{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PEC Monte Carlo simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Start by importing MagmaPEC and MagmaPandas and any other packages you want to use. Here we also import Pandas for importing pressure data. For details on the use of MagmaPandas, please see it's [documentation](https://magmapandas.readthedocs.io/en/latest/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import MagmaPEC as mpc\n",
    "import MagmaPandas as mp\n",
    "\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the next few steps we import all relevant data and set up the melt initial FeO prediction model. These steps are identical to the [PEC model example](https://magmapec.readthedocs.io/en/latest/notebooks/pec_corr.html#)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import melt inclusion and olivine data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "melt_file = \"./data/melt.csv\"\n",
    "olivine_file = \"./data/olivine.csv\"\n",
    "\n",
    "melt = mp.read_melt(melt_file, index_col=[\"name\"])\n",
    "olivine = mp.read_olivine(olivine_file, index_col=[\"name\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import inclusion internal pressures or calculate them if you have measured melt CO2 (and H2O). See the [PEC model example](https://magmapec.readthedocs.io/en/latest/notebooks/pec_corr.html) for details on how to do the calculation. Here we import them from a file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "pressure_file =\"./data/pressure.csv\"\n",
    "pressure = pd.read_csv(pressure_file, index_col = [\"name\"]).squeeze()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set up the melt initial FeO prediction model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "wholerock_file = \"./data/wholerock.csv\"\n",
    "wholerock = mp.read_melt(wholerock_file, index_col=[\"name\"])\n",
    "\n",
    "x = wholerock.drop(columns=[\"FeO\"])\n",
    "FeOi_predict = mpc.FeOi_prediction(x=x, FeO=wholerock[\"FeO\"])\n",
    "\n",
    "do_not_use = [\"MnO\", \"P2O5\", \"Cr2O3\", \"total\"]\n",
    "\n",
    "model_fits = FeOi_predict.calculate_model_fits(exclude=do_not_use)\n",
    "FeOi_predict.select_predictors(idx=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we need to set up the object that handles the random sampling of errors in the Monte Carlo simulation. This is done with the *PEC_MC_parameters* class and it includes the following parameters for error propagation:\n",
    "\n",
    "- **melt_errors**\n",
    "        \n",
    "    propagate errors on melt composition by providing one standard deviation errors per element as a pandas Series (fixed errors for all inclusions) or DataFrame (errors per inclusion).\n",
    "\n",
    "- **olivine_errors**\n",
    "\n",
    "    propagate errors on olivine composition by providing one standard deviation errors per element as a pandas Series (fixed errors for all inclusions) or DataFrame (errors per inclusion).\n",
    "\n",
    "- **FeOi_errors**\n",
    "\n",
    "    propagate errors on estimate melt initial FeO contents. Fixed errors can be provided either for the whole dataset, or per inclusion. Alternatively, an [FeOi_prediction object](https://magmapec.readthedocs.io/en/latest/notebooks/FeOi.html) can be provided to propagate errors on predictions models.\n",
    "\n",
    "- **Fe3Fe2**\n",
    "\n",
    "    Propagate errors on modelled melt Fe<sup>2+</sup>/Fe<sup>3+</sup> ratios. Errors are automatically calculated by MagmaPandas based on the selected model. Pass *True* to this parameter to activate it.\n",
    "\n",
    "- **Kd**\n",
    "\n",
    "    Propagate errors on modelled olivine-melt Fe-Mg partition coefficients. Errors are automatically calculated by MagmaPandas based on the selected model. Pass *True* to this parameter to activate it.\n",
    "\n",
    "By default errors are not propagated - you explicitely need to tell MagmaPEC to do so when initialising the *PEC_MC_parameters* object"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example we will use all error propagation options, which means we need to provide melt and olivine composition errors. We import these from .csv files containing error data for individual inclusions and olivines. This is just an example with randomly generated errors, normally you should use analytical errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "melt_errors_file = \"./data/melt_errors.csv\"\n",
    "olivine_errors_file = \"./data/olivine_errors.csv\"\n",
    "\n",
    "melt_errors = pd.read_csv(melt_errors_file, index_col=[0])\n",
    "olivine_errors = pd.read_csv(olivine_errors_file, index_col=[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make very sure that the elements in the error data have identical sorting to the melt and olivine dataframes, otherwise errors will be applied to the wrong elements. \n",
    "We can force this by sorting the columns of the error dataframes (or series) with the *elements* attributes of the melt and olivine MagmaFrames:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "melt_errors = melt_errors[melt.elements]\n",
    "olivine_errors = olivine_errors[olivine.elements]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what they look like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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>SiO2</th>\n",
       "      <th>Al2O3</th>\n",
       "      <th>MgO</th>\n",
       "      <th>CaO</th>\n",
       "      <th>FeO</th>\n",
       "      <th>Na2O</th>\n",
       "      <th>K2O</th>\n",
       "      <th>MnO</th>\n",
       "      <th>TiO2</th>\n",
       "      <th>P2O5</th>\n",
       "      <th>Cr2O3</th>\n",
       "      <th>CO2</th>\n",
       "      <th>H2O</th>\n",
