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1.041695 0.059135 0.1000 + z_m_limit 11 17.0 3 2.180201 0.197294 0.1000 + z_m_limit 12 18.0 3 1.355358 0.089641 0.1000 + z_m_limit 13 19.0 3 1.301685 0.074906 0.1000 + z_m_limit 14 21.0 3 2.564522 0.309317 0.1000 + z_m_limit 15 25.0 3 1.653818 1.653818 0.1000 + z_m_limit 16 26.0 3 10.295902 4.957629 0.1000 + newton 1 + mult_wcs 3 + sigposArcsec 0.44271887242357316 + end +grille + nombre 128 + polaire 0 + nlentille 149 + nlens_opt 5 + end +potentiel O1 + profil 81 + x_centre -0.979130 + y_centre 0.562751 + ellipticite 0.679974 + angle_pos 546.307537 + core_radius_kpc 72.823746 + cut_radius_kpc 1500.000000 + v_disp 974.871092 + z_lens 0.3900 + end +limit O1 + x_centre 3 -1.690695 1.548630 0.010000 + y_centre 3 0.494555 0.494555 0.010000 + ellipticite 3 0.671254 0.102648 0.000000 + angle_pos 3 545.282208 2.515631 0.100000 + core_radius_kpc 3 69.326783 20.178728 0.100000 + v_disp 3 940.938928 94.281629 0.100000 + end +potentiel O2 + profil 81 + x_centre 0.000000 + y_centre 0.000000 + ellipticite 0.161000 + angle_pos 29.200000 + core_radius_kpc 0.739248 + cut_radius_kpc 15.484341 + v_disp 348.735025 + z_lens 0.3900 + end +limit O2 + core_radius_kpc 3 1.142028 1.142028 0.100000 + cut_radius_kpc 3 25.088747 19.646797 0.100000 + v_disp 3 316.964704 63.444421 0.100000 + end +potentiel O3 + profil 81 + x_centre 35.018340 + y_centre 25.622865 + ellipticite 0.556698 + angle_pos 42.852676 + core_radius_kpc 1.043435 + cut_radius_kpc 196.972088 + v_disp 250.659203 + z_lens 0.3900 + end +limit O3 + x_centre 3 32.291342 4.171206 0.100000 + y_centre 3 23.224141 2.499710 0.100000 + ellipticite 3 0.665503 0.130670 0.000000 + angle_pos 3 35.846426 31.934088 0.100000 + core_radius_kpc 3 6.066072 6.066072 0.100000 + cut_radius_kpc 3 257.462815 144.350330 0.100000 + v_disp 3 241.703609 45.110533 0.100000 + end +potentiel O4 + profil 81 + x_centre 42.168551 + y_centre 0.264105 + ellipticite 0.356369 + angle_pos 37.047764 + core_radius_kpc 69.138007 + cut_radius_kpc 419.309414 + v_disp 426.762398 + z_lens 0.3900 + end +limit O4 + x_centre 3 43.411593 3.161986 0.100000 + y_centre 3 3.392387 3.392387 0.100000 + ellipticite 3 0.161926 0.161926 0.000000 + angle_pos 3 38.106823 35.681892 0.100000 + core_radius_kpc 3 86.009097 28.294007 0.100000 + cut_radius_kpc 3 385.526459 136.141412 0.100000 + v_disp 3 512.266665 188.463832 0.100000 + end +potentiel O5 + profil 81 + x_centre -13.636774 + y_centre -4.423680 + ellipticite 0.188572 + angle_pos 6.044797 + core_radius_kpc 4.928694 + cut_radius_kpc 51.369572 + v_disp 3.994717 + z_lens 0.3900 + end +limit O5 + ellipticity 1 0.0 0.6 0.01 + angle_pos 1 -90.0 90.0 0.1 + core_radius_kpc 3 3.343167 3.343167 0.100000 + cut_radius_kpc 3 91.255679 60.195571 0.100000 + v_disp 1 0.1 300.0 0.1 + end +potentiel O1 + profil 81 + x_centre -8.821696 + y_centre 87.105960 + ellipticite 0.763811 + angle_pos -51.100000 + core_radius_kpc 0.220664 + cut_radius_kpc 4.413278 + v_disp 60.644302 + mag 18.281800 + z_lens 0.3900 + end +limit O1 + end +potentiel O2 + profil 81 + x_centre 35.046789 + y_centre 25.268400 + ellipticite 0.010711 + angle_pos -40.600000 + core_radius_kpc 0.190771 + cut_radius_kpc 3.815410 + v_disp 56.387132 + mag 18.597900 + z_lens 0.3900 + end +limit O2 + end +potfile0 + filein 3 galcat.cat + zlens 0.390000 + type 81 + corekpc 0.150000 + mag0 19.120000 + sigma 3 110.504757 19.479206 + cutkpc 3 51.525067 27.573461 + slope 0 4.000000 0.000000 + vdslope 0 4.000000 0.000000 + vdscatter 0 0.000000 0.000000 + rcutscatter 0 0.000000 0.000000 + end +cline + nplan 0 + dmax 50.000000 + algorithm MARCHINGSQUARES + limitHigh 1.0 + limitLow 0.100000 + end +grande + iso 0 0 0.000000 0.000000 0.000000 + name best + profil 0 0 + contour 1 0 + large_dist 0.300000 + end +cosmologie + model 1 + H0 70.000000 + omegaM 0.300000 + omegaX 0.700000 + omegaK 0. + wX -1.000000 + wa 0.000000 + end +cosmolimit + omegaM 0 0.000000 0.000000 + omegaX 0 0.000000 0.000000 + wX 0 0.000000 0.000000 + wa 0 0.000000 0.000000 + end +champ + xmin -80.000000 + xmax 80.000000 + ymin -80.000000 + ymax 80.000000 + end +fini diff --git a/Notebooks/Clusters/mock_cluster_data.ipynb b/Notebooks/Clusters/mock_cluster_data.ipynb new file mode 100644 index 0000000..9b76bee --- /dev/null +++ b/Notebooks/Clusters/mock_cluster_data.ipynb @@ -0,0 +1,1548 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Modelling of mock catalogue data\n", + "$\\texttt{lenstronomy}$ was originally developed to simulate and model imaging data. The modular design allows to model and sample data in catalogue form too. In this notebook, we create mock data for multiple sources multiply imaged by a galaxy cluster.\n", + "\n", + "In the first step, we create in the necessary data:\n", + "- lens parameters; including position and redshift\n", + "- image parameters; including positions, apparent magnitudes, relative time delays and image brightnesses\n", + "\n", + "and perform some calculations:\n", + "- each lensing galaxy's eccentricity, absolute magnitude, luminosity, distance, velocity dispersion, Einstein radius, and realtive mass\n", + "- relative time delays of images\n", + "\n", + "The multiple images are then grouped together based on the number of sources and the known groups of multiple images.\n", + "\n", + "\n", + "In a second step, we use this mock data to sample the lens model parameter space. The modelling can also be used if only partial information is available (e.g. no time delays and/or flux ratio measurements) are available.\n", + "\n", + "The notebook also describes the different possibilities in folding in the positional information in the modeling when the underlying requirement is that the images come from the same source and how to enforce this when evaluating the time delay prediction." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Installing packages\n", + "The first block of packages all provide helpful methods to perform calculations, access constant values, and make plots. astropy and scipy contain relevant astrophysical constants and tools. math, numpy, and random all provide useful mathematical methods that are otherwise tedious to code. copy makes it easy to quickly duplicate useful information, leaving one as a reference and the other available to perform calculations on or update. corner and matplotlib contain plotting functions, making the creation of informative and interesting plots easier. pandas allows for easier organization of data through the pandas data frame.\n", + "\n", + "$\\texttt{lenstronomy}$ is the basis of this notebook, using the packages listed below for various purposes. LensModel creates the class used to generate images later, using the lens_plot functions. We also need the Extenstions and EquationsSolver packages in order to backward ray trace to determine source locations, among other uses. The PointSource class is used to later calculate the RMSE of the source positions, which helps tell us if the model is a good fit to the data. $\\texttt{lenstronomy clusters functions}$ is a new small package that helps to sort and collect the labels and data for the corner plots from the MCMC posteriors." + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": {}, + "outputs": [], + "source": [ + "# import the necessary python modules\n", + "import astropy\n", + "import copy\n", + "import corner\n", + "import math\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import pandas as pd\n", + "import random\n", + "import scipy\n", + "import time\n", + "from astropy.cosmology import FlatLambdaCDM\n", + "\n", + "from lenstronomy.LensModel.lens_model import LensModel\n", + "from lenstronomy.LensModel.lens_model_extensions import LensModelExtensions\n", + "from lenstronomy.LensModel.Solver.lens_equation_solver import LensEquationSolver\n", + "from lenstronomy.Cosmo.lens_cosmo import LensCosmo\n", + "from lenstronomy.Util import constants\n", + "from lenstronomy.Util import param_util\n", + "from lenstronomy.Plots import lens_plot\n", + "from lenstronomy.PointSource.point_source import PointSource\n", + "import lenstronomy_clusters_functions.clusters_functions\n", + "\n", + "%matplotlib inline\n", + "\n", + "measurement_realization = True # if True, draws measurement values from the uncertainties, if not, keeps the true value" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Generating the mock data.\n", + "Data for each galaxy cluster member is generated, along with the data for each source. We choose to create 10 cluster members in addition to the main dark matter halo and 20 background sources at varying redshifts.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# the redshifts of lens and source and the cosmology is only used when predicting the relative time delays between the images\n", + "random.seed(50)\n", + "\n", + "num_cluster_members = 10\n", + "z_lenses = []\n", + "for i in range(num_cluster_members):\n", + " z_lenses.append(0.5)\n", + "z_lens_nfw = 0.5\n", + "\n", + "\n", + "# set the redshifts of the background sources at various redshifts\n", + "num_sources = 20\n", + "z_sources = []\n", + "for i in range(num_sources):\n", + " z_sources.append(random.uniform(1,5))\n", + "z_source_convention = 1.5\n", + "\n", + "# choose the desired cosmology\n", + "cosmo = FlatLambdaCDM(H0=70, Om0=0.3, Ob0=0.)\n", + "lensCosmo = LensCosmo(cosmo=cosmo, z_lens=z_lens_nfw, z_source=z_source_convention)\n", + "\n", + "# make choice of lens model and make class instances for each. In this case, we use the dPIED and NFW_CSE for the member galaxies and the dark matter halo respectively\n", + "lens_model_list = []\n", + "for i in range(num_cluster_members):\n", + " lens_model_list.append('PJAFFE_ELLIPSE_POTENTIAL')\n", + "lens_model_list.append('NFW_ELLIPSE_CSE')\n", + "\n", + "# make instance of LensModel class. uses python class functionality. Essentially formats the data for future use\n", + "lensModel = LensModel(lens_model_list=lens_model_list, cosmo=cosmo, z_lens=z_lens_nfw, z_source_convention=z_source_convention, z_source=z_sources[0])\n", + "# we require routines accessible in the LensModelExtensions class. Gives us access to both the lens model extentions and equation solver code\n", + "lensModelExtensions = LensModelExtensions(lensModel=lensModel)\n", + "# make instance of LensEquationSolver to solve the lens equation\n", + "lensEquationSolver = LensEquationSolver(lensModel=lensModel)\n", + "\n", + "# generate the source and lens positions\n", + "x_sources = []\n", + "y_sources = []\n", + "x_cluster_members = []\n", + "y_cluster_members = []\n", + "# we chose a source position (in units angle)\n", + "for i in range(num_sources):\n", + " x_sources.append(random.uniform(-7, 7))\n", + " y_sources.append(random.uniform(-4, 4))\n", + "for i in range(num_cluster_members):\n", + " x_cluster_members.append(random.uniform(-15, 15))\n", + " y_cluster_members.append(random.uniform(-15, 15))\n", + "\n", + "\n", + "# for the given lens models, generate the necessary data according to the lenstronomy documentation\n", + "# for the dPIED models:\n", + "e1s = [random.uniform(-0.1, 0.1) for i in range(num_cluster_members)]\n", + "e2s = [random.uniform(-0.1, 0.1) for i in range(num_cluster_members)]\n", + "Ras = [random.uniform(0, 1) for i in range(num_cluster_members)]\n", + "Rss = [random.uniform(1, 10) for i in range(num_cluster_members)]\n", + "sigmaVs = [random.uniform(175, 325) for i in range(num_cluster_members)] # velocity dispersion around 200-300\n", + "sigma0s = [] # projected density normalization\n", + "thetaEs = []\n", + "# calculate a reasonable density normalization for each dPIED model\n", + "for i in range(num_cluster_members):\n", + " sigma0 = float((lensCosmo.vel_disp_dPIED_sigma0(vel_disp=sigmaVs[i], Ra=Ras[i], Rs=Rss[i])))\n", + " sigma0s.append(sigma0)\n", + " thetaE = float(lensCosmo.sis_sigma_v2theta_E(sigmaVs[i]))\n", + " thetaEs.append(thetaE)\n", + "# for the NFW model\n", + "nfw_e1 = 0.1\n", + "nfw_e2 = -0.3\n", + "nfw_x = 0\n", + "nfw_y = 0\n", + "nfw_sigmaV = 150\n", + "nfw_thetaE = float(lensCosmo.sis_sigma_v2theta_E(nfw_sigmaV))\n", + "nfw_mass = 10**14.5 # solar masses, mass of a galaxy cluster's halo\n", + "concentration = 10 # ratio of r200 to Rs\n", + "nfw_Rs, nfw_alpha_Rs = lensCosmo.nfw_physical2angle(nfw_mass, concentration) # outputs Rs angle and alpha Rs. See google slides 1/27/25\n", + "\n", + "\n", + "## create the keyword arguments for the lens and fix the relative scaling of one deflector and another\n", + "# mass_scaling = False # if True, samples scaling parameters\n", + "# num_scale_factor = 1 # number of scaling parameters being sampled\n", + "kwargs_lens = []\n", + "mass_scaling_list = []\n", + "for i in range(num_cluster_members):\n", + " kwargs_lens.append({'sigma0': sigma0s[i], \"e1\": e1s[i], \"e2\": e2s[i], 'Ra': Ras[i], 'Rs': Rss[i], 'center_x': x_cluster_members[i], \"center_y\": y_cluster_members[i]})\n", + " mass_scaling_list.append(1)\n", + "kwargs_lens.append({\"Rs\": nfw_Rs, \"alpha_Rs\": nfw_alpha_Rs, \"e1\": nfw_e1, \"e2\": nfw_e2, \"center_x\": nfw_x, \"center_y\": nfw_y})\n", + "mass_scaling_list.append(False)" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1, 5, 3, 9, 3, 3, 1, 5, 5, 5, 5, 3, 5, 5, 1, 3, 5, 5, 1, 5]\n" + ] + } + ], + "source": [ + "# we solve for the image position(s) of the provided source position and lens model\n", + "x_imgs = []\n", + "y_imgs = []\n", + "for i in range(num_sources):\n", + " # update redshift for each source\n", + " lensEquationSolver.lensModel.change_source_redshift(z_source=z_sources[i])\n", + " x_img_temp, y_img_temp = lensEquationSolver.image_position_from_source(kwargs_lens=kwargs_lens, sourcePos_x=x_sources[i], sourcePos_y=y_sources[i], search_window=150)\n", + " x_imgs.append(x_img_temp)\n", + " y_imgs.append(y_img_temp)\n", + "\n", + "num_images_list = []\n", + "for i in range(num_sources):\n", + " num_images_list.append(len(x_imgs[i]))\n", + "print(num_images_list)" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0\n", + "6\n", + "14\n", + "18\n", + "[5, 3, 9, 3, 3, 5, 5, 5, 5, 3, 5, 5, 3, 5, 5, 5]\n" + ] + } + ], + "source": [ + "# do not run this code block more than once in a row!!!\n", + "# removes sources, their redshifts, and the num_images from the respective lists\n", + "\n", + "num_sources = 20\n", + "num = 0\n", + "single_images = []\n", + "for i in range(num_sources):\n", + " if len(x_imgs[i]) == 1:\n", + " print(i)\n", + " num+=1\n", + " single_images.append(i)\n", + "\n", + "num_sources -= num\n", + "single_image_sources = []\n", + "for item in single_images[::-1]:\n", + " single_image_sources.append(item)\n", + "\n", + "for i in range(len(single_image_sources)):\n", + " x_sources.pop(single_image_sources[i])\n", + " y_sources.pop(single_image_sources[i])\n", + " z_sources.pop(single_image_sources[i])\n", + " x_imgs.pop(single_image_sources[i])\n", + " y_imgs.pop(single_image_sources[i])\n", + " num_images_list.pop(single_image_sources[i])\n", + "\n", + "# we now have a revised list of sources that include only sources that produce multiple images\n", + "print(num_images_list)" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": {}, + "outputs": [], + "source": [ + "image_ids = []\n", + "for i in range(num_sources):\n", + " for j in range(len(x_imgs[i])):\n", + " image_ids.append(str(i+1)+'.'+str(j+1))" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "point source magnification: [ 4.05958217 2.93307485 -1.27332527 -1.82404073 0.12146693]\n", + "source size in arcsec: [np.float64(0.0013266197473033032), np.float64(0.001843025597768968), np.float64(0.001214753891368082), np.float64(0.0015365738780623768), np.float64(0.0017544569241995356), np.float64(0.0017318437249481198), np.float64(0.0015298640122022136), np.float64(0.0019664417132685477), np.float64(0.0014751006751977415), np.float64(0.0021061595857312996), np.float64(0.002163748238476515), np.float64(0.001859340001654938), np.float64(0.002315284620557126), np.float64(0.001475939840537608), np.float64(0.002335853247897363), np.float64(0.001239889941889914)]\n", + "finite magnification: [array([ 2.17465208, 10.58094154, 6.9769299 , 5.21863821, 0.30068666]), array([2.32094137, 2.44494163, 0.75174101]), array([2.36498484, 5.40139208, 5.93524521, 3.09974108, 2.97613867,\n", + " 0.92090018, 3.02114586, 2.67027292, 0.2110031 ]), array([2.68580909, 4.6342153 , 5.06607017]), array([2.76208896, 3.83020447, 1.98542829]), array([2.876089 , 3.90743006, 1.71968234, 2.34070748, 1.11334388]), array([2.22082896, 4.19793145, 2.45022735, 2.50491312, 0.14125965]), array([3.36380121, 3.5483828 , 2.19078296, 2.57256387, 1.16160826]), array([2.53620128, 6.29485904, 2.64535807, 2.41468165, 0.22557598]), array([2.04116913, 4.87063901, 0.43303732]), array([2.07746745, 7.14079487, 5.04199991, 2.07220285, 0.11016382]), array([2.21099183, 4.99214592, 4.47340137, 1.56908285, 0.17443896]), array([2.50933994, 1.80574046, 0.69858235]), array([2.31049438, 7.88076922, 7.17074778, 4.52069801, 3.22190121]), array([3.45814875, 2.91857951, 2.45920881, 1.36733196, 0.05583936]), array([4.05960961, 2.93307502, 1.27332542, 1.82404122, 0.14326062])]\n", + "time delays: [array([-22715.81785838, -12996.30266199, -12935.59101661, -11414.10275639,\n", + " -10771.88977115]), array([-24128.52553461, -10636.26427087, -10556.57788154]), array([-20792.14188637, -14216.62330021, -14122.67605812, -14098.1849247 ,\n", + " -14093.86895208, -14088.82846572, -13657.30623043, -11714.18831155,\n", + " -11176.22951635]), array([-20922.45997181, -19367.35328429, -18820.97228881]), array([-22144.47410647, -20015.53185314, -18906.49766759]), array([-20161.5721062 , -16933.09483265, -15914.38482873, -11021.76302252,\n", + " -10998.6712417 ]), array([-24534.67308936, -14066.72003155, -13272.52781382, -12330.27362095,\n", + " -10806.05265773]), array([-16020.31006505, -15969.98257414, -14126.4360405 , -11323.84159755,\n", + " -11304.76934621]), array([-19714.86873899, -13798.34170752, -13175.63902416, -11730.09398658,\n", + " -11175.68731593]), array([-26444.79273813, -10620.39093343, -10227.37964691]), array([-25262.78369919, -14218.16805476, -13870.90140067, -12755.46302 ,\n", + " -10803.09326777]), array([-21474.82969536, -15114.93690195, -14698.94492478, -11764.86086715,\n", + " -11023.46070436]), array([-24411.20590417, -10240.69389526, -10191.51405629]), array([-21862.87426134, -15456.7705475 , -15377.35473725, -10828.80891322,\n", + " -10826.77897017]), array([-20531.92535713, -17754.77718472, -15199.22856703, -12893.52059628,\n", + " -11335.93690877]), array([-19401.36858126, -19209.97228614, -15784.19576566, -12213.83740631,\n", + " -11363.8626036 ])]\n" + ] + } + ], + "source": [ + "# compute image positions and their (finite) magnifications\n", + "# the infinitesimal magnification at the position of the images is:\n", + "mag_infs = []\n", + "for i in range(num_sources):\n", + " lensEquationSolver.lensModel.change_source_redshift(z_source=z_sources[i])\n", + " mag_inf = lensModel.magnification(x_imgs[i], y_imgs[i], kwargs_lens)\n", + " mag_infs.append(mag_inf)\n", + "print('point source magnification: ', mag_inf)\n", + "\n", + "# we chose a finite source size of the emitting 'point source' region\n", + "source_sizes_pc = [random.uniform(10, 20) for i in range(num_sources)] # Gaussian source size in units of parsec\n", + "# we convert the units of pc into arcseconds given the redshift of the lens and the cosmology\n", + "D_s = lensCosmo.ds\n", + "source_sizes_arcsec = []\n", + "for i in range(num_sources):\n", + " source_size_arcsec = source_sizes_pc[i] / 10**6 / D_s / constants.arcsec\n", + " source_sizes_arcsec.append(source_size_arcsec)\n", + "print('source size in arcsec: ', source_sizes_arcsec)\n", + "\n", + "# we compute the finite magnification by rendering a grid around the point source position and add up all the flux coming from the extended source in this window\n", + "window_size = 0.1 # units of arcseconds\n", + "grid_number = 100 # supersampled window (per axis)\n", + "\n", + "# and here are the finite magnifications computed\n", + "mag_finites = []\n", + "for i in range(num_sources):\n", + " lensEquationSolver.lensModel.change_source_redshift(z_source=z_sources[i])\n", + " mag_finite = lensModelExtensions.magnification_finite(x_pos=x_imgs[i], y_pos=y_imgs[i], kwargs_lens=kwargs_lens, \n", + " source_sigma=source_size_arcsec, window_size=window_size,\n", + " grid_number=grid_number)\n", + " mag_finites.append(mag_finite)\n", + "print('finite magnification: ', mag_finites)\n", + "\n", + "# here are the predicted time delays in units of days\n", + "t_days = []\n", + "for i in range(num_sources):\n", + " lensEquationSolver.lensModel.change_source_redshift(z_source=z_sources[i])\n", + " t_days_temp = lensModel.arrival_time(x_imgs[i], y_imgs[i], kwargs_lens)\n", + " t_days.append(t_days_temp)\n", + "print('time delays: ', t_days)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plots\n", + "These plots show the convergence, the critical curves and caustics, and the calculated image positions. This uses three key word arguments from the lens_model_plot function, and produces a plot using that and the point_source_plot function. The three key arguments are:\n", + "- with_convergence=True: for the first plot, this creates the map of the mass distribution based on the lens model parameters that have been input.