.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/_4_unorganized/plot_olivine_control_line.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples__4_unorganized_plot_olivine_control_line.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples__4_unorganized_plot_olivine_control_line.py:


MELTS: Calculate Olivine Control Line
=====================================

Extrapolates a melt composition to a more primitive composition under the assumption that only olivine has crystallised from the melt. This calculation might be used for estimating primary melt compositions, or the effect of post-entrapment crystallisation on olivine-hosted melt inclusions.

The calculation uses the rhyoliteMELTS v1.2 model.

Open this code in an executable MyBinder instance (MyBinder links may be slow to load-- please be patient!):

.. image:: https://mybinder.org/badge_logo.svg
  :target: https://mybinder.org/v2/gl/swmatthews-research%2FThermoEngineLite/main?urlpath=%2Fdoc%2Ftree%2F.%2Fdoc%2Fsource%2Fauto_examples%2F_4_unorganized%2Fplot_olivine_control_line.ipynb

.. GENERATED FROM PYTHON SOURCE LINES 17-21

Initialization
--------------

Import the necessary packages

.. GENERATED FROM PYTHON SOURCE LINES 21-29

.. code-block:: Python


    from thermoengine import model, magmaforge, redox
    from thermoengine.core import chem
    import pandas as pd
    import numpy as np
    from scipy.optimize import root_scalar
    import matplotlib.pyplot as plt








.. GENERATED FROM PYTHON SOURCE LINES 30-31

Retrieve the MELTS v1.2 database and extract the olivine and liquid models.

.. GENERATED FROM PYTHON SOURCE LINES 31-36

.. code-block:: Python


    db = model.Database("MELTS_v1_2")
    liq = db.get_phase('Liq')
    olv = db.get_phase('Ol')








.. GENERATED FROM PYTHON SOURCE LINES 37-39

Set up the Calculations
-----------------------

.. GENERATED FROM PYTHON SOURCE LINES 41-44

This section sets up the algorithm for incrementally finding the equilibrium olivine composition at the liquidus, adding a small amount of it into the melt, and repeating.

 You must run the cells below, but you do not need to change anything inside them to run a calculation.

.. GENERATED FROM PYTHON SOURCE LINES 44-184

.. code-block:: Python


    def calculate_olivine_control_line(
            starting_comp : pd.Series,
            P_bar : float,
            target_Mgn : float,
            step_size : float = 0.005
            ) -> tuple[pd.DataFrame,
                       pd.DataFrame]:
        """
        Calculate an olivine control line, starting at the start composition and
        ending when the equilibrium olivine has the target Mgn. The Fe3/tFe ratio
        must be set in the starting_comp.

        Inputs
        ------
        starting_comp : pd.Series
            The starting composition in weight percent (or grams) of oxides
        P_bar : float
            The pressure in bars
        target_Mgn : float
            The olivine Mgn at which to terminate the calculation
        step_size : float
            The moles of olivine to add to the liquid composition at each step
    
        Outputs
        -------
        pd.DataFrame
            The melt compositions at each step on the olivine control line
        pd.DataFrame
            The olivine compositions at each step on the olivine control line
        """

        if 'Fe2O3' not in starting_comp or starting_comp['Fe2O3'] == 0.0:
            print("Warning: Fe2O3 set to 0.0")
        if 'FeO' not in starting_comp or starting_comp['FeO'] == 0.0:
            print("Warning: FeO is set to 0.0")
    
        if target_Mgn > 1 and target_Mgn < 100:
            target_Mgn = target_Mgn / 100
        elif target_Mgn > 100 or target_Mgn < 0:
            assert False, "Bad target Mg number."

        start_comp_arr = np.zeros(len(chem.OXIDE_ORDER))
        for i, ox in zip(range(len(chem.OXIDE_ORDER)), chem.OXIDE_ORDER):
            if ox in starting_comp:
                start_comp_arr[i] = starting_comp[ox]
            else:
                start_comp_arr[i] = 0.0
        start_comp_arr = start_comp_arr / np.sum(start_comp_arr) * 100

        liq_moles = magmaforge.System.convert_wtoxides_to_liquid_endmems(
            starting_comp, liq, oxides=starting_comp.index)
    
        olv_omni_comps = _calc_omni_comps_for_phases(olv, liq)