       "      <th>F</th>\n",
       "      <th>S</th>\n",
       "      <th>Cl</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>PI032-04-01</th>\n",
       "      <td>1.02</td>\n",
       "      <td>0.64</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.47</td>\n",
       "      <td>0.69</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.18</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.17</td>\n",
       "      <td>0.21</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI032-04-02</th>\n",
       "      <td>1.06</td>\n",
       "      <td>0.84</td>\n",
       "      <td>0.29</td>\n",
       "      <td>0.46</td>\n",
       "      <td>0.54</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.18</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.13</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI041-02-02</th>\n",
       "      <td>1.04</td>\n",
       "      <td>0.90</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.55</td>\n",
       "      <td>0.49</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.21</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.16</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.23</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.17</td>\n",
       "      <td>0.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI041-03-01</th>\n",
       "      <td>0.98</td>\n",
       "      <td>0.64</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.40</td>\n",
       "      <td>0.53</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.36</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI041-03-03</th>\n",
       "      <td>1.02</td>\n",
       "      <td>0.54</td>\n",
       "      <td>0.31</td>\n",
       "      <td>0.42</td>\n",
       "      <td>0.68</td>\n",
       "      <td>0.18</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.18</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.13</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             SiO2  Al2O3   MgO   CaO   FeO  Na2O   K2O   MnO  TiO2  P2O5  \\\n",
       "PI032-04-01  1.02   0.64  0.14  0.47  0.69  0.10  0.08  0.05  0.18  0.05   \n",
       "PI032-04-02  1.06   0.84  0.29  0.46  0.54  0.05  0.03  0.01  0.06  0.18   \n",
       "PI041-02-02  1.04   0.90  0.09  0.55  0.49  0.22  0.21  0.01  0.16  0.04   \n",
       "PI041-03-01  0.98   0.64  0.10  0.40  0.53  0.12  0.12  0.08  0.01  0.03   \n",
       "PI041-03-03  1.02   0.54  0.31  0.42  0.68  0.18  0.03  0.02  0.11  0.06   \n",
       "\n",
       "             Cr2O3   CO2   H2O     F     S    Cl  \n",
       "PI032-04-01   0.05  0.17  0.21  0.22  0.10  0.12  \n",
       "PI032-04-02   0.04  0.24  0.12  0.13  0.12  0.04  \n",
       "PI041-02-02   0.00  0.15  0.23  0.04  0.17  0.06  \n",
       "PI041-03-01   0.00  0.05  0.36  0.06  0.14  0.04  \n",
       "PI041-03-03   0.10  0.18  0.08  0.13  0.06  0.15  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "melt_errors.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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>SiO2</th>\n",
       "      <th>FeO</th>\n",
       "      <th>MgO</th>\n",
       "      <th>NiO</th>\n",
       "      <th>MnO</th>\n",
       "      <th>Al2O3</th>\n",
       "      <th>CaO</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>PI032-04-01</th>\n",
       "      <td>1.06</td>\n",
       "      <td>0.60</td>\n",
       "      <td>1.22</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI032-04-02</th>\n",
       "      <td>0.85</td>\n",
       "      <td>0.57</td>\n",
       "      <td>1.28</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.07</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI041-02-02</th>\n",
       "      <td>1.11</td>\n",
       "      <td>0.44</td>\n",
       "      <td>1.30</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI041-03-01</th>\n",
       "      <td>0.99</td>\n",
       "      <td>0.50</td>\n",
       "      <td>1.31</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.16</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI041-03-03</th>\n",
       "      <td>0.95</td>\n",
       "      <td>0.64</td>\n",
       "      <td>1.21</td>\n",
       "      <td>0.13</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             SiO2   FeO   MgO   NiO   MnO  Al2O3   CaO\n",
       "PI032-04-01  1.06  0.60  1.22  0.01  0.09   0.08  0.02\n",
       "PI032-04-02  0.85  0.57  1.28  0.14  0.07   0.24  0.06\n",
       "PI041-02-02  1.11  0.44  1.30  0.08  0.10   0.01  0.19\n",
       "PI041-03-01  0.99  0.50  1.31  0.14  0.16   0.15  0.01\n",
       "PI041-03-03  0.95  0.64  1.21  0.13  0.11   0.10  0.15"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "olivine_errors.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Together with the *FeOi_prediction* object, we pass these as arguments to the *PEC_MC_parameters* object. We also set *Fe3Fe2* and *Kd* to *True* in order to propagate their model errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "mc_parameters = mpc.PEC_MC_parameters(melt_errors=melt_errors, olivine_errors=olivine_errors, FeOi_errors=FeOi_predict, Fe3Fe2=True, Kd=True, temperature=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can create the Monte Carlo model with the *PEC_MC* object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "pec_mc_model = mpc.PEC_MC(inclusions=melt, olivines=olivine, P_bar=pressure, FeO_target=FeOi_predict, MC_parameters=mc_parameters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And finally run the Monte Carlo simulation with *n* iterations. To get representative errors, a minimum of 50 iterations is recommended."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Monte Carlo loop\n",
      "050/050\n",
      "Equilibrating ... |██████████████████████████████| 100% [10/10] in 2.2s \n",