\n", + "- with_caustics=True: for the second plot, this shows the critical curves in red and the caustics in green. Critical curves represent a line of positions where the lens will infinitely magnify a source, and the caustics represent where the images formed by that critical curve would appear on the image plane.\n", + "- images_from_data=True: for the third plot, the places a diamond at each point an image appears from the input ps kwargs and scales the diamond according to the calculated magnifications.\n", + "\n", + "After that, we plot each of the finite sources as seen at the different image positions." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# # here we plot the lens model, the caustics and critical curves, and the image positions\n", + "\n", + "# Create figure and axes\n", + "f, ax = plt.subplots(1, 3, figsize=(18, 5), sharex=True, sharey=True)\n", + "\n", + "#Name_list = None is the default, replace none with a list of strings (ex below) to have custom labels. When plotting, choose one of the lists, as shown below.\n", + "Name_list = [[\".1\", \".2\", \".3\", \".4\", \".5\", \".6\", \".7\", \".8\", \".9\", \".10\", \".11\", \".12\", \".13\", \".14\", \".15\", \".16\", \".17\", \".18\", \".19\", \".20\"], [\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\", \"L\", \"M\", \"N\", \"O\", \"P\", \"Q\", \"R\", \"S\", \"T\", \"U\", \"V\", \"W\", \"X\", \"Y\", \"Z\"]] # if using a custom Name_list, insert: name_list=Name_list[i] into the list of parameters for plotting.\n", + "num_Names = len(Name_list)\n", + "color_list = ['k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y'] # should be at least as long as the number of sources\n", + "\n", + "lensModel.change_source_redshift(z_source=z_sources[0])\n", + "lens_plot.lens_model_plot(ax[0], lensModel=lensModel, kwargs_lens=kwargs_lens, images_x=[], images_y=[],\n", + " mag_images=None, index=0, color_value=color_list[0], name_list=Name_list[0], point_source=True,\n", + " images_from_data=False, with_caustics=False, numPix=110, deltaPix=1.0, with_convergence=True,\n", + " fontsize=5\n", + " )\n", + "\n", + "rgba_transparent = (1.0, 1.0, 1.0, 0.0)\n", + "lens_plot.lens_model_plot(ax[1], lensModel=lensModel, kwargs_lens=kwargs_lens, images_x=[], images_y=[],\n", + " mag_images=None, index=0, color_value=color_list[0], name_list=Name_list[0], point_source=True,\n", + " images_from_data=False, with_caustics=True, numPix=110, deltaPix=1.0, with_convergence=False,\n", + " fontsize=5\n", + " )\n", + "for i in range(num_sources):\n", + " lensModel.change_source_redshift(z_source=z_sources[i])\n", + " lens_plot.lens_model_plot(ax[2], lensModel=lensModel, kwargs_lens=kwargs_lens, images_x=x_imgs[i], images_y=y_imgs[i], \n", + " mag_images=mag_finites[i], index=i, color_value=color_list[i], name_list=Name_list[0], point_source=True,\n", + " images_from_data=False, with_caustics=False, numPix=110, deltaPix=1.0, with_convergence=False,\n", + " fontsize=5\n", + " )\n", + "# Show the plot\n", + "plt.show()\n", + "\n", + "# kappa = lens.kappa(x_grid_rot, y_grid_rot, kwargs_lens)" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": {}, + "outputs": [], + "source": [ + "# Image properties\n", + "# this groups the images according to the sources that they came from, each list contains lists of the associated image ID's, positions, and redshifts. Used for plotting purposes.\n", + "\n", + "grouped_ids = []\n", + "grouped_z_images = []\n", + "z_images = []\n", + "\n", + "cutoff = 0\n", + "for i in range(num_sources):\n", + " ids_temp = []\n", + " z_temp = []\n", + " for j in range(num_images_list[i]):\n", + " ids_temp.append(image_ids[j+cutoff])\n", + " z_temp = z_sources[i]*np.ones(num_images_list[i])\n", + " cutoff += num_images_list[i]\n", + " grouped_ids.append(ids_temp)\n", + " grouped_z_images.append(z_temp)" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Users\\earth\\AppData\\Local\\Temp\\ipykernel_22240\\1363722647.py:46: RuntimeWarning: divide by zero encountered in log10\n", + " ax.matshow(np.log10(image), vmin=0, vmax=5, origin='lower')\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# here we plot the finite sources as seen at the different image positions\n", + "label_lists = []\n", + "for i in range(num_sources):\n", + " label_list_temp = [None] * len(x_imgs[i])\n", + " label_lists.append(label_list_temp)\n", + "\n", + "if (Name_list is not None) & (num_Names == 1):\n", + " for i in range(num_sources):\n", + " lensModelExtensions._lensModel.change_source_redshift(z_source=z_sources[i])\n", + " x_img_indexed = x_imgs[i]\n", + " y_img_indexed = y_imgs[i]\n", + " f, axes = plt.subplots(1, len(x_img_indexed), figsize=(5*5, 5*len(x_img_indexed)), sharex=False, sharey=False)\n", + " for j in range(len(x_imgs[i])):\n", + " label_lists[i][j] = grouped_ids[i][j]\n", + " for k in range(len(x_img_indexed)):\n", + " lensModelExtensions._lensModel.change_source_redshift(z_source=z_sources[i])\n", + " image = lensModelExtensions.zoom_source(x_pos=x_img_indexed[k], y_pos=y_img_indexed[k], kwargs_lens=kwargs_lens, \n", + " source_sigma=source_sizes_arcsec[i], window_size=window_size,\n", + " grid_number=grid_number)\n", + " if len(x_img_indexed) == 1:\n", + " axes.matshow(np.log10(image), vmin=0, vmax=5, origin='lower')\n", + " axes.set_title(label_lists[i][k], color=color_list[i])\n", + " else:\n", + " ax = axes[k]\n", + " ax.matshow(np.log10(image), vmin=0, vmax=5, origin='lower')\n", + " ax.set_title(label_lists[i][k], color=color_list[i])\n", + " plt.show()\n", + "elif (Name_list is not None) & (num_Names > 1):\n", + " for i in range(num_sources):\n", + " lensModelExtensions._lensModel.change_source_redshift(z_source=z_sources[i])\n", + " x_img_indexed = x_imgs[i]\n", + " y_img_indexed = y_imgs[i]\n", + " f, axes = plt.subplots(1, len(x_img_indexed), figsize=(5*5, 5*len(x_img_indexed)), sharex=False, sharey=False)\n", + " for j in range(len(x_imgs[i])):\n", + " label_lists[i][j] = grouped_ids[i][j]\n", + " for k in range(len(x_img_indexed)):\n", + " lensModelExtensions._lensModel.change_source_redshift(z_source=z_sources[i])\n", + " image = lensModelExtensions.zoom_source(x_pos=x_img_indexed[k], y_pos=y_img_indexed[k], kwargs_lens=kwargs_lens, \n", + " source_sigma=source_sizes_arcsec[i], window_size=window_size,\n", + " grid_number=grid_number)\n", + " if len(x_img_indexed) == 1:\n", + " axes.matshow(np.log10(image), vmin=0, vmax=5, origin='lower')\n", + " axes.set_title(label_lists[i][k], color=color_list[i])\n", + " else:\n", + " ax = axes[k]\n", + " ax.matshow(np.log10(image), vmin=0, vmax=5, origin='lower')\n", + " ax.set_title(label_lists[i][k], color=color_list[i])\n", + " plt.show()\n", + "else:\n", + " for i in range(num_sources):\n", + " x_img_indexed = x_imgs[i]\n", + " y_img_indexed = y_imgs[i]\n", + " f, axes = plt.subplots(1, len(x_img_indexed), figsize=(5*5, 5*len(x_img_indexed)), sharex=False, sharey=False)\n", + " label_list = [f\"{i+1}A\", f\"{i+1}B\", f\"{i+1}C\", f\"{i+1}D\", f\"{i+1}E\", f\"{i+1}F\", f\"{i+1}G\", f\"{i+1}H\", f\"{i+1}I\", f\"{i+1}J\", f\"{i+1}K\"]\n", + " for j in range(len(x_img_indexed)):\n", + " lensModelExtensions._lensModel.change_source_redshift(z_source=z_sources[i])\n", + " image = lensModelExtensions.zoom_source(x_pos=x_img_indexed[i], y_pos=y_img_indexed[i], kwargs_lens=kwargs_lens, \n", + " source_sigma=source_sizes_arcsec[j], window_size=window_size,\n", + " grid_number=grid_number)\n", + " if len(x_img_indexed) == 1:\n", + " axes.matshow(np.log10(image), vmin=0, vmax=5, origin='lower')\n", + " axes.set_title(label_lists[i][j], color=color_list[i])\n", + " else:\n", + " ax = axes[j]\n", + " ax.matshow(np.log10(image), vmin=0, vmax=5, origin='lower')\n", + " ax.set_title(label_lists[i][j], color=color_list[i])\n", + " plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Set up data for modeling\n", + "Now that we have read in all our data and completed the necessary calculations, we can explicitly set up the data in the way we want to use for modeling.\n", + "This includes set up of the uncertainty for each value, including flux ratios, time delays, and image positions.\n", + "\n", + "In this section, we explicitly set up the data products that we want to use for the modeling. You can replace this box with the values for the lens you want to model." + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "flux_ratios_list: [array([4.86553074, 3.20825089, 2.39976194, 0.13914263]), array([1.05342351, 0.32389271]), array([2.28389813, 2.50960739, 1.31065662, 1.25838737, 0.3893625 ,\n", + " 1.27744749, 1.12908579, 0.08884872]), array([1.72544364, 1.88623479]), array([1.38670537, 0.71881258]), array([1.35859305, 0.59792442, 0.81384018, 0.38709224]), array([1.89025375, 1.10328845, 1.12791773, 0.06696097]), array([1.05487233, 0.65128184, 0.76476275, 0.34530991]), array([2.48200395, 1.04303876, 0.95208496, 0.09024353]), array([2.38620114, 0.21232589]), array([3.43724495, 2.42699042, 0.99746551, 0.05690163]), array([2.25787465, 2.02325169, 0.70967365, 0.07671182]), array([0.71960509, 0.27839031]), array([3.41082951, 3.10352676, 1.95575709, 1.39362762]), array([0.84397142, 0.71113439, 0.3953941 , 0.01964236]), array([0.72250658, 0.31365919, 0.44931736, 0.02992104])]\n" + ] + } + ], + "source": [ + "## Here we calculate the flux ratio between the different images from the same source. We then also add a sigma to the values to account for error\n", + "\n", + "flux_error = 0.02\n", + "flux_ratios_list = []\n", + "flux_ratio_errors_list = []\n", + "flux_ratios_measured_list = []\n", + "\n", + "for i in range(num_sources):\n", + " lensModel.change_source_redshift(z_source=z_sources[i])\n", + " if len(mag_infs[i]) <= 1:\n", + " flux_ratios = []\n", + " flux_ratios_measured = []\n", + " flux_ratio_errors = []\n", + " else:\n", + " image_amps = np.abs(mag_infs[i])\n", + " flux_ratios = image_amps[1:]/image_amps[0]\n", + " flux_ratio_errors = flux_error*np.ones(len(flux_ratios))\n", + " flux_ratios_measured = flux_ratios + np.random.normal(0, flux_ratio_errors)\n", + " if measurement_realization:\n", + " flux_ratios_measured = flux_ratios + np.random.normal(0, flux_ratio_errors)\n", + " else:\n", + " flux_ratios_measured = flux_ratios\n", + " flux_ratios_list.append(flux_ratios)\n", + " flux_ratio_errors_list.append(flux_ratio_errors)\n", + " flux_ratios_measured_list.append(flux_ratios_measured)\n", + "print('flux_ratios_list: %s' %(flux_ratios_list))\n", + "\n", + "# image positions in relative RA (arc seconds)\n", + "astrometry_sigma = 0.005 # 1-sigma astrometric uncertainties of the image positions (assuming equal precision for all images in RA/DEC directions)\n", + "\n", + "## Here we loop to calculate the time delays\n", + "d_dts = []\n", + "d_dt_sigmas = []\n", + "d_dt_measured_list = []\n", + "ximg_measured_list = []\n", + "yimg_measured_list = []\n", + "\n", + "for i in range(num_sources):\n", + " lensModel.change_source_redshift(z_source=z_sources[i])\n", + " if len(t_days[i]) <= 1:\n", + " d_dt_measured = []\n", + " else:\n", + " d_dt = t_days[i][1:] - t_days[i][0] # lenstronomy definition of relative time delay is in respect of first image in the list (full covariance is in planning)\n", + " d_dt_sigma = 0.5 * np.ones(len(d_dt))\n", + " d_dts.append(d_dt)\n", + " d_dt_sigmas.append(d_dt_sigma)\n", + " \n", + " if measurement_realization:\n", + " d_dt_measured = d_dt + np.random.normal(0, d_dt_sigma)\n", + " else:\n", + " d_dt_measured = d_dt\n", + " \n", + " if measurement_realization: \n", + " ximg_measured = x_imgs[i] + np.random.normal(0, astrometry_sigma, len(x_imgs[i]))\n", + " yimg_measured = y_imgs[i] + np.random.normal(0, astrometry_sigma, len(y_imgs[i]))\n", + " else:\n", + " ximg_measured = x_imgs[i]\n", + " yimg_measured = y_imgs[i]\n", + " \n", + " d_dt_measured_list.append(d_dt_measured)\n", + " ximg_measured_list.append(ximg_measured)\n", + " yimg_measured_list.append(yimg_measured)\n", + "\n", + "# here we create a keyword list with all the data elements. If you only have partial information about your lens, only provide the quantities you have.\n", + "# kwargs_time_delays_list = []\n", + "# kwargs_time_delay_uncertainties_list = []\n", + "# kwargs_flux_ratios_list = []\n", + "# kwargs_flux_ratio_errors_list = []\n", + "kwargs_ra_image_list = []\n", + "kwargs_dec_image_list = []\n", + "\n", + "\n", + "for i in range(num_sources):\n", + " # kwargs_time_delays_list.append(d_dt_measured_list[i])\n", + " # kwargs_time_delay_uncertainties_list.append(d_dt_sigmas[i])\n", + " # kwargs_flux_ratios_list.append(flux_ratios_measured_list[i])\n", + " # kwargs_flux_ratio_errors_list.append(flux_ratio_errors_list[i])\n", + " kwargs_ra_image_list.append(ximg_measured_list[i])\n", + " kwargs_dec_image_list.append(yimg_measured_list[i])\n", + "\n", + "kwargs_data_joint = {'ra_image_list': kwargs_ra_image_list, 'dec_image_list': kwargs_dec_image_list}\n", + " # 'time_delays_measured': kwargs_time_delays_list,\n", + " # 'time_delays_uncertainties': kwargs_time_delay_uncertainties_list,\n", + " # 'flux_ratios': kwargs_flux_ratios_list, \n", + " # 'flux_ratio_errors': kwargs_flux_ratio_errors_list,\n", + " # don't add this: 'point_source_redshift_list': z_sources_new}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Model settings\n", + "Here we set up the modeling. For each lens mass and the dark matter halo, a new instance of the initial guess of the parameters, uncertainties and lower and upper bounds must be included, each added to the appropriate kwargs dictionary. These values should match what is used in the lensing profiles that were chosen.\n", + "In this example, we use the same lens model as we chose earlier to generate the plots, etc. In the pure modeling notebook, as we choose the same lens model for both, we might expect a perfect fit. However, with real data, this is less likely.\n", + "\n", + "This part is equal to the imaging simulation of lenstronomy. We refer to other notebooks and the documentation for more details: https://github.com/lenstronomy/lenstronomy-tutorials/blob/main/Notebooks/LensModeling/modelling_of_catalogue_data.ipynb." + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "kwargs_lens_init len: 11, data: [{'sigma0': 1.6692528302621406, 'e1': -0.005963408814306501, 'e2': 0.028987851267885584, 'Ra': 0.14304486684040685, 'Rs': 1.2392323340379334, 'center_x': 14.350432185244088, 'center_y': 10.507883203188516}, {'sigma0': 1.6123234300962002, 'e1': -0.019381253240776858, 'e2': 0.00389378054598169, 'Ra': 0.3109810179929473, 'Rs': 5.446534280757485, 'center_x': 9.864069865313613, 'center_y': 9.084495076292722}, {'sigma0': 0.832609131993273, 'e1': -0.027495130819679095, 'e2': -0.00043695108768342095, 'Ra': 0.7377212185003087, 'Rs': 4.888959751509585, 'center_x': -8.274476193873594, 'center_y': 6.7747609852849635}, {'sigma0': 0.4356712373068588, 'e1': 0.05504092392155169, 'e2': -0.039701154589705405, 'Ra': 0.9584017571471027, 'Rs': 5.858424003261759, 'center_x': -12.062407619149372, 'center_y': -10.894292312232903}, {'sigma0': 19.329534879379587, 'e1': -0.09616365720698761, 'e2': -0.014049996143097293, 'Ra': 0.0158259658431944, 'Rs': 3.0125643439316905, 'center_x': -3.7177397734945767, 'center_y': -7.62749224842974}, {'sigma0': 0.36023619596464546, 'e1': -0.011290117102994948, 'e2': 0.08529733715705598, 'Ra': 0.5001592416526002, 'Rs': 1.2410942144861468, 'center_x': -13.994888298334637, 'center_y': 0.5361494527350157}, {'sigma0': 2.9896992887714195, 'e1': 0.027883740613810493, 'e2': -0.07754063210022671, 'Ra': 0.24099452480013428, 'Rs': 6.445000794146591, 'center_x': 13.973840666024458, 'center_y': -12.637756471040511}, {'sigma0': 0.6449741639027774, 'e1': -0.09823286934577538, 'e2': -0.08241796193834168, 'Ra': 0.8992930107381696, 'Rs': 8.438867426282116, 'center_x': -7.886403795566914, 'center_y': 12.789474039244972}, {'sigma0': 0.2811116430505816, 'e1': -0.03663566134079339, 'e2': -0.06807016561599841, 'Ra': 0.99582487574195, 'Rs': 4.018405669577006, 'center_x': 0.8500299054061937, 'center_y': -1.047980060232474}, {'sigma0': 0.6276138534808254, 'e1': -0.0306414760060449, 'e2': -0.08996744903604065, 'Ra': 0.6975025131484497, 'Rs': 4.402434594440141, 'center_x': -2.452017865745983, 'center_y': 9.62920085879659}, {'Rs': np.float64(19.243410455349796), 'alpha_Rs': np.float64(12.429447589643214), 'e1': 0.1, 'e2': -0.3, 'center_x': 0, 'center_y': 0}]\n", + "fixed_lens len: 11, data: [{'sigma0': 1.6692528302621406, 'e1': -0.005963408814306501, 'e2': 0.028987851267885584, 'Ra': 0.14304486684040685, 'Rs': 1.2392323340379334, 'center_x': 14.350432185244088, 'center_y': 10.507883203188516}, {'sigma0': 1.6123234300962002, 'e1': -0.019381253240776858, 'e2': 0.00389378054598169, 'Ra': 0.3109810179929473, 'Rs': 5.446534280757485, 'center_x': 9.864069865313613, 'center_y': 9.084495076292722}, {'sigma0': 0.832609131993273, 'e1': -0.027495130819679095, 'e2': -0.00043695108768342095, 'Ra': 0.7377212185003087, 'Rs': 4.888959751509585, 'center_x': -8.274476193873594, 'center_y': 6.7747609852849635}, {'sigma0': 0.4356712373068588, 'e1': 0.05504092392155169, 'e2': -0.039701154589705405, 'Ra': 0.9584017571471027, 'Rs': 5.858424003261759, 'center_x': -12.062407619149372, 'center_y': -10.894292312232903}, {'sigma0': 19.329534879379587, 'e1': -0.09616365720698761, 'e2': -0.014049996143097293, 'Ra': 0.0158259658431944, 'Rs': 3.0125643439316905, 'center_x': -3.7177397734945767, 'center_y': -7.62749224842974}, {'sigma0': 0.36023619596464546, 'e1': -0.011290117102994948, 'e2': 0.08529733715705598, 'Ra': 0.5001592416526002, 'Rs': 1.2410942144861468, 'center_x': -13.994888298334637, 'center_y': 0.5361494527350157}, {'sigma0': 2.9896992887714195, 'e1': 0.027883740613810493, 'e2': -0.07754063210022671, 'Ra': 0.24099452480013428, 'Rs': 6.445000794146591, 'center_x': 13.973840666024458, 'center_y': -12.637756471040511}, {'sigma0': 0.6449741639027774, 'e1': -0.09823286934577538, 'e2': -0.08241796193834168, 'Ra': 0.8992930107381696, 'Rs': 8.438867426282116, 'center_x': -7.886403795566914, 'center_y': 12.789474039244972}, {'sigma0': 0.2811116430505816, 'e1': -0.03663566134079339, 'e2': -0.06807016561599841, 'Ra': 0.99582487574195, 'Rs': 4.018405669577006, 'center_x': 0.8500299054061937, 'center_y': -1.047980060232474}, {'sigma0': 0.6276138534808254, 'e1': -0.0306414760060449, 'e2': -0.08996744903604065, 'Ra': 0.6975025131484497, 'Rs': 4.402434594440141, 'center_x': -2.452017865745983, 'center_y': 9.62920085879659}, {'Rs': np.float64(19.243410455349796), 'alpha_Rs': np.float64(12.429447589643214), 'e1': 0.1, 'e2': -0.3, 'center_x': 0, 'center_y': 0}]\n", + "kwargs_lens_sigma_list len: 11, data: [{'sigma0': 0.01, 'e1': 0.01, 'e2': 0.01, 'Ra': 1.0, 'Rs': 17, 'center_x': 0.1, 'center_y': 0.1}, {'sigma0': 0.01, 'e1': 0.01, 'e2': 0.01, 'Ra': 1.0, 'Rs': 17, 'center_x': 0.1, 'center_y': 0.1}, {'sigma0': 0.01, 'e1': 0.01, 'e2': 0.01, 'Ra': 1.0, 'Rs': 17, 'center_x': 0.1, 'center_y': 0.1}, {'sigma0': 0.01, 'e1': 0.01, 'e2': 0.01, 'Ra': 1.0, 'Rs': 17, 'center_x': 0.1, 'center_y': 0.1}, {'sigma0': 0.01, 'e1': 0.01, 'e2': 0.01, 'Ra': 1.0, 'Rs': 17, 'center_x': 0.1, 'center_y': 0.1}, {'sigma0': 0.01, 'e1': 0.01, 'e2': 0.01, 'Ra': 1.0, 'Rs': 17, 'center_x': 0.1, 'center_y': 0.1}, {'sigma0': 0.01, 'e1': 0.01, 'e2': 0.01, 'Ra': 1.0, 'Rs': 17, 'center_x': 0.1, 'center_y': 0.1}, {'sigma0': 0.01, 'e1': 0.01, 'e2': 0.01, 'Ra': 1.0, 'Rs': 17, 'center_x': 0.1, 'center_y': 0.1}, {'sigma0': 0.01, 'e1': 0.01, 'e2': 0.01, 'Ra': 1.0, 'Rs': 17, 'center_x': 0.1, 'center_y': 0.1}, {'sigma0': 0.01, 'e1': 0.01, 'e2': 0.01, 'Ra': 1.0, 'Rs': 17, 'center_x': 0.1, 'center_y': 0.1}, {'Rs': 0.1, 'alpha_Rs': 0.1, 'e1': 0.01, 'e2': 0.01, 'center_x': 0.01, 'center_y': 0.01}]\n", + "kwargs_lower_lens_list len: 11, data: [{'sigma0': 0, 'e1': -0.5, 'e2': -0.5, 'Ra': 0, 'Rs': 0, 'center_x': -100, 'center_y': -100}, {'sigma0': 0, 'e1': -0.5, 'e2': -0.5, 'Ra': 0, 'Rs': 0, 'center_x': -100, 'center_y': -100}, {'sigma0': 0, 'e1': -0.5, 'e2': -0.5, 'Ra': 0, 'Rs': 0, 'center_x': -100, 'center_y': -100}, {'sigma0': 0, 'e1': -0.5, 'e2': -0.5, 'Ra': 0, 'Rs': 0, 'center_x': -100, 'center_y': -100}, {'sigma0': 0, 'e1': -0.5, 'e2': -0.5, 'Ra': 0, 'Rs': 0, 'center_x': -100, 'center_y': -100}, {'sigma0': 0, 'e1': -0.5, 'e2': -0.5, 'Ra': 0, 'Rs': 0, 'center_x': -100, 'center_y': -100}, {'sigma0': 0, 'e1': -0.5, 'e2': -0.5, 'Ra': 0, 'Rs': 0, 'center_x': -100, 'center_y': -100}, {'sigma0': 0, 'e1': -0.5, 'e2': -0.5, 'Ra': 0, 'Rs': 0, 'center_x': -100, 'center_y': -100}, {'sigma0': 0, 'e1': -0.5, 'e2': -0.5, 'Ra': 0, 'Rs': 0, 'center_x': -100, 'center_y': -100}, {'sigma0': 0, 'e1': -0.5, 'e2': -0.5, 'Ra': 0, 'Rs': 0, 'center_x': -100, 'center_y': -100}, {'Rs': 0, 'alpha_Rs': 0, 'e1': -0.5, 'e2': -0.5, 'center_x': -100, 'center_y': -100}]\n", + "kwargs_upper_lens_list len: 11, data: [{'sigma0': 1000, 'e1': 0.5, 'e2': 0.5, 'Ra': 100, 'Rs': 100, 'center_x': 100, 'center_y': 100}, {'sigma0': 1000, 'e1': 0.5, 'e2': 0.5, 'Ra': 100, 'Rs': 100, 'center_x': 100, 'center_y': 100}, {'sigma0': 1000, 'e1': 0.5, 'e2': 0.5, 'Ra': 100, 'Rs': 100, 'center_x': 100, 'center_y': 100}, {'sigma0': 1000, 'e1': 0.5, 'e2': 0.5, 'Ra': 100, 'Rs': 100, 'center_x': 100, 'center_y': 100}, {'sigma0': 1000, 'e1': 0.5, 'e2': 0.5, 'Ra': 100, 'Rs': 100, 'center_x': 100, 'center_y': 100}, {'sigma0': 1000, 'e1': 0.5, 'e2': 0.5, 'Ra': 100, 'Rs': 100, 'center_x': 100, 'center_y': 100}, {'sigma0': 1000, 'e1': 0.5, 'e2': 0.5, 'Ra': 100, 'Rs': 100, 'center_x': 100, 'center_y': 100}, {'sigma0': 1000, 'e1': 0.5, 'e2': 0.5, 'Ra': 100, 'Rs': 100, 'center_x': 100, 'center_y': 100}, {'sigma0': 1000, 'e1': 0.5, 'e2': 0.5, 'Ra': 100, 'Rs': 100, 'center_x': 100, 'center_y': 100}, {'sigma0': 1000, 'e1': 0.5, 'e2': 0.5, 'Ra': 100, 'Rs': 100, 'center_x': 100, 'center_y': 100}, {'Rs': 10000, 'alpha_Rs': 1000, 'e1': 0.5, 'e2': 0.5, 'center_x': 100, 'center_y': 100}]\n" + ] + } + ], + "source": [ + "# ==================\n", + "# lens model choices\n", + "# ==================\n", + "# could also add things that are known very well to the fixed_lens.append({}) list, ie. this could be not empty!