orbit_plots.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "from astropy.time import Time\n",
    "from astropy import units as u, constants as cst\n",
    "\n",
    "from orbitize.results import Results\n",
    "from orbitize.sampler import MCMC\n",
    "from orbitize.lnlike import chi2_lnlike\n",
    "from orbitize.system import transform_errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# load the posteriors from the various orbit fits\n",
    "\n",
    "nograv_results = Results()\n",
    "nograv_results.load_results(\"results/with_literature_astrom/chains.hdf5\")\n",
    "\n",
    "onegrav_results = Results()\n",
    "onegrav_results.load_results(\n",
    "    \"results/with_literature_astromwith_first_vlti_point/chains.hdf5\"\n",
    ")\n",
    "\n",
    "other_onegrav_results = Results()\n",
    "other_onegrav_results.load_results(\n",
    "    \"results/with_literature_astromwith_second_vlti_point/chains.hdf5\"\n",
    ")\n",
    "\n",
    "threegrav_results = Results()\n",
    "threegrav_results.load_results(\n",
    "    \"results/with_literature_astromwith_first_vlti_pointwith_second_vlti_pointwith_third_vlti_point/chains.hdf5\"\n",
    ")\n",
    "\n",
    "onlygrav_results = Results()\n",
    "onlygrav_results.load_results(\n",
    "    \"results/with_first_vlti_pointwith_second_vlti_point/chains.hdf5\"\n",
    ")\n",
    "\n",
    "fixed_ecc_results = Results()\n",
    "fixed_ecc_results.load_results(\n",
    "    \"results/with_literature_astromwith_first_vlti_pointwith_second_vlti_pointwith_third_vlti_point_fixed_ecc/chains.hdf5\"\n",
    ")\n",
    "\n",
    "lin_ecc_results = Results()\n",
    "lin_ecc_results.load_results(\n",
    "    \"results/with_literature_astromwith_first_vlti_pointwith_second_vlti_pointwith_third_vlti_point_linear_ecc/chains.hdf5\"\n",
    ")\n",
    "\n",
    "all_results = {\n",
    "    nograv_results: [\"literature data only\", \"results/with_literature_astrom/\"],\n",
    "    onegrav_results: [\n",
    "        \"literature + GRAVITY epoch 1\",\n",
    "        \"results/with_literature_astromwith_first_vlti_point/\",\n",
    "    ],\n",
    "    other_onegrav_results: [\n",
    "        \"literature + GRAVITY epoch 2\",\n",
    "        \"results/with_literature_astromwith_second_vlti_point/\",\n",
    "    ],\n",
    "    threegrav_results: [\n",
    "        \"all data\",\n",
    "        \"results/with_literature_astromwith_first_vlti_pointwith_second_vlti_pointwith_third_vlti_point/\",\n",
    "    ],\n",
    "    onlygrav_results: [\n",
    "        \"first two GRAVITY data only\",\n",
    "        \"results/with_first_vlti_pointwith_second_vlti_point/\",\n",
    "    ],\n",
    "    fixed_ecc_results: [\n",
    "        \"all data, e fixed to 0\",\n",
    "        \"results/with_literature_astromwith_first_vlti_pointwith_second_vlti_pointwith_third_vlti_point_fixed_ecc/\",\n",
    "    ],\n",
    "    lin_ecc_results: [\n",
    "        \"all data, decreasing e prior\",\n",
    "        \"results/with_literature_astromwith_first_vlti_pointwith_second_vlti_pointwith_third_vlti_point_linear_ecc/\",\n",
    "    ],\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    epoch      object  quant1 quant1_err ... quant12_corr quant_type instrument\n",
      "-------------- ------ ------- ---------- ... ------------ ---------- ----------\n",
      "57538.42600476      1   830.4        4.9 ...          nan      seppa     SPHERE\n",
      "57565.51000561      1   830.1        3.2 ...          nan      seppa     SPHERE\n",
      "       57791.0      1   827.6        1.5 ...          nan      seppa     SPHERE\n",
      "     57793.055      1   828.8        1.5 ...          nan      seppa     SPHERE\n",
      "       57891.0      1   832.0        3.0 ...          nan      seppa       NACO\n",
      "       57892.0      1   850.0       20.0 ...          nan      seppa       NACO\n",
      "     58250.035      1   822.9        2.0 ...          nan      seppa     SPHERE\n",
      "     58250.035      1   826.4        2.4 ...          nan      seppa     SPHERE\n",
      "       58263.5      1    14.0       15.0 ...          nan         rv      defrv\n",
      "     59221.312      1 415.613   0.107484 ...    -0.095039      radec    GRAVITY\n",
      "     59602.271      1 416.269      0.035 ...       -0.224      radec    GRAVITY\n",
      "     60071.208      1  416.98      0.281 ...        0.954      radec    GRAVITY\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:root:Too few points to create valid contours\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    epoch      object  quant1 quant1_err ... quant12_corr quant_type instrument\n",
      "-------------- ------ ------- ---------- ... ------------ ---------- ----------\n",
      "57538.42600476      1   830.4        4.9 ...          nan      seppa     SPHERE\n",
      "57565.51000561      1   830.1        3.2 ...          nan      seppa     SPHERE\n",
      "       57791.0      1   827.6        1.5 ...          nan      seppa     SPHERE\n",
      "     57793.055      1   828.8        1.5 ...          nan      seppa     SPHERE\n",
      "       57891.0      1   832.0        3.0 ...          nan      seppa       NACO\n",
      "       57892.0      1   850.0       20.0 ...          nan      seppa       NACO\n",
      "     58250.035      1   822.9        2.0 ...          nan      seppa     SPHERE\n",
      "     58250.035      1   826.4        2.4 ...          nan      seppa     SPHERE\n",
      "       58263.5      1    14.0       15.0 ...          nan         rv      defrv\n",
      "     59221.312      1 415.613   0.107484 ...    -0.095039      radec    GRAVITY\n",
      "     59602.271      1 416.269      0.035 ...       -0.224      radec    GRAVITY\n",
      "     60071.208      1  416.98      0.281 ...        0.954      radec    GRAVITY\n",
