├── .gitignore ├── README.rst ├── Step 1 - Loading stellar population models.ipynb ├── Step 2 - Setting up your filter curves.ipynb ├── Step 3 - Converting your stellar models to photometric fluxes.ipynb ├── Step 4 - Loading observational data.ipynb ├── Step 5 - First steps towards fitting models to data.ipynb ├── Step 6 - Grid-based fitting.ipynb ├── data ├── UltraVISTA_catalogue.cat ├── filters │ ├── CFHT_g.txt │ ├── CFHT_i+i2.txt │ ├── CFHT_r.txt │ ├── CFHT_u.txt │ ├── CFHT_z.txt │ ├── IRAC1 │ ├── IRAC2 │ ├── VISTA_H.txt │ ├── VISTA_J.txt │ ├── VISTA_Ks.txt │ ├── VISTA_Y.txt │ └── subaru_z └── spectra-bin-imf135_300.z020.dat └── final_code.py /.gitignore: -------------------------------------------------------------------------------- 1 | 2 | 3 | ################################# 4 | 5 | # Standard .gitignore from github: 6 | 7 | # Byte-compiled / optimized / DLL files 8 | __pycache__/ 9 | *.py[cod] 10 | *$py.class 11 | 12 | # C extensions 13 | *.so 14 | 15 | # Distribution / packaging 16 | .Python 17 | build/ 18 | develop-eggs/ 19 | dist/ 20 | downloads/ 21 | eggs/ 22 | .eggs/ 23 | lib/ 24 | lib64/ 25 | parts/ 26 | sdist/ 27 | var/ 28 | wheels/ 29 | *.egg-info/ 30 | .installed.cfg 31 | *.egg 32 | MANIFEST 33 | 34 | # PyInstaller 35 | # Usually these files are written by a python script from a template 36 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 37 | *.manifest 38 | *.spec 39 | 40 | # Installer logs 41 | pip-log.txt 42 | pip-delete-this-directory.txt 43 | 44 | # Unit test / coverage reports 45 | htmlcov/ 46 | .tox/ 47 | .coverage 48 | .coverage.* 49 | .cache 50 | nosetests.xml 51 | coverage.xml 52 | *.cover 53 | .hypothesis/ 54 | .pytest_cache/ 55 | 56 | # Translations 57 | *.mo 58 | *.pot 59 | 60 | # Django stuff: 61 | *.log 62 | .static_storage/ 63 | .media/ 64 | local_settings.py 65 | 66 | # Flask stuff: 67 | instance/ 68 | .webassets-cache 69 | 70 | # Scrapy stuff: 71 | .scrapy 72 | 73 | # Sphinx documentation 74 | docs/_build/ 75 | 76 | # PyBuilder 77 | target/ 78 | 79 | # Jupyter Notebook 80 | .ipynb_checkpoints 81 | 82 | # pyenv 83 | .python-version 84 | 85 | # celery beat schedule file 86 | celerybeat-schedule 87 | 88 | # SageMath parsed files 89 | *.sage.py 90 | 91 | # Environments 92 | .env 93 | .venv 94 | env/ 95 | venv/ 96 | ENV/ 97 | env.bak/ 98 | venv.bak/ 99 | 100 | # Spyder project settings 101 | .spyderproject 102 | .spyproject 103 | 104 | # Rope project settings 105 | .ropeproject 106 | 107 | # mkdocs documentation 108 | /site 109 | 110 | # mypy 111 | .mypy_cache/ -------------------------------------------------------------------------------- /README.rst: -------------------------------------------------------------------------------- 1 | SED Fitting Tutorial 2 | ==================== 3 | 4 | This repository contains a series of iPython notebooks which will teach you how to perform very basic SED fitting. The assumption is that you're familiar with the basic concepts (e.g. by having read Section 2 of `Conroy 2013 `_), and now want to start implementing those concepts in Python. 5 | 6 | I wrote the tutorial in the hope that it might be useful either for students who wanted to start writing their own SED fitting package, or for people who are using other people's SED fitting tools and want to understand a little better how they work. 7 | 8 | The method the code applies is grid-based chi-squared minimisation. It fits age, mass and redshift for simple stellar population models from BPASS. The code is deliberately inefficient in order to make the syntax as clear as possible. 9 | 10 | If you're working off this code as a starting point, suggestions for developing it further are as follows: 11 | - Vectorise mathematical operations with numpy to speed up the code, although beware running out of memory. 12 | - Perform analytic chi-squared minimisation to determine the best fitting mass and only grid over age and redshift. 13 | - Add a function to apply the Calzetti et al. (2000) dust law and add Av as another grid parameter. 14 | - Add the ability to fit grids of stellar models at different metallicities. 15 | - Add the ability to fit and more complex star-formation histories by adding SSP models together. 16 | - Put the whole thing inside a class so you're not accessing variables from the global namespace within functions. 17 | - Replace the grid method with a functional minimisation (e.g. scipy.optimise) or MCMC (e.g. emcee) routine. 18 | 19 | At that point you've already got a highly competitive SED fitting code, where you go from there is up to you... 20 | 21 | Or you could just used `Bagpipes `_. -------------------------------------------------------------------------------- /Step 4 - Loading observational data.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Step 4 - Loading observational data\n", 8 | "\n", 9 | "We've now developed everything we need to start fitting. All we need is some data to try it out on. I've uploaded a few objects from UltraVISTA to practice on to a catalogue in the \"data\" folder called \"UltraVISTA_catalogue.cat\". Let's write some code to load the data up." 10 | ] 11 | }, 12 | { 13 | "cell_type": "code", 14 | "execution_count": 1, 15 | "metadata": {}, 16 | "outputs": [], 17 | "source": [ 18 | "import numpy as np\n", 19 | "\n", 20 | "def load_data(row_no):\n", 21 | " \"\"\" Load UltraVISTA photometry from catalogue. \"\"\"\n", 22 | "\n", 23 | " # load up the relevant columns from the catalogue.