\n", + "\n", + "### for Setting the galaxy lens parameters\n", + "# combine the append of all these at the same time as the lens_model_list\n", + "\n", + "## we have previously defined our lens_model_list as we needed it for calculations/plotting above. If not defined above, uncomment it below.\n", + "# lens_model_list = []\n", + "# for i in range(len(gal_data_arcsec)):\n", + "# lens_model_list.append('PJAFFE_ELLIPSE_POTENTIAL')\n", + "# lens_model_list.append('NFW_ELLIPSE_CSE')\n", + "\n", + "## fixed_lens values here. Switch which lines are commented to change if the lens model is fixed or not\n", + "fixed_lens = []\n", + "for i in range(num_cluster_members):\n", + " # fixed_lens.append({})\n", + " fixed_lens.append({'sigma0': sigma0s[i], \"e1\": e1s[i], \"e2\": e2s[i], 'Ra': Ras[i], 'Rs': Rss[i], 'center_x': x_cluster_members[i], \"center_y\": y_cluster_members[i]})\n", + "fixed_lens.append({\"Rs\": nfw_Rs, \"alpha_Rs\": nfw_alpha_Rs, \"e1\": nfw_e1, \"e2\": nfw_e2, \"center_x\": nfw_x, \"center_y\": nfw_y})\n", + "# fixed_lens.append({})\n", + "\n", + "kwargs_lens_init = []\n", + "kwargs_lens_sigma = []\n", + "kwargs_lower_lens = []\n", + "kwargs_upper_lens = []\n", + "\n", + "# SPEMD parameters\n", + "# for i in range(len(lens_model_list)):\n", + "# fixed_lens.append({})\n", + "\n", + "# append once for each of the cluster members, then once for the dark matter halo\n", + "for i in range(num_cluster_members):\n", + " # initial parameter guess\n", + " kwargs_lens_init.append({'sigma0': sigma0s[i], \"e1\": e1s[i], \"e2\": e2s[i], 'Ra': Ras[i], 'Rs': Rss[i], 'center_x': x_cluster_members[i], \"center_y\": y_cluster_members[i]})\n", + " # initial particle cloud\n", + " kwargs_lens_sigma.append({'sigma0': 0.01, 'e1': 0.01, 'e2': 0.01, 'Ra': 1.0, 'Rs': 17, 'center_x': 0.1, 'center_y': 0.1})\n", + " # hard lower bound limit of parameters\n", + " kwargs_lower_lens.append({'sigma0': 0, 'e1': -0.5, 'e2': -0.5, 'Ra': 0, 'Rs': 0, 'center_x': -100, 'center_y': -100})\n", + " # hard upper bound limit of parameters\n", + " kwargs_upper_lens.append({'sigma0': 1000, 'e1': 0.5, 'e2': 0.5, 'Ra': 100, 'Rs': 100, 'center_x': 100, 'center_y': 100})\n", + "\n", + "# same kwargs but for the nfw dark matter halo\n", + "kwargs_lens_init.append({\"Rs\": nfw_Rs, \"alpha_Rs\": nfw_alpha_Rs, \"e1\": nfw_e1, \"e2\": nfw_e2, \"center_x\": nfw_x, \"center_y\": nfw_y})\n", + "kwargs_lens_sigma.append({\"Rs\": 0.1, \"alpha_Rs\": 0.1, \"e1\": 0.01, \"e2\": 0.01, \"center_x\": 0.01 , \"center_y\": 0.01})\n", + "kwargs_lower_lens.append({\"Rs\": 0, \"alpha_Rs\": 0, \"e1\": -0.5, \"e2\": -0.5, \"center_x\": -100, \"center_y\": -100})\n", + "kwargs_upper_lens.append({\"Rs\": 10000, \"alpha_Rs\": 1000, \"e1\": 0.5, \"e2\": 0.5, \"center_x\": 100, \"center_y\": 100})\n", + "\n", + "# combine all parameter options for lenstronomy\n", + "lens_params = [kwargs_lens_init, kwargs_lens_sigma, fixed_lens, kwargs_lower_lens, kwargs_upper_lens]\n", + "print('kwargs_lens_init len: %s, data: %s' %(len(kwargs_lens_init), kwargs_lens_init))\n", + "print('fixed_lens len: %s, data: %s' %(len(fixed_lens), fixed_lens))\n", + "print('kwargs_lens_sigma_list len: %s, data: %s' %(len(kwargs_lens_sigma), kwargs_lens_sigma))\n", + "print('kwargs_lower_lens_list len: %s, data: %s' %(len(kwargs_lower_lens), kwargs_lower_lens))\n", + "print('kwargs_upper_lens_list len: %s, data: %s' %(len(kwargs_upper_lens), kwargs_upper_lens))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we do the same for the image parameters, including an initial guess, uncertainty, and upper and lower limits for each instance. This is also where we can choose to include 'special' parameters, such as astrometric perturbations, time delay distances, or quasar soruce information if relevant.\n", + "We can choose here to fix the x and y position parameters if desired, removing one degree of freedom from our model." + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "special_params: [{'scale_factor': [1]}, {'scale_factor': [0.2]}, {}, {'scale_factor': [0]}, {'scale_factor': [10]}]\n", + "point_source_list: ['LENSED_POSITION', 'LENSED_POSITION', 'LENSED_POSITION', 'LENSED_POSITION', 'LENSED_POSITION', 'LENSED_POSITION', 'LENSED_POSITION', 'LENSED_POSITION', 'LENSED_POSITION', 'LENSED_POSITION', 'LENSED_POSITION', 'LENSED_POSITION', 'LENSED_POSITION', 'LENSED_POSITION', 'LENSED_POSITION', 'LENSED_POSITION']\n", + "fixed_lens: [{'sigma0': 1.6692528302621406, 'e1': -0.005963408814306501, 'e2': 0.028987851267885584, 'Ra': 0.14304486684040685, 'Rs': 1.2392323340379334, 'center_x': 14.350432185244088, 'center_y': 10.507883203188516}, {'sigma0': 1.6123234300962002, 'e1': -0.019381253240776858, 'e2': 0.00389378054598169, 'Ra': 0.3109810179929473, 'Rs': 5.446534280757485, 'center_x': 9.864069865313613, 'center_y': 9.084495076292722}, {'sigma0': 0.832609131993273, 'e1': -0.027495130819679095, 'e2': -0.00043695108768342095, 'Ra': 0.7377212185003087, 'Rs': 4.888959751509585, 'center_x': -8.274476193873594, 'center_y': 6.7747609852849635}, {'sigma0': 0.4356712373068588, 'e1': 0.05504092392155169, 'e2': -0.039701154589705405, 'Ra': 0.9584017571471027, 'Rs': 5.858424003261759, 'center_x': -12.062407619149372, 'center_y': -10.894292312232903}, {'sigma0': 19.329534879379587, 'e1': -0.09616365720698761, 'e2': -0.014049996143097293, 'Ra': 0.0158259658431944, 'Rs': 3.0125643439316905, 'center_x': -3.7177397734945767, 'center_y': -7.62749224842974}, {'sigma0': 0.36023619596464546, 'e1': -0.011290117102994948, 'e2': 0.08529733715705598, 'Ra': 0.5001592416526002, 'Rs': 1.2410942144861468, 'center_x': -13.994888298334637, 'center_y': 0.5361494527350157}, {'sigma0': 2.9896992887714195, 'e1': 0.027883740613810493, 'e2': -0.07754063210022671, 'Ra': 0.24099452480013428, 'Rs': 6.445000794146591, 'center_x': 13.973840666024458, 'center_y': -12.637756471040511}, {'sigma0': 0.6449741639027774, 'e1': -0.09823286934577538, 'e2': -0.08241796193834168, 'Ra': 0.8992930107381696, 'Rs': 8.438867426282116, 'center_x': -7.886403795566914, 'center_y': 12.789474039244972}, {'sigma0': 0.2811116430505816, 'e1': -0.03663566134079339, 'e2': -0.06807016561599841, 'Ra': 0.99582487574195, 'Rs': 4.018405669577006, 'center_x': 0.8500299054061937, 'center_y': -1.047980060232474}, {'sigma0': 0.6276138534808254, 'e1': -0.0306414760060449, 'e2': -0.08996744903604065, 'Ra': 0.6975025131484497, 'Rs': 4.402434594440141, 'center_x': -2.452017865745983, 'center_y': 9.62920085879659}, {'Rs': np.float64(19.243410455349796), 'alpha_Rs': np.float64(12.429447589643214), 'e1': 0.1, 'e2': -0.3, 'center_x': 0, 'center_y': 0}]\n", + "fixed_ps: [{}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}]\n", + "fixed_special: {}\n", + "kwargs_special_init: {'scale_factor': [1]}\n" + ] + } + ], + "source": [ + "# =========================\n", + "# image position parameters\n", + "# =========================\n", + "\n", + "# we chose to model the image positions in the lensed plane (we know where they appear) and fix the image position coordinates\n", + "point_source_list = []\n", + "fixed_ps = []\n", + "kwargs_ps_init = []\n", + "kwargs_ps_sigma = []\n", + "kwargs_lower_ps = []\n", + "kwargs_upper_ps = []\n", + "\n", + "for i in range(num_sources):\n", + " point_source_list.append('LENSED_POSITION')\n", + " # fixed_ps.append({'ra_image': ximg_measured_list[i], 'dec_image': yimg_measured_list[i]}) # we fix the image position coordinates\n", + " fixed_ps.append({})\n", + " kwargs_ps_init.append({'ra_image': ximg_measured_list[i], 'dec_image': yimg_measured_list[i]})\n", + " kwargs_ps_sigma.append({'ra_image': 0.01 * np.ones(len(x_imgs[i])), 'dec_image': 0.01 * np.ones(len(y_imgs[i]))})\n", + " kwargs_lower_ps.append({'ra_image': -100 * np.ones(len(x_imgs[i])), 'dec_image': -100 * np.ones(len(y_imgs[i]))})\n", + " kwargs_upper_ps.append({'ra_image': 100* np.ones(len(x_imgs[i])), 'dec_image': 100 * np.ones(len(y_imgs[i]))})\n", + "\n", + "# combine all parameter options for lenstronomy\n", + "ps_params = [kwargs_ps_init, kwargs_ps_sigma, fixed_ps, kwargs_lower_ps, kwargs_upper_ps]\n", + "\n", + "fixed_special = {}\n", + "kwargs_special_init = {}\n", + "kwargs_special_sigma = {}\n", + "kwargs_lower_special = {}\n", + "kwargs_upper_special = {}\n", + "\n", + "# =========================\n", + "# astrometric perturbations\n", + "# =========================\n", + "# astrometric perturbations are modeled in lenstronomy with 'delta_x_image' and 'delta_y_image'.\n", + "# These perturbations place the 'actual' point source at the difference to 'ra_image'.\n", + "# we let some freedom in how well the actual image positions are matching those given by the data (indicated as 'ra_image', 'dec_image' and held fixed while fitting)\n", + "\n", + "#kwargs_special_init['delta_x_image'], kwargs_special_init['delta_y_image'] = np.zeros_like(ximg), np.zeros_like(yimg)\n", + "#kwargs_special_sigma['delta_x_image'], kwargs_special_sigma['delta_y_image'] = np.ones_like(ximg) * astrometry_sigma, np.ones_like(yimg) * astrometry_sigma\n", + "#kwargs_lower_special['delta_x_image'], kwargs_lower_special['delta_y_image'] = np.ones_like(ximg) * (-1), np.ones_like(yimg) * (-1)\n", + "#kwargs_upper_special['delta_x_image'], kwargs_upper_special['delta_y_image'] = np.ones_like(ximg) * (1), np.ones_like(yimg) * (1)\n", + "\n", + "# ==================\n", + "# quasar source size\n", + "# ==================\n", + "# # If you want to keep the source size fixed during the fitting, don't comment the line below (or comment the line to let it vary).\n", + "# fixed_special['source_size'] = [source_size_arcsec, source_size_arcsec2]\n", + "# kwargs_special_init['source_size'] = [source_size_arcsec, source_size_arcsec2]\n", + "# kwargs_special_sigma['source_size'] = [source_size_arcsec, source_size_arcsec2]\n", + "# or:\n", + "# kwargs_special_init['source_size'] = source_sizes_arcsec[0]\n", + "# kwargs_special_sigma['source_size'] = source_sizes_arcsec[0]\n", + "# fixed_special['source_size'] = source_sizes_arcsec[0]\n", + "\n", + "# kwargs_lower_special['source_size'] = 0.0001\n", + "# kwargs_upper_special['source_size'] = 1\n", + "\n", + "\n", + "# ===================\n", + "# Time-delay distance\n", + "# ===================\n", + "# with time-delay information, we can measure the time-delay distance (units physical Mpc)\n", + "\n", + "# if you want to fix the cosmology and instead use the time-delay information to constrain the lens model, out-comment the line below\n", + " # essentially, choose either the first line of the above block of code, or the first line of the below block of code\n", + "#fixed_special['D_dt'] = lensCosmo.D_dt\n", + "# kwargs_special_init['D_dt'] = lensCosmo.ddt\n", + "# kwargs_special_sigma['D_dt'] = 2000\n", + "# kwargs_lower_special['D_dt'] = 0\n", + "# kwargs_upper_special['D_dt'] = 10000\n", + "\n", + "# mass scaling parameter configuraiton\n", + "kwargs_special_init['scale_factor'] = [1] #### Does this get replaced with the mass scaling relationships from the calculations above?\n", + "kwargs_special_sigma['scale_factor'] = [0.2]\n", + "kwargs_lower_special['scale_factor'] = [0]\n", + "kwargs_upper_special['scale_factor'] = [10]\n", + "\n", + "special_params = [kwargs_special_init, kwargs_special_sigma, fixed_special, kwargs_lower_special, kwargs_upper_special]\n", + "print(\"special_params:\", special_params)\n", + "\n", + "# combined parameter settings\n", + "kwargs_params = {'lens_model': lens_params,\n", + " 'point_source_model': ps_params,\n", + " 'special': special_params}\n", + "\n", + "# our model choices\n", + "kwargs_model = {'lens_model_list': lens_model_list, \n", + " 'point_source_model_list': point_source_list,\n", + " 'point_source_redshift_list': z_sources, # add this for changing redshifts of sources!\n", + " 'z_source_convention': z_source_convention,\n", + " 'z_lens': z_lens_nfw,\n", + " 'cosmo': cosmo}\n", + "\n", + "print(\"point_source_list:\", point_source_list)\n", + "print(\"fixed_lens:\", fixed_lens)\n", + "print(\"fixed_ps:\", fixed_ps)\n", + "print(\"fixed_special:\", fixed_special)\n", + "print(\"kwargs_special_init:\", kwargs_special_init)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## setup options for likelihood and parameter sampling\n", + "In $\\texttt{lenstronomy}$ the likelihood settings (which likelihood gets evaluated) and the parameter sampling options (which parameters get sampled) are separated. It is upon the user to decide the appropriate parameters to be sampled for the given choice of likelihood and information." + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": {}, + "outputs": [], + "source": [ + "# so I'd have to turn these on or off depending on what model/information I have\n", + "time_delay_likelihood = False # bool, set this True or False depending on whether time-delay information is available and you want to make use of its information content.\n", + "flux_ratio_likelihood = False # bool, modeling the flux ratios of the images\n", + "image_position_likelihood = True # bool, evaluating the image position likelihood (in combination with astrometric errors)\n", + "\n", + "kwargs_flux_compute = {'source_type': 'INF', # you can either chose 'INF' which is a infinetesimal source size, 'GAUSSIAN' or 'TORUS'\n", + " 'window_size': window_size, # window size to compute the finite source magnification (only when 'GAUSSIAN' or 'TORUS' are chosen.)\n", + " 'grid_number': grid_number} # number of grid points (per axis) to compute the extended source surface brightness within the window_size around the image position\n", + "\n", + "kwargs_constraints = {'num_point_source_list': num_images_list,\n", + " # 'Ddt_sampling': time_delay_likelihood,\n", + " 'mass_scaling_list': mass_scaling_list\n", + " } # sampling of the time-delay distance\n", + "\n", + "# ATTENTION: make sure that the numerical options are chosen to provide accurate computations for the finite source magnifications!\n", + "if kwargs_flux_compute['source_type'] in ['GAUSSIAN', 'TORUS'] and flux_ratio_likelihood is True:\n", + " kwargs_constraints['source_size'] = True # explicit sampling of finite source size parameter (only use when source_type='GAUSSIAN' or 'TORUS')\n", + "\n", + "# we can define un-correlated Gaussian priors on specific parameters explicitly\n", + "# e.g. power-law mass slope of the main deflector\n", + "# prior_lens = [[0, 'center_x', 0, 0.01], [0, 'center_y', 0, 0.01]] # [[0, 'gamma', 2, 0.1],[index_model, 'param_name', mean, 1-sigma error], [...], ...]\n", + "# e.g. source size of the emission region\n", + "# prior_lens_light = []\n", + "# prior_special = []\n", + " \n", + "kwargs_likelihood = {'image_position_uncertainty': astrometry_sigma, # astrometric uncertainty of image positions\n", + " 'image_position_likelihood': True, # evaluate point source likelihood given the measured image positions\n", + " 'time_delay_likelihood': False, # evaluating the time-delay likelihood\n", + " 'flux_ratio_likelihood': False, # enables the flux ratio likelihood \n", + " 'kwargs_flux_compute': kwargs_flux_compute, # source_type='INF' will lead to point source\n", + " # 'prior_lens': prior_lens,\n", + " # 'prior_lens_light': prior_lens_light,\n", + " # 'prior_special': prior_special,\n", + " 'check_bounds': True # check parameter bounds and punish them\n", + " }" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Multiple image position constraints\n", + "Matching multiple image position constraints from the same source is a difficult and computationally tedious task. Here we discuss a few different approaches, their pros and cons and how they are implemented in lenstronomy. You can find more on these methods in another notebook: https://github.com/lenstronomy/lenstronomy-tutorials/blob/main/Notebooks/LensModeling/modelling_of_catalogue_data.ipynb." + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": {}, + "outputs": [], + "source": [ + "# setting the non-linear solver accoring to option (3)\n", + "kwargs_constraints['solver_type'] = 'NONE' # 'PROFILE_SHEAR', 'NONE', # any proposed lens model must satisfy the image positions appearing at the position of the point sources being sampeled\n", + "\n", + "# checking for matched source position in ray-tracing the image position back to the source plane.\n", + "# This flag should be set =True when dealing with option (2) and (3)\n", + "# kwargs_likelihood['check_matched_source_position'] = True # check non-linear solver and discard non-solutions # removed by simon in a recent PR\n", + "kwargs_likelihood['source_position_tolerance'] = 15 # hard bound tolerance on r.m.s. scatter in the source plane to be met in the sampling\n", + "\n", + "# desired precision on r.m.s. scatter in the source plane to achive. \n", + "# This is implemented as a Gaussian likelihood term and is met when the model is sufficient in describing the data\n", + "# This precision must be set when using option (2). Option (3) should guarantee a very high precision except in some failures of the solver.\n", + "kwargs_likelihood['source_position_sigma'] = astrometry_sigma\n", + "\n", + "# setting to propagate the astrometric uncertainties in image position into a likelihood in the source position.\n", + "# Option (4) above. This option can be used SEPARATE to the solver or the source position tolerance (see below)\n", + "# Care has to be taken when requiring time-delay predictions.