{
 "cells": [
  {
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   "metadata": {},
   "source": [
    "# Isotopically Non-Stationary 13C-MFA\n",
    "INCA is capable of analyzing isotopically non-stationary (INST) data. I such data sets the fluxes are still assumed to be constant, however the isotopologue distribution vector are allow to vary dynamically (See plot further down).\n",
    "\n",
    "The INCAWrapper can setup INCA models to fit INST datasets. In this example we will show how by estimating the flux distribution from a simulated INST dataset.\n",
    "\n",
    "The simulated dataset is produced using the simple model [1,2], which we have also used in earlier tutorials. This time however, we simulated the isotopically non-stationary data. To inspect how the data was simulated see https://github.com/biosustain/incawrapper/tree/main/docs/examples/Literature%20data/simple%20model/simple_model_inst_simulation.py."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import pathlib\n",
    "import incawrapper\n",
    "import ast\n",
    "PROJECT_DIR = pathlib.Path().cwd().parents[1].resolve()\n",
    "data_folder = PROJECT_DIR / pathlib.Path(\"docs/examples/Literature data/simple model\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To fit fluxes to a INST dataset INCA as minimum requires:\n",
    "\n",
    "- Reaction data\n",
    "- Tracer data\n",
    "- MS measurements\n",
    "\n",
    "Furthermore, it is possible to use \n",
    "- Flux measurements\n",
    "- Pool size measurement, i.e. concentrations of metabolites\n",
    "\n",
    "For completeness, we will here consider the data where we have ms, pool size, and flux measurements. We will load both the measurements and the tracer and reaction information here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "tracers_data = pd.read_csv(data_folder / \"tracers.csv\", \n",
    "   converters={'atom_mdv':ast.literal_eval, 'atom_ids':ast.literal_eval} # a trick to read lists from csv\n",
    ").query(\"experiment_id == 'exp1'\") # we only simulated experiment 1\n",
    "\n",
    "reactions_data = pd.read_csv(data_folder / \"reactions.csv\")\n",
    "ms_data = pd.read_csv(data_folder / 'simulated_data' / \"mdv_no_noise.csv\", \n",
    "   converters={'labelled_atom_ids': ast.literal_eval} # a trick to read lists from csv\n",
    ")\n",
    "pool_sizes = pd.read_csv(data_folder / 'simulated_data' / \"pool_sizes_measurement_no_noise.csv\")\n",
    "flux_measurements = pd.read_csv(data_folder / 'simulated_data' / \"flux_measurements_no_noise.csv\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The toy model has 5 reactions that we will show here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>model</th>\n",
       "      <th>rxn_id</th>\n",
       "      <th>rxn_eqn</th>\n",
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       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>simple_model</td>\n",
       "      <td>R1</td>\n",
       "      <td>A (abc) -&gt; B (abc)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>simple_model</td>\n",
       "      <td>R2</td>\n",
       "      <td>B (abc) &lt;-&gt; D (abc)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>simple_model</td>\n",
       "      <td>R3</td>\n",
       "      <td>B (abc) -&gt; C (bc) + E (a)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>simple_model</td>\n",
       "      <td>R4</td>\n",
       "      <td>B (abc) + C (de) -&gt; D (bcd) + E (a) + E (e)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>simple_model</td>\n",
       "      <td>R5</td>\n",
       "      <td>D (abc) -&gt; F (abc)</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          model rxn_id                                      rxn_eqn\n",
       "0  simple_model     R1                           A (abc) -> B (abc)\n",
       "1  simple_model     R2                          B (abc) <-> D (abc)\n",
       "2  simple_model     R3                    B (abc) -> C (bc) + E (a)\n",
       "3  simple_model     R4  B (abc) + C (de) -> D (bcd) + E (a) + E (e)\n",
       "4  simple_model     R5                           D (abc) -> F (abc)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reactions_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We consider one experiment with a single labelled substrate, A, which is labelled at carbon position 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>experiment_id</th>\n",
       "      <th>met_id</th>\n",
       "      <th>tracer_id</th>\n",
       "      <th>atom_ids</th>\n",
       "      <th>ratio</th>\n",
       "      <th>atom_mdv</th>\n",
       "      <th>enrichment</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>exp1</td>\n",
       "      <td>A</td>\n",
       "      <td>[2-13C]A</td>\n",
       "      <td>[2]</td>\n",
       "      <td>1.0</td>\n",
       "      <td>[0, 1]</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  experiment_id met_id tracer_id atom_ids  ratio atom_mdv  enrichment\n",
       "0          exp1      A  [2-13C]A      [2]    1.0   [0, 1]           1"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tracers_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When analysing INST data, we have mass distribution vectors of the same metabolite at multiple time points. These are specified by adding the timepoint in the `time` column."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>experiment_id</th>\n",
       "      <th>met_id</th>\n",
       "      <th>ms_id</th>\n",
       "      <th>measurement_replicate</th>\n",
       "      <th>labelled_atom_ids</th>\n",
       "      <th>unlabelled_atoms</th>\n",
       "      <th>mass_isotope</th>\n",
       "      <th>intensity_std_error</th>\n",
       "      <th>time</th>\n",
       "      <th>intensity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>exp1</td>\n",
       "      <td>B</td>\n",
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       "      <td>1</td>\n",
       "      <td>[1, 2, 3]</td>\n",
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       "      <td>0</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>exp1</td>\n",
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       "      <td>[1, 2, 3]</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>exp1</td>\n",
       "      <td>B</td>\n",
       "      <td>B1</td>\n",
       "      <td>1</td>\n",
       "      <td>[1, 2, 3]</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>exp1</td>\n",
       "      <td>B</td>\n",
       "      <td>B1</td>\n",
       "      <td>1</td>\n",
       "      <td>[1, 2, 3]</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>exp1</td>\n",
       "      <td>F</td>\n",
       "      <td>F1</td>\n",
       "      <td>1</td>\n",
       "      <td>[1, 2, 3]</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  experiment_id met_id ms_id  measurement_replicate labelled_atom_ids  \\\n",
       "0          exp1      B    B1                      1         [1, 2, 3]   \n",
       "1          exp1      B    B1                      1         [1, 2, 3]   \n",
       "2          exp1      B    B1                      1         [1, 2, 3]   \n",
       "3          exp1      B    B1                      1         [1, 2, 3]   \n",
       "4          exp1      F    F1                      1         [1, 2, 3]   \n",
       "\n",
       "   unlabelled_atoms  mass_isotope  intensity_std_error  time  intensity  \n",
       "0               NaN             0                0.003     0        1.0  \n",
       "1               NaN             1                0.003     0        0.0  \n",
       "2               NaN             2                0.003     0        0.0  \n",
       "3               NaN             3                0.003     0        0.0  \n",
       "4               NaN             0                0.003     0        1.0  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ms_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get a better idea of what the data looks like we can visualise the time series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/s143838/.virtualenvs/incawrapper-dev/lib/python3.10/site-packages/seaborn/axisgrid.py:123: UserWarning: The figure layout has changed to tight\n",
      "  self._figure.tight_layout(*args, **kwargs)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x123ee1630>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1005.36x300 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "g = sns.FacetGrid(ms_data, col=\"ms_id\", hue=\"mass_isotope\")\n",
    "g.map_dataframe(sns.lineplot, data=ms_data, x=\"time\", y=\"intensity\")\n",
    "\n",
    "# add overall legend\n",
