From d4c97b8f3e14473dbf0c98d369ce170cbfc4bfe1 Mon Sep 17 00:00:00 2001 From: emilyhunt Date: Mon, 29 Sep 2025 12:24:36 +0200 Subject: [PATCH] Add notebook with basic use examples --- examples/basic_use.ipynb | 400 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 400 insertions(+) create mode 100644 examples/basic_use.ipynb diff --git a/examples/basic_use.ipynb b/examples/basic_use.ipynb new file mode 100644 index 0000000..84ddd00 --- /dev/null +++ b/examples/basic_use.ipynb @@ -0,0 +1,400 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "157221af", + "metadata": {}, + "source": [ + "# Basic use of the package\n", + "\n", + "The following notebook shows you the basics of querying and using the models, following the examples in the library readme." + ] + }, + { + "cell_type": "markdown", + "id": "8a5c0477", + "metadata": {}, + "source": [ + "## Imports" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "8be3e85e", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from hr_selection_function import HR24SelectionFunction, NStarsPredictor\n", + "from astropy.coordinates import SkyCoord\n", + "from astropy import units as u" + ] + }, + { + "cell_type": "markdown", + "id": "fe8e1865", + "metadata": {}, + "source": [ + "## The selection function\n", + "\n", + "The selection function is super easy to use. It takes three arguments: Gaia data density ($\\rho_\\mathrm{data}$ in the paper), number of stars, and median parallax error.\n", + "\n", + "Data download will happen automatically the first time you use the package." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "3fde06f8", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Pick some basic things\n", + "n_stars = np.geomspace(5, 200)\n", + "median_parallax_error = np.full(50, 0.1)\n", + "threshold = np.full(50, 3)\n", + "\n", + "# Query the selection function\n", + "model = HR24SelectionFunction()\n", + "\n", + "\n", + "fig, ax = plt.subplots()\n", + "for density in [100, 1000, 10000, 100000]:\n", + " gaia_density = np.full(50, density)\n", + " result = model(gaia_density, n_stars, median_parallax_error, threshold)\n", + " ax.plot(n_stars, result, label=f\"Data density: {density:.0f}\")\n", + "\n", + "ax.set(xscale=\"log\", xlabel=\"Number of stars\", ylabel=\"Detection probability\")\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "4e2040d4", + "metadata": {}, + "source": [ + "It also works if you specify coordinates instead, in cases where you don't know the data density." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "03649c60", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[None, Text(0.5, 0, 'Number of stars'), Text(0, 0.5, 'Detection probability')]" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "n_stars = np.geomspace(5, 200)\n", + "median_parallax_error = np.full(50, 0.1)\n", + "threshold = np.full(50, 3)\n", + "\n", + "coordinates = SkyCoord(\n", + " l=np.full(50, 0)*u.deg,\n", + " b=np.full(50, 0)*u.deg,\n", + " pm_l_cosb=np.full(50, 0)*u.mas/u.yr,\n", + " pm_b=np.full(50, 0)*u.mas/u.yr,\n", + " distance=np.full(50, 2000)*u.pc,\n", + " frame=\"galactic\"\n", + ")\n", + "\n", + "\n", + "fig, ax = plt.subplots()\n", + "result = model(coordinates, n_stars, median_parallax_error, threshold)\n", + "ax.plot(n_stars, result, label=f\"Data density: {density:.0f}\")\n", + "\n", + "ax.set(xscale=\"log\", xlabel=\"Number of stars\", ylabel=\"Detection probability\")" + ] + }, + { + "cell_type": "markdown", + "id": "f155c1ec", + "metadata": {}, + "source": [ + "We can also query different samples of the walkers, and query the model probabilistically! This is useful if you want to incorporate **systematic errors** in the model fit into your eventual work - every time you query the function, you could take a randomly sampled model." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "abadd0de", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Pick some basic things\n", + "n_stars = np.geomspace(5, 100)\n", + "median_parallax_error = np.full(50, 0.1)\n", + "threshold = np.full(50, 3)\n", + "gaia_density = np.full(50, 1000)\n", + "\n", + "fig, ax = plt.subplots(nrows=2, sharex=True)\n", + "result_median = model(gaia_density, n_stars, median_parallax_error, threshold)\n", + "for i in range(50):\n", + " result = model(\n", + " gaia_density, n_stars, median_parallax_error, threshold, mode=\"random_sample\"\n", + " )\n", + " ax[0].plot(n_stars, result, \"k-\", alpha=0.05, lw=0.5)\n", + " ax[1].plot(n_stars, result - result_median, \"k-\", alpha=0.5, lw=0.5)\n", + "\n", + "ax[0].set(ylabel=\"Detection