\n", + "kwargs_likelihood['source_position_likelihood'] = True # evaluates how close the different image positions match the source positons]\n", + "kwargs_likelihood['image_position_uncertainty'] = astrometry_sigma # this option (4) uses the 'image_position_uncertainty' to translate to a source position uncertainty (see also Birrer & Treu 2019)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## log_likelihood test" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Prior likelihood = 0\n", + "source position likelihood -147.03755783843414\n", + "image position likelihood 0.0\n", + "-147.03755783843414\n" + ] + } + ], + "source": [ + "from lenstronomy.Workflow.fitting_sequence import FittingSequence\n", + "fitting_seq = FittingSequence(kwargs_data_joint, kwargs_model, kwargs_constraints, kwargs_likelihood, kwargs_params)\n", + "\n", + "kwargs_truth = {\"kwargs_ps\": kwargs_ps_init, \"kwargs_lens\": kwargs_lens_init, \"kwargs_source\": {}, \"kwargs_special\": kwargs_special_init,\n", + " \"kwargs_lens_light\": None, \"kwargs_tracer_source\": None}\n", + "log_likelihood = fitting_seq.likelihoodModule.log_likelihood(kwargs_truth, verbose=True)\n", + "\n", + "# for more detailed feedback for your inital guess, uncomment the lines below\n", + "# args = fitting_seq.param_class.kwargs2args(**kwargs_truth)\n", + "# kwargs_test = fitting_seq.param_class.args2kwargs(args)\n", + "# print(kwargs_test)\n", + "# kwargs_ps_test = kwargs_test['kwargs_ps']\n", + "# for kwargs in kwargs_ps_test:\n", + "# print(kwargs)\n", + "# fitting_seq.likelihoodModule.logL(args, verbose=True)\n", + "\n", + "print(log_likelihood)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Distance and Root Mean Square Error calculations of the source positions" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Distances (x): [array([-0.00167908, -0.0017614 , -0.00251431, -0.00203619, 0.00799099]), array([-0.00466145, 0.00435131, 0.00031014]), array([-2.19586898e-03, 7.52362680e-05, 3.31506381e-03, 4.45506775e-03,\n", + " -5.65079774e-04, -8.87835944e-04, 4.10671925e-04, 2.59597362e-03,\n", + " -7.20322867e-03]), array([ 0.00403599, -0.00328874, -0.00074725]), array([ 0.00084219, -0.00310425, 0.00226206]), array([-0.00058571, 0.00026265, 0.00225894, -0.00514401, 0.00320813]), array([ 0.00124545, -0.00331879, -0.00323023, 0.00126667, 0.0040369 ]), array([ 0.00276431, 0.00761466, 0.00441653, -0.00523136, -0.00956414]), array([-0.001771 , 0.00445985, 0.00315823, 0.00608851, -0.01193559]), array([ 0.00329806, 0.00020453, -0.00350259]), array([ 0.0021508 , 0.00362703, -0.00325494, -0.00026361, -0.00225928]), array([ 0.00393888, -0.00288165, 0.00117057, -0.00929393, 0.00706614]), array([ 0.00041373, 0.00405669, -0.00447043]), array([-0.00897244, -0.00056826, -0.00201612, 0.00150962, 0.0100472 ]), array([ 0.00079423, -0.00774474, -0.00501112, -0.00453809, 0.01649972]), array([-0.00189087, 0.00602749, 0.0073523 , -0.00265477, -0.00883416])]\n", + "Distances (y): [array([-0.00027837, -0.00329531, 0.005122 , 0.00252711, -0.00407542]), array([-0.00182411, 0.00581596, -0.00399184]), array([-0.00026885, 0.00258076, 0.00068248, -0.00060053, -0.00499418,\n", + " 0.00257483, -0.00257966, -0.00186459, 0.00446973]), array([-0.0012174 , 0.0001352 , 0.00108219]), array([ 0.00345489, 0.00055123, -0.00400613]), array([ 0.0017399 , 0.00520004, -0.00238252, -0.01014189, 0.00558447]), array([ 0.00146929, 0.00411859, -0.00237656, -0.00298139, -0.00022994]), array([ 0.00265072, 0.00775588, 0.00411841, -0.00320814, -0.01131686]), array([ 0.00029895, 0.00551926, 0.00342389, 0.01029044, -0.01953255]), array([ 0.00052513, -0.00557374, 0.00504862]), array([-0.00199393, 0.00104732, -0.00141493, -0.00509022, 0.00745176]), array([ 0.00227973, -0.00050322, -0.00209049, -0.00391652, 0.0042305 ]), array([-0.00265733, 0.00512061, -0.00246327]), array([-0.00214794, -0.00371642, -0.00618949, 0.00332263, 0.00873123]), array([-0.0019702 , -0.00636423, -0.00845671, -0.00828279, 0.02507393]), array([-0.00558125, 0.01084944, 0.00033982, -0.00475509, -0.00085293])]\n", + "RMSE (x, y): 0.004910067708845705, 0.005882910585260102\n" + ] + } + ], + "source": [ + "# calculate the source positions\n", + "func_x_source, func_y_source = fitting_seq.likelihoodModule.PointSource.source_position(kwargs_ps_init, kwargs_lens)\n", + "\n", + "# calculate the distance between the mean of a source's calculated positions and each individual position\n", + "func_diffs_x, func_diffs_y = fitting_seq.likelihoodModule._position_likelihood.source_position_dist(kwargs_ps=kwargs_ps_init, kwargs_lens=kwargs_lens, lens_model=lensModel, z_sources=z_sources)\n", + "print('Distances (x): %s' %(func_diffs_x))\n", + "print('Distances (y): %s' %(func_diffs_y))\n", + "\n", + "# calculate the RMSE for the source positions\n", + "func_rmse_x, func_rmse_y = fitting_seq.likelihoodModule._position_likelihood.source_position_rmse(kwargs_ps=kwargs_ps_init, kwargs_lens=kwargs_lens, lens_model=lensModel, z_sources=z_sources)\n", + "print('RMSE (x, y): %s, %s' %(func_rmse_x, func_rmse_y))" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# historgram of the distances calculated in the above cell\n", + "f, ax = plt.subplots(1, 2, figsize=(10, 5), sharex=True, sharey=True)\n", + "\n", + "x_data = []\n", + "y_data = []\n", + "\n", + "for i in range(len(func_diffs_x)):\n", + " for j in range(len(func_diffs_x[i])):\n", + " x_data.append(func_diffs_x[i][j])\n", + " y_data.append(func_diffs_y[i][j])\n", + "\n", + "values_x, bins_x, bars_x = ax[0].hist(x_data, bins=20, edgecolor='black')\n", + "values_y, bins_y, bars_y = ax[1].hist(y_data, bins=20, edgecolor='black')\n", + "\n", + "ax[0].set_ylabel('Frequency')\n", + "ax[1].set_ylabel('Frequency')\n", + "\n", + "ax[0].set_xlabel('Source position-mean residual (x) [arcsec]')\n", + "ax[1].set_xlabel('Source position-mean residual (y) [arcsec]')\n", + "\n", + "ax[0].bar_label(bars_x, fontsize=10, color='blue')\n", + "ax[1].bar_label(bars_y, fontsize=10, color='blue')\n", + "\n", + "ax[0].margins(x=0.01, y=0.1)\n", + "ax[1].margins(x=0.01, y=0.1)\n", + "\n", + "ax[0].set_title('')\n", + "ax[1].set_title('')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 2D histogram just for fun, helps visualize how close your calculations are to the truth\n", + "plt.hexbin(x_data, y_data, gridsize=30, cmap='Blues')\n", + "plt.xlabel('RMS scatter for source x position [arcsec]')\n", + "plt.ylabel('RMS scatter for source y position [arcsec]')\n", + "plt.title('2D Histogram')\n", + "plt.colorbar()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Run the modeling - Particle Swarm Optimization to find a maxima in the likelihood" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fitting_kwargs_list = [['PSO', {'sigma_scale': .1, 'n_particles': 100, 'n_iterations': 200}]] #['update_settings', {'lens_add_fixed': [[0, ['gamma']]]}]]\n", + " # you can add additional fixed parameters in the line above if you want\n", + "\n", + "start_time = time.time()\n", + "chain_list_pso = fitting_seq.fit_sequence(fitting_kwargs_list)\n", + "kwargs_result = fitting_seq.best_fit()\n", + "end_time = time.time()\n", + "print(end_time - start_time, 'total time needed for computation')\n", + "print('============ CONGRATULATIONS, YOUR JOB WAS SUCCESSFUL ================ ')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fitting_seq.best_fit_likelihood(verbose=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "kwargs_result = fitting_seq.best_fit(bijective=True)\n", + "args_result = fitting_seq.param_class.kwargs2args(**kwargs_result)\n", + "logL = fitting_seq.likelihoodModule.logL(args_result, verbose=True)\n", + "\n", + "from lenstronomy.Plots import chain_plot\n", + "for i in range(len(chain_list_pso)):\n", + " chain_plot.plot_chain_list(chain_list_pso, i)\n", + "\n", + "print(\"kwargs_results\", kwargs_result)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## MCMC posterior sampling" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#and now we run the MCMC\n", + "fitting_kwargs_list = [\n", + " ['MCMC', {'n_burn': 200, 'n_run': 400, 'walkerRatio': 10,'sigma_scale': 0.1}]\n", + "]\n", + "chain_list_mcmc = fitting_seq.fit_sequence(fitting_kwargs_list)\n", + "\n", + "kwargs_result = fitting_seq.best_fit()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "## we want the logL (log likelihood) to stay fairly flat across the plot, that means its a decent guess.\n", + "chain_plot.plot_chain_list(chain_list_mcmc)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Post-processing the chains " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "sampler_type, samples_mcmc, param_mcmc, dist_mcmc = chain_list_mcmc[0]\n", + "\n", + "print(\"number of non-linear parameters in the MCMC process: \", len(param_mcmc))\n", + "print(\"parameters in order: \", param_mcmc)\n", + "print(\"number of evaluations in the MCMC process: \", np.shape(samples_mcmc)[0])\n", + "\n", + "# import the parameter handling class #\n", + "from lenstronomy.Sampling.parameters import Param\n", + "import lenstronomy.Util.param_util as param_util\n", + "# make instance of parameter class with given model options, constraints and fixed parameters\n", + "# this allows to recover the full parameters of all model components, not just the ones being sampled.\n", + "\n", + "param = Param(kwargs_model, fixed_lens, kwargs_fixed_ps=fixed_ps, kwargs_fixed_special=fixed_special, \n", + " kwargs_lens_init=kwargs_result['kwargs_lens'], **kwargs_constraints)\n", + "# the number of non-linear parameters and their names #\n", + "num_param, param_list = param.num_param()\n", + "\n", + "lensModel = LensModel(kwargs_model['lens_model_list'])\n", + "lensModelExtensions = LensModelExtensions(lensModel=lensModel)\n", + "print(\"parameter values: \", param)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "np.save('samples_mcmc_cluster', samples_mcmc)\n", + "np.save('sampler_type_cluster', sampler_type)\n", + "np.save('param_cluster', param)\n", + "np.save('lens_model_list_cluster', lens_model_list)\n", + "np.save('kwargs_constraints_cluster', kwargs_constraints)\n", + "np.save('special_params_cluster', special_params)\n", + "for i in range(num_sources):\n", + " np.save('x_imgs_cluster'+str(i), x_imgs[i])\n", + " np.save('y_imgs_cluster'+str(i), y_imgs[i])\n", + " np.save('label_list_cluster'+str(i), label_lists[i])\n", + "np.save('param_mcmc_cluster', param_mcmc)\n", + "np.save('dist_mcmc_cluster', dist_mcmc)\n", + "np.save('num_param_cluster', num_param)\n", + "np.save('param_list_cluster', param_list)\n", + "np.save('kwargs_result_cluster', kwargs_result)\n", + "for i in range(4):\n", + " np.save('chain_list_mcmc_cluster'+str(i), chain_list_mcmc[0][i])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "num_sources_ = 20\n", + "\n", + "samples_mcmc_ = np.load('samples_mcmc_cluster.npy')\n", + "sampler_type_ = np.load('sampler_type_cluster.npy')\n", + "lens_model_list_ = np.load('lens_model_list_cluster.npy')\n", + "x_imgs_ = []\n", + "label_lists_ = []\n", + "for i in range(num_sources_):\n", + " x_imgs_.append(np.load('x_imgs_cluster'+str(i)+'.npy'))\n", + " label_lists_.append(np.load('label_list_cluster'+str(i)+'.npy'))\n", + "param_mcmc_ = np.load('param_mcmc_cluster.npy')\n", + "dist_mcmc_ = np.load('dist_mcmc_cluster.npy')\n", + "num_param_ = np.load('num_param_cluster.npy')\n", + "param_list_ = np.load('param_list_cluster.npy')\n", + "param_ = np.load('param_cluster.npy', allow_pickle=True)\n", + "kwargs_constraints_ = np.load('kwargs_constraints_cluster.npy', allow_pickle=True)\n", + "special_params_ = np.load('special_params_cluster.npy', allow_pickle=True)\n", + "kwargs_result_ = np.load('kwargs_result_cluster.npy', allow_pickle=True)\n", + "chain_list_mcmc_ = []\n", + "for i in range(4):\n", + " chain_list_mcmc_.append(np.load('chain_list_mcmc_cluster'+str(i)+'.npy'))\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "param_ = np.ndarray.tolist(param_)\n", + "samples_mcmc_ = np.ndarray.tolist(samples_mcmc_)\n", + "sampler_type_ = np.ndarray.tolist(sampler_type_)\n", + "lens_model_list_ = np.ndarray.tolist(lens_model_list_)\n", + "for i in range(len(x_imgs_)):\n", + " x_imgs_[i] = np.ndarray.tolist(x_imgs_[i])\n", + "\n", + "for i in range(len(label_lists_)):\n", + " label_lists_[i] = np.ndarray.tolist(label_lists_[i])\n", + "param_mcmc_ = np.ndarray.tolist(param_mcmc_)\n", + "dist_mcmc_ = np.ndarray.tolist(dist_mcmc_)\n", + "num_param_ = np.ndarray.tolist(num_param_)\n", + "param_list_ = np.ndarray.tolist(param_list_)\n", + "kwargs_constraints_ = np.ndarray.tolist(kwargs_constraints_)\n", + "special_params_ = np.ndarray.tolist(special_params_)\n", + "kwargs_result_ = np.ndarray.tolist(kwargs_result_)\n", + "for i in range(4):\n", + " chain_list_mcmc_[i] = np.ndarray.tolist(chain_list_mcmc_[i])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "labels_new = []\n", + "for i in range(num_cluster_members):\n", + " labels_new.extend(['sigma0_lens_'+str(i), 'Ra_lens_'+str(i), 'Rs_lens_'+str(i), 'e1_lens_'+str(i), 'e2_lens_'+str(i), 'center_x_lens'+str(i), 'center_y_lens'+str(i)])\n", + "labels_new.extend(['Rs_nfw_lens', 'alphaRs_nfw_lens', 'e1_nfw_lens', 'e2_nfw_lens', 'center_x_nfw_lens', 'center_y_nfw_lens'])\n", + "\n", + "lenstronomy_clusters_functions.clusters_functions.real_image_pos_labels(num_sources, x_imgs, labels_new, label_lists, image_position_likelihood=True)\n", + "lenstronomy_clusters_functions.clusters_functions.flux_ratio_labels(num_sources, x_imgs, labels_new, label_lists, flux_ratio_likelihood=False)\n", + "lenstronomy_clusters_functions.clusters_functions.source_size_labels(kwargs_constraints, labels_new, special_params=special_params)\n", + "lenstronomy_clusters_functions.clusters_functions.time_delay_labels(labels_new, time_delay_likelihood=True)\n", + "\n", + "print(labels_new)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "new_chain = []\n", + "mcmc_new_list_cluster = []\n", + "\n", + "mcmc_new_list_cluster = lenstronomy_clusters_functions.clusters_functions.samples2posterior_plot(samples=samples_mcmc_, mcmc_list=mcmc_new_list_cluster, param_class=param_, lens_model_list=lens_model_list_, kwargs_constraints=kwargs_constraints_, special_params=special_params_, image_position_likelihood=True, with_flux_ratios=False, time_delay_likelihood=False)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# np.save('mcmc_new_list_cluster', mcmc_new_list_cluster)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "mcmc_new_list_cluster_ = np.load('mcmc_new_list_cluster.npy')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# import code for legend on corner plot\n", + "import matplotlib.lines as mlines\n", + "\n", + "# purple_line = mlines.Line2D([], [], color='purple', label=str(num_sources_data)+\" Sources, varied z\")\n", + "blue_line = mlines.Line2D([], [], color='blue', label='Clusters, const z')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "samples_cluster = np.array(mcmc_new_list_cluster[269500:308000])\n", + "\n", + "figure = corner.corner(samples_cluster, labels=labels_new, color='blue', show_titles=True) # fig=plot should put the one with reduced data and the full one on top of each other... reduced = blue, original = gray\n", + "\n", + "plt.legend(handles=[blue_line], bbox_to_anchor=(-2, 4., 1., .0), loc=1)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# input truth time-delay distance [Mpc]\n", + "lensCosmo.ddt" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Notebooks/Clusters/modelling_SMACS0723_cluster_data.ipynb b/Notebooks/Clusters/modelling_SMACS0723_cluster_data.ipynb new file mode 100644 index 0000000..8269260 --- /dev/null +++ b/Notebooks/Clusters/modelling_SMACS0723_cluster_data.ipynb @@ -0,0 +1,1807 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Modelling of catalogue data\n", + "$\\texttt{lenstronomy}$ was originally developed to simulate and model imaging data. The modular design allows to model and sample data in catalogue form too. In this notebook, we read in data from the Mahler et al. paper for multiple sources multiply imaged by a galaxy cluster.\n", + "\n", + "In the first step, we read in the necessary data:\n", + "- lens parameters; including position and redshift\n", + "- image parameters; including positions, apparent magnitudes, \n", + "\n", + "and perform some calculations:\n", + "- each lensing galaxy's eccentricity, absolute magnitude, luminosity, distance, velocity dispersion, Einstein radius, and realtive mass\n", + "- relative time delays of images\n", + "\n", + "The multiple images are then grouped together based on the number of sources and the known groups of multiple images.\n", + "\n", + "\n", + "In a second step, we use this data to sample the lens model parameter space. The modelling can also be used if only partial information is available (e.g. no time delays and/or flux ratio measurements) are available." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Installing packages\n", + "The first block of packages all provide helpful methods to perform calculations, access constant values, and make plots. astropy and scipy contain relevant astrophysical constants and tools. math, numpy, and random all provide useful mathematical methods that are otherwise tedious to code. copy makes it easy to quickly duplicate useful information, leaving one as a reference and the other available to perform calculations on or update. corner and matplotlib contain plotting functions, making the creation of informative and interesting plots easier. pandas allows for easier organization of data through the pandas data frame.\n", + "\n", + "$\\texttt{lenstronomy}$ is the basis of this notebook, using the packages listed below for various purposes. LensModel creates the class used to generate images later, using the lens_plot functions. We also need the Extenstions and EquationsSolver packages in order to backward ray trace to determine source locations, among other uses. The PointSource class is used to later calculate the RMSE of the source positions, which helps tell us if the model is a good fit to the data. $\\texttt{lenstronomy clusters functions}$ is a new small package that helps to sort and collect the labels and data for the corner plots from the MCMC posteriors." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# import the necessary python modules\n", + "import astropy\n", + "import copy\n", + "import corner\n", + "import math\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import pandas as pd\n", + "import random\n", + "import scipy\n", + "import time\n", + "from astropy.cosmology import FlatLambdaCDM\n", + "\n", + "from lenstronomy.LensModel.lens_model import LensModel\n", + "from lenstronomy.LensModel.lens_model_extensions import LensModelExtensions\n", + "from lenstronomy.LensModel.Solver.lens_equation_solver import LensEquationSolver\n", + "from lenstronomy.Cosmo.lens_cosmo import LensCosmo\n", + "from lenstronomy.Util import constants\n", + "from lenstronomy.Util import param_util\n", + "from lenstronomy.Plots import lens_plot\n", + "from lenstronomy.PointSource.point_source import PointSource\n", + "import lenstronomy_clusters_functions.clusters_functions\n", + "\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# important initial values\n", + "\n", + "random.seed(10)\n", + "measurement_realization = True # if True, draws measurement values from the uncertainties, if not, keeps the true value" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# mini functions to check if something is a float or not, and to find the value of a float before the decimal point (rounding down)\n", + "def is_float(string):\n", + " try:\n", + " float(string)\n", + " return True\n", + " except ValueError:\n", + " return False\n", + "\n", + "def find_value_before_decimal(list, target_value):\n", + " count = 0\n", + " for decimal in list:\n", + " decimal = float(decimal)\n", + " if math.floor(decimal) == target_value:\n", + " count += 1\n", + " return count" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Reading in catalogue data\n", + "The data used is from the Mahler et al. 2023 paper (https://arxiv.org/pdf/2207.07101) and its data files (SMACS0723-mahler2022 found on GitHub at: https://github.com/guillaumemahler/SMACS0723-mahler2022 under the ICLv1 folder).\n", + "- The first file, 'input.par' is a parameter file which is generally in a format used for another lens modeling program, $\\texttt{lenstool}$. It is separated into headers with various associated properties listed after and then the limits of each property. For example, under a given \"potentiel\" header, there are coordinates for the center, ellipticity, angle position, core radius (kpc), cut radius (kpc), velocity dispersion, and redshift of the lens. Values with uncertainties have those listed below the profile under a separate \"limit\" header.\n", + "- The second file read in is the 'galcat.cat' file. This is a catalog file contains lists of information regarding a numbered galaxy cluster member. Each is indexed as referenced in the paper, and the information includes the coordinates (ra and dec in degrees), the major and minor axis lengths, reference angle θ, apparent magnitude, and redshift.\n", + "- The final data file read in is the 'arcs.dat' file, a data file that contains all the information regarding the multiple image positions from the various background sources. Each image is labeled with the source number and multiple image number (ie. 1.2), then the coordinates (relative degrees), the uncertainties, and redshifts. Some redshifts are optimzed in the modeling by Mahler et al., so the values here are not what is used. The values used are input by hand." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# READING IN AND CONVERTING DATA - LENS PARAMETERS\n", + "\n", + "# reading in the data, just a mess because the file is not normalized\n", + "with open('input.par', 'r') as input:\n", + " params = []\n", + " for line in input:\n", + " if line.find(\":\") != -1 or line.find(\" \") != -1:\n", + " if line.find(\":\") != -1:\n", + " name, value = line.split(\":\")\n", + " if line.find('\\t') != -1:\n", + " line = line.replace('\\t', \" \")\n", + " line = line.lstrip()\n", + " line = line.rstrip()\n", + " if line.count(\" \") >= 2:\n", + " name, value = line.split(\" \", 1)\n", + " name = name.strip()\n", + " value = value.lstrip()\n", + " value = value.rstrip()\n", + " value = value.split(\" \")\n", + " for x in value:\n", + " if is_float(x) is True:\n", + " x = float(x)\n", + " else:\n", + " x = x\n", + " else:\n", + " name, value = line.split(\" \")\n", + " if line.find(\":\") != -1:\n", + " name = name.replace(\":\", \" \")\n", + " name = name.strip()\n", + " value = value.lstrip()\n", + " value = value.rstrip()\n", + " if is_float(value) is True:\n", + " value = float(value)\n", + " params.append([name, value])\n", + " elif line.find(\" \") == -1:\n", + " line = line.lstrip()\n", + " line = line.rstrip()\n", + " params.append(line)\n", + "input.close()\n", + "\n", + "input_data_frame = pd.DataFrame(params, columns=[\"Variable\", \"Value\", \"\", \"\", \"\", \"\", \"\", \"\", \"\", \"\"])\n", + "\n", + "reference_point = [float(input_data_frame['Value'].iloc[9][1]), float(input_data_frame['Value'].iloc[9][2])]\n", + "# [110.82675, -73.454628] from the Mahler paper" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# reading in the data from the Mahler galaxy catalog. Formatting is aweful, so a lot of data normalization. Then we get out data on each cluster member's:\n", + " # Galaxy ID, RA, DEC, a, b, theta, apparent magnitude, z. The ra and dec are converted form degrees to arcsec. a and b are used to calculate the ellipticity\n", + "\n", + "with open('galcat.cat', 'r') as file:\n", + " gal_cat = file.read()\n", + "\n", + "lines = gal_cat.splitlines()\n", + "\n", + "for i in range(len(lines)):\n", + " lines[i]=lines[i].lstrip('#')\n", + " lines[i]=lines[i].lstrip(str(chr(32)))\n", + "\n", + "gal_data=[]\n", + "for i in range(len(lines)):\n", + " gal_data.append(lines[i].split(' '))\n", + "\n", + "# We don't need blank lines, so find them...