        T, olv_mols = find_liquidus_olivine(P_bar, liq_moles, olv_omni_comps)
        Mgn = olv_mols[5]/(olv_mols[1]+olv_mols[5])    
    
        MAX_ITER = 1000
        iternum = 0

        check_phase_sat(T, P_bar, starting_comp)

        # Initialise dataframes for results
        liq_comps = np.zeros([MAX_ITER, len(chem.OXIDE_ORDER)])
        olv_comps = np.zeros([MAX_ITER, olv.endmember_num+1])
        liq_comps[0,:] = start_comp_arr
        olv_comps[0,:-1] = olv_mols
        olv_comps[0,-1] = Mgn 
        T_seq = [T]

        while Mgn < target_Mgn and iternum < MAX_ITER:
            liq_moles += step_size * olv_omni_comps.T.dot(olv_mols)

            T, olv_mols = find_liquidus_olivine(P_bar, liq_moles, olv_omni_comps, T0=T)
            Mgn = olv_mols[5]/(olv_mols[1]+olv_mols[5])

            liq_mol_ox = liq.endmember_mol_oxide_comps.T.dot(liq_moles)
            liq_wtpt = chem.mol_to_wt_oxide(liq_mol_ox, chem.OXIDE_ORDER)
            liq_wtpt = liq_wtpt/np.sum(liq_wtpt) * 100
            liq_comps[iternum+1,:] = liq_wtpt


            olv_comps[iternum+1,:-1] = olv_mols
            olv_comps[iternum+1, -1] = Mgn
            T_seq.append(T)
            iternum += 1
    
        liq_comps = pd.DataFrame(liq_comps[:iternum+1,:], columns=chem.OXIDE_ORDER, index=T_seq)
        olv_comps = pd.DataFrame(olv_comps[:iternum+1,:], 
                                 columns=list(olv.endmember_names)+['Mg#'], 
                                 index=T_seq)
    
        return liq_comps, olv_comps


    def find_liquidus_olivine(P, liq_moles, olv_omni_comps, T0=1500.0):
        res = root_scalar(_affncomp_root, x0=T0, args=(P, liq_moles, olv_omni_comps))
        assert res.converged, "Something has gone wrong when finding the temperature, check inputs."
        T = res.root
        affn, comp = get_olv_affncomp_from_liq(T, P, liq_moles, olv_omni_comps)
        return T, comp

    
    def _affncomp_root(T, P, liq_moles, omni_comps):
        return get_olv_affncomp_from_liq(T, P, liq_moles, omni_comps)[0]

    def get_olv_affncomp_from_liq(T, P, liq_moles, omni_comps):
        liq_mu = liq.chem_potential(T, P, mol=liq_moles)
        olv_mu = omni_comps.dot(liq_mu)
        affn, comp = olv.affinity_and_comp(T, P, olv_mu)
        return (affn, comp)

    def _calc_omni_comps_for_phases(phase, omni_phase):
        """
        Calculates the matrix for conversion of phase compositions into
        omni_component endmembers.
        """

        omni_element_comps = omni_phase.endmember_element_comps
        inv_omni_element_comps = np.linalg.pinv(omni_element_comps)

        TOL = 1e-12

        phs_element_comps = phase.endmember_element_comps
        phs_omni_comps = phs_element_comps.dot(inv_omni_element_comps)

        phs_omni_comps[np.abs(phs_omni_comps) <= TOL] = 0
        
        return phs_omni_comps

    def check_phase_sat(T, P, oxide_wtpt):
        sys = magmaforge.System(oxide_wtpt, T_K=T, P_bar=P, database='MELTS_v1_2')
        phs_mass = sys._system_calculator._total_mass_of_every_phase

        for phs in phs_mass:
            if phs not in ['Liquid', 'Olivine'] and phs_mass[phs] > 0.0:
                print(f"Warning: {phs} is saturated: {phs_mass[phs]:.2f} wt% present at olvine-saturation temperature.")








.. GENERATED FROM PYTHON SOURCE LINES 185-189

User Inputs
-----------

Provide the starting composition of the magma here. You must have already determined the amount of FeO and Fe2O3 in the magma.