    "g.add_legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the measured mass isotopologue distribution changes over time especially for the B and F metabolites. While it only changes a little for the E metabolite.\n",
    "\n",
    "We also have measurements of one uptake rate and one secretion rate. A core assumption for INST 13C-MFA is that the fluxes are constant, thus there is only one measurement for each flux."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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>rxn_id</th>\n",
       "      <th>flux</th>\n",
       "      <th>experiment_id</th>\n",
       "      <th>flux_std_error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>R1</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>exp1</td>\n",
       "      <td>0.300000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>R5</td>\n",
       "      <td>80.566147</td>\n",
       "      <td>exp1</td>\n",
       "      <td>0.241698</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  rxn_id        flux experiment_id  flux_std_error\n",
       "0     R1  100.000000          exp1        0.300000\n",
       "1     R5   80.566147          exp1        0.241698"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flux_measurements.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we are ready to create the inca script. This is done very similar to the other examples. The main difference is that `sim_ss=False` this tells inca that don't wish to assume steady state in the isotopologue distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "output_file = PROJECT_DIR / pathlib.Path(\"docs/examples/Literature data/simple model/simple_model_inst_fitting.mat\")\n",
    "script = incawrapper.create_inca_script_from_data(\n",
    "    reactions_data=reactions_data, \n",
    "    tracer_data=tracers_data, \n",
    "    flux_measurements=flux_measurements,\n",
    "    pool_measurements=pool_sizes,\n",
    "    ms_measurements=ms_data, \n",
    "    experiment_ids=[\"exp1\"]\n",
    ")\n",
    "script.add_to_block(\"options\", \n",
    "    incawrapper.define_options(\n",
    "        fit_starts=10, # Number of flux estimation restarts\n",
    "        sim_na=False, # Do not simulate natural abundance\n",
    "        sim_ss=False # Do INST 13C MFA\n",
    "    )\n",
    ")\n",
    "script.add_to_block(\"runner\", incawrapper.define_runner(output_file, run_estimate=True, run_continuation=True))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the script is ready to run in matlab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "ms_exp1 = 1x3 msdata object\n",
      " \n",
      "fields: atoms  id  [idvs]  more  on  state  \n",
      " \n",
      "B1 E1 F1\n",
      " \n",
      " \n",
      "ms_exp1 = 1x3 msdata object\n",
      " \n",
      "fields: atoms  id  [idvs]  more  on  state  \n",
      " \n",
      "B1 E1 F1\n",
      " \n",
      " \n",
      "ms_exp1 = 1x3 msdata object\n",
      " \n",
      "fields: atoms  id  [idvs]  more  on  state  \n",
      " \n",
      "B1 E1 F1\n",
      " \n",
      " \n",
      "m = 1x1 model object\n",
      " \n",
      "fields: [expts]  [mets]  notes  [options]  [rates]  [states]  \n",
      " \n",
      "\t5 reactions (6 fluxes)                                  \n",
      "\t6 states (3 balanced, 1 source, 2 sink and 0 unbalanced)\n",
      "\t6 metabolites                                           \n",
      "\t1 experiments                                           \n",
      " \n",
      "\n",
      "                                         Directional \n",
      " Iteration      Residual     Step-size    derivative        Lambda\n",
      "     0       8.80347e+07\n",
      "     1       4.64462e+07         0.277      -6.3e+07      0.111111\n",
      "     2       4.56521e+07       0.00865     -4.57e+07      0.111111\n",
      "     3       4.53763e+07       0.00304     -4.52e+07      0.111111\n",
      "     4       1.51334e+07          0.43     -2.54e+07      0.111111\n",
      "     5       7.19864e+06         0.319        -1e+07      0.111111\n",
      "     6            182600             1     -7.37e+04      0.111111\n",
      "     7           32453.9             1     -7.59e+03      0.037037\n",
      "     8           16919.7             1          -508     0.0123457\n",
      "     9           15454.6             1         -22.7    0.00411523\n",
      "    10           15076.6             1         -62.9    0.00361073\n",
      "    11            9817.3         0.231      8.36e+03    0.00293036\n",
      "    12           326.457         0.838     -1.54e+03    0.00293036\n",
      "    13           7.07087             1         -1.21    0.00293036\n",
      "                                                    \n",
      " Optimization terminated: Constrained optimum found.\n",
      " Parameters converged to within tolerance.          \n",
      "\n",
      "                                         Directional \n",
      " Iteration      Residual     Step-size    derivative        Lambda\n",
      "     0       8.39765e+07\n",
      "     1       8.29154e+07       0.00637     -8.29e+07      0.150157\n",
      "     2       1.64973e+07         0.564     -3.58e+07      0.150157\n",
      "     3       1.63743e+07       0.00379     -1.62e+07      0.150157\n",
      "     4       1.62851e+07       0.00277     -1.61e+07      0.150157\n",
      "     5       9.97697e+06         0.224     -1.23e+07      0.150157\n",
      "     6            289203             1     -8.72e+04      0.150157\n",
      "     7           51116.1             1     -2.65e+04     0.0500524\n",
      "     8           31359.8             1      3.73e+03     0.0166841\n",
      "     9           29942.9         0.162     -3.85e+03      0.013746\n",
      "    10           29186.1             1         2e+03      0.013746\n",
      "    11           23393.2         0.207     -1.22e+04     0.0172162\n",
      "    12           15050.3             1          -231     0.0172162\n",
      "    13           15029.5             1         0.194    0.00573872\n",
      "    14           15028.2             1       -0.0383     0.0025289\n",
      "    15           6665.92         0.634      2.23e+04   0.000842965\n",
      "    16           1784.18             1          35.8   0.000842965\n",
      "    17           162.149             1          -140   0.000280988\n",
      "    18           10.0179             1         -17.1   0.000120214\n",
      "    19           7.08585         0.941        -0.316   4.00712e-05\n",
      "    20            7.0415             1       -0.0016   4.00712e-05\n",
      "    21           7.04135             1     -2.78e-06   1.33571e-05\n",
      "                                                      \n",
      " Optimization terminated: Unconstrained optimum found.\n",
      " Norm of gradient less than tolerance.                \n",
      "\n",
      "                                         Directional \n",
      " Iteration      Residual     Step-size    derivative        Lambda\n",
      "     0        8.6554e+07\n",
      "     1        8.4608e+07        0.0114     -8.48e+07      0.111111\n",
      "     2       5.56033e+07         0.192     -6.76e+07      0.111111\n",
      "     3       5.52764e+07       0.00296     -5.51e+07      0.111111\n",
      "     4       1.46314e+07         0.494     -2.75e+07      0.111111\n",
      "     5       7.60619e+06         0.287     -1.01e+07      0.111111\n",
      "     6            204376             1     -7.78e+04      0.111111\n",
      "     7           34893.8             1      -1.1e+04      0.037037\n",
      "     8           31657.4             1      4.66e+03     0.0123457\n",
      "     9           28833.9             1      1.86e+03     0.0125963\n",
      "    10           15177.7             1          -551     0.0126071\n",
      "    11           10023.6         0.385      3.54e+04    0.00420237\n",
      "    12           1676.12             1          14.8    0.00420237\n",
      "    13           159.443             1          -111    0.00140079\n",
      "    14           45.1375         0.523         -63.7   0.000631376\n",
      "    15           2.74157             1         -3.82   0.000631376\n",
      "    16           2.32142             1        -0.024   0.000210459\n",
      "                                                    \n",
      " Optimization terminated: Constrained optimum found.\n",
      " Parameters converged to within tolerance.          \n",
      "\n",
      "                                         Directional \n",
      " Iteration      Residual     Step-size    derivative        Lambda\n",
      "     0       8.82926e+07\n",
      "     1        8.6347e+07        0.0112     -8.65e+07      0.111111\n",
