Grade Tonnage

The “Grade Tonnage” curve is often used to characterise an entire deposit. It is a cumulative view that presents the “mass (tonnes) and head grade” with increasing cut-off grade.

They are useful in comparing deposits.

import pandas as pd
import plotly

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

import xarray as xr

Create a MassComposition object

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

df_data: pd.DataFrame = iron_ore_sample_data()
name = 'A072391'
df_data.drop(columns=['Na2O', 'CaO', 'MnO', 'TiO2', 'P', 'K2O', 'MgO'], inplace=True)

print(df_data.shape)
df_data.head()

(126, 8)

	mass_dry	H2O	Al2O3	Fe	SiO2	DHID	interval_from	interval_to
index
6	2.12	0.35	1.48	64.30	3.23	CBS02	26.60	26.85
7	2.06	0.23	1.28	64.91	2.90	CBS02	26.85	27.10
9	1.91	0.23	1.01	65.09	2.39	CBS02	27.70	28.00
10	1.96	0.36	0.99	65.03	2.22	CBS02	28.00	28.30
12	2.06	0.40	0.75	65.87	1.69	CBS02	28.60	28.95

obj_mc: MassComposition = MassComposition(df_data, name=name)

Demonstrate the aggregate function

i.e. weight average of the dataset, a.k.a. head grade

print(obj_mc.aggregate())
print(obj_mc.aggregate(as_dataframe=False))

res: xr.Dataset = obj_mc.binned_mass_composition(cutoff_var='Fe', bin_width=1.0, cumulative=True, as_dataframe=False)
res

            mass_wet  mass_dry       H2O     Al2O3         Fe     SiO2
name
A072391  2029.617808  1981.688  2.361519  1.773585  60.443938  2.82721
<xarray.Dataset> Size: 48B
Dimensions:   (index: 1)
Dimensions without coordinates: index
Data variables:
    mass_wet  (index) float64 8B 2.03e+03
    mass_dry  (index) float64 8B 1.982e+03
    H2O       (index) float64 8B 2.362
    Al2O3     (index) float64 8B 1.774
    Fe        (index) float64 8B 60.44
    SiO2      (index) float64 8B 2.827
Attributes:
    mc_name:            Aggregate of A072391
    mc_vars_mass:       ['mass_wet', 'mass_dry']
    mc_vars_chem:       ['Al2O3', 'Fe', 'SiO2']
    mc_vars_attrs:      []
    mc_interval_edges:  {}
/home/runner/work/mass-composition/mass-composition/elphick/mass_composition/mc_xarray.py:157: 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`.

<xarray.Dataset> Size: 560B
Dimensions:   (Fe_bins: 10)
Coordinates:
  * Fe_bins   (Fe_bins) object 80B (57.0, 58.0] (58.0, 59.0] ... (66.0, 67.0]
Data variables:
    mass_wet  (Fe_bins) float64 80B 2.03e+03 1.966e+03 1.832e+03 ... 23.58 5.575
    mass_dry  (Fe_bins) float64 80B 1.982e+03 1.921e+03 1.791e+03 ... 23.44 5.52
    H2O       (Fe_bins) float64 80B 2.362 2.321 2.27 ... 0.6308 0.5975 0.9911
    Al2O3     (Fe_bins) float64 80B 1.774 1.722 1.665 ... 1.039 0.8941 0.873
    Fe        (Fe_bins) float64 80B 60.44 60.54 60.68 ... 65.17 65.69 66.19
    SiO2      (Fe_bins) float64 80B 2.827 2.778 2.689 2.545 ... 2.304 2.049 2.0
Attributes:
    mc_name:            Aggregate of A072391 with group Fe
    mc_vars_mass:       ['mass_wet', 'mass_dry']
    mc_vars_chem:       ['Al2O3', 'Fe', 'SiO2']
    mc_vars_attrs:      []
    mc_interval_edges:  {}

xarray.Dataset

• Dimensions:
  • Fe_bins: 10
• Coordinates: (1)
  • Fe_bins
    (Fe_bins)
    object
    (57.0, 58.0] ... (66.0, 67.0]

    units :

    %

    standard_name :

    Fe

    mc_type :

    chemistry

    mc_col_orig :

    Fe

    array([Interval(57.0, 58.0, closed='right'),
           Interval(58.0, 59.0, closed='right'),
           Interval(59.0, 60.0, closed='right'),
           Interval(60.0, 61.0, closed='right'),
           Interval(61.0, 62.0, closed='right'),
           Interval(62.0, 63.0, closed='right'),
           Interval(63.0, 64.0, closed='right'),
           Interval(64.0, 65.0, closed='right'),
           Interval(65.0, 66.0, closed='right'),
           Interval(66.0, 67.0, closed='right')], dtype=object)

• Data variables: (6)
  • mass_wet
    (Fe_bins)
    float64
    2.03e+03 1.966e+03 ... 23.58 5.575

    units :

    mass_units

    standard_name :

    Wet Mass

    mc_type :

    mass

    mc_col_orig :

    None

    array([2029.61780764, 1966.24413201, 1832.40451244, 1273.23539711,
            480.49695225,  190.52509456,   94.35518418,   51.13254505,
             23.58088726,    5.57525784])

  • mass_dry
    (Fe_bins)
    float64
    1.982e+03 1.921e+03 ... 23.44 5.52

    units :

    mass_units

    standard_name :

    Dry Mass

    mc_type :

    mass

    mc_col_orig :

    mass_dry

    array([1981.688, 1920.608, 1790.808, 1249.318,  472.378,  188.678,
             93.78 ,   50.81 ,   23.44 ,    5.52 ])

  • H2O
    (Fe_bins)
    float64
    2.362 2.321 2.27 ... 0.5975 0.9911

    units :