.. GENERATED FROM PYTHON SOURCE LINES 189-208

.. code-block:: Python


    oxide_comp = pd.Series({
                            'SiO2':  48.32,
                            'TiO2':   0.93,
                            'Al2O3': 15.99,
                            'Fe2O3':  0.67,
                            'FeO':    8.36,
                            'MnO':    0.16,
                            'MgO':   10.56,
                            'CaO':   14.01,
                            'Na2O':   1.72,
                            'K2O':    0.05,
                            'P2O5':   0.03,
                            'H2O':    0.3,
                            'CO2':    0.05
                            })
    # Composition of olivine-saturated glass from Kistufell, Iceland (Breddam, 2002)









.. GENERATED FROM PYTHON SOURCE LINES 209-210

Provide the pressure of crystallisation and the target Mg# for the equilibrium olivine:

.. GENERATED FROM PYTHON SOURCE LINES 210-214

.. code-block:: Python


    pressure_bar = 1000.0
    target_Mgn = 90.0








.. GENERATED FROM PYTHON SOURCE LINES 215-216

Run the calculation:

.. GENERATED FROM PYTHON SOURCE LINES 216-224

.. code-block:: Python


    liq_comp, olv_comp = calculate_olivine_control_line(
                                                oxide_comp, 
                                                P_bar=1000.0, 
                                                target_Mgn=90.0
                                                )









.. GENERATED FROM PYTHON SOURCE LINES 225-229

Results
-------

We can see the results as tables of the liquid and olivine compositions along the extrapolated liquid line of descent:

.. GENERATED FROM PYTHON SOURCE LINES 229-232

.. code-block:: Python


    liq_comp






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
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          <th>Fe2O3</th>
          <th>Cr2O3</th>
          <th>FeO</th>
          <th>MnO</th>
          <th>MgO</th>
          <th>NiO</th>
          <th>CoO</th>
          <th>CaO</th>
          <th>Na2O</th>
          <th>K2O</th>
          <th>P2O5</th>
          <th>H2O</th>
          <th>CO2</th>
        </tr>
      </thead>
      <tbody>
        <tr>
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          <td>8.264953</td>
          <td>0.158181</td>
          <td>10.439941</td>
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          <td>0.0</td>
          <td>13.850717</td>
          <td>1.700445</td>
          <td>0.049432</td>
          <td>0.029659</td>
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          <td>0.0</td>
          <td>8.601571</td>
          <td>0.163671</td>
          <td>14.774027</td>
          <td>0.0</td>
          <td>0.0</td>
          <td>12.295010</td>
          <td>1.502227</td>
          <td>0.043669</td>
          <td>0.026202</td>
          <td>0.262016</td>
          <td>0.043669</td>
        </tr>
        <tr>
          <th>1613.925060</th>
          <td>46.886007</td>
          <td>0.807062</td>
          <td>13.876258</td>
          <td>0.581432</td>
          <td>0.0</td>
          <td>8.608117</td>
          <td>0.163780</td>
          <td>14.992167</td>
          <td>0.0</td>
          <td>0.0</td>
          <td>12.219389</td>
          <td>1.492631</td>
          <td>0.043390</td>
          <td>0.026034</td>
          <td>0.260343</td>
          <td>0.043390</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 233-236

