.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/113_partition_models.py"
.. LINE NUMBERS ARE GIVEN BELOW.
.. only:: html
.. note::
:class: sphx-glr-download-link-note
Click :ref:`here <sphx_glr_download_auto_examples_113_partition_models.py>`
to download the full example code
.. rst-class:: sphx-glr-example-title
.. _sphx_glr_auto_examples_113_partition_models.py:
Partition Models
================
Partition models, (a.k.a. partition curves) define the separation of a unit operation / process.
In the one dimensional case, the Partition Number (PN) is represents the probability that a particle will
report to the defined reference stream.
Consider a desliming cyclone that aims to separate a slurry at 150 micron. The reference stream is defined as
the Underflow (UF), since that is the "stream of value" in our simple example.
.. Admonition:: TODO
Add a reference to partition curves.
.. GENERATED FROM PYTHON SOURCE LINES 18-34
.. code-block:: default
from functools import partial
import numpy as np
import pandas as pd
import plotly
import plotly.graph_objects as go
from scipy.interpolate import PchipInterpolator
from elphick.mass_composition import MassComposition
from elphick.mass_composition.datasets.sample_data import size_by_assay
from elphick.mass_composition.flowsheet import Flowsheet
from elphick.mass_composition.utils.partition import napier_munn
from elphick.mass_composition.utils.pd_utils import calculate_partition
# sphinx_gallery_thumbnail_number = -1
.. GENERATED FROM PYTHON SOURCE LINES 35-39
Create a mass-composition object
--------------------------------
We get some demo data in the form of a pandas DataFrame
.. GENERATED FROM PYTHON SOURCE LINES 40-45
.. code-block:: default
df_data: pd.DataFrame = size_by_assay()
mc_feed: MassComposition = MassComposition(df_data, name='size sample')
print(mc_feed)
.. 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'}}
.. GENERATED FROM PYTHON SOURCE LINES 46-51
Define and Apply the Partition
------------------------------
We partially initialise the 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 51-54
.. code-block:: default
part_cyclone = partial(napier_munn, d50=0.150, ep=0.1, dim='size')
.. GENERATED FROM PYTHON SOURCE LINES 55-56
Separate the object using the defined partitions. UF = Underflow, OF = Overflow
.. GENERATED FROM PYTHON SOURCE LINES 56-64
.. code-block:: default
mc_uf, mc_of = mc_feed.split_by_partition(partition_definition=part_cyclone, name_1='underflow', name_2='overflow')
fs: Flowsheet = Flowsheet().from_streams([mc_feed, mc_uf, mc_of])
fig = fs.table_plot(table_pos='left',
sankey_color_var='Fe', sankey_edge_colormap='copper_r', sankey_vmin=50, sankey_vmax=70)
fig
.. raw:: html
<div class="output_subarea output_html rendered_html output_result">
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<br />
<br />
.. GENERATED FROM PYTHON SOURCE LINES 65-66
We'll now get the partition data from the objects
.. GENERATED FROM PYTHON SOURCE LINES 66-70
.. code-block:: default
df_partition: pd.DataFrame = mc_feed.calculate_partition(ref=mc_uf)
df_partition
.. rst-class:: sphx-glr-script-out
.. code-block:: none
/home/runner/work/mass-composition/mass-composition/elphick/mass_composition/mass_composition.py:1386: FutureWarning:
The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
.. 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>da</th>
<th>PN</th>
</tr>
<tr>
<th>size</th>
<th></th>
<th></th>
</tr>
</thead>
<tbody>
<tr>
<th>[0.85, 2.0)</th>
<td>1.303840</td>
<td>0.999997</td>
</tr>
<tr>
<th>[0.5, 0.85)</th>
<td>0.651920</td>
<td>0.995995</td>
</tr>
<tr>
<th>[0.15, 0.5)</th>
<td>0.273861</td>
<td>0.795960</td>
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<th>[0.075, 0.15)</th>
<td>0.106066</td>
<td>0.381583</td>
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<tr>
<th>[0.045, 0.075)</th>
<td>0.058095</td>
<td>0.266972</td>
</tr>
<tr>
<th>[0.0, 0.045)</th>
<td>0.020855</td>
<td>0.194771</td>
</tr>
</tbody>
</table>
</div>
</div>
<br />
<br />
.. GENERATED FROM PYTHON SOURCE LINES 71-72
Create an interpolator from the data. As a Callable, the spline can be used to split a MassComposition object.
