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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "ORIGEN v2.2 Benchmark Study\n",
      "===========================\n",
      "This notebook attemps to benchmark the symbolic decayer to ORIGEN v2.2 results.  The basic strategy is that at $t=0$, a single kg of a pure nuclude is decayed for 0.01, 0.1, 1.0, 10, 100 times that nuclide's half life.  If the nuclide is stable then the decay calculation is run for 0.01, 0.1, 1.0, 10, 100 seconds.\n",
      "\n",
      "Throughout this benchmark I use the mean relative error as the basis for comparison. For any points $x$ and $y$:\n",
      "\n",
      "$e = \\frac{2|x - y|}{x + y} $ \n",
      "\n",
      "This may also be given in a mass-weighted form, $w$, for mass $m$.\n",
      "\n",
      "$w = m\\cdot e$\n",
      "\n",
      "The mass weighted form is useful to discrimnate against species that have a high relative error but are virtually absent in the decayed material. Let's start with some imports!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import os\n",
      "import sys\n",
      "import shutil\n",
      "import warnings\n",
      "import subprocess\n",
      "from functools import lru_cache\n",
      "\n",
      "import numpy as np\n",
      "import matplotlib\n",
      "%matplotlib inline\n",
      "import pandas as pd\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "from pyne.utils import QAWarning\n",
      "warnings.simplefilter('ignore', QAWarning)\n",
      "from pyne import nucname\n",
      "from pyne import data\n",
      "from pyne import origen22\n",
      "from pyne.material import Material, MaterialLibrary\n",
      "\n",
      "import sys\n",
      "sys.path.insert(0, '/home/scopatz/pyne/src')\n",
      "import decaygen\n",
      "\n",
      "exp2 = np.exp2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Load in the ORIGEN Materials\n",
      "-----------------------------"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "H5NAME = 'origen-benchmark-py{0}k.h5'.format(sys.version_info[0])\n",
      "mats = MaterialLibrary(H5NAME)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Load Origen Half-Lives\n",
      "-----------------------\n",
      "Testing the decayer is meaningless if the half-lives that are used do not match each other. This adds a function to compare the relative error of the pyne half life to the origen one."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t9 = origen22.parse_tape9('TAPE9.INP')\n",
      "for key in list(t9.keys()):\n",
      "    if key not in [1, 2, 3]:\n",
      "        del t9[key]\n",
      "        \n",
      "def t9_half_life(nuc):\n",
      "    nuczz = nucname.zzaaam(nuc)\n",
      "    hl = None\n",
      "    for i in [1, 2, 3]:\n",
      "        hl = t9[i]['half_life'].get(nuczz, None)\n",
      "        if hl is not None:\n",
      "            break\n",
      "    return hl\n",
      "\n",
      "@lru_cache()\n",
      "def hl_relerr(nuc):\n",
      "    \"\"\"Half-life relative error.\"\"\"\n",
      "    dhl = data.half_life(nuc) or np.inf\n",
      "    ohl = t9_half_life(nuc) or np.inf\n",
      "    if np.isinf(ohl) and np.isinf(dhl):\n",
      "        return 0.0\n",
      "    hlre = np.abs(ohl - dhl) * 2 / (ohl + dhl)\n",
      "    return np.inf if np.isnan(hlre) else hlre"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import json\n",
      "t9hls = {}\n",
      "for i in [1, 2, 3]:\n",
      "    t9hls.update({nucname.id(int(nuc)): v for nuc, v in t9[i]['half_life'].items()})\n",
      "with open('o2hls.json', 'w') as f:\n",
      "    json.dump(t9hls, f, sort_keys=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Pivot Mats Keys\n",
      "----------------\n",
      "This puts the material keys into a dict mapping nuclides to the data set names (eg 'origen_922350000_3').  This filters out any data sets that contain high relative errors in the half-lives.  It also filters out species for which Origen has weird metastable behavior that seems unphysical."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "metastable_blacklist = {\n",
      "    771940001,  # have 2+ metastables that ORIGEN lumps together, or\n",
      "    340830001,  # ...\n",
      "    350830000,  # decay to metastables without reason.\n",
      "    340830000,  # ...\n",
      "    481170000,  # ...\n",
      "    461110000,  # ...\n",
      "    441030000,  # ...\n",
      "    471110001,  # missing branch in origen\n",
      "    501130001,  # ...\n",
      "}\n",
      "nuc_keys = {}\n",
      "for key in mats.keys():\n",
      "    _, nuc, t = key.split('_')\n",
      "    nuc = int(nuc)\n",
