initial upload

scientific-computing-2/auto_examples_jupyter_3/solutions/plot_periodicity_finder.ipynb

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+{
+  "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
+}