\n", 24 | " catalogue = np.loadtxt(\"data/UltraVISTA_catalogue.cat\",\n", 25 | " usecols=(0,3,4,5,6,7,8,9,10,11,12,13,14,15,\n", 26 | " 16,17,18,19,20,21,22,23,24,25,26))\n", 27 | " \n", 28 | " # Extract the object we're interested in from the catalogue.\n", 29 | " fluxes = catalogue[row_no, 1:13]\n", 30 | " fluxerrs = catalogue[row_no, 13:25]\n", 31 | "\n", 32 | " # Convert to microjanskys\n", 33 | " fluxes = fluxes*10**29\n", 34 | " fluxerrs = fluxerrs*10**29\n", 35 | " \n", 36 | " # Put an error floor into the data at the 20 sigma level.\n", 37 | " # This is normally done to account for systematic uncertainties.\n", 38 | " for i in range(fluxes.shape[0]):\n", 39 | " if fluxerrs[i] < fluxes[i]/20:\n", 40 | " fluxerrs[i] = fluxes[i]/20\n", 41 | "\n", 42 | " return fluxes, fluxerrs\n", 43 | "\n", 44 | "fluxes, fluxerrs = load_data(1)" 45 | ] 46 | }, 47 | { 48 | "cell_type": "markdown", 49 | "metadata": {}, 50 | "source": [ 51 | "I guess that's all there is to it, moving quickly on..." 52 | ] 53 | }, 54 | { 55 | "cell_type": "code", 56 | "execution_count": null, 57 | "metadata": {}, 58 | "outputs": [], 59 | "source": [] 60 | } 61 | ], 62 | "metadata": { 63 | "kernelspec": { 64 | "display_name": "Python 2", 65 | "language": "python", 66 | "name": "python2" 67 | }, 68 | "language_info": { 69 | "codemirror_mode": { 70 | "name": "ipython", 71 | "version": 2 72 | }, 73 | "file_extension": ".py", 74 | "mimetype": "text/x-python", 75 | "name": "python", 76 | "nbconvert_exporter": "python", 77 | "pygments_lexer": "ipython2", 78 | "version": "2.7.14" 79 | } 80 | }, 81 | "nbformat": 4, 82 | "nbformat_minor": 2 83 | } 84 | -------------------------------------------------------------------------------- /Step 5 - First steps towards fitting models to data.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Step 5 - First steps towards fitting models to data\n", 8 | "\n", 9 | "In the first three steps we've built up a framework that allows us to load stellar models, filter curves and combine them at any observed redshift, briefly we'll re-input that code, each of the three functions below are condensed versions of the ground we covered in the first three examples respectively." 10 | ] 11 | }, 12 | { 13 | "cell_type": "code", 14 | "execution_count": 2, 15 | "metadata": {}, 16 | "outputs": [], 17 | "source": [ 18 | "import numpy as np\n", 19 | "\n", 20 | "from astropy.cosmology import FlatLambdaCDM\n", 21 | "\n", 22 | "cosmo = FlatLambdaCDM(H0=70., Om0=0.3)\n", 23 | "\n", 24 | "\n", 25 | "def get_model_grid():\n", 26 | " \"\"\" Loads up the BPASS grid of stellar models and \n", 27 | " resamples it onto a coarser wavelength grid. See Step 1. \"\"\"\n", 28 | " \n", 29 | " model_path = \"data/spectra-bin-imf135_300.z020.dat\"\n", 30 | " raw_wavelengths = np.loadtxt(model_path, usecols=0)\n", 31 | " raw_grid = np.loadtxt(model_path)[:,1:]\n", 32 | " \n", 33 | " grid = np.zeros((wavelengths.shape[0], raw_grid.shape[1]))\n", 34 | "\n", 35 | " for i in range(grid.shape[1]):\n", 36 | " grid[:,i] = np.interp(wavelengths, raw_wavelengths, raw_grid[:,i])\n", 37 | " \n", 38 | " grid *= (3.827*10**33)/(10**6)\n", 39 | "\n", 40 | " return grid\n", 41 | "\n", 42 | " \n", 43 | "def blueshift_filters(redshift):\n", 44 | " \"\"\" A function that resamples filters onto the same wavelength\n", 45 | " basis as the model spectrum at the specified redshift. See Step 2. \"\"\"\n", 46 | " \n", 47 | " resampled_filter_curves = []\n", 48 | "\n", 49 | " for filt in filter_curves:\n", 50 | " blueshifted_wavs = filt[:, 0]/(1 + redshift)\n", 51 | " \n", 52 | " resampled_filt = np.interp(wavelengths,\n", 53 | " blueshifted_wavs, filt[:, 1],\n", 54 | " left=0, right=0)\n", 55 | " \n", 56 | " resampled_filter_curves.append(resampled_filt)\n", 57 | " \n", 58 | " return resampled_filter_curves\n", 59 | "\n", 60 | "\n", 61 | "def get_model_photometry(redshift, age_index):\n", 62 | " \"\"\" For a row in the model grid return model\n", 63 | " photometry at the specified redshifts. See Step 3. \"\"\"\n", 64 | "\n", 65 | " ssp_model = np.copy(grid[:, age_index])\n", 66 | " \n", 67 | " luminosity_distance = (3.086*10**24)*cosmo.luminosity_distance(redshift).value\n", 68 | "\n", 69 | " ssp_model /= 4*np.pi*(1 + redshift)*luminosity_distance**2\n", 70 | "\n", 71 | " filter_curves_z = blueshift_filters(redshift)\n", 72 | "\n", 73 | " photometry = np.zeros(len(filter_curves))\n", 74 | "\n", 75 | " redshifted_wavs = wavelengths*(1 + redshift)\n", 76 | " \n", 77 | " for i in range(photometry.shape[0]):\n", 78 | " flux_contributions = filter_curves_z[i]*ssp_model\n", 79 | " photometry[i] = np.trapz(flux_contributions, x=redshifted_wavs)\n", 80 | " photometry[i] /= np.trapz(filter_curves_z[i], x=redshifted_wavs)\n", 81 | " \n", 82 | " return photometry\n" 83 | ] 84 | }, 85 | { 86 | "cell_type": "markdown", 87 | "metadata": {}, 88 | "source": [ 89 | "Let's also re-input the function we wrote in Step 4 to load up observational data." 90 | ] 91 | }, 92 | { 93 | "cell_type": "code", 94 | "execution_count": 3, 95 | "metadata": {}, 96 | "outputs": [], 97 | "source": [ 98 | "def load_data(row_no):\n", 99 | " \"\"\" Load UltraVISTA photometry from catalogue. See Step 4. \"\"\"\n", 100 | "\n", 101 | " # load up the relevant columns from the catalogue.