Likelihood_timing.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from isochrones.dartmouth import Dartmouth_Isochrone\n",
    "dar = Dartmouth_Isochrone()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from isochrones.utils import addmags\n",
    "import numpy as np\n",
    "M1 = 1.\n",
    "M2 = 0.7\n",
    "age = np.log10(5e9)\n",
    "feh = 0.0\n",
    "distance = 200\n",
    "AV = 0.1\n",
    "\n",
    "#Simulate true magnitudes\n",
    "unresolved_bands = ['J','H','K']\n",
    "resolved_bands = ['i']\n",
    "args = (age, feh, distance, AV)\n",
    "unresolved = {b:addmags(dar.mag[b](M1, *args), dar.mag[b](M2, *args)) for b in unresolved_bands}\n",
    "resolved_1 = {b:dar.mag['i'](M1, *args) for b in resolved_bands}\n",
    "resolved_2 = {b:dar.mag['i'](M2, *args) for b in resolved_bands}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>band</th>\n",
       "      <th>e_mag</th>\n",
       "      <th>mag</th>\n",
       "      <th>name</th>\n",
       "      <th>pa</th>\n",
       "      <th>relative</th>\n",
       "      <th>resolution</th>\n",
       "      <th>separation</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>J</td>\n",
       "      <td>0.02</td>\n",
       "      <td>9.925142</td>\n",
       "      <td>twomass</td>\n",
       "      <td>0.0</td>\n",
       "      <td>False</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>H</td>\n",
       "      <td>0.02</td>\n",
       "      <td>9.533282</td>\n",
       "      <td>twomass</td>\n",
       "      <td>0.0</td>\n",
       "      <td>False</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>K</td>\n",
       "      <td>0.02</td>\n",
       "      <td>9.475713</td>\n",
       "      <td>twomass</td>\n",
       "      <td>0.0</td>\n",
       "      <td>False</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>i</td>\n",
       "      <td>0.10</td>\n",
       "      <td>11.028637</td>\n",
       "      <td>RAO</td>\n",
       "      <td>0.0</td>\n",
       "      <td>True</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>i</td>\n",
       "      <td>0.10</td>\n",
       "      <td>13.180917</td>\n",
       "      <td>RAO</td>\n",
       "      <td>100.0</td>\n",
       "      <td>True</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   band  e_mag        mag     name     pa relative  resolution  separation\n",
       "2     J   0.02   9.925142  twomass    0.0    False         4.0         0.0\n",
       "4     H   0.02   9.533282  twomass    0.0    False         4.0         0.0\n",
       "6     K   0.02   9.475713  twomass    0.0    False         4.0         0.0\n",
       "8     i   0.10  11.028637      RAO    0.0     True         0.1         0.0\n",
       "10    i   0.10  13.180917      RAO  100.0     True         0.1         0.5"
      ]
     },
     "execution_count": 227,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "instruments = ['twomass','RAO']\n",
    "bands = {'twomass':['J','H','K'],\n",
    "          'RAO':['i']}\n",
    "mag_unc = {'twomass': 0.02, 'RAO':0.1}\n",
    "resolution = {'twomass':4.0, 'RAO':0.1}\n",
    "relative = {'twomass':False, 'RAO':True}\n",
    "separation = 0.5\n",
    "PA = 100.\n",
    "\n",
    "columns = ['name', 'band', 'resolution', 'relative', 'separation', 'pa', 'mag', 'e_mag']\n",
    "df = pd.DataFrame(columns=columns)\n",
    "i=2\n",
    "for inst in ['twomass']:  #Unresolved observations\n",
    "    for b in bands[inst]:\n",
    "        row = {}\n",
    "        row['name'] = inst\n",