      "Error in callback <function flush_figures at 0x7fac4d7b4560> (for post_execute):\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m/data/user/sblunt/miniconda3/envs/python3.7/lib/python3.7/site-packages/ipykernel/pylab/backend_inline.py\u001b[0m in \u001b[0;36mflush_figures\u001b[0;34m()\u001b[0m\n\u001b[1;32m    119\u001b[0m         \u001b[0;31m# ignore the tracking, just draw and close all figures\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    120\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 121\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    122\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mException\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    123\u001b[0m             \u001b[0;31m# safely show traceback if in IPython, else raise\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/data/user/sblunt/miniconda3/envs/python3.7/lib/python3.7/site-packages/ipykernel/pylab/backend_inline.py\u001b[0m in \u001b[0;36mshow\u001b[0;34m(close, block)\u001b[0m\n\u001b[1;32m     41\u001b[0m             display(\n\u001b[1;32m     42\u001b[0m                 \u001b[0mfigure_manager\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcanvas\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 43\u001b[0;31m                 \u001b[0mmetadata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0m_fetch_figure_metadata\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfigure_manager\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcanvas\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     44\u001b[0m             )\n\u001b[1;32m     45\u001b[0m     \u001b[0;32mfinally\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/data/user/sblunt/miniconda3/envs/python3.7/lib/python3.7/site-packages/IPython/core/display.py\u001b[0m in \u001b[0;36mdisplay\u001b[0;34m(include, exclude, metadata, transient, display_id, *objs, **kwargs)\u001b[0m\n\u001b[1;32m    311\u001b[0m             \u001b[0mpublish_display_data\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmetadata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mmetadata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    312\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 313\u001b[0;31m             \u001b[0mformat_dict\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmd_dict\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minclude\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0minclude\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexclude\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mexclude\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    314\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mformat_dict\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    315\u001b[0m                 \u001b[0;31m# nothing to display (e.g. _ipython_display_ took over)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/data/user/sblunt/miniconda3/envs/python3.7/lib/python3.7/site-packages/IPython/core/formatters.py\u001b[0m in \u001b[0;36mformat\u001b[0;34m(self, obj, include, exclude)\u001b[0m\n\u001b[1;32m    178\u001b[0m             \u001b[0mmd\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    179\u001b[0m             \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 180\u001b[0;31m                 \u001b[0mdata\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mformatter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    181\u001b[0m             \u001b[0;32mexcept\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    182\u001b[0m                 \u001b[0;31m# FIXME: log the exception\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<decorator-gen-9>\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, obj)\u001b[0m\n",
      "\u001b[0;32m/data/user/sblunt/miniconda3/envs/python3.7/lib/python3.7/site-packages/IPython/core/formatters.py\u001b[0m in \u001b[0;36mcatch_format_error\u001b[0;34m(method, self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    222\u001b[0m     \u001b[0;34m\"\"\"show traceback on failed format call\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    223\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 224\u001b[0;31m         \u001b[0mr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmethod\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    225\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    226\u001b[0m         \u001b[0;31m# don't warn on NotImplementedErrors\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/data/user/sblunt/miniconda3/envs/python3.7/lib/python3.7/site-packages/IPython/core/formatters.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, obj)\u001b[0m\n\u001b[1;32m    339\u001b[0m                 \u001b[0;32mpass\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    340\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 341\u001b[0;31m                 \u001b[0;32mreturn\u001b[0m \u001b[0mprinter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    342\u001b[0m             \u001b[0;31m# Finally look for special method names\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    343\u001b[0m             \u001b[0mmethod\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_real_method\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprint_method\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/data/user/sblunt/miniconda3/envs/python3.7/lib/python3.7/site-packages/IPython/core/pylabtools.py\u001b[0m in \u001b[0;36m<lambda>\u001b[0;34m(fig)\u001b[0m\n\u001b[1;32m    246\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    247\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0;34m'png'\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mformats\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 248\u001b[0;31m         \u001b[0mpng_formatter\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfor_type\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mFigure\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mprint_figure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfig\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'png'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    249\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0;34m'retina'\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mformats\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0;34m'png2x'\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mformats\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    