\n", + "str_to_find = ''\n", + "Is = []\n", + "for i in range(len(gal_data)):\n", + " blank_in_data = np.isin(str_to_find, gal_data[i])\n", + " if blank_in_data == True:\n", + " Is.append(i)\n", + "Is.reverse()\n", + "# ... and now get rid of them\n", + "for i in range(len(Is)):\n", + " row_to_remove = Is[i]\n", + " gal_data.remove(gal_data[row_to_remove])\n", + "# Convert the position from deg to arcsec\n", + "gal_data_deg = copy.deepcopy(gal_data)\n", + "\n", + "# convert values from strings to floats\n", + "for i in range(len(gal_data_deg)):\n", + " for j in range(len(gal_data_deg[i])):\n", + " gal_data_deg[i][j] = float(gal_data[i][j])\n", + "\n", + "# subtract reference point from galaxy positions in degrees\n", + "for i in range(len(gal_data_deg)):\n", + " gal_data_deg[i][1] = (gal_data_deg[i][1] - reference_point[0])*math.cos(reference_point[1])\n", + " gal_data_deg[i][2] = (gal_data_deg[i][2] - reference_point[1])\n", + "\n", + "gal_data_corr = copy.deepcopy(gal_data_deg)\n", + "\n", + "# convert coordinates to arcsec\n", + "for i in range(len(gal_data_corr)):\n", + " gal_data_corr[i][1] = gal_data_deg[i][1]*3600\n", + " gal_data_corr[i][2] = gal_data_deg[i][2]*3600\n", + "\n", + "# make data frame\n", + "columns = ['Galaxy ID', 'RA', 'DEC', 'a', 'b', 'theta', 'magnitude', 'z']\n", + "\n", + "gal_data_arcsec = pd.DataFrame(gal_data_corr, columns=columns)\n", + "\n", + "# the Mahler data has the redshift listed as 0.0 for each of the cluster members relative to the main lens mass. For this code, we need the individual member redshifts\n", + "# so we will assume each of them to be 0.39, like the lens mass. This is most likely to simple of an assumption, but for now it will have to do.\n", + "\n", + "z_cluster_members = []\n", + "for i in range(len(gal_data_arcsec)):\n", + " z_cluster_members.append(0.39)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[3, 3, 4, 3, 3, 3, 3, 2, 2, 3, 2, 3, 4, 3, 2, 3, 3, 3, 3, 3, 2]\n" + ] + } + ], + "source": [ + "## load in the new image data and convert to make it useable\n", + "# this reads in the Mahler data on the multiple image systems. Each arc is then sorted, and the refernce ra and dec are recorded in arcsec.\n", + "# the image redshifts are input by hand as listed in the Mahler paper.\n", + "\n", + "#process for data in a .dat file with ' ' as delimiter\n", + "with open('arcs.dat', 'r') as file:\n", + " arcs_data = file.read()\n", + "lines = arcs_data.splitlines()\n", + "arcs_data_deg=[]\n", + "for i in range(len(lines)):\n", + " arcs_data_deg.append(lines[i].split(' '))\n", + "\n", + "arcs_data_corr = copy.deepcopy(arcs_data_deg) # deepcopy ensures there are no rounding errors\n", + "\n", + "for i in range(len(arcs_data_corr)):\n", + " for j in range(len(arcs_data_deg[i])-1):\n", + " arcs_data_corr[i][j] = float(arcs_data_deg[i][j])\n", + "\n", + "for i in range(len(arcs_data_corr)):\n", + " arcs_data_corr[i][1] = (arcs_data_corr[i][1] - reference_point[0])*math.cos(reference_point[1])\n", + " arcs_data_corr[i][2] = arcs_data_corr[i][2] - reference_point[1]\n", + "\n", + "arcs_data_arcsec = copy.deepcopy(arcs_data_corr)\n", + "\n", + "# convert to arcsec\n", + "for i in range(len(arcs_data_arcsec)):\n", + " arcs_data_arcsec[i][1] = arcs_data_corr[i][1]*3600\n", + " arcs_data_arcsec[i][2] = arcs_data_corr[i][2]*3600\n", + "\n", + "ra_list = []\n", + "dec_list = []\n", + "for i in range(len(arcs_data_deg)):\n", + " ra_list.append(arcs_data_deg[i][1])\n", + " dec_list.append(arcs_data_deg[i][2])\n", + "\n", + "x_pos_list = []\n", + "y_pos_list = []\n", + "for i in range(len(arcs_data_arcsec)):\n", + " x_pos_list.append(arcs_data_arcsec[i][1])\n", + " y_pos_list.append(arcs_data_arcsec[i][2])\n", + "\n", + "# create a list of image ids\n", + "num_images=len(arcs_data_arcsec)\n", + "image_ids = []\n", + "for i in range(num_images):\n", + " image_ids.append(str(arcs_data_arcsec[i][0]))\n", + "\n", + "## caluculate number of sources from image list\n", + "num_images_list = []\n", + "sources_list = []\n", + "for i in range(len(arcs_data_arcsec)):\n", + " index = find_value_before_decimal(image_ids, i+1)\n", + " if index != 0:\n", + " num_images_list.append(index)\n", + " sources_list.append(i+1)\n", + "print(num_images_list)\n", + "total_images = sum(num_images_list)\n", + "num_sources_data = len(sources_list)\n", + "\n", + "# z for the images from the Mahler paper. In the future, would want to read these in, but not listed in the data set\n", + "z_sources_new = [1.449, 1.449, 1.449, 1.3779, 1.3779, 1.3779, 1.9914, 1.9914, 1.9914, 1.9914,\n", + " 2.31, 2.31, 2.31, 1.425, 1.425, 1.425, 1.70, 1.70, 1.70, 5.17, 5.17, 5.17, \n", + " 14.39, 14.39, 3.01, 3.01, 1.43, 1.43, 1.43, 1.73, 1.73, 1.73, 1.81, 1.81, \n", + " 1.81, 3.34, 3.34, 3.34, 2.04, 2.04, 2.04, 1.09, 1.09, 2.12, 2.12, 2.12, 1.37, \n", + " 1.37, 1.37, 1.37, 1.37, 1.37, 2.60, 2.60, 2.60, 3.93, 3.93, 3.93, 2.88, 2.88]" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "# Image properties\n", + "# this groups the images according to the sources that they came from, each list contains lists of the associated image ID's, positions, and redshifts. Used for plotting purposes.\n", + "\n", + "grouped_ids = []\n", + "grouped_x_imgs = []\n", + "grouped_y_imgs = []\n", + "grouped_z_sources = []\n", + "\n", + "cutoff = 0\n", + "for i in range(num_sources_data):\n", + " ids_temp = []\n", + " images_x_temp = []\n", + " images_y_temp = []\n", + " z_temp = []\n", + " for j in range(num_images_list[i]):\n", + " ids_temp.append(image_ids[j+cutoff])\n", + " images_x_temp.append(x_pos_list[j+cutoff])\n", + " images_y_temp.append(y_pos_list[j+cutoff])\n", + " z_temp.append(z_sources_new[j+cutoff])\n", + " cutoff += num_images_list[i]\n", + " grouped_ids.append(ids_temp)\n", + " grouped_x_imgs.append(images_x_temp)\n", + " grouped_y_imgs.append(images_y_temp)\n", + " grouped_z_sources.append(z_temp)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "# Input for lens properties\n", + "# This includes the assumed cosmology, the lens parameters for each dPIED member galaxy, and the NFW dark matter halo\n", + "\n", + "import astropy.units as u\n", + "\n", + "z_lens = float(input_data_frame['Value'].iloc[50][0])\n", + "\n", + "# source properties\n", + "z_source_convention= 1.5\n", + "\n", + "v_disp = float(input_data_frame['Value'].iloc[68][0])\n", + "Ra = float(input_data_frame['Value'].iloc[66][0])\n", + "Rs = float(input_data_frame['Value'].iloc[67][0])\n", + "\n", + "cosmo = FlatLambdaCDM(H0=70, Om0=0.3, Ob0=0.) # H_0 {km/s/Mpc}, omega_0 (= (ρ / ρ_critical) where ρ is the actual density of the universe and ρ_critical is the critical density), Omega_b (Baryon density today)\n", + "lensCosmo = LensCosmo(cosmo=cosmo, z_lens=z_lens, z_source=z_source_convention)\n", + "\n", + "# for the astropy calculation of the luminosity distances or the cluster member galaxies\n", + "astro_cosmo = FlatLambdaCDM(H0=70*u.km / u.s / u.Mpc, Tcmb0=2.725*u.K, Om0=0.3)\n", + "\n", + "# make class instances for a chosen lens model type. Chose a lens model\n", + "lens_model_list = []\n", + "for i in range(len(gal_data_arcsec)):\n", + " lens_model_list.append('PJAFFE_ELLIPSE_POTENTIAL')\n", + "lens_model_list.append('NFW_ELLIPSE_CSE')\n", + "\n", + "# make instance of LensModel class. Only one here, the shifting of the sources will happen in the computing bit further down in this block\n", + "lensModel = LensModel(lens_model_list=lens_model_list, cosmo=cosmo, z_lens=z_lens, z_source_convention=z_source_convention, z_source=z_sources_new[0])\n", + "\n", + "# we require routines accessible in the LensModelExtensions class, then make instance of LensEquationSolver to solve the lens equation\n", + "lensModelExtensions = LensModelExtensions(lensModel=lensModel)\n", + "lensEquationSolver = LensEquationSolver(lensModel=lensModel)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "q: 0.161, ecc: 0.7226528854435831, e1: 0.18932996344052383, e2: 0.307751463284245\n" + ] + } + ], + "source": [ + "phi = 0.1\n", + "gamma = 0.1\n", + "gamma1, gamma2 = param_util.shear_polar2cartesian(phi=0.1, gamma=0.1)\n", + "# chose the data where the lens is centered at (0,0)\n", + "\n", + "# calculate the eccentricities in a way that matches lenstronomy's definitions\n", + "angle_rads=[]\n", + "qs = []\n", + "eccentricities = []\n", + "e1s = []\n", + "e2s = []\n", + "for i in range(len(gal_data_arcsec)):\n", + " angle_rad = (gal_data_arcsec['theta'].iloc[i])*(math.pi/180) # 'theta' is defined as: ellipticity of the matter density\n", + " q = ((gal_data_arcsec['b'].iloc[i])/(gal_data_arcsec['a'].iloc[i]))\n", + " ecc = (1-q)/(1+q)\n", + " e1 = float(ecc * (math.cos(2*angle_rad)) * 0.5)\n", + " e2 = float(ecc * (math.sin(2*angle_rad)) * 0.5)\n", + "\n", + " angle_rads.append(angle_rad)\n", + " qs.append(q)\n", + " eccentricities.append(ecc)\n", + " e1s.append(e1)\n", + " e2s.append(e2)\n", + "\n", + "nfw_angle_rad = (float(input_data_frame['Value'].iloc[65][0]))*(math.pi/180) # now based on the 'angle_pos' value, not the 'theta' value. Is there something similar for the member galaxies?\n", + "nfw_q = float(input_data_frame['Value'].iloc[64][0])\n", + "nfw_ecc = (1-nfw_q)/(1+nfw_q)\n", + "nfw_e1 = float(nfw_ecc * (math.cos(2*nfw_angle_rad)) * 0.5)\n", + "nfw_e2 = float(nfw_ecc * (math.sin(2*nfw_angle_rad)) * 0.5) # check the orientation\n", + "\n", + "print('q: %s, ecc: %s, e1: %s, e2: %s' %(nfw_q, nfw_ecc, nfw_e1, nfw_e2))" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "23.177739657126313 13.696467308568057\n", + "[-0.04904835144227604, 0.0004096789801026205, 0.013853329148482103, -0.021693684005130647, -0.04280093462643234, 0.012975965144632111, 2.116184797134287e-18, 0.03284400066076623, -0.0029387904961787597, -0.008495642398291883, -0.08262735602655073, -0.0006031537779170575, -0.06969730999316877, -0.011369648927660486, 0.03967822983514242, -0.057352591942256496, 0.021688234624488708, 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watts, luminosity of the sun = 3.8*10**33 ergs/sec = 10**26 joules/sec\n", + "L_mw = float(L_sun * 10**(0.4*(M_sun-M_mw))) # this equation works!\n", + "L_andromeda = (2.6*10**10)*L_sun\n", + "L_star = 3*10**10 * L_sun # watts, luminosity of a typical, milky way-type galaxy\n", + "\n", + "L_ratio_star = L_star/L_mw\n", + "L_ratio_andromeda = L_andromeda/L_mw\n", + "L_ratios = []\n", + "\n", + "sigma_v_star = 160 # km/s, central Velocity Dispersion of a typical, milky way-type galaxy\n", + "mass_star = 6*(10**42) # kg, mass of a milky way type galaxy\n", + "alpha = 0.7 # tunes the size of the galaxy halo\n", + "\n", + "D_l_andromeda = 765000\n", + "D_l_Mpcs = [] # luminosity distance in Mpc\n", + "D_l_pcs = [] # luminosity distance in pc\n", + "\n", + "Ms = []\n", + "Ls = [] # watts, luminosity of the galaxy\n", + "\n", + "sie_sigma_vs = []\n", + "sie_theta_Es = []\n", + "dPIED_sigma_0s = []\n", + "\n", + "for i in range(len(gal_data_arcsec)):\n", + " D_l_Mpc = astro_cosmo.luminosity_distance(z_cluster_members[i]) # this is in units of MPC\n", + " D_l_Mpcs.append(D_l_Mpc)\n", + " D_l_pc = float(D_l_Mpc / u.Mpc * (10**6)) # convert to pc for the absolute magnitude calculation\n", + " D_l_pcs.append(D_l_pc) # --> *(3.086*(10**19)) to m\n", + " M = float(ms.iloc[i] - 5*(math.log(D_l_pc, 10)) + 5) # this gives M around -23\n", + " Ms.append(M)\n", + " # convert magnitude to luminosity, use Milky Way as a reference:\n", + " L = float(L_mw * 10**(0.4*(M_mw-Ms[i]))) # L = L_sun * 10**((M_sun-Mags.iloc[i])/2.5) # L = L_sun * 10**((4.83-M[i])/2.5)\n", + " Ls.append(L)\n", + " L_ratio = float(L/L_mw)\n", + " sie_sigma_v = float(sigma_v_star * (Ls[i]/L_star)**(0.25) - 65) # km/s # from the Faber-Jackson relation\n", + " sie_theta_E = float(lensCosmo.sis_sigma_v2theta_E(sie_sigma_v)) # arcsec\n", + " dPIED_sigma_0 = float(lensCosmo.vel_disp_dPIED_sigma0(vel_disp=sie_sigma_v, Ra=float(gal_data_arcsec['a'].iloc[i]), Rs=Rt_star_kpc)) ## Ra is the core radius, Rs is the truncation radius\n", + " L_ratios.append(L_ratio)\n", + " sie_sigma_vs.append(sie_sigma_v)\n", + " sie_theta_Es.append(sie_theta_E)\n", + " dPIED_sigma_0s.append(dPIED_sigma_0)\n", + "\n", + "# solve for the mass scaling\n", + "masses = [] # milky way-masses, masses of each member galaxy\n", + "massV2 = []\n", + "mw_mass = 1.5*10**12 # solar masses, mass of the milky way\n", + "Ts = []\n", + "\n", + "for i in range(len(gal_data_arcsec)):\n", + " mL_scaling_relationship = ((1/grav))*((sigma_v_star)**2)*(Rt_star*(Ls[i]/L_star)**(0.5 + alpha)) ## Natarajan & Kneib 1997\n", + " T = 12 * (sigma_v_star/240)**2 * (Rt_star_kpc/30) * (Ls[i]/L_star)**(alpha - 0.5)\n", + " Ts.append(T)\n", + " masses.append(mL_scaling_relationship) # closer to kg, mass of the given galaxy\n", + "\n", + "nfw_mass = 10**14.5 # solar masses, mass of a galaxy cluster's halo\n", + "concentration = 10 # ratio of r200 to Rs\n", + "nfw_Rs, nfw_alpha_Rs = lensCosmo.nfw_physical2angle(nfw_mass, concentration) # outputs Rs angle and alpha Rs. See google slides 1/27/25\n", + "nfw_sigma_v = float(input_data_frame['Value'].iloc[68][0])\n", + "\n", + "for i in range(len(gal_data_arcsec)):\n", + " kwargs_lens.append({'sigma0': dPIED_sigma_0s[i], \"e1\": e1s[i], \"e2\": e2s[i], 'Ra': float(gal_data_arcsec['a'].iloc[i]), 'Rs': Rt_star_kpc, 'center_x': float(gal_data_arcsec['RA'].iloc[i]), \"center_y\": float(gal_data_arcsec['DEC'].iloc[i])})\n", + "kwargs_lens.append({\"Rs\": nfw_Rs, \"alpha_Rs\": nfw_alpha_Rs, \"e1\": nfw_e1, \"e2\": nfw_e2, \"center_x\": float(input_data_frame['Value'].iloc[62][0]), \"center_y\": float(input_data_frame['Value'].iloc[63][0])})\n", + "\n", + "print(nfw_Rs, nfw_alpha_Rs)\n", + "print(e1s)\n", + "print(e2s)\n", + "print(float(gal_data_arcsec['a'].iloc[2]))\n", + "print(Rt_star_kpc)\n", + "\n", + "# Definitions:\n", + "# dPIED\n", + " # :param sigma0: sigma0/sigma_crit (see class documentation above)\n", + " # :param Ra: core radius (see class documentation above)\n", + " # :param Rs: transition radius from logarithmic slope -2 to -4 (see class documentation)\n", + " # :param e1: eccentricity component in x-direction\n", + " # :param e2: eccentricity component in y-direction\n", + " # :param center_x: center of profile\n", + " # :param center_y: center of profile\n", + "\n", + "# NFW:\n", + "# :param Rs: turn over point in the slope of the NFW profile in angular units. transition radius from 1 to 3 power law (arcsec), alpha Rs is the defelction angle at that radius\n", + "# :param alpha_Rs: deflection (angular units) at projected Rs\n", + " # :param e1: eccentricity component in x-direction\n", + " # :param e2: eccentricity component in y-direction\n", + "# :param center_x: center of halo (in angular units)\n", + "# :param center_y: center of halo (in angular units)" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1745.5423064934434\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "c:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\LightModel\\Profiles\\gaussian.py:43: RuntimeWarning: divide by zero encountered in scalar divide\n", + " c = amp / (2 * np.pi * sigma**2)\n", + "c:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\LightModel\\Profiles\\gaussian.py:44: RuntimeWarning: divide by zero encountered in divide\n", + " r2 = (x - center_x) ** 2 / sigma**2 + (y - center_y) ** 2 / sigma**2\n", + "c:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\LightModel\\Profiles\\gaussian.py:45: RuntimeWarning: invalid value encountered in multiply\n", + " return c * np.exp(-r2 / 2.0)\n" + ] + } + ], + "source": [ + "# use image positions and calculate their (finite) magnifications\n", + "mag_infs = []\n", + "source_sizes_pc = []\n", + "source_sizes_arcsec = []\n", + "mag_finites = []\n", + "t_days = []\n", + "\n", + "D_s = lensCosmo.ds # angular distance\n", + "print(D_s)\n", + "\n", + "# we compute the finite magnification by rendering a grid around the point source position and add up all the flux coming from the extended source in this window\n", + "window_size = 0.1 # units of arcseconds\n", + "grid_number = 100 # supersampled window (per axis)\n", + "\n", + "for i in range(num_sources_data):\n", + " lensEquationSolver.change_source_redshift(z_source=z_sources_new[i]) # here is where we change the redshift\n", + "\n", + " mag_inf_temp = lensModel.magnification(grouped_x_imgs[i], grouped_y_imgs[i], kwargs_lens)\n", + " mag_infs.append(mag_inf_temp)\n", + "\n", + " source_size_pc_temp = random.randrange(0, 15)\n", + " source_sizes_pc.append(source_size_pc_temp)\n", + " source_size_arcsec_temp = source_sizes_pc[i] / 10**6 / D_s / constants.arcsec\n", + " source_sizes_arcsec.append(source_size_arcsec_temp)\n", + "\n", + " mag_finite_temp = lensModelExtensions.magnification_finite(x_pos=grouped_x_imgs[i], y_pos=grouped_y_imgs[i], kwargs_lens=kwargs_lens, source_sigma=source_sizes_arcsec[i], window_size=window_size, grid_number=grid_number)\n", + " mag_finites.append(mag_finite_temp)\n", + " \n", + " t_days_temp = lensModel.arrival_time(grouped_x_imgs[i], grouped_y_imgs[i], kwargs_lens)\n", + " t_days.append(t_days_temp)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plots in comparison to the Mahler et al. paper\n", + "We then plot the convergence (or mass distribution), critical curves and caustics, and the image positions. This uses three key word arguments from the lens_model_plot function, and produces a plot using that and the point_source_plot function. The three key arguments are:\n", + "- with_convergence=True: for the first plot, this creates the map of the mass distribution based on the lens model parameters that have been input.\n", + "- with_caustics=True: for the second plot, this shows the critical curves in red and the caustics in green. Critical curves represent a line of positions where the lens will infinitely magnify a source, and the caustics represent where the images formed by that critical curve would appear on the image plane.\n", + "- images_from_data=True: for the third plot, the places a diamond at each point an image appears from the input ps kwargs and scales the diamond according to the calculated magnifications.\n", + "\n", + "Below that are rows of plots. These are grouped by each source's set of multiple images and show what our model predicts each image would look like according to its position and hte lens mass distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Create figure and axes\n", + "f, ax = plt.subplots(1, 3, figsize=(18, 5), sharex=True, sharey=True)\n", + "\n", + "#Name_list = None is the default, replace none with a list of strings (ex below) to have custom labels. When plotting, choose one of the lists, as shown below.\n", + "Name_list = [[\".1\", \".2\", \".3\", \".4\", \".5\", \".6\", \".7\", \".8\", \".9\", \".10\"], [\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\", \"I\", \"J\", \"K\", \"L\", \"M\", \"N\", \"O\", \"P\", \"Q\", \"R\", \"S\", \"T\", \"U\", \"V\", \"W\", \"X\", \"Y\", \"Z\"]] # if using a custom Name_list, insert: name_list=Name_list[i] into the list of parameters for plotting.