pygradations 0.1.0

A Python package for analyzing and manipulating size distributions (gradations) from mineral processing streams

pygradations

A Python package for analyzing and manipulating size distributions (gradations) from mineral processing streams.

Overview

Gradations are size distributions typically represented as dataframes with the following columns:

• sieve: sieve aperture in mm
• p: weight % retained in each sieve
• wr: cumulative % retained (cumsum of p)
• wp: % passing through each sieve (100 - wr)

Features

• Data Loading: Import gradation data from CSV and Excel files
• Curve Fitting: Fit various distribution models to gradation data:
  • Gaudin-Schuhmann distribution
  • Rosin-Rammler distribution
  • Cubic spline interpolation
• Visualization: Plot gradation curves with fitted distributions
• Analysis: Calculate characteristic sizes (D10, D30, D50, D60, D90) and coefficients
• Interpolation: Interpolate gradation data to standard sieve sizes
• Comparison: Compare multiple gradations on the same scale

Installation

pip install pygradations

Quick Start

Loading Data

import pygradations as pg

# Load from CSV file
gradation = pg.load_gradation_from_csv("sample_data.csv", name="Sample 1")

# Load from Excel file
gradation = pg.load_gradation_from_excel("sample_data.xlsx", sheet_name="Sheet1", name="Sample 2")

Basic Usage

import pygradations as pg
import pandas as pd

# Example gradation data
data = pd.DataFrame({
    'sieve': [63.50, 50.80, 38.10, 31.75, 25.40, 19.05, 12.70, 9.53, 6.73, 4.76],
    'p': [0.0, 3.65, 29.37, 18.26, 14.74, 9.86, 9.22, 3.59, 3.11, 1.87],
    'wr': [0.0, 3.65, 33.02, 51.28, 66.02, 75.88, 85.1, 88.69, 91.8, 93.67],
    'wp': [100.0, 96.35, 66.98, 48.72, 33.98, 24.12, 14.9, 11.31, 8.2, 6.33]
})

# Create Gradation object
grad = pg.Gradation(data, name="Example Gradation")

# Get basic information
print(grad)
print(f"Number of sieves: {len(grad.data)}")
print(f"Sieve sizes: {grad.get_sieve_sizes()}")

Curve Fitting

import matplotlib.pyplot as plt

# Get data for fitting
sieve_sizes = grad.get_sieve_sizes()
passing_percentages = grad.get_passing_percentages()

# Fit different models
k, m, r_sq_gs = pg.gaudin_schuhmann_fit(sieve_sizes, passing_percentages)
x_63, n, r_sq_rr = pg.rosin_rammler_fit(sieve_sizes, passing_percentages)

print(f"Gaudin-Schuhmann: k={k:.2f}, m={m:.2f}, R²={r_sq_gs:.3f}")
print(f"Rosin-Rammler: x₆₃={x_63:.2f}, n={n:.2f}, R²={r_sq_rr:.3f}")

# Plot fitted curves
fig, axes = plt.subplots(1, 3, figsize=(15, 5))

pg.plot_fitted_curve(sieve_sizes, passing_percentages, 'gaudin_schuhmann', ax=axes[0])
pg.plot_fitted_curve(sieve_sizes, passing_percentages, 'rosin_rammler', ax=axes[1])
pg.plot_fitted_curve(sieve_sizes, passing_percentages, 'cubic_spline', ax=axes[2])

plt.tight_layout()
plt.show()

Analysis

# Calculate characteristic sizes
char_sizes = pg.get_characteristic_sizes(grad.data)
print("Characteristic sizes:")
for size_name, size_value in char_sizes.items():
    print(f"  {size_name}: {size_value:.2f} mm")

# Calculate coefficients
uniformity = pg.calculate_uniformity_coefficient(grad.data)
curvature = pg.calculate_curvature_coefficient(grad.data)
print(f"Uniformity coefficient: {uniformity:.2f}")
print(f"Curvature coefficient: {curvature:.2f}")

Interpolation

# Interpolate to standard sieve sizes
standard_sieves = pg.create_standard_sieve_series()
interpolated = pg.interpolate_to_sieves(grad.data, standard_sieves, method='cubic_spline')

print("Interpolated data:")
print(interpolated.head())

Multiple Gradations

# Create a dictionary of gradations
gradations = {
    "Sample 1": grad.data,
    "Sample 2": another_grad.data,
    "Sample 3": third_grad.data
}

# Compare gradations
comparison = pg.compare_gradations(gradations)
print(comparison.head())

# Export results
pg.export_gradation_to_csv(comparison, "comparison_results.csv")

API Reference

Core Classes

Gradation(data, name)

Main class for representing gradation data.

Methods:

• get_sieve_sizes(): Return sieve sizes as numpy array
• get_passing_percentages(): Return passing percentages as numpy array
• get_retained_percentages(): Return retained percentages as numpy array
• get_cumulative_retained(): Return cumulative retained percentages as numpy array

Data Loading

load_gradation_from_csv(filepath, name=None)

Load gradation data from CSV file.

load_gradation_from_excel(filepath, sheet_name=0, name=None)

Load gradation data from Excel file.

Curve Fitting

gaudin_schuhmann_fit(sieve_sizes, passing_percentages)

Fit Gaudin-Schuhmann distribution. Returns (k, m, r_squared).

rosin_rammler_fit(sieve_sizes, passing_percentages)

Fit Rosin-Rammler distribution. Returns (x_63, n, r_squared).

cubic_spline_fit(sieve_sizes, passing_percentages)

Fit cubic spline. Returns CubicSpline object.

plot_fitted_curve(sieve_sizes, passing_percentages, fit_type, ax=None)

Plot original data and fitted curve.

Analysis

get_characteristic_sizes(data)

Calculate D10, D30, D50, D60, D90 characteristic sizes.

calculate_uniformity_coefficient(data)

Calculate uniformity coefficient (D60/D10).

calculate_curvature_coefficient(data)

Calculate curvature coefficient (D30²/(D10*D60)).

Utilities

calculate_cumulative_percentages(data)

Calculate wr and wp from individual retained percentages.

validate_gradation_data(data)

Validate gradation data format and consistency.

create_standard_sieve_series()

Get standard sieve sizes for interpolation.

compare_gradations(gradations, target_sieves=None)

Compare multiple gradations by interpolating to same sieve sizes.

Data Format

The package expects gradation data in the following format:

sieve (mm)	p (%)	wr (%)	wp (%)
63.50	0.0	0.0	100.0
50.80	3.65	3.65	96.35
38.10	29.37	33.02	66.98
...	...	...	...

Where:

• sieve: Sieve aperture in mm
• p: Weight % retained in each sieve
• wr: Cumulative % retained (cumsum of p)
• wp: % passing through each sieve (100 - wr)

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

License

This project is licensed under the MIT License - see the LICENSE file for details.