.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/400_mass_balancing.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_400_mass_balancing.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_400_mass_balancing.py:


Mass Balancing
==============

In the examples so far, Flowsheet objects are created by math operations, so they inherently balance.
A common problem in Mineral Processing (Metallurgy/Chemical/Process Engineering) is mass (or metallurgical) balancing.
When auditing a processing plant the data is collected by measurement and sampling/assaying. This data will never
balance of course due to sampling and measurement errors.

There exists a fundamental optimisation process that can balance the overall mass and components across a
system (network/flowsheet).  This example demonstrates that functionality.

.. GENERATED FROM PYTHON SOURCE LINES 14-28

.. code-block:: default

    import logging
    from functools import partial
    from typing import Dict

    import numpy as np
    import pandas as pd
    import plotly

    from elphick.mass_composition import MassComposition
    from elphick.mass_composition.balance import MCBalance
    from elphick.mass_composition.flowsheet import Flowsheet
    from elphick.mass_composition.utils.partition import napier_munn
    from elphick.mass_composition.datasets.sample_data import size_by_assay








.. GENERATED FROM PYTHON SOURCE LINES 29-33

.. code-block:: default

    logging.basicConfig(level=logging.INFO,
                        format='%(asctime)s %(levelname)s %(module)s - %(funcName)s: %(message)s',
                        datefmt='%Y-%m-%dT%H:%M:%S%z')








.. GENERATED FROM PYTHON SOURCE LINES 34-38

Create a MassComposition object
-------------------------------

We get some demo data in the form of a pandas DataFrame

.. GENERATED FROM PYTHON SOURCE LINES 39-43

.. code-block:: default


    df_data: pd.DataFrame = size_by_assay()
    df_data






.. 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></th>
          <th>mass_dry</th>
          <th>fe</th>
          <th>sio2</th>
          <th>al2o3</th>
        </tr>
        <tr>
          <th>size_retained</th>
          <th>size_passing</th>
          <th></th>
          <th></th>
          <th></th>
          <th></th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0.850</th>
          <th>2.000</th>
          <td>3.3</td>
          <td>64.15</td>
          <td>2.04</td>
          <td>2.68</td>
        </tr>
        <tr>
          <th>0.500</th>
          <th>0.850</th>
          <td>9.9</td>
          <td>64.33</td>
          <td>2.05</td>
          <td>2.23</td>
        </tr>
        <tr>
          <th>0.150</th>
          <th>0.500</th>
          <td>26.5</td>
          <td>64.52</td>
          <td>1.84</td>
          <td>2.19</td>
        </tr>
        <tr>
          <th>0.075</th>
          <th>0.150</th>
          <td>2.5</td>
          <td>62.65</td>
          <td>2.88</td>
          <td>3.32</td>
        </tr>
        <tr>
          <th>0.045</th>
          <th>0.075</th>
          <td>8.8</td>
          <td>62.81</td>
          <td>2.12</td>
          <td>2.25</td>
        </tr>
        <tr>
          <th>0.000</th>
          <th>0.045</th>
          <td>49.0</td>
          <td>55.95</td>
          <td>6.39</td>
          <td>6.34</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 44-45

Create the object

.. GENERATED FROM PYTHON SOURCE LINES 45-50

.. code-block:: default


    mc_size: MassComposition = MassComposition(df_data, name='size sample')
    print(mc_size)
    mc_size.aggregate()





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    size sample
    <xarray.Dataset> Size: 336B
    Dimensions:   (size: 6)
    Coordinates:
      * size      (size) object 48B [0.85, 2.0) [0.5, 0.85) ... [0.0, 0.045)
    Data variables:
        mass_wet  (size) float64 48B 3.3 9.9 26.5 2.5 8.8 49.0
        mass_dry  (size) float64 48B 3.3 9.9 26.5 2.5 8.8 49.0
        H2O       (size) float64 48B 0.0 0.0 0.0 0.0 0.0 0.0
        Fe        (size) float64 48B 64.15 64.33 64.52 62.65 62.81 55.95
        SiO2      (size) float64 48B 2.04 2.05 1.84 2.88 2.12 6.39
        Al2O3     (size) float64 48B 2.68 2.23 2.19 3.32 2.25 6.34
    Attributes:
        mc_name:            size sample
        mc_vars_mass:       ['mass_wet', 'mass_dry']
        mc_vars_chem:       ['Fe', 'SiO2', 'Al2O3']
        mc_vars_attrs:      []
        mc_interval_edges:  {'size': {'left': 'retained', 'right': 'passing'}}


.. 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>mass_wet</th>
          <th>mass_dry</th>
          <th>H2O</th>
          <th>Fe</th>
          <th>SiO2</th>
          <th>Al2O3</th>
        </tr>
        <tr>
          <th>name</th>
          <th></th>
          <th></th>
          <th></th>
          <th></th>
          <th></th>
          <th></th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>size sample</th>
          <td>100.0</td>
          <td>100.0</td>
          <td>0.0</td>
          <td>60.09245</td>
          <td>4.14753</td>
          <td>4.27716</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 51-53