.. GENERATED FROM PYTHON SOURCE LINES 72-77
.. code-block:: default
da = np.linspace(0.01, df_partition.index.right.max(), num=500)
spline_partition = PchipInterpolator(x=df_partition.sort_index()['da'], y=df_partition.sort_index()['PN'])
pn_extracted = spline_partition(da)
.. GENERATED FROM PYTHON SOURCE LINES 78-79
Plot the extracted data, and the spline on the input partition curve to visually validate.
.. GENERATED FROM PYTHON SOURCE LINES 79-94
.. code-block:: default
pn_original = part_cyclone(da) / 100
fig = go.Figure(go.Scatter(x=da, y=pn_original, name='Input Partition', line=dict(width=5, color='DarkSlateGrey')))
fig.add_trace(go.Scatter(x=df_partition['da'], y=df_partition['PN'], name='Extracted Partition Data', mode='markers',
marker=dict(size=12, color='red', line=dict(width=2, color='DarkSlateGrey'))))
fig.add_trace(
go.Scatter(x=da, y=pn_extracted, name='Extracted Partition Curve', line=dict(width=2, color='red', dash='dash')))
fig.update_xaxes(type="log")
fig.update_layout(title='Partition Round Trip Check', xaxis_title='da', yaxis_title='PN', yaxis_range=[0, 1.05])
# noinspection PyTypeChecker
plotly.io.show(fig)
.. raw:: html
:file: images/sphx_glr_113_partition_models_001.html
.. GENERATED FROM PYTHON SOURCE LINES 95-98
There are differences in the re-created partition at the coarser sizes. It would be interesting to
investigate if up-sampling in advance of partition generation would reduce this difference. Alternatively,
the `napier_munn` parameteric partition function could be fitted to reduce the difference.
.. GENERATED FROM PYTHON SOURCE LINES 100-104
Pandas Function
---------------
The same functionality is available in pandas
.. GENERATED FROM PYTHON SOURCE LINES 104-109
.. code-block:: default
df_partition_2: pd.DataFrame = mc_feed.data.to_dataframe().pipe(calculate_partition, df_ref=mc_uf.data.to_dataframe(),
col_mass_dry='mass_dry')
df_partition_2
.. 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>da</th>
<th>PN</th>
</tr>
<tr>
<th>size</th>
<th></th>
<th></th>
</tr>
</thead>
<tbody>
<tr>
<th>[0.85, 2.0)</th>
<td>1.303840</td>
<td>0.999997</td>
</tr>
<tr>
<th>[0.5, 0.85)</th>
<td>0.651920</td>
<td>0.995995</td>
</tr>
<tr>
<th>[0.15, 0.5)</th>
<td>0.273861</td>
<td>0.795960</td>
</tr>
<tr>
<th>[0.075, 0.15)</th>
<td>0.106066</td>
<td>0.381583</td>
</tr>
<tr>
<th>[0.045, 0.075)</th>
<td>0.058095</td>
<td>0.266972</td>
</tr>
<tr>
<th>[0.0, 0.045)</th>
<td>0.020855</td>
<td>0.194771</td>
</tr>
</tbody>
</table>
</div>
</div>
<br />
<br />
.. GENERATED FROM PYTHON SOURCE LINES 110-111
.. code-block:: default
pd.testing.assert_frame_equal(df_partition, df_partition_2)
.. rst-class:: sphx-glr-timing
**Total running time of the script:** ( 0 minutes 0.496 seconds)
.. _sphx_glr_download_auto_examples_113_partition_models.py:
.. only:: html
.. container:: sphx-glr-footer sphx-glr-footer-example
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download Python source code: 113_partition_models.py <113_partition_models.py>`
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: 113_partition_models.ipynb <113_partition_models.ipynb>`
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_