      "     2       1.73613e+07         0.561     -3.75e+07      0.111111\n",
      "     3        1.7096e+07       0.00781     -1.69e+07      0.111111\n",
      "     4       1.70153e+07        0.0024     -1.68e+07      0.111111\n",
      "     5       1.08075e+07         0.209     -1.31e+07      0.111111\n",
      "     6            315592             1     -8.82e+04      0.111111\n",
      "     7           59173.2             1     -3.39e+04      0.037037\n",
      "     8           31776.2             1      4.14e+03     0.0123457\n",
      "     9           31119.9        0.0615     -5.28e+03     0.0093034\n",
      "    10           28729.8             1      1.87e+03     0.0093034\n",
      "    11           15078.2             1          -482    0.00931513\n",
      "    12           9217.01         0.436      3.28e+04    0.00310504\n",
      "    13           1783.34             1         -21.2    0.00310504\n",
      "    14           174.025             1          -141    0.00103501\n",
      "    15           9.42444             1         -16.6   0.000469196\n",
      "    16           6.81875             1        -0.165   0.000156399\n",
      "    17           6.80275             1      -0.00032   5.21329e-05\n",
      "    18           6.80278             1     -3.23e-07   1.73776e-05\n",
      "    19           6.80271             1     -3.05e-07   3.47553e-05\n",
      "                                                      \n",
      " Optimization terminated: Unconstrained optimum found.\n",
      " Norm of gradient less than tolerance.                \n",
      "\n",
      "                                         Directional \n",
      " Iteration      Residual     Step-size    derivative        Lambda\n",
      "     0       8.46555e+07\n",
      "     1       8.41799e+07       0.00283     -8.39e+07      0.118315\n",
      "     2       1.66314e+07         0.565     -3.62e+07      0.118315\n",
      "     3       1.64206e+07       0.00648     -1.62e+07      0.118315\n",
      "     4       1.62829e+07       0.00427     -1.61e+07      0.118315\n",
      "     5       1.01792e+07         0.215     -1.24e+07      0.118315\n",
      "     6            288455             1      -8.8e+04      0.118315\n",
      "     7           51316.3             1      -2.6e+04     0.0394383\n",
      "     8           31947.8             1      4.28e+03     0.0131461\n",
      "     9             31025        0.0861     -5.09e+03     0.0113623\n",
      "    10           29443.6             1       2.1e+03     0.0113623\n",
      "    11           24686.2         0.156     -1.45e+04     0.0120989\n",
      "    12           15059.2             1          -283     0.0120989\n",
      "    13           15029.3             1          -1.5    0.00403297\n",
      "    14           6509.86         0.648      2.15e+04    0.00134432\n",
      "    15           1784.12             1          34.1    0.00134432\n",
      "    16           164.004             1          -140   0.000448107\n",
      "    17           10.0513             1         -17.3   0.000192713\n",
      "    18           7.05527             1        -0.166   6.42377e-05\n",
      "                                                    \n",
      " Optimization terminated: Constrained optimum found.\n",
      " Parameters converged to within tolerance.          \n",
      "\n",
      "                                         Directional \n",
      " Iteration      Residual     Step-size    derivative        Lambda\n",
      "     0       8.61807e+07\n",
      "     1       8.40101e+07        0.0128     -8.44e+07      0.111111\n",
      "     2       8.32141e+07       0.00477     -8.31e+07      0.111111\n",
      "     3       7.86841e+07        0.0278     -8.03e+07      0.111111\n",
      "     4       1.30696e+07         0.604     -3.08e+07      0.111111\n",
      "     5       8.36853e+06         0.206        -1e+07      0.111111\n",
      "     6            273024             1      -8.7e+04      0.111111\n",
      "     7           46586.2             1     -2.23e+04      0.037037\n",
      "     8           31571.9             1      4.32e+03     0.0123457\n",
      "     9           28264.4         0.699          -116      0.011244\n",
      "    10           28174.2             1           915      0.011244\n",
      "    11           26809.6             1          -157     0.0198663\n",
      "    12           27272.5         0.177      2.23e+05     0.0182072\n",
      "    13           28673.8        0.0434      8.77e+05     0.0364144\n",
      "    14           28580.9        0.0455      8.37e+05      0.145658\n",
      "    15           27752.9        0.0649      5.94e+05       1.16526\n",
      "    16           21769.4         0.219      1.95e+05       9.32208\n",
      "    17           2320.73             1           108       9.32208\n",
      "    18           341.687             1          -189       3.10736\n",
      "    19           19.1996             1         -45.9       1.97299\n",
      "    20           6.91169             1         -0.92      0.657663\n",
      "    21           6.80925             1      -0.00994      0.219221\n",
      "    22           6.80286             1       -0.0017     0.0730736\n",
      "    23           6.80258             1     -0.000107     0.0434197\n",
      "                                                      \n",
      " Optimization terminated: Unconstrained optimum found.\n",
      " Parameters converged to within tolerance.            \n",
      "\n",
      "                                         Directional \n",
      " Iteration      Residual     Step-size    derivative        Lambda\n",
      "     0       8.84086e+07\n",
      "     1       8.54262e+07        0.0172      -8.6e+07      0.111111\n",
      "     2       7.87759e+07          0.04     -8.12e+07      0.111111\n",
      "     3       7.78237e+07       0.00609     -7.79e+07      0.111111\n",
      "     4       1.42459e+07         0.583     -3.21e+07      0.111111\n",
      "     5       8.96799e+06         0.213     -1.09e+07      0.111111\n",
      "     6            277905             1     -8.61e+04      0.111111\n",
      "     7           47679.4             1     -2.37e+04      0.037037\n",
      "     8           31235.7             1      4.22e+03     0.0123457\n",
      "     9           28586.6             1      1.79e+03     0.0107715\n",
      "    10           15080.6             1          -538     0.0107789\n",
      "    11           14308.9        0.0267     -1.37e+04    0.00359297\n",
      "    12           10830.2         0.359      5.13e+04    0.00359297\n",
      "    13           1664.99             1          72.8    0.00359297\n",
      "    14           167.287             1         -95.7    0.00119766\n",
      "    15           6.23418             1         -17.7   0.000562941\n",
      "    16           2.32666             1        -0.174   0.000187647\n",
      "    17            2.3195             1      0.000911    6.2549e-05\n",
      "    18           2.31572             1      5.95e-05   6.49149e-05\n",
      "    19            2.3207             1     -5.69e-06   2.16383e-05\n",
      "    20           2.32065             1     -6.27e-06   4.32766e-05\n",
      "                                                      \n",
      " Optimization terminated: Unconstrained optimum found.\n",
      " Parameters converged to within tolerance.            \n",
      "\n",
      "                                         Directional \n",
      " Iteration      Residual     Step-size    derivative        Lambda\n",
      "     0       8.66582e+07\n",
      "     1       1.70442e+07         0.566     -3.72e+07      0.111111\n",
      "     2       1.68174e+07        0.0068     -1.66e+07      0.111111\n",
      "     3       1.66502e+07       0.00508     -1.64e+07      0.111111\n",
      "     4       1.05707e+07         0.209     -1.28e+07      0.111111\n",
      "     5            310368             1     -8.84e+04      0.111111\n",
      "     6           57589.1             1     -3.23e+04      0.037037\n",
      "     7           31814.2             1      4.18e+03     0.0123457\n",
      "     8           31021.5        0.0749     -5.16e+03     0.0095651\n",
      "     9             29295             1      2.24e+03     0.0095651\n",
      "    10           22163.2         0.277     -1.06e+04    0.00995642\n",
      "    11           15049.1             1          -197    0.00995642\n",
      "    12           15028.9             1        -0.981    0.00331881\n",
      "    13           15028.6         0.349        -0.281    0.00110627\n",