250\u001b[0m         \u001b[0mpng_formatter\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfor_type\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mFigure\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mretina_figure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfig\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/data/user/sblunt/miniconda3/envs/python3.7/lib/python3.7/site-packages/IPython/core/pylabtools.py\u001b[0m in \u001b[0;36mprint_figure\u001b[0;34m(fig, fmt, bbox_inches, **kwargs)\u001b[0m\n\u001b[1;32m    130\u001b[0m         \u001b[0mFigureCanvasBase\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfig\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    131\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 132\u001b[0;31m     \u001b[0mfig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcanvas\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprint_figure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbytes_io\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkw\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    133\u001b[0m     \u001b[0mdata\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbytes_io\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgetvalue\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    134\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mfmt\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'svg'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/data/user/sblunt/miniconda3/envs/python3.7/lib/python3.7/site-packages/matplotlib/backend_bases.py\u001b[0m in \u001b[0;36mprint_figure\u001b[0;34m(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, **kwargs)\u001b[0m\n\u001b[1;32m   2080\u001b[0m                     \u001b[0morientation\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0morientation\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2081\u001b[0m                     \u001b[0mbbox_inches_restore\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0m_bbox_inches_restore\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2082\u001b[0;31m                     **kwargs)\n\u001b[0m\u001b[1;32m   2083\u001b[0m             \u001b[0;32mfinally\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2084\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mbbox_inches\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mrestore_bbox\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/data/user/sblunt/miniconda3/envs/python3.7/lib/python3.7/site-packages/matplotlib/backends/backend_agg.py\u001b[0m in \u001b[0;36mprint_png\u001b[0;34m(self, filename_or_obj, metadata, pil_kwargs, *args, **kwargs)\u001b[0m\n\u001b[1;32m    525\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    526\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 527\u001b[0;31m             \u001b[0mFigureCanvasAgg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdraw\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    528\u001b[0m             \u001b[0mrenderer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_renderer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    529\u001b[0m             \u001b[0;32mwith\u001b[0m \u001b[0mcbook\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_setattr_cm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrenderer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdpi\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdpi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m\\\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/data/user/sblunt/miniconda3/envs/python3.7/lib/python3.7/site-packages/matplotlib/backends/backend_agg.py\u001b[0m in \u001b[0;36mdraw\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    386\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrenderer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_renderer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcleared\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    387\u001b[0m         \u001b[0;32mwith\u001b[0m \u001b[0mRendererAgg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlock\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 388\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdraw\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrenderer\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    389\u001b[0m             \u001b[0;31m# A GUI class may be need to update a window using this draw, so\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    390\u001b[0m             \u001b[0;31m# don't forget to call the superclass.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/data/user/sblunt/miniconda3/envs/python3.7/lib/python3.7/site-packages/matplotlib/artist.py\u001b[0m in \u001b[0;36mdraw_wrapper\u001b[0;34m(artist, renderer, *args, **kwargs)\u001b[0m\n\u001b[1;32m     36\u001b[0m                 \u001b[0mrenderer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstart_filter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     37\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 38\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mdraw\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0martist\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrenderer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     39\u001b[0m         \u001b[0;32mfinally\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     40\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0martist\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_agg_filter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/data/user/sblunt/miniconda3/envs/python3.7/lib/python3.7/site-packages/matplotlib/figure.py\u001b[0m in \u001b[0;36mdraw\u001b[0;34m(self, renderer)\u001b[0m\n\u001b[1;32m   1707\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpatch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdraw\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrenderer\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1708\u001b[0m             mimage._draw_list_compositing_images(\n\u001b[0;32m-> 1709\u001b[0;31m                 renderer, self, artists, self.suppressComposite)\n\u001b[0m\u001b[1;32m   