\n", + "num_Names = len(Name_list)\n", + "color_list = ['k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y', 'k', 'b', 'g', 'r', 'c', 'm', 'y'] # should be at least as long as the number of sources\n", + "\n", + "\n", + "# Define ellipse parameters\n", + "gals = []\n", + "for i in range(len(gal_data_arcsec)): # angle in degrees\n", + " gals.append({\"xy\":(gal_data_arcsec['RA'].iloc[i], gal_data_arcsec['DEC'].iloc[i]), \"width\":gal_data_arcsec['a'].iloc[i], \"height\":gal_data_arcsec['b'].iloc[i], \"angle\":gal_data_arcsec['theta'].iloc[i]})\n", + "\n", + "lensModel.change_source_redshift(z_source=grouped_z_sources[0][0])\n", + "lens_plot.lens_model_plot(ax[0], lensModel=lensModel, kwargs_lens=kwargs_lens, images_x=[], images_y=[],\n", + " mag_images=None, index=0, color_value=color_list[0], name_list=Name_list[0], point_source=True,\n", + " images_from_data=False, with_caustics=False, numPix=110, deltaPix=1.0, with_convergence=True,\n", + " fontsize=5\n", + " )\n", + "\n", + "rgba_transparent = (1.0, 1.0, 1.0, 0.0)\n", + "lens_plot.lens_model_plot(ax[1], lensModel=lensModel, kwargs_lens=kwargs_lens, images_x=[], images_y=[],\n", + " mag_images=None, index=0, color_value=color_list[0], name_list=Name_list[0], point_source=True,\n", + " images_from_data=False, with_caustics=True, numPix=110, deltaPix=1.0, with_convergence=False,\n", + " fontsize=5\n", + " )\n", + "for i in range(num_sources_data):\n", + " lens_plot.lens_model_plot(ax[2], lensModel=lensModel, kwargs_lens=kwargs_lens, images_x=grouped_x_imgs[i], images_y=grouped_y_imgs[i], \n", + " mag_images=None, index=i, color_value=color_list[i], name_list=Name_list[0], point_source=True,\n", + " images_from_data=True, with_caustics=False, numPix=110, deltaPix=1.0, with_convergence=False,\n", + " fontsize=5\n", + " )\n", + "# Show the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Users\\earth\\AppData\\Local\\Temp\\ipykernel_27772\\707012058.py:38: RuntimeWarning: divide by zero encountered in log10\n", + " ax.matshow(np.log10(image), vmin=0, vmax=5, origin='lower')\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# here we plot the finite sources as seen at the different image positions\n", + "label_lists = []\n", + "for i in range(num_sources_data):\n", + " label_list_temp = [None] * len(grouped_x_imgs[i])\n", + " label_lists.append(label_list_temp)\n", + "\n", + "if (Name_list is not None) & (num_Names == 1):\n", + " for i in range(num_sources_data):\n", + " lensModelExtensions._lensModel.change_source_redshift(z_source=z_sources_new[i])\n", + " x_img_indexed = grouped_x_imgs[i]\n", + " y_img_indexed = grouped_y_imgs[i]\n", + " f, axes = plt.subplots(1, len(x_img_indexed), figsize=(5*5, 5*len(x_img_indexed)), sharex=False, sharey=False)\n", + " for j in range(len(grouped_x_imgs[i])):\n", + " label_lists[i][j] = grouped_ids[i][j]\n", + " for k in range(len(x_img_indexed)):\n", + " lensModelExtensions._lensModel.change_source_redshift(z_source=z_sources_new[i])\n", + " image = lensModelExtensions.zoom_source(x_pos=x_img_indexed[k], y_pos=y_img_indexed[k], kwargs_lens=kwargs_lens, \n", + " source_sigma=source_sizes_arcsec[i], window_size=window_size,\n", + " grid_number=grid_number)\n", + " ax = axes[k]\n", + " ax.matshow(np.log10(image), vmin=0, vmax=5, origin='lower')\n", + " ax.set_title(label_lists[i][k], color=color_list[i])\n", + " plt.show()\n", + "elif (Name_list is not None) & (num_Names > 1):\n", + " for i in range(num_sources_data):\n", + " lensModelExtensions._lensModel.change_source_redshift(z_source=z_sources_new[i])\n", + " x_img_indexed = grouped_x_imgs[i]\n", + " y_img_indexed = grouped_y_imgs[i]\n", + " f, axes = plt.subplots(1, len(x_img_indexed), figsize=(5*5, 5*len(x_img_indexed)), sharex=False, sharey=False)\n", + " for j in range(len(grouped_x_imgs[i])):\n", + " label_lists[i][j] = grouped_ids[i][j]\n", + " for k in range(len(x_img_indexed)):\n", + " lensModelExtensions._lensModel.change_source_redshift(z_source=z_sources_new[i])\n", + " image = lensModelExtensions.zoom_source(x_pos=x_img_indexed[k], y_pos=y_img_indexed[k], kwargs_lens=kwargs_lens, \n", + " source_sigma=source_sizes_arcsec[i], window_size=window_size,\n", + " grid_number=grid_number)\n", + " ax = axes[k]\n", + " ax.matshow(np.log10(image), vmin=0, vmax=5, origin='lower')\n", + " ax.set_title(label_lists[i][k], color=color_list[i])\n", + " plt.show()\n", + "else:\n", + " for i in range(num_sources_data):\n", + " x_img_indexed = grouped_x_imgs[i]\n", + " y_img_indexed = grouped_y_imgs[i]\n", + " f, axes = plt.subplots(1, len(x_img_indexed), figsize=(5*5, 5*len(x_img_indexed)), sharex=False, sharey=False)\n", + " label_list = [f\"{i+1}A\", f\"{i+1}B\", f\"{i+1}C\", f\"{i+1}D\", f\"{i+1}E\", f\"{i+1}F\", f\"{i+1}G\", f\"{i+1}H\", f\"{i+1}I\", f\"{i+1}J\", f\"{i+1}K\"]\n", + " for j in range(len(x_img_indexed)):\n", + " lensModelExtensions._lensModel.change_source_redshift(z_source=z_sources_new[i])\n", + " image = lensModelExtensions.zoom_source(x_pos=x_img_indexed[i], y_pos=y_img_indexed[i], kwargs_lens=kwargs_lens, \n", + " source_sigma=source_sizes_arcsec[j], window_size=window_size,\n", + " grid_number=grid_number)\n", + " ax = axes[i]\n", + " ax.matshow(np.log10(image), vmin=0, vmax=5, origin='lower')\n", + " ax.set_title(label_list[i], color=color_list[i])\n", + " plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Set up data for modeling\n", + "Now that we have read in all our data and completed the necessary calculations, we can explicitly set up the data in the way we want to use for modeling.\n", + "This includes set up of the uncertainty for each value, including flux ratios, time delays, and image positions.\n", + "\n", + "In this section, we explicitly set up the data products that we want to use for the modeling. You can replace this box with the values for the lens you want to model." + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "flux_ratios_list: [array([2.48143117, 6.96033332]), array([7.5821401 , 6.05038333]), array([1.08781962, 1.64915666, 1.9357879 ]), array([1.40553419, 1.72949596]), array([0.08508568, 0.05400981]), array([1.72691319, 0.79889613]), array([1.10154266, 1.00032676]), array([1.27134665]), array([1.32483809]), array([0.20272076, 0.19210771]), array([1.20630712]), array([1.88949098, 0.68965758]), array([0.8889793 , 0.85663596, 1.52030375]), array([2.07127584, 0.69912625]), array([0.94631609]), array([2.80480536, 0.25544793]), array([0.37504151, 0.24992134]), array([0.23765046, 0.1542041 ]), array([1.55948269, 0.59984678]), array([1.52860002, 0.91235299]), array([1.02694846])]\n" + ] + } + ], + "source": [ + "## Here we calculate the flux ratio between the different images from the same source. We then also add a sigma to the values to account for error\n", + "\n", + "flux_error = 0.02 # flux ratio error based on the Mahler et al. paper\n", + "flux_ratios_list = []\n", + "flux_ratio_errors_list = []\n", + "flux_ratios_measured_list = []\n", + "\n", + "for i in range(num_sources_data):\n", + " image_amps = np.abs(mag_infs[i])\n", + " flux_ratios = image_amps[1:]/image_amps[0]\n", + " flux_ratio_errors = flux_error*np.ones(len(flux_ratios))\n", + " flux_ratios_measured = flux_ratios + np.random.normal(0, flux_ratio_errors)\n", + " if measurement_realization:\n", + " flux_ratios_measured = flux_ratios + np.random.normal(0, flux_ratio_errors)\n", + " else:\n", + " flux_ratios_measured = flux_ratios\n", + " flux_ratios_list.append(flux_ratios)\n", + " flux_ratio_errors_list.append(flux_ratio_errors)\n", + " flux_ratios_measured_list.append(flux_ratios_measured)\n", + "print('flux_ratios_list: %s' %(flux_ratios_list))\n", + "\n", + "# image positions in relative RA (arc seconds)\n", + "astrometry_sigma = 0.005 # 1-sigma astrometric uncertainties of the image positions (assuming equal precision for all images in RA/DEC directions)\n", + "\n", + "## Here we loop to calculate the time delays\n", + "d_dts = []\n", + "d_dt_sigmas = []\n", + "d_dt_measured_list = []\n", + "ximg_measured_list = []\n", + "yimg_measured_list = []\n", + "\n", + "for i in range(num_sources_data):\n", + " d_dt = t_days[i][1:] - t_days[i][0] # lenstronomy definition of relative time delay is in respect of first image in the list (full covariance is in planning)\n", + " d_dt_sigma = 0.5 * np.ones(len(d_dt))\n", + " d_dts.append(d_dt)\n", + " d_dt_sigmas.append(d_dt_sigma)\n", + " \n", + " if measurement_realization:\n", + " d_dt_measured = d_dt + np.random.normal(0, d_dt_sigma)\n", + " ximg_measured = grouped_x_imgs[i] + np.random.normal(0, astrometry_sigma, len(grouped_x_imgs[i]))\n", + " yimg_measured = grouped_y_imgs[i] + np.random.normal(0, astrometry_sigma, len(grouped_y_imgs[i]))\n", + " else:\n", + " d_dt_measured = d_dt\n", + " ximg_measured = grouped_x_imgs[i]\n", + " yimg_measured = grouped_y_imgs[i]\n", + "\n", + " d_dt_measured_list.append(d_dt_measured)\n", + " ximg_measured_list.append(ximg_measured)\n", + " yimg_measured_list.append(yimg_measured)\n", + "\n", + "# here we create a keyword list with all the data elements. If you only have partial information about your lens, only provide the quantities you have.\n", + "# kwargs_time_delays_list = []\n", + "# kwargs_time_delay_uncertainties_list = []\n", + "# kwargs_flux_ratios_list = []\n", + "# kwargs_flux_ratio_errors_list = []\n", + "kwargs_ra_image_list = []\n", + "kwargs_dec_image_list = []\n", + "\n", + "\n", + "for i in range(num_sources_data):\n", + " # kwargs_time_delays_list.append(d_dt_measured_list[i])\n", + " # kwargs_time_delay_uncertainties_list.append(d_dt_sigmas[i])\n", + " # kwargs_flux_ratios_list.append(flux_ratios_measured_list[i])\n", + " # kwargs_flux_ratio_errors_list.append(flux_ratio_errors_list[i])\n", + " kwargs_ra_image_list.append(ximg_measured_list[i])\n", + " kwargs_dec_image_list.append(yimg_measured_list[i])\n", + "\n", + "kwargs_data_joint = {'ra_image_list': kwargs_ra_image_list, 'dec_image_list': kwargs_dec_image_list}\n", + " # 'time_delays_measured': kwargs_time_delays_list,\n", + " # 'time_delays_uncertainties': kwargs_time_delay_uncertainties_list,\n", + " # 'flux_ratios': kwargs_flux_ratios_list, \n", + " # 'flux_ratio_errors': kwargs_flux_ratio_errors_list,\n", + " # 'point_source_redshift_list': z_sources_new}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Model settings\n", + "Here we set up the modeling. For each lens mass and the dark matter halo, a new instance of the initial guess of the parameters, uncertainties and lower and upper bounds must be included, each added to the appropriate kwargs dictionary. These values should match what is used in the lensing profiles that were chosen.\n", + "In this example, we use the same lens model as we chose earlier to generate the plots, etc. In the pure modeling notebook, as we choose the same lens model for both, we might expect a perfect fit. However, with real data, this is less likely.\n", + "\n", + "This part is equal to the imaging simulation of lenstronomy. We refer to other notebooks and the documentation for more details: https://github.com/lenstronomy/lenstronomy-tutorials/blob/main/Notebooks/LensModeling/modelling_of_catalogue_data.ipynb." + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [], + "source": [ + "# ==================\n", + "# lens model choices\n", + "# ==================\n", + "### for Setting the galaxy lens parameters\n", + "\n", + "## settings for kwargs_constraints (Param() class)\n", + "# mass_scaling = True # if True, samples scaling parameters\n", + "# num_scale_factor = 1 # number of scaling parameters being sampled\n", + "\n", + "mass_scaling_list = [] # False or integer for each mass model, integer, model theta_E gets multiplied with the saling parameter[integer - 1]\n", + "for i in range(len(gal_data_arcsec)):\n", + " mass_scaling_list.append(1)\n", + "mass_scaling_list.append(False)\n", + "\n", + "\n", + "## we have previously defined our lens_model_list as we needed it for calculations/plotting above. If not defined above, uncomment it below.\n", + "# lens_model_list = []\n", + "# for i in range(len(gal_data_arcsec)):\n", + "# lens_model_list.append('PJAFFE_ELLIPSE_POTENTIAL')\n", + "# lens_model_list.append('NFW_ELLIPSE_CSE')\n", + "\n", + "## fixed_lens values here\n", + "fixed_lens = []\n", + "for i in range(len(gal_data_arcsec)):\n", + " fixed_lens.append({'sigma0': dPIED_sigma_0s[i], \"e1\": e1s[i], \"e2\": e2s[i], 'Ra': float(gal_data_arcsec['a'].iloc[i]), 'Rs': Rt_star_kpc, 'center_x': float(gal_data_arcsec['RA'].iloc[i]), \"center_y\": float(gal_data_arcsec['DEC'].iloc[i])})\n", + "fixed_lens.append({\"Rs\": nfw_Rs, \"alpha_Rs\": nfw_alpha_Rs, \"e1\": nfw_e1, \"e2\": nfw_e2, \"center_x\": float(input_data_frame['Value'].iloc[62][0]), \"center_y\": float(input_data_frame['Value'].iloc[63][0])})\n", + "\n", + "kwargs_lens_init = []\n", + "kwargs_lens_sigma = []\n", + "kwargs_lower_lens = []\n", + "kwargs_upper_lens = []\n", + "\n", + "# SPEMD parameters\n", + "# for i in range(len(lens_model_list)):\n", + "# fixed_lens.append({})\n", + "\n", + "# append once for each of the cluster members, then once for the dark matter halo\n", + "for i in range(len(gal_data_arcsec)):\n", + " # initial parameter guess\n", + " kwargs_lens_init.append({'sigma0': dPIED_sigma_0s[i], \"e1\": e1s[i], \"e2\": e2s[i], 'Ra': float(gal_data_arcsec['a'].iloc[i]), 'Rs': Rt_star_kpc, 'center_x': float(gal_data_arcsec['RA'].iloc[i]), \"center_y\": float(gal_data_arcsec['DEC'].iloc[i])}) # (kwargs_lens[i]) # {\"theta_E\": 0.2, \"e1\": e1s[i], \"e2\": e2s[i], \"center_x\": gal_data_arcsec['RA'].iloc[i], \"center_y\": gal_data_arcsec['DEC'].iloc[i]})\n", + " # initial particle cloud\n", + " kwargs_lens_sigma.append({'sigma0': 0.01, 'e1': 0.01, 'e2': 0.01, 'Ra': 1.0, 'Rs': 17, 'center_x': 0.1, 'center_y': 0.1})\n", + " # hard lower bound limit of parameters\n", + " kwargs_lower_lens.append({'sigma0': 0, 'e1': -0.5, 'e2': -0.5, 'Ra': 0, 'Rs': 0, 'center_x': -100, 'center_y': -100})\n", + " # hard upper bound limit of parameters\n", + " kwargs_upper_lens.append({'sigma0': 10, 'e1': 0.5, 'e2': 0.5, 'Ra': 100, 'Rs': 100, 'center_x': 100, 'center_y': 100})\n", + "\n", + "# same kwargs but for the nfw dark matter halo\n", + "kwargs_lens_init.append({\"Rs\": nfw_Rs, \"alpha_Rs\": nfw_alpha_Rs, \"e1\": nfw_e1, \"e2\": nfw_e2, \"center_x\": float(input_data_frame['Value'].iloc[62][0]), \"center_y\": float(input_data_frame['Value'].iloc[63][0])}) # (kwargs_lens[-1]) # {\"Rs\": nfw_Rs, \"alpha_Rs\": nfw_alpha_Rs, \"e1\": nfw_e1, \"e2\": nfw_e2, \"center_x\": float(input_data_frame['Value'].iloc[62][0]), \"center_y\": float(input_data_frame['Value'].iloc[63][0])})\n", + "kwargs_lens_sigma.append({\"Rs\": 0.1, \"alpha_Rs\": 0.1, \"e1\": 0.01, \"e2\": 0.01, \"center_x\": 0.1 , \"center_y\": 0.01})\n", + "kwargs_lower_lens.append({\"Rs\": 0, \"alpha_Rs\": 0, \"e1\": -0.5, \"e2\": -0.5, \"center_x\": -100, \"center_y\": -100})\n", + "kwargs_upper_lens.append({\"Rs\": 100, \"alpha_Rs\": 10, \"e1\": 0.5, \"e2\": 0.5, \"center_x\": 100, \"center_y\": 100})\n", + "\n", + "# SHEAR parameters\n", + "# we keep the center of shear definition fixed at (0,0). Want to make sure that things aren't moving, they're just being sheared?\n", + "# for i in range(len(lens_model_list)):\n", + " # fixed_lens.append({'ra_0': 0, 'dec_0': 0})\n", + " # kwargs_lens_init.append({'gamma1': 0.0, 'gamma2': 0.0})\n", + " # kwargs_lens_sigma.append({'gamma1': 0.1, 'gamma2': 0.1})\n", + " # kwargs_lower_lens.append({'gamma1': -0.3, 'gamma2': -0.3})\n", + " # kwargs_upper_lens.append({'gamma1': 0.3, 'gamma2': 0.3})\n", + "\n", + "# combine all parameter options for lenstronomy\n", + "lens_params = [kwargs_lens_init, kwargs_lens_sigma, fixed_lens, kwargs_lower_lens, kwargs_upper_lens]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we do the same for the image parameters, including an initial guess, uncertainty, and upper and lower limits for each instance. This is also where we can choose to include 'special' parameters, such as astrometric perturbations, time delay distances, or quasar soruce information if relevant.\n", + "We can choose here to fix the x and y position parameters if desired, removing one degree of freedom from our model." + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": {}, + "outputs": [], + "source": [ + "# =========================\n", + "# image position parameters\n", + "# =========================\n", + "\n", + "# we chose to model the image positions in the lensed plane (we know where they appear) and fix the image position coordinates\n", + "point_source_list = []\n", + "fixed_ps = []\n", + "kwargs_ps_init = []\n", + "kwargs_ps_sigma = []\n", + "kwargs_lower_ps = []\n", + "kwargs_upper_ps = []\n", + "\n", + "for i in range(num_sources_data):\n", + " point_source_list.append('LENSED_POSITION')\n", + " fixed_ps.append({'ra_image': ximg_measured_list[i], 'dec_image': yimg_measured_list[i]}) # we fix the image position coordinates\n", + " kwargs_ps_init.append({'ra_image': ximg_measured_list[i], 'dec_image': yimg_measured_list[i]})\n", + " kwargs_ps_sigma.append({'ra_image': 0.01 * np.ones(len(grouped_x_imgs[i])), 'dec_image': 0.01 * np.ones(len(grouped_y_imgs[i]))})\n", + " kwargs_lower_ps.append({'ra_image': -10 * np.ones(len(grouped_x_imgs[i])), 'dec_image': -10 * np.ones(len(grouped_y_imgs[i]))})\n", + " kwargs_upper_ps.append({'ra_image': 10* np.ones(len(grouped_x_imgs[i])), 'dec_image': 10 * np.ones(len(grouped_y_imgs[i]))})\n", + "\n", + "# combine all parameter options for lenstronomy\n", + "ps_params = [kwargs_ps_init, kwargs_ps_sigma, fixed_ps, kwargs_lower_ps, kwargs_upper_ps]\n", + "\n", + "fixed_special = {}\n", + "kwargs_special_init = {}\n", + "kwargs_special_sigma = {}\n", + "kwargs_lower_special = {}\n", + "kwargs_upper_special = {}\n", + "\n", + "# =========================\n", + "# astrometric perturbations\n", + "# =========================\n", + "# astrometric perturbations are modeled in lenstronomy with 'delta_x_image' and 'delta_y_image'.\n", + "# These perturbations place the 'actual' point source at the difference to 'ra_image'.\n", + "# we let some freedom in how well the actual image positions are matching those given by the data (indicated as 'ra_image', 'dec_image' and held fixed while fitting)\n", + "\n", + "#kwargs_special_init['delta_x_image'], kwargs_special_init['delta_y_image'] = np.zeros_like(ximg), np.zeros_like(yimg)\n", + "#kwargs_special_sigma['delta_x_image'], kwargs_special_sigma['delta_y_image'] = np.ones_like(ximg) * astrometry_sigma, np.ones_like(yimg) * astrometry_sigma\n", + "#kwargs_lower_special['delta_x_image'], kwargs_lower_special['delta_y_image'] = np.ones_like(ximg) * (-1), np.ones_like(yimg) * (-1)\n", + "#kwargs_upper_special['delta_x_image'], kwargs_upper_special['delta_y_image'] = np.ones_like(ximg) * (1), np.ones_like(yimg) * (1)\n", + "\n", + "# ==================\n", + "# quasar source size\n", + "# ==================\n", + "# # If you want to keep the source size fixed during the fitting, don't comment the line below (or comment the line to let it vary).\n", + "# fixed_special['source_size'] = [source_size_arcsec, source_size_arcsec2]\n", + "# kwargs_special_init['source_size'] = [source_size_arcsec, source_size_arcsec2]\n", + "# kwargs_special_sigma['source_size'] = [source_size_arcsec, source_size_arcsec2]\n", + "# or:\n", + "# kwargs_special_init['source_size'] = source_sizes_arcsec[0]\n", + "# kwargs_special_sigma['source_size'] = source_sizes_arcsec[0]\n", + "# fixed_special['source_size'] = source_sizes_arcsec[0]\n", + "\n", + "# kwargs_lower_special['source_size'] = 0.0001\n", + "# kwargs_upper_special['source_size'] = 1\n", + "\n", + "\n", + "# ===================\n", + "# Time-delay distance\n", + "# ===================\n", + "# with time-delay information, we can measure the time-delay distance (units physical Mpc)\n", + "\n", + "# if you want to fix the cosmology and instead use the time-delay information to constrain the lens model, out-comment the line below\n", + " # essentially, choose either the first line of the above block of code, or the first line of the below block of code\n", + "#fixed_special['D_dt'] = lensCosmo.D_dt\n", + "# kwargs_special_init['D_dt'] = lensCosmo.ddt\n", + "# kwargs_special_sigma['D_dt'] = 2000\n", + "# kwargs_lower_special['D_dt'] = 0\n", + "# kwargs_upper_special['D_dt'] = 10000\n", + "\n", + "# mass scaling parameter configuraiton\n", + "kwargs_special_init['scale_factor'] = [1] #### Does this get replaced with the mass scaling relationships from the calculations above?\n", + "kwargs_special_sigma['scale_factor'] = [0.2]\n", + "kwargs_lower_special['scale_factor'] = [0]\n", + "kwargs_upper_special['scale_factor'] = [10]\n", + "\n", + "special_params = [kwargs_special_init, kwargs_special_sigma, fixed_special, kwargs_lower_special, kwargs_upper_special]\n", + "\n", + "# combined parameter settings\n", + "kwargs_params = {'lens_model': lens_params,\n", + " 'point_source_model': ps_params,\n", + " 'special': special_params}\n", + "\n", + "# our model choices\n", + "kwargs_model = {'lens_model_list': lens_model_list, \n", + " 'point_source_model_list': point_source_list,\n", + " 'point_source_redshift_list': z_sources_new, # add this for changing redshifts of sources!\n", + " 'z_source_convention': z_source_convention,\n", + " 'z_lens': z_lens,\n", + " 'cosmo': cosmo}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## setup options for likelihood and parameter sampling\n", + "In $\\texttt{lenstronomy}$ the likelihood settings (which likelihood gets evaluated) and the parameter sampling options (which parameters get sampled) are separated. It is upon the user to decide the appropriate parameters to be sampled for the given choice of likelihood and information." + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": {}, + "outputs": [], + "source": [ + "# so I'd have to turn these on or off depending on what model/information I have\n", + "time_delay_likelihood = False # bool, set this True or False depending on whether time-delay information is available and you want to make use of its information content.