      "    if nuc in metastable_blacklist:\n",
      "        continue\n",
      "    chains = decaygen.genchains([(nuc,)])\n",
      "    maxrelerr = max([max(list(map(hl_relerr, c))) for c in chains])\n",
      "    if maxrelerr > 0.1:\n",
      "        continue\n",
      "    t = int(t)\n",
      "    if nuc not in nuc_keys:\n",
      "        nuc_keys[nuc] = []\n",
      "    nuc_keys[nuc].append(key)\n",
      "sfunc = lambda x: int(x.rsplit('_', 1)[1])\n",
      "for keys in nuc_keys.values():\n",
      "    keys.sort(key=sfunc)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Material Relative Error\n",
      "------------------------\n",
      "Unitly functions to convert materials to pandas Series and compute the relative error of each nuclide bewteen two materials."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def mat_to_series(x):\n",
      "    xmass = x.mult_by_mass()\n",
      "    s = pd.Series(list(x.values()), list(map(int, x.keys())))\n",
      "    return s\n",
      "\n",
      "def matdiff(x, y):\n",
      "    if not isinstance(x, pd.Series):\n",
      "        x = mat_to_series(x)\n",
      "    if not isinstance(y, pd.Series):\n",
      "        y = mat_to_series(y)\n",
      "    return (x - y).abs() * (2 / (x + y))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Perform the Comparison\n",
      "-----------------------\n",
      "This constructs a new data frame that compares the origen decayed material to the pyne material decay.  The comparison stores:\n",
      "\n",
      "* the parent nuclide, nuc\n",
      "* the decay time, t\n",
      "* the maximum relative error over all nuclides, relerr\n",
      "* the nuclide with the maximum relative error, child\n",
      "* The mass of the child, childmass\n",
      "* the child's mass weighted relative error, weightederr\n",
      "\n",
      "Note that this also filters by when Origen itself has messed up by gaining or lossing too much mass (1%). Furthermore, the maximum relative error is only computed for species that have a certain threshold mass (1e-3).  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "idx = []\n",
      "err = []\n",
      "for nuc, keys in list(nuc_keys.items()):\n",
      "    fresh = mats[keys[0]]\n",
      "    for matkey in keys[1:]:\n",
      "        mat = mats[matkey]\n",
      "        if (mat.mass < 0.99) or (mat.mass > 1.1):\n",
      "            # Origen lost too much mass\n",
      "            continue\n",
      "        t = mat.metadata['decay_time']\n",
      "        dmat = fresh.decay(t)\n",
      "        oser = mat_to_series(mat)\n",
      "        dser = mat_to_series(dmat)\n",
      "        md = matdiff(oser, dser)\n",
      "        md = md.fillna(value=0.0)\n",
      "        mask = (dser > 1e-3) | (oser > 1e-3)\n",
      "        mdmasked = md.where(mask)\n",
      "        maxmd = mdmasked.max()\n",
      "        child = mdmasked.argmax()\n",
      "        if np.isnan(child):\n",
      "            continue\n",
      "        childmass = max(dser[child], oser[child])\n",
      "        weightederr = maxmd * childmass\n",
      "        idx.append(matkey)\n",
      "        err.append((nuc, t, maxmd, child, childmass, weightederr))\n",
      "df = pd.DataFrame(err, index=idx, columns=['nuc', 't', 'relerr', 'child', 'childmass', 'weightederr'])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Helper\n",
      "------\n",
      "A utility function for printing out nuclide summaries"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def nucsummary(nuc, i=None):\n",
      "    print('Nulcide:', nucname.name(nuc))\n",
      "    print(\"origen half life:\", t9_half_life(nuc))\n",
      "    print(\"data.half_life():\", data.half_life(nuc))\n",
      "    print('relerr half life:', hl_relerr(nuc))\n",
      "    print()\n",
      "    subdf = df[df['nuc'] == nuc]\n",
      "    plt.figure(figsize=(10, 6))\n",
      "    subdf.plot(x='t', y='relerr', logx=True, label=nucname.name(int(nuc)))\n",
      "    plt.legend(loc=0)\n",
      "    plt.ylabel('t [sec]')\n",
      "    plt.ylabel('Relative Error')\n",
      "    if i is not None:\n",
      "        okey = 'origen_{0}_{1}'.format(nuc, i)\n",
      "        fkey = 'fresh_{0}_0'.format(nuc)\n",
      "        omat = mats[okey]\n",
      "        fresh = mats[fkey]\n",
      "        t = omat.metadata['decay_time']\n",
      "        dmat = fresh.decay(t)\n",
      "        md = matdiff(omat, dmat)\n",
      "        print(omat)\n",
      "        print()\n",
      "        print(dmat)\n",
      "        print()\n",
      "        print(md)\n",
      "    print(subdf.to_latex())\n",