1710\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1711\u001b[0m             \u001b[0mrenderer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclose_group\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'figure'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/data/user/sblunt/miniconda3/envs/python3.7/lib/python3.7/site-packages/matplotlib/image.py\u001b[0m in \u001b[0;36m_draw_list_compositing_images\u001b[0;34m(renderer, parent, artists, suppress_composite)\u001b[0m\n\u001b[1;32m    133\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mnot_composite\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mhas_images\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    134\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0ma\u001b[0m \u001b[0;32min\u001b[0m \u001b[0martists\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 135\u001b[0;31m             \u001b[0ma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdraw\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrenderer\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    136\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    137\u001b[0m         \u001b[0;31m# Composite any adjacent images together\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/data/user/sblunt/miniconda3/envs/python3.7/lib/python3.7/site-packages/matplotlib/artist.py\u001b[0m in \u001b[0;36mdraw_wrapper\u001b[0;34m(artist, renderer, *args, **kwargs)\u001b[0m\n\u001b[1;32m     36\u001b[0m                 \u001b[0mrenderer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstart_filter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     37\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 38\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mdraw\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0martist\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrenderer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     39\u001b[0m         \u001b[0;32mfinally\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     40\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0martist\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_agg_filter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/data/user/sblunt/miniconda3/envs/python3.7/lib/python3.7/site-packages/matplotlib/axes/_base.py\u001b[0m in \u001b[0;36mdraw\u001b[0;34m(self, renderer, inframe)\u001b[0m\n\u001b[1;32m   2645\u001b[0m             \u001b[0mrenderer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstop_rasterizing\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2646\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2647\u001b[0;31m         \u001b[0mmimage\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_draw_list_compositing_images\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrenderer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0martists\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2648\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2649\u001b[0m         \u001b[0mrenderer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclose_group\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'axes'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/data/user/sblunt/miniconda3/envs/python3.7/lib/python3.7/site-packages/matplotlib/image.py\u001b[0m in \u001b[0;36m_draw_list_compositing_images\u001b[0;34m(renderer, parent, artists, suppress_composite)\u001b[0m\n\u001b[1;32m    133\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mnot_composite\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mhas_images\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    134\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0ma\u001b[0m \u001b[0;32min\u001b[0m \u001b[0martists\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 135\u001b[0;31m             \u001b[0ma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdraw\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrenderer\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    136\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    137\u001b[0m         \u001b[0;31m# Composite any adjacent images together\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/data/user/sblunt/miniconda3/envs/python3.7/lib/python3.7/site-packages/matplotlib/artist.py\u001b[0m in \u001b[0;36mdraw_wrapper\u001b[0;34m(artist, renderer, *args, **kwargs)\u001b[0m\n\u001b[1;32m     36\u001b[0m                 \u001b[0mrenderer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstart_filter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     37\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 38\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mdraw\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0martist\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrenderer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     39\u001b[0m         \u001b[0;32mfinally\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     40\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0martist\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_agg_filter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/data/user/sblunt/miniconda3/envs/python3.7/lib/python3.7/site-packages/matplotlib/lines.py\u001b[0m in \u001b[0;36mdraw\u001b[0;34m(self, renderer)\u001b[0m\n\u001b[1;32m    867\u001b[0m                 renderer.draw_markers(gc, marker_path, marker_trans,\n\u001b[1;32m    868\u001b[0m                                       \u001b[0msubsampled\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maffine\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfrozen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 869\u001b[0;31m                                       fc_rgba)\n\u001b[0m\u001b[1;32m    870\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    871\u001b[0m                 \u001b[0malt_marker_path\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmarker\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_alt_path\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "from fit_orbit import confidence_ellipse\n",
    "from orbitize.system import seppa2radec\n",
    "\n",