\n", 102 | " catalogue = np.loadtxt(\"data/UltraVISTA_catalogue.cat\",\n", 103 | " usecols=(0,3,4,5,6,7,8,9,10,11,12,13,14,15,\n", 104 | " 16,17,18,19,20,21,22,23,24,25,26))\n", 105 | " \n", 106 | " # Extract the object we're interested in from the catalogue.\n", 107 | " fluxes = catalogue[row_no, 1:13]\n", 108 | " fluxerrs = catalogue[row_no, 13:25]\n", 109 | "\n", 110 | " # Convert to microjanskys\n", 111 | " fluxes = fluxes*10**29\n", 112 | " fluxerrs = fluxerrs*10**29\n", 113 | " \n", 114 | " # Put an error floor into the data at the 20 sigma level.\n", 115 | " # This is normally done to account for systematic uncertainties.\n", 116 | " for i in range(fluxes.shape[0]):\n", 117 | " if fluxerrs[i] < fluxes[i]/20:\n", 118 | " fluxerrs[i] = fluxes[i]/20\n", 119 | "\n", 120 | " return fluxes, fluxerrs\n", 121 | "\n", 122 | "fluxes, fluxerrs = load_data(1)" 123 | ] 124 | }, 125 | { 126 | "cell_type": "markdown", 127 | "metadata": {}, 128 | "source": [ 129 | "There's also some other basic setting up we should do to define the variables we're going to need." 130 | ] 131 | }, 132 | { 133 | "cell_type": "code", 134 | "execution_count": 4, 135 | "metadata": {}, 136 | "outputs": [], 137 | "source": [ 138 | "# Define our basic quantities.\n", 139 | "wavelengths = np.arange(1000., 60000., 10.)\n", 140 | "ages = np.arange(2, 53)\n", 141 | "ages = 10**(6+0.1*(ages-2))\n", 142 | "\n", 143 | "grid = get_model_grid()\n", 144 | "\n", 145 | "# Load the curves up.\n", 146 | "filter_names = [\"data/filters/CFHT_u.txt\",\n", 147 | " \"data/filters/CFHT_g.txt\",\n", 148 | " \"data/filters/CFHT_r.txt\",\n", 149 | " \"data/filters/CFHT_i+i2.txt\",\n", 150 | " \"data/filters/CFHT_z.txt\",\n", 151 | " \"data/filters/subaru_z\",\n", 152 | " \"data/filters/VISTA_Y.txt\",\n", 153 | " \"data/filters/VISTA_J.txt\",\n", 154 | " \"data/filters/VISTA_H.txt\",\n", 155 | " \"data/filters/VISTA_Ks.txt\",\n", 156 | " \"data/filters/IRAC1\",\n", 157 | " \"data/filters/IRAC2\"]\n", 158 | "\n", 159 | "filter_curves = []\n", 160 | "\n", 161 | "for name in filter_names:\n", 162 | " filter_curves.append(np.loadtxt(name))\n", 163 | " \n", 164 | "eff_wavs = np.zeros(len(filter_curves))\n", 165 | "\n", 166 | "# Calculate the effective wavelengths of the filter curves\n", 167 | "for i in range(len(filter_curves)):\n", 168 | " filt = filter_curves[i]\n", 169 | "\n", 170 | " wav_weights = filt[:,1]*filt[:,0]\n", 171 | " \n", 172 | " eff_wavs[i] = np.trapz(wav_weights, x=filt[:,0])\n", 173 | "\n", 174 | " eff_wavs[i] /= np.trapz(filt[:, 1], x=filt[:,0])" 175 | ] 176 | }, 177 | { 178 | "cell_type": "markdown", 179 | "metadata": {}, 180 | "source": [ 181 | "# Now that that's over with...\n", 182 | "\n", 183 | "Having got all that out of the way let's think about how to go about fitting to data. The simplest way to do this is grid-based fitting. Basically we're going to pick a bunch of redshift, age and mass values making up a 3D grid, then calculate chi-squared values at each point and see which one is smallest. Let's start with a single point to develop the idea.\n", 184 | "\n", 185 | "We can only use discrete fixed age values corresponding to the ages we have spectra for in the BPASS model grid, so let's just leave things in terms of the column index in the grid instead of actual ages in years for now." 186 | ] 187 | }, 188 | { 189 | "cell_type": "code", 190 | "execution_count": 5, 191 | "metadata": {}, 192 | "outputs": [], 193 | "source": [ 194 | "mass = 10**10 # Solar masses\n", 195 | "redshift = 1.\n", 196 | "age_index = 25\n", 197 | "\n", 198 | "# Our photometry is in erg/s/cm^2/A per Solar mass of stars\n", 199 | "model_photometry = get_model_photometry(redshift, age_index)\n", 200 | "\n", 201 | "# Convert to erg/s/cm^2/A by multiplying by the total mass we want.\n", 202 | "model_photometry *= mass\n", 203 | "\n", 204 | "# Our observational data is in microJanskys.\n", 205 | "fluxes, fluxerrs = load_data(1)" 206 | ] 207 | }, 208 | { 209 | "cell_type": "markdown", 210 | "metadata": {}, 211 | "source": [ 212 | "Would you look at that, we have a not-at-all-contrived unit mismatch between our model and our photometric data. Converting between flux per unit Angstrom and flux per unit frequency is the bane of my (and I presume other people in the field's too) existance, I always have to work it out from scratch every time.\n", 213 | "\n", 214 | "Let's turn our microJansky observational data into erg/s/cm^2/A and quickly plot the result." 215 | ] 216 | }, 217 | { 218 | "cell_type": "code", 219 | "execution_count": 6, 220 | "metadata": {}, 221 | "outputs": [], 222 | "source": [ 223 | "# Convert from muJy to erg/s/cm^2/Hz.\n", 224 | "fluxes = fluxes*10**-29\n", 225 | "fluxerrs = fluxerrs*10**-29\n", 226 | "\n", 227 | "# Convert from erg/s/cm^2/Hz to erg/s/cm^2/A.\n", 228 | "fluxes = fluxes*2.9979*10**18/eff_wavs**2\n", 229 | "fluxerrs = fluxerrs*2.9979*10**18/eff_wavs**2" 230 | ] 231 | }, 232 | { 233 | "cell_type": "code", 234 | "execution_count": 9, 235 | "metadata": {}, 236 | "outputs": [ 237 | { 238 | "data": { 239 | "image/png": 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\n", 240 | "text/plain": [ 241 | "