      "    return subdf"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 58
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Data!\n",
      "----------\n",
      "The data frame, sorted by relative error, childmass, and nuclide."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df.sort(['relerr', 'childmass', 'nuc'], ascending=[False, False, True])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
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        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>nuc</th>\n",
        "      <th>t</th>\n",
        "      <th>relerr</th>\n",
        "      <th>child</th>\n",
        "      <th>childmass</th>\n",
        "      <th>weightederr</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>origen_420930001_4</th>\n",
        "      <td> 420930001</td>\n",
        "      <td> 2.466000e+05</td>\n",
        "      <td> 1.994709</td>\n",
        "      <td> 410930000</td>\n",
        "      <td> 0.001168</td>\n",
        "      <td> 0.002330</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_420930001_5</th>\n",
        "      <td> 420930001</td>\n",
        "      <td> 2.466000e+06</td>\n",
        "      <td> 1.948262</td>\n",
        "      <td> 410930000</td>\n",
        "      <td> 0.001181</td>\n",
        "      <td> 0.002302</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_781930001_5</th>\n",
        "      <td> 781930001</td>\n",
        "      <td> 3.741120e+07</td>\n",
        "      <td> 1.629114</td>\n",
        "      <td> 771930000</td>\n",
        "      <td> 0.016067</td>\n",
        "      <td> 0.026175</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_781930001_4</th>\n",
        "      <td> 781930001</td>\n",
        "      <td> 3.741120e+06</td>\n",
        "      <td> 1.581632</td>\n",
        "      <td> 771930000</td>\n",
        "      <td> 0.001406</td>\n",
        "      <td> 0.002223</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_420990000_1</th>\n",
        "      <td> 420990000</td>\n",
        "      <td> 2.375136e+03</td>\n",
        "      <td> 1.557261</td>\n",
        "      <td> 430990000</td>\n",
        "      <td> 0.006907</td>\n",
        "      <td> 0.010757</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_491140000_4</th>\n",
        "      <td> 491140000</td>\n",
        "      <td> 7.190000e+02</td>\n",
        "      <td> 1.483783</td>\n",
        "      <td> 481140000</td>\n",
        "      <td> 0.033710</td>\n",
        "      <td> 0.050018</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_491140000_5</th>\n",
        "      <td> 491140000</td>\n",
        "      <td> 7.190000e+03</td>\n",
        "      <td> 1.483744</td>\n",
        "      <td> 481140000</td>\n",
        "      <td> 0.033740</td>\n",
        "      <td> 0.050062</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_491140000_3</th>\n",
        "      <td> 491140000</td>\n",
        "      <td> 7.190000e+01</td>\n",
        "      <td> 1.483744</td>\n",
        "      <td> 481140000</td>\n",
        "      <td> 0.016870</td>\n",
        "      <td> 0.025031</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_491140000_2</th>\n",
        "      <td> 491140000</td>\n",
        "      <td> 7.190000e+00</td>\n",
        "      <td> 1.483651</td>\n",
        "      <td> 481140000</td>\n",
        "      <td> 0.002259</td>\n",
        "      <td> 0.003352</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_380910000_1</th>\n",
        "      <td> 380910000</td>\n",
        "      <td> 3.474000e+02</td>\n",
        "      <td> 0.803749</td>\n",
        "      <td> 390910000</td>\n",
        "      <td> 0.006907</td>\n",
        "      <td> 0.005552</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_491140001_4</th>\n",
        "      <td> 491140001</td>\n",
        "      <td> 4.277664e+07</td>\n",
        "      <td> 0.674001</td>\n",
        "      <td> 481140000</td>\n",
        "      <td> 0.075220</td>\n",
        "      <td> 0.050698</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_491140001_5</th>\n",
        "      <td> 491140001</td>\n",
        "      <td> 4.277664e+08</td>\n",
        "      <td> 0.673959</td>\n",
        "      <td> 481140000</td>\n",
        "      <td> 0.075290</td>\n",
        "      <td> 0.050742</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_491140001_3</th>\n",
        "      <td> 491140001</td>\n",
        "      <td> 4.277664e+06</td>\n",
        "      <td> 0.673843</td>\n",
        "      <td> 481140000</td>\n",
        "      <td> 0.037640</td>\n",
        "      <td> 0.025363</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_491140001_2</th>\n",
