├── .gitignore ├── LICENSE.txt ├── README.md ├── preisach ├── __init__.py ├── plot_preisach_widget.py ├── preisach_python.py └── weights.py ├── pyproject.toml └── setup.py /.gitignore: -------------------------------------------------------------------------------- 1 | # Python 2 | *.egg-info/ 3 | *.pyc 4 | MANIFEST 5 | build/ 6 | dist/ 7 | 8 | # Environments 9 | venv/ 10 | -------------------------------------------------------------------------------- /LICENSE.txt: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2023 Isaac Kramer 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Python implementation of the Preisach model of hysteresis 2 | 3 | This GitHub repository contains code that can be used to execute the Preisach model of hysteresis. The interactive notebooks featured here were produced for the published article [Hysteresis in soil hydraulic conductivity as driven by salinity and sodicity – a modeling framework](https://hess.copernicus.org/articles/25/1993/2021/). 4 | The corresponding GitHub repository for that project can be found [here](https://github.com/isaackramer/soil-hysteresis). 5 | 6 | This repository contains: 7 | 8 | * Widgets designed to give users an intuitive sense of how the Preisach framework works. 9 | * Basic implementation of the Preisach framework using Python. 10 | 11 | ## Widgets 12 | 13 | ##### 1. Geometric Intepretation of the Preisach Framework 14 | 15 | This widget demonstrates how hysterons, the core of the Preisach framework, are used to model hysteresis. To run the widget, click the Launch Binder. Wait for the notebook to load (this can take several minutes) and then click Cell → Run All. 16 | 17 | [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/yairmau/hysteresis-python/master?filepath=Hysteron%20Widget%20Vertical%20Version.ipynb) 18 | 19 | 20 | ##### 2. The Weight Function 21 | 22 | In this widget we demonstrate how weight functions affect the system's output. With this widget, the user can compare different weight functions, including how each affects output. To run the widget, click the Launch Binder. Wait for the notebook to load (this can take several minutes) and then click Cell → Run All. 23 | 24 | [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/yairmau/hysteresis-python/master?filepath=Weights%20Widget.ipynb) 25 | 26 | 27 | -------------------------------------------------------------------------------- /preisach/__init__.py: -------------------------------------------------------------------------------- 1 | """ 2 | Python implementation of the Preisach model of hysteresis 3 | """ 4 | 5 | __version__ = "0.1.0" 6 | -------------------------------------------------------------------------------- /preisach/plot_preisach_widget.py: -------------------------------------------------------------------------------- 1 | """One input widget""" 2 | 3 | import matplotlib.gridspec as gridspec 4 | import matplotlib.pyplot as plt 5 | import numpy as np 6 | 7 | from matplotlib.widgets import Slider, Button 8 | from palettable.colorbrewer.sequential import YlGnBu_9 9 | 10 | from preisach.preisach_python import preisach_single_value 11 | from preisach.weights import weights 12 | 13 | 14 | # number of hysterons on each side of the triangle 15 | hys_per_side = 101 16 | 17 | # create meshgrid with location of hysterons 18 | beta_values = np.around(np.linspace(0, 1, hys_per_side), 2) 19 | alpha_values = np.around(np.linspace(1, 0, hys_per_side), 2) 20 | beta_grid, alpha_grid = np.meshgrid(beta_values, alpha_values) 21 | 22 | # create array showing whether hysterons on/off 23 | # inital values: all hysterons set to 0 (negative saturation) and 24 | # values outside of preisach triangle set to np.nan 25 | preisach_triangle = np.where(alpha_grid >= beta_grid, 0, np.nan) 26 | 27 | # assign weights: "uniform", "linear", "bottom_heavy", "top_heavy", 28 | # "left_heavy", "right_heavy" "center_light_alpha", "center_light_beta", 29 | # "center_heavy_alpha", "center_heavy_beta" 30 | mu = weights("irreversible", beta_grid, alpha_grid) 31 | mass = np.nansum(mu) 32 | mu = mu / mass 33 | 34 | 35 | # initial state of system 36 | initial_input = 0 37 | inputs = np.array([initial_input]) 38 | outputs = np.array([np.nansum(preisach_triangle)]) 39 | 40 | 41 | # Begin plotting 42 | plt.ion() 43 | plt.clf() 44 | 45 | fig = plt.figure(1) 46 | gs = gridspec.GridSpec(2, 2, width_ratios=[2, 1], height_ratios=[1, 1]) 47 | gs.update(left=0.1, right=0.95, bottom=0.25, top=0.9, wspace=0.3) 48 | 49 | 50 | ax1 = plt.subplot(gs[:, 0]) # Input/output 51 | ax2 = plt.subplot(gs[0, 1]) # Preisach plane 52 | ax3 = plt.subplot(gs[1, 1]) # Weights 53 | 54 | (plot1,) = ax1.plot(inputs[0], 1 - outputs[0], color="red") 55 | plot2 = ax2.pcolormesh(beta_grid, alpha_grid, preisach_triangle, cmap=YlGnBu_9.mpl_colormap) 56 | plot3 = ax3.scatter(beta_grid, alpha_grid, c=mu, cmap=YlGnBu_9.mpl_colormap, s=0.2) 57 | 58 | 59 | # axis limits 60 | ax1.set_xlim([-0.05, 1.05]) 61 | ax1.set_ylim([-0.05, 1.05]) 62 | ax2.set_xlim([-0.05, 1.05]) 63 | ax2.set_ylim([-0.05, 1.05]) 64 | 65 | # add slider (rect = [left, bottom, width, height]) 66 | axcolor = "lightgoldenrodyellow" 67 | axinputs = plt.axes([0.25, 0.1, 0.65, 0.03], facecolor=axcolor) 68 | sinputs = Slider(axinputs, "input", valmin=0, valmax=1, valinit=0.0) 69 | 70 | # function to update plots based on slider input 71 | def update(val): 72 | global inputs, outputs, preisach_triangle 73 | inputs = np.concatenate((inputs, np.array([sinputs.val]))) 74 | outputs, preisach_triangle = preisach_single_value( 75 | inputs, alpha_grid, beta_grid, mu, preisach_triangle, outputs 76 | ) 77 | plot1.set_ydata(outputs) 78 | plot1.set_xdata(inputs) 79 | ax2.pcolormesh(beta_grid, alpha_grid, preisach_triangle) 80 | fig.canvas.draw_idle() 81 | 82 | 83 | # for the slider to remain responsive you must maintain a reference to it. 84 | # Call on_changed() to connect to the slider event. 85 | sinputs.on_changed(update) 86 | -------------------------------------------------------------------------------- /preisach/preisach_python.py: -------------------------------------------------------------------------------- 1 | """Functions used for calculating preisach output based on given input""" 2 | 3 | import numpy as np 4 | 5 | 6 | def preisach_single_value( 7 | inputs, alpha_grid, beta_grid, mu, preisach_triangle, outputs 8 | ): 9 | """Preisach function with single input""" 10 | 11 | # compare new input to previous input value and change hysteron values accordingly 12 | if inputs[-1] > inputs[-2]: # if input increases 13 | preisach_triangle = np.where(inputs[-1] > alpha_grid, 1, preisach_triangle) 14 | elif inputs[-1] < inputs[-2]: # if input increases 15 | preisach_triangle = np.where(inputs[-1] < beta_grid, 0, preisach_triangle) 16 | 17 | # values outside the presiach half-plane are set to nan 18 | preisach_triangle = np.where(alpha_grid >= beta_grid, preisach_triangle, np.nan) 19 | 20 | # calculate weighted presiach triangle 21 | weighted_preisach = preisach_triangle * mu 22 | 23 | # new output value 24 | f = np.nansum(weighted_preisach) 25 | outputs = np.concatenate((outputs, np.array([f]))) 26 | return outputs, preisach_triangle 27 | 28 | 29 | def preisach_array(inputs, alpha_grid, beta_grid, mu, starting_value): 30 | """Preisach function for array of input values""" 31 | 32 | preisach_triangle = np.where(alpha_grid >= beta_grid, starting_value, np.nan) 33 | outputs = np.array([np.nansum(preisach_triangle * mu)]) 34 | 35 | for ii in range(len(inputs) - 1): 36 | new_input = inputs[ii + 1] 37 | old_input = inputs[ii] 38 | 39 | if new_input > old_input: # if input increases 40 | preisach_triangle = np.where(new_input > alpha_grid, 1, preisach_triangle) 41 | elif new_input < old_input: # if input increases 42 | preisach_triangle = np.where(new_input < beta_grid, 0, preisach_triangle) 43 | 44 | preisach_triangle = np.where(alpha_grid >= beta_grid, preisach_triangle, np.nan) 