      "Correcting    ... |██████████████████████████████| 100% [10/10] in 13.4s \n"
     ]
    }
   ],
   "source": [
    "pec_mc_model.run(n=50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Results are stored internally in the following attributes:\n",
    "\n",
    "- **pec**: pandas DataFrame\n",
    "\n",
    "    Average PEC extents (%) of the MC model and their one standard deviation errors.\n",
    "\n",
    "- **inclusions_corr**: MagmaPandas Melt frame\n",
    "\n",
    "    Averages of corrected melt inclusion compositions (wt. %)\n",
    "\n",
    "- **inclusions_stddev**: pandas DataFrame\n",
    "\n",
    "    One standard deviation errors on inclusions_corr (wt. %)\n",
    "\n",
    "- **pec_MC**: pandas DataFrame\n",
    "\n",
    "    PEC extents for individual iterations\n",
    "\n",
    "- **inclusions_MC**: dictionary of MagmaPandas Melt frames\n",
    "\n",
    "    corrected melt inclusion compositions for individual iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "pec = pec_mc_model.pec\n",
    "inclusions_corrected = pec_mc_model.inclusions_corr\n",
    "inclusions_errors = pec_mc_model.inclusions_stddev\n",
    "\n",
    "pec_mc = pec_mc_model.pec_MC\n",
    "inclusions_MC = pec_mc_model.inclusions_MC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>pec</th>\n",
       "      <th>stddev</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>name</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>PI032-04-01</th>\n",
       "      <td>9.596699</td>\n",
       "      <td>4.571030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI032-04-02</th>\n",
       "      <td>10.571102</td>\n",
       "      <td>4.999259</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI041-02-02</th>\n",
       "      <td>0.029676</td>\n",
       "      <td>3.332411</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI041-03-01</th>\n",
       "      <td>12.122017</td>\n",
       "      <td>5.592136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI041-03-03</th>\n",
       "      <td>12.350934</td>\n",
       "      <td>5.439491</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI041-05-04</th>\n",
       "      <td>-4.324584</td>\n",
       "      <td>2.935303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI041-05-06</th>\n",
       "      <td>1.761258</td>\n",
       "      <td>3.100318</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI041-07-01</th>\n",
       "      <td>11.755184</td>\n",
       "      <td>4.999059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI041-07-02</th>\n",
       "      <td>10.548042</td>\n",
       "      <td>4.990837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI052-01-02</th>\n",
       "      <td>-8.153084</td>\n",
       "      <td>2.932983</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   pec    stddev\n",
       "name                            \n",
       "PI032-04-01   9.596699  4.571030\n",
       "PI032-04-02  10.571102  4.999259\n",
       "PI041-02-02   0.029676  3.332411\n",
       "PI041-03-01  12.122017  5.592136\n",
       "PI041-03-03  12.350934  5.439491\n",
       "PI041-05-04  -4.324584  2.935303\n",
       "PI041-05-06   1.761258  3.100318\n",
       "PI041-07-01  11.755184  4.999059\n",
       "PI041-07-02  10.548042  4.990837\n",
       "PI052-01-02  -8.153084  2.932983"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SiO2</th>\n",
       "      <th>Al2O3</th>\n",
       "      <th>MgO</th>\n",
       "      <th>CaO</th>\n",
       "      <th>FeO</th>\n",
       "      <th>Na2O</th>\n",
       "      <th>K2O</th>\n",
       "      <th>MnO</th>\n",
       "      <th>TiO2</th>\n",
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       "      <th>CO2</th>\n",
       "      <th>H2O</th>\n",
       "      <th>F</th>\n",
       "      <th>S</th>\n",
       "      <th>Cl</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>name</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
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       "      <th></th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>PI032-04-01</th>\n",
       "      <td>49.038185</td>\n",
       "      <td>13.965831</td>\n",
       "      <td>7.548374</td>\n",
       "      <td>9.712050</td>\n",
       "      <td>10.270587</td>\n",
       "      <td>3.587690</td>\n",
       "      <td>0.679658</td>\n",
       "      <td>0.131731</td>\n",
       "      <td>2.450270</td>\n",
       "      <td>0.282972</td>\n",
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       "      <td>0.601138</td>\n",
       "      <td>1.385841</td>\n",
       "      <td>0.138570</td>\n",
       "      <td>0.147149</td>\n",
       "      <td>0.059956</td>\n",
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       "    <tr>\n",
       "      <th>PI032-04-02</th>\n",
       "      <td>48.554467</td>\n",
       "      <td>14.659704</td>\n",
       "      <td>7.477362</td>\n",
       "      <td>9.371954</td>\n",
       "      <td>10.352409</td>\n",
       "      <td>3.458443</td>\n",
       "      <td>0.909402</td>\n",
       "      <td>0.135773</td>\n",
       "      <td>2.574248</td>\n",
       "      <td>0.318282</td>\n",
       "      <td>0.00000</td>\n",
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       "      <td>0.086511</td>\n",
       "      <td>0.166056</td>\n",
       "      <td>0.040240</td>\n",
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       "    <tr>\n",
       "      <th>PI041-02-02</th>\n",
       "      <td>49.194844</td>\n",
       "      <td>16.869946</td>\n",
       "      <td>4.745780</td>\n",
       "      <td>9.219521</td>\n",
       "      <td>10.209481</td>\n",
       "      <td>3.815880</td>\n",
       "      <td>1.081526</td>\n",