        "      <td> 491140001</td>\n",
        "      <td> 4.277664e+05</td>\n",
        "      <td> 0.673820</td>\n",
        "      <td> 481140000</td>\n",
        "      <td> 0.005041</td>\n",
        "      <td> 0.003397</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_230540000_4</th>\n",
        "      <td> 230540000</td>\n",
        "      <td> 4.980000e+02</td>\n",
        "      <td> 0.633013</td>\n",
        "      <td> 230540000</td>\n",
        "      <td> 0.001881</td>\n",
        "      <td> 0.001191</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_360790001_4</th>\n",
        "      <td> 360790001</td>\n",
        "      <td> 5.000000e+02</td>\n",
        "      <td> 0.610648</td>\n",
        "      <td> 360790001</td>\n",
        "      <td> 0.001835</td>\n",
        "      <td> 0.001121</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_561330001_4</th>\n",
        "      <td> 561330001</td>\n",
        "      <td> 1.401480e+06</td>\n",
        "      <td> 0.587649</td>\n",
        "      <td> 551330000</td>\n",
        "      <td> 0.002970</td>\n",
        "      <td> 0.001745</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_842110000_4</th>\n",
        "      <td> 842110000</td>\n",
        "      <td> 5.160000e+00</td>\n",
        "      <td> 0.531242</td>\n",
        "      <td> 842110000</td>\n",
        "      <td> 0.001683</td>\n",
        "      <td> 0.000894</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_952420001_4</th>\n",
        "      <td> 952420001</td>\n",
        "      <td> 4.449622e+10</td>\n",
        "      <td> 0.519896</td>\n",
        "      <td> 942380000</td>\n",
        "      <td> 0.001293</td>\n",
        "      <td> 0.000672</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_80190000_4</th>\n",
        "      <td>  80190000</td>\n",
        "      <td> 2.688000e+02</td>\n",
        "      <td> 0.496765</td>\n",
        "      <td>  80190000</td>\n",
        "      <td> 0.001622</td>\n",
        "      <td> 0.000806</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_741890000_4</th>\n",
        "      <td> 741890000</td>\n",
        "      <td> 6.420000e+03</td>\n",
        "      <td> 0.472665</td>\n",
        "      <td> 741890000</td>\n",
        "      <td> 0.001581</td>\n",
        "      <td> 0.000747</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_320710001_4</th>\n",
        "      <td> 320710001</td>\n",
        "      <td> 2.041000e-01</td>\n",
        "      <td> 0.462447</td>\n",
        "      <td> 320710001</td>\n",
        "      <td> 0.001564</td>\n",
        "      <td> 0.000723</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_802050000_4</th>\n",
        "      <td> 802050000</td>\n",
        "      <td> 3.084000e+03</td>\n",
        "      <td> 0.448400</td>\n",
        "      <td> 802050000</td>\n",
        "      <td> 0.001541</td>\n",
        "      <td> 0.000691</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_461110001_1</th>\n",
        "      <td> 461110001</td>\n",
        "      <td> 1.980000e+02</td>\n",
        "      <td> 0.402345</td>\n",
        "      <td> 471110000</td>\n",
        "      <td> 0.002104</td>\n",
        "      <td> 0.000846</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_40100000_4</th>\n",
        "      <td>  40100000</td>\n",
        "      <td> 4.765198e+14</td>\n",
        "      <td> 0.387555</td>\n",
        "      <td>  40100000</td>\n",
        "      <td> 0.001446</td>\n",
        "      <td> 0.000560</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_781910000_4</th>\n",
        "      <td> 781910000</td>\n",
        "      <td> 2.445120e+06</td>\n",
        "      <td> 0.387555</td>\n",
        "      <td> 781910000</td>\n",
        "      <td> 0.001446</td>\n",
        "      <td> 0.000560</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_561310000_4</th>\n",
        "      <td> 561310000</td>\n",
        "      <td> 9.936000e+06</td>\n",
        "      <td> 0.346184</td>\n",
        "      <td> 551310000</td>\n",
        "      <td> 0.005383</td>\n",
        "      <td> 0.001864</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_280590000_4</th>\n",
        "      <td> 280590000</td>\n",
        "      <td> 2.398378e+13</td>\n",
        "      <td> 0.344502</td>\n",
        "      <td> 280590000</td>\n",
        "      <td> 0.001383</td>\n",
        "      <td> 0.000476</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_461090001_3</th>\n",
        "      <td> 461090001</td>\n",
        "      <td> 2.817600e+02</td>\n",
        "      <td> 0.341814</td>\n",
        "      <td> 471090000</td>\n",
