uo3lHeWrzU6TkpzCt/zTu\n7WxgRwYhrpAkhxqWXZhNZEYk29K3EZEewcnikwC09W5LeFA4A4MGEhoQWuMDVs4qM5cRfyK+4s4m\n7kQcZm3Gw8mD/oH9GRho+WBs5dXKbkbklpnL2JO9pyJZxJ+Mx6zNNHJuRP/m/Sv+XVo2bnnZ1+T3\ntN/515Z/4eTgxLuD3zWkTUaImiTJoRZprTmYe5DIDEtVx87jOykxleDk4ETvZr0rPqg7+3W+7Cl5\ntdYcKzhWkYx2ZO7gdNlpHJQD3f27V9y59Gzas0a/JddneSV5FQ3v29K3kXY6DYBgz2DCAsMIDwpn\nQOCAai24orVm+d7lvB/zPu192vPB9R8Q7Blc2y9BiFonyaEOlZhKiDkew7YMyzfYAzkHAPB29a74\nUBoYOJBAz8C/PE5eSR5RGVEVx6n84Xa2yqR/8/42sZqUrdNak1KQUpEotmdur0iuFe0wgQO5qulV\nF7QdlJhKeDXiVb5L+o7hrYbzxqA3au2OUIi6JsnBQCeKThCVEWXpOpoeSVZRFgCtvVpXVHW4Obqx\nO3s3Pq4+ZBVlEZkeWVEt4unseU61SIvGLeymqqi2lJvLK6rlItIjiD8Rj0mb8HDyoF/zfhV3Ysl5\nybwZ9SbHC4/zZK8nmdBzglx70aBIcrARWmsOnzps7S67jejMaIpNxeds44DDOX36uzfpbjN9+huq\nsw362zIs1XYpBSnnPO/s4MzSG5fWm9HaQlSXJAcbVWoq5c3IN/km8Rs0GgccGNfTMvWCME5KQQrv\n7HiHzSmbActI7Um9JzG2x1iDIxOiZslKcDbKxdGFOzvciaujK47KERdHF64OvtrosOxei8YteLT7\no7g5uuGoHGt9gJEQtk7uHAxiK4PPxLnk30U0dFKtJIQQ4gJSrSSEEOKy2UxyUEqNUEolKKUSlVLT\njI5HCCHsmU0kB6WUI/Ah8DegKzBKKdXV2KiEEMJ+2URyAPoDiVrrJK11KfA5cLvBMQkhhN2yleQQ\nDFQehZRqLRNCCGEAW0kO1aKUGq+UilZKRWdnZxsdjhBCNFi2MkdDGlB5aa8Qa9k5tNaLgEUASqls\npVRy3YRXa5oAJ4wOwobI9fgfuRbnkutxriu5Hq2qs5FNjHNQSjkBB4GhWJLCDuB+rfVeQwOrZUqp\n6Or0N7YXcj3+R67FueR6nKsurodN3DlorcuVUpOA9YAjsLShJwYhhLBlNpEcALTWPwA/GB2HEEKI\netYg3QAtMjoAGyPX43/kWpxLrse5av162ESbgxBCCNsidw5CCCEuIMmhDiilWiilNiul9iml9iql\npljL/ZRSG5RSh6y/fY2OtS4ppRyVUruUUt9Z/7bb66GU8lFKfaWUOqCU2q+UGmiv10Mp9bT1fRKv\nlFqplHKzp2uhlFqqlMpSSsVXKrvo61dKPW+dky5BKXVjTcUhyaFulAPPaK27AmHAk9a5o6YBG7XW\nHYCN1r/tyRRgf6W/7fl6zAV+0lp3Bq7Ccl3s7noopYKBp4BQrXV3LL0X78O+rsXHwIjzyv709Vs/\nR+4Duln3mW+dq+6KSXKoA1rrDK11jPVxAZY3fjCW+aOWWzdbDtxhTIR1TykVAtwMLKlUbJfXQynl\nDVwLfASgtS7VWp/CTq8Hll6U7tbxTx5AOnZ0LbTWvwE55xVf7PXfDnyutS7RWh8BErHMVXfFJDnU\nMaVUa6A3EAUEaK0zrE9lAgEGhWWEOcC/AHOlMnu9Hm2AbGCZtZptiVKqEXZ4PbTWacBs4BiQAeRp\nrX/GDq/FeS72+mttXjpJDnVIKeUJfA1M1VrnV35OW7qN2UXXMaXULUCW1nrnxbaxp+uB5ZtyH2CB\n1ro3cIbzqk3s5XpY69Jvx5Iwg4BGSqnRlbexl2txMXX1+iU51BGllDOWxPCp1nq1tfi4UirQ+nwg\nkGVUfHVsEHCbUuoolunZr1dKfYL9Xo9UIFVrHWX9+yssycIer8cw4IjWOltrXQasBsKxz2tR2cVe\nf7XmpbsckhzqgFJKYalP3q+1fq/SU+uAMdbHY4C1dR2bEbTWz2utQ7TWrbE0pm3SWo/Gfq9HJpCi\nlOpkLRoK7MM+r8cxIEwp5WF93wzF0kZnj9eisou9/nXAfUopV6VUG6ADsL0mTiiD4OqAUupqYCsQ\nx//q2F/A0u6wCmgJJAMjtdbnN0Q1aEqpwcCzWutblFL+2On1UEr1wtI47wIkAY9g+fJmd9dDKfUa\ncC+WXn67gLGAJ3ZyLZRSK4HBWGZePQ68AqzhIq9fKfUi8CiW6zVVa/1jjcQhyUEIIcT5pFpJCCHE\nBSQ5CCGEuIAkByGEEBeQ5CCEEOICkhyEEEJcQJKDEEKIC0hyEEIIcQFJDkIIIS7w//vs0KQaCCVV\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7f7ea677f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(vdplorenz1_data[0], vdplorenz1_data[1], '.-')\n",
    "plt.plot(vdplorenz1_burst_data0[0], vdplorenz1_burst_data0[1], '.-')\n",
    "plt.plot(vdplorenz1_burst_data05[0], vdplorenz1_burst_data05[1], '.-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fast Van der Pol, slow Lorenz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "poly_order = 3\n",
    "coefficient_threshold = .002\n",
    "tol = 1e-10\n",
    "\n",
    "mu=5\n",
    "sigma=10.\n",
    "rho=28.\n",
    "beta=8/3\n",
    "c1=.005\n",
    "c2=10\n",
    "\n",
    "x0 = [0.0, 2.0, -8.0, 7.0, 27.0]\n",
    "\n",
    "lorenz_base_period_length = .759\n",
    "vdp_base_period_length = 11.45015"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Uniform sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "num_periods_simulate = 1.5\n",
    "sampling_rate_simulate_exponent = 14\n",
    "sampling_rate_simulate = 2**sampling_rate_simulate_exponent\n",
    "\n",
    "frequency_multipliers = np.arange(10,110,10)\n",
    "test_durations = np.arange(.1,1.5,.1)\n",
    "\n",
    "sampling_rate_exponent = 12\n",
    "sampling_rate = 2**sampling_rate_exponent\n",