       "      <td>0.150459</td>\n",
       "      <td>2.795936</td>\n",
       "      <td>0.565836</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.469872</td>\n",
       "      <td>0.668820</td>\n",
       "      <td>0.059603</td>\n",
       "      <td>0.116337</td>\n",
       "      <td>0.036158</td>\n",
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       "    <tr>\n",
       "      <th>PI041-03-01</th>\n",
       "      <td>45.887674</td>\n",
       "      <td>15.778030</td>\n",
       "      <td>6.993274</td>\n",
       "      <td>11.021453</td>\n",
       "      <td>10.686971</td>\n",
       "      <td>3.348819</td>\n",
       "      <td>1.140917</td>\n",
       "      <td>0.110142</td>\n",
       "      <td>3.161059</td>\n",
       "      <td>0.555012</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.794686</td>\n",
       "      <td>0.281567</td>\n",
       "      <td>0.086593</td>\n",
       "      <td>0.098787</td>\n",
       "      <td>0.055019</td>\n",
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       "    <tr>\n",
       "      <th>PI041-03-03</th>\n",
       "      <td>45.368272</td>\n",
       "      <td>15.883119</td>\n",
       "      <td>7.006869</td>\n",
       "      <td>11.180753</td>\n",
       "      <td>10.760509</td>\n",
       "      <td>3.410114</td>\n",
       "      <td>1.166775</td>\n",
       "      <td>0.085819</td>\n",
       "      <td>3.245916</td>\n",
       "      <td>0.500428</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.807792</td>\n",
       "      <td>0.302871</td>\n",
       "      <td>0.112784</td>\n",
       "      <td>0.093646</td>\n",
       "      <td>0.074334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI041-05-04</th>\n",
       "      <td>47.905434</td>\n",
       "      <td>18.758468</td>\n",
       "      <td>3.554904</td>\n",
       "      <td>9.522532</td>\n",
       "      <td>9.319479</td>\n",
       "      <td>4.639602</td>\n",
       "      <td>1.619916</td>\n",
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       "      <td>0.124218</td>\n",
       "      <td>0.059425</td>\n",
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       "    <tr>\n",
       "      <th>PI041-05-06</th>\n",
       "      <td>46.439516</td>\n",
       "      <td>16.934260</td>\n",
       "      <td>4.558820</td>\n",
       "      <td>9.115684</td>\n",
       "      <td>11.523588</td>\n",
       "      <td>3.992881</td>\n",
       "      <td>1.468084</td>\n",
       "      <td>0.171794</td>\n",
       "      <td>3.682809</td>\n",
       "      <td>0.630996</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.645502</td>\n",
       "      <td>0.529145</td>\n",
       "      <td>0.113611</td>\n",
       "      <td>0.127881</td>\n",
       "      <td>0.065430</td>\n",
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       "    <tr>\n",
       "      <th>PI041-07-01</th>\n",
       "      <td>45.782869</td>\n",
       "      <td>15.466512</td>\n",
       "      <td>7.094071</td>\n",
       "      <td>9.641606</td>\n",
       "      <td>11.520774</td>\n",
       "      <td>3.130550</td>\n",
       "      <td>1.273328</td>\n",
       "      <td>0.146889</td>\n",
       "      <td>3.518325</td>\n",
       "      <td>0.558488</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.465974</td>\n",
       "      <td>1.035865</td>\n",
       "      <td>0.099808</td>\n",
       "      <td>0.170116</td>\n",
       "      <td>0.094825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI041-07-02</th>\n",
       "      <td>45.851318</td>\n",
       "      <td>15.577426</td>\n",
       "      <td>6.675896</td>\n",
       "      <td>10.248314</td>\n",
       "      <td>11.446601</td>\n",
       "      <td>3.240330</td>\n",
       "      <td>1.380481</td>\n",
       "      <td>0.139995</td>\n",
       "      <td>3.559769</td>\n",
       "      <td>0.619597</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.393779</td>\n",
       "      <td>0.600101</td>\n",
       "      <td>0.074141</td>\n",
       "      <td>0.135176</td>\n",
       "      <td>0.057076</td>\n",
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       "    <tr>\n",
       "      <th>PI052-01-02</th>\n",
       "      <td>49.173977</td>\n",
       "      <td>17.128900</td>\n",
       "      <td>3.790439</td>\n",
       "      <td>10.484961</td>\n",
       "      <td>8.417258</td>\n",
       "      <td>4.937496</td>\n",
       "      <td>1.554145</td>\n",
       "      <td>0.235262</td>\n",
       "      <td>1.747572</td>\n",
       "      <td>0.716371</td>\n",
       "      <td>0.07623</td>\n",
       "      <td>0.288786</td>\n",
       "      <td>1.088326</td>\n",
       "      <td>0.169099</td>\n",
       "      <td>0.132997</td>\n",
       "      <td>0.058181</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "                  SiO2      Al2O3       MgO        CaO        FeO      Na2O  \\\n",
       "name                                                                          \n",
       "PI032-04-01  49.038185  13.965831  7.548374   9.712050  10.270587  3.587690   \n",
       "PI032-04-02  48.554467  14.659704  7.477362   9.371954  10.352409  3.458443   \n",
       "PI041-02-02  49.194844  16.869946  4.745780   9.219521  10.209481  3.815880   \n",
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       "PI041-03-03  45.368272  15.883119  7.006869  11.180753  10.760509  3.410114   \n",
       "PI041-05-04  47.905434  18.758468  3.554904   9.522532   9.319479  4.639602   \n",
       "PI041-05-06  46.439516  16.934260  4.558820   9.115684  11.523588  3.992881   \n",
       "PI041-07-01  45.782869  15.466512  7.094071   9.641606  11.520774  3.130550   \n",
       "PI041-07-02  45.851318  15.577426  6.675896  10.248314  11.446601  3.240330   \n",