        "      <td> 0.001102</td>\n",
        "      <td> 0.000377</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_812040000_2</th>\n",
        "      <td> 812040000</td>\n",
        "      <td> 1.193824e+07</td>\n",
        "      <td> 0.331065</td>\n",
        "      <td> 802040000</td>\n",
        "      <td> 0.001955</td>\n",
        "      <td> 0.000647</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>...</th>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_802040000_2</th>\n",
        "      <td> 802040000</td>\n",
        "      <td> 1.000000e-01</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 802040000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_802040000_3</th>\n",
        "      <td> 802040000</td>\n",
        "      <td> 1.000000e+00</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 802040000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_802040000_4</th>\n",
        "      <td> 802040000</td>\n",
        "      <td> 1.000000e+01</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 802040000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_802040000_5</th>\n",
        "      <td> 802040000</td>\n",
        "      <td> 1.000000e+02</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 802040000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_812030000_1</th>\n",
        "      <td> 812030000</td>\n",
        "      <td> 1.000000e-02</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 812030000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_812030000_2</th>\n",
        "      <td> 812030000</td>\n",
        "      <td> 1.000000e-01</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 812030000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_812030000_3</th>\n",
        "      <td> 812030000</td>\n",
        "      <td> 1.000000e+00</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 812030000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_812030000_4</th>\n",
        "      <td> 812030000</td>\n",
        "      <td> 1.000000e+01</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 812030000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_812030000_5</th>\n",
        "      <td> 812030000</td>\n",
        "      <td> 1.000000e+02</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 812030000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_812050000_1</th>\n",
        "      <td> 812050000</td>\n",
        "      <td> 1.000000e-02</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 812050000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_812050000_2</th>\n",
        "      <td> 812050000</td>\n",
        "      <td> 1.000000e-01</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 812050000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_812050000_3</th>\n",
        "      <td> 812050000</td>\n",
        "      <td> 1.000000e+00</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 812050000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_812050000_4</th>\n",
        "      <td> 812050000</td>\n",
        "      <td> 1.000000e+01</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 812050000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_812050000_5</th>\n",
        "      <td> 812050000</td>\n",
        "      <td> 1.000000e+02</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 812050000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_822060000_1</th>\n",
        "      <td> 822060000</td>\n",
        "      <td> 1.000000e-02</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 822060000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_822060000_2</th>\n",
        "      <td> 822060000</td>\n",
        "      <td> 1.000000e-01</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 822060000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_822060000_3</th>\n",
        "      <td> 822060000</td>\n",
        "      <td> 1.000000e+00</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 822060000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_822060000_4</th>\n",
        "      <td> 822060000</td>\n",
        "      <td> 1.000000e+01</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 822060000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_822060000_5</th>\n",
        "      <td> 822060000</td>\n",
        "      <td> 1.000000e+02</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 822060000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_822070000_1</th>\n",
        "      <td> 822070000</td>\n",
        "      <td> 1.000000e-02</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 822070000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_822070000_2</th>\n",