45 | weighted_preisach = preisach_triangle * mu 46 | 47 | f = np.nansum(weighted_preisach) 48 | outputs = np.concatenate((outputs, np.array([f]))) 49 | 50 | return outputs, preisach_triangle 51 | -------------------------------------------------------------------------------- /preisach/weights.py: -------------------------------------------------------------------------------- 1 | """function for creating different weight functions""" 2 | import numpy as np 3 | 4 | from numpy import where, nan, nansum 5 | 6 | 7 | def weights(method, beta, alpha): 8 | distance = (alpha - beta) / np.sqrt(2) 9 | mu = { 10 | "uniform": where(alpha >= beta, 1, nan), 11 | "linear": where(alpha == beta, 1, nan), 12 | "top_heavy": where(alpha >= beta, alpha, nan), 13 | "bottom_heavy": where(alpha >= beta, 1 - alpha, nan), 14 | "right_heavy": where(alpha >= beta, beta, nan), 15 | "left_heavy": where(alpha >= beta, 1 - beta, nan), 16 | "center_light_alpha": where(alpha >= beta, np.abs(0.5 - alpha), nan), 17 | "center_light_beta": where(alpha >= beta, np.abs(0.5 - beta), nan), 18 | "single_line": where(np.logical_and(0.3 < beta, beta < 0.5), 1, 0), 19 | "upper_left": where(np.logical_and(0.6 > beta, alpha > 0.90), 1, 0), 20 | "near_diagonal": where((alpha - beta) < 0.2, 1, 0), 21 | "far_diagonal": where((alpha - beta) < 0.5, 0, 1), 22 | "dirac_detal": where(np.logical_and(0.5 == beta, alpha == 0.5), 1, 0), 23 | "irreversible": where(alpha >= beta, distance, 0), 24 | "reversible": where(alpha >= beta, (1 - distance) ** 4, 0), 25 | "set_1": where(alpha >= beta, (1 - distance), nan), 26 | "set_2": where(alpha >= beta, (1 - distance) ** 2, nan), 27 | "set_3": where(alpha >= beta, (1 - distance) ** 4, nan), 28 | "mcneal": where( 29 | np.logical_and( 30 | np.logical_or(0.3 > beta, 0.8 < beta), 31 | alpha > 0.8 32 | ), 33 | 1, 34 | 0 35 | ), 36 | }[method] 37 | mu = where(alpha >= beta, mu, nan) 38 | mass = nansum(mu) 39 | mu = mu / mass 40 | return mu 41 | -------------------------------------------------------------------------------- /pyproject.toml: -------------------------------------------------------------------------------- 1 | [project] 2 | name = "preisach" 3 | dynamic = ["version"] 4 | authors = [ 5 | { name="Isaac Kramer", email="43068145+isaackramer@users.noreply.github.com" }, 6 | { name="Peter Hillerström", email="peter.hillerstrom@gmail.com" }, 7 | ] 8 | description = "Python implementation of the Preisach model of hysteresis" 9 | readme = "README.md" 10 | keywords = [ 11 | "hysteresis", 12 | ] 13 | license.text = "MIT License" 14 | classifiers = [ 15 | "License :: OSI Approved :: MIT License", 16 | "Programming Language :: Python :: 3", 17 | "Topic :: Scientific/Engineering :: Physics", 18 | ] 19 | requires-python = ">=3.7" 20 | dependencies = [ 21 | "numpy >= 1.23.5", 22 | "palettable >= 3.3.0", 23 | ] 24 | 25 | [project.optional-dependencies] 26 | dev = [ 27 | "black >= 22.1.0", 28 | "flake8 >= 6.0.0", 29 | "pycodestyle >= 2.10.0", 30 | "pylint >= 2.15.10", 31 | ] 32 | notebook = [ 33 | "jupyter ~= 1.0.0", 34 | ] 35 | plot = [ 36 | "matplotlib ~= 3.4.3", 37 | ] 38 | 39 | # [project.gui-scripts] 40 | # preisach-widget = preisach.plot_preisach_widget:main [plot] 41 | 42 | [project.urls] 43 | "Source code" = "https://github.com/isaackramer/python-preisach" 44 | "Issue tracker" = "https://github.com/isaackramer/python-preisach/issues" 45 | 46 | [tool.setuptools] 47 | packages = ["preisach"] 48 | 49 | [tool.setuptools.dynamic] 50 | version.attr = "preisach.__version__" 51 | 52 | [build-system] 53 | requires = ["setuptools", "setuptools-scm"] 54 | build-backend = "setuptools.build_meta" 55 | -------------------------------------------------------------------------------- /setup.py: -------------------------------------------------------------------------------- 1 | from setuptools import setup 2 | 3 | setup() 4 | --------------------------------------------------------------------------------