probability\")\n", + "ax[1].set(xscale=\"log\", xlabel=\"Number of stars\", ylabel=\"Residual\")\n", + "\n", + "fig.subplots_adjust(hspace=0.)" + ] + }, + { + "cell_type": "markdown", + "id": "62396b03", + "metadata": {}, + "source": [ + "## The number of stars predictor\n", + "\n", + "If you don't know n_stars or median_parallax_error for your cluster, you can predict it with the `NStarsPredictor` in this library." + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "6bc25f8d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Querying model 10 of 10\n" + ] + }, + { + "data": { + "text/plain": [ + "[Text(0.5, 0, 'Mass [MSun]'), Text(0, 0.5, 'Number of stars')]" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Initialize with lower models number to make it faster for demo\n", + "nstars_model = NStarsPredictor(models=10)\n", + "\n", + "# Pick values to query\n", + "mass = np.linspace(50, 5000)\n", + "extinction = np.full(50, 1)\n", + "log_age = np.full(50, 7.5)\n", + "metallicity = np.full(50, 0.0)\n", + "differential_extinction = np.full(50, 0.2)\n", + "\n", + "coordinates = SkyCoord(\n", + " l=np.full(50, 0)*u.deg,\n", + " b=np.full(50, 0)*u.deg,\n", + " pm_l_cosb=np.full(50, 0)*u.mas/u.yr,\n", + " pm_b=np.full(50, 0)*u.mas/u.yr,\n", + " distance=np.full(50, 2000)*u.pc,\n", + " frame=\"galactic\"\n", + ")\n", + "\n", + "n_stars_predicted, median_parallax_error_predicted = nstars_model(\n", + " coordinates, \n", + " mass=mass, \n", + " extinction=extinction, \n", + " log_age=log_age, \n", + " metallicity=metallicity, \n", + " differential_extinction=differential_extinction\n", + ")\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "ax.scatter(mass, n_stars_predicted)\n", + "ax.set(xlabel=\"Mass [MSun]\", ylabel=\"Number of stars\")" + ] + }, + { + "cell_type": "markdown", + "id": "c3cc4790", + "metadata": {}, + "source": [ + "The bouncing around is because it's an _ensemble_ model, and it (sort of) randomly samples the number of stars that a given mass might have.\n", + "\n", + "We can use up to 250 models (the full ensemble) to get the most accurate prediction. **This will take longer to load and run, however.**\n", + "\n", + "We can also ask for full predictions from each model and use them to estimate uncertainties!" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "id": "4b7ac723", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Querying model 250 of 250\n" + ] + }, + { + "data": { + "text/plain": [ + "[Text(0.5, 0, 'Mass [MSun]'), Text(0, 0.5, 'Number of stars')]" + ] + }, + "execution_count": 59, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Initialize with lower models number to make it faster for demo\n", + "nstars_model = NStarsPredictor(models=250)\n", + "\n", + "# Pick values to query\n", + "mass = np.linspace(50, 5000)\n", + "extinction = np.full(50, 1)\n", + "log_age = np.full(50, 7.5)\n", + "metallicity = np.full(50, 0.0)\n", + "differential_extinction = np.full(50, 0.2)\n", + "\n", + "coordinates = SkyCoord(\n", + " l=np.full(50, 0) * u.deg,\n", + " b=np.full(50, 0) * u.deg,\n", + " pm_l_cosb=np.full(50, 0) * u.mas / u.yr,\n", + " pm_b=np.full(50, 0) * u.mas / u.yr,\n", + " distance=np.full(50, 2000) * u.pc,\n", + " frame=\"galactic\",\n", + ")\n", + "\n", + "n_stars_predicted, median_parallax_error_predicted = nstars_model(\n", + " coordinates,\n", + " mass=mass,\n", + " extinction=extinction,\n", + " log_age=log_age,\n", + " metallicity=metallicity,\n", + " differential_extinction=differential_extinction,\n", + " mode=\"full\",\n", + ")\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "median = np.median(n_stars_predicted, axis=1)\n", + "errors = (\n", + " median - np.percentile(n_stars_predicted, 16, axis=1),\n", + " np.percentile(n_stars_predicted, 84, axis=1) - median,\n", + " )\n", + "ax.errorbar(\n", + " mass,\n", + " median,\n", + " yerr=errors,\n", + " fmt=\".\",\n", + " capsize=2\n", + ")\n", + "ax.set(xlabel=\"Mass [MSun]\", ylabel=\"Number of stars\")" + ] + }, + { + "cell_type": "markdown", + "id": "f8367419", + "metadata": {}, + "source": [ + "There is still some scatter here (which is to be expected based on sampling & the fact that XGBoost isn't perfect), but this is still an accurate way to go from cluster parameters to number of stars." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "hr-selection-function", + "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": "3.12.9" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} -- 2.51.2