" 242 | ] 243 | }, 244 | "metadata": {}, 245 | "output_type": "display_data" 246 | } 247 | ], 248 | "source": [ 249 | "import matplotlib.pyplot as plt\n", 250 | "\n", 251 | "plt.figure(figsize=(15, 5))\n", 252 | "plt.errorbar(eff_wavs, fluxes, yerr=fluxerrs, lw=1.0, linestyle=\" \", capsize=3, capthick=1, color=\"black\")\n", 253 | "plt.scatter(eff_wavs, fluxes, s=75, linewidth=1, facecolor=\"blue\", edgecolor=\"black\")\n", 254 | "plt.xscale(\"log\")\n", 255 | "plt.xlim(1000.*(1 + redshift), 60000.*(1 + redshift))\n", 256 | "plt.show()" 257 | ] 258 | }, 259 | { 260 | "cell_type": "markdown", 261 | "metadata": {}, 262 | "source": [ 263 | "Ok, now we have our units the same let's calculate a chi-squared value." 264 | ] 265 | }, 266 | { 267 | "cell_type": "code", 268 | "execution_count": 10, 269 | "metadata": {}, 270 | "outputs": [ 271 | { 272 | "name": "stdout", 273 | "output_type": "stream", 274 | "text": [ 275 | "Chi-squared value: 3505.00879547\n" 276 | ] 277 | } 278 | ], 279 | "source": [ 280 | "diffs = fluxes - model_photometry\n", 281 | "\n", 282 | "chisq = np.sum(diffs**2/fluxerrs**2)\n", 283 | "\n", 284 | "print \"Chi-squared value:\", chisq" 285 | ] 286 | }, 287 | { 288 | "cell_type": "markdown", 289 | "metadata": {}, 290 | "source": [ 291 | "Not great, let's see if we can iterate towards a better solution. First plot this model over the data." 292 | ] 293 | }, 294 | { 295 | "cell_type": "code", 296 | "execution_count": 11, 297 | "metadata": {}, 298 | "outputs": [ 299 | { 300 | "data": { 301 | "image/png": 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\n", 302 | "text/plain": [ 303 | "
" 304 | ] 305 | }, 306 | "metadata": {}, 307 | "output_type": "display_data" 308 | } 309 | ], 310 | "source": [ 311 | "plt.figure(figsize=(15, 5))\n", 312 | "plt.errorbar(eff_wavs, fluxes, yerr=fluxerrs, lw=1.0, linestyle=\" \", capsize=3, capthick=1, color=\"black\")\n", 313 | "plt.scatter(eff_wavs, fluxes, s=75, linewidth=1, facecolor=\"blue\", edgecolor=\"black\")\n", 314 | "plt.scatter(eff_wavs, model_photometry, s=75, facecolor=\"orange\")\n", 315 | "plt.xscale(\"log\")\n", 316 | "plt.xlim(1000.*(1 + redshift), 60000.*(1 + redshift))\n", 317 | "plt.show()" 318 | ] 319 | }, 320 | { 321 | "cell_type": "markdown", 322 | "metadata": {}, 323 | "source": [ 324 | "Whilst it may not be obvious if you're new to this, once you've spent a long time looking at these kind of plots you'll be able to tell that it looks like the redshift is pretty good, but we've underestimated the age and the mass. Let's try again by stepping up by 0.5 dex in mass and 5 in our age index." 325 | ] 326 | }, 327 | { 328 | "cell_type": "code", 329 | "execution_count": 12, 330 | "metadata": {}, 331 | "outputs": [ 332 | { 333 | "name": "stdout", 334 | "output_type": "stream", 335 | "text": [ 336 | "Chi-squared value: 164.328659021\n" 337 | ] 338 | }, 339 | { 340 | "data": { 341 | "image/png": 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\n", 342 | "text/plain": [ 343 | "
" 344 | ] 345 | }, 346 | "metadata": {}, 347 | "output_type": "display_data" 348 | } 349 | ], 350 | "source": [ 351 | "mass = 10**10.5 # Solar masses\n", 352 | "redshift = 1.\n", 353 | "age_index = 30\n", 354 | "\n", 355 | "# Our photometry is in erg/s/cm^2/A per Solar mass of stars\n", 356 | "model_photometry = get_model_photometry(redshift, age_index)\n", 357 | "\n", 358 | "# Convert to erg/s/cm^2/A by multiplying by the total mass we want.\n", 359 | "model_photometry *= mass\n", 360 | "\n", 361 | "diffs = fluxes - model_photometry\n", 362 | "\n", 363 | "chisq = np.sum(diffs**2/fluxerrs**2)\n", 364 | "\n", 365 | "print \"Chi-squared value:\", chisq\n", 366 | "\n", 367 | "plt.figure(figsize=(15, 5))\n", 368 | "plt.errorbar(eff_wavs, fluxes, yerr=fluxerrs, lw=1.0, linestyle=\" \", capsize=3, capthick=1, color=\"black\")\n", 369 | "plt.scatter(eff_wavs, fluxes, s=75, linewidth=1, facecolor=\"blue\", edgecolor=\"black\")\n", 370 | "plt.scatter(eff_wavs, model_photometry, s=75, facecolor=\"orange\", zorder=10)\n", 371 | "plt.xscale(\"log\")\n", 372 | "plt.xlim(1000.*(1 + redshift), 60000.*(1 + redshift))\n", 373 | "plt.show()" 374 | ] 375 | }, 376 | { 377 | "cell_type": "markdown", 378 | "metadata": {}, 379 | "source": [ 380 | "We're already doing a lot better, but it's still going to take forever to get anywhere this way. Let's go to the next step and iterate over a grid of points in order to make things faster." 381 | ] 382 | }, 383 | { 384 | "cell_type": "code", 385 | "execution_count": null, 386 | "metadata": {}, 387 | "outputs": [], 388 | "source": [] 389 | } 390 | ], 391 | "metadata": { 392 | "kernelspec": { 393 | "display_name": "Python 2", 394 | "language": "python", 395 | "name": "python2" 396 | }, 397 | "language_info": { 398 | "codemirror_mode": { 399 | "name": "ipython", 400 | "version": 2 401 | }, 402 | "file_extension": ".py", 403 | "mimetype": "text/x-python", 404 | "name": "python", 405 | "nbconvert_exporter": "python", 406 | "pygments_lexer": "ipython2", 407 | "version": "2.7.14" 408 | } 409 | }, 410 | "nbformat": 4, 411 | "nbformat_minor": 2 412 | } 413 | -------------------------------------------------------------------------------- /Step 6 - Grid-based fitting.