{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Using the `SigmaA` Class\n", "\n", "The surface density with respect to semi-major axis, $\\Sigma(a)$ is defined through the `SigmaA` class. This class must be initialised for the pipeline, and is directly used when computing the final $\\bar\\Sigma(r)$ profile. \n", "\n", "The class comes with a host of pre-built $\\Sigma(a)$ profiles but also supports any supplied functional form. This page demonstrates all of the built in functionalities within the class." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Getting Started: Class Functionality\n", "\n", "To begin using the class, the user must first initialise it by specifying the following:\n", "\n", "- The minimum and maximum semi-major axes, set via the `a_min` and `a_max` arguments (these define the truncation bounds)\n", "- The overall amplitude or normalisation factor, specified using `sigma0`\n", "- The desired profile type, selected through the `profile_type` argument\n", "\n", "In addition to these required parameters, each built-in profile type accepts its own specific keyword arguments, which must also be supplied at initialisation. These profile-specific arguments are summarised in the table below and explained in more detail in the following sections:\n", "\n", "| Profile Type | Required Parameters |\n", "|-------------------|--------------------------------|\n", "| `'power_law'` | `power` |\n", "| `'gaussian'` | `gauss_width`, `gauss_center` |\n", "| `'step_up'` | `step` |\n", "| `'step_down'` | `step` |\n", "| `'custom'` | `custom_func` (callable) |" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Initialising the Class\n", "\n", "This is an example on how to initialise the class with a power-law profile. Each built-in profile has its own arguments that must be defined. See the next sections for demonstrations with the other built-in profiles. In the case of the power-law, the user must define the `power` parameter." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# First import the class\n", "from debrispy import SigmaA\n", "import numpy as np\n", "\n", "# Initialise\n", "sigma_a_profile = SigmaA(a_min=1, a_max=4, profile_type='power_law', sigma0=1, power=0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Getting Information about the Class via Print\n", "\n", "Once initialised, the user can get check information about the class parameters, such as the profile type and semi-major axis range, by simply printing the class." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SigmaA(type=power_law, a_min=1, a_max=4, sigma0=1, power=0.5)\n" ] } ], "source": [ "print(sigma_a_profile)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculating and Returning the $\\Sigma(a)$ Values\n", "\n", "Once initialised, the user can obtain the $\\Sigma(a)$ values for a chosen array of $a$ values by using the `get_values` method or by simply calling the class as a function, which internally uses the same method." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0. 0.99627096 0.70622455 0.57710986 0.5 ]\n" ] } ], "source": [ "# Define the a values to calculate the profile over\n", "a_vals = np.linspace(0.01, 4, 5)\n", "\n", "# Option 1: Return the values through the 'get_values' method\n", "sigma_a_vals = sigma_a_profile.get_values(a_vals)\n", "\n", "# Option 2: Return the values by calling the initialised class directly\n", "sigma_a_vals = sigma_a_profile(a_vals)\n", "\n", "print(sigma_a_vals)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualising the Profile\n", "\n", "The `Sigma(a)` class also a plotting tool, which can be called through the `plot` method. This method has a host of arguments to change appearance of the plot, and also has support for any `plt.plot` keyword arguments (e.g. `linewidth`, `linestyle`), which the method automatically applies." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a_vals = np.linspace(0.01, 5, 1_000)\n", "\n", "sigma_a_profile.plot(a_vals = a_vals, save=False, show = True, \n", " filename = \"figures/sigma_a.png\", figsize = (8, 6))\n", "\n", "sigma_a_profile.plot(a_vals = a_vals, save=False, show = True, \n", " filename = \"figures/sigma_a.png\", figsize = (8, 6), \n", " linestyle = \"--\", linewidth = 4, color = 'red')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculating the Area\n", "\n", "After initialisation, the user can calculate the area of the curve via the `get_area` method. This uses the adaptive quadrature through `scipy.integrate.quad` internally." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The area is: 2.0\n" ] } ], "source": [ "area_value = sigma_a_profile.compute_area()\n", "print(f\"The area is: {area_value}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Built-In Profile Types" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Power-Law Profile\n", "\n", "The power-law profile is called using the `profile_type = 'power_law'` argument, and is defined as, \n", "\n", "$$\n", "\\Sigma(a) = \\Sigma_0 \\left( \\frac{a_\\text{min}}{a} \\right)^p,\n", "$$\n", "\n", "where $\\Sigma_0$ is set using the `sigma0` argument, and $p$ is set using the `power` argument" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Area: 1.386\n" ] } ], "source": [ "power_law_profile = SigmaA(a_min=1, a_max=4, profile_type='power_law', sigma0=1, power=1)\n", "\n", "a_vals = np.linspace(0.01, 5, 10000)\n", "power_law_profile.plot(a_vals)\n", "\n", "print(f\"Area: {power_law_profile.compute_area():.3f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Gaussian Profile\n", "\n", "The Gaussian profile is called using the `profile_type = 'gaussian'` argument and is defines as,\n", "\n", "$$\n", " \\Sigma(a) = \\frac{\\Sigma_0}{\\sqrt{2\\pi}\\sigma} \\exp{\\left[ -\\frac{(a - a_0)^2}{2\\sigma^2} \\right]},\n", "$$\n", "\n", "where $\\Sigma_0$ is set using the `sigma0` argument, $\\sigma$ is set using the `gauss_width` argument and $a_0$ is set with the `gauss_center` argument.