ScaleFactorvsTimeDE.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8bd112c3-179b-4b57-86fc-7e9408fcb315",
   "metadata": {},
   "source": [
    "# Lookback time (different dark energy models movie)\n",
    "Florent Leclercq<br/>\n",
    "Institut d'Astrophysique de Paris<br/>\n",
    "20 July 2023"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a4edcc84-f45f-4503-8651-1c01068fc03f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.animation import FuncAnimation\n",
    "%matplotlib widget\n",
    "plt.rcParams.update({'lines.linewidth': 2})\n",
    "plt.rcParams.update({'text.usetex': True})\n",
    "plt.rcParams.update({'text.latex.preamble': r\"\\usepackage{amsmath}\\usepackage{upgreek}\"})\n",
    "plt.rcParams.update({'font.family': 'serif'})\n",
    "plt.rcParams.update({'font.size': 10})\n",
    "plt.rcParams.update({'figure.max_open_warning': 20})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a2110b62-056f-4a51-a2f9-f855d11347e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "from LookbackTimeLib import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f4eb6922-ee53-44e9-ba1e-26d859d9e85d",
   "metadata": {},
   "outputs": [],
   "source": [
    "class movie:\n",
    "    def __init__(self, t, a4=None, a5=None, a6=None, a7=None):\n",
    "        self.fig, self.ax = plt.subplots(1,1, figsize=(6,4))\n",
    "        self.steps = len(t)\n",
    "        self.a4, self.a5, self.a6, self.a7 = a4, a5, a6, a7\n",
    "        self.t = t\n",
    "\n",
    "    def show(self):\n",
    "        self.fig.show()\n",
    "    \n",
    "    # Initialization function\n",
    "    def init(self):\n",
    "        ax = self.ax\n",
    "        a4, a5, a6, a7 = self.a4, self.a5, self.a6, self.a7\n",
    "        t = self.t\n",
    "        frame = 0\n",
    "        Nstart = 0\n",
    "        ax.set_xlim([tminDE-1.,tmaxDE])\n",
    "        ax.set_ylim([0.,5.])\n",
    "        if a4 is not None:\n",
    "            self.plot1, = ax.plot(t[Nstart:frame], a4[Nstart:frame], color=\"C9\")\n",
    "        else:\n",
    "            self.plot1 = None\n",
    "        if a5 is not None:\n",
    "            self.plot2, = ax.plot(t[Nstart:frame], a5[Nstart:frame], color=c_phantom)\n",
    "        else:\n",
    "            self.plot2 = None\n",
    "        if a6 is not None:\n",
    "            self.plot3, = ax.plot(t[Nstart:frame], a6[Nstart:frame], color=c_freezing)\n",
    "        else:\n",
    "            self.plot3 = None\n",
    "        if a7 is not None:\n",
    "            self.plot4, = ax.plot(t[Nstart:frame], a7[Nstart:frame], color=c_thawing)\n",
    "        else:\n",
    "            self.plot4 = None\n",
    "        return self.plot1, self.plot2, self.plot3, self.plot4, \n",
    "    \n",
    "    # Update function\n",
    "    def update(self, frame):\n",
    "        a4, a5, a6, a7 = self.a4, self.a5, self.a6, self.a7\n",
    "        t = self.t\n",
    "        Nstart = NpastDE if frame>NpastDE else 0\n",
    "        \n",
    "        if a4 is not None:\n",
    "            self.plot1.set_data(t[Nstart:frame], a4[Nstart:frame])\n",
    "        if a5 is not None:\n",
    "            self.plot2.set_data(t[Nstart:frame], a5[Nstart:frame])\n",
    "        if a6 is not None:\n",
    "            self.plot3.set_data(t[Nstart:frame], a6[Nstart:frame])\n",
    "        if a7 is not None:\n",
    "            self.plot4.set_data(t[Nstart:frame], a7[Nstart:frame])\n",
    "        return self.plot1, self.plot2, self.plot3, self.plot4, \n",
    "        \n",
    "    # Create the animation\n",
    "    def animate(self):\n",
    "        animation = FuncAnimation(self.fig, self.update, frames=len(t), init_func=self.init, blit=False)\n",
    "        return animation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4f715da2-c626-4309-9023-242dfd9c8084",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "model_id": "b9c5d8947b874593a265670d73ebea8c",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=600.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "i=Nframes-1\n",
    "frame = movie(tDE, a4DE, a5DE, a6DE, a7DE)\n",
    "frame.init();\n",
    "frame.update(i);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d9d99cd2-a2c5-440f-8599-e7acd4f6e6d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "de6df23d63304aee9cee34595873d833",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img src='data:image/png;base64,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' width=600.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "this_movie = movie(tDE, a4DE, a5DE, a6DE, a7DE)\n",
    "animation = this_movie.animate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fe536247-bc2c-4d9f-83b4-37e126e33362",
   "metadata": {},
   "outputs": [],
   "source": [
    "animation.save(\"output/ScaleFactorvsTimeDE.mp4\", dpi=300, fps=48)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "615a3f44-8109-414d-aa2d-3f3293dbf6ad",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}