{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "\n# Crude periodicity finding\n\nDiscover the periods in evolution of animal populations\n(:download:`../../../../data/populations.txt`)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Load the data\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import numpy as np\n\ndata = np.loadtxt(\"../../../../data/populations.txt\")\nyears = data[:, 0]\npopulations = data[:, 1:]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Plot the data\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\n\nplt.figure()\nplt.plot(years, populations * 1e-3)\nplt.xlabel(\"Year\")\nplt.ylabel(r\"Population number ($\\cdot10^3$)\")\nplt.legend([\"hare\", \"lynx\", \"carrot\"], loc=1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Plot its periods\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import scipy as sp\n\nft_populations = sp.fft.fft(populations, axis=0)\nfrequencies = sp.fft.fftfreq(populations.shape[0], years[1] - years[0])\nperiods = 1 / frequencies\n\nplt.figure()\nplt.plot(periods, abs(ft_populations) * 1e-3, \"o\")\nplt.xlim(0, 22)\nplt.xlabel(\"Period\")\nplt.ylabel(r\"Power ($\\cdot10^3$)\")\n\nplt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "There's probably a period of around 10 years (obvious from the\nplot), but for this crude a method, there's not enough data to say\nmuch more.\n\n"
      ]
    }
  ],
  "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": "3.12.11"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}