      "    14           15028.2             1      -0.00905    0.00110627\n",
      "    15           6667.07         0.634      2.24e+04   0.000368756\n",
      "    16           1784.09             1          35.7   0.000368756\n",
      "    17           164.009             1          -140   0.000122919\n",
      "    18           10.0516             1         -17.3    5.2864e-05\n",
      "    19           7.05545             1        -0.166   1.76213e-05\n",
      "    20           7.05123             1     -0.000427   5.87378e-06\n",
      "    21           7.04731             1      8.06e-07   5.91445e-06\n",
      "    22           7.04093         0.347     -1.42e-06   1.97148e-06\n",
      "    23            7.0411             1      6.87e-08   1.97148e-06\n",
      "    24            7.0411             1      8.11e-08   3.94297e-06\n",
      "    25            7.0411             1      9.03e-08   1.57719e-05\n",
      "                                                    \n",
      " Optimization terminated: Constrained optimum found.\n",
      " Parameters converged to within tolerance.          \n",
      "\n",
      "                                         Directional \n",
      " Iteration      Residual     Step-size    derivative        Lambda\n",
      "     0       8.78969e+07\n",
      "     1       8.27101e+07        0.0303     -8.43e+07      0.111111\n",
      "     2       7.96693e+07        0.0187     -8.05e+07      0.111111\n",
      "     3       4.44252e+07         0.256     -5.86e+07      0.111111\n",
      "     4       3.01012e+07         0.179      -3.6e+07      0.111111\n",
      "     5       9.00943e+06         0.462     -1.59e+07      0.111111\n",
      "     6            368485          0.87     -1.19e+06      0.111111\n",
      "     7           38818.5             1     -1.88e+04      0.111111\n",
      "     8           28813.4             1           464      0.037037\n",
      "     9           27531.2             1           229     0.0123457\n",
      "    10           19415.2         0.888      1.88e+04     0.0123429\n",
      "    11             17095             1          13.7     0.0123429\n",
      "    12           15405.7             1          -102     0.0041143\n",
      "    13           15054.6             1         -59.9    0.00287209\n",
      "    14           5608.04         0.746      1.77e+04   0.000957364\n",
      "    15           1784.37             1          18.9   0.000957364\n",
      "    16           163.871             1          -141   0.000319121\n",
      "    17           9.28104             1         -15.8   0.000137885\n",
      "    18           6.81873             1        -0.145   4.59616e-05\n",
      "    19           6.80896             1     -0.000271   1.53205e-05\n",
      "    20           6.81233             1      -6.9e-07   5.10684e-06\n",
      "    21           6.80902             1     -2.53e-07   1.02137e-05\n",
      "                                                      \n",
      " Optimization terminated: Unconstrained optimum found.\n",
      " Parameters converged to within tolerance.            \n",
      "\n",
      "                                         Directional \n",
      " Iteration      Residual     Step-size    derivative        Lambda\n",
      "     0       8.95343e+07\n",
      "     1       7.42695e+07        0.0903     -8.08e+07      0.111111\n",
      "     2       7.30822e+07       0.00804     -7.36e+07      0.111111\n",
      "     3       4.89482e+07         0.183     -5.91e+07      0.111111\n",
      "     4       1.33372e+06         0.869     -6.39e+06      0.111111\n",
      "     5            129221             1     -8.12e+04      0.111111\n",
      "     6           18347.2             1     -3.13e+03      0.037037\n",
      "     7           2089.56             1           442     0.0123457\n",
      "     8           305.929             1          -180    0.00411523\n",
      "     9           105.718         0.469          -147    0.00263209\n",
      "    10           4.34867             1         -11.7    0.00263209\n",
      "    11            2.3313             1        -0.126   0.000877365\n",
      "                                                    \n",
      " Optimization terminated: Constrained optimum found.\n",
      " Parameters converged to within tolerance.          \n",
      "\n",
      "                                         Directional \n",
      " Iteration      Residual     Step-size    derivative        Lambda\n",
      "     0           2.31572\n",
      "     1           2.19873             1     -5.43e-05   9.88143e-09\n",
      "     2           2.14707         0.279        -0.193   3.29381e-09\n",
      "     3          0.177144             1         0.248   3.29381e-09\n",
      "     4         0.0375023             1        0.0379   1.16041e-09\n",
      "     5         0.0278745             1       0.00169   3.89766e-10\n",
      "     6           0.02766             1       0.00025   1.29922e-10\n",
      "     7         0.0174713             1      0.000507   1.24112e-10\n",
      "     8         0.0166539             1      7.26e-05   7.36839e-11\n",
      "                                                      \n",
      " Optimization terminated: Unconstrained optimum found.\n",
      " Parameters converged to within tolerance.            \n",
      "\n",
      "\tEstimation completed in 39.5600 seconds.\n",
      "\n",
      "\tPreprocessing time:     9.7600 s\n",
      "\n",
      "\tComputation time:       29.5700 s\n",
      "\n",
      "\tPostprocessing time:    0.2300 s\n",
      "\n",
      "\n",
      " ========== Varying R1 upward from 99.99 ==========\n",
      "\n",
      "                Delta        Delta                       Predictor    Corrector   Corrector   Failed\n",
      " Iteration      residual     parameter     Step-size         error    adjustment  iterations   steps     h/hopt        Lambda\n",
      "     1          0.754745      0.215778      0.215778      0.005972      0.019519      3          0            1   9.88142e-09\n",
      "     2          1.517117      0.306032     0.0902535     -0.003133      0.002786     12          0            1   3.29381e-09\n",
      "     3          1.719718      0.325427     0.0193951      0.004318      0.000989      1          0         0.28   1.09794e-09\n",
      "     4          2.486981      0.391547     0.0661198     -0.000187      0.000842      1          0            1   1.09794e-09\n",
      "     5          3.253886      0.448067       0.05652     -0.001386      0.000000      3          0            1   3.65979e-10\n",
      "     6          4.021580      0.498288      0.050221      0.000971      0.001569      1          0            1   1.21993e-10\n",
      "\n",
      " ========== Varying R1 downward from 99.99 ==========\n",
      "\n",
      "                Delta        Delta                       Predictor    Corrector   Corrector   Failed\n",
      " Iteration      residual     parameter     Step-size         error    adjustment  iterations   steps     h/hopt        Lambda\n",
      "     1          0.772019      0.215673      0.215673      0.017932      0.014205     11          0            1   9.88142e-09\n",
      "     2          1.542067       0.30482     0.0891473      0.004471      0.002715     11          0            1   3.29381e-09\n",
      "     3          2.312094      0.373107     0.0682867      0.002637      0.000903     10          0            1   1.09794e-09\n",
      "     4          3.080986      0.430594     0.0574866      0.001495      0.000895     11          0            1   3.65979e-10\n",
      "     5          3.776696      0.476568      0.045974      0.001914      0.000593      1          0        0.908   1.21993e-10\n",
      "     6          4.553611      0.522706     0.0461386      0.008624      0.000000      1          0            1   1.21993e-10\n",
      "\n",
      " ========== Varying R2 net upward from 61.15 ==========\n",
      "\n",
      "                Delta        Delta                       Predictor    Corrector   Corrector   Failed\n",
      " Iteration      residual     parameter     Step-size         error    adjustment  iterations   steps     h/hopt        Lambda\n",
      "     1          0.719768      0.339624      0.339624     -0.014601      0.023062     13          0        0.993   9.88142e-09\n",
      "     2          0.798777       0.35994     0.0203157     -0.000351      0.000768      8          0        0.139   9.88142e-09\n",
      "     3          0.884681      0.379857     0.0199165     -0.000141      0.000607      6          0        0.145   9.88142e-09\n",
