L-curve.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e25836d2-68d1-4e10-b2fc-e4ce0a787958",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2024-07-04 22:07:14.067710: I tensorflow/core/util/port.cc:113] oneDNN custom operations are on. You may see slightly different numerical results due to floating-point round-off errors from different computation orders. To turn them off, set the environment variable `TF_ENABLE_ONEDNN_OPTS=0`.\n",
      "2024-07-04 22:07:14.068229: I external/local_tsl/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.\n",
      "2024-07-04 22:07:14.071047: I external/local_tsl/tsl/cuda/cudart_stub.cc:32] Could not find cuda drivers on your machine, GPU will not be used.\n",
      "2024-07-04 22:07:14.102242: I tensorflow/core/platform/cpu_feature_guard.cc:210] This TensorFlow binary is optimized to use available CPU instructions in performance-critical operations.\n",
      "To enable the following instructions: AVX2 AVX_VNNI FMA, in other operations, rebuild TensorFlow with the appropriate compiler flags.\n",
      "2024-07-04 22:07:14.826718: W tensorflow/compiler/tf2tensorrt/utils/py_utils.cc:38] TF-TRT Warning: Could not find TensorRT\n"
     ]
    }
   ],
   "source": [
    "from src.l_curve import create_L_curve\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import os\n",
    "import firedrake"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a4dad06d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_lcurve(l_curve,loglog=False):\n",
    "    # Plot\n",
    "    plt.figure(figsize=(10, 6))\n",
    "\n",
    "    # Plot scatter points\n",
    "    if loglog:\n",
    "        plt.loglog(l_curve['J1'], l_curve['J2'], marker='o', linestyle='', label='Regularization constant')\n",
    "    else:\n",
    "        plt.plot(l_curve['J1'], l_curve['J2'], marker='o', linestyle='', label='Regularization constant')\n",
    "\n",
    "    # Plot line connecting the points\n",
    "    if loglog:\n",
    "        plt.loglog(l_curve['J1'], l_curve['J2'], marker='', linestyle='-')\n",
    "    else:\n",
    "        plt.plot(l_curve['J1'], l_curve['J2'], marker='', linestyle='-')\n",
    "\n",
    "    # Annotate points with regularization values\n",
    "    for i, txt in enumerate(l_curve['reg']):\n",
    "        plt.annotate(txt, (l_curve['J1'][i], l_curve['J2'][i]))\n",
    "\n",
    "    plt.xlabel('E')\n",
    "    plt.ylabel('R')\n",
    "    plt.title('Log-Log Plot of E vs R with Regularization Constants')\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f3cc44e6",
   "metadata": {},
   "outputs": [],
   "source": [
    "variable = 'simultaneous'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6e689a9",
   "metadata": {},
   "source": [
    "#### Thwaites L-curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3c916289",
   "metadata": {},
   "outputs": [],
   "source": [
    "l_curve = create_L_curve(None, variable, outline='data/geojson/thwaites.geojson', mesh='thwaites', invert_iter = 170, workers = 2,  lcar=9e3, nosigma_lossfcn = 'nosigma', drichlet_ids = [1,2,5,6], regularization_grad_fcn = True, constant_val=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1d3d5065",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = {\n",
    "    'reg': [0.01, 0.1, 1, 10],\n",
    "    'J1': [568.5430921059252, 200.15193884090579, 125.05111469154097, 131.02607789480362],\n",
    "    'J2': [0.029821845834902418, 0.5584096178962419, 10.077985527278557, 16.01170699159037]\n",
    "}\n",
    "\n",
    "l_curve = pd.DataFrame(data)\n",
    "l_curve = l_curve.sort_values('reg')\n",
    "l_curve\n",
    "\n",
    "l_curve = pd.DataFrame(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "110d80df",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_lcurve(l_curve, loglog=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16ce9bd9",
   "metadata": {},
   "source": [
    "#### Dotson L-curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4f32911e",
   "metadata": {},
   "outputs": [],
   "source": [
    "l_curve = create_L_curve(None, variable, outline='data/geojson/dotson-crosson.geojson', mesh='dotson', invert_iter = 300, workers = 2,  lcar=10e3, nosigma_lossfcn = 'nosigma', drichlet_ids = [1,2,5,6,7,8,9,10,11], regularization_grad_fcn = True, constant_val=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "43f6c2a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>reg</th>\n",
       "      <th>J1</th>\n",
       "      <th>J2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.01</td>\n",
       "      <td>1940.085759</td>\n",
       "      <td>0.088330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.10</td>\n",
       "      <td>552.569799</td>\n",
       "      <td>1.827576</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.00</td>\n",
       "      <td>260.436310</td>\n",
       "      <td>45.853066</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>100.00</td>\n",
       "      <td>224.773247</td>\n",
       "      <td>323.206872</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      reg           J1          J2\n",
       "0    0.01  1940.085759    0.088330\n",
       "1    0.10   552.569799    1.827576\n",
       "2    1.00   260.436310   45.853066\n",
       "3  100.00   224.773247  323.206872"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = {\n",
    "    'reg': [0.01, 0.1, 1, 100],\n",
    "    'J1': [1940.0857585219212, 552.5697993920149, 260.4363104810728, 224.77324734206692],\n",
    "    'J2': [0.08833021365283901, 1.8275757046578123, 45.85306601609634, 323.2068724742969]\n",
    "}\n",
    "\n",
    "l_curve = pd.DataFrame(data)\n",
    "l_curve\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "31e94c20",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_lcurve(l_curve, loglog=False)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "firedrake",
   "language": "python",
   "name": "firedrake"
  },
  "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
}