Constrain

A simple example that demonstrates the constrain method of mass-composition.

It is possible that a MassComposition object is created from a Machine Learning Model estimation. If either the ML model is over-fitted, or the features supplied to create the estimation are out of range, improbable results can be generated. The constrain method will provide a way to manage these outliers.

import pandas as pd

from elphick.mass_composition import MassComposition
from elphick.mass_composition.datasets.sample_data import sample_data

Create a MassComposition object

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

df_data: pd.DataFrame = sample_data()
df_data

	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

obj_mc: MassComposition = MassComposition(df_data)
obj_mc.data.to_dataframe()

	mass_wet	mass_dry	H2O	Fe	SiO2	Al2O3	LOI	group
index
0	100.0	90.0	10.000000	57.0	5.2	3.0	5.0	grp_1
1	90.0	80.0	11.111111	59.0	3.1	1.7	4.0	grp_1
2	110.0	90.0	18.181818	61.0	2.2	0.9	3.0	grp_2

Constraining by Clip

Constraining by clip simpy clips the mass or composition values. The simplest way to constrain is with a tuple of the limits.

obj_1: MassComposition = obj_mc.constrain(clip_mass=(85, 100))
obj_1.data.to_dataframe()

	mass_wet	mass_dry	H2O	Fe	SiO2	Al2O3	LOI	group
index
0	100.0	90.0	10.000000	57.0	5.2	3.0	5.0	grp_1
1	90.0	85.0	5.555556	59.0	3.1	1.7	4.0	grp_1
2	100.0	90.0	10.000000	61.0	2.2	0.9	3.0	grp_2

Notice that the mass has been constrained for some records and the H2O has been modified accordingly.

More granularity is possible by passing a dict[variable: tuple_of_limits]

obj_2: MassComposition = obj_mc.constrain(clip_mass={'mass_wet': (0, 100)})
obj_2.data.to_dataframe()

	mass_wet	mass_dry	H2O	Fe	SiO2	Al2O3	LOI	group
index
0	100.0	90.0	10.000000	57.0	5.2	3.0	5.0	grp_1
1	90.0	80.0	11.111111	59.0	3.1	1.7	4.0	grp_1
2	100.0	90.0	10.000000	61.0	2.2	0.9	3.0	grp_2

Constraining Relative to Another Object

Sometimes constraining relative to another object is useful. This can be described as “constraining by recovery”. The object is converted to absolute mass (where components are converted to mass units) and divided by the reference (other) object, also converted to mass units. In mineral processing, this is known as recovery.

First we’ll make another object to act as our reference.

obj_other: MassComposition = obj_mc.add(obj_mc, name='feed')

obj_3: MassComposition = obj_mc.constrain(relative_mass=(0.0, 0.1), other=obj_other)
obj_3.data.to_dataframe()

	mass_wet	mass_dry	H2O	Fe	SiO2	Al2O3	LOI	group
index
0	20.0	18.0	10.000000	57.0	5.2	3.0	5.0	grp_1
1	18.0	16.0	11.111111	59.0	3.1	1.7	4.0	grp_1
2	22.0	18.0	18.181818	61.0	2.2	0.9	3.0	grp_2

Here we constrain Fe to 10% recovery of 2 x the original object…

obj_4: MassComposition = obj_mc.constrain(relative_composition={'Fe': (0.0, 0.1)}, other=obj_other)
obj_4.data.to_dataframe()

	mass_wet	mass_dry	H2O	Fe	SiO2	Al2O3	LOI	group
index
0	100.0	90.0	10.000000	11.4	5.2	3.0	5.0	grp_1
1	90.0	80.0	11.111111	11.8	3.1	1.7	4.0	grp_1
2	110.0	90.0	18.181818	12.2	2.2	0.9	3.0	grp_2

Arguments can be combined to perform multiple constraints in one call.

obj_5: MassComposition = obj_mc.constrain(clip_mass=(85, 100),
                                          relative_composition={'Fe': (0.0, 0.1)}, other=obj_other)
obj_5.data.to_dataframe()

	mass_wet	mass_dry	H2O	Fe	SiO2	Al2O3	LOI	group
index
0	100.0	90.0	10.000000	11.4	5.2	3.0	5.0	grp_1
1	90.0	80.0	11.111111	11.8	3.1	1.7	4.0	grp_1
2	110.0	90.0	18.181818	12.2	2.2	0.9	3.0	grp_2