       "PI052-01-02  49.173977  17.128900  3.790439  10.484961   8.417258  4.937496   \n",
       "\n",
       "                  K2O       MnO      TiO2      P2O5    Cr2O3       CO2  \\\n",
       "name                                                                     \n",
       "PI032-04-01  0.679658  0.131731  2.450270  0.282972  0.00000  0.601138   \n",
       "PI032-04-02  0.909402  0.135773  2.574248  0.318282  0.00000  0.591418   \n",
       "PI041-02-02  1.081526  0.150459  2.795936  0.565836  0.00000  0.469872   \n",
       "PI041-03-01  1.140917  0.110142  3.161059  0.555012  0.00000  0.794686   \n",
       "PI041-03-03  1.166775  0.085819  3.245916  0.500428  0.00000  0.807792   \n",
       "PI041-05-04  1.619916  0.130669  2.506853  0.830447  0.00000  0.488603   \n",
       "PI041-05-06  1.468084  0.171794  3.682809  0.630996  0.00000  0.645502   \n",
       "PI041-07-01  1.273328  0.146889  3.518325  0.558488  0.00000  0.465974   \n",
       "PI041-07-02  1.380481  0.139995  3.559769  0.619597  0.00000  0.393779   \n",
       "PI052-01-02  1.554145  0.235262  1.747572  0.716371  0.07623  0.288786   \n",
       "\n",
       "                  H2O         F         S        Cl  \n",
       "name                                                 \n",
       "PI032-04-01  1.385841  0.138570  0.147149  0.059956  \n",
       "PI032-04-02  1.303731  0.086511  0.166056  0.040240  \n",
       "PI041-02-02  0.668820  0.059603  0.116337  0.036158  \n",
       "PI041-03-01  0.281567  0.086593  0.098787  0.055019  \n",
       "PI041-03-03  0.302871  0.112784  0.093646  0.074334  \n",
       "PI041-05-04  0.448569  0.090882  0.124218  0.059425  \n",
       "PI041-05-06  0.529145  0.113611  0.127881  0.065430  \n",
       "PI041-07-01  1.035865  0.099808  0.170116  0.094825  \n",
       "PI041-07-02  0.600101  0.074141  0.135176  0.057076  \n",
       "PI052-01-02  1.088326  0.169099  0.132997  0.058181  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
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    }
   ],
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  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SiO2_stddev</th>\n",
       "      <th>Al2O3_stddev</th>\n",
       "      <th>MgO_stddev</th>\n",
       "      <th>CaO_stddev</th>\n",
       "      <th>FeO_stddev</th>\n",
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       "      <th>CO2_stddev</th>\n",
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       "      <th>S_stddev</th>\n",
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       "      <th>name</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>PI032-04-01</th>\n",
       "      <td>0.684140</td>\n",
       "      <td>0.767229</td>\n",
       "      <td>1.429579</td>\n",
       "      <td>0.528847</td>\n",
       "      <td>0.318606</td>\n",
       "      <td>0.195741</td>\n",
       "      <td>0.082248</td>\n",
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       "      <td>0.077634</td>\n",
       "      <td>0.068188</td>\n",
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       "    <tr>\n",
       "      <th>PI032-04-02</th>\n",
       "      <td>0.675087</td>\n",
       "      <td>1.020384</td>\n",
       "      <td>1.429734</td>\n",
       "      <td>0.518800</td>\n",
       "      <td>0.277615</td>\n",
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       "      <td>0.014049</td>\n",
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       "      <td>0.135802</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.204367</td>\n",
       "      <td>0.137161</td>\n",
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       "      <td>0.085342</td>\n",
       "      <td>0.033133</td>\n",
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       "    <tr>\n",
       "      <th>PI041-02-02</th>\n",
       "      <td>0.921795</td>\n",
       "      <td>1.078272</td>\n",
       "      <td>1.085552</td>\n",
       "      <td>0.573999</td>\n",
       "      <td>0.378420</td>\n",
       "      <td>0.214054</td>\n",
       "      <td>0.177747</td>\n",
       "      <td>0.015982</td>\n",
       "      <td>0.136563</td>\n",
       "      <td>0.048991</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.148134</td>\n",
       "      <td>0.277951</td>\n",
       "      <td>0.034226</td>\n",
       "      <td>0.113298</td>\n",
       "      <td>0.035241</td>\n",
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       "    <tr>\n",
       "      <th>PI041-03-01</th>\n",
       "      <td>0.683158</td>\n",
       "      <td>0.912316</td>\n",
       "      <td>1.736349</td>\n",
       "      <td>0.649194</td>\n",
       "      <td>0.159993</td>\n",
       "      <td>0.196658</td>\n",
       "      <td>0.120308</td>\n",
       "      <td>0.062801</td>\n",
       "      <td>0.140206</td>\n",
       "      <td>0.040101</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.061839</td>\n",
       "      <td>0.228635</td>\n",
       "      <td>0.045563</td>\n",
       "      <td>0.098435</td>\n",
       "      <td>0.036972</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI041-03-03</th>\n",
       "      <td>0.621632</td>\n",
       "      <td>0.789395</td>\n",
       "      <td>1.602801</td>\n",
       "      <td>0.546556</td>\n",
       "      <td>0.215348</td>\n",
       "      <td>0.198945</td>\n",
       "      <td>0.064844</td>\n",
       "      <td>0.021529</td>\n",
       "      <td>0.151684</td>\n",
       "      <td>0.068454</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.134119</td>\n",
       "      <td>0.070433</td>\n",
       "      <td>0.110846</td>\n",
       "      <td>0.052602</td>\n",