    %

    standard_name :

    H2O

    mc_type :

    moisture

    mc_col_orig :

    H2O

    array([2.36151888, 2.32097995, 2.27005075, 1.8784741 , 1.68969901,
           0.96947574, 0.60959468, 0.63080186, 0.59746379, 0.99112614])

  • Al2O3
    (Fe_bins)
    float64
    1.774 1.722 1.665 ... 0.8941 0.873

    units :

    %

    standard_name :

    Al2O3

    mc_type :

    chemistry

    mc_col_orig :

    Al2O3

    array([1.7735851 , 1.72190358, 1.66513797, 1.58723432, 1.33057763,
           1.24445616, 1.13898806, 1.03876993, 0.8940913 , 0.87298913])

  • Fe
    (Fe_bins)
    float64
    60.44 60.54 60.68 ... 65.69 66.19

    units :

    %

    standard_name :

    Fe

    mc_type :

    chemistry

    mc_col_orig :

    Fe

    array([60.4439379 , 60.54429733, 60.68122032, 61.12485812, 62.29731211,
           63.40437359, 64.39875773, 65.17139146, 65.68619881, 66.19458333])

  • SiO2
    (Fe_bins)
    float64
    2.827 2.778 2.689 ... 2.049 2.0

    units :

    %

    standard_name :

    SiO2

    mc_type :

    chemistry

    mc_col_orig :

    SiO2

    array([2.82721018, 2.77829082, 2.68893448, 2.54513781, 2.35429631,
           2.39765039, 2.28791533, 2.3042964 , 2.04941553, 1.99981884])

• Indexes: (1)
  • Fe_bins
    PandasIndex

    PandasIndex(IntervalIndex([(57.0, 58.0], (58.0, 59.0], (59.0, 60.0], (60.0, 61.0],
                   (61.0, 62.0], (62.0, 63.0], (63.0, 64.0], (64.0, 65.0],
                   (65.0, 66.0], (66.0, 67.0]],
                  dtype='interval[float64, right]', name='Fe_bins'))

• Attributes: (5)

  mc_name :

  Aggregate of A072391 with group Fe

  mc_vars_mass :

  ['mass_wet', 'mass_dry']

  mc_vars_chem :

  ['Al2O3', 'Fe', 'SiO2']

  mc_vars_attrs :

  []

  mc_interval_edges :

  {}

Tabular Grade bin data

res: pd.DataFrame = obj_mc.binned_mass_composition(cutoff_var='Fe', bin_width=1.0, cumulative=True,
                                                   direction='ascending', as_dataframe=True)
res

/home/runner/work/mass-composition/mass-composition/elphick/mass_composition/mc_xarray.py:157: 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`.

	mass_wet	mass_dry	H2O	Al2O3	Fe	SiO2
Fe_bins
(57.0, 58.0]	63.373676	61.080	3.619288	3.398666	57.288222	4.365437
(58.0, 59.0]	197.213295	190.880	3.211394	2.791020	58.217789	4.124492
(59.0, 60.0]	756.382411	732.370	3.174639	2.091473	59.282386	3.308385
(60.0, 61.0]	1549.120855	1509.310	2.569900	1.912236	59.863876	2.975221
(61.0, 62.0]	1839.092713	1793.010	2.505731	1.829265	60.132412	2.872413
(62.0, 63.0]	1935.262623	1887.908	2.446935	1.805108	60.247486	2.853999
(63.0, 64.0]	1978.485263	1930.878	2.406248	1.792921	60.319538	2.840970
(64.0, 65.0]	2006.036920	1958.248	2.382255	1.784113	60.381189	2.836520
(65.0, 66.0]	2024.042550	1976.168	2.365294	1.776101	60.427875	2.829521
(66.0, 67.0]	2029.617808	1981.688	2.361519	1.773585	60.443938	2.827210

res: pd.DataFrame = obj_mc.binned_mass_composition(cutoff_var='Fe', bin_width=1.0, cumulative=True,
                                                   direction='descending', as_dataframe=True)
res

/home/runner/work/mass-composition/mass-composition/elphick/mass_composition/mc_xarray.py:157: 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`.

	mass_wet	mass_dry	H2O	Al2O3	Fe	SiO2
Fe_bins
(57.0, 58.0]	2029.617808	1981.688	2.361519	1.773585	60.443938	2.827210
(58.0, 59.0]	1966.244132	1920.608	2.320980	1.721904	60.544297	2.778291
(59.0, 60.0]	1832.404512	1790.808	2.270051	1.665138	60.681220	2.688934
(60.0, 61.0]	1273.235397	1249.318	1.878474	1.587234	61.124858	2.545138
(61.0, 62.0]	480.496952	472.378	1.689699	1.330578	62.297312	2.354296
(62.0, 63.0]	190.525095	188.678	0.969476	1.244456	63.404374	2.397650
(63.0, 64.0]	94.355184	93.780	0.609595	1.138988	64.398758	2.287915
(64.0, 65.0]	51.132545	50.810	0.630802	1.038770	65.171391	2.304296
(65.0, 66.0]	23.580887	23.440	0.597464	0.894091	65.686199	2.049416
(66.0, 67.0]	5.575258	5.520	0.991126	0.872989	66.194583	1.999819

Plot the Grade Bins

fig = obj_mc.plot_bins(variables=['mass_dry', 'Fe', 'SiO2', 'Al2O3'],
                       cutoff_var='Fe',
                       bin_width=1.0,
                       cumulative=True,
                       direction='descending')
# noinspection PyTypeChecker
plotly.io.show(fig)  # this call to show will set the thumbnail for the gallery

/home/runner/work/mass-composition/mass-composition/elphick/mass_composition/mc_xarray.py:157: 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`.