    "data = threegrav_results.data\n",
    "print(data)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 10))\n",
    "\n",
    "for i in range(len(data)):\n",
    "    datapoint = data[i]\n",
    "\n",
    "    # skip plotting the point with huge errors\n",
    "    if datapoint[\"quant1_err\"] > 10:\n",
    "        continue\n",
    "\n",
    "    if datapoint[\"quant_type\"] == \"seppa\":\n",
    "        sep, pa, sep_err, pa_err = (\n",
    "            datapoint[\"quant1\"],\n",
    "            datapoint[\"quant2\"],\n",
    "            datapoint[\"quant1_err\"],\n",
    "            datapoint[\"quant2_err\"],\n",
    "        )\n",
    "        raerr, decerr, corr = transform_errors(sep, pa, sep_err, pa_err, 0, seppa2radec)\n",
    "        facecolor = \"hotpink\"\n",
    "        alpha = 0.05 * (i + 1)\n",
    "    elif datapoint[\"quant_type\"] == \"radec\":\n",
    "        raerr, decerr, corr = (\n",
    "            datapoint[\"quant1_err\"],\n",
    "            datapoint[\"quant2_err\"],\n",
    "            datapoint[\"quant12_corr\"],\n",
    "        )\n",
    "        facecolor = \"rebeccapurple\"\n",
    "        alpha = 0.07 * (i + 1)\n",
    "    else:\n",
    "        continue\n",
    "\n",
    "    ellipse = confidence_ellipse(\n",
    "        0, 0, corr, raerr, decerr, ax, n_std=1, alpha=alpha, facecolor=facecolor\n",
    "    )\n",
    "\n",
    "plt.xlabel(\"$\\Delta$R.A. [mas]\")\n",
    "plt.ylabel(\"$\\Delta$decl. [mas]\")\n",
    "plt.xlim(5, -5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.savefig(\"results/plots/art.png\", dpi=250)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# make MCMC convergence plots\n",
    "params = {\"ecc1\": \"e\", \"pan1\": \"$\\\\Omega$\", \"aop1\": \"$\\\\omega$\"}\n",
    "for param in params.keys():\n",
    "    for res in all_results:\n",
    "        smas = res.post[:, res.system.param_idx[param]]\n",
    "\n",
    "        num_walkers = 1000\n",
    "        n_steps = len(smas) // num_walkers\n",
    "        chn = smas.reshape((num_walkers, n_steps))\n",
    "\n",
    "        walkers_to_plot = np.random.choice(num_walkers, size=100, replace=False)\n",
    "        plt.figure()\n",
    "        chop_after = 0\n",
    "        for w in walkers_to_plot:\n",
    "            plt.plot(chn[w, :][chop_after:], color=\"k\", alpha=0.005)\n",
    "        plt.xlabel(\"step number / 100\")\n",
    "        plt.ylabel(params[param])\n",
    "        plt.title(\"{}\".format(all_results[res][0]))\n",
    "        plt.savefig(\"{}{}chains.png\".format(all_results[res][1], param), dpi=250)\n",
    "        plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x792 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot all the sma, ecc, and inc posteriors\n",
    "fig, ax = plt.subplots(3, 1, figsize=(8, 11))\n",
    "\n",
    "ax[0].set_xlabel(\"a [au]\")\n",
    "ax[1].set_xlabel(\"e\")\n",
    "ax[2].set_xlabel(\"inc [deg]\")\n",
    "\n",
    "plot_dict = {\n",
    "    nograv_results: {\"ec\": None, \"fc\": \"grey\", \"alpha\": 0.5, \"histtype\": \"stepfilled\"},\n",
    "    onegrav_results: {\"ec\": \"hotpink\", \"fc\": \"white\", \"histtype\": \"step\"},\n",
    "    other_onegrav_results: {\"ec\": \"pink\", \"fc\": \"white\", \"histtype\": \"step\"},\n",
    "    threegrav_results: {\"ec\": \"purple\", \"fc\": \"white\", \"histtype\": \"step\"},\n",
    "    onlygrav_results: {\n",
    "        \"ec\": None,\n",
    "        \"fc\": \"skyblue\",\n",
    "        \"histtype\": \"stepfilled\",\n",
    "        \"alpha\": 0.5,\n",
    "    },\n",
    "}\n",
    "\n",
    "for res, lab in zip(\n",
    "    [\n",
    "        nograv_results,\n",
    "        onegrav_results,\n",
    "        other_onegrav_results,\n",
    "        threegrav_results,\n",
    "        onlygrav_results,\n",
    "    ],\n",
    "    [\n",
    "        \"lit. only\",\n",
    "        \"lit. + 1st GRAV.\",\n",
    "        \"lit. + 2nd GRAV.\",\n",
    "        \"lit. + 3 GRAV.\",\n",
    "        \"2 GRAV. only\",\n",
    "    ],\n",
    "):\n",
    "    ax[0].hist(\n",
    "        res.post[:, res.system.param_idx[\"sma1\"]],\n",
    "        bins=75,\n",
    "        range=(40, 200),\n",
    "        label=lab,\n",
    "        **plot_dict[res],\n",
    "        density=True\n",
    "    )\n",
    "    ax[1].hist(\n",
    "        res.post[:, res.system.param_idx[\"ecc1\"]],\n",
    "        bins=25,\n",
    "        **plot_dict[res],\n",
    "        density=True\n",
    "    )\n",
    "    ax[2].hist(\n",
    "        np.degrees(res.post[:, res.system.param_idx[\"inc1\"]]),\n",
    "        range=(70, 175),\n",
    "        bins=50,\n",
    "        **plot_dict[res],\n",
    "        density=True\n",
    "    )\n",
    "\n",
    "for a in ax:\n",
    "    a.set_ylabel(\"relative probability\")\n",
    "    # a.set_yticks([])\n",
    "ax[0].legend()\n",
    "plt.savefig(\"results/plots/orbit_compare.png\", dpi=250)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the planetary RV vs the measurement\n",
    "\n",
    "rv_epoch = threegrav_results.data[threegrav_results.data[\"quant_type\"] == \"rv\"][\n",
    "    \"epoch\"\n",
    "].value[0]\n",
    "\n",
    "# compute the planetary RV at the measured epoch for each posterior sample\n",
    "_, _, rv_out = threegrav_results.system.compute_all_orbits(\n",
    "    threegrav_results.post.T, epochs=np.array([rv_epoch])\n",
    ")\n",
    "\n",
    "rv_predictions = rv_out[0, 1, :]\n",
    "plt.figure()\n",
    "plt.hist(\n",
    "    rv_predictions,\n",
    "    bins=25,\n",
    "    density=True,\n",
    "    label=\"vals. from orbit fit\",\n",
    "    histtype=\"step\",\n",
    "    color=\"purple\",\n",
    ")\n",
    "\n",
    "# overplot the RV measurement and uncertainty\n",
    "rv_meas = threegrav_results.data[threegrav_results.data[\"quant_type\"] == \"rv\"][\n",
    "    \"quant1\"\n",
    "].value[0]\n",
    "rv_unc = threegrav_results.data[threegrav_results.data[\"quant_type\"] == \"rv\"][\n",
    "    \"quant1_err\"\n",
    "].value[0]\n",
    "\n",
    "rv2plot = np.linspace(-10, 40, int(1e3))\n",
    "\n",
    "\n",
    "def norm(x, mu, sig):\n",