       "      <td>0.088702</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI041-05-04</th>\n",
       "      <td>0.767873</td>\n",
       "      <td>0.978518</td>\n",
       "      <td>0.898687</td>\n",
       "      <td>0.418429</td>\n",
       "      <td>0.343335</td>\n",
       "      <td>0.253467</td>\n",
       "      <td>0.127715</td>\n",
       "      <td>0.126536</td>\n",
       "      <td>0.093800</td>\n",
       "      <td>0.034276</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.249720</td>\n",
       "      <td>0.167424</td>\n",
       "      <td>0.096160</td>\n",
       "      <td>0.010195</td>\n",
       "      <td>0.009643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI041-05-06</th>\n",
       "      <td>0.859292</td>\n",
       "      <td>0.986402</td>\n",
       "      <td>0.975461</td>\n",
       "      <td>0.432861</td>\n",
       "      <td>0.399822</td>\n",
       "      <td>0.375694</td>\n",
       "      <td>0.213302</td>\n",
       "      <td>0.185424</td>\n",
       "      <td>0.197941</td>\n",
       "      <td>0.043942</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.217330</td>\n",
       "      <td>0.236147</td>\n",
       "      <td>0.087190</td>\n",
       "      <td>0.059650</td>\n",
       "      <td>0.030361</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI041-07-01</th>\n",
       "      <td>0.577925</td>\n",
       "      <td>1.078946</td>\n",
       "      <td>1.408947</td>\n",
       "      <td>0.504997</td>\n",
       "      <td>0.248594</td>\n",
       "      <td>0.136789</td>\n",
       "      <td>0.045372</td>\n",
       "      <td>0.075074</td>\n",
       "      <td>0.143228</td>\n",
       "      <td>0.026259</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.056172</td>\n",
       "      <td>0.185572</td>\n",
       "      <td>0.096999</td>\n",
       "      <td>0.027073</td>\n",
       "      <td>0.091682</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI041-07-02</th>\n",
       "      <td>0.535806</td>\n",
       "      <td>0.957769</td>\n",
       "      <td>1.528439</td>\n",
       "      <td>0.551789</td>\n",
       "      <td>0.227877</td>\n",
       "      <td>0.166253</td>\n",
       "      <td>0.147385</td>\n",
       "      <td>0.059076</td>\n",
       "      <td>0.138005</td>\n",
       "      <td>0.025977</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.166085</td>\n",
       "      <td>0.174210</td>\n",
       "      <td>0.002745</td>\n",
       "      <td>0.045242</td>\n",
       "      <td>0.063498</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI052-01-02</th>\n",
       "      <td>0.906649</td>\n",
       "      <td>0.888955</td>\n",
       "      <td>0.877843</td>\n",
       "      <td>0.435415</td>\n",
       "      <td>0.402362</td>\n",
       "      <td>0.134263</td>\n",
       "      <td>0.073166</td>\n",
       "      <td>0.024505</td>\n",
       "      <td>0.097982</td>\n",
       "      <td>0.228803</td>\n",
       "      <td>0.097102</td>\n",
       "      <td>0.008038</td>\n",
       "      <td>0.151310</td>\n",
       "      <td>0.162627</td>\n",
       "      <td>0.060260</td>\n",
       "      <td>0.017870</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             SiO2_stddev  Al2O3_stddev  MgO_stddev  CaO_stddev  FeO_stddev  \\\n",
       "name                                                                         \n",
       "PI032-04-01     0.684140      0.767229    1.429579    0.528847    0.318606   \n",
       "PI032-04-02     0.675087      1.020384    1.429734    0.518800    0.277615   \n",
       "PI041-02-02     0.921795      1.078272    1.085552    0.573999    0.378420   \n",
       "PI041-03-01     0.683158      0.912316    1.736349    0.649194    0.159993   \n",
       "PI041-03-03     0.621632      0.789395    1.602801    0.546556    0.215348   \n",
       "PI041-05-04     0.767873      0.978518    0.898687    0.418429    0.343335   \n",
       "PI041-05-06     0.859292      0.986402    0.975461    0.432861    0.399822   \n",
       "PI041-07-01     0.577925      1.078946    1.408947    0.504997    0.248594   \n",
       "PI041-07-02     0.535806      0.957769    1.528439    0.551789    0.227877   \n",
       "PI052-01-02     0.906649      0.888955    0.877843    0.435415    0.402362   \n",
       "\n",
       "             Na2O_stddev  K2O_stddev  MnO_stddev  TiO2_stddev  P2O5_stddev  \\\n",
       "name                                                                         \n",
       "PI032-04-01     0.195741    0.082248    0.046226     0.169112     0.057255   \n",
       "PI032-04-02     0.147678    0.044618    0.014049     0.106298     0.135802   \n",
       "PI041-02-02     0.214054    0.177747    0.015982     0.136563     0.048991   \n",
       "PI041-03-01     0.196658    0.120308    0.062801     0.140206     0.040101   \n",
       "PI041-03-03     0.198945    0.064844    0.021529     0.151684     0.068454   \n",
       "PI041-05-04     0.253467    0.127715    0.126536     0.093800     0.034276   \n",
       "PI041-05-06     0.375694    0.213302    0.185424     0.197941     0.043942   \n",
       "PI041-07-01     0.136789    0.045372    0.075074     0.143228     0.026259   \n",
       "PI041-07-02     0.166253    0.147385    0.059076     0.138005     0.025977   \n",
       "PI052-01-02     0.134263    0.073166    0.024505     0.097982     0.228803   \n",
       "\n",
       "             Cr2O3_stddev  CO2_stddev  H2O_stddev  F_stddev  S_stddev  \\\n",
       "name                                                                    \n",
       "PI032-04-01      0.000000    0.150842    0.203130  0.130984  0.077634   \n",
       "PI032-04-02      0.000000    0.204367    0.137161  0.093134  0.085342   \n",
       "PI041-02-02      0.000000    0.148134    0.277951  0.034226  0.113298   \n",