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Step 6 - Grid-based fitting\n", 8 | "\n", 9 | "In the previous step we were painfully inching our way towards the right answer, now let's just automate things and search for the right answer over a 3D grid of points in age, redshift and mass. I've updated the functions from Steps 3 and 4 to handle the mass and unit conversions from Step 5 respectively to tidy up the bit of the code that's going to be new." 10 | ] 11 | }, 12 | { 13 | "cell_type": "code", 14 | "execution_count": 3, 15 | "metadata": {}, 16 | "outputs": [], 17 | "source": [ 18 | "import numpy as np\n", 19 | "\n", 20 | "from astropy.cosmology import FlatLambdaCDM\n", 21 | "\n", 22 | "cosmo = FlatLambdaCDM(H0=70., Om0=0.3)\n", 23 | "\n", 24 | "\n", 25 | "def get_model_grid():\n", 26 | " \"\"\" Loads up the BPASS grid of stellar models and \n", 27 | " resamples it onto a coarser wavelength grid. See Step 1. \"\"\"\n", 28 | " \n", 29 | " model_path = \"data/spectra-bin-imf135_300.z020.dat\"\n", 30 | " raw_wavelengths = np.loadtxt(model_path, usecols=0)\n", 31 | " raw_grid = np.loadtxt(model_path)[:,1:]\n", 32 | " \n", 33 | " grid = np.zeros((wavelengths.shape[0], raw_grid.shape[1]))\n", 34 | "\n", 35 | " for i in range(grid.shape[1]):\n", 36 | " grid[:,i] = np.interp(wavelengths, raw_wavelengths, raw_grid[:,i])\n", 37 | " \n", 38 | " grid *= (3.827*10**33)/(10**6)\n", 39 | "\n", 40 | " return grid\n", 41 | "\n", 42 | " \n", 43 | "def blueshift_filters(redshift):\n", 44 | " \"\"\" A function that resamples filters onto the same wavelength\n", 45 | " basis as the model spectrum at the specified redshift. See Step 2. \"\"\"\n", 46 | " \n", 47 | " resampled_filter_curves = []\n", 48 | "\n", 49 | " for filt in filter_curves:\n", 50 | " blueshifted_wavs = filt[:, 0]/(1 + redshift)\n", 51 | " \n", 52 | " resampled_filt = np.interp(wavelengths,\n", 53 | " blueshifted_wavs, filt[:, 1],\n", 54 | " left=0, right=0)\n", 55 | " \n", 56 | " resampled_filter_curves.append(resampled_filt)\n", 57 | " \n", 58 | " return resampled_filter_curves\n", 59 | "\n", 60 | "\n", 61 | "def get_model_photometry(redshift, age_index, mass):\n", 62 | " \"\"\" For a row in the model grid return model\n", 63 | " photometry at the specified redshifts. See Step 3. \"\"\"\n", 64 | "\n", 65 | " ssp_model = np.copy(grid[:, age_index])\n", 66 | " \n", 67 | " luminosity_distance = (3.086*10**24)*cosmo.luminosity_distance(redshift).value\n", 68 | "\n", 69 | " ssp_model /= 4*np.pi*(1 + redshift)*luminosity_distance**2\n", 70 | "\n", 71 | " filter_curves_z = blueshift_filters(redshift)\n", 72 | "\n", 73 | " photometry = np.zeros(len(filter_curves))\n", 74 | "\n", 75 | " redshifted_wavs = wavelengths*(1 + redshift)\n", 76 | " \n", 77 | " for i in range(photometry.shape[0]):\n", 78 | " flux_contributions = filter_curves_z[i]*ssp_model\n", 79 | " photometry[i] = np.trapz(flux_contributions, x=redshifted_wavs)\n", 80 | " photometry[i] /= np.trapz(filter_curves_z[i], x=redshifted_wavs)\n", 81 | " \n", 82 | " photometry = photometry*mass \n", 83 | " \n", 84 | " return photometry\n", 85 | "\n", 86 | "\n", 87 | "\n", 88 | "\n", 89 | "def load_data(row_no):\n", 90 | " \"\"\" Load UltraVISTA photometry from catalogue. See Step 4. \"\"\"\n", 91 | "\n", 92 | " # load up the relevant columns from the catalogue.\n", 93 | " catalogue = np.loadtxt(\"data/UltraVISTA_catalogue.cat\",\n", 94 | " usecols=(0,3,4,5,6,7,8,9,10,11,12,13,14,15,\n", 95 | " 16,17,18,19,20,21,22,23,24,25,26))\n", 96 | " \n", 97 | " # Extract the object we're interested in from the catalogue.\n", 98 | " fluxes = catalogue[row_no, 1:13]\n", 99 | " fluxerrs = catalogue[row_no, 13:25]\n", 100 | "\n", 101 | " # Fluxes come in erg/s/cm^2/Hz.\n", 102 | "\n", 103 | " # Put an error floor into the data at the 20 sigma level.\n", 104 | " # This is normally done to account for systematic uncertainties.\n", 105 | " for i in range(fluxes.shape[0]):\n", 106 | " if fluxerrs[i] < fluxes[i]/20:\n", 107 | " fluxerrs[i] = fluxes[i]/20\n", 108 | "\n", 109 | " # Convert from erg/s/cm^2/Hz to erg/s/cm^2/A.\n", 110 | " fluxes = fluxes*2.9979*10**18/eff_wavs**2\n", 111 | " fluxerrs = fluxerrs*2.9979*10**18/eff_wavs**2\n", 112 | " \n", 113 | " return fluxes, fluxerrs\n", 114 | "\n", 115 | "\n", 116 | "# Define our basic quantities.\n", 117 | "wavelengths = np.arange(1000., 60000., 10.)\n", 118 | "ages = np.arange(2, 53)\n", 119 | "ages = 10**(6+0.1*(ages-2))\n", 120 | "\n", 121 | "grid = get_model_grid()\n", 122 | "\n", 123 | "# Load the curves up.\n", 124 | "filter_names = [\"data/filters/CFHT_u.txt\",\n", 125 | " \"data/filters/CFHT_g.txt\",\n", 126 | " \"data/filters/CFHT_r.txt\",\n", 127 | " \"data/filters/CFHT_i+i2.txt\",\n", 128 | " \"data/filters/CFHT_z.txt\",\n", 129 | " \"data/filters/subaru_z\",\n", 130 | " \"data/filters/VISTA_Y.txt\",\n", 131 | " \"data/filters/VISTA_J.txt\",\n", 132 | " \"data/filters/VISTA_H.txt\",\n", 133 | " \"data/filters/VISTA_Ks.txt\",\n", 134 | " \"data/filters/IRAC1\",\n", 135 | " \"data/filters/IRAC2\"]\n", 136 | "\n", 137 | "filter_curves = []\n", 138 | "\n", 139 | "for name in filter_names:\n", 140 | " filter_curves.append(np.loadtxt(name))\n", 141 | " \n", 142 | "eff_wavs = np.zeros(len(filter_curves))\n", 143 | "\n", 144 | "# Calculate the effective wavelengths of the filter curves\n", 145 | "for i in range(len(filter_curves)):\n", 146 | " filt = filter_curves[i]\n", 147 | "\n", 148 | " wav_weights = filt[:,1]*filt[:,0]\n", 149 | " \n", 150 | " eff_wavs[i] = np.trapz(wav_weights, x=filt[:,0])\n", 151 | "\n", 152 | " eff_wavs[i] /= np.trapz(filt[:, 1], x=filt[:,0])" 153 | ] 154 | }, 155 | { 156 | "cell_type": "markdown", 157 | "metadata": {}, 158 | "source": [ 159 | "Right, now the interesting bit, let's load up our data, define a grid of points to sample over and find out best fit. This may take a while, but at least we can go away and do something else now instead of manually fiddling with the parameters." 