    "    return 1 / (sig * np.sqrt(2 * np.pi)) * np.exp(-0.5 * ((x - mu) / sig) ** 2)\n",
    "\n",
    "\n",
    "plt.plot(\n",
    "    rv2plot,\n",
    "    10 * norm(rv2plot, rv_meas, rv_unc),\n",
    "    label=\"Petrus (2021) meas.\",\n",
    "    color=\"k\",\n",
    "    ls=\"--\",\n",
    ")\n",
    "# plt.yticks([])\n",
    "plt.ylabel(\"relative probability\")\n",
    "plt.xlabel(\"RV$_{{\\\\rm pl}}$ - RV$_{{*}}$ [km s$^{{-1}}$]\")\n",
    "plt.xlim(-10, 40)\n",
    "\n",
    "onesig_rvrange = np.linspace(rv_meas - rv_unc, rv_meas + rv_unc, int(1e3))\n",
    "plt.fill_between(\n",
    "    onesig_rvrange,\n",
    "    np.zeros(int(1e3)),\n",
    "    10 * norm(onesig_rvrange, rv_meas, rv_unc),\n",
    "    color=\"k\",\n",
    "    alpha=0.1,\n",
    "    ec=None,\n",
    ")\n",
    "\n",
    "plt.legend()\n",
    "plt.savefig(\"results/plots/rv_meas.png\", dpi=250)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9266284403669721\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# compare the eccentricity posteriors using different priors\n",
    "\n",
    "plt.figure()\n",
    "colors = [\"hotpink\", \"purple\"]\n",
    "histtypes = [\"stepfilled\", \"step\"]\n",
    "labels = [\"linear post.\", \"uniform post.\"]\n",
    "for i, res in enumerate([lin_ecc_results, threegrav_results]):\n",
    "    plt.hist(\n",
    "        res.post[:, res.system.param_idx[\"ecc1\"]],\n",
    "        bins=25,\n",
    "        alpha=0.6,\n",
    "        color=colors[i],\n",
    "        density=True,\n",
    "        histtype=histtypes[i],\n",
    "        label=labels[i],\n",
    "    )\n",
    "\n",
    "# overplot the prior in each case\n",
    "m = -2.18\n",
    "b = 2.01\n",
    "xplot = np.array([0, -b / m, 1])\n",
    "norm = -0.5 * b**2 / m\n",
    "print(norm)\n",
    "yplot = (m * xplot + b) / norm\n",
    "yplot[-1] = 0\n",
    "\n",
    "plt.plot(xplot, yplot, color=colors[0], ls=\"--\", label=\"linear prior\")\n",
    "plt.plot(xplot, np.ones(len(xplot)), color=colors[1], ls=\"-.\", label=\"uniform prior\")\n",
    "plt.xlim(0, 1)\n",
    "plt.legend()\n",
    "# plt.yticks([])\n",
    "plt.ylabel(\"relative probability\")\n",
    "\n",
    "plt.xlabel(\"e\")\n",
    "plt.savefig(\"results/plots/ecc_compare.png\", dpi=250)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n",
      "0.29660732319546323\n",
      "-15.514103819525001\n",
      "-15.490626142760085\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(16.5, 17.5)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the log-likelihoods for the fixed eccentricity posterior vs the accepted one\n",
    "\n",
    "\n",
    "plt.figure()\n",
    "labels = [\"Fixed e\", \"Accepted\"]\n",
    "colors = [\"hotpink\", \"purple\"]\n",
    "for i, res in enumerate([fixed_ecc_results, threegrav_results]):\n",
    "    plt.hist(\n",
    "        res.lnlike,\n",
    "        bins=50,\n",
    "        alpha=0.3,\n",
    "        density=True,\n",
    "        label=labels[i],\n",
    "        color=colors[i],\n",
    "        range=(-30, -16),\n",
    "    )\n",
    "    print(res.post[:, 1][np.argmax(res.lnlike)])\n",
    "    # plt.hist(res.lnlike[res.post[:,1] > 0.4], density=True, alpha=0.5,bins=50, range=(-30,-16))\n",
    "plt.yticks([])\n",
    "plt.legend()\n",
    "plt.xlim(-30, -16)\n",
    "plt.xlabel(\"log(L)\")\n",
    "plt.savefig(\"results/plots/ecc_lnlike_compare.png\", dpi=250)\n",
    "\n",
    "plt.figure()\n",
    "for i, res in enumerate([fixed_ecc_results, threegrav_results]):\n",
    "    ecc_post = res.post[:, 1]\n",
    "    plt.scatter(ecc_post, -1 * res.lnlike)\n",
    "    print(np.max(res.lnlike))\n",
    "plt.ylim(16.5, 17.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best lnlike for e=0.000: 15.536\n",
      "Best lnlike for e=0.042: 15.538\n",
      "Best lnlike for e=0.084: 15.558\n",
      "Best lnlike for e=0.126: 15.558\n",
      "Best lnlike for e=0.168: 15.552\n",
      "Best lnlike for e=0.211: 15.555\n",
      "Best lnlike for e=0.253: 15.537\n",
      "Best lnlike for e=0.295: 15.559\n",
      "Best lnlike for e=0.337: 15.525\n",
      "Best lnlike for e=0.379: 15.527\n",
      "Best lnlike for e=0.421: 15.517\n",
      "Best lnlike for e=0.463: 15.515\n",
      "Best lnlike for e=0.505: 15.527\n",
      "Best lnlike for e=0.547: 15.527\n",
      "Best lnlike for e=0.589: 15.533\n",
      "Best lnlike for e=0.632: 15.543\n",
      "Best lnlike for e=0.674: 15.556\n",
      "Best lnlike for e=0.716: 15.581\n",
      "Best lnlike for e=0.758: 15.578\n",
      "Best lnlike for e=0.800: 15.674\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.optimize import minimize\n",
    "\n",
    "plt.figure(figsize=(5, 5))\n",
    "for e in np.linspace(0, 0.8, 20):\n",
    "    e_sampler = MCMC(threegrav_results.system)\n",
    "\n",
    "    def neg_lnlike_func(x):\n",
    "        sma, inc, aop, pan, tau = x\n",
    "        if (\n",
    "            sma < 0\n",
    "            or inc < 0\n",
    "            or inc > np.pi\n",
    "            or pan < 0\n",
    "            or pan > np.pi\n",
    "            or tau < 0\n",
    "            or tau > 1\n",
    "        ):\n",
    "            return np.inf\n",
    "        return -1 * e_sampler._logl([sma, e, inc, aop, pan, tau, 9.28, 1.96])\n",
    "\n",
    "    p0 = [70, np.radians(110), np.radians(200), np.radians(160), 0.5]\n",
    "    res = minimize(\n",
    "        neg_lnlike_func,\n",
    "        p0,\n",
    "        method=\"Nelder-Mead\",\n",
    "        options={\"maxiter\": int(1e9), \"maxfev\": int(1e10)},\n",
    "    )\n",
    "\n",
    "    best_lnlike = res.fun\n",
    "    print(\"Best lnlike for e={:.3f}: {:.3f}\".format(e, best_lnlike))\n",
    "\n",
    "    plt.scatter([e], [-best_lnlike], color=\"rebeccapurple\")\n",
    "\n",
    "plt.xlabel(\"e\")\n",
    "plt.ylabel(\"log$\\\\mathcal{{L}}_{{\\\\mathrm{{max}}}}$\")\n",
    "# plt.ylim(-17.5, -16.9)\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"results/plots/ecc_lnlike.png\", dpi=250)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.22413729289585405 0.043884864392431666 0.0\n"
     ]
    }
   ],
   "source": [