       "PI041-03-01      0.000000    0.061839    0.228635  0.045563  0.098435   \n",
       "PI041-03-03      0.000000    0.134119    0.070433  0.110846  0.052602   \n",
       "PI041-05-04      0.000000    0.249720    0.167424  0.096160  0.010195   \n",
       "PI041-05-06      0.000000    0.217330    0.236147  0.087190  0.059650   \n",
       "PI041-07-01      0.000000    0.056172    0.185572  0.096999  0.027073   \n",
       "PI041-07-02      0.000000    0.166085    0.174210  0.002745  0.045242   \n",
       "PI052-01-02      0.097102    0.008038    0.151310  0.162627  0.060260   \n",
       "\n",
       "             Cl_stddev  \n",
       "name                    \n",
       "PI032-04-01   0.068188  \n",
       "PI032-04-02   0.033133  \n",
       "PI041-02-02   0.035241  \n",
       "PI041-03-01   0.036972  \n",
       "PI041-03-03   0.088702  \n",
       "PI041-05-04   0.009643  \n",
       "PI041-05-06   0.030361  \n",
       "PI041-07-01   0.091682  \n",
       "PI041-07-02   0.063498  \n",
       "PI052-01-02   0.017870  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inclusions_errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>name</th>\n",
       "      <th>PI032-04-01</th>\n",
       "      <th>PI032-04-02</th>\n",
       "      <th>PI041-02-02</th>\n",
       "      <th>PI041-03-01</th>\n",
       "      <th>PI041-03-03</th>\n",
       "      <th>PI041-05-04</th>\n",
       "      <th>PI041-05-06</th>\n",
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       "      <th>PI041-07-02</th>\n",
       "      <th>PI052-01-02</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>iteration</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.814795</td>\n",
       "      <td>1.06189</td>\n",
       "      <td>-7.713281</td>\n",
       "      <td>3.010327</td>\n",
       "      <td>2.955713</td>\n",
       "      <td>-9.099756</td>\n",
       "      <td>-0.522314</td>\n",
       "      <td>2.185376</td>\n",
       "      <td>0.01543</td>\n",
       "      <td>-14.604492</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12.524048</td>\n",
       "      <td>4.575262</td>\n",
       "      <td>-1.423328</td>\n",
       "      <td>8.784961</td>\n",
       "      <td>8.0</td>\n",
       "      <td>-5.385857</td>\n",
       "      <td>1.880664</td>\n",
       "      <td>10.16709</td>\n",
       "      <td>10.0</td>\n",
       "      <td>-10.747681</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.789526</td>\n",
       "      <td>4.0</td>\n",
       "      <td>-0.382031</td>\n",
       "      <td>6.201294</td>\n",
       "      <td>6.136987</td>\n",
       "      <td>-7.401428</td>\n",
       "      <td>-1.350854</td>\n",
       "      <td>7.808716</td>\n",
       "      <td>6.187897</td>\n",
       "      <td>-11.27063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11.8</td>\n",
       "      <td>8.137012</td>\n",
       "      <td>-1.426172</td>\n",
       "      <td>7.44588</td>\n",
       "      <td>9.01008</td>\n",
       "      <td>-6.124573</td>\n",
       "      <td>-2.069324</td>\n",
       "      <td>10.4</td>\n",
       "      <td>9.422449</td>\n",
       "      <td>-8.559125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.243164</td>\n",
       "      <td>2.316284</td>\n",
       "      <td>-2.730713</td>\n",
       "      <td>5.905371</td>\n",
       "      <td>6.262866</td>\n",
       "      <td>-8.778662</td>\n",
       "      <td>0.838452</td>\n",
       "      <td>6.921082</td>\n",
       "      <td>4.375781</td>\n",
       "      <td>-11.380933</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "name      PI032-04-01 PI032-04-02 PI041-02-02 PI041-03-01 PI041-03-03  \\\n",
       "iteration                                                               \n",
       "0            2.814795     1.06189   -7.713281    3.010327    2.955713   \n",
       "1           12.524048    4.575262   -1.423328    8.784961         8.0   \n",
       "2            3.789526         4.0   -0.382031    6.201294    6.136987   \n",
       "3                11.8    8.137012   -1.426172     7.44588     9.01008   \n",
       "4            2.243164    2.316284   -2.730713    5.905371    6.262866   \n",
       "\n",
       "name      PI041-05-04 PI041-05-06 PI041-07-01 PI041-07-02 PI052-01-02  \n",
       "iteration                                                              \n",
       "0           -9.099756   -0.522314    2.185376     0.01543  -14.604492  \n",
       "1           -5.385857    1.880664    10.16709        10.0  -10.747681  \n",
       "2           -7.401428   -1.350854    7.808716    6.187897   -11.27063  \n",
       "3           -6.124573   -2.069324        10.4    9.422449   -8.559125  \n",
       "4           -8.778662    0.838452    6.921082    4.375781  -11.380933  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pec_mc.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dataframes in *inclusions_MC* also have *isothermal_equilibration* and *Kd_equilibration* columns. These columns show if equilibration during stage [1] and [2] respectively was successful. In extreme cases, error propagation of melt and olivine compositions by random sampling can result in melt-olivine pairs that cannot be equilibrated without crystallising more than the entire inclusion or exchanging more Mg or Fe than is present in the inclusion. If that is the case, no corrected compositions are calculated and eiher the isothermal- of Kd-equilibration column is set to *False*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SiO2</th>\n",
       "      <th>Al2O3</th>\n",
       "      <th>MgO</th>\n",
       "      <th>CaO</th>\n",
       "      <th>FeO</th>\n",
       "      <th>Na2O</th>\n",
       "      <th>K2O</th>\n",