160 | ] 161 | }, 162 | { 163 | "cell_type": "code", 164 | "execution_count": 4, 165 | "metadata": {}, 166 | "outputs": [ 167 | { 168 | "name": "stdout", 169 | "output_type": "stream", 170 | "text": [ 171 | "Tried 0 / 520251 models.\n", 172 | "Tried 10000 / 520251 models.\n", 173 | "Tried 20000 / 520251 models.\n", 174 | "Tried 30000 / 520251 models.\n", 175 | "Tried 40000 / 520251 models.\n", 176 | "Tried 50000 / 520251 models.\n", 177 | "Tried 60000 / 520251 models.\n", 178 | "Tried 70000 / 520251 models.\n", 179 | "Tried 80000 / 520251 models.\n", 180 | "Tried 90000 / 520251 models.\n", 181 | "Tried 100000 / 520251 models.\n", 182 | "Tried 110000 / 520251 models.\n", 183 | "Tried 120000 / 520251 models.\n", 184 | "Tried 130000 / 520251 models.\n", 185 | "Tried 140000 / 520251 models.\n", 186 | "Tried 150000 / 520251 models.\n", 187 | "Tried 160000 / 520251 models.\n", 188 | "Tried 170000 / 520251 models.\n", 189 | "Tried 180000 / 520251 models.\n", 190 | "Tried 190000 / 520251 models.\n", 191 | "Tried 200000 / 520251 models.\n", 192 | "Tried 210000 / 520251 models.\n", 193 | "Tried 220000 / 520251 models.\n", 194 | "Tried 230000 / 520251 models.\n", 195 | "Tried 240000 / 520251 models.\n", 196 | "Tried 250000 / 520251 models.\n", 197 | "Tried 260000 / 520251 models.\n", 198 | "Tried 270000 / 520251 models.\n", 199 | "Tried 280000 / 520251 models.\n", 200 | "Tried 290000 / 520251 models.\n", 201 | "Tried 300000 / 520251 models.\n", 202 | "Tried 310000 / 520251 models.\n", 203 | "Tried 320000 / 520251 models.\n", 204 | "Tried 330000 / 520251 models.\n", 205 | "Tried 340000 / 520251 models.\n", 206 | "Tried 350000 / 520251 models.\n", 207 | "Tried 360000 / 520251 models.\n", 208 | "Tried 370000 / 520251 models.\n", 209 | "Tried 380000 / 520251 models.\n", 210 | "Tried 390000 / 520251 models.\n", 211 | "Tried 400000 / 520251 models.\n", 212 | "Tried 410000 / 520251 models.\n", 213 | "Tried 420000 / 520251 models.\n", 214 | "Tried 430000 / 520251 models.\n", 215 | "Tried 440000 / 520251 models.\n", 216 | "Tried 450000 / 520251 models.\n", 217 | "Tried 460000 / 520251 models.\n", 218 | "Tried 470000 / 520251 models.\n", 219 | "Tried 480000 / 520251 models.\n", 220 | "Tried 490000 / 520251 models.\n", 221 | "Tried 500000 / 520251 models.\n", 222 | "Tried 510000 / 520251 models.\n", 223 | "Tried 520000 / 520251 models.\n", 224 | "best chi-squared value: 51.42339121433705\n", 225 | "('best parameters (z, mass, age):', 0.8800000000000003, 10.179999999999996, 0.7943282347242822)\n" 226 | ] 227 | } 228 | ], 229 | "source": [ 230 | "fluxes, fluxerrs = load_data(1)\n", 231 | "\n", 232 | "redshifts = np.arange(0.5, 1.501, 0.01)\n", 233 | "masses = 10**np.arange(10, 11.001, 0.01)\n", 234 | "age_indices = np.arange(51)\n", 235 | "\n", 236 | "best_chisq = np.inf\n", 237 | "best_point = [0.,0.,0.]\n", 238 | "\n", 239 | "n_redshifts = redshifts.shape[0]\n", 240 | "n_masses = masses.shape[0]\n", 241 | "n_ages = ages.shape[0]\n", 242 | "n_models = n_redshifts*n_masses*n_ages\n", 243 | "\n", 244 | "for i in range(n_redshifts):\n", 245 | " for j in range(n_masses):\n", 246 | " for k in range(n_ages):\n", 247 | " \n", 248 | " model_no = k + j*n_ages + i*n_masses*n_ages\n", 249 | " \n", 250 | " if not model_no % 10000:\n", 251 | " print \"Tried\", model_no, \"/\", n_models, \"models.\"\n", 252 | " \n", 253 | " redshift = redshifts[i]\n", 254 | " mass = masses[j]\n", 255 | " age_ind = age_indices[k]\n", 256 | "\n", 257 | " model_photometry = get_model_photometry(redshift, age_ind, mass)\n", 258 | " \n", 259 | " diffs = fluxes - model_photometry\n", 260 | "\n", 261 | " chisq = np.sum(diffs**2/fluxerrs**2)\n", 262 | " \n", 263 | " if chisq < best_chisq:\n", 264 | " best_chisq = chisq\n", 265 | " best_point = [i,j,k]\n", 266 | " \n", 267 | "print \"best chi-squared value:\", best_chisq\n", 268 | "print (\"best parameters (z, mass, age):\",\n", 269 | " redshifts[best_point[0]],\n", 270 | " np.log10(masses[best_point[1]]),\n", 271 | " ages[age_indices[best_point[2]]]*10**-9)" 272 | ] 273 | }, 274 | { 275 | "cell_type": "markdown", 276 | "metadata": {}, 277 | "source": [ 278 | "By a wild coincidence this code generats models at about the same rate as BAGPIPES, though obviously there's a lot more going on under the hood in BAGPIPES, and it certainly doesn't take half a million iterations to converge on a 3 parameter problem! I haven't checked but I suspect the bottleneck here is the astropy luminosity_distance function.\n", 279 | "\n", 280 | "Let's plot the solution our grid search has come up with and see what we think." 281 | ] 282 | }, 283 | { 284 | "cell_type": "code", 285 | "execution_count": 6, 286 | "metadata": {}, 287 | "outputs": [ 288 | { 289 | "data": { 290 | "image/png": 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\n", 291 | "text/plain": [ 292 | "