        "      <td> 822070000</td>\n",
        "      <td> 1.000000e-01</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 822070000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_822070000_3</th>\n",
        "      <td> 822070000</td>\n",
        "      <td> 1.000000e+00</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 822070000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_822070000_4</th>\n",
        "      <td> 822070000</td>\n",
        "      <td> 1.000000e+01</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 822070000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_822070000_5</th>\n",
        "      <td> 822070000</td>\n",
        "      <td> 1.000000e+02</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 822070000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_822080000_1</th>\n",
        "      <td> 822080000</td>\n",
        "      <td> 1.000000e-02</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 822080000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_822080000_2</th>\n",
        "      <td> 822080000</td>\n",
        "      <td> 1.000000e-01</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 822080000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_822080000_3</th>\n",
        "      <td> 822080000</td>\n",
        "      <td> 1.000000e+00</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 822080000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_822080000_4</th>\n",
        "      <td> 822080000</td>\n",
        "      <td> 1.000000e+01</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 822080000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_822080000_5</th>\n",
        "      <td> 822080000</td>\n",
        "      <td> 1.000000e+02</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 822080000</td>\n",
        "      <td> 1.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_721780001_3</th>\n",
        "      <td> 721780001</td>\n",
        "      <td> 4.000000e+00</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 721780001</td>\n",
        "      <td> 0.500000</td>\n",
        "      <td> 0.000000</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>2802 rows \u00d7 6 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "                          nuc             t    relerr      child  childmass  \\\n",
        "origen_420930001_4  420930001  2.466000e+05  1.994709  410930000   0.001168   \n",
        "origen_420930001_5  420930001  2.466000e+06  1.948262  410930000   0.001181   \n",
        "origen_781930001_5  781930001  3.741120e+07  1.629114  771930000   0.016067   \n",
        "origen_781930001_4  781930001  3.741120e+06  1.581632  771930000   0.001406   \n",
        "origen_420990000_1  420990000  2.375136e+03  1.557261  430990000   0.006907   \n",
        "origen_491140000_4  491140000  7.190000e+02  1.483783  481140000   0.033710   \n",
        "origen_491140000_5  491140000  7.190000e+03  1.483744  481140000   0.033740   \n",
        "origen_491140000_3  491140000  7.190000e+01  1.483744  481140000   0.016870   \n",
        "origen_491140000_2  491140000  7.190000e+00  1.483651  481140000   0.002259   \n",
        "origen_380910000_1  380910000  3.474000e+02  0.803749  390910000   0.006907   \n",
        "origen_491140001_4  491140001  4.277664e+07  0.674001  481140000   0.075220   \n",
        "origen_491140001_5  491140001  4.277664e+08  0.673959  481140000   0.075290   \n",
        "origen_491140001_3  491140001  4.277664e+06  0.673843  481140000   0.037640   \n",
        "origen_491140001_2  491140001  4.277664e+05  0.673820  481140000   0.005041   \n",
        "origen_230540000_4  230540000  4.980000e+02  0.633013  230540000   0.001881   \n",
        "origen_360790001_4  360790001  5.000000e+02  0.610648  360790001   0.001835   \n",
        "origen_561330001_4  561330001  1.401480e+06  0.587649  551330000   0.002970   \n",
        "origen_842110000_4  842110000  5.160000e+00  0.531242  842110000   0.001683   \n",
        "origen_952420001_4  952420001  4.449622e+10  0.519896  942380000   0.001293   \n",
        "origen_80190000_4    80190000  2.688000e+02  0.496765   80190000   0.001622   \n",
        "origen_741890000_4  741890000  6.420000e+03  0.472665  741890000   0.001581   \n",
        "origen_320710001_4  320710001  2.041000e-01  0.462447  320710001   0.001564   \n",
        "origen_802050000_4  802050000  3.084000e+03  0.448400  802050000   0.001541   \n",
        "origen_461110001_1  461110001  1.980000e+02  0.402345  471110000   0.002104   \n",
        "origen_40100000_4    40100000  4.765198e+14  0.387555   40100000   0.001446   \n",