    "# compute AIC & WAIC for each of the three various-eccentricity-prior fits\n",
    "# ref: http://www.stat.columbia.edu/~gelman/research/published/waic_understand3.pdf\n",
    "# I like the WAIC because it is v Bayesian and ya girl is v Bayesian. I'll include a pedantic rant in the paper about it.\n",
    "\n",
    "from scipy.special import logsumexp\n",
    "\n",
    "\n",
    "def calc_lnlikes(system, params):\n",
    "    model, jitter = system.compute_model(params)\n",
    "\n",
    "    # fold data/errors to match model output shape. In particualr, quant1/quant2 are interleaved\n",
    "    data = np.array([system.data_table[\"quant1\"], system.data_table[\"quant2\"]]).T\n",
    "\n",
    "    # errors below required for lnlike function below\n",
    "    errs = np.array(\n",
    "        [system.data_table[\"quant1_err\"], system.data_table[\"quant2_err\"]]\n",
    "    ).T\n",
    "\n",
    "    corrs = system.data_table[\"quant12_corr\"]\n",
    "\n",
    "    # grab all seppa indices\n",
    "    seppa_indices = system.all_seppa\n",
    "\n",
    "    # compute lnlike\n",
    "    lnlikes = chi2_lnlike(data, errs, corrs, model, jitter, seppa_indices)\n",
    "\n",
    "    return lnlikes\n",
    "\n",
    "\n",
    "def waic(results, N=100000):\n",
    "    # lots of this code stolen from pymc3 which has an excellent stats module\n",
    "\n",
    "    # compute log-pointwise predictive density for in-sample data\n",
    "    random_idx = np.random.choice(np.arange(len(results.post)), size=N)\n",
    "    lnlikes = calc_lnlikes(results.system, results.post[random_idx,].T)\n",
    "\n",
    "    # for RVs, second dimension of a data point (x1, x2) is nan\n",
    "    lnlikes_i = lnlikes[:, 0, :] + np.nan_to_num(lnlikes[:, 1, :])\n",
    "\n",
    "    # this is the log pointwise predictive density of each data point (i.e. the average likelihood of each posterior sample)\n",
    "    lppd_i = logsumexp(lnlikes_i, axis=1, b=1 / N)  # eq 5 of Gelman paper linked above\n",
    "    lppd = np.sum(lppd_i)\n",
    "    vars_lpd = np.var(lnlikes_i, axis=1)\n",
    "    # TODO: warning if vars_lpd > 0.4\n",
    "    p_waic = np.sum(vars_lpd)\n",
    "\n",
    "    # draw S samples from posterior\n",
    "    # compute log-likelihood of one data point across all models, and add together, then divide by S and add across all models\n",
    "    # second term computes variance of log-chi2 probability for each data point then adds over data points\n",
    "    # multiply by -2 to put on same scale as AIC\n",
    "\n",
    "    return -2 * (lppd - p_waic)\n",
    "\n",
    "\n",
    "# intuition: want lppd to be as large as possible (i.e. want average probability of data given model to be large), so want WAIC to be as small as possible\n",
    "e_uniform_waic = waic(threegrav_results)\n",
    "e_dec_waic = waic(lin_ecc_results)\n",
    "e_fixed_waic = waic(fixed_ecc_results)\n",
    "print(\n",
    "    e_uniform_waic - e_fixed_waic,\n",
    "    e_dec_waic - e_fixed_waic,\n",
    "    e_fixed_waic - e_fixed_waic,\n",
    ")\n",
    "\n",
    "# AIC = -2 * MLE + 2k, where k = # free params. The MLE is essentially the same for all three models (~15.5), so the deltaAIC is 6 (\"evidence is positive but not strong\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "literature data only & $92.5^{+88.7}_{-32.0}$ & $0.58^{+0.29}_{-0.38}$ & $109.5^{+20.5}_{-11.2}$ & $181.6^{+107.6}_{-128.9}$ & $171.9^{+163.9}_{-45.3}$ & $0.36^{+0.30}_{-0.17}$ & $9.30\\pm{0.03}$ & $1.96\\pm{0.04}$ \\\\\n",
      "literature + GRAVITY epoch 1 & $66.1^{+28.3}_{-12.7}$ & $0.64^{+0.26}_{-0.31}$ & $105.6^{+13.9}_{-5.0}$ & $195.6^{+74.0}_{-95.9}$ & $156.9^{+171.0}_{-8.1}$ & $0.44\\pm{0.15}$ & $9.30\\pm{0.03}$ & $1.96\\pm{0.04}$ \\\\\n",
      "literature + GRAVITY epoch 2 & $66.3^{+27.2}_{-13.0}$ & $0.63\\pm{0.27}$ & $105.4^{+14.9}_{-4.8}$ & $194.3^{+70.5}_{-101.6}$ & $156.5^{+172.2}_{-7.6}$ & $0.43\\pm{0.15}$ & $9.30\\pm{0.03}$ & $1.96\\pm{0.04}$ \\\\\n",
      "all data & $62.2^{+14.7}_{-7.2}$ & $0.55\\pm{0.19}$ & $109.2^{+6.3}_{-3.9}$ & $189.3^{+33.3}_{-32.3}$ & $155.1^{+9.0}_{-4.9}$ & $0.44\\pm{0.10}$ & $9.30\\pm{0.03}$ & $1.96\\pm{0.04}$ \\\\\n",
      "first two GRAVITY data only & $61.4^{+9.7}_{-5.1}$ & $0.55\\pm{0.14}$ & $109.6^{+4.4}_{-2.9}$ & $190.3^{+25.8}_{-19.3}$ & $155.4^{+7.2}_{-3.6}$ & $0.44\\pm{0.07}$ & $9.30\\pm{0.03}$ & $1.96\\pm{0.04}$ \\\\\n",
      "all data, ecc. fixed to 0 & $91.2\\pm{0.4}$ & =0 & $103.1\\pm{0.5}$ & -- & $153.2^{+179.9}_{-0.3}$ & -- & $9.30\\pm{0.03}$ & $1.96\\pm{0.04}$ \\\\\n",
      "all data, decreasing ecc. prior & $74.6^{+14.9}_{-10.0}$ & $0.30\\pm{0.17}$ & $105.2^{+2.5}_{-1.9}$ & $187.6^{+50.5}_{-47.2}$ & $153.8^{+5.9}_{-2.5}$ & $0.46\\pm{0.14}$ & $9.30\\pm{0.03}$ & $1.96\\pm{0.04}$ \\\\\n"
     ]
    }
   ],
   "source": [
    "# make an overleaf table of all of the fit results\n",
    "\n",
    "\n",
    "def format_post(\n",
    "    results_obj, el_label, n_decimals=1, degrees=False, dont_print_circ_toggle=False\n",
    "):\n",
    "    quants = np.quantile(\n",
    "        results_obj.post[:, results_obj.system.param_idx[el_label]], [0.16, 0.50, 0.84]\n",
    "    )\n",
    "\n",
    "    if dont_print_circ_toggle:\n",
    "        return \"--\"\n",
    "\n",
    "    if degrees:\n",
    "        quants = np.degrees(quants)\n",
    "\n",
    "    med = quants[1]\n",
    "    up_lim = quants[2] - quants[1]\n",
    "    lo_lim = quants[1] - quants[0]\n",
    "\n",
    "    if up_lim == lo_lim:\n",
    "        if el_label == \"ecc1\":\n",
    "            return \"=0\"\n",
    "\n",
    "    if np.abs(up_lim - lo_lim) <= 1 / (10 * n_decimals):\n",
    "        return \"${:.{prec}f}\\\\pm{{{:.{prec}f}}}$\".format(med, up_lim, prec=n_decimals)\n",
    "\n",
    "    return \"${:.{prec}f}^{{+{:.{prec}f}}}_{{-{:.{prec}f}}}$\".format(\n",
    "        med, up_lim, lo_lim, prec=n_decimals\n",
    "    )\n",
    "\n",
    "\n",
    "for res in all_results.keys():\n",
    "    dont_print_circ_toggle = False\n",
    "    if all_results[res][0] == \"all data, ecc. fixed to 0\":\n",
    "        dont_print_circ_toggle = True\n",
    "\n",
    "    print(\n",
