{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Constrained Models\n", "\n", "AstroPhot models can have very complex constraints which allow for specialized and powerful fitting problems to be solved. Here you will learn how to take advantage of these capabilities." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import astrophot as ap\n", "import numpy as np\n", "import torch\n", "from astropy.io import fits\n", "import matplotlib.pyplot as plt\n", "from time import time\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Range limits\n", "\n", "The simplest form of constraint on a parameter is to restrict its range to within some limit. This is done at creation of the variable and you simply indicate the endpoints (non-inclusive) of the limits." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "got an AssertionError with message: center has upper limit [10.0, 20.0]\n" ] } ], "source": [ "target = ap.image.Target_Image(data = np.zeros((100,100)), center = [0,0], pixelscale = 1)\n", "gal1 = ap.models.AstroPhot_Model(\n", " name = \"galaxy1\",\n", " model_type = \"sersic galaxy model\",\n", " parameters = {\n", " \"center\": {\"value\": [0,0], \"limits\": [[-10,-20], [10,20]]}, # here we set the limits, note it can be different for each value\n", " },\n", " target = target,\n", ")\n", "\n", "# Now if we try to set a value outside the range we get an error\n", "try:\n", " gal1[\"center\"].value = [25,25]\n", "except ap.errors.InvalidParameter as e:\n", " print(\"got an AssertionError with message: \", e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Internal functions in AstroPhot track these limits and so will not go outside those limits under normal circumstances (contact us if you find it happening!). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Equality constraints\n", "\n", "Another form of constraint is an equality constraint. You can fix one parameter to track another's value so that they will always be equal." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "gals:\n", "center: [-25.0, -25.0] +- [0.1, 0.1] [arcsec]\n", "q: 0.9 +- 0.03 [b/a], limits: (0.0, 1.0)\n", "PA: 0.0 +- 0.06 [radians], limits: (0.0, 3.141592653589793), cyclic\n", "n: 2.0 +- 0.05 [none], limits: (0.36, 8.0)\n", "Re: 5.0 [arcsec], limits: (0.0, None)\n", "Ie: 1.0 [log10(flux/arcsec^2)]\n", "center: [25.0, 25.0] +- [0.1, 0.1] [arcsec]\n", "q: 0.9 +- 0.03 [b/a], limits: (0.0, 1.0)\n", "PA: 0.0 +- 0.06 [radians], limits: (0.0, 3.141592653589793), cyclic\n", "Ie: 1.0 [log10(flux/arcsec^2)]\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "target = ap.image.Target_Image(data = np.zeros((100,100)), center = [0,0], pixelscale = 1)\n", "gal1 = ap.models.AstroPhot_Model(\n", " name = \"galaxy1\",\n", " model_type = \"sersic galaxy model\",\n", " parameters = {\"center\": [-25,-25], \"PA\": 0, \"q\": 0.9, \"n\": 2, \"Re\": 5, \"Ie\": 1.},\n", " target = target,\n", ")\n", "gal2 = ap.models.AstroPhot_Model(\n", " name = \"galaxy2\",\n", " model_type = \"sersic galaxy model\",\n", " parameters = {\"center\": [25,25], \"PA\": 0, \"q\": 0.9, \"Ie\": 1.},\n", " target = target,\n", ")\n", "\n", "# here we set the equality constraint, setting the values for gal2 equal to the parameters of gal1\n", "gal2[\"n\"].value = gal1[\"n\"]\n", "gal2[\"Re\"].value = gal1[\"Re\"]\n", "\n", "# we make a group model to use both star models together\n", "gals = ap.models.AstroPhot_Model(\n", " name = \"gals\",\n", " model_type = \"group model\",\n", " models = [gal1, gal2],\n", " target = target,\n", ")\n", "\n", "print(gals.parameters)\n", "\n", "fig, ax = plt.subplots()\n", "ap.plots.model_image(fig, ax, gals)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# We can now change a parameter value and both models will change\n", "gal1[\"n\"].value = 1\n", "\n", "fig, ax = plt.subplots()\n", "ap.plots.model_image(fig, ax, gals)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that these two parameters are linked, optimization algorithms in AstroPhot will take this into account and fit the constrained set of parameters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Function constraints\n", "\n", "In some situations one may be able to impose a constraint on a set of parameters using some function. Some concrete examples of this include:\n", "\n", "- A spatially varying PSF can be forced to obey some smoothing function such as a plane or spline\n", "- The SED of a multiband fit may be constrained to follow some pre-determined form\n", "- An astrometry correction in multi-image fitting can be included for each image to ensure precise alignment\n", "\n", "The possibilities with this kind of constraint capability are quite extensive. If you do something creative with these functional constraints please let us know!" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Here we will demo a spatially varying PSF where the moffat \"n\" parameter changes across the image\n", "target = ap.image.Target_Image(data = np.zeros((100,100)), center = [0,0], pixelscale = 1)\n", "\n", "psf_target = ap.image.PSF_Image(data = np.zeros((25,25)), pixelscale = 1)\n", "\n", "# First we make all the star objects\n", "allstars = []\n", "allpsfs = []\n", "for x in [-30,0,30]:\n", " for y in [-30,0,30]:\n", " allpsfs.append(\n", " ap.models.AstroPhot_Model(\n", " name = \"psf\",\n", " model_type = \"moffat psf model\",\n", " parameters = {\"Rd\": 2},\n", " target = psf_target,\n", " )\n", " )\n", " allstars.append(\n", " ap.models.AstroPhot_Model(\n", " name = f\"star {x} {y}\",\n", " model_type = \"point model\",\n", " parameters = {\"center\": [x,y], \"flux\": 1},\n", " target = target,\n", " psf = allpsfs[-1],\n", " )\n", " )\n", " allpsfs[-1][\"n\"].link(allstars[-1][\"center\"])# see we need to link the center as well so that it can be used in the function\n", "\n", "# we link the Rd parameter for all the PSFs so that they are the same\n", "for psf in allpsfs[1:]:\n", " psf[\"Rd\"].value = allpsfs[0][\"Rd\"]\n", " \n", "# next we need the parameters for the spatially varying PSF plane\n", "P_intercept = ap.param.Parameter_Node(\n", " name = \"intercept\",\n", " value = 3,\n", ")\n", "P_slope = ap.param.Parameter_Node(\n", " name = \"slope\",\n", " value = [1/50, -1/50],\n", ")\n", "\n", "# next we define the function which takes the parameters as input and returns the value for n\n", "def constrained_moffat_n(params):\n", " return params[\"intercept\"].value + torch.sum(params[\"slope\"].value * params[\"center\"].value)\n", "\n", "# finally we assign this parameter function to the \"n\" parameter for each moffat\n", "for psf in allpsfs:\n", " psf[\"n\"].value = constrained_moffat_n\n", " psf[\"n\"].link(P_intercept)\n", " psf[\"n\"].link(P_slope)\n", " \n", "# A group model holds all the stars together\n", "MODEL = ap.models.AstroPhot_Model(\n", " name = \"spatial PSF\",\n", " model_type = \"group model\",\n", " models = allstars,\n", " target = target,\n", ")\n", "\n", "fig, ax = plt.subplots()\n", "ap.plots.model_image(fig, ax, MODEL)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "See how the PSF parameters vary across the image, this model could now be optimized to fit some data and the parameters of the plane (`intercept` and `slope`) will be optimized alongside everything else to give the best possible optimized parameter values accounting for everything in the image!" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.5" } }, "nbformat": 4, "nbformat_minor": 4 }