      "     4          0.980513      0.400214     0.0203571     -0.000536      0.000488      3          0        0.156   9.88142e-09\n",
      "     5          1.077754      0.419233     0.0190197     -0.000810      0.000000      1          0        0.155   9.88142e-09\n",
      "     6          1.829426      0.536339      0.117106     -0.016549      0.000070      1          0            1   9.88142e-09\n",
      "     7          2.579316      0.625327     0.0889879     -0.018402      0.000000      9          0            1   3.29381e-09\n",
      "     8          3.328514      0.700059     0.0747311     -0.018794      0.000300     11          0            1   1.09794e-09\n",
      "     9          4.076962      0.765748     0.0656895     -0.019844      0.000000      9          0            1   3.65979e-10\n",
      "\n",
      " ========== Varying R2 net downward from 61.15 ==========\n",
      "\n",
      "                Delta        Delta                       Predictor    Corrector   Corrector   Failed\n",
      " Iteration      residual     parameter     Step-size         error    adjustment  iterations   steps     h/hopt        Lambda\n",
      "     1          0.400717      0.259767      0.259767      0.005865      0.047144      2          0        0.759   9.88142e-09\n",
      "     2          0.961683      0.403076      0.143309     -0.015632      0.013534      5          0        0.809   9.88142e-09\n",
      "     3          1.497588      0.503522      0.100446     -0.021859      0.005349      1          0         0.76   9.88142e-09\n",
      "     4          2.225975      0.614464      0.110943     -0.038871      0.001034     10          0            1   9.88142e-09\n",
      "     5          2.951371      0.707698     0.0932337     -0.033971      0.000000     11          0        0.989   3.29381e-09\n",
      "     6          3.688137       0.79167     0.0839715     -0.026450      0.005076      2          0            1   3.29381e-09\n",
      "     7          4.408092       0.86774       0.07607     -0.035817      0.012520     13          0            1   1.09794e-09\n",
      "\n",
      " ========== Varying R2 exch upward from 49.85 ==========\n",
      "\n",
      "                Delta        Delta                       Predictor    Corrector   Corrector   Failed\n",
      " Iteration      residual     parameter     Step-size         error    adjustment  iterations   steps     h/hopt        Lambda\n",
      "     1          0.655792       1.75246       1.75246     -0.090681      0.021818      3          0            1   9.88142e-09\n",
      "     2          1.365163       2.54916      0.796708     -0.055353      0.003568      2          0            1   3.29381e-09\n",
      "     3          2.076718       3.16658      0.617412     -0.056240      0.000498      2          0            1   1.09794e-09\n",
      "     4          2.786908       3.69248        0.5259     -0.057975      0.000126      2          0            1   3.65979e-10\n",
      "     5          3.499706       4.16062      0.468143     -0.055460      0.000034      9          0            1   1.21993e-10\n",
      "     6          3.538924       4.18505     0.0244282     -0.001988      0.000686      5          0       0.0572   4.06643e-11\n",
      "     7          4.256895       4.60873      0.423679     -0.050321      0.000000      1          0            1   4.06643e-11\n",
      "\n",
      " ========== Varying R2 exch downward from 49.85 ==========\n",
      "\n",
      "                Delta        Delta                       Predictor    Corrector   Corrector   Failed\n",
      " Iteration      residual     parameter     Step-size         error    adjustment  iterations   steps     h/hopt        Lambda\n",
      "     1          0.040027      0.425982      0.425982     -0.003053      0.002419     11          0        0.243   9.88142e-09\n",
      "     2          0.253571       1.00613      0.580152     -0.009291      0.000348      1          0         0.46   9.88142e-09\n",
      "     3          0.988168       1.89255      0.886413     -0.033090      0.000604      1          0            1   9.88142e-09\n",
      "     4          1.724774       2.45808      0.565537     -0.031652      0.000034      1          0            1   3.29381e-09\n",
      "     5          2.461663       2.90638      0.448299     -0.031403      0.000000      1          0            1   1.09794e-09\n",
      "     6          3.199023        3.2883      0.381922     -0.030865      0.000066      1          0            1   3.65979e-10\n",
      "     7          3.935789       3.62597      0.337663     -0.031526      0.000000      1          0            1   1.21993e-10\n",
      "\n",
      " ========== Varying R4 upward from 19.42 ==========\n",
      "\n",
      "                Delta        Delta                       Predictor    Corrector   Corrector   Failed\n",
      " Iteration      residual     parameter     Step-size         error    adjustment  iterations   steps     h/hopt        Lambda\n",
      "     1          0.355862       0.16074       0.16074      0.002414      0.043132      8          0        0.719   9.88142e-09\n",
      "     2          1.077407      0.280094      0.119355     -0.031781      0.014966     11          0            1   9.88142e-09\n",
      "     3          1.809057      0.362946     0.0828514     -0.033713      0.002929      2          0            1   3.29381e-09\n",
      "     4          2.543757      0.430852     0.0679058     -0.032610      0.000981     10          0            1   1.09794e-09\n",
      "     5          3.275071      0.489761     0.0589089     -0.036697      0.000280     10          0            1   3.65979e-10\n",
      "     6          3.321450      0.493826    0.00406522      0.000546      0.010633     10          0       0.0773   1.21993e-10\n",
      "     7          3.376941      0.497548    0.00372172      0.006055      0.002324     11          0       0.0708   1.21993e-10\n",
      "     8          3.425789      0.501173    0.00362591      0.001900      0.004108      8          0       0.0698   1.21993e-10\n",
      "     9          3.477358       0.50468    0.00350684      0.001989      0.000134      1          0       0.0679   1.21993e-10\n",
      "    10          4.208963      0.556197     0.0515164     -0.036148      0.000538     11          0            1   1.21993e-10\n",
      "\n",
      " ========== Varying R4 downward from 19.42 ==========\n",
      "\n",
      "                Delta        Delta                       Predictor    Corrector   Corrector   Failed\n",
      " Iteration      residual     parameter     Step-size         error    adjustment  iterations   steps     h/hopt        Lambda\n",
      "     1          0.694953      0.217096      0.217096     -0.007211      0.023116      5          0        0.972   9.88142e-09\n",
      "     2          1.451063      0.313258     0.0961621     -0.011916      0.000265      1          0            1   9.88142e-09\n",
      "     3          2.204853      0.377803     0.0645456     -0.014348      0.000154     10          0            1   3.29381e-09\n",
      "     4          2.957479      0.429872     0.0520682     -0.015583      0.000083     11          0            1   1.09794e-09\n",
      "     5          3.709188      0.474717     0.0448453     -0.016416      0.000167      9          0            1   3.65979e-10\n",
      "     6          4.461267      0.514699     0.0399826     -0.016025      0.000188      8          0            1   1.21993e-10\n",
      "\n",
      " ========== Varying R5 upward from 80.57 ==========\n",
      "\n",
      "                Delta        Delta                       Predictor    Corrector   Corrector   Failed\n",
      " Iteration      residual     parameter     Step-size         error    adjustment  iterations   steps     h/hopt        Lambda\n",
      "     1          0.754751      0.178404      0.178404      0.012833      0.026374     11          0            1   9.88142e-09\n",
      "     2          1.510010      0.253403     0.0749992     -0.008718      0.004315     12          0            1   3.29381e-09\n",
      "     3          2.024710       0.29369     0.0402868     -0.004239      0.002605      4          0        0.701   1.09794e-09\n",
      "     4          2.792842       0.34471     0.0510205     -0.000043      0.000116      1          0            1   1.09794e-09\n",
      "     5          3.560295      0.388088     0.0433775     -0.000789      0.000050      1          0            1   3.65979e-10\n",
      "     6          4.327208      0.426484     0.0383967     -0.001359      0.000020      1          0            1   1.21993e-10\n",
      "\n",
      " ========== Varying R5 downward from 80.57 ==========\n",