    "spacing = sampling_rate_simulate//sampling_rate\n",
    "\n",
    "total_samples = np.zeros((frequency_multipliers.size, test_durations.size))\n",
    "extra_coefficients = np.zeros((frequency_multipliers.size, test_durations.size))\n",
    "\n",
    "for idx,frequency_multiplier in enumerate(frequency_multipliers):\n",
    "    tau_lorenz = 2*frequency_multiplier\n",
    "    tau_vdp = 2*lorenz_base_period_length/vdp_base_period_length\n",
    "\n",
    "    fast_period_length = tau_vdp*vdp_base_period_length\n",
    "    slow_period_length = tau_lorenz*lorenz_base_period_length\n",
    "\n",
    "    Xi_true = np.zeros((56,5))\n",
    "    Xi_true[2,0] = 1\n",
    "    Xi_true[3,0] = c1\n",
    "    Xi_true[1,1] = -1\n",
    "    Xi_true[2,1] = mu\n",
    "    Xi_true[22,1] = -mu\n",
    "    Xi_true[:,0:2] /= tau_vdp\n",
    "    Xi_true[1,2] = c2\n",
    "    Xi_true[3,2] = -sigma\n",
    "    Xi_true[4,2] = sigma\n",
    "    Xi_true[3,3] = rho\n",
    "    Xi_true[4,3] = -1\n",
    "    Xi_true[17,3] = -1\n",
    "    Xi_true[5,4] = -beta\n",
    "    Xi_true[16,4] = 1\n",
    "    Xi_true[:,2:] /= tau_lorenz\n",
    "    \n",
    "    t_simulate = np.linspace(0, num_periods_simulate*slow_period_length,\n",
    "                    int(num_periods_simulate*sampling_rate_simulate*slow_period_length/fast_period_length))\n",
    "    dt_simulate = t_simulate[1]-t_simulate[0]\n",
    "    \n",
    "    initial_samples = 6*sampling_rate_simulate\n",
    "    vdp_lorenz_simulation = utils.simulate_coupled_vdp_lorenz(dt_simulate, t_simulate.size+initial_samples, x0=x0,\n",
    "                                                 mu=mu, sigma=sigma, rho=rho, beta=beta, c1=c1, c2=c2,\n",
    "                                                 tau1=tau_vdp, tau2=tau_lorenz)[0][:,initial_samples:]\n",
    "    \n",
    "    for i,duration in enumerate(test_durations):\n",
    "        # get subsamples\n",
    "        t_max_idx = int(duration*frequency_multiplier*sampling_rate_simulate)+1\n",
    "\n",
    "        t_sample = t_simulate[:t_max_idx:spacing]\n",
    "        dt_sample = t_sample[1] - t_sample[0]\n",
    "        total_samples[idx,i] = t_sample.size\n",
    "\n",
    "        sampled_data = vdp_lorenz_simulation[:,:t_max_idx:spacing]\n",
    "\n",
    "        sindy = utils.SINDy()\n",
    "        sindy.fit(sampled_data, poly_order, t=dt_sample, coefficient_threshold=coefficient_threshold)\n",
    "        extra_coefficients[idx,i] = np.where(((np.abs(Xi_true) < tol) & (np.abs(sindy.Xi) > tol))\\\n",
    "                                              | ((np.abs(Xi_true) > tol) & (np.abs(sindy.Xi) < tol)))[0].size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "vdplorenz2_data = [frequency_multipliers,\n",
    "                   find_boundary(extra_coefficients, test_durations, 0)*frequency_multipliers*sampling_rate]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Burst sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(3)\n",
    "\n",
    "frequency_multipliers = np.arange(10,110,10)\n",
    "subsample_chunks_exponent = np.arange(2,13)\n",
    "\n",
    "subsample_chunk_size_exponent = 3\n",
    "subsample_chunk_size = 2**subsample_chunk_size_exponent\n",
    "\n",
    "extra_coefficients = np.zeros((frequency_multipliers.size, subsample_chunks_exponent.size))\n",
    "incorrect_trial_fraction = np.zeros((frequency_multipliers.size, subsample_chunks_exponent.size))\n",
    "total_samples = np.zeros((frequency_multipliers.size, subsample_chunks_exponent.size))\n",
    "\n",
    "subsample_duration = 2\n",
    "num_trials=100\n",
    "\n",