" 293 | ] 294 | }, 295 | "metadata": {}, 296 | "output_type": "display_data" 297 | } 298 | ], 299 | "source": [ 300 | "import matplotlib.pyplot as plt\n", 301 | "\n", 302 | "model_photometry = get_model_photometry(redshifts[best_point[0]], \n", 303 | " age_indices[best_point[2]], \n", 304 | " masses[best_point[1]])\n", 305 | "\n", 306 | "plt.figure(figsize=(15, 5))\n", 307 | "plt.errorbar(eff_wavs, fluxes, yerr=fluxerrs, lw=1.0, linestyle=\" \", \n", 308 | " capsize=3, capthick=1, color=\"black\")\n", 309 | "\n", 310 | "plt.scatter(eff_wavs, fluxes, s=75, linewidth=1, \n", 311 | " facecolor=\"blue\", edgecolor=\"black\")\n", 312 | "\n", 313 | "plt.scatter(eff_wavs, model_photometry, s=75, \n", 314 | " facecolor=\"orange\", zorder=10)\n", 315 | "\n", 316 | "plt.xscale(\"log\")\n", 317 | "plt.xlim(1000.*(1 + redshift), 60000.*(1 + redshift))\n", 318 | "plt.show()" 319 | ] 320 | }, 321 | { 322 | "cell_type": "markdown", 323 | "metadata": {}, 324 | "source": [ 325 | "You can see this model isn't a perfect fit to the data, but it isn't half bad given the simplifying assumptions we've made. Our minimum reduced chi-squared value is about 5.7, and I believe the spectroscopic redshift from Lega-C is around 0.92, so we're within 0.05.\n", 326 | "\n", 327 | "That's it for the tutorial, I hope you found it useful!" 328 | ] 329 | } 330 | ], 331 | "metadata": { 332 | "kernelspec": { 333 | "display_name": "Python 2", 334 | "language": "python", 335 | "name": "python2" 336 | }, 337 | "language_info": { 338 | "codemirror_mode": { 339 | "name": "ipython", 340 | "version": 2 341 | }, 342 | "file_extension": ".py", 343 | "mimetype": "text/x-python", 344 | "name": "python", 345 | "nbconvert_exporter": "python", 346 | "pygments_lexer": "ipython2", 347 | "version": "2.7.14" 348 | } 349 | }, 350 | "nbformat": 4, 351 | "nbformat_minor": 2 352 | } 353 | -------------------------------------------------------------------------------- /data/UltraVISTA_catalogue.cat: -------------------------------------------------------------------------------- 1 | # ID RA Dec u g r i z z_sub Y J H K IRAC1 IRAC2 u_err g_err r_err i_err z_err z_sub_err Y_err J_err H_err K_err IRAC1_err IRAC2_err med_zphot cat_flag 2 | 9.005200000000000000e+04 1.504182179500000132e+02 2.016852062299999915e+00 4.784149999999999674e-31 1.066950999999999929e-30 4.092548000000000211e-30 1.377000000000000031e-29 2.553288999999999721e-29 2.850824999999999945e-29 4.042347999999999781e-29 7.372301999999999549e-29 1.143512000000000003e-28 1.923006000000000023e-28 3.256411000000000223e-28 2.352991000000000023e-28 1.345679999999999891e-31 1.374680000000000093e-31 2.309479999999999842e-31 6.884999999999999978e-31 1.276645000000000068e-30 1.425413000000000076e-30 2.021174000000000171e-30 3.686151000000000195e-30 5.717560000000000016e-30 9.615030000000000396e-30 3.256410999999999774e-29 2.352990999999999967e-29 9.000000000000000222e-01 2.000000000000000000e+00 3 | 9.697600000000000000e+04 1.504443243800000118e+02 2.038632248999999952e+00 2.227856999999999886e-30 3.853693000000000244e-30 1.223257000000000024e-29 3.419206000000000097e-29 6.419618999999999534e-29 7.164044000000000245e-29 9.255203000000000274e-29 1.239207000000000094e-28 1.606604000000000078e-28 2.082824000000000152e-28 2.570925999999999963e-28 1.668960999999999896e-28 1.280610000000000064e-31 1.926846000000000107e-31 6.116284999999999593e-31 1.709602999999999909e-30 3.209809999999999940e-30 3.582022000000000123e-30 4.627601999999999750e-30 6.196034999999999908e-30 8.033020000000000109e-30 1.041411999999999936e-29 2.570925999999999851e-29 1.668961000000000064e-29 9.399999999999999467e-01 1.000000000000000000e+00 4 | 1.022160000000000000e+05 1.504296549299999981e+02 2.057103832400000165e+00 2.821050000000000002e-31 9.717879999999999363e-31 6.480127999999999725e-30 2.018247999999999917e-29 4.401966999999999930e-29 -9.900000000000000000e+01 7.168065999999999565e-29 1.109757000000000056e-28 1.644593999999999927e-28 2.316034999999999921e-28 3.087351000000000095e-28 2.026277000000000203e-28 1.413400000000000038e-31 1.286559999999999960e-31 3.240063999999999950e-31 1.009123999999999959e-30 2.200984000000000068e-30 -9.900000000000000000e+01 3.584033000000000343e-30 5.548785000000000281e-30 8.222969999999999353e-30 1.158017999999999965e-29 3.087350999999999758e-29 2.026277000000000091e-29 9.456999999999999851e-01 1.000000000000000000e+00 5 | 1.184820000000000000e+05 1.503732196999999928e+02 2.105747718299999960e+00 1.123342000000000081e-30 7.540046999999999521e-30 3.180553999999999773e-29 8.354774000000000519e-29 1.249370000000000016e-28 1.378198999999999942e-28 1.828988999999999960e-28 2.791500999999999864e-28 4.274577000000000203e-28 5.996345999999999643e-28 5.723603999999999608e-28 3.566050000000000060e-28 1.159289999999999970e-31 3.770024000000000039e-31 1.590277000000000167e-30 4.177387000000000259e-30 6.246849999999999662e-30 6.890994999999999993e-30 9.144944999999999801e-30 1.395751000000000133e-29 2.137289000000000078e-29 2.998172999999999822e-29 5.723604000000000281e-29 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2.520525999999999930e-03 213 | 1.015500000000000000e+04 2.220941000000000148e-03 214 | -------------------------------------------------------------------------------- /final_code.