docs/ipynb/exporting-data.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exporting data\n",
    "\n",
    "There are fundamentally two different data types:\n",
    "\n",
    "- spatially averaged data (as in the `odt` [OOMMF Data Table] file)\n",
    "- spatially resolved data (as in the `omf`, `omv` files)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Access the raw OOMMF output files\n",
    "\n",
    "When Jupyter OOMMF needs a micromagnetic calculation to be carried out, it is writing a `mif` file, and then asks OOMMF to execute that miffile, and export data to the file system.\n",
    "\n",
    "It it thus possible to read the output files from the disk as one would normally with OOMMF. This allows re-use of all existing tools to analyse OOMMF data (including muview, ovf2vtk, ...)\n",
    "\n",
    "Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2018/6/26 12:2: Calling OOMMF (example-macrospin/example-macrospin.mif) ... [0.7s]\n"
     ]
    }
   ],
   "source": [
    "import oommfc as oc\n",
    "system = oc.examples.macrospin()\n",
    "td = oc.TimeDriver()\n",
    "td.drive(system, t=0.1e-9, n=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the last output line, we can see that the OOMMF data is stored in the directory `example-macrospin`. We can display the content:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "example-macrospin.mif\r\n",
      "example-macrospin.odt\r\n",
      "example-macrospin-Oxs_TimeDriver-Magnetization-00-0000036.omf\r\n",
      "example-macrospin-Oxs_TimeDriver-Magnetization-01-0000066.omf\r\n",
      "example-macrospin-Oxs_TimeDriver-Magnetization-02-0000092.omf\r\n",
      "example-macrospin-Oxs_TimeDriver-Magnetization-03-0000113.omf\r\n",
      "example-macrospin-Oxs_TimeDriver-Magnetization-04-0000130.omf\r\n",
      "m0.omf\r\n"
     ]
    }
   ],
   "source": [
    "!ls example-macrospin/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exporting the OOMMF Data Table\n",
    "The file `example-macrospin.odt` is automatically read and available as a pandas data table in the `system.dt` object. We can thus use all the export functionality that pandas supports. For example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>E</th>\n",
       "      <th>Ecount</th>\n",
       "      <th>max_dm/dt</th>\n",
       "      <th>dE/dt</th>\n",
       "      <th>deltaE</th>\n",
       "      <th>E_Zeeman</th>\n",
       "      <th>iteration</th>\n",
       "      <th>stage_iteration</th>\n",
       "      <th>stage</th>\n",
       "      <th>mx</th>\n",
       "      <th>my</th>\n",
       "      <th>mz</th>\n",
       "      <th>last_time_step</th>\n",
       "      <th>t</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-5.033171e-18</td>\n",
       "      <td>217.0</td>\n",
       "      <td>37867.797392</td>\n",
       "      <td>-1.241326e-07</td>\n",
       "      <td>-4.522273e-20</td>\n",
       "      <td>-5.033171e-18</td>\n",
       "      <td>36.0</td>\n",
       "      <td>36.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.597360</td>\n",
       "      <td>-0.038383</td>\n",
       "      <td>0.801054</td>\n",
       "      <td>3.586075e-13</td>\n",
       "      <td>2.000000e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-6.131373e-18</td>\n",
       "      <td>392.0</td>\n",
       "      <td>13822.238704</td>\n",
       "      <td>-1.653875e-08</td>\n",
       "      <td>-6.256125e-21</td>\n",
       "      <td>-6.131373e-18</td>\n",
       "      <td>66.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.216713</td>\n",
       "      <td>0.027838</td>\n",
       "      <td>0.975838</td>\n",
       "      <td>3.708125e-13</td>\n",
       "      <td>4.000000e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-6.266081e-18</td>\n",
       "      <td>543.0</td>\n",
       "      <td>4664.609034</td>\n",
       "      <td>-1.883547e-09</td>\n",
       "      <td>-1.210170e-21</td>\n",
       "      <td>-6.266081e-18</td>\n",
       "      <td>92.0</td>\n",
       "      <td>25.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>-0.072403</td>\n",
       "      <td>-0.013953</td>\n",
       "      <td>0.997278</td>\n",
       "      <td>6.216520e-13</td>\n",
       "      <td>6.000000e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-6.281233e-18</td>\n",
       "      <td>664.0</td>\n",
       "      <td>1577.051840</td>\n",
       "      <td>-2.152969e-10</td>\n",
       "      <td>-2.059347e-22</td>\n",
       "      <td>-6.281233e-18</td>\n",
