{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Unique Eccentricity Profiles\n", "\n", "Unique eccentricity profiles refer to profiles where eccentricity is a unique function of semi-major axis, $e = e(a)$, which can also be written as $\\psi(e, a) = \\delta(e - e(a))$. Such eccentricity profiles are defined through the `UniqueEccentricity` class." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Initialising the `UniqueEccentricity` Class\n", "\n", "When initialising the eccentricity class, the user must firstly supply the `a_min` and `a_max` values, defining the range of semi-major axes.\n", "\n", "In terms of the profile being used, there are two ways to initialise the class:\n", "\n", "1. Using the **built-in power-law profile**, \n", "$$\n", "e(a) = e_0 \\left(\\frac{a_{\\min}}{a}\\right)^{p}\n", "$$\n", "\n", "2. Providing a **custom function**,\n", "\n", "$$\n", "e(a) = e_0 \\cdot e(a)_\\text{custom}\n", "$$\n", "\n", "In both cases, the class automatically checks that the returned eccentricities lie within the physically valid range $0 \\leq e(a) < 1$.\n", "\n", "Unlike the `SigmaA` class, the eccentricity is **not truncated** outside of $[a_{\\min}, a_{\\max}]$. The `UniqueEccentricity` class is primarily a lightweight, object-oriented wrapper for storing and evaluating $e(a)$, and is designed for direct use with the `Kernel` class when computing the ASD." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Built-In Eccentricity Profile\n", "\n", "The class defaults to the built-in power-law profile, for which the user must define the scaling factor, `e0`, and the `power` argument." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Import the class\n", "from debrispy import UniqueEccentricity\n", "import numpy as np\n", "\n", "# Initialise\n", "power_law = UniqueEccentricity(a_min=1, a_max=4, e0=0.5, power=0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Custom Eccentricity Profile\n", "\n", "Alternatively, the user can override the power law profile by supplying their own function through the `eccentricity_func` argument. Even in this case, the user is free to define the normalisation, `e0`, which defaults to 1 if unspecified.\n", "\n", "⚠️ **Important:** If providing a custom eccentricity function, it should be vectorised (so scalar Python conditionals such as ``if``/``else`` will usually fail, use NumPy-aware operations instead), and be provided in such a way that the semi-major axis, $a$, is the only parameter. This can be done by wrapping the function manually or using a `lambda` function." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def ecc(a, b, c):\n", " return np.abs(np.sin(a*b))*c\n", "\n", "custom = UniqueEccentricity(a_min=1, a_max=4, e0=1, \n", " eccentricity_func=lambda a: ecc(a, b=0.5, c=0.5))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Returning Eccentricity Values & Profile Information" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Profile information can be obtained via the `print` functionality." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "UniqueEccentricity(a_min=1, a_max=4, e0=0.5, power=0.5)\n", "UniqueEccentricity(a_min=1, a_max=4, e0=1, custom_func=True)\n" ] } ], "source": [ "print(power_law)\n", "print(custom)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One can evaluate the eccentricty at specific a values, either by calling the `eccentricity` method, or by simply calling the class as a function (which internally also uses the same method)." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.35355339 0.31622777 0.28867513]\n", "[0.35355339 0.31622777 0.28867513]\n" ] } ], "source": [ "a_vals = [2, 2.5, 3]\n", "print(power_law(a_vals))\n", "print(power_law.eccentricity(a_vals))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculating the Derivative\n", "\n", "In addition, the class contains a `derivative` method to calculate $de/da$. This is not directly part of the ASD pipeline, however can be an effective way to determine or visualise sharply peaked regions. This is calculated for arbitrary eccentricity distributions numerically using the central differences method." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.21939564 0.13507558 0.0176843 -0.10403671]\n" ] } ], "source": [ "a_vals = [1, 2, 3, 4]\n", "custom_profile_derivatives = custom.derivative(a_vals)\n", "print(custom_profile_derivatives)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualising the Eccentricity Profile\n", "\n", "The `plot()` method of the `UniqueEccentricity` class provides a flexible interface for visualising the eccentricity profile.\n", "\n", "By default, it will:\n", "\n", "- Generate 500 points uniformly in the interval $[a_{\\min}, a_{\\max}]$\n", "- Plot \\( e(a) \\) on linear axes\n", "- Label the axes and show a grid\n", "- Display the figure unless `save=True` is specified (note that `filename` must be provided if `save=True`)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "custom.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Some useful keyword arguments include:\n", "\n", "**Plot appearance:**\n", "\n", "- `color`: Line colour (e.g. `'k'`, `'C1'`, `'#FF0000'`)\n", "- `linestyle`: `'-'`, `'--'`, `':'`, etc.\n", "- `linewidth` or `lw`: Line width\n", "- `marker`: Marker style (`'o'`, `'.'`, `'s'`, etc.)\n", "- `alpha`: Line transparency\n", "- `label`: Legend label\n", "\n", "**Axes and layout:**\n", "\n", "- `xlim`, `ylim`: Axis ranges\n", "- `xlabel`, `ylabel`, `title`: Override axis labels and title\n", "- `grid`: Show/hide grid\n", "- `log`: If `True`, use log scale for y-axis\n", "- `save=True, filename=\"...\"`: Save figure instead of displaying" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ecc = UniqueEccentricity(a_min=40, a_max=100, e0=0.1, power=1.5)\n", "\n", "ecc.plot(\n", " color='green',\n", " linestyle='--',\n", " linewidth=5,\n", " alpha=0.5,\n", " xlim=(30, 110),\n", " ylim=(0, 0.15),\n", " title='Eccentricity Profile (Power Law)',\n", " grid=True\n", ")" ] } ], "metadata": { "kernelspec": { "display_name": "env_debris", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.14" } }, "nbformat": 4, "nbformat_minor": 2 }