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import matplotlib.pyplot as plt 3 | 4 | from astropy.cosmology import FlatLambdaCDM 5 | 6 | cosmo = FlatLambdaCDM(H0=70., Om0=0.3) 7 | 8 | 9 | def get_model_grid(): 10 | """ Loads up the BPASS grid of stellar models and 11 | resamples it onto a coarser wavelength grid. See Step 1. """ 12 | 13 | model_path = "data/spectra-bin-imf135_300.z020.dat" 14 | raw_wavelengths = np.loadtxt(model_path, usecols=0) 15 | raw_grid = np.loadtxt(model_path)[:,1:] 16 | 17 | grid = np.zeros((wavelengths.shape[0], raw_grid.shape[1])) 18 | 19 | for i in range(grid.shape[1]): 20 | grid[:,i] = np.interp(wavelengths, raw_wavelengths, raw_grid[:,i]) 21 | 22 | grid *= (3.827*10**33)/(10**6) 23 | 24 | return grid 25 | 26 | 27 | def blueshift_filters(redshift): 28 | """ A function that resamples filters onto the same wavelength 29 | basis as the model spectrum at the specified redshift. See Step 2. """ 30 | 31 | resampled_filter_curves = [] 32 | 33 | for filt in filter_curves: 34 | blueshifted_wavs = filt[:, 0]/(1 + redshift) 35 | 36 | resampled_filt = np.interp(wavelengths, 37 | blueshifted_wavs, filt[:, 1], 38 | left=0, right=0) 39 | 40 | resampled_filter_curves.append(resampled_filt) 41 | 42 | return resampled_filter_curves 43 | 44 | 45 | def get_model_photometry(redshift, age_index, mass): 46 | """ For a row in the model grid return model 47 | photometry at the specified redshifts. See Step 3. """ 48 | 49 | ssp_model = np.copy(grid[:, age_index]) 50 | 51 | luminosity_distance = (3.086*10**24)*cosmo.luminosity_distance(redshift) 52 | 53 | ssp_model /= 4*np.pi*(1 + redshift)*luminosity_distance.value**2 54 | 55 | filter_curves_z = blueshift_filters(redshift) 56 | 57 | photometry = np.zeros(len(filter_curves)) 58 | 59 | redshifted_wavs = wavelengths*(1 + redshift) 60 | 61 | for i in range(photometry.shape[0]): 62 | flux_contributions = filter_curves_z[i]*ssp_model 63 | photometry[i] = np.trapz(flux_contributions, x=redshifted_wavs) 64 | photometry[i] /= np.trapz(filter_curves_z[i], x=redshifted_wavs) 65 | 66 | photometry = photometry*mass 67 | 68 | return photometry 69 | 70 | 71 | def load_data(row_no): 72 | """ Load UltraVISTA photometry from catalogue. See Step 4. """ 73 | 74 | # load up the relevant columns from the catalogue. 75 | catalogue = np.loadtxt("data/UltraVISTA_catalogue.cat", 76 | usecols=(0,3,4,5,6,7,8,9,10,11,12,13,14,15, 77 | 16,17,18,19,20,21,22,23,24,25,26)) 78 | 79 | # Extract the object we're interested in from the catalogue. 80 | fluxes = catalogue[row_no, 1:13] 81 | fluxerrs = catalogue[row_no, 13:25] 82 | 83 | # Fluxes come in erg/s/cm^2/Hz. 84 | 85 | # Put an error floor into the data at the 20 sigma level. 86 | # This is normally done to account for systematic uncertainties. 87 | for i in range(fluxes.shape[0]): 88 | if fluxerrs[i] < fluxes[i]/20: 89 | fluxerrs[i] = fluxes[i]/20 90 | 91 | # Convert from erg/s/cm^2/Hz to erg/s/cm^2/A. 92 | fluxes = fluxes*2.9979*10**18/eff_wavs**2 93 | fluxerrs = fluxerrs*2.9979*10**18/eff_wavs**2 94 | 95 | return fluxes, fluxerrs 96 | 97 | 98 | # Define our basic quantities. 99 | wavelengths = np.arange(1000., 60000., 10.) 100 | ages = np.arange(2, 53) 101 | ages = 10**(6+0.1*(ages-2)) 102 | 103 | grid = get_model_grid() 104 | 105 | # Load the curves up. 106 | filter_names = ["data/filters/CFHT_u.txt", 107 | "data/filters/CFHT_g.txt", 108 | "data/filters/CFHT_r.txt", 109 | "data/filters/CFHT_i+i2.txt", 110 | "data/filters/CFHT_z.txt", 111 | "data/filters/subaru_z", 112 | "data/filters/VISTA_Y.txt", 113 | "data/filters/VISTA_J.txt", 114 | "data/filters/VISTA_H.txt", 115 | "data/filters/VISTA_Ks.txt", 116 | "data/filters/IRAC1", 117 | "data/filters/IRAC2"] 118 | 119 | filter_curves = [] 120 | 121 | for name in filter_names: 122 | filter_curves.append(np.loadtxt(name)) 123 | 124 | eff_wavs = np.zeros(len(filter_curves)) 125 | 126 | # Calculate the effective wavelengths of the filter curves 127 | for i in range(len(filter_curves)): 128 | filt = filter_curves[i] 129 | 130 | wav_weights = filt[:,1]*filt[:,0] 131 | 132 | eff_wavs[i] = np.trapz(wav_weights, x=filt[:,0]) 133 | 134 | eff_wavs[i] /= np.trapz(filt[:, 1], x=filt[:,0]) 135 | 136 | # Load observational data 137 | fluxes, fluxerrs = load_data(1) 138 | 139 | # Set grid ranges and steps 140 | redshifts = np.arange(0.5, 1.501, 0.01) 141 | masses = 10**np.arange(10, 11.001, 0.01) 142 | age_indices = np.arange(51) 143 | 144 | best_chisq = np.inf 145 | best_point = [0.,0.,0.] 146 | 147 | n_redshifts = redshifts.shape[0] 148 | n_masses = masses.shape[0] 149 | n_ages = ages.shape[0] 150 | n_models = n_redshifts*n_masses*n_ages 151 | 152 | # Iterate over the grid 153 | for i in range(n_redshifts): 154 | for j in range(n_masses): 155 | for k in range(n_ages): 156 | 157 | model_no = k + j*n_ages + i*n_masses*n_ages 158 | 159 | if not model_no % 10000: 160 | print "Tried", model_no, "/", n_models, "models." 161 | 162 | redshift = redshifts[i] 163 | mass = masses[j] 164 | age_ind = age_indices[k] 165 | 166 | model_photometry = get_model_photometry(redshift, age_ind, mass) 167 | 168 | diffs = fluxes - model_photometry 169 | 170 | chisq = np.sum(diffs**2/fluxerrs**2) 171 | 172 | if chisq < best_chisq: 173 | best_chisq = chisq 174 | best_point = [i,j,k] 175 | 176 | print "best chi-squared value:", best_chisq 177 | 178 | print ("best parameters (z, mass, age):", 179 | redshifts[best_point[0]], 180 | np.log10(masses[best_point[1]]), 181 | ages[age_indices[best_point[2]]]*10**-9) 182 | 183 | # Plot the results 184 | best_photometry = get_model_photometry(redshifts[best_point[0]], 185 | age_indices[best_point[2]], 186 | masses[best_point[1]]) 187 | 188 | plt.figure(figsize=(15, 5)) 189 | plt.errorbar(eff_wavs, fluxes, yerr=fluxerrs, lw=1.0, linestyle=" ", 190 | capsize=3, capthick=1, color="black") 191 | 192 | plt.scatter(eff_wavs, fluxes, s=75, linewidth=1, 193 | facecolor="blue", edgecolor="black") 194 | 195 | plt.scatter(eff_wavs, best_photometry, s=75, facecolor="orange", zorder=10) 196 | plt.xscale("log") 197 | plt.xlim(1000.*(1 + redshift), 60000.*(1 + redshift)) 198 | plt.show() 199 | --------------------------------------------------------------------------------