\n", "\n", "**Note**: Since the profile is properly normalised, `sigma0` also effectively sets the area under the curve." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Area: 1.000\n" ] } ], "source": [ "gaussian_profile = SigmaA(a_min=1, a_max=4, profile_type='gaussian', \n", " sigma0=1, gauss_center = 2.5, gauss_width = 0.3)\n", "gaussian_profile.plot(a_vals)\n", "\n", "print(f\"Area: {gaussian_profile.compute_area():.3f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is also possible to get truncated Gaussian profiles using this setup:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Area: 0.954\n" ] } ], "source": [ "gaussian_profile_trunc = SigmaA(a_min=1.5, a_max=3.5, profile_type='gaussian', \n", " sigma0=1, gauss_center = 2.5, gauss_width = 0.5)\n", "gaussian_profile_trunc.plot(a_vals)\n", "\n", "print(f\"Area: {gaussian_profile_trunc.compute_area():.3f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Step-Function Profile\n", "\n", "The step-function profiles are accesed by setting `profile_type = 'step_up'`, which is defined as, \n", "\n", "$$\n", " \\Sigma(a) = \\Sigma_0 \\quad \\text{for} \\quad a > s\n", "$$\n", "\n", " or `profile_type = 'step_down'`, which is defined as, \n", "\n", "$$\n", " \\Sigma(a) = \\Sigma_0 \\quad \\text{for} \\quad a < s\n", "$$\n", "\n", " In both cases, the position of the step, $s$, is defined via the `step` argument." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "step_up_profile = SigmaA(a_min=1, a_max=4, profile_type='step_up', step=2)\n", "step_up_profile.plot()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "step_down_profile = SigmaA(a_min=1, a_max=4, profile_type='step_down', step=2.5)\n", "step_down_profile.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example Code (Manual Plotting)\n", "\n", "Of course, the user can choose to return the $\\Sigma(a)$ values and plot manually for full control. This is an example showing how to obtain $\\Sigma(a)$ profiles using all of the built-in methods and the plotting them together." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "fig, (ax1, ax2, ax3, ax4) = plt.subplots(1, 4, figsize=(15, 5))\n", "\n", "a_vals = np.linspace(0.01, 5, 1_000)\n", "a_vals2 = np.linspace(0.01, 4, 1_000)\n", "a_vals3 = np.linspace(1, 4, 1_000)\n", "\n", "\n", "# Plot data on each subplot\n", "ax1.plot(a_vals, power_law_profile(a_vals), 'b-', lw = 2, \n", " label = r\"$p = -0.5$\")\n", "ax1.set_title('Power Law', fontsize = 18)\n", "ax1.set_xlabel(r'$a$', fontsize = 18)\n", "ax1.set_ylabel(r'$\\Sigma_a(a)$', fontsize = 18)\n", "\n", "ax2.plot(a_vals, gaussian_profile(a_vals), 'r-', lw = 2, \n", " label = r\"$a_0 = 2.5$\" + \"\\n\" + r\"$\\sigma = 0.3$\")\n", "ax2.set_title('Gaussian', fontsize = 18)\n", "ax2.set_xlabel(r'$a$', fontsize = 18)\n", "\n", "ax3.plot(a_vals2, step_up_profile(a_vals2), 'g-', lw = 2, \n", " label = r\"$a_\\mathrm{step} = 2$\")\n", "ax3.set_title('Step Up', fontsize = 18)\n", "ax3.set_xlabel(r'$a$', fontsize = 18)\n", "\n", "ax4.plot(a_vals3, step_down_profile(a_vals3), 'm-', lw = 2, \n", " label = r\"$a_\\mathrm{step} = 2.5$\")\n", "ax4.set_title('Step Down', fontsize = 18)\n", "ax4.set_xlabel(r'$a$', fontsize = 18)\n", "\n", "\n", "for ax in (ax1, ax2, ax3, ax4):\n", " ax.set_ylim(0, 1.35)\n", " ax.tick_params(axis='both', which='major', labelsize=13)\n", " ax.legend(fontsize = 19, loc = 'upper right', framealpha=1.0, \n", " edgecolor='black', handlelength=0, handletextpad=0)\n", " ax.grid()\n", "\n", "for ax in (ax2, ax3, ax4):\n", " ax.set_yticklabels([])\n", "\n", "plt.tight_layout()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using a Custom Profile Type\n", "\n", "The `SigmaA` class can be initialised with any user-supplied function. \n", "\n", "⚠️ **Important:** The supplied function 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": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define the custom profile\n", "def sig_a_smooth(a, *pars):\n", " plaw = pars[0] \n", " sigma0 = pars[1] \n", " a_in = pars[2] \n", " a_out = pars[3] \n", " w_in = pars[4] \n", " w_out = pars[5] \n", " \n", " f_1 = sigma0*(a_in/a)**plaw\n", " f_2 = 0.5*(1.0+np.tanh((a-a_in)/w_in))\n", " f_3 = 0.5*(1.0+np.tanh((a_out-a)/w_out))\n", "\n", " return f_1*f_2*f_3\n", "\n", "parameters = [1.0, 1.0, 4.0, 15.0, 0.2, 0.2]\n", "\n", "# Initialise the class\n", "custom_profile = SigmaA(a_min=3, a_max=16, profile_type = 'custom', \n", " sigma_func = lambda a: sig_a_smooth(a, *parameters))\n", "custom_profile.plot()" ] } ], "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 }