check_timeseries_stationarity.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "Import the necessary modules. We need stationarity from ntrfc and some other modules for the definition of a signal and for rendering a plot"
   ],
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     "name": "#%% md\n"
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   }
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "outputs": [],
   "source": [
    "from ntrfc.timeseries.stationarity import stationarity\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Lets define a signal generator. We want to generate a signal with some noise, an initial transient and a constant deterministic fluctuation."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
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  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "outputs": [],
   "source": [
    "def signalgen_abatingsine(amplitude, noiseamplitude, frequency, mean, abate, time):\n",
    "    resolution = 2048\n",
    "    step = (resolution * frequency ** -1) ** -1\n",
    "\n",
    "    times = np.arange(0, time, step)\n",
    "    noise = np.random.normal(-1, 1, len(times)) * noiseamplitude\n",
    "\n",
    "    values = amplitude * np.sin(frequency * (2 * np.pi) * times) + mean + np.e ** -(times * abate) + noise\n",
    "    return times, values"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
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  },
  {
   "cell_type": "markdown",
   "source": [
    "Lets define the input arguments for the signal generator and lets generate a signal."
   ],
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    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
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   "cell_type": "code",
   "execution_count": 11,
   "outputs": [],
   "source": [
    "test_amplitudes = 0.1\n",
    "test_noiseamplitude = 0.01\n",
    "test_frequencies = 6\n",
    "test_times = 40\n",
    "test_mean = -1\n",
    "test_abate = 1\n",
    "\n",
    "\n",
    "timesteps, values = signalgen_abatingsine(amplitude=test_amplitudes, noiseamplitude=test_noiseamplitude,\n",
    "                                          frequency=test_frequencies, mean=test_mean, time=test_times,\n",
    "                                          abate=test_abate)\n"
   ],
   "metadata": {
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    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Lets compute the index of the stationary timestep."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "outputs": [],
   "source": [
    "stationary_timestep = stationarity(timesteps, values)\n",
    "\n",
    "well_computed_stationarity_limit = -np.log(0.05) / abate\n",
    "well_computed_stationary_time = timesteps[-1] - well_computed_stationarity_limit\n",
    "stationary_time = timesteps[-1] - stationary_timestep\n"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Lets plot the result"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [
    "plt.figure()\n",
    "plt.plot(timesteps, values)\n",
    "plt.axvline(stationary_timestep, color=\"green\")\n",
    "plt.show()\n"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  }
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