    "for idx,frequency_multiplier in enumerate(frequency_multipliers):\n",
    "    tau_lorenz = 2*frequency_multiplier\n",
    "    tau_vdp = 2*lorenz_base_period_length/vdp_base_period_length\n",
    "\n",
    "    fast_period_length = tau_vdp*vdp_base_period_length\n",
    "    slow_period_length = tau_lorenz*lorenz_base_period_length\n",
    "\n",
    "    Xi_true = np.zeros((56,5))\n",
    "    Xi_true[2,0] = 1\n",
    "    Xi_true[3,0] = c1\n",
    "    Xi_true[1,1] = -1\n",
    "    Xi_true[2,1] = mu\n",
    "    Xi_true[22,1] = -mu\n",
    "    Xi_true[:,0:2] /= tau_vdp\n",
    "    Xi_true[1,2] = c2\n",
    "    Xi_true[3,2] = -sigma\n",
    "    Xi_true[4,2] = sigma\n",
    "    Xi_true[3,3] = rho\n",
    "    Xi_true[4,3] = -1\n",
    "    Xi_true[17,3] = -1\n",
    "    Xi_true[5,4] = -beta\n",
    "    Xi_true[16,4] = 1\n",
    "    Xi_true[:,2:] /= tau_lorenz\n",
    "    \n",
    "    num_periods_simulate = 2.5\n",
    "    sampling_rate_simulate_exponent = 12\n",
    "    sampling_rate_simulate = 2**sampling_rate_simulate_exponent\n",
    "    t_simulate = np.linspace(0, num_periods_simulate*slow_period_length,\n",
    "                    int(num_periods_simulate*sampling_rate_simulate*frequency_multiplier))\n",
    "    dt_simulate = t_simulate[1]-t_simulate[0]\n",
    "\n",
    "    sampling_rate_base_exponent = 12\n",
    "    sampling_rate_base = 2**sampling_rate_base_exponent\n",
    "    spacing = 2**(sampling_rate_simulate_exponent - sampling_rate_base_exponent)\n",
    "    t_sample = t_simulate[::spacing]\n",
    "    dt_sample = t_sample[1] - t_sample[0]\n",
    "    \n",
    "    initial_samples = 5*sampling_rate_simulate\n",
    "    vdp_lorenz_simulation = utils.simulate_coupled_vdp_lorenz(dt_simulate, t_simulate.size+initial_samples, x0=x0,\n",
    "                                                 mu=mu, sigma=sigma, rho=rho, beta=beta, c1=c1, c2=c2,\n",
    "                                                 tau1=tau_vdp, tau2=tau_lorenz)[0][:,initial_samples:]\n",
    "    vdp_lorenz_solution = vdp_lorenz_simulation[:,::spacing]\n",
    "        \n",
    "    for j,subsample_chunk_exponent in enumerate(subsample_chunks_exponent):\n",
    "        subsample_chunk = 2**subsample_chunk_exponent\n",
    "\n",
    "        expected_samples = subsample_chunk*subsample_chunk_size\n",
    "        t_max_idx = int(subsample_duration*frequency_multiplier*sampling_rate_base)+1\n",
    "\n",
    "        subsample_start_idxs = np.linspace(0, t_max_idx-subsample_chunk_size, subsample_chunk).astype(int)\n",
    "        sample_separation = subsample_start_idxs[1] - subsample_chunk_size\n",
    "        if (expected_samples/t_max_idx > .9) or (sample_separation <= 5):\n",
    "            total_samples[idx,j] = np.nan\n",
    "            extra_coefficients[idx,j] = np.nan\n",
    "            incorrect_trial_fraction[idx,j] = np.nan\n",
    "            continue\n",
    "\n",
    "        for trial in range(num_trials):    \n",
    "            subsample_start_idxs = np.linspace(0, t_max_idx-subsample_chunk_size, subsample_chunk).astype(int)\n",
    "            sample_separation = subsample_start_idxs[1] - subsample_chunk_size\n",
    "            subsample_offsets = np.random.randint(sample_separation-1, size=subsample_chunk-2)\\\n",
    "                                - (sample_separation-1)//2\n",
    "            subsample_start_idxs[1:-1] += subsample_offsets\n",
    "            subsample_idxs = np.unique(np.sort((subsample_start_idxs[:,np.newaxis] \\\n",
    "                                                + np.arange(subsample_chunk_size)).flatten()))\n",
    "\n",