       "      <th>MnO</th>\n",
       "      <th>TiO2</th>\n",
       "      <th>P2O5</th>\n",
       "      <th>Cr2O3</th>\n",
       "      <th>CO2</th>\n",
       "      <th>H2O</th>\n",
       "      <th>F</th>\n",
       "      <th>S</th>\n",
       "      <th>Cl</th>\n",
       "      <th>isothermal_equilibration</th>\n",
       "      <th>Kd_equilibration</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>iteration</th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th>0</th>\n",
       "      <td>49.659755</td>\n",
       "      <td>15.346003</td>\n",
       "      <td>4.765847</td>\n",
       "      <td>9.638317</td>\n",
       "      <td>10.297186</td>\n",
       "      <td>3.761251</td>\n",
       "      <td>0.883066</td>\n",
       "      <td>0.117185</td>\n",
       "      <td>2.604499</td>\n",
       "      <td>0.349611</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.524141</td>\n",
       "      <td>1.289585</td>\n",
       "      <td>0.384034</td>\n",
       "      <td>0.217611</td>\n",
       "      <td>0.161906</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>49.021621</td>\n",
       "      <td>13.406203</td>\n",
       "      <td>8.494789</td>\n",
       "      <td>8.91942</td>\n",
       "      <td>10.763932</td>\n",
       "      <td>3.410622</td>\n",
       "      <td>0.6347</td>\n",
       "      <td>0.251858</td>\n",
       "      <td>2.50811</td>\n",
       "      <td>0.199926</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.692912</td>\n",
       "      <td>1.483525</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.163488</td>\n",
       "      <td>0.048894</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>48.247397</td>\n",
       "      <td>15.670665</td>\n",
       "      <td>5.687451</td>\n",
       "      <td>10.352983</td>\n",
       "      <td>10.144835</td>\n",
       "      <td>3.799917</td>\n",
       "      <td>0.579199</td>\n",
       "      <td>0.116463</td>\n",
       "      <td>2.703525</td>\n",
       "      <td>0.313039</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.678262</td>\n",
       "      <td>1.34723</td>\n",
       "      <td>0.029433</td>\n",
       "      <td>0.053967</td>\n",
       "      <td>0.275634</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>48.691004</td>\n",
       "      <td>13.595075</td>\n",
       "      <td>7.825504</td>\n",
       "      <td>10.155966</td>\n",
       "      <td>10.394342</td>\n",
       "      <td>3.6004</td>\n",
       "      <td>0.633725</td>\n",
       "      <td>0.139596</td>\n",
       "      <td>2.580742</td>\n",
       "      <td>0.192747</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.491091</td>\n",
       "      <td>1.477336</td>\n",
       "      <td>0.145906</td>\n",
       "      <td>0.064359</td>\n",
       "      <td>0.012207</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>49.668286</td>\n",
       "      <td>14.139461</td>\n",
       "      <td>5.626875</td>\n",
       "      <td>10.317219</td>\n",
       "      <td>10.487224</td>\n",
       "      <td>3.856336</td>\n",
       "      <td>0.609107</td>\n",
       "      <td>0.118617</td>\n",
       "      <td>2.712715</td>\n",
       "      <td>0.264858</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.482999</td>\n",
       "      <td>1.367683</td>\n",
       "      <td>0.159937</td>\n",
       "      <td>0.188682</td>\n",
       "      <td>0.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                SiO2      Al2O3       MgO        CaO        FeO      Na2O  \\\n",
       "iteration                                                                   \n",
       "0          49.659755  15.346003  4.765847   9.638317  10.297186  3.761251   \n",
       "1          49.021621  13.406203  8.494789    8.91942  10.763932  3.410622   \n",
       "2          48.247397  15.670665  5.687451  10.352983  10.144835  3.799917   \n",
       "3          48.691004  13.595075  7.825504  10.155966  10.394342    3.6004   \n",
       "4          49.668286  14.139461  5.626875  10.317219  10.487224  3.856336   \n",
       "\n",
       "                K2O       MnO      TiO2      P2O5 Cr2O3       CO2       H2O  \\\n",
       "iteration                                                                     \n",
       "0          0.883066  0.117185  2.604499  0.349611   0.0  0.524141  1.289585   \n",
       "1            0.6347  0.251858   2.50811  0.199926   0.0  0.692912  1.483525   \n",
       "2          0.579199  0.116463  2.703525  0.313039   0.0  0.678262   1.34723   \n",
       "3          0.633725  0.139596  2.580742  0.192747   0.0  0.491091  1.477336   \n",
       "4          0.609107  0.118617  2.712715  0.264858   0.0  0.482999  1.367683   \n",
       "\n",
       "                  F         S        Cl isothermal_equilibration  \\\n",
       "iteration                                                          \n",
       "0          0.384034  0.217611  0.161906                      NaN   \n",
       "1               0.0  0.163488  0.048894                      NaN   \n",
       "2          0.029433  0.053967  0.275634                      NaN   \n",
       "3          0.145906  0.064359  0.012207                      NaN   \n",
       "4          0.159937  0.188682       0.0                      NaN   \n",
       "\n",
       "          Kd_equilibration  \n",
       "iteration                   \n",
       "0                      NaN  \n",
       "1                      NaN  \n",
       "2                      NaN  \n",
       "3                      NaN  \n",
       "4                      NaN  "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inclusions_MC[\"PI032-04-01\"].head()"
   ]
  }
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