      "\n",
      "                Delta        Delta                       Predictor    Corrector   Corrector   Failed\n",
      " Iteration      residual     parameter     Step-size         error    adjustment  iterations   steps     h/hopt        Lambda\n",
      "     1          0.745374      0.178537      0.178537      0.001932      0.024850      2          0            1   9.88142e-09\n",
      "     2          1.500599      0.253168     0.0746316     -0.009236      0.003831      8          0            1   3.29381e-09\n",
      "     3          2.243867      0.310409     0.0572408     -0.015132      0.009892     11          0            1   1.09794e-09\n",
      "     4          2.779080      0.344793     0.0343838      0.005914      0.002910      5          0        0.708   3.65979e-10\n",
      "     5          2.963252      0.356035     0.0112424     -0.002741      0.000000     10          0        0.255   3.65979e-10\n",
      "     6          3.722591      0.398899     0.0428638     -0.007937      0.001015      5          0            1   3.65979e-10\n",
      "     7          4.480816      0.437568     0.0386684     -0.009390      0.000676     10          0            1   1.21993e-10\n",
      "\n",
      " ========== Varying B pool upward from 100 ==========\n",
      "\n",
      "                Delta        Delta                       Predictor    Corrector   Corrector   Failed\n",
      " Iteration      residual     parameter     Step-size         error    adjustment  iterations   steps     h/hopt        Lambda\n",
      "     1          0.768378     0.0131457     0.0131457      0.000092      0.000007      1          0            1   9.88142e-09\n",
      "     2          1.536713     0.0185907    0.00544498      0.000045      0.000002      1          0            1   3.29381e-09\n",
      "     3          2.305045     0.0227688    0.00417809      0.000040      0.000000      1          0            1   1.09794e-09\n",
      "     4          3.073376     0.0262911     0.0035223      0.000039      0.000000      1          0            1   3.65979e-10\n",
      "     5          3.841705     0.0293943    0.00310321      0.000038      0.000000      1          0            1   1.21993e-10\n",
      "\n",
      " ========== Varying B pool downward from 100 ==========\n",
      "\n",
      "                Delta        Delta                       Predictor    Corrector   Corrector   Failed\n",
      " Iteration      residual     parameter     Step-size         error    adjustment  iterations   steps     h/hopt        Lambda\n",
      "     1          0.768306     0.0131456     0.0131456      0.000019      0.000004      1          0            1   9.88142e-09\n",
      "     2          1.536660     0.0185906    0.00544498      0.003021      0.002959     12          0            1   3.29381e-09\n",
      "     3          2.304970     0.0227687    0.00417809      0.000018      0.000000      1          0            1   1.09794e-09\n",
      "     4          3.075278      0.026291     0.0035223      0.002615      0.000598     12          0            1   3.65979e-10\n",
      "     5          3.843587     0.0293942     0.0031032      0.000017      0.000000     11          0            1   1.21993e-10\n",
      "\n",
      " ========== Varying C pool upward from 1.088 ==========\n",
      "\n",
      "                Delta        Delta                       Predictor    Corrector   Corrector   Failed\n",
      " Iteration      residual     parameter     Step-size         error    adjustment  iterations   steps     h/hopt        Lambda\n",
      "     1          0.062401      0.424544      0.424544      0.025503      0.006728      1          0        0.237   9.88142e-09\n",
      "     2          1.157927       1.63827       1.21373      0.475314      0.148081      5          0            1   9.88142e-09\n",
      "     3          2.067374       2.13973      0.501451      0.157436      0.016281      5          0            1   1.00135e-08\n",
      "     4          2.962081         2.526      0.386279      0.136967      0.010552      4          0            1   7.95522e-09\n",
      "     5          3.845004       2.85128      0.325278      0.120845      0.006214      2          0            1    5.8359e-09\n",
      "\n",
      " ========== Varying C pool downward from 1.088 ==========\n",
      "\n",
      "                Delta        Delta                       Predictor    Corrector   Corrector   Failed\n",
      " Iteration      residual     parameter     Step-size         error    adjustment  iterations   steps     h/hopt        Lambda\n",
      "     1          0.366521       1.08825       1.08825      0.105858      0.021167      1          0        0.606   9.88142e-09\n",
      "\n",
      " ========== Varying D pool upward from 1.136 ==========\n",
      "\n",
      "                Delta        Delta                       Predictor    Corrector   Corrector   Failed\n",
      " Iteration      residual     parameter     Step-size         error    adjustment  iterations   steps     h/hopt        Lambda\n",
      "     1          0.650722      0.707908      0.707908      0.191529      0.023452      1          0        0.793   9.88142e-09\n",
      "     2          1.529677       1.03607      0.328162      0.114525      0.003861      1          0            1   9.88142e-09\n",
      "     3          2.386104       1.24317      0.207096      0.090352      0.002217      1          0            1   6.46484e-09\n",
      "     4          3.237277       1.40838      0.165208      0.084799      0.001918      1          0            1   3.57286e-09\n",
      "     5          4.085773       1.55005      0.141676      0.081959      0.001755      1          0            1   1.88222e-09\n",
      "\n",
      " ========== Varying D pool downward from 1.136 ==========\n",
      "\n",
      "                Delta        Delta                       Predictor    Corrector   Corrector   Failed\n",
      " Iteration      residual     parameter     Step-size         error    adjustment  iterations   steps     h/hopt        Lambda\n",
      "     1          0.114740      0.286824      0.286824      0.042387      0.008584      1          0        0.323   9.88142e-09\n",
      "     2          1.277177      0.870987      0.584162      0.455712      0.061566      1          0            1   9.88142e-09\n",
      "     3          2.260803       1.13548      0.264492      0.227337      0.012003      1          0            1   9.94531e-09\n",
      "     4          2.299622       1.13639   0.000909441      0.036193      0.000548      1          0      0.00446   9.26885e-09\n",
      "\n",
      " ========== Varying E pool upward from 0.7071 ==========\n",
      "\n",
      "                Delta        Delta                       Predictor    Corrector   Corrector   Failed\n",
      " Iteration      residual     parameter     Step-size         error    adjustment  iterations   steps     h/hopt        Lambda\n",
      "     1          0.877125       6.10247       6.10247      0.155340      0.046507     12          0            1   9.88142e-09\n",
      "     2          1.209838        7.1837       1.08122      0.019435      0.000905      1          0        0.448    7.7934e-09\n",
      "     3          1.979379       9.24119       2.05749      0.004022      0.002772      1          0            1    7.7934e-09\n",
      "     4          2.742069       10.8507       1.60955     -0.004132      0.001470      1          0            1    2.5978e-09\n",
      "     5          3.500968       12.2294       1.37864     -0.008475      0.000918      1          0            1   8.65934e-10\n",
      "     6          4.257429       13.4615       1.23214     -0.011211      0.000620      1          0            1   2.88645e-10\n",
      "\n",
      " ========== Varying E pool downward from 0.7071 ==========\n",
      "\n",
      "                Delta        Delta                       Predictor    Corrector   Corrector   Failed\n",
      " Iteration      residual     parameter     Step-size         error    adjustment  iterations   steps     h/hopt        Lambda\n",
      "     1          0.012546      0.707109      0.707109      0.003231      0.001103      1          0        0.116   9.88142e-09\n",
      "\n",
      " ========== Varying F pool upward from 100 ==========\n",
      "\n",
      "                Delta        Delta                       Predictor    Corrector   Corrector   Failed\n",
      " Iteration      residual     parameter     Step-size         error    adjustment  iterations   steps     h/hopt        Lambda\n",
