{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Introduction\n",
    "\n",
    "Compare the different ways to determine the noise color from the power spectral density."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-02-19T15:07:35.818923Z",
     "start_time": "2020-02-19T15:07:35.816648Z"
    }
   },
   "source": [
    "## Standard imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-02-19T15:07:49.271141Z",
     "start_time": "2020-02-19T15:07:48.697097Z"
    }
   },
   "outputs": [],
   "source": [
    "# Data manipulation\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# Options for pandas\n",
    "pd.options.display.max_columns = 50\n",
    "pd.options.display.max_rows = 30\n",
    "\n",
    "from IPython import get_ipython\n",
    "ipython = get_ipython()\n",
    "\n",
    "# autoreload extension\n",
    "if 'autoreload' not in ipython.extension_manager.loaded:\n",
    "    %load_ext autoreload\n",
    "\n",
    "%autoreload 2\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import gridspec\n",
    "%matplotlib inline\n",
    "\n",
    "import time\n",
    "np.random.seed(int(time.time()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-02-19T15:08:03.406470Z",
     "start_time": "2020-02-19T15:08:03.386828Z"
    }
   },
   "source": [
    "## Specific imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-02-19T15:11:03.503582Z",
     "start_time": "2020-02-19T15:11:03.052492Z"
    }
   },
   "outputs": [],
   "source": [
    "from generate_timeseries import Timeseries\n",
    "from noise_parameters import NOISE\n",
    "from noise_properties_plotting import example_noise_fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Settings figures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-02-19T15:10:23.964569Z",
     "start_time": "2020-02-19T15:10:23.819750Z"
    }
   },
   "outputs": [],
   "source": [
    "from elife_settings import set_elife_settings, ELIFE\n",
    "\n",
    "set_elife_settings()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-02-19T15:08:47.556507Z",
     "start_time": "2020-02-19T15:08:47.536376Z"
    }
   },
   "source": [
    "# Compare fits for noise color determination"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-02-19T15:12:38.990256Z",
     "start_time": "2020-02-19T15:12:37.399413Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 396.85x144 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 50\n",
    "    \n",
    "steadystate = np.logspace(-2,2,50)[::-1]\n",
    "\n",
    "params = {}\n",
    "\n",
    "# no immigration\n",
    "params['immigration_rate'] = np.zeros([N, 1])\n",
    "\n",
    "omega = np.random.normal(0,0.1,[N, N]); # np.zeros([N,N]);\n",
    "np.fill_diagonal(omega, -1)\n",
    "params['interaction_matrix'] = omega\n",
    "\n",
    "# growthrates determined by the steady state\n",
    "g = - omega.dot(steadystate).reshape([N,1])\n",
    "params['growth_rate'] = g\n",
    "\n",
    "initcond = np.array([np.random.normal(abundance, 0.1*abundance) \n",
    "                     for abundance in steadystate]).reshape([N,1])\n",
    "\n",
    "params['initial_condition'] = initcond\n",
    "params['noise_linear'] = 1e-1\n",
    "\n",
    "x = Timeseries(params, noise_implementation = NOISE.LANGEVIN_LINEAR,\n",
    "                    dt=0.01, tskip=4, T=100.0).timeseries\n",
    "\n",
    "fig = plt.figure(figsize=(ELIFE.TEXTWIDTH,2))\n",
    "\n",
    "gs = gridspec.GridSpec(2,2,wspace=0.3, hspace=0.5, top=0.9, right=0.95, bottom=0.18,\n",
    "                       width_ratios=[0.75,1], height_ratios=[1,1.5])\n",
    "ax_ts = fig.add_subplot(gs[0])\n",
    "ax_pws = fig.add_subplot(gs[:,1])\n",
    "ax_leg = fig.add_subplot(gs[2])\n",
    "ax_leg.axis('off')\n",
    "ax_left = fig.add_subplot(gs[:,0])\n",
    "ax_left.axis('off')\n",
    "ax_left.text(0.05, 1.1, 'A', transform=ax_left.transAxes, fontsize=10, fontweight='bold', \n",
    "                  va='top', ha='right')\n",
    "ax_pws.text(0.05, 1.1, 'B', transform=ax_pws.transAxes, fontsize=10, fontweight='bold', \n",
    "                  va='top', ha='right')\n",
    "\n",
    "ax_ts.set_yscale('log')\n",
    "ax_ts.set_ylabel('Abundance')\n",
    "ax_ts.set_xlabel('Time', ha='right', x=1)\n",
    "\n",
    "\n",
    "for j in range(1, N+1, int(N/5)):\n",
    "    ax_ts.plot(x['time'][::10], x['species_%d'%j][::10])\n",
    "\n",
    "    example_noise_fit(ax_pws, x['species_%d'%j], spline=True, linear_all=True)\n",
    "\n",
    "ax_pws.set_xlabel('log$_{10}$(frequency)', ha='right', x=1)\n",
    "\n",
    "handles, labels = ax_pws.get_legend_handles_labels()\n",
    "ax_leg.legend(handles, labels, title='Linear with cutoff | Linear | Spline', loc=2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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  "hide_input": true,
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  },
  "toc": {
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