We partially initialise a partition function
The dim argument is added to inform the split method which dimension to apply the function/split to

.. GENERATED FROM PYTHON SOURCE LINES 54-57

.. code-block:: default


    partition = partial(napier_munn, d50=0.150, ep=0.1, dim='size')








.. GENERATED FROM PYTHON SOURCE LINES 58-62

Create a Network that balances
------------------------------

Separate the object using the defined partition

.. GENERATED FROM PYTHON SOURCE LINES 62-71

.. code-block:: default


    mc_coarse, mc_fine = mc_size.split_by_partition(partition_definition=partition, name_1='coarse', name_2='fine')

    fs: Flowsheet = Flowsheet().from_streams([mc_size, mc_coarse, mc_fine])
    print(fs.balanced)

    fig = fs.table_plot(plot_type='network', table_pos='left', table_area=0.3)
    fig





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    True


.. raw:: html

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    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 72-73

Demonstrate that the data balances with the balance plot

.. GENERATED FROM PYTHON SOURCE LINES 74-79

.. code-block:: default


    fig = fs.plot_balance()
    # noinspection PyTypeChecker
    plotly.io.show(fig)  # this call to show will set the thumbnail for the gallery




.. raw:: html
    :file: images/sphx_glr_400_mass_balancing_001.html





.. GENERATED FROM PYTHON SOURCE LINES 80-81

The balance plot can be colored by a specified column or index/dimension.

.. GENERATED FROM PYTHON SOURCE LINES 82-86

.. code-block:: default


    fig = fs.plot_balance(color='size')
    fig






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>                        <script type="text/javascript">window.PlotlyConfig = {MathJaxConfig: 'local'};</script>
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    <br />

.. GENERATED FROM PYTHON SOURCE LINES 87-91

Create an imbalanced network
----------------------------

Modify one stream to corrupt the balance

.. GENERATED FROM PYTHON SOURCE LINES 91-103

.. code-block:: default


    df_coarse_2 = mc_coarse.data.to_dataframe().apply(lambda x: np.random.normal(loc=x, scale=np.std(x)))
    mc_coarse_2: MassComposition = MassComposition(data=df_coarse_2, name='coarse')
    mc_coarse_2 = mc_coarse_2.set_parent_node(mc_size)

    # create a new network - which does not balance
    fs_ub: Flowsheet = Flowsheet().from_streams([mc_size, mc_coarse_2, mc_fine])
    print(fs_ub.balanced)

    fig = fs_ub.table_plot(plot_type='network', table_pos='left', table_area=0.3)
    fig





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    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 108-110

Balance the Flowsheet
---------------------

.. GENERATED FROM PYTHON SOURCE LINES 112-115

..  note::

    This example has not yet been completed...

.. GENERATED FROM PYTHON SOURCE LINES 115-135

.. code-block:: default


    mcb: MCBalance = MCBalance(fs=fs_ub)

    # SD configuration
    # df_sds: pd.DataFrame = mcb.create_balance_config(best_measurements='input')

    # cost functions
    cfs: Dict = mcb._create_cost_functions()
    # check for a zero cost when passing the measured values
    for k, v in cfs.items():
        x = mcb.fs.to_dataframe().loc[k, :].drop(columns=['mass_wet']).values.ravel()
        y = v(x=x)
        print(k, y)

    df_bal: pd.DataFrame = mcb.optimise()

    # create a network using the balanced data
    fs_bal: Flowsheet = Flowsheet.from_dataframe(df=df_bal, name='balanced', mc_name_col='name')
    fig = fs_bal.plot_parallel(color='name')
    fig.show()




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:72: RuntimeWarning:

    invalid value encountered in divide

    [0.85, 2.0) 44.18414624507857
    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:72: RuntimeWarning:

    invalid value encountered in divide

    [0.5, 0.85) 102.68716348473487
    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:72: RuntimeWarning:

    invalid value encountered in divide

    [0.15, 0.5) 6822.474633349426
    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:72: RuntimeWarning:

    invalid value encountered in divide

    [0.075, 0.15) 1299.7196730403964
    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:72: RuntimeWarning:

    invalid value encountered in divide

    [0.045, 0.075) 12.624316443587384
    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:72: RuntimeWarning:

    invalid value encountered in divide

    [0.0, 0.045) 44.12603423431622
    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:202: RuntimeWarning:

    Method powell cannot handle constraints.