\n", + "flux_ratio_likelihood = False # bool, modeling the flux ratios of the images\n", + "image_position_likelihood = True # bool, evaluating the image position likelihood (in combination with astrometric errors)\n", + "\n", + "kwargs_flux_compute = {'source_type': 'INF', # you can either chose 'INF' which is a infinetesimal source size, 'GAUSSIAN' or 'TORUS'\n", + " 'window_size': window_size, # window size to compute the finite source magnification (only when 'GAUSSIAN' or 'TORUS' are chosen.)\n", + " 'grid_number': grid_number} # number of grid points (per axis) to compute the extended source surface brightness within the window_size around the image position\n", + "\n", + "kwargs_constraints = {'num_point_source_list': num_images_list,\n", + " # 'Ddt_sampling': time_delay_likelihood,\n", + " 'mass_scaling_list': mass_scaling_list\n", + " } # sampling of the time-delay distance\n", + "\n", + "# ATTENTION: make sure that the numerical options are chosen to provide accurate computations for the finite source magnifications!\n", + "if kwargs_flux_compute['source_type'] in ['GAUSSIAN', 'TORUS'] and flux_ratio_likelihood is True:\n", + " kwargs_constraints['source_size'] = True # explicit sampling of finite source size parameter (only use when source_type='GAUSSIAN' or 'TORUS')\n", + "\n", + "# we can define un-correlated Gaussian priors on specific parameters explicitly\n", + "# e.g. power-law mass slope of the main deflector\n", + "# prior_lens = [[0, 'center_x', 0, 0.01], [0, 'center_y', 0, 0.01]] # [[0, 'gamma', 2, 0.1],[index_model, 'param_name', mean, 1-sigma error], [...], ...]\n", + "# e.g. source size of the emission region\n", + "# prior_lens_light = []\n", + "# prior_special = []\n", + " \n", + "kwargs_likelihood = {'image_position_uncertainty': astrometry_sigma, # astrometric uncertainty of image positions\n", + " 'image_position_likelihood': True, # evaluate point source likelihood given the measured image positions\n", + " 'time_delay_likelihood': False, # evaluating the time-delay likelihood\n", + " 'flux_ratio_likelihood': False, # enables the flux ratio likelihood \n", + " 'kwargs_flux_compute': kwargs_flux_compute, # source_type='INF' will lead to point source\n", + " # 'prior_lens': prior_lens,\n", + " # 'prior_lens_light': prior_lens_light,\n", + " # 'prior_special': prior_special,\n", + " 'check_bounds': True # check parameter bounds and punish them\n", + " }" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Multiple image position constraints\n", + "Matching multiple image position constraints from the same source is a difficult and computationally tedious task. Here we discuss a few different approaches, their pros and cons and how they are implemented in lenstronomy. You can find more on these methods in another notebook: https://github.com/lenstronomy/lenstronomy-tutorials/blob/main/Notebooks/LensModeling/modelling_of_catalogue_data.ipynb." + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": {}, + "outputs": [], + "source": [ + "# setting the non-linear solver accoring to option (3)\n", + "kwargs_constraints['solver_type'] = 'NONE' # 'PROFILE_SHEAR', 'NONE', # any proposed lens model must satisfy the image positions appearing at the position of the point sources being sampeled\n", + "\n", + "# checking for matched source position in ray-tracing the image position back to the source plane.\n", + "# This flag should be set =True when dealing with option (2) and (3)\n", + "# kwargs_likelihood['check_matched_source_position'] = True # check non-linear solver and discard non-solutions # removed by simon in a recent PR\n", + "kwargs_likelihood['source_position_tolerance'] = 15 # hard bound tolerance on r.m.s. scatter in the source plane to be met in the sampling\n", + "\n", + "# desired precision on r.m.s. scatter in the source plane to achive. \n", + "# This is implemented as a Gaussian likelihood term and is met when the model is sufficient in describing the data\n", + "# This precision must be set when using option (2). Option (3) should guarantee a very high precision except in some failures of the solver.\n", + "kwargs_likelihood['source_position_sigma'] = astrometry_sigma\n", + "\n", + "# setting to propagate the astrometric uncertainties in image position into a likelihood in the source position.\n", + "# Option (4) above. This option can be used SEPARATE to the solver or the source position tolerance (see below)\n", + "# Care has to be taken when requiring time-delay predictions.\n", + "kwargs_likelihood['source_position_likelihood'] = True # evaluates how close the different image positions match the source positons]\n", + "kwargs_likelihood['image_position_uncertainty'] = astrometry_sigma # this option (4) uses the 'image_position_uncertainty' to translate to a source position uncertainty (see also Birrer & Treu 2019)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## log_likelihood test" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Prior likelihood = 0\n", + "source position likelihood -74897143.03469963\n", + "image position likelihood 0.0\n", + "-74897143.03469963\n" + ] + } + ], + "source": [ + "from lenstronomy.Workflow.fitting_sequence import FittingSequence\n", + "fitting_seq = FittingSequence(kwargs_data_joint, kwargs_model, kwargs_constraints, kwargs_likelihood, kwargs_params)\n", + "\n", + "kwargs_truth = {\"kwargs_ps\": kwargs_ps_init, \"kwargs_lens\": kwargs_lens, \"kwargs_source\": {}, \"kwargs_special\": kwargs_special_init,\n", + " \"kwargs_lens_light\": None, \"kwargs_tracer_source\": None}\n", + "log_likelihood = fitting_seq.likelihoodModule.log_likelihood(kwargs_truth, verbose=True)\n", + "\n", + "print(log_likelihood)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Distance and Root Mean Square Error calculations of the source positions" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Distances (x): [array([ 0.24803471, 0.0446136 , -0.29264831]), array([ 0.31334984, 0.48108156, -0.79443139]), array([ 0.83948437, 2.4643706 , -1.17245752, -2.13139745]), array([ 0.51153718, 1.26773459, -1.77927177]), array([ 0.99026363, -0.32488509, -0.66537854]), array([ 0.77384476, 0.92853563, -1.70238039]), array([ 1.27791097, 0.82208091, -2.09999188]), array([-0.70693473, 0.70693473]), array([-0.45814933, 0.45814933]), array([ 1.41708193, -0.61806376, -0.79901816]), array([-0.10411472, 0.10411472]), array([ 2.24279917, -1.4364209 , -0.80637827]), array([ 0.9799139 , -3.03860353, -0.85018002, 2.90886966]), array([ 0.3918785 , 0.05983456, -0.45171306]), array([ 0.09267644, -0.09267644]), array([-0.52923623, -1.17328707, 1.7025233 ]), array([ 1.86268225, -1.45555166, -0.40713058]), array([ 1.60751302, -1.31259982, -0.2949132 ]), array([-0.18240145, 0.48291211, -0.30051066]), array([ 0.99497887, 0.31896879, -1.31394766]), array([-0.0563877, 0.0563877])]\n", + "Distances (y): [array([ 3.95554534, -1.69068587, -2.26485947]), array([ 3.28679621, -2.08398998, -1.20280623]), array([ 5.78408981, -2.71364979, -4.34180161, 1.27136159]), array([-6.90297236, 0.48344624, 6.41952612]), array([ 1.15295887, 1.00396564, -2.15692451]), array([ 2.68982088, 0.75783347, -3.44765435]), array([-0.89297809, -0.39314057, 1.28611865]), array([-5.43554447, 5.43554447]), array([-3.92911606, 3.92911606]), array([-0.00960444, 0.44878887, -0.43918444]), array([-0.51821164, 0.51821164]), array([ 1.70300637, 1.75130513, -3.4543115 ]), array([ 5.69077631, 2.51423353, -5.8911714 , -2.31383844]), array([ 4.97551049, 1.0599819 , -6.03549239]), array([-0.05136053, 0.05136053]), array([-3.48539194, -1.5956808 , 5.08107274]), array([ 0.1738166 , 1.87658578, -2.05040239]), array([ 0.2672908 , 1.87321896, -2.14050976]), array([ 5.55640798, 1.91406053, -7.47046851]), array([-0.40738092, -0.31193517, 0.7193161 ]), array([-0.81555291, 0.81555291])]\n", + "RMSE (x, y): 1.1738724000607654, 3.238176683048879\n" + ] + } + ], + "source": [ + "func_x_source, func_y_source = fitting_seq.likelihoodModule.PointSource.source_position(kwargs_ps_init, kwargs_lens)\n", + "\n", + "func_diffs_x, func_diffs_y = fitting_seq.likelihoodModule._position_likelihood.source_position_dist(kwargs_ps=kwargs_ps_init, kwargs_lens=kwargs_lens, lens_model=lensModel, z_sources=z_sources_new)\n", + "print('Distances (x): %s' %(func_diffs_x))\n", + "print('Distances (y): %s' %(func_diffs_y))\n", + "\n", + "func_rmse_x, func_rmse_y = fitting_seq.likelihoodModule._position_likelihood.source_position_rmse(kwargs_ps=kwargs_ps_init, kwargs_lens=kwargs_lens, lens_model=lensModel, z_sources=z_sources_new)\n", + "print('RMSE (x, y): %s, %s' %(func_rmse_x, func_rmse_y))" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "f, ax = plt.subplots(1, 2, figsize=(10, 5), sharex=True, sharey=True)\n", + "\n", + "x_data = []\n", + "y_data = []\n", + "\n", + "for i in range(len(func_diffs_x)):\n", + " for j in range(len(func_diffs_x[i])):\n", + " x_data.append(func_diffs_x[i][j])\n", + " y_data.append(func_diffs_y[i][j])\n", + "\n", + "values_x, bins_x, bars_x = ax[0].hist(x_data, bins=20, edgecolor='black')\n", + "values_y, bins_y, bars_y = ax[1].hist(y_data, bins=20, edgecolor='black')\n", + "\n", + "ax[0].set_ylabel('Frequency')\n", + "ax[1].set_ylabel('Frequency')\n", + "\n", + "ax[0].set_xlabel('Source position-mean residual (x) [arcsec]')\n", + "ax[1].set_xlabel('Source position-mean residual (y) [arcsec]')\n", + "\n", + "ax[0].bar_label(bars_x, fontsize=10, color='blue')\n", + "ax[1].bar_label(bars_y, fontsize=10, color='blue')\n", + "\n", + "ax[0].margins(x=0.01, y=0.1)\n", + "ax[1].margins(x=0.01, y=0.1)\n", + "\n", + "ax[0].set_title('')\n", + "ax[1].set_title('')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.hexbin(x_data, y_data, gridsize=30, cmap='Blues')\n", + "plt.xlabel('RMS scatter for source x position [arcsec]')\n", + "plt.ylabel('RMS scatter for source y position [arcsec]')\n", + "plt.title('2D Histogram')\n", + "plt.colorbar()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Run the modeling - Particle Swarm Optimization to find a maxima in the likelihood" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Computing the PSO ...\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + " 0%| | 2/800 [58:54<384:15:23, 1733.49s/it]" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "PSO: Exception while calling your likelihood function:\n", + " params: [0.7370853121420735]\n", + " args: []\n", + " kwargs: {}\n", + " exception:\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Traceback (most recent call last):\n", + " File \"c:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\Sampling\\Samplers\\pso.py\", line 472, in __call__\n", + " return self.f(x, *self.args, **self.kwargs)\n", + " ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n", + " File \"c:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\Sampling\\likelihood.py\", line 352, in logL\n", + " return self.log_likelihood(kwargs_return, verbose=verbose)\n", + " ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n", + " File \"c:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\Sampling\\likelihood.py\", line 428, in log_likelihood\n", + " logL += self._position_likelihood.logL(\n", + " ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n", + " File \"c:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\Sampling\\Likelihoods\\position_likelihood.py\", line 128, in logL\n", + " logL -= 10.0**5\n", + " ^\n", + " File \"c:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\Sampling\\Likelihoods\\position_likelihood.py\", line 278, in source_position_likelihood\n", + " if k_list is not None:\n", + " \n", + " File \"c:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\LensModel\\lens_model.py\", line 412, in hessian\n", + " def hessian(self, x, y, kwargs, k=None, diff=None, diff_method=\"square\"):\n", + " ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n", + " File \"c:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\LensModel\\single_plane.py\", line 152, in hessian\n", + " f_xx, f_xy, f_yx, f_yy = self.func_list[k].hessian(x, y, **kwargs[k])\n", + " ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n", + " File \"c:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\LensModel\\Profiles\\pseudo_jaffe_ellipse_potential.py\", line 101, in hessian\n", + " alpha_ra_dx, alpha_dec_dx = self.derivatives(\n", + " ^^^^^^^^^^^^^^^^^\n", + " File \"c:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\LensModel\\Profiles\\pseudo_jaffe_ellipse_potential.py\", line 85, in derivatives\n", + " f_x_prim, f_y_prim = self.spherical.derivatives(\n", + " ^^^^^^^^^^^^^^^^^^^^^^^^^^^\n", + " File \"c:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\LensModel\\Profiles\\pseudo_jaffe.py\", line 247, in derivatives\n", + " r = max(self._s, r)\n", + " ^^^^^^^^^^^^^^^\n", + "KeyboardInterrupt\n", + " 0%| | 2/800 [9:15:15<3692:25:52, 16657.58s/it]\n" + ] + }, + { + "ename": "KeyboardInterrupt", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)", + "Cell \u001b[1;32mIn[50], line 5\u001b[0m\n\u001b[0;32m 2\u001b[0m \u001b[38;5;66;03m# you can add additional fixed parameters in the line above if you want\u001b[39;00m\n\u001b[0;32m 4\u001b[0m start_time \u001b[38;5;241m=\u001b[39m time\u001b[38;5;241m.\u001b[39mtime()\n\u001b[1;32m----> 5\u001b[0m chain_list_pso \u001b[38;5;241m=\u001b[39m \u001b[43mfitting_seq\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mfit_sequence\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfitting_kwargs_list\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 6\u001b[0m kwargs_result \u001b[38;5;241m=\u001b[39m fitting_seq\u001b[38;5;241m.\u001b[39mbest_fit()\n\u001b[0;32m 7\u001b[0m end_time \u001b[38;5;241m=\u001b[39m time\u001b[38;5;241m.\u001b[39mtime()\n", + "File \u001b[1;32mc:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\Workflow\\fitting_sequence.py:132\u001b[0m, in \u001b[0;36mFittingSequence.fit_sequence\u001b[1;34m(self, fitting_list)\u001b[0m\n\u001b[0;32m 129\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mflux_calibration(\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[0;32m 131\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m fitting_type \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mPSO\u001b[39m\u001b[38;5;124m\"\u001b[39m:\n\u001b[1;32m--> 132\u001b[0m kwargs_result, chain, param \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mpso\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 133\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_updateManager\u001b[38;5;241m.\u001b[39mupdate_param_state(\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs_result)\n\u001b[0;32m 135\u001b[0m chain_list\u001b[38;5;241m.\u001b[39mappend([fitting_type, chain, param])\n", + "File \u001b[1;32mc:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\Workflow\\fitting_sequence.py:428\u001b[0m, in \u001b[0;36mFittingSequence.pso\u001b[1;34m(self, n_particles, n_iterations, sigma_scale, print_key, threadCount)\u001b[0m\n\u001b[0;32m 426\u001b[0m \u001b[38;5;66;03m# run PSO\u001b[39;00m\n\u001b[0;32m 427\u001b[0m sampler \u001b[38;5;241m=\u001b[39m Sampler(likelihoodModule\u001b[38;5;241m=\u001b[39m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mlikelihoodModule)\n\u001b[1;32m--> 428\u001b[0m result, chain \u001b[38;5;241m=\u001b[39m \u001b[43msampler\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mpso\u001b[49m\u001b[43m(\u001b[49m\n\u001b[0;32m 429\u001b[0m \u001b[43m \u001b[49m\u001b[43mn_particles\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m 430\u001b[0m \u001b[43m \u001b[49m\u001b[43mn_iterations\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m 431\u001b[0m \u001b[43m \u001b[49m\u001b[43mlower_start\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m 432\u001b[0m \u001b[43m \u001b[49m\u001b[43mupper_start\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m 433\u001b[0m \u001b[43m \u001b[49m\u001b[43minit_pos\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43minit_pos\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m 434\u001b[0m \u001b[43m \u001b[49m\u001b[43mthreadCount\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mthreadCount\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m 435\u001b[0m \u001b[43m \u001b[49m\u001b[43mmpi\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_mpi\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m 436\u001b[0m \u001b[43m \u001b[49m\u001b[43mprint_key\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mprint_key\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m 437\u001b[0m \u001b[43m \u001b[49m\u001b[43mverbose\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_verbose\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m 438\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 439\u001b[0m kwargs_result \u001b[38;5;241m=\u001b[39m param_class\u001b[38;5;241m.\u001b[39margs2kwargs(result, bijective\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m)\n\u001b[0;32m 440\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m kwargs_result, chain, param_list\n", + "File \u001b[1;32mc:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\Sampling\\sampler.py:120\u001b[0m, in \u001b[0;36mSampler.pso\u001b[1;34m(self, n_particles, n_iterations, lower_start, upper_start, threadCount, init_pos, mpi, print_key, verbose)\u001b[0m\n\u001b[0;32m 116\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mComputing the \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m ...\u001b[39m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m print_key)\n\u001b[0;32m 118\u001b[0m time_start \u001b[38;5;241m=\u001b[39m time\u001b[38;5;241m.\u001b[39mtime()\n\u001b[1;32m--> 120\u001b[0m result, [log_likelihood_list, pos_list, vel_list] \u001b[38;5;241m=\u001b[39m \u001b[43mpso\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43moptimize\u001b[49m\u001b[43m(\u001b[49m\n\u001b[0;32m 121\u001b[0m \u001b[43m \u001b[49m\u001b[43mn_iterations\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mverbose\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mverbose\u001b[49m\n\u001b[0;32m 122\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 124\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m pool\u001b[38;5;241m.\u001b[39mis_master():\n\u001b[0;32m 125\u001b[0m kwargs_return \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mchain\u001b[38;5;241m.\u001b[39mparam\u001b[38;5;241m.\u001b[39margs2kwargs(result)\n", + "File \u001b[1;32mc:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\Sampling\\Samplers\\pso.py:235\u001b[0m, in \u001b[0;36mParticleSwarmOptimizer.optimize\u001b[1;34m(self, max_iter, verbose, c1, c2, p, m, n, early_stop_tolerance)\u001b[0m\n\u001b[0;32m 233\u001b[0m num_iter \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0\u001b[39m\n\u001b[0;32m 234\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m tqdm(total\u001b[38;5;241m=\u001b[39mmax_iter) \u001b[38;5;28;01mas\u001b[39;00m pbar:\n\u001b[1;32m--> 235\u001b[0m \u001b[43m \u001b[49m\u001b[38;5;28;43;01mfor\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43m_\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;129;43;01min\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msample\u001b[49m\u001b[43m(\u001b[49m\n\u001b[0;32m 236\u001b[0m \u001b[43m \u001b[49m\u001b[43mmax_iter\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mc1\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mc2\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mp\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mm\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mn\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mearly_stop_tolerance\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mverbose\u001b[49m\n\u001b[0;32m 237\u001b[0m \u001b[43m 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early_stop_tolerance, verbose)\u001b[0m\n\u001b[0;32m 192\u001b[0m particle\u001b[38;5;241m.\u001b[39mvelocity \u001b[38;5;241m=\u001b[39m (part_vel \u001b[38;5;241m+\u001b[39m cog_vel \u001b[38;5;241m+\u001b[39m soc_vel)\u001b[38;5;241m.\u001b[39mtolist()\n\u001b[0;32m 193\u001b[0m particle\u001b[38;5;241m.\u001b[39mposition \u001b[38;5;241m=\u001b[39m (\n\u001b[0;32m 194\u001b[0m np\u001b[38;5;241m.\u001b[39marray(particle\u001b[38;5;241m.\u001b[39mposition) \u001b[38;5;241m+\u001b[39m np\u001b[38;5;241m.\u001b[39marray(particle\u001b[38;5;241m.\u001b[39mvelocity)\n\u001b[0;32m 195\u001b[0m )\u001b[38;5;241m.\u001b[39mtolist()\n\u001b[1;32m--> 197\u001b[0m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_get_fitness\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mswarm\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 199\u001b[0m swarm \u001b[38;5;241m=\u001b[39m []\n\u001b[0;32m 200\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m particle \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mswarm:\n", + "File \u001b[1;32mc:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\Sampling\\Samplers\\pso.py:263\u001b[0m, in \u001b[0;36mParticleSwarmOptimizer._get_fitness\u001b[1;34m(self, swarm)\u001b[0m\n\u001b[0;32m 261\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m 262\u001b[0m map_func \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpool\u001b[38;5;241m.