    "            t_subsample = t_sample[subsample_idxs]\n",
    "\n",
    "            total_samples[idx,j] = t_subsample.size\n",
    "            subsampled_data = vdp_lorenz_solution[:,subsample_idxs]\n",
    "            sindy = utils.SINDy()\n",
    "            sindy.fit(subsampled_data, poly_order, t_subsample, dt_max=1.5*dt_sample,\n",
    "                      coefficient_threshold=coefficient_threshold)\n",
    "            tmp = np.where(((np.abs(Xi_true) < tol) & (np.abs(sindy.Xi) > tol))\\\n",
    "                            | ((np.abs(Xi_true) > tol) & (np.abs(sindy.Xi) < tol)))[0].size\n",
    "            extra_coefficients[idx,j] += tmp\n",
    "            if tmp>0:\n",
    "                incorrect_trial_fraction[idx,j] += 1\n",
    "\n",
    "extra_coefficients /= num_trials\n",
    "incorrect_trial_fraction /= num_trials\n",
    "\n",
    "vdplorenz2_burst_data0 = [frequency_multipliers,\n",
    "                         (2**find_boundary(incorrect_trial_fraction,\n",
    "                                           subsample_chunks_exponent, 0))*(2**subsample_chunk_size_exponent)]\n",
    "vdplorenz2_burst_data05 = [frequency_multipliers,\n",
    "                         (2**find_boundary(incorrect_trial_fraction,\n",
    "                                           subsample_chunks_exponent, 0.05))*(2**subsample_chunk_size_exponent)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f7f887e0908>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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gMCBSIC9TdWJ0eXBlIC9UeXBlMyAvTmFtZSAvRGVqYVZ1U2FucwovRm9udEJCb3ggWyAt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\nCnN0YXJ0eHJlZgo2NDcxCiUlRU9GCg==\n",
      "image/png": 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j91vwajKzlmb2YtA+18z61prnSjNbHVyurK8nLSL1rzoc4abnPmVnRYhHLh9D+1apsS5J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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7f50e68240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(vdplorenz2_data[0], vdplorenz2_data[1], '.-')\n",
    "plt.plot(vdplorenz2_burst_data0[0], vdplorenz2_burst_data0[1], '.-')\n",
    "plt.plot(vdplorenz2_burst_data05[0], vdplorenz2_burst_data05[1], '.-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot all results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/pdf": 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KZW5kc3RyZWFtCmVuZG9iagoyOCAwIG9iago8PCAvTGVuZ3RoIDkwIC9GaWx0ZXIgL0Zs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\n",
      "image/png": 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hXkRExGekpaWxdm3uHW6TJ0+mS5cudOnSxeFUFUszgUiFOX/+PH/605/I/XwAYWFhvPXW\nWxriRUREfIa1lsjISLKysnj++efp3r2705EqhcvpAFI1Xb9+nQULFniLP2MMrVq1UvEnIiI+5dix\nY5w+fZpatWoxefLkanNfus4ASrmLiYnh008/JSsrC8gt/gIDA3XPn4iI+JSMjAxWrlwJwPjx46vV\n7UkqAKXcuN1u1q1bx44dOwDo0aMH4eHhfPPNN1X6RloREfFPq1ev5u7du4SEhNC/f3+n41QqFYBS\nLgoP8TJ+/HheeukljDGEhoY6HU9ERKSAs2fP8vXXXxMUFMTUqVO9Q79UFyoApcwuXrxIREQE6enp\n1K9fn9mzZ9OxY0enY4mIiDxSVlYWkZGRAIwaNYpmzZo5nKjyqQCUUrPWsnv3bj7//HM8Hg8dOnRg\n9uzZNGjQwOloIiIij7VhwwZu3bpF69atGTp0qNNxHKECUEolKyuLZcuWcfToUQCGDBnCuHHj1MtX\nRER8WmJiIrt378blcjFt2rRq+76lAlBK7Nq1a8ybN4+UlBRq1qzJ9OnT6dGjh9OxREREnignJ4cl\nS5ZgrWXo0KG0adPG6UiOUQEoJRITE8PixYt58OABzZs3Z86cOTRv3tzpWCIiIkXatm0bycnJPP30\n04wePdrpOI5SASjF8qghXqZNm0ZwcLDDyURERIqWkpLCli1bAHjzzTepUaOGw4mcpQJQipSens78\n+fO5cOHCD4Z4ERER8XUej4elS5eSk5PDgAED6NSpk9ORHKcCUJ4o/xAvDRo0YPbs2XTo0MHpWCIi\nIsW2d+9eEhISqF+/PuPHj3c6jk9QASiPVHiIl44dO/LOO+9oiBcREfErt2/fZt26dQBMnjyZ2rVr\nO5zIN6gAlB+IjY1l9erVJCUlATB06FDGjh1bbbvKi4iIf7LWEhkZyYMHD+jevTsvvPCC05F8hgpA\nKeDo0aMsWLDA+3jMmDGMHDnSwUQiIiKlc/ToUc6cOUOtWrWYPHmy03F8SvWa+E6eKDo6mk8++cT7\n2Bijjh4iIuKXMjIyWLlyJQCvv/66bmEqRGcABbfbzdq1a9m5cyfwv4VfQEAAISEhDqcTEREpuVWr\nVpGRkUGnTp3o37+/03F8TpEFoDFmETAKSLXWdn3E+kHAeiAxb9Faa+1/lGdIqTjp6elERERw8eJF\nXC4XEyZM4Ec/+hHx8fGEhITQvn17pyOKiIiUyJkzZzh8+DBBQUFMnTpVV7MeoThnABcDHwJLnrBN\nlLV2VLkkkkpz4cIFIiIiuHPnDg0bNuSdd97xDvGiwk9ERPxRVlYWkZGRAIwePZqmTZs6nMg3FVkA\nWmv3GWPaVnwUqSzWWnbt2sWaNWvweDyEhITwzjvvUL9+faejiYiIlMn69eu5ffs2bdq0YciQIU7H\n8VnldQ9gP2PMKSAJ+Cdr7dly2q+Us6ysLJYsWUJ0dDQAw4YN47XXXtMQLyIi4vcSEhL46quvcLlc\nTJs2Te9tT1AeBWAM0MZam2GMGQl8AXR81IbGmNnAbIA2bdqUw6GlJFJSUpg3bx7Xrl0jODiY6dOn\na0wkP6B2I1JyajfVT05ODkuXLsVay8svv0zr1q2djuTTyjwMjLX2jrU2I+/7LUCQMabJY7aNsNaG\nWWvDnn766bIeWkogOjqaP/zhD1y7do0WLVrw29/+VsWfn1C7ESk5tZvq57PPPiMlJYVGjRrxyiuv\nOB3H55X5DKAx5hngurXWGmN6kVtU3ipzMikXbrebNWvWsGvXLgB69uzJ1KlTCQ4OdjiZiIhI+di1\naxcHDhwA4O7du1y5ckWdGYtQnGFglgODgCbGmKvA/wWCAKy184DXgZ8bY3KATGCStdZWWGIptkcN\n8fLTn/5U3eFFRKRKSEtLY/Xq1d772gE8Hg/x8fEqAItQnF7AT5w7xVr7IbnDxIgPiY+PZ/78+d4h\nXmbPnq3GICIiVUJOTg47d+5ky5YtPHjwgICAAL4/96RJDIpHM4FUMdZadu7cydq1azXEi4iIVDnn\nzp1jxYoVXL9+HYAXXniBCRMmkJaWpkkMSkAFYBWSlZXFp59+SkxMDKAhXkREpOq4ffs2q1at4vjx\n4wA0a9aMSZMm8dxzzwHw1FNPqfArARWAVcThw4e98x4GBwczY8YMunfv7nQsERGRMsnOzmbHjh1s\n2bKF7OxsatasyciRIxkyZAiBgSpjSkvPXBWwefNmNmzY4H08depUFX8iIuL3zpw5w8qVK0lNTQWg\nR48eTJgwgUaNGjmczP+pAPRjbrebzz//nN27d3uXuVwubt686WAqERGRsrl58yarV6/mxIkTADRv\n3pyJEycSGhrqcLKqQwWgn/ruu++IiIggISEBYwwulwtrrXo/iYiI38rOzmb79u18+eWX3su9o0aN\nYvDgwbrcW870bPqhRw3x8v1y9X4SERF/dPr0aVauXMmNGzeA3IkLxo8fr8u9FUQFoB+x1rJjxw7W\nrVuHx+OhU6dOvP32294hXlT4iYiIv7l58yarVq3i5MmTALRo0YJJkybRqVMnh5NVbSoA/URmZiZL\nlizxDvHy8ssvM2bMGA3xIiIifunhw4esWLGCQ4cO4fF4CA4O9l7u1XtbxVMB6AeSk5OZN28e169f\nJzg4mJkzZ/L88887HUtERKRUTp48SWRkJOnp6UBuB8ZZs2bRrVs3h5NVHyoAfdzRo0dZunQpDx48\noEWLFrz77rs0a9bM6VgiIiIlduPGDVauXMnp06d/sC4pKUkFYCVSAeijcnJyWLNmjXeIl169ejF1\n6lRq1qzpcDIREZGSefjwIVu3bmXbtm3k5OQQHBxMv379iIqKwu12awQLB6gA9EH5h3gJCAhgwoQJ\nDBo0CGOM09FERESKzVrLyZMnWbVqFbdu3QKgT58+jBs3jgYNGhAWFqYRLByiAtDHFB7iZc6cObRr\n187pWCIiIiVy/fp1Vq5cydmzZwFo1aoVkydPpkOHDt5t2rdvr8LPISoAfURRQ7yIiIj4gwcPHvDl\nl1+yY8cOcnJyqFWrFmPGjGHgwIHq3etDVAD6gMzMTD799FOOHz8OwPDhw3n11VfVUERExG9Yazl+\n/DirVq0iLS0NgH79+jF27FidzPBBKgAdpiFeRETE3127do0VK1YQGxsLQOvWrZk8ebIu7/owFYAO\n2rRpE1u2bMHtdtOyZUveffddmjZt6nQsERGRYsnKymLLli3s3LkTt9tN7dq1ee211wgPD8flcjkd\nT55ABaADcnJyWLhwoXdWD5fLxcSJE1X8iYiIX7DWEhMTw+rVq72XewcMGMBrr71GvXr1HE4nxVFk\nAWiMWQSMAlKttV0fsd4AHwAjgfvADGttTHkHrSrS0tKYP38+CQkJBZZfunRJ8x6KiIjPO3LkCBs2\nbODGjRsAtGnThilTpvDss886nExKojhnABcDHwJLHrN+BNAx76s38Le8f6WQuLg45s+fz927d6lX\nrx6ZmZl4PB4NgCkiIj4vKyuLyMhIjhw54l02bNgwxo4dq8u9fqjIAtBau88Y0/YJm4wBllhrLfC1\nMaahMaa5tTalnDL6PWst27dvZ926dVhr6dy5M2+//TapqakaAFNERHyatZZjx47x+eef891333mX\nG2OoXbu2ij8/VR73ALYEruR7fDVv2Q8KQGPMbGA25J4yrg4yMzNZvHgxJ06cAGDEiBG8+uqruFwu\n6tWrp8JPilQd241IWandlI/k5GRWrFhBXFwcAM888ww3b97U1asqoFI7gVhrI4AIgLCwMFuZx3ZC\nUlIS8+bNIzU1lVq1ajFz5kx+8pOfOB1L/Ex1azci5UHtpmwyMzPZtGkTu3fvxuPxUKdOHcaNG0e/\nfv1ITEzU1asqoDwKwCSgdb7HrfKWVWtHjhxh6dKlPHz4kFatWjFnzhz18hUREZ9mreXIkSOsWbOG\n9PR0jDG8+OKLjBkzhjp16gCavq2qKI8CcAPwS2PMCnI7f6RX5/v/cnJyWL16NXv27AFyJ73+2c9+\nRo0aNZwNJiLiI+7fv8/evXu5ffs2ffr0UTHhI5KSkli+fDkXLlwA4Nlnn2XKlCm6hF5FFWcYmOXA\nIKCJMeYq8H+BIABr7TxgC7lDwFwkdxiYmRUV1telpaURERHBpUuXCAgIYOLEiQwcOJDckXJERKqn\nnJwcLl26RGxsLLGxsSQmJnrXHTp0iLlz56oIdFBmZiYbNmxgz549eDwe6tWrx9ixY+nbt686eFRh\nxekFPLmI9Rb4Rbkl8lPnz59nwYIF3L17l0aNGjFnzhyNiSQi1ZK1lpSUFG/BFx8fz4MHD7zrjTHk\nvnWA2+0mPj5eBaADrLV8/fXXrF27ljt37mCMYdCgQbz66qvey71SdWkmkDKy1rJt2za++OILrLWE\nhoYya9YsjYQuItVKeno6sbGxnD9/ntjY2ALDhQA0b96c0NBQnnvuOQIDA/nrX/+K2+1WT1KHXLly\nheXLl3snJWjfvj2TJ0+mdevWRfykVBUqAMvgSUO8iIhUZQ8fPiQ+Pt57li8pqWDfv/r169O5c2ee\ne+45OnfuTKNGjQqsnzt3rnqSOuD+/fvey73WWurVq8f48ePp06ePbleqZlQAlpKGeBGR6ubgwYMc\nPXqUjIwMkpOTycnJ8