{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import packages\n",
    "import h5py                     # hdf5 reader\n",
    "import numpy as np              # numpy\n",
    "import matplotlib.pyplot as plt # plotting\n",
    "\n",
    "plt.rcParams.update({\n",
    "    \"pgf.texsystem\": \"pdflatex\",  # Use pdflatex for compatibility\n",
    "    \"text.usetex\": True,           # Use LaTeX for text rendering\n",
    "    \"font.family\": \"serif\",        # Use serif fonts\n",
    "    \"pgf.preamble\": r\"\\usepackage{amsmath}\",  # Add any necessary packages\n",
    "    \"pgf.rcfonts\": False,          # Disable rc fonts to avoid extra font definitions\n",
    "    \"font.size\": 22,\n",
    "    \"figure.figsize\": (6,6)\n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "wave1_path = 'training-results/32ksamples_wave1-NN.hdf'\n",
    "wave4_path = 'training-results/32ksamples_wave4-NN.hdf'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#helper function\n",
    "def load_hdf5_list(file, levels, dataset):\n",
    "    l = list()\n",
    "    for L in levels:\n",
    "        l.append(file[dataset+'/'+str(L)][:])\n",
    "    return l\n",
    "\n",
    "#load data\n",
    "wave1_f = h5py.File(wave1_path, 'r')\n",
    "wave1_N = wave1_f['number_of_training_samples'][:]\n",
    "wave1_POD_ranks = wave1_f['POD_rank'][:]\n",
    "wave1_f.close()\n",
    "wave4_f = h5py.File(wave4_path, 'r')\n",
    "wave4_N = wave4_f['number_of_training_samples'][:]\n",
    "wave4_POD_ranks = wave4_f['POD_rank'][:]\n",
    "wave4_f.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#plotting\n",
    "plt.clf()\n",
    "p=1./4.5\n",
    "plt.subplots(constrained_layout=True)\n",
    "plt.loglog(wave1_N, wave1_N, \"-+\")\n",
    "plt.loglog(wave1_N, wave1_POD_ranks, \"-+\")\n",
    "plt.loglog(wave4_N, wave4_POD_ranks, \"-+\")\n",
    "plt.loglog(wave4_N, 8e2*wave4_N**(1/(2*(1/p-1))), \"--\", color=\"black\")\n",
    "plt.title('POD ranks obtained from snapshots')\n",
    "plt.xlabel('number of snapshots N')\n",
    "plt.legend(['N', 'POD rank $J$, $\\kappa=1$', 'POD rank $J$, $\\kappa=4$', 'rate $1/(2(1/p-1))$'], loc='lower right')\n",
    "plt.savefig('plots/POD_ranks.eps')"
   ]
  }
 ],
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