       "      <td>113.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.024163</td>\n",
       "      <td>0.006131</td>\n",
       "      <td>0.999689</td>\n",
       "      <td>9.181643e-13</td>\n",
       "      <td>8.000000e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-6.282947e-18</td>\n",
       "      <td>761.0</td>\n",
       "      <td>550.439309</td>\n",
       "      <td>-2.622797e-11</td>\n",
       "      <td>-3.440007e-23</td>\n",
       "      <td>-6.282947e-18</td>\n",
       "      <td>130.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>-0.008347</td>\n",
       "      <td>-0.002458</td>\n",
       "      <td>0.999962</td>\n",
       "      <td>1.290222e-12</td>\n",
       "      <td>1.000000e-10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              E  Ecount     max_dm/dt         dE/dt        deltaE  \\\n",
       "0 -5.033171e-18   217.0  37867.797392 -1.241326e-07 -4.522273e-20   \n",
       "1 -6.131373e-18   392.0  13822.238704 -1.653875e-08 -6.256125e-21   \n",
       "2 -6.266081e-18   543.0   4664.609034 -1.883547e-09 -1.210170e-21   \n",
       "3 -6.281233e-18   664.0   1577.051840 -2.152969e-10 -2.059347e-22   \n",
       "4 -6.282947e-18   761.0    550.439309 -2.622797e-11 -3.440007e-23   \n",
       "\n",
       "       E_Zeeman  iteration  stage_iteration  stage        mx        my  \\\n",
       "0 -5.033171e-18       36.0             36.0    0.0 -0.597360 -0.038383   \n",
       "1 -6.131373e-18       66.0             29.0    1.0  0.216713  0.027838   \n",
       "2 -6.266081e-18       92.0             25.0    2.0 -0.072403 -0.013953   \n",
       "3 -6.281233e-18      113.0             20.0    3.0  0.024163  0.006131   \n",
       "4 -6.282947e-18      130.0             16.0    4.0 -0.008347 -0.002458   \n",
       "\n",
       "         mz  last_time_step             t  \n",
       "0  0.801054    3.586075e-13  2.000000e-11  \n",
       "1  0.975838    3.708125e-13  4.000000e-11  \n",
       "2  0.997278    6.216520e-13  6.000000e-11  \n",
       "3  0.999689    9.181643e-13  8.000000e-11  \n",
       "4  0.999962    1.290222e-12  1.000000e-10  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# display beginning of data table in notebook\n",
    "system.dt.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MS Excel, html, latex, json"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "system.dt.to_excel(\"data-odt.xlsx\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "system.dt.to_html(\"data-odt.html\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "system.dt.to_latex(\"data-odt.tex\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "system.dt.to_json(\"data-odt.json\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numpy arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given a pandas table, we can extract each column as a (Pandas) Series:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    2.000000e-11\n",
       "1    4.000000e-11\n",
       "2    6.000000e-11\n",
       "3    8.000000e-11\n",
       "4    1.000000e-10\n",
       "Name: t, dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_series = system.dt['t']\n",
    "t_series"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or convert this into a numpy array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "t_array = np.array(system.dt['t'])\n",
    "mx_array = np.array(system.dt['mx'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "for example to plot the data in some custom way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f84587defd0>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "fig, axes = plt.subplots()\n",
    "axes.plot(t_array, mx_array)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To see which data columns are available in the table, we can use:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['E', 'Ecount', 'max_dm/dt', 'dE/dt', 'deltaE', 'E_Zeeman', 'iteration',\n",
       "       'stage_iteration', 'stage', 'mx', 'my', 'mz', 'last_time_step', 't'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "system.dt.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['E',\n",
       " 'Ecount',\n",
       " 'max_dm/dt',\n",
       " 'dE/dt',\n",
       " 'deltaE',\n",
       " 'E_Zeeman',\n",
       " 'iteration',\n",
       " 'stage_iteration',\n",
       " 'stage',\n",
       " 'mx',\n",
       " 'my',\n",
       " 'mz',\n",
       " 'last_time_step',\n",
       " 't']"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(system.dt.columns)"
   ]
  }
 ],
 "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}