    "        row['band'] = b\n",
    "        row['resolution'] = resolution[inst]\n",
    "        row['relative'] = relative[inst]\n",
    "        row['separation'] = 0.\n",
    "        row['pa'] = 0.\n",
    "        row['mag'] = unresolved[b]\n",
    "        row['e_mag'] = mag_unc[inst]\n",
    "        df = df.append(pd.DataFrame(row, index=[i]))\n",
    "        i += 2\n",
    "\n",
    "for inst in ['RAO']:  #Resolved observations\n",
    "    for b in bands[inst]:\n",
    "        mags = [resolved_1[b], resolved_2[b]]\n",
    "        pas = [0, PA]\n",
    "        seps = [0., separation]\n",
    "        for mag,sep,pa in zip(mags,seps,pas):\n",
    "            row = {}\n",
    "            row['name'] = inst\n",
    "            row['band'] = b\n",
    "            row['resolution'] = resolution[inst]\n",
    "            row['relative'] = relative[inst]\n",
    "            row['separation'] = sep\n",
    "            row['pa'] = pa\n",
    "            row['mag'] = mag\n",
    "            row['e_mag'] = mag_unc[inst]\n",
    "            df = df.append(pd.DataFrame(row, index=[i]))\n",
    "            i += 2\n",
    "            \n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from isochrones.observation import ObservationTree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First\n",
      " ╚═ twomass H=(9.53, 0.02) @(0.00, 0 [4.00])\n",
      "    ╚═ twomass J=(9.93, 0.02) @(0.00, 0 [4.00])\n",
      "       ╚═ twomass K=(9.48, 0.02) @(0.00, 0 [4.00])\n",
      "          ╠═ RAO i=(11.03, 0.10) @(0.00, 0 [0.10])\n",
      "          ║  ╚═ 0_0\n",
      "          ╚═ RAO i=(13.18, 0.10) @(0.50, 100 [0.10])\n",
      "             ╚═ 0_1\n"
     ]
    }
   ],
   "source": [
    "t = ObservationTree.from_df(df, name='First')\n",
    "t.define_models(dar)\n",
    "t.print_ascii()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from isochrones.starmodel import StarModel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mod = StarModel(dar, obs=t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 13.60 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "10000 loops, best of 3: 88.5 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit mod.lnlike(p = [1.0,1.0,10,0.0,200,0.1],use_cache=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First\n",
      " ╚═ some telescopes W1=(9.45, 0.02) @(0.00, 0 [5.00])\n",
      "    ╚═ twomass H=(9.53, 0.02) @(0.00, 0 [4.00])\n",
      "       ╚═ twomass J=(9.93, 0.02) @(0.00, 0 [4.00])\n",
      "          ╚═ twomass K=(9.48, 0.02) @(0.00, 0 [4.00])\n",
      "             ╠═ RAO i=(11.03, 0.10) @(0.00, 0 [0.10])\n",
      "             ║  ╚═ 0_0\n",
      "             ╚═ RAO i=(13.18, 0.10) @(0.50, 100 [0.10])\n",
      "                ╚═ 0_1\n"
     ]
    }
   ],
   "source": [
    "mag = addmags(dar.mag['W1'](M1, *args), dar.mag['W1'](M2, *args))\n",
    "e_mag = 0.02\n",
    "              \n",
    "row = {}\n",
    "row['name'] = 'some telescopes'\n",
    "row['band'] = 'W1'\n",
    "row['resolution'] = 5.0\n",
    "row['relative'] = False\n",
    "row['separation'] = 0.\n",
    "row['pa'] = 0.\n",
    "row['mag'] = mag\n",
    "row['e_mag'] = e_mag\n",
    "df = df.append(pd.DataFrame(row, index=[0]))\n",
    "\n",
    "t = ObservationTree.from_df(df, name='First')\n",
    "t.define_models(dar)\n",
