diff --git a/docs/apps/FourierTransforms/app.md b/docs/apps/FourierTransforms/app.md index fe87851..732006c 100644 --- a/docs/apps/FourierTransforms/app.md +++ b/docs/apps/FourierTransforms/app.md @@ -5,6 +5,7 @@ categories: - Mathematics tags: - Fourier Transform + - Draft date: 2025-11-02 hide: - toc diff --git a/docs/apps/FractionalDerivatives/app.md b/docs/apps/FractionalDerivatives/app.md new file mode 100644 index 0000000..5d9cc30 --- /dev/null +++ b/docs/apps/FractionalDerivatives/app.md @@ -0,0 +1,16 @@ +--- +authors: + - ptuemmler +categories: + - Mathematics +tags: + - Fourier Transform + - Draft +date: 2025-11-05 +hide: + - toc +draft: true +--- +# Fractional Derivatives + +{{embed_app("100%", "860px")}} diff --git a/docs/apps/FractionalDerivatives/app.py b/docs/apps/FractionalDerivatives/app.py new file mode 100644 index 0000000..f9f8dc3 --- /dev/null +++ b/docs/apps/FractionalDerivatives/app.py @@ -0,0 +1,124 @@ +import numpy as np +import matplotlib.pyplot as plt +import re +from shiny import App, Inputs, Outputs, Session, render, ui, reactive + +app_ui = ui.page_sidebar( + ui.sidebar( + ui.input_text( + "function", + "Function f(x)", + value="e**(-x**2)", + placeholder="Enter function like: sin(x), cos(x), exp(x), x**2, etc." + ), + ui.input_slider( + "order", + "Derivative order", + min=0, + max=4, + value=1, + step=0.1, + animate=True + ), + ui.input_dark_mode(id='dark_mode'), + open='always' + ), + ui.output_plot("plot", width="100%", height="800px"), +) + + +def server(input: Inputs, output: Outputs, session: Session): + xrange = 10 # Fixed x-range for plotting + factor = 10 # Oversampling factor for better accuracy + npix_real = int(2**14) + 1 + + @reactive.calc + def clean_function(): + """Clean and validate the input function""" + func_str = input.function().strip() + + # Replace common mathematical functions with numpy equivalents + replacements = { + 'sin': 'np.sin', + 'cos': 'np.cos', + 'tan': 'np.tan', + 'exp': 'np.exp', + 'log': 'np.log', + 'sqrt': 'np.sqrt', + 'abs': 'np.abs', + } + + # Apply replacements only to function names (not as part of other words) + for old, new in replacements.items(): + func_str = re.sub(r'\b' + old + r'\b', new, func_str) + + # Replace 'x' with the actual variable name for evaluation + return func_str + + @reactive.calc + def evaluate_function(): + """Evaluate the function at given x values""" + func_str = clean_function() + + x = np.linspace(-xrange*factor, xrange*factor, npix_real) + try: + # Create a safe namespace for evaluation + namespace = {'x': x, 'np': np, 'pi': np.pi, 'e': np.e} + y = eval(func_str, {"__builtins__": {}}, namespace) + return x, y, func_str + except Exception as e: + # Return a default function if evaluation fails + ui.notification_show(f"Error evaluating function: {func_str}. Using default e**(-x**2).", duration=10, type="error") + return x, np.exp(-x**2), "e**(-x**2)" + + + @render.plot() + def plot(): + if input.dark_mode() == "dark": + style_label = 'dark_background' + else: + style_label = 'seaborn-v0_8' + + with plt.style.context(style_label): + x, y_true, func_str = evaluate_function() + order = input.order() + + fig, ax = plt.subplots(2,1, sharex=True) + + # Plot original function + ax[0].plot(x, y_true, linewidth=2, label=r'$f(x)$') + + # Compute non-integer derivative using Fourier transform method + Y = np.fft.fft(y_true) + k = np.fft.fftfreq(len(x), d=(x[1]-x[0])) * 2 * np.pi # Angular frequency + + Y_deriv = Y * ((1j * k) ** order) + y_deriv = np.real(np.fft.ifft(Y_deriv)) + + # Plot derivative + ax[1].plot([0], [0]) # Dummy plot to ensure proper scaling + ax[1].plot(x, y_deriv, linewidth=2, label=r'$f^{(' + f'{order}' + ')}(x)$') + + ax[0].set_ylabel(r'$f(x)$') + ax[1].set_ylabel(r'$\frac{d}{dx}^{' + f'{order}' + '}f(x)$') + + ax[1].set_xlabel('x') + # Set reasonable y-limits based on the data + + y_min = np.min(y_true[np.abs(x)<=xrange]) + y_max = np.max(y_true[np.abs(x)<=xrange]) + y_range = y_max - y_min + ax[0].set_ylim(y_min - 0.1 * y_range, y_max + 0.1 * y_range) + + y_min = np.min(y_deriv[np.abs(x)<=xrange]) + y_max = np.max(y_deriv[np.abs(x)<=xrange]) + y_range = y_max - y_min + ax[1].set_ylim(y_min - 0.1 * y_range, y_max + 0.1 * y_range) + + ax[0].set_xlim(-xrange, xrange) + ax[1].set_xlim(-xrange, xrange) + return fig + + +app = App(app_ui, server) + diff --git a/docs/apps/FractionalDerivatives/requirements.txt b/docs/apps/FractionalDerivatives/requirements.txt new file mode 100644 index 0000000..a46db3e --- /dev/null +++ b/docs/apps/FractionalDerivatives/requirements.txt @@ -0,0 +1,3 @@ +numpy +palmerpenguins +matplotlib \ No newline at end of file diff --git a/docs/apps/MinkowskiSpaceTime/app.md b/docs/apps/MinkowskiSpaceTime/app.md index 2ecffbe..f4c9324 100644 --- a/docs/apps/MinkowskiSpaceTime/app.md +++ b/docs/apps/MinkowskiSpaceTime/app.md @@ -6,6 +6,7 @@ categories: - Physics tags: - Relativity + - Draft date: 2025-11-03 hide: - toc diff --git a/docs/license.md b/docs/license.md index 5f2586b..17afcec 100644 --- a/docs/license.md +++ b/docs/license.md @@ -1,3 +1,426 @@ # License ## CC BY 4.0 (for teaching materials) +??? info + ```text + + Attribution 4.0 International + + ======================================================================= + + Creative Commons Corporation ("Creative Commons") is not a law firm and + does not provide legal services or legal advice. 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For + the avoidance of doubt, this paragraph does not form part of the public + licenses. + + Creative Commons may be contacted at creativecommons.org. + ``` + ## MIT License (for code examples) +??? info + ```text + MIT License + Copyright (c) 2025 Paul Tuemmler + + Permission is hereby granted, free of charge, to any person obtaining a copy + of this software and associated documentation files (the "Software"), to deal + in the Software without restriction, including without limitation the rights + to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + copies of the Software, and to permit persons to whom the Software is + furnished to do so, subject to the following conditions: + + The above copyright notice and this permission notice shall be included in all + copies or substantial portions of the Software. + + THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. 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