a4LCgoiJCTEe5avRYsWTywo1JO0cl28eJGdO3cSFxfH/fv3McYwePBgRo8e\nTe3atZ2OJw5QAVhCCQkJ7Nq1ixMnTuB2u2nVqhXvvvsuTz/9tNPRREQqxIULF1i5ciVXrlwpsPxH\nP/qRt+Br164dQUFBDiWUJzl48CBLlizx3nfZsmVL3nrrLVq1auVwMnGSCsASiI+P5/3338fj8QDQ\ntWtX5syZoyFeRKRcJSQk+MTl0YSEBDZu3EhsbGyB5cYYRowYwZgxYxxKJsVx79491q9fz969e73L\njDH07NlTxZ+oACyutLQ0Fi1a5C3+jDF06NBBxZ+IlBtrLRs3bmTz5s0ABAYG8qtf/YqOHTtWao7E\nxEQ2btzI2bNnAQgODqZHjx4cOXLE23Gja9eulZpJis/j8XDw4EHWrVtHRkYGxhjv5Xh1upHvqQAs\nhtjYWBYsWEBGRgaQW/wFBgaqEYlIubl79y6RkZEcP37cuywnJ4cPP/yQwYMH079/f5o0aVKhGS5f\nvsyGDRs4ffo0ADVr1uSll15iyJAh1KlTh/79+/vEmUl5vG+++YYVK1Z4x1oMCQlh0qRJZGVl6f9O\nClAB+AQej4dt27axfv167xAvQ4YM4cqVK2pEIlJuTp48ybJly7hz5w41atTA7XbjdrsByMrKYsuW\nLWzZsoXOnTvTv39/unfvXq732129epWNGzd6RzSoUaMGgwcPZujQodStW9e7nTpu+K6MjAzWr19P\nVFQU1loaNGjA66+/Ts+ePb1n//R/J/mpAHyM+/fvs3jxYk6ePAnAyJEjGT16NC6XS5c+RKRcZGZm\nsnr1ag4cOADknq2ZPn066enp3rM1brebAwcOEB0dzfnz5zl//jy1a9emd+/e9O/fv0zjtiUnJ7Np\n0yaio6OB3J68gwYNYtiwYdSvX79cfkepWB6Ph/379/PFF19w7949XC4XQ4YMYdSoUQQHBzsdT3yY\nCsBHuHr1Kh9//DGpqanUrl2bmTNn0q1bN6djiUgVEh8fz+LFi7l16xaBgYGMHTuWwYMH43K5aNKk\nSYGzNSEhIUycOJGjR4+yf/9+Ll++zFdffcVXX33Fj370IwYMGEDPnj2pVatWsY597do1Nm3axLFj\nx7DWEhgYyMCBAxk+fDgNGjSoqF9ZylliYiLLly/n22+/BaBTp05MmjSJFi1aOJxM/IEKwEK+/vpr\nli1bRnZ2toZ4EZFyl52dzfr169m5cyfWWtq0acPMmTOLfNOuXbs2L774Ii+++CKXL1/mwIEDHDly\nhG+//ZZvv/2WVatWERYWRv/+/enQocMjx+BLTU1l8+bNHD582Fv4DRgwgOHDh/9goGbxXRkZGaxb\nt44DBw5graVhw4ZMmDCBHj16aDBnKTYVgHmys7NZvXq1t7t83759mTJlinr5iki5uXz5MosWLSIl\nJQWXy8XIkSN55ZVXCAgIKNF+2rRpQ5s2bRg/fjzHjx/nwIEDxMXFcejQIQ4dOkSzZs3o378/ffv2\n5caNG5zEB7ZKAAAXVklEQVQ4cYKUlBTOnj2Lx+PB5XIRHh7OiBEjeOqppyrot5Xy5vF4iIqK4osv\nvuD+/fsEBAQwZMgQRo4cqcu9UmIqAIHbt28TERFBYmIigYGBTJw4kfDwcH2SEpFy4Xa72bp1K5s2\nbcLj8dCsWTNmzpzJs88+W6b91qhRg969e9O7d29SU1M5ePAgBw8e5Pr166xdu5Z169YBeAcANsbQ\nv39/Ro4cWeE9iqV8Xbp0ieXLl3P58mUAQkNDmTRpEs8884zDycRfVfsCMP8QL0899RRz5syhbdu2\nTscSkSri2rVrfPLJJ3zzzTcADB48mLFjx5b71YWmTZvy2muvMXr0aM6ePcv+/fs5deqUt/gDGDJk\nCK+//nq5Hlcq1p07d1i3bh0HDx4EoFGjRrzxxht0795dJymkTKptAejxeNi6dSsbNmzAWstzzz3H\nrFmzCgx5ICJSWh6Ph71797JmzRqys7Np1KgR06dPJzQ0tEKPGxAQQLdu3ejWrRunTp1i3rx5eDwe\nAgMD6d69e4UeW8qPx+NhzZo17N27l+zsbAIDAxk6dCgjRoygZs2aTseTKqBaFoCFh3h55ZVXGDVq\nFC6Xy+FkIlIV3L59myVLlninUOvTpw8TJ06kdu3alZqjW7du/PrXv9YAwH4mISGBxYsXk5qaCuRe\nup8xYwY9e/Z0OJlUJdWuALxy5Qoff/wxN27coHbt2rz11lv8+Mc/djqWiFQB1loOHz7MihUryMzM\npG7duvzsZz/jhRdecCyTBm/2H3fu3GHt2rUcOnSowHJjDDdv3nQolVRV1aoAPHToEJGRkWRnZ9O6\ndWvmzJmjIV5EpFycOXOGNWvWkJycDOSefXvzzTc1oLIUye12s3fvXjZs2EBmZiaBgYH07NmTY8eO\neede1tSjUt6qRQEYFxfH2rVrvTdh9+vXj8mTJ2uIFxEpk4yMDOLi4vj66685deqUd/mIESMYM2aM\nbtKXIl24cIEVK1Zw9epVALp27crEiRNp2rQp4eHhunwvFaZYBaAxZjjwARAALLDW/rHQ+kHAeiAx\nb9Faa+1/lGPOUjt16hQfffSRtyfc8OHDGTt2rMOpRMQfZWdnk5CQQGxsLLGxsVy+fLlAL1vIvVxX\ns2ZNFX/yROnp6axZs4bDhw8D0LhxYyZOnEi3bt0KzN2rwk8qSpEFoDEmAPgrMBS4Chw1xmyw1p4r\ntGmUtXZUBWQstbS0ND799NMCY2BpsEwRKS5rLUlJScTGxnLu3DkuXLhAdna2d31gYCDt27enWbNm\nHDx4EI/Ho8t18kRut5uvvvqKjRs3kpWVRWBgIMOHD+fll1/WVSmpVMU5A9gLuGitvQRgjFkBjAEK\nF4A+5ebNm7z//vtkZGR4P00FBgbqD7OIPFFaWpr3DF9sbCx3794tsL5Vq1aEhobSuXNnQkJCvG/a\nffr00eU6eaL4+HiWL19e4D7RN954Q/eiiyOKUwC2BK7ke3wV6P2I7foZY04BScA/WWvPFt7AGDMb\nmA25UxlVlGvXrvGnP/2JtLQ02rZty6uvvsrly5f1h1n8UmW1m+ooISGBc+fOUbNmTW/hl5KSUmCb\nhg0bEhoa6i36GjRo8Mh96XKdb/GldvPdd9+xZs0ajhw5AkCTJk2YNGmSRqAQR5VXJ5AYoI21NsMY\nMxL4AuhYeCNrbQQQARAWFmYLry8PSUlJvP/++9y9e5cOHTrwy1/+klq1atGlS5eKOJxIhauMdlMd\n7d27l+XLl//gHr6aNWsSEhLiLfqaN2+u+/n8kC+0G7fbze7du9m4cSMPHjwgKCjIe7k3KCjIiUgi\nXsUpAJOA1vket8pb5mWtvZPv+y3GmI+MMU2stZU6cNE333zDn//8Z+7du0doaCg///nPNWK6iBRw\n//591q1bx759+wos79SpE6NGjaJdu3YEBlaLARKkAp0/f54VK1Z4zyg///zzTJgwQXMwi88ozl+5\no0BHY8yz5BZ+k4Ap+TcwxjwDXLfWWmNML8AF3CrvsE9y8eJF/vKXv5CVlUW3bt2YPXu2PmGJiJe1\nlmPHjrFq1Sru3LlTYOafgIAAxowZo0u4UmYnTpxgw4YNJCXlnidp2rQpEydOpGvXrg4nEymoyALQ\nWptjjPklsI3cYWAWWWvPGmPezVs/D3gd+LkxJgfIBCbZwtdVKlBsbCwfffQRDx8+JCwsjLfeeouA\ngIDKOryI+LibN2+yfPlyzpw5A+Terzd16lQyMzPVcUPKzOPxcOHCBXbs2MHp06e9y8PDw5k4caJO\nRohPKtZ1DmvtFmBLoWXz8n3/IfBh+UYrnlOnTvHxxx+Tk5ND3759mTZtmub0FREg9x6snTt3snHj\nRrKzs6lVqxbjxo1jwIAB3r8TKvyktJKSkjh8+DBHjhwhLS2twDpjDI0bN1bxJz7Lr290iY6OZsGC\nBXg8Hl588UUmTZqk4k9EAEhMTGTZsmXeGRZ69uzJhAkTHtuLV6Q40tLSOHLkCEeOHPG+tiB3IOeO\nHTty7NgxjQcpfsFvC8BDhw55B3keNmwY48aNU089ESEzM5P169ezZ88erLU0btyYKVOm6B4sKbXM\nzExiYmI4fPgw8fHx3p7jtWvXJiwsjN69e9OuXTtcLhcDBw7UbQXiF/yyANy7dy+fffYZAKNGjWLU\nqFEq/kSE48ePs2LFCr777jtcLhdDhw5l1KhRFT4aQGZmJu+//z4xMTF07tyZDh06lGl/Fy9e5Pz5\n81V+X6mpqcycOZO+ffuWaV8VIScnh7Nnz3L48GFOnTrlnQEmMDCQbt260bt3b7p06fKDS7waD1L8\nhd8VgDt27ODzzz8HYPz48QwbNszhRCLitNu3b7NixQpOnjwJQNu2bZk6dSqtW7cu4ifL5u7du/zt\nb3/jj3/84w/uAZPiWbZsGbt27fKJItBay6VLlzh8+DDHjh3j3r173nUhISH07t2bF154gdq1azuY\nUqR8+E0BaK1l8+bNbNy4EYDJkyczaNAgZ0OJiKM8Hg9fffUV69ev58GDBwQHB/Paa6/x4osvVuj9\nwLdu3eLPf/4zf/nLXx5583/37t1LPcvD6dOniYmJqTb7evjwIXv27HG0ADx69Cj79u3j+vXrpKen\ne5e3aNGC3r1706tXL5566inH8olUBL8oAK21rF27lu3bt2OMYfr06T7xaVFEnHP58mWWLVvGt99+\nC0D37t2ZOHEijRo1qrBjpqSk8N///d/MmzfPe3ZowIABjBs3jn/913/l4cOH1KhRgw8//LDUf6MO\nHTrESy+9VK325eSH+UWLFnH48GHv47p169KvXz969+5Nq1atHMslUtF8vgD0eDysXLmSPXv24HK5\nmDVrFmFhYU7HEhGHxMbGsnHjRhISEgBo1KgRkydP5ic/+UmFHTMxMZH//M//ZNGiRTx8+BCA4cOH\n8y//8i+Eh4cD0KdPH/bs2cOgQYPK9AG1b9++7Nq1S/tygDGGl156iZEjRzodRaTCmUocr7mAsLAw\ne+zYsSdu4/F4WLp0KQcPHiQwMJDZs2dX6B95kYpijIm21pb5k0tx2o0/y8nJ4e7du9y5c4c7d+78\n4Pvr1697z/gBhIWF8eabbxIcHFwhec6dO8cf//hHPvvsM9xuN8YYxo0bx29/+1t69OhRIceU/1UZ\n7ebChQt88MEHuN1uAgICmDt3rjpxiF8rbrvx2TOAFy5cYPny5SQlJREUFMTf/d3f8dxzzzkdS0RK\n4eTJk5w9e5bGjRtTp04db1FXuMi7f/9+sfdpjKFVq1YVUvxFR0fz+9//nrVr1wK5U8VNmzaNf/7n\nfyY0NLTcjyfO6dixI3PnztXQLVLt+GQBGBcXx/vvv+8da2nChAkq/kT8yP379zl//jyxsbGcOnWK\n7777rlg/53K5qFu3LvXr1/d+1atXz/v9vXv3WLt2bYUMtGutJSoqit/97nds374dgJo1a/LWW2/x\nm9/8hmeffbbcjiW+RUO3SHXkkwXgzp07vcWfMaZEZwVEpPLl5ORw6dIlYmNjiY2N5ZtvvuFxt5e0\nadOG0NDQRxZ4derUKbL3btu2bcv1bI21lq1bt/K73/2OAwcOAFCnTh1+/vOf84//+I80b968zMcQ\nEfE1PlkA9urVi2XLlnH79m2aNGlCz5492bJlS9E/+BixsbGkpKQwbtw4+vXrV45J5Unu3bvH0qVL\nuXjxop77KsZaS0pKCufOnSM2NpYLFy7w4MED7/qAgADatWtHaGgoAQEB/P73v+f69es0adKEXr16\nERwczMOHD7l58yY3b94s0bFjY2M5ffo0P/7xj8t8OfbQoUMsXLiQlJQUILdDyXvvvcd7772nYT+k\nxG7dukVkZCQxMTHl8vosz9e6r+4rLi6OGzduMHr0aJ/pDFRd+GQnkL/+9a/88pe/rJDjDh48mLFj\nxxIeHk7Xrl0JCAiokONUR7dv32b//v1ERUURFRXFsWPHcLvd3vXV+bmvrE4gCQkJFXYvU3p6uvcM\n3/nz539wWbdFixaEhobStGlTkpOTOXz4MFFRUZw4ceKxZwN9yS9+8Qv+8Ic/UK9ePaejSB5f7zx1\n5coVoqKi2LdvH1FRUZw7d67cj1FdGGN45ZVXGD9+POHh4bRr104zfJWSX3cCiY+PL/C4LG9m378h\nfm/37t3s3r0bgAYNGtC/f38GDhxIeHg4YWFh1KhRo/TBq5mrV696i72oqCjOnDlTYH3hxqvnvmLt\n37+fyMhIPB4PLpeLvn378vTTTxMUFERQUBCBgYHF+vf77xMTEzly5AjZ2dkkJyeTnJxc4Hj169en\nc+fONGjQgBs3bhAdHc1nn332g/brcrkKFIDl2Z7La18BAQG0bNlSxZ88lrWWuLi4AgVf/h7pkDtN\nXE5OjvexL77WfXVf1lo2bdrEpk2bgNwPlOHh4d6vrl27Vujg7tWRT54BLDxIaFmmCcq/r6CgIN57\n7z2Sk5Mf2XiDg4Pp06eP9wXXt29f6tatW6rjVjXWWi5cuOD9wxcVFUViYmKBbWrWrEmvXr28z19g\nYCCvvvpqgec+KSmJqKgoLl++XOBnq/pzXxlnMiIiIoiOji7rIR6rRo0atG/fntq1a3Pz5k1Onz5N\nVFQUSUlJBbarU6cOffv29f5fArzyyivl3p59aV9SMZw8A5iTk8PJkye9Bd/+/fu5ceNGgW2+/yAb\nHh7OwIEDyc7OZsSIET73+vSHfX0/1Nv3Z1Vv3bpVYNtGjRp5n+vw8HB69OihkwaPUdx245MFIOS+\nMMprkNDH7evy5csFzmAVPn0fEBDACy+84H3BDRgwgAsXLlR4Ll/Y1+7du2nZsiXp6ene5yc1NbXA\ndvXq1Svwxy8sLOwHQ3IU9dx/X1DGxsYW+Lmq9txXxhvZ0aNH+cMf/sDVq1dp2bIlY8eOpW7dumRn\nZ5OTk1Osf7//PjMzk+TkZJKSkqhVqxYtWrQgIyODgwcP/mDqs6eeeqrAJ/Xu3bsTFBRU4ueouHx1\nX1L+KqsAPHToEDt37qRx48bcvn2bqKgoDh48SEZGRoHtnnnmGe/rfODAgY+8lcVXX5/+tC+Px8P5\n8+e97z379u3jypUrBX6uVq1aPzhpcOrUKb/5HStyX35fADrh5s2bBe5hi4mJKXAPG+Re1rTW4nK5\neP7552nQoEGpjpWens6JEye8l+