.. code-block:: Python


    olv_comp






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>Tephroite</th>
          <th>Fayalite</th>
          <th>Coolivine</th>
          <th>Niolivine</th>
          <th>Monticellite</th>
          <th>Forsterite</th>
          <th>Mg#</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>1499.443504</th>
          <td>0.002446</td>
          <td>0.133909</td>
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          <th>1506.843444</th>
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          <td>0.014584</td>
          <td>0.851877</td>
          <td>0.866598</td>
        </tr>
        <tr>
          <th>1514.052214</th>
          <td>0.002361</td>
          <td>0.128498</td>
          <td>0.0</td>
          <td>0.0</td>
          <td>0.014396</td>
          <td>0.854745</td>
          <td>0.869312</td>
        </tr>
        <tr>
          <th>1521.078311</th>
          <td>0.002322</td>
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          <td>0.014210</td>
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          <td>0.871899</td>
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        <tr>
          <th>1527.929701</th>
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        <tr>
          <th>1534.613862</th>
          <td>0.002247</td>
          <td>0.121293</td>
          <td>0.0</td>
          <td>0.0</td>
          <td>0.013859</td>
          <td>0.862601</td>
          <td>0.876721</td>
        </tr>
        <tr>
          <th>1541.137830</th>
          <td>0.002212</td>
          <td>0.119102</td>
          <td>0.0</td>
          <td>0.0</td>
          <td>0.013691</td>
          <td>0.864995</td>
          <td>0.878974</td>
        </tr>
        <tr>
          <th>1547.508210</th>
          <td>0.002178</td>
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          <td>0.881130</td>
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          <th>1553.731227</th>
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          <td>0.883197</td>
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        <tr>
          <th>1559.812738</th>
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        </tr>
        <tr>
          <th>1565.758290</th>
          <td>0.002084</td>
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          <td>0.873644</td>
          <td>0.887083</td>
        </tr>
        <tr>
          <th>1571.573099</th>
          <td>0.002055</td>
          <td>0.109423</td>
          <td>0.0</td>
          <td>0.0</td>
          <td>0.012920</td>
          <td>0.875602</td>
          <td>0.888913</td>
        </tr>
        <tr>
          <th>1577.262098</th>
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        <tr>
          <th>1582.829955</th>
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        </tr>
        <tr>
          <th>1588.281088</th>
          <td>0.001973</td>
          <td>0.104463</td>
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          <td>0.881060</td>
          <td>0.894002</td>
        </tr>
        <tr>
          <th>1593.619682</th>
          <td>0.001948</td>
          <td>0.102927</td>
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        </tr>
        <tr>
          <th>1598.849698</th>
          <td>0.001923</td>
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          <td>0.897098</td>
        </tr>
        <tr>
          <th>1603.974914</th>
          <td>0.001899</td>
          <td>0.100011</td>
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          <td>0.0</td>
          <td>0.012117</td>
          <td>0.885972</td>
          <td>0.898567</td>
        </tr>
        <tr>
          <th>1608.998902</th>
          <td>0.001876</td>
          <td>0.098626</td>
          <td>0.0</td>
          <td>0.0</td>
          <td>0.011994</td>
          <td>0.887504</td>
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        </tr>
        <tr>
          <th>1613.925060</th>
          <td>0.001853</td>
          <td>0.097287</td>
          <td>0.0</td>
          <td>0.0</td>
          <td>0.011874</td>
          <td>0.888986</td>
          <td>0.901359</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 237-238

We can save the tables (which can be downloaded if you are running this in a binder):

.. GENERATED FROM PYTHON SOURCE LINES 238-242

.. code-block:: Python


    liq_comp.to_csv('liquid_compositions.csv')
    olv_comp.to_csv('olivine_compositions.csv')








.. GENERATED FROM PYTHON SOURCE LINES 243-244

But we can also plot the results:

.. GENERATED FROM PYTHON SOURCE LINES 244-260

.. code-block:: Python


    fig, ax = plt.subplots(3,1, figsize=(3.75, 7))

    ax[0].plot(liq_comp['MgO'], liq_comp['FeO'], marker='s', markersize=3)
    ax[1].plot(liq_comp['MgO'], olv_comp['Mg#']*100, marker='s', markersize=3)
    ax[2].plot(liq_comp['MgO'], liq_comp.index - 273.15, marker='s', markersize=3)

    for a in ax:
        a.set_xlabel('MgO (wt%)')

    ax[0].set_ylabel('FeO (wt%)')
    ax[1].set_ylabel('Fo (mol%)')
    ax[2].set_ylabel('Temperature (°C)')

    fig.tight_layout()

    plt.show()


.. image-sg:: /auto_examples/_4_unorganized/images/sphx_glr_plot_olivine_control_line_001.png
   :alt: plot olivine control line
   :srcset: /auto_examples/_4_unorganized/images/sphx_glr_plot_olivine_control_line_001.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.418 seconds)


.. _sphx_glr_download_auto_examples__4_unorganized_plot_olivine_control_line.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_olivine_control_line.ipynb <plot_olivine_control_line.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_olivine_control_line.py <plot_olivine_control_line.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_olivine_control_line.zip <plot_olivine_control_line.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_