    "t.print_ascii()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mod = StarModel(dar, obs=t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 27.38 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "10000 loops, best of 3: 101 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit mod.lnlike(p = [1.0,1.0,10,0.0,200,0.1],use_cache=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First\n",
      " ╚═ some telescopes W1=(9.45, 0.02) @(0.00, 0 [5.00])\n",
      "    ╚═ some telescopes W2=(9.49, 0.02) @(0.00, 0 [5.00])\n",
      "       ╚═ twomass H=(9.53, 0.02) @(0.00, 0 [4.00])\n",
      "          ╚═ twomass J=(9.93, 0.02) @(0.00, 0 [4.00])\n",
      "             ╚═ twomass K=(9.48, 0.02) @(0.00, 0 [4.00])\n",
      "                ╠═ RAO i=(11.03, 0.10) @(0.00, 0 [0.10])\n",
      "                ║  ╚═ 0_0\n",
      "                ╚═ RAO i=(13.18, 0.10) @(0.50, 100 [0.10])\n",
      "                   ╚═ 0_1\n"
     ]
    }
   ],
   "source": [
    "mag = addmags(dar.mag['W2'](M1, *args), dar.mag['W2'](M2, *args))\n",
    "e_mag = 0.02\n",
    "              \n",
    "row = {}\n",
    "row['name'] = 'some telescopes'\n",
    "row['band'] = 'W2'\n",
    "row['resolution'] = 5.0\n",
    "row['relative'] = False\n",
    "row['separation'] = 0.\n",
    "row['pa'] = 0.\n",
    "row['mag'] = mag\n",
    "row['e_mag'] = e_mag\n",
    "df = df.append(pd.DataFrame(row, index=[1]))\n",
    "\n",
    "t = ObservationTree.from_df(df, name='First')\n",
    "t.define_models(dar)\n",
    "t.print_ascii()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mod = StarModel(dar, obs=t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 14.68 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "10000 loops, best of 3: 113 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit mod.lnlike(p = [1.0,1.0,10,0.0,200,0.1],use_cache=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First\n",
      " ╚═ some telescopes W1=(9.45, 0.02) @(0.00, 0 [5.00])\n",
      "    ╚═ some telescopes W2=(9.49, 0.02) @(0.00, 0 [5.00])\n",
      "       ╚═ twomass H=(9.53, 0.02) @(0.00, 0 [4.00])\n",
      "          ╚═ twomass J=(9.93, 0.02) @(0.00, 0 [4.00])\n",
      "             ╚═ twomass K=(9.48, 0.02) @(0.00, 0 [4.00])\n",
      "                ╚═ some telescopes r=(11.05, 0.01) @(0.00, 0 [3.50])\n",
      "                   ╠═ RAO i=(11.03, 0.10) @(0.00, 0 [0.10])\n",
      "                   ║  ╚═ 0_0\n",
      "                   ╚═ RAO i=(13.18, 0.10) @(0.50, 100 [0.10])\n",
      "                      ╚═ 0_1\n"
     ]
    }
   ],
   "source": [
    "mag = addmags(dar.mag['r'](M1, *args), dar.mag['r'](M2, *args))\n",
    "e_mag = 0.01\n",
    "              \n",
    "row = {}\n",
    "row['name'] = 'some telescopes'\n",
    "row['band'] = 'r'\n",
    "row['resolution'] = 3.5\n",
    "row['relative'] = False\n",
    "row['separation'] = 0.\n",
    "row['pa'] = 0.\n",
    "row['mag'] = mag\n",
    "row['e_mag'] = e_mag\n",
    "df = df.append(pd.DataFrame(row, index=[3]))\n",
    "\n",
    "t = ObservationTree.from_df(df, name='First')\n",
    "t.define_models(dar)\n",
    "t.print_ascii()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mod = StarModel(dar, obs=t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 14.76 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "10000 loops, best of 3: 125 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit mod.lnlike(p = [1.0,1.0,10,0.0,200,0.1],use_cache=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First\n",
      " ╚═ some telescopes W1=(9.45, 0.02) @(0.00, 0 [5.00])\n",
      "    ╚═ some telescopes W2=(9.49, 0.02) @(0.00, 0 [5.00])\n",
      "       ╚═ twomass H=(9.53, 0.02) @(0.00, 0 [4.00])\n",