t8cV+FNW3atMAfv27dupXbfXzfP/ffF4THjx/3q+feWktwcPBj\nPw1XxhvZX/7yF371q1+Vy++VmprK2bNnH7muVatW3kv34eHhhIaG6tKMVIjKaDf/8R//wb//+78/\n8m9e+/btvX/vwsPDad++ve5Lc8i3335boCA8f/58gfUBAQF4PB6ffY/wyfcba60jXz169LC+7u7d\nu3b79u323/7t3+yLL75oAwMDLVCtvrp3727nz59v4+LirMfjqbTn/s6dO3733AcEBNjf//73j/x9\ngGO2gtvNG2+8UWG/W8+ePe2SJUtsYmJipb4OpHqrjHYzatSoAq/1Pn362JUrV9qkpKSK+8WkzFJT\nU+3atWvt3LlzbY8ePawxxvH3AH97v9EZwBLYu3cvL7/8MtnZ2QQFBfFf//VfdOnSpVT7Onv2LL/5\nzW98dl85OTk+dV+Urz/3RT1flXEmY9OmTbz++utV+nUg1UtltJsvvviCiRMn4na79Vr3Yzt37mTU\nqFE++x7hi+83xSoAjTHDgQ+AAGCBtfaPhdabvPUjgfvADGttzJP26Y8FIPj3fQFO7Ks8+erv6Cv3\nABY3S3H56utAqg9/bDfiHF/9++er7zdFFoDGmAAgHhgKXAWOApOttefybTMS+HtyC8DewAfW2t5P\n2q+/FoAipeHr45mJ+CK1G5GSK267Kc6d272Ai9baS9bah8AKYEyhbcYAS/IuP38NNDTGaP4kERER\nER9UnIGgWwL5+19fJfcsX1HbtARS8m9kjJkNzM57mGGMiStR2rJpApRszqnKoVwl46+5flTaHavd\nPJJylYy/5lK7KV/KVTL+mqtY7aZSZwKx1kYAEZV5zO8ZY46Vx6WE8qZcJVMdc6nd/JBylUx1zKV2\n80PKVTJVPVdxLgEnAa3zPW6Vt6yk24iIiIiIDyhOAXgU6GiMedYYUwOYBGwotM0GYJrJ1QdIt9am\nFN6RiIiIiDivyEvA1tocY8wvgW3kDgOzyFp71hjzbt76ecAWcnsAXyR3GJiZFRe51By5FFAMylUy\nylW5fPX3Uq6SUa7K5au/l3KVTJXO5dhA0CIiIiLiDE3gKSIiIlLNqAAUERERqWaqXAFojGltjPnK\nGHPOGHPWGPMPecufMsbsMMZcyPu3kUP5Aowxx40xm3wllzGmoTHmc2PMeWNMrDGmr4/kmpv3f3jG\nGLPcGBPsRC5jzCJjTKox5ky+ZY/NYYz5rTHmojEmzhjzckXnKw9qN6XKpHbz5BxqN2o3j8qkdvPk\nHJXWbqpcAQjkAL+21j4H9AF+YYx5DvhnYJe1tiOwK++xE/4BiM332BdyfQBstdZ2Bn6Sl8/RXMaY\nlsB7QJi1tiu5HZAmOZRrMTC80LJH5sh7rU0CuuT9zEcmdzpFX6d2U3JqN0+2GLUbtZsfUrt5ssVU\nVrux1lbpL2A9ufMYxwHN85Y1B+IcyNIq7z9vMLApb5mjuYAGQCJ5HYLyLXc61/ezyzxFbm/1TcAw\np3IBbYEzRT0/wG+B3+bbbhvQt7Jfa+Xw+6rdPDmT2k3x8qjdqN3kz6R2U7w8ldJuquIZQC9jTFug\nO3AYaGb/d2zCa0AzByL9Cfj/AE++ZU7neha4AXySd6lggTGmjtO5rLVJwP8PXCZ3SsF0a+12p3Pl\n87gcj5sW0W+o3RSL2k3pqN1UHrWbYqqu7abKFoDGmLrAGuBX1to7+dfZ3FK5Use/McaMAlKttdGP\n28aJXOR+2nkB+Ju1tjtwj0KnuR16vhoBY8j9g9ECqGOMmep0rkfxlRzlQe2m2NRuyshXcpQHtZti\nU7spo/LMUSULQGNMELmNMdJauzZv8XVjTPO89c2B1EqO1R941RjzDbACGGyMWeYDua4CV621h/Me\nf05uA3U61xAg0Vp7w1qbDawF+vlAru89LoffTouodlMiajelo3ZTOdRuSqZatpsqVwAaYwywEIi1\n1v5PvlUbgOl5308n916NSmOt/a21tpW1ti25N23uttZO9YFc14ArxphOeYteAs45nYvcU/F9jDG1\n8/5PXyL3ZmGnc33vcTk2AJOMMTWNMc8CHYEjDuQrEbWbEudSuykdtZtKoHZTYtWz3ZTnjYu+8AUM\nIPf06CngRN7XSKAxuTfEXgB2Ak85mHEQ/3tTruO5gOeBY3nP2RdAIx/J9e/AeeAMsBSo6UQuYDm5\n94Vkk/sJdtaTcgD/CiSQe+PuCKdeZyX8HdVuSp5H7ebJOdRu1G4elUft5sk5Kq3daCo4ERERkWqm\nyl0CFhEREZEnUwEoIiIiUs2oABQRERGpZlQAioiIiFQzKgBFREREqhkVgCIiIiLVjApAERERkWrm\n/wFvDaSAjGzH2QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7f97a9ce10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(9,3))\n",
    "\n",
    "plt.subplot(1,3,1)\n",
    "plt.plot(vdp_data[0], vdp_data[1], '.-', color='#666666', linewidth=2)\n",
    "plt.plot(vdp_burst_data0[0], vdp_burst_data0[1], '.-k', linewidth=2)\n",
    "plt.ylim([0,3e5])\n",
    "# plt.yticks(np.arange(0,3.5e5,5e4), np.arange(0,3.5,.5))\n",
    "plt.ticklabel_format(style='sci', axis='y', scilimits=(0,4))\n",
    "\n",
    "plt.subplot(1,3,2)\n",
    "plt.plot(vdplorenz1_data[0], vdplorenz1_data[1], '.-', color='#666666',\n",
    "         linewidth=2)\n",
    "plt.plot(vdplorenz1_burst_data0[0], vdplorenz1_burst_data0[1], '.-k', linewidth=2)\n",
    "plt.ylim([0,3e5])\n",
    "plt.yticks(np.arange(0,3.5e5,5e4), [])\n",
    "\n",
    "plt.subplot(1,3,3)\n",
    "plt.plot(vdplorenz2_data[0], vdplorenz2_data[1], '.-', color='#666666',\n",
    "        linewidth=2)\n",
    "plt.plot(vdplorenz2_burst_data0[0], vdplorenz2_burst_data0[1], '.-k', linewidth=2)\n",
    "plt.ylim([0,3e5])\n",
    "plt.yticks(np.arange(0,3.5e5,5e4), [])\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.savefig('figures/04.pdf', format='pdf', dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}