      "     1          0.768288     0.0131468     0.0131468      0.000017      0.000022      1          0            1   9.88142e-09\n",
      "     2          1.536581     0.0185923    0.00544553      0.000002      0.000000      0          0            1   3.29381e-09\n",
      "     3          2.304878     0.0227708     0.0041785      0.000005      0.000000      0          0            1   1.09794e-09\n",
      "     4          3.073178     0.0262935    0.00352264      0.000008      0.000000      0          0            1   3.65979e-10\n",
      "     5          3.841478      0.029397    0.00310351      0.000009      0.000000      0          0            1   1.21993e-10\n",
      "\n",
      " ========== Varying F pool downward from 100 ==========\n",
      "\n",
      "                Delta        Delta                       Predictor    Corrector   Corrector   Failed\n",
      " Iteration      residual     parameter     Step-size         error    adjustment  iterations   steps     h/hopt        Lambda\n",
      "     1          0.768329     0.0131468     0.0131468      0.000037      0.000000      1          0            1   9.88142e-09\n",
      "     2          1.536693     0.0185923    0.00544553      0.003440      0.003367     12          0            1   3.29381e-09\n",
      "     3          2.304997     0.0227708     0.0041785      0.000012      0.000000      1          0            1   1.09794e-09\n",
      "     4          3.075355     0.0262934    0.00352264      0.003247      0.001181     12          0            1   3.65979e-10\n",
      "     5          3.843608     0.0293969     0.0031035     -0.000038      0.000000     11          0            1   1.21993e-10\n",
      "\n",
      "\tContinuation completed in 48.3100 seconds.\n",
      "\n",
      "\tPreprocessing time:     0.9300 s\n",
      "\n",
      "\tComputation time:       47.3800 s\n",
      "\n",
      "\tSimulation completed in 0.9100 seconds.\n",
      "\n",
      "\tPreprocessing time:     0.0700 s\n",
      "\n",
      "\tComputation time:       0.8100 s\n",
      "\n",
      "\tPostprocessing time:    0.0300 s\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%%capture\n",
    "import dotenv\n",
    "inca_directory = pathlib.Path(dotenv.get_key(dotenv.find_dotenv(), \"INCA_base_directory\"))\n",
    "incawrapper.run_inca(script, INCA_base_directory=inca_directory)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now read the results from INCA using the `INCAResults` object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "res = incawrapper.INCAResults(output_file)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Typically, the first thing we want to inspect is the goodness of fit. This can be accessed as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fit accepted: False\n",
      "Confidence level: 0.05\n",
      "Chi-square value (SSR): 0.016653922841033397\n",
      "Expected chi-square range: [17.53873858 48.23188959]\n"
     ]
    }
   ],
   "source": [
    "res.fitdata.get_goodness_of_fit()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the SSR value is below the expected range, thus this indicate that we are overfitting the data. However, in this scenario it is not surprising, because we used the exact simulated values with out measurement noise.\n",
    "\n",
    "We can inspect the flux estimates as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>type</th>\n",
       "      <th>id</th>\n",
       "      <th>eqn</th>\n",
       "      <th>val</th>\n",
       "      <th>std</th>\n",
       "      <th>lb</th>\n",
       "      <th>ub</th>\n",
       "      <th>unit</th>\n",
       "      <th>free</th>\n",
       "      <th>alf</th>\n",
       "      <th>chi2s</th>\n",
       "      <th>cont</th>\n",
       "      <th>cor</th>\n",
       "      <th>cov</th>\n",
       "      <th>vals</th>\n",
       "      <th>base</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Net flux</td>\n",
       "      <td>R1</td>\n",
       "      <td>A -&gt; B</td>\n",
       "      <td>99.992277</td>\n",
       "      <td>0.190251</td>\n",
       "      <td>99.51167</td>\n",
       "      <td>100.479345</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>0.05</td>\n",
       "      <td>[4.570265356139303, 3.793349715129606, 3.09763...</td>\n",
       "      <td>0</td>\n",
       "      <td>[1.0, -0.15515765338290124, 0.0203688527219357...</td>\n",
       "      <td>[0.036195387046629834, -0.008826206497164618, ...</td>\n",
       "      <td>[99.46957072161385, 99.515709324456, 99.561683...</td>\n",
       "      <td>{'id': []}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Net flux</td>\n",
       "      <td>R2 net</td>\n",
       "      <td>B &lt;-&gt; D</td>\n",
       "      <td>61.150708</td>\n",
       "      <td>0.299002</td>\n",
       "      <td>60.342355</td>\n",
       "      <td>61.896734</td>\n",
       "      <td>[]</td>\n",
       "      <td>1</td>\n",
       "      <td>0.05</td>\n",
       "      <td>[4.424745896389132, 3.7047908218400725, 2.9680...</td>\n",
       "      <td>0</td>\n",
       "      <td>[-0.15515765338299395, 1.0000000000000002, -0....</td>\n",
       "      <td>[-0.008826206497169892, 0.0894022682485085, -0...</td>\n",
       "      <td>[60.282968518148586, 60.359038522070044, 60.44...</td>\n",
       "      <td>{'id': []}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Exch flux</td>\n",
       "      <td>R2 exch</td>\n",
       "      <td>B &lt;-&gt; D</td>\n",
       "      <td>49.849456</td>\n",
       "      <td>1.736105</td>\n",
       "      <td>46.264288</td>\n",
       "      <td>54.217439</td>\n",
       "      <td>[]</td>\n",
       "      <td>1</td>\n",
       "      <td>0.05</td>\n",
       "      <td>[3.952443057055, 3.2156770572216344, 2.4783166...</td>\n",
       "      <td>0</td>\n",
       "      <td>[0.020368852719712092, -0.05313916272317603, 1...</td>\n",
       "      <td>[0.006727739232202212, -0.02758448914464573, 3...</td>\n",
       "      <td>[46.22348883339175, 46.56115197844941, 46.9430...</td>\n",
       "      <td>{'id': []}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Net flux</td>\n",
       "      <td>R3</td>\n",
       "      <td>B -&gt; C + E</td>\n",
       "      <td>19.420784</td>\n",
       "      <td>0.189242</td>\n",
       "      <td>18.938698</td>\n",
       "      <td>19.950753</td>\n",
       "      <td>[]</td>\n",
       "      <td>1</td>\n",
       "      <td>0.05</td>\n",
       "      <td>[4.477920913249516, 3.7258415870429094, 2.9741...</td>\n",
       "      <td>0</td>\n",
       "      <td>[0.6252401109640534, -0.8679919809953349, 0.05...</td>\n",
       "      <td>[0.022510796771899863, -0.04911423737283656, 0...</td>\n",
       "      <td>[18.906085016756712, 18.946067593473966, 18.99...</td>\n",
       "      <td>{'id': []}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Net flux</td>\n",
       "      <td>R4</td>\n",
       "      <td>B + C -&gt; D + E + E</td>\n",
       "      <td>19.420784</td>\n",
       "      <td>0.189242</td>\n",
       "      <td>18.938698</td>\n",
       "      <td>19.950753</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>0.05</td>\n",
       "      <td>[4.477920913249516, 3.7258415870429094, 2.9741...</td>\n",
       "      <td>0</td>\n",
       "      <td>[0.6252401109640534, -0.8679919809953349, 0.05...</td>\n",
       "      <td>[0.022510796771899863, -0.04911423737283656, 0...</td>\n",
       "      <td>[18.906085016756712, 18.946067593473966, 18.99...</td>\n",
       "      <td>{'id': []}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Net flux</td>\n",
       "      <td>R5</td>\n",
       "      <td>D -&gt; F</td>\n",
       "      <td>80.571493</td>\n",
       "      <td>0.164275</td>\n",
       "      <td>80.16627</td>\n",
       "      <td>80.97421</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>0.05</td>\n",
       "      <td>[4.497470340629002, 3.7392448695467877, 2.9799...</td>\n",
       "      <td>0</td>\n",
       "      <td>[0.43785814143479984, 0.8202193590233617, -0.0...</td>\n",
       "      <td>[0.013684590274729971, 0.04028803087567194, -0...</td>\n",
       "      <td>[80.13392503277558, 80.17259342556605, 80.2154...</td>\n",
       "      <td>{'id': []}</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        type       id                 eqn        val       std         lb  \\\n",
       "0   Net flux       R1              A -> B  99.992277  0.190251   99.51167   \n",
       "1   Net flux   R2 net             B <-> D  61.150708  0.299002  60.342355   \n",
       "2  Exch flux  R2 exch             B <-> D  49.849456  1.736105  46.264288   \n",
       "3   Net flux       R3          B -> C + E  19.420784  0.189242  18.938698   \n",