\u001b[39mmap\n\u001b[1;32m--> 263\u001b[0m ln_probability \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mlist\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mmap_func\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mfunc\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mposition\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 265\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m i, particle \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28menumerate\u001b[39m(swarm):\n\u001b[0;32m 266\u001b[0m particle\u001b[38;5;241m.\u001b[39mfitness \u001b[38;5;241m=\u001b[39m ln_probability[i]\n", + "File \u001b[1;32mc:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\Sampling\\Samplers\\pso.py:472\u001b[0m, in \u001b[0;36m_FunctionWrapper.__call__\u001b[1;34m(self, x)\u001b[0m\n\u001b[0;32m 470\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m__call__\u001b[39m(\u001b[38;5;28mself\u001b[39m, x):\n\u001b[0;32m 471\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[1;32m--> 472\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mf\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 473\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m: \u001b[38;5;66;03m# pragma: no cover\u001b[39;00m\n\u001b[0;32m 474\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mtraceback\u001b[39;00m\n", + "File \u001b[1;32mc:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\Sampling\\likelihood.py:352\u001b[0m, in \u001b[0;36mLikelihoodModule.logL\u001b[1;34m(self, args, verbose)\u001b[0m\n\u001b[0;32m 350\u001b[0m \u001b[38;5;66;03m# extract parameters\u001b[39;00m\n\u001b[0;32m 351\u001b[0m kwargs_return \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mparam\u001b[38;5;241m.\u001b[39margs2kwargs(args)\n\u001b[1;32m--> 352\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlog_likelihood\u001b[49m\u001b[43m(\u001b[49m\u001b[43mkwargs_return\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mverbose\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mverbose\u001b[49m\u001b[43m)\u001b[49m\n", + "File \u001b[1;32mc:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\Sampling\\likelihood.py:428\u001b[0m, in \u001b[0;36mLikelihoodModule.log_likelihood\u001b[1;34m(self, kwargs_return, verbose)\u001b[0m\n\u001b[0;32m 426\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m verbose \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mTrue\u001b[39;00m:\n\u001b[0;32m 427\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mkinematic logL = \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m logL_kinematic_2d)\n\u001b[1;32m--> 428\u001b[0m logL \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_position_likelihood\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlogL\u001b[49m\u001b[43m(\u001b[49m\n\u001b[0;32m 429\u001b[0m \u001b[43m \u001b[49m\u001b[43mkwargs_lens\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkwargs_ps\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkwargs_special\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mverbose\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mverbose\u001b[49m\n\u001b[0;32m 430\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 431\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_tracer_likelihood \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mTrue\u001b[39;00m:\n\u001b[0;32m 432\u001b[0m logL_tracer \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mtracer_likelihood\u001b[38;5;241m.\u001b[39mlogL(param\u001b[38;5;241m=\u001b[39mparam, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs_return)\n", + "File \u001b[1;32mc:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\Sampling\\Likelihoods\\position_likelihood.py:128\u001b[0m, in \u001b[0;36mPositionLikelihood.logL\u001b[1;34m(self, kwargs_lens, kwargs_ps, kwargs_special, verbose)\u001b[0m\n\u001b[0;32m 120\u001b[0m \u001b[38;5;28mprint\u001b[39m(\n\u001b[0;32m 121\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mNumber of images found \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m exceeded the limited number allowed \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m 122\u001b[0m \u001b[38;5;241m%\u001b[39m (\u001b[38;5;28mlen\u001b[39m(ra_image_list[\u001b[38;5;241m0\u001b[39m]), \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_max_num_images)\n\u001b[0;32m 123\u001b[0m )\n\u001b[0;32m 124\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m (\n\u001b[0;32m 125\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_source_position_likelihood \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mTrue\u001b[39;00m\n\u001b[0;32m 126\u001b[0m \u001b[38;5;129;01mor\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_bound_source_position_tolerance \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m\n\u001b[0;32m 127\u001b[0m ):\n\u001b[1;32m--> 128\u001b[0m logL_source_pos \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msource_position_likelihood\u001b[49m\u001b[43m(\u001b[49m\n\u001b[0;32m 129\u001b[0m \u001b[43m \u001b[49m\u001b[43mkwargs_lens\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m 130\u001b[0m \u001b[43m \u001b[49m\u001b[43mkwargs_ps\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m 131\u001b[0m \u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_source_position_sigma\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m 132\u001b[0m \u001b[43m \u001b[49m\u001b[43mhard_bound_rms\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_bound_source_position_tolerance\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m 133\u001b[0m \u001b[43m \u001b[49m\u001b[43mverbose\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mverbose\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m 134\u001b[0m \u001b[43m 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277\u001b[0m )\n\u001b[1;32m--> 278\u001b[0m f_xx, f_xy, f_yx, f_yy \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_lensModel\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mhessian\u001b[49m\u001b[43m(\u001b[49m\n\u001b[0;32m 279\u001b[0m \u001b[43m \u001b[49m\u001b[43mx_image\u001b[49m\u001b[43m[\u001b[49m\u001b[43mi\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my_image\u001b[49m\u001b[43m[\u001b[49m\u001b[43mi\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkwargs_lens\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mk\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mk_lens\u001b[49m\n\u001b[0;32m 280\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 281\u001b[0m A \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39marray([[\u001b[38;5;241m1\u001b[39m \u001b[38;5;241m-\u001b[39m f_xx, \u001b[38;5;241m-\u001b[39mf_xy], [\u001b[38;5;241m-\u001b[39mf_yx, \u001b[38;5;241m1\u001b[39m \u001b[38;5;241m-\u001b[39m f_yy]])\n\u001b[0;32m 282\u001b[0m Sigma_theta \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39marray([[\u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m0\u001b[39m], [\u001b[38;5;241m0\u001b[39m, \u001b[38;5;241m1\u001b[39m]]) \u001b[38;5;241m*\u001b[39m sigma\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m2\u001b[39m\n", + "File \u001b[1;32mc:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\LensModel\\lens_model.py:412\u001b[0m, in \u001b[0;36mLensModel.hessian\u001b[1;34m(self, x, y, kwargs, k, diff, diff_method)\u001b[0m\n\u001b[0;32m 396\u001b[0m \u001b[38;5;250m\u001b[39m\u001b[38;5;124;03m\"\"\"Hessian matrix.\u001b[39;00m\n\u001b[0;32m 397\u001b[0m \n\u001b[0;32m 398\u001b[0m \u001b[38;5;124;03m:param x: x-position (preferentially arcsec)\u001b[39;00m\n\u001b[1;32m (...)\u001b[0m\n\u001b[0;32m 409\u001b[0m \u001b[38;5;124;03m:return: f_xx, f_xy, f_yx, f_yy components\u001b[39;00m\n\u001b[0;32m 410\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[0;32m 411\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m diff \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m--> 412\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlens_model\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mhessian\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mk\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mk\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 413\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m diff_method \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124msquare\u001b[39m\u001b[38;5;124m\"\u001b[39m:\n\u001b[0;32m 414\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_hessian_differential_square(x, y, kwargs, k\u001b[38;5;241m=\u001b[39mk, diff\u001b[38;5;241m=\u001b[39mdiff)\n", + "File \u001b[1;32mc:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\LensModel\\single_plane.py:152\u001b[0m, in \u001b[0;36mSinglePlane.hessian\u001b[1;34m(self, x, y, kwargs, k)\u001b[0m\n\u001b[0;32m 150\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m i, func \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28menumerate\u001b[39m(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mfunc_list):\n\u001b[0;32m 151\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m bool_list[i] \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mTrue\u001b[39;00m:\n\u001b[1;32m--> 152\u001b[0m f_xx_i, f_xy_i, f_yx_i, f_yy_i \u001b[38;5;241m=\u001b[39m \u001b[43mfunc\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mhessian\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m[\u001b[49m\u001b[43mi\u001b[49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 153\u001b[0m f_xx \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m f_xx_i\n\u001b[0;32m 154\u001b[0m f_xy \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m f_xy_i\n", + "File \u001b[1;32mc:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\LensModel\\Profiles\\pseudo_jaffe_ellipse_potential.py:101\u001b[0m, in \u001b[0;36mPseudoJaffeEllipsePotential.hessian\u001b[1;34m(self, x, y, sigma0, Ra, Rs, e1, e2, center_x, center_y)\u001b[0m\n\u001b[0;32m 97\u001b[0m alpha_ra, alpha_dec \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mderivatives(\n\u001b[0;32m 98\u001b[0m x, y, sigma0, Ra, Rs, e1, e2, center_x, center_y\n\u001b[0;32m 99\u001b[0m )\n\u001b[0;32m 100\u001b[0m diff \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_diff\n\u001b[1;32m--> 101\u001b[0m alpha_ra_dx, alpha_dec_dx \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mderivatives\u001b[49m\u001b[43m(\u001b[49m\n\u001b[0;32m 102\u001b[0m \u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m+\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mdiff\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43msigma0\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mRa\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mRs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43me1\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43me2\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcenter_x\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcenter_y\u001b[49m\n\u001b[0;32m 103\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 104\u001b[0m alpha_ra_dy, alpha_dec_dy \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mderivatives(\n\u001b[0;32m 105\u001b[0m x, y \u001b[38;5;241m+\u001b[39m diff, sigma0, Ra, Rs, e1, e2, center_x, center_y\n\u001b[0;32m 106\u001b[0m )\n\u001b[0;32m 108\u001b[0m f_xx \u001b[38;5;241m=\u001b[39m (alpha_ra_dx \u001b[38;5;241m-\u001b[39m alpha_ra) \u001b[38;5;241m/\u001b[39m diff\n", + "File \u001b[1;32mc:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\LensModel\\Profiles\\pseudo_jaffe_ellipse_potential.py:85\u001b[0m, in \u001b[0;36mPseudoJaffeEllipsePotential.derivatives\u001b[1;34m(self, x, y, sigma0, Ra, Rs, e1, e2, center_x, center_y)\u001b[0m\n\u001b[0;32m 83\u001b[0m cos_phi \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mcos(phi_G)\n\u001b[0;32m 84\u001b[0m sin_phi \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39msin(phi_G)\n\u001b[1;32m---> 85\u001b[0m f_x_prim, f_y_prim \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mspherical\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mderivatives\u001b[49m\u001b[43m(\u001b[49m\n\u001b[0;32m 86\u001b[0m \u001b[43m \u001b[49m\u001b[43mx_\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my_\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43msigma0\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mRa\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mRs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcenter_x\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mcenter_y\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m0\u001b[39;49m\n\u001b[0;32m 87\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 88\u001b[0m f_x_prim \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39msqrt(\u001b[38;5;241m1\u001b[39m \u001b[38;5;241m-\u001b[39m e)\n\u001b[0;32m 89\u001b[0m f_y_prim \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39msqrt(\u001b[38;5;241m1\u001b[39m \u001b[38;5;241m+\u001b[39m e)\n", + "File \u001b[1;32mc:\\users\\earth\\documents\\graduate school\\stony brook\\research\\lenstronomy\\lenstronomy\\LensModel\\Profiles\\pseudo_jaffe.py:247\u001b[0m, in \u001b[0;36mPseudoJaffe.derivatives\u001b[1;34m(self, x, y, sigma0, Ra, Rs, center_x, center_y)\u001b[0m\n\u001b[0;32m 245\u001b[0m r \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39msqrt(x_\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m2\u001b[39m \u001b[38;5;241m+\u001b[39m y_\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m2\u001b[39m)\n\u001b[0;32m 246\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(r, \u001b[38;5;28mint\u001b[39m) \u001b[38;5;129;01mor\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(r, \u001b[38;5;28mfloat\u001b[39m):\n\u001b[1;32m--> 247\u001b[0m r \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mmax\u001b[39;49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_s\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mr\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m 248\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m 249\u001b[0m r[r \u001b[38;5;241m<\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_s] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_s\n", + "\u001b[1;31mKeyboardInterrupt\u001b[0m: " + ] + } + ], + "source": [ + "fitting_kwargs_list = [['PSO', {'sigma_scale': 1., 'n_particles': 400, 'n_iterations': 800}]] #['update_settings', {'lens_add_fixed': [[0, ['gamma']]]}]]\n", + " # you can add additional fixed parameters in the line above if you want\n", + "\n", + "start_time = time.time()\n", + "chain_list_pso = fitting_seq.fit_sequence(fitting_kwargs_list)\n", + "kwargs_result = fitting_seq.best_fit()\n", + "end_time = time.time()\n", + "print(end_time - start_time, 'total time needed for computation')\n", + "print('============ CONGRATULATIONS, YOUR JOB WAS SUCCESSFUL ================ ')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fitting_seq.best_fit_likelihood(verbose=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "kwargs_result = fitting_seq.best_fit(bijective=True)\n", + "args_result = fitting_seq.param_class.kwargs2args(**kwargs_result)\n", + "logL = fitting_seq.likelihoodModule.logL(args_result, verbose=True)\n", + "\n", + "from lenstronomy.Plots import chain_plot\n", + "for i in range(len(chain_list_pso)):\n", + " chain_plot.plot_chain_list(chain_list_pso, i)\n", + "\n", + "print(\"kwargs_results\", kwargs_result)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## MCMC posterior sampling" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#and now we run the MCMC\n", + "fitting_kwargs_list = [\n", + " ['MCMC', {'n_burn': 400, 'n_run': 600, 'walkerRatio': 10,'sigma_scale': 0.1}]\n", + "]\n", + "chain_list_mcmc = fitting_seq.fit_sequence(fitting_kwargs_list)\n", + "\n", + "kwargs_result = fitting_seq.best_fit()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "## we want the logL (log likelihood) to stay fairly flat across the plot, that means its a decent guess.\n", + "chain_plot.plot_chain_list(chain_list_mcmc)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Post-processing the chains " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "sampler_type, samples_mcmc, param_mcmc, dist_mcmc = chain_list_mcmc[0]\n", + "\n", + "print(\"number of non-linear parameters in the MCMC process: \", len(param_mcmc))\n", + "print(\"parameters in order: \", param_mcmc)\n", + "print(\"number of evaluations in the MCMC process: \", np.shape(samples_mcmc)[0])\n", + "\n", + "# import the parameter handling class #\n", + "from lenstronomy.Sampling.parameters import Param\n", + "import lenstronomy.Util.param_util as param_util\n", + "# make instance of parameter class with given model options, constraints and fixed parameters\n", + "# this allows to recover the full parameters of all model components, not just the ones being sampled.\n", + "\n", + "param = Param(kwargs_model, fixed_lens, kwargs_fixed_ps=fixed_ps, kwargs_fixed_special=fixed_special, \n", + " kwargs_lens_init=kwargs_result['kwargs_lens'], **kwargs_constraints)\n", + "# the number of non-linear parameters and their names #\n", + "num_param, param_list = param.num_param()\n", + "\n", + "lensModel = LensModel(kwargs_model['lens_model_list'])\n", + "lensModelExtensions = LensModelExtensions(lensModel=lensModel)\n", + "print(\"parameter values: \", param)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "labels_new = [r\"$\\theta_E$\", r\"$\\gamma$\", r\"$\\phi_{lens}$\", r\"$q$\", r\"$\\phi_{ext}$\", r\"$\\gamma_{ext}$\"]\n", + "\n", + "lenstronomy_clusters_functions.clusters_functions.real_image_pos_labels(num_sources_data, grouped_x_imgs, labels_new, label_lists, image_position_likelihood=False)\n", + "lenstronomy_clusters_functions.clusters_functions.flux_ratio_labels(num_sources_data, grouped_x_imgs, labels_new, label_lists, flux_ratio_likelihood=False)\n", + "lenstronomy_clusters_functions.clusters_functions.source_size_labels(kwargs_constraints, labels_new, special_params=special_params)\n", + "lenstronomy_clusters_functions.clusters_functions.time_delay_labels(labels_new, time_delay_likelihood=True)\n", + " \n", + "print(labels_new)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# mcmc_new_list = samples2posterior_plot(samples=samples_mcmc, mcmc_list=mcmc_new_list, param_class=param, kwargs_constraints=kwargs_constraints, with_flux_ratios=True)\n", + "\n", + "new_chain = []\n", + "mcmc_new_list_cluster = []\n", + "\n", + "mcmc_new_list_cluster = lenstronomy_clusters_functions.clusters_functions.samples2posterior_plot(samples=samples_mcmc, mcmc_list=mcmc_new_list_cluster, param_class=param, kwargs_constraints=kwargs_constraints, special_params=special_params, image_position_likelihood=False, with_flux_ratios=False, time_delay_likelihood=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "np.save('mcmc_new_list_cluster', mcmc_new_list_cluster)\n", + "print(mcmc_new_list_cluster[0])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(np.shape(mcmc_new_list_cluster))\n", + "print(len(labels_new))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# import code for legend on corner plot\n", + "import matplotlib.lines as mlines\n", + "\n", + "# purple_line = mlines.Line2D([], [], color='purple', label=str(num_sources_data)+\" Sources, varied z\")\n", + "blue_line = mlines.Line2D([], [], color='blue', label='Clusters, const z')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# mcmc_new_list_cluster = np.load('mcmc_new_list_cluster.npy')\n", + "# mcmc_new_list_05 = np.load('mcmc_new_list_05.npy')\n", + "# samples5 = np.array(mcmc_new_list_05[87000:198000])\n", + "samples_cluster = np.array(mcmc_new_list_cluster[75000:150000])\n", + "\n", + "figure = corner.corner(samples_cluster, labels=labels_new, color='blue', show_titles=True) # fig=plot should put the one with reduced data and the full one on top of each other... reduced = blue, original = gray\n", + "# figure = corner.corner(samples_variedz, labels=labels_new, color='blue', show_titles=False) \n", + "# plot = corner.corner(samples_constz, fig=figure, labels=labels_new, color='purple', truth_color = 'orange', show_titles=True)\n", + " # truths=[kwargs_lens[0]['theta_E'], gamma1, phi, q, 0.1, gamma2, lensCosmo.ddt], truth_color='orange', show_titles=True)\n", + "# theta_E = 1.0\n", + "# gamma = 2.0\n", + "# phi_lens = -0.7\n", + "# q = 0.9\n", + "# phi_ext = 0.1\n", + "# gamma_ext = 0.1\n", + "# Ddt = lensCosmo.ddt\n", + "#plot = corner.corner(samples8, fig=figure, labels=labels_new, color='purple', show_titles=False, truths=[theta_, gamma, phi_lens, q, phi_ext, gamma_ext, d_dt], truth_color='orange')\n", + "\n", + "\n", + "plt.legend(handles=[blue_line], bbox_to_anchor=(-2, 4., 1., .0), loc=1)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# input truth time-delay distance [Mpc]\n", + "lensCosmo.ddt" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.10" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}