    "        \"{} & {} & {} & {} & {} & {} & {} & {} & {} \\\\\\\\\".format(\n",
    "            all_results[res][0],\n",
    "            format_post(res, \"sma1\", n_decimals=1),\n",
    "            format_post(res, \"ecc1\", n_decimals=2),\n",
    "            format_post(res, \"inc1\", n_decimals=1, degrees=True),\n",
    "            format_post(\n",
    "                res,\n",
    "                \"aop1\",\n",
    "                n_decimals=1,\n",
    "                degrees=True,\n",
    "                dont_print_circ_toggle=dont_print_circ_toggle,\n",
    "            ),\n",
    "            format_post(res, \"pan1\", n_decimals=1, degrees=True),\n",
    "            format_post(\n",
    "                res, \"tau1\", n_decimals=2, dont_print_circ_toggle=dont_print_circ_toggle\n",
    "            ),\n",
    "            format_post(res, \"plx\", n_decimals=2),\n",
    "            format_post(res, \"mtot\", n_decimals=2),\n",
    "        )\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2056700173384229\n",
      "0.06993503916549973\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([0.        , 0.        , 0.        , 0.        , 0.        ,\n",
       "        0.        , 0.        , 0.        , 0.        , 0.        ,\n",
       "        0.        , 0.        , 0.        , 0.        , 0.        ,\n",
       "        0.        , 0.        , 0.        , 0.        , 0.        ,\n",
       "        0.        , 0.        , 0.        , 0.        , 0.        ,\n",
       "        0.21306818, 0.42613636, 2.34375   , 2.62784091, 3.33806818,\n",
       "        4.33238636, 4.75852273, 5.53977273, 6.10795455, 4.75852273,\n",
       "        4.75852273, 3.83522727, 2.69886364, 1.5625    , 0.99431818,\n",
       "        0.56818182, 0.21306818, 0.42613636, 0.21306818, 0.        ,\n",
       "        0.28409091, 0.        , 0.        , 0.        , 0.        ]),\n",
       " array([0.  , 0.02, 0.04, 0.06, 0.08, 0.1 , 0.12, 0.14, 0.16, 0.18, 0.2 ,\n",
       "        0.22, 0.24, 0.26, 0.28, 0.3 , 0.32, 0.34, 0.36, 0.38, 0.4 , 0.42,\n",
       "        0.44, 0.46, 0.48, 0.5 , 0.52, 0.54, 0.56, 0.58, 0.6 , 0.62, 0.64,\n",
       "        0.66, 0.68, 0.7 , 0.72, 0.74, 0.76, 0.78, 0.8 , 0.82, 0.84, 0.86,\n",
       "        0.88, 0.9 , 0.92, 0.94, 0.96, 0.98, 1.  ]),\n",
       " <a list of 50 Patch objects>)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# run the accepted orbit fit posteriors forward in time; plot deltaRA & deltaDec by eccentricity\n",
    "date = {\"year\": 2023, \"month\": 5, \"day\": 15}\n",
    "epoch = Time(date, format=\"ymdhms\")\n",
    "\n",
    "n_to_plot = 3000\n",
    "indx = np.random.choice(len(threegrav_results.post), size=n_to_plot)\n",
    "\n",
    "raoff, deoff, rv = threegrav_results.system.compute_all_orbits(\n",
    "    threegrav_results.post[indx, :].T, epochs=np.array([epoch.mjd])\n",
    ")\n",
    "raoff_pl = raoff[:, 1, :][0]\n",
    "deoff_pl = deoff[:, 1, :][0]\n",
    "rv_pl = rv[:, 1, :][0] - rv[:, 0, :][0]\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "eccentricities = threegrav_results.post[indx, :][:, 1]\n",
    "plt.scatter(raoff_pl, deoff_pl, color=cm.rainbow(eccentricities), alpha=0.75, s=2)\n",
    "\n",
    "indx = np.random.choice(len(fixed_ecc_results.post), size=n_to_plot)\n",
    "raoff, deoff, rv = fixed_ecc_results.system.compute_all_orbits(\n",
    "    fixed_ecc_results.post[indx, :].T, epochs=np.array([epoch.mjd])\n",
    ")\n",
    "raoff_pl = raoff[:, 1, :][0]\n",
    "deoff_pl = deoff[:, 1, :][0]\n",
    "rv_pl_e0 = rv[:, 1, :][0] - rv[:, 0, :][0]\n",
    "\n",
    "plt.scatter(raoff_pl, deoff_pl, color=cm.rainbow(np.zeros(n_to_plot)), alpha=0.5, s=2)\n",
    "plt.ylabel(\"$\\Delta$Dec.\")\n",
    "plt.xlabel(\"$\\Delta$R.A.\")\n",
    "ax.set_xlim((ax.get_xlim()[1], ax.get_xlim()[0]))\n",
    "ax.set_aspect(\"equal\")\n",
    "\n",
    "ax_cbar = plt.colorbar()\n",
    "ax_cbar.set_label(\"eccentricity\")\n",
    "plt.tight_layout()\n",
    "plt.savefig(\n",
    "    \"results/plots/orbit_predict{}-{}.png\".format(date[\"month\"], date[\"year\"]), dpi=250\n",
    ")\n",
    "\n",
    "plt.figure()\n",
    "plt.hist(\n",
    "    np.abs(rv_pl[eccentricities >= 0.5]),\n",
    "    bins=50,\n",
    "    color=\"rebeccapurple\",\n",
    "    alpha=0.5,\n",
    "    label=\"e $\\\\geq$ 0.5\",\n",
    "    density=True,\n",
    ")\n",
    "plt.hist(\n",
    "    np.abs(rv_pl[eccentricities < 0.5]),\n",
    "    bins=50,\n",
    "    color=\"rebeccapurple\",\n",
    "    label=\"0 < e < 0.5\",\n",
    "    density=True,\n",
    "    histtype=\"step\",\n",
    ")\n",
    "\n",
    "crires_rvprec = 0.4\n",
    "plt.hist(\n",
    "    np.abs(rv_pl_e0),\n",
    "    bins=50,\n",
    "    color=\"pink\",\n",
    "    alpha=0.5,\n",
    "    label=\"e=0\",\n",
    "    density=True,\n",
    ")\n",
    "plt.xlabel(\"|RV$_{{\\\\mathrm{{pl}}}}$ -RV$_{{\\\\mathrm{{*}}}}$|  [km/s]\")\n",
    "plt.errorbar(\n",
    "    [1],\n",
    "    [2],\n",
    "    [0],\n",
    "    [crires_rvprec],\n",
    "    fmt=\"o\",\n",
    "    color=\"rebeccapurple\",\n",
    "    label=\"CRIRES+ RV precision\",\n",
    ")\n",
    "plt.yticks([])\n",
    "plt.legend()\n",
    "plt.savefig(\n",
    "    \"results/plots/rv_predict{}-{}.png\".format(date[\"month\"], date[\"year\"]), dpi=250\n",
    ")\n",
    "\n",
    "# estimate posterior improvement given a crires+ measurement\n",
    "updated_ecc = eccentricities[(rv_pl > 2 - crires_rvprec) & (rv_pl < 2 + crires_rvprec)]\n",
    "plt.figure()\n",
    "plt.hist(\n",
    "    eccentricities,\n",
    "    alpha=0.5,\n",
    "    color=\"rebeccapurple\",\n",
    "    range=(0, 1),\n",
    "    bins=50,\n",
    "    density=True,\n",
    ")\n",
    "print(np.std(eccentricities))\n",
    "print(np.std(updated_ecc))\n",
    "plt.hist(updated_ecc, alpha=0.5, color=\"pink\", range=(0, 1), bins=50, density=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "display_name": "python3.8",
   "language": "python",
   "name": "python3"
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    "name": "ipython",
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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