       "4   Net flux       R4  B + C -> D + E + E  19.420784  0.189242  18.938698   \n",
       "5   Net flux       R5              D -> F  80.571493  0.164275   80.16627   \n",
       "\n",
       "           ub unit  free   alf  \\\n",
       "0  100.479345   []     0  0.05   \n",
       "1   61.896734   []     1  0.05   \n",
       "2   54.217439   []     1  0.05   \n",
       "3   19.950753   []     1  0.05   \n",
       "4   19.950753   []     0  0.05   \n",
       "5    80.97421   []     0  0.05   \n",
       "\n",
       "                                               chi2s  cont  \\\n",
       "0  [4.570265356139303, 3.793349715129606, 3.09763...     0   \n",
       "1  [4.424745896389132, 3.7047908218400725, 2.9680...     0   \n",
       "2  [3.952443057055, 3.2156770572216344, 2.4783166...     0   \n",
       "3  [4.477920913249516, 3.7258415870429094, 2.9741...     0   \n",
       "4  [4.477920913249516, 3.7258415870429094, 2.9741...     0   \n",
       "5  [4.497470340629002, 3.7392448695467877, 2.9799...     0   \n",
       "\n",
       "                                                 cor  \\\n",
       "0  [1.0, -0.15515765338290124, 0.0203688527219357...   \n",
       "1  [-0.15515765338299395, 1.0000000000000002, -0....   \n",
       "2  [0.020368852719712092, -0.05313916272317603, 1...   \n",
       "3  [0.6252401109640534, -0.8679919809953349, 0.05...   \n",
       "4  [0.6252401109640534, -0.8679919809953349, 0.05...   \n",
       "5  [0.43785814143479984, 0.8202193590233617, -0.0...   \n",
       "\n",
       "                                                 cov  \\\n",
       "0  [0.036195387046629834, -0.008826206497164618, ...   \n",
       "1  [-0.008826206497169892, 0.0894022682485085, -0...   \n",
       "2  [0.006727739232202212, -0.02758448914464573, 3...   \n",
       "3  [0.022510796771899863, -0.04911423737283656, 0...   \n",
       "4  [0.022510796771899863, -0.04911423737283656, 0...   \n",
       "5  [0.013684590274729971, 0.04028803087567194, -0...   \n",
       "\n",
       "                                                vals        base  \n",
       "0  [99.46957072161385, 99.515709324456, 99.561683...  {'id': []}  \n",
       "1  [60.282968518148586, 60.359038522070044, 60.44...  {'id': []}  \n",
       "2  [46.22348883339175, 46.56115197844941, 46.9430...  {'id': []}  \n",
       "3  [18.906085016756712, 18.946067593473966, 18.99...  {'id': []}  \n",
       "4  [18.906085016756712, 18.946067593473966, 18.99...  {'id': []}  \n",
       "5  [80.13392503277558, 80.17259342556605, 80.2154...  {'id': []}  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "estimated_fluxes = res.fitdata.fitted_parameters.query(\"type.str.contains('flux')\")\n",
    "estimated_fluxes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we will compare the estimated fluxes to the know simulated fluxes. This is off course only possible because we use simulated data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import true parameter values\n",
    "true_fluxes = pd.read_csv(data_folder / 'simulated_data' / \"true_fluxes.csv\")\n",
    "true_pool_sizes = pd.read_csv(data_folder / 'simulated_data' / \"true_pool_sizes.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x13cf71d20>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "errbars = estimated_fluxes[['lb', 'ub']].subtract(estimated_fluxes['val'], axis=0).abs().T\n",
    "ax.errorbar(x=estimated_fluxes['id'], y=estimated_fluxes['val'], yerr=errbars, color='black', fmt='none', label='95% CI of fitted value')\n",
    "ax.scatter(x=estimated_fluxes['id'], y=estimated_fluxes['val'], color='black', label='fitted value')\n",
    "ax.scatter(x=true_fluxes['rxn_id'], y=true_fluxes['flux'], color='red', label='True flux', s=10)\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that INCAWrapper and INCA was able to obtain unbiased estimates of the true fluxes using INST 13C-MFA. The R2 exchange flux still has some uncertainty, but it is common for exchange fluxes not to be well determined [3]. Lets also inspect the numerical values of the fitted and true fluxes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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>type</th>\n",
       "      <th>id</th>\n",
       "      <th>eqn</th>\n",
       "      <th>true_flux</th>\n",
       "      <th>fitted_flux</th>\n",
       "      <th>std</th>\n",
       "      <th>lb</th>\n",
       "      <th>ub</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Net flux</td>\n",
       "      <td>R1</td>\n",
       "      <td>A -&gt; B</td>\n",
       "      <td>100.000</td>\n",
       "      <td>99.992</td>\n",
       "      <td>0.190</td>\n",
       "      <td>99.51167</td>\n",
       "      <td>100.479345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Net flux</td>\n",
       "      <td>R2 net</td>\n",
       "      <td>B &lt;-&gt; D</td>\n",
       "      <td>61.132</td>\n",
       "      <td>61.151</td>\n",
       "      <td>0.299</td>\n",
       "      <td>60.342355</td>\n",
       "      <td>61.896734</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Exch flux</td>\n",
       "      <td>R2 exch</td>\n",
       "      <td>B &lt;-&gt; D</td>\n",
       "      <td>49.806</td>\n",
       "      <td>49.849</td>\n",
       "      <td>1.736</td>\n",
       "      <td>46.264288</td>\n",
       "      <td>54.217439</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Net flux</td>\n",
       "      <td>R3</td>\n",
       "      <td>B -&gt; C + E</td>\n",
       "      <td>19.434</td>\n",
       "      <td>19.421</td>\n",
       "      <td>0.189</td>\n",
       "      <td>18.938698</td>\n",
       "      <td>19.950753</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Net flux</td>\n",
       "      <td>R4</td>\n",
       "      <td>B + C -&gt; D + E + E</td>\n",
       "      <td>19.434</td>\n",
       "      <td>19.421</td>\n",
       "      <td>0.189</td>\n",
       "      <td>18.938698</td>\n",
       "      <td>19.950753</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Net flux</td>\n",
       "      <td>R5</td>\n",
       "      <td>D -&gt; F</td>\n",
       "      <td>80.566</td>\n",
       "      <td>80.571</td>\n",
       "      <td>0.164</td>\n",
       "      <td>80.16627</td>\n",
       "      <td>80.97421</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        type       id                 eqn  true_flux  fitted_flux    std  \\\n",
       "0   Net flux       R1              A -> B    100.000       99.992  0.190   \n",
       "1   Net flux   R2 net             B <-> D     61.132       61.151  0.299   \n",
       "2  Exch flux  R2 exch             B <-> D     49.806       49.849  1.736   \n",
       "3   Net flux       R3          B -> C + E     19.434       19.421  0.189   \n",
       "4   Net flux       R4  B + C -> D + E + E     19.434       19.421  0.189   \n",
       "5   Net flux       R5              D -> F     80.566       80.571  0.164   \n",
       "\n",
       "          lb          ub  \n",
       "0   99.51167  100.479345  \n",
       "1  60.342355   61.896734  \n",
       "2  46.264288   54.217439  \n",
       "3  18.938698   19.950753  \n",
       "4  18.938698   19.950753  \n",
       "5   80.16627    80.97421  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fitted_and_true_fluxes = (\n",
    "    estimated_fluxes\n",
    "    .merge(true_fluxes, left_on=\"id\", right_on=\"rxn_id\")\n",
    "    .rename(columns={\"val\": \"fitted_flux\", \"flux\": \"true_flux\"})\n",
    ")\n",
    "fitted_and_true_fluxes[['type', 'id', 'eqn', 'true_flux', 'fitted_flux', 'std', 'lb', 'ub']].round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again here we see that the incawrapper (and INCA) finds a good estimate of the true flux distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "[1] M. R. Antoniewicz, J. K. Kelleher, and G. Stephanopoulos, “Determination of confidence intervals of metabolic fluxes estimated from stable isotope measurements,” Metabolic Engineering, vol. 8, no. 4, pp. 324–337, Jul. 2006, doi: 10.1016/j.ymben.2006.01.004.\n",
    "\n",
    "[2] M. R. Antoniewicz, J. K. Kelleher, and G. Stephanopoulos, “Elementary metabolite units (EMU): A novel framework for modeling isotopic distributions,” Metabolic Engineering, vol. 9, no. 1, pp. 68–86, Jan. 2007, doi: 10.1016/j.ymben.2006.09.001.\n",
    "\n",
    "[3] W. Wiechert and K. Nöh, “Quantitative Metabolic Flux Analysis Based on Isotope Labeling,” in Metabolic Engineering, 1st ed., J. Nielsen, G. Stephanopoulos, and S. Y. Lee, Eds., Wiley, 2021, pp. 73–136. doi: 10.1002/9783527823468.ch3.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "bfair-testing",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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