      "          ╚═ twomass J=(9.93, 0.02) @(0.00, 0 [4.00])\n",
      "             ╚═ twomass K=(9.48, 0.02) @(0.00, 0 [4.00])\n",
      "                ╚═ some telescopes r=(11.05, 0.01) @(0.00, 0 [3.50])\n",
      "                   ╠═ some instruments z=(11.00, 0.02) @(0.00, 0 [0.15])\n",
      "                   ║  ╚═ RAO i=(11.03, 0.10) @(0.00, 0 [0.10])\n",
      "                   ║     ╚═ 0_0\n",
      "                   ╚═ some instruments z=(12.98, 0.02) @(0.50, 100 [0.15])\n",
      "                      ╚═ RAO i=(13.18, 0.10) @(0.50, 100 [0.10])\n",
      "                         ╚═ 0_1\n"
     ]
    }
   ],
   "source": [
    "resolved_1 = {'z':dar.mag['z'](M1, *args)}\n",
    "resolved_2 = {'z':dar.mag['z'](M2, *args)}\n",
    "e_mag = 0.02\n",
    "              \n",
    "mags = [resolved_1['z'], resolved_2['z']]\n",
    "pas = [0, PA]\n",
    "seps = [0., separation]\n",
    "for mag,sep,pa in zip(mags,seps,pas):\n",
    "    row = {}\n",
    "    row['name'] = 'some instruments'\n",
    "    row['band'] = 'z'\n",
    "    row['resolution'] = 0.15\n",
    "    row['relative'] = True\n",
    "    row['separation'] = sep\n",
    "    row['pa'] = pa\n",
    "    row['mag'] = mag\n",
    "    row['e_mag'] = e_mag\n",
    "    df = df.append(pd.DataFrame(row, index=[7]))\n",
    "\n",
    "t = ObservationTree.from_df(df, name='First')\n",
    "t.define_models(dar)\n",
    "t.print_ascii()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mod = StarModel(dar, obs=t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 14.64 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "10000 loops, best of 3: 143 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit mod.lnlike(p = [1.0,1.0,10,0.0,200,0.1], use_cache=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First\n",
      " ╚═ some telescopes W1=(9.45, 0.02) @(0.00, 0 [5.00])\n",
      "    ╚═ some telescopes W2=(9.49, 0.02) @(0.00, 0 [5.00])\n",
      "       ╚═ twomass H=(9.53, 0.02) @(0.00, 0 [4.00])\n",
      "          ╚═ twomass J=(9.93, 0.02) @(0.00, 0 [4.00])\n",
      "             ╚═ twomass K=(9.48, 0.02) @(0.00, 0 [4.00])\n",
      "                ╚═ some telescopes r=(11.05, 0.01) @(0.00, 0 [3.50])\n",
      "                   ╠═ some instruments z=(11.00, 0.02) @(0.00, 0 [0.15])\n",
      "                   ║  ╚═ RAO i=(11.03, 0.10) @(0.00, 0 [0.10])\n",
      "                   ║     ╚═ some instruments Kepler=(11.10, 0.01) @(0.00, 0 [0.10])\n",
      "                   ║        ╚═ 0_0\n",
      "                   ╚═ some instruments z=(12.98, 0.02) @(0.50, 100 [0.15])\n",
      "                      ╚═ RAO i=(13.18, 0.10) @(0.50, 100 [0.10])\n",
      "                         ╚═ some instruments Kepler=(13.52, 0.01) @(0.55, 95 [0.10])\n",
      "                            ╚═ 0_1\n"
     ]
    }
   ],
   "source": [
    "resolved_1 = {'Kepler':dar.mag['Kepler'](M1, *args)}\n",
    "resolved_2 = {'Kepler':dar.mag['Kepler'](M2, *args)}\n",
    "e_mag = 0.01\n",
    "              \n",
    "mags = [resolved_1['Kepler'], resolved_2['Kepler']]\n",
    "pas = [0, 95]\n",
    "seps = [0., 0.55]\n",
    "for mag,sep,pa in zip(mags,seps,pas):\n",
    "    row = {}\n",
    "    row['name'] = 'some instruments'\n",
    "    row['band'] = 'Kepler'\n",
    "    row['resolution'] = 0.1\n",
    "    row['relative'] = True\n",
    "    row['separation'] = sep\n",
    "    row['pa'] = pa\n",
    "    row['mag'] = mag\n",
    "    row['e_mag'] = e_mag\n",
