Splitting and Partitioning Objects

Demonstrate splitting by mass and partitioning along dimensions.

import plotly
import pandas as pd
from functools import partial

from elphick.mass_composition.flowsheet import Flowsheet
from elphick.mass_composition.utils.partition import perfect
from elphick.mass_composition.datasets.sample_data import sample_data, size_by_assay
from elphick.mass_composition import MassComposition

# sphinx_gallery_thumbnail_number = -1

Create a mass-composition (mc) enabled Xarray Dataset

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

df_data: pd.DataFrame = sample_data()
df_data.head()

	wet_mass	mass_dry	FE	SIO2	al2o3	LOI	group
index
0	100.0	90.0	57.0	5.2	3.0	5.0	grp_1
1	90.0	80.0	59.0	3.1	1.7	4.0	grp_1
2	110.0	90.0	61.0	2.2	0.9	3.0	grp_2

# Construct a MassComposition object and standardise the chemistry variables

obj_mc: MassComposition = MassComposition(df_data, name='test data')
print(obj_mc)
obj_mc.aggregate()

test data
<xarray.Dataset> Size: 216B
Dimensions:   (index: 3)
Coordinates:
  * index     (index) int64 24B 0 1 2
Data variables:
    mass_wet  (index) float64 24B 100.0 90.0 110.0
    mass_dry  (index) float64 24B 90.0 80.0 90.0
    H2O       (index) float64 24B 10.0 11.11 18.18
    Fe        (index) float64 24B 57.0 59.0 61.0
    SiO2      (index) float64 24B 5.2 3.1 2.2
    Al2O3     (index) float64 24B 3.0 1.7 0.9
    LOI       (index) float64 24B 5.0 4.0 3.0
    group     (index) object 24B 'grp_1' 'grp_1' 'grp_2'
Attributes:
    mc_name:            test data
    mc_vars_mass:       ['mass_wet', 'mass_dry']
    mc_vars_chem:       ['Fe', 'SiO2', 'Al2O3', 'LOI']
    mc_vars_attrs:      ['group']
    mc_interval_edges:  {}

	mass_wet	mass_dry	H2O	Fe	SiO2	Al2O3	LOI
name
test data	300.0	260.0	13.333333	59.0	3.515385	1.873077	4.0

Split by Mass

Split the original Dataset by mass and return both the defined split and complement objects. Splitting with a float, splits mass but does not modify the absolute grade of the input.

obj_mc_split, obj_mc_comp = obj_mc.split(fraction=0.1)
print(obj_mc_split)
obj_mc_split.aggregate()

(0.1 * test data)
<xarray.Dataset> Size: 216B
Dimensions:   (index: 3)
Coordinates:
  * index     (index) int64 24B 0 1 2
Data variables:
    mass_wet  (index) float64 24B 10.0 9.0 11.0
    mass_dry  (index) float64 24B 9.0 8.0 9.0
    H2O       (index) float64 24B 10.0 11.11 18.18
    Fe        (index) float64 24B 57.0 59.0 61.0
    SiO2      (index) float64 24B 5.2 3.1 2.2
    Al2O3     (index) float64 24B 3.0 1.7 0.9
    LOI       (index) float64 24B 5.0 4.0 3.0
    group     (index) object 24B 'grp_1' 'grp_1' 'grp_2'
Attributes:
    mc_name:            (0.1 * test data)
    mc_vars_mass:       ['mass_wet', 'mass_dry']
    mc_vars_chem:       ['Fe', 'SiO2', 'Al2O3', 'LOI']
    mc_vars_attrs:      ['group']
    mc_interval_edges:  {}

	mass_wet	mass_dry	H2O	Fe	SiO2	Al2O3	LOI
name
(0.1 * test data)	30.0	26.0	13.333333	59.0	3.515385	1.873077	4.0

obj_mc_comp.aggregate()

	mass_wet	mass_dry	H2O	Fe	SiO2	Al2O3	LOI
name
(0.9 * test data)	270.0	234.0	13.333333	59.0	3.515385	1.873077	4.0

Add the split and complement parts using the mc.add method

obj_mc_sum: MassComposition = obj_mc_split + obj_mc_comp
obj_mc_sum.aggregate()

	mass_wet	mass_dry	H2O	Fe	SiO2	Al2O3	LOI
name
((0.1 * test data) + (0.9 * test data))	300.0	260.0	13.333333	59.0	3.515385	1.873077	4.0

Confirm the sum of the splits is materially equivalent to the starting object.

pd.testing.assert_frame_equal(obj_mc.data.to_dataframe(), obj_mc_sum.data.to_dataframe())

Partition by Dimension

In mineral processing, unit operations separate particles based on one (or more) property. Consider a sizing screen, separating by size. The characteristics of such separations can be defined by a function. The function is often called a partition curve or tromp curve.

First we load a size x assay dataset, with size fractions as the index. While the data is multidimensional (considering all assays), from the MassComposition object definition it is a 1D dataset (indexed by size).

df_data: pd.DataFrame = size_by_assay()
df_data

		mass_dry	fe	sio2	al2o3
size_retained	size_passing
0.850	2.000	3.3	64.15	2.04	2.68
0.500	0.850	9.9	64.33	2.05	2.23
0.150	0.500	26.5	64.52	1.84	2.19
0.075	0.150	2.5	62.65	2.88	3.32
0.045	0.075	8.8	62.81	2.12	2.25
0.000	0.045	49.0	55.95	6.39	6.34

Create the object

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

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'}}

	mass_wet	mass_dry	H2O	Fe	SiO2	Al2O3
name
size sample	100.0	100.0	0.0	60.09245	4.14753	4.27716

Visualise the data

fig = mc_size.plot_parallel(color='Fe')
fig

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

partition = partial(perfect, d50=0.150, dim='size')

Separate the object using the defined partition

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

fs: Flowsheet = Flowsheet().from_streams([mc_size, mc_coarse, mc_fine])
fig = fs.plot_network()
fig.show()

fig = fs.table_plot(table_pos='top',
                     sankey_color_var='Fe', sankey_edge_colormap='copper_r', sankey_vmin=50, sankey_vmax=70)
# noinspection PyTypeChecker
plotly.io.show(fig)  # this call to show will set the thumbnail for use in the gallery