    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:202: OptimizeWarning:

    Unknown solver options: xatol

    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:72: RuntimeWarning:

    invalid value encountered in divide

    Optimization terminated successfully.
             Current function value: 2.850809
             Iterations: 5
             Function evaluations: 1457
                    Al2O3        Fe        H2O          SiO2      mass_dry  size
    name                                                                        
    Node_in -7.002935e-05 -0.034756   0.000000  1.314848e-05 -5.095644e-02   NaN
    coarse   1.096296e-02  3.196257 -14.036747 -8.560657e-04  4.524572e+00   NaN
    fine     2.213041e-08  0.000011   0.000000  2.603801e-09  5.310747e-11   NaN
    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:202: RuntimeWarning:

    Method powell cannot handle constraints.

    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:202: OptimizeWarning:

    Unknown solver options: xatol

    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:72: RuntimeWarning:

    invalid value encountered in divide

    Optimization terminated successfully.
             Current function value: 6.922607
             Iterations: 11
             Function evaluations: 2729
                Al2O3        Fe        H2O      SiO2  mass_dry  size
    name                                                            
    Node_in  0.000078 -0.018427   0.000000 -0.000417  0.003000   NaN
    coarse  -0.003995  1.305829 -32.769922  0.082481  7.984925   NaN
    fine    -0.002750  0.683671   0.000000  0.014384 -3.448308   NaN
    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:202: RuntimeWarning:

    Method powell cannot handle constraints.

    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:202: OptimizeWarning:

    Unknown solver options: xatol

    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:72: RuntimeWarning:

    invalid value encountered in divide

    Optimization terminated successfully.
             Current function value: 1.994857
             Iterations: 52
             Function evaluations: 10763
                Al2O3        Fe         H2O      SiO2   mass_dry  size
    name                                                              
    Node_in  0.001444 -0.191930    0.000000  0.001535  -0.985332   NaN
    coarse  -0.031624 -1.757421  -24.001292 -0.010482  10.265487   NaN
    fine    -0.073742  0.038438 -357.364351 -0.080776  -7.259364   NaN
    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:202: RuntimeWarning:

    Method powell cannot handle constraints.

    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:202: OptimizeWarning:

    Unknown solver options: xatol

    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:72: RuntimeWarning:

    invalid value encountered in divide

    Optimization terminated successfully.
             Current function value: 21.834363
             Iterations: 6
             Function evaluations: 1501
                Al2O3         Fe         H2O      SiO2  mass_dry  size
    name                                                              
    Node_in -0.000113  -0.178690    0.000000 -0.000048 -0.060996   NaN
    coarse   0.014591  10.036741  277.107219  0.004394  6.440876   NaN
    fine     0.004370   5.484283    0.000000  0.001844  0.562201   NaN
    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:202: RuntimeWarning:

    Method powell cannot handle constraints.

    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:202: OptimizeWarning:

    Unknown solver options: xatol

    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:72: RuntimeWarning:

    invalid value encountered in divide

    Optimization terminated successfully.
             Current function value: 0.410410
             Iterations: 6
             Function evaluations: 1497
                Al2O3        Fe        H2O      SiO2  mass_dry  size
    name                                                            
    Node_in  0.000040 -0.003939   0.000000 -0.000010  0.017871   NaN
    coarse   0.000738 -0.044401  19.263268 -0.000028 -0.102159   NaN
    fine    -0.004298 -0.122773   0.000000  0.001070 -2.807691   NaN
    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:202: RuntimeWarning:

    Method powell cannot handle constraints.

    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:202: OptimizeWarning:

    Unknown solver options: xatol

    /home/runner/work/mass-composition/mass-composition/elphick/mass_composition/balance.py:72: RuntimeWarning:

    invalid value encountered in divide

    Optimization terminated successfully.
             Current function value: 1.042026
             Iterations: 26
             Function evaluations: 4708
                Al2O3        Fe       H2O      SiO2  mass_dry  size
    name                                                           
    Node_in  0.003753 -0.012161  0.000000 -0.013599 -0.080565   NaN
    coarse  -0.081375 -0.100791 -0.081055  0.599332  0.897935   NaN
    fine    -0.219394  0.237840  9.380482  0.684675  3.839377   NaN

    Preparing MassComposition data:   0%|          | 0/3 [00:00<?, ?it/s]
    Preparing MassComposition data: 100%|##########| 3/3 [00:00<00:00, 552.20it/s]

    Creating MassComposition objects:   0%|          | 0/3 [00:00<?, ?it/s]
    Creating MassComposition objects: 100%|##########| 3/3 [00:00<00:00, 22.76it/s]
    Creating MassComposition objects: 4it [00:00, 30.28it/s]                       





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

   **Total running time of the script:** ( 0 minutes  4.521 seconds)


.. _sphx_glr_download_auto_examples_400_mass_balancing.py:

.. only:: html

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


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

      :download:`Download Python source code: 400_mass_balancing.py <400_mass_balancing.py>`

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

      :download:`Download Jupyter notebook: 400_mass_balancing.ipynb <400_mass_balancing.ipynb>`


.. only:: html

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

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