    "    df = df.append(pd.DataFrame(row, index=[11]))\n",
    "\n",
    "t = ObservationTree.from_df(df, name='First')\n",
    "t.define_models(dar)\n",
    "t.print_ascii()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mod = StarModel(dar, obs=t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 14.54 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "10000 loops, best of 3: 163 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit mod.lnlike(p = [1.0,1.0,10,0.0,200,0.1], use_cache=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First\n",
      " ╚═ some telescopes W1=(9.45, 0.02) @(0.00, 0 [5.00])\n",
      "    ╚═ some telescopes W2=(9.49, 0.02) @(0.00, 0 [5.00])\n",
      "       ╚═ twomass H=(9.53, 0.02) @(0.00, 0 [4.00])\n",
      "          ╚═ twomass J=(9.93, 0.02) @(0.00, 0 [4.00])\n",
      "             ╚═ twomass K=(9.48, 0.02) @(0.00, 0 [4.00])\n",
      "                ╚═ some telescopes r=(11.05, 0.01) @(0.00, 0 [3.50])\n",
      "                   ╠═ some instruments z=(11.00, 0.02) @(0.00, 0 [0.15])\n",
      "                   ║  ╚═ RAO i=(11.03, 0.10) @(0.00, 0 [0.10])\n",
      "                   ║     ╚═ some instruments Kepler=(11.10, 0.01) @(0.00, 0 [0.10])\n",
      "                   ║        ╚═ some instruments g=(11.69, 0.02) @(0.00, 0 [0.09])\n",
      "                   ║           ╚═ 0_0\n",
      "                   ╚═ some instruments z=(12.98, 0.02) @(0.50, 100 [0.15])\n",
      "                      ╚═ RAO i=(13.18, 0.10) @(0.50, 100 [0.10])\n",
      "                         ╚═ some instruments Kepler=(13.52, 0.01) @(0.55, 95 [0.10])\n",
      "                            ╚═ some instruments g=(14.77, 0.02) @(0.54, 96 [0.09])\n",
      "                               ╚═ 0_1\n"
     ]
    }
   ],
   "source": [
    "resolved_1 = {'g':dar.mag['g'](M1, *args)}\n",
    "resolved_2 = {'g':dar.mag['g'](M2, *args)}\n",
    "e_mag = 0.02\n",
    "              \n",
    "mags = [resolved_1['g'], resolved_2['g']]\n",
    "pas = [0, 96]\n",
    "seps = [0., 0.54]\n",
    "for mag,sep,pa in zip(mags,seps,pas):\n",
    "    row = {}\n",
    "    row['name'] = 'some instruments'\n",
    "    row['band'] = 'g'\n",
    "    row['resolution'] = 0.09\n",
    "    row['relative'] = True\n",
    "    row['separation'] = sep\n",
    "    row['pa'] = pa\n",
    "    row['mag'] = mag\n",
    "    row['e_mag'] = e_mag\n",
    "    df = df.append(pd.DataFrame(row, index=[13]))\n",
    "\n",
    "t = ObservationTree.from_df(df, name='First')\n",
    "t.define_models(dar)\n",
    "t.print_ascii()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mod = StarModel(dar, obs=t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 14.58 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "10000 loops, best of 3: 181 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit mod.lnlike(p = [1.0,1.0,10,0.0,200,0.1], use_cache=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = range(4,11,1)\n",
    "y = [88.5,101,113,125,143,163,181]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fa511c6df90>"
      ]
     },
     "execution_count": 259,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAEZCAYAAABrUHmEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa511fd6d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x,y)\n",
    "plt.xlabel('numbers of nodes')\n",
    "plt.ylabel(r'time($\\mu$s)')\n",
    "plt.title('time it takes to run lnlike method vs nodes')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}