        "origen_781910000_4  781910000  2.445120e+06  0.387555  781910000   0.001446   \n",
        "origen_561310000_4  561310000  9.936000e+06  0.346184  551310000   0.005383   \n",
        "origen_280590000_4  280590000  2.398378e+13  0.344502  280590000   0.001383   \n",
        "origen_461090001_3  461090001  2.817600e+02  0.341814  471090000   0.001102   \n",
        "origen_812040000_2  812040000  1.193824e+07  0.331065  802040000   0.001955   \n",
        "...                       ...           ...       ...        ...        ...   \n",
        "origen_802040000_2  802040000  1.000000e-01  0.000000  802040000   1.000000   \n",
        "origen_802040000_3  802040000  1.000000e+00  0.000000  802040000   1.000000   \n",
        "origen_802040000_4  802040000  1.000000e+01  0.000000  802040000   1.000000   \n",
        "origen_802040000_5  802040000  1.000000e+02  0.000000  802040000   1.000000   \n",
        "origen_812030000_1  812030000  1.000000e-02  0.000000  812030000   1.000000   \n",
        "origen_812030000_2  812030000  1.000000e-01  0.000000  812030000   1.000000   \n",
        "origen_812030000_3  812030000  1.000000e+00  0.000000  812030000   1.000000   \n",
        "origen_812030000_4  812030000  1.000000e+01  0.000000  812030000   1.000000   \n",
        "origen_812030000_5  812030000  1.000000e+02  0.000000  812030000   1.000000   \n",
        "origen_812050000_1  812050000  1.000000e-02  0.000000  812050000   1.000000   \n",
        "origen_812050000_2  812050000  1.000000e-01  0.000000  812050000   1.000000   \n",
        "origen_812050000_3  812050000  1.000000e+00  0.000000  812050000   1.000000   \n",
        "origen_812050000_4  812050000  1.000000e+01  0.000000  812050000   1.000000   \n",
        "origen_812050000_5  812050000  1.000000e+02  0.000000  812050000   1.000000   \n",
        "origen_822060000_1  822060000  1.000000e-02  0.000000  822060000   1.000000   \n",
        "origen_822060000_2  822060000  1.000000e-01  0.000000  822060000   1.000000   \n",
        "origen_822060000_3  822060000  1.000000e+00  0.000000  822060000   1.000000   \n",
        "origen_822060000_4  822060000  1.000000e+01  0.000000  822060000   1.000000   \n",
        "origen_822060000_5  822060000  1.000000e+02  0.000000  822060000   1.000000   \n",
        "origen_822070000_1  822070000  1.000000e-02  0.000000  822070000   1.000000   \n",
        "origen_822070000_2  822070000  1.000000e-01  0.000000  822070000   1.000000   \n",
        "origen_822070000_3  822070000  1.000000e+00  0.000000  822070000   1.000000   \n",
        "origen_822070000_4  822070000  1.000000e+01  0.000000  822070000   1.000000   \n",
        "origen_822070000_5  822070000  1.000000e+02  0.000000  822070000   1.000000   \n",
        "origen_822080000_1  822080000  1.000000e-02  0.000000  822080000   1.000000   \n",
        "origen_822080000_2  822080000  1.000000e-01  0.000000  822080000   1.000000   \n",
        "origen_822080000_3  822080000  1.000000e+00  0.000000  822080000   1.000000   \n",
        "origen_822080000_4  822080000  1.000000e+01  0.000000  822080000   1.000000   \n",
        "origen_822080000_5  822080000  1.000000e+02  0.000000  822080000   1.000000   \n",
        "origen_721780001_3  721780001  4.000000e+00  0.000000  721780001   0.500000   \n",
        "\n",
        "                    weightederr  \n",
        "origen_420930001_4     0.002330  \n",
        "origen_420930001_5     0.002302  \n",
        "origen_781930001_5     0.026175  \n",
        "origen_781930001_4     0.002223  \n",
        "origen_420990000_1     0.010757  \n",
        "origen_491140000_4     0.050018  \n",
        "origen_491140000_5     0.050062  \n",
        "origen_491140000_3     0.025031  \n",
        "origen_491140000_2     0.003352  \n",
        "origen_380910000_1     0.005552  \n",
        "origen_491140001_4     0.050698  \n",
        "origen_491140001_5     0.050742  \n",
        "origen_491140001_3     0.025363  \n",
        "origen_491140001_2     0.003397  \n",
        "origen_230540000_4     0.001191  \n",
        "origen_360790001_4     0.001121  \n",
        "origen_561330001_4     0.001745  \n",
        "origen_842110000_4     0.000894  \n",
        "origen_952420001_4     0.000672  \n",
        "origen_80190000_4      0.000806  \n",
        "origen_741890000_4     0.000747  \n",
        "origen_320710001_4     0.000723  \n",
        "origen_802050000_4     0.000691  \n",
        "origen_461110001_1     0.000846  \n",
        "origen_40100000_4      0.000560  \n",
        "origen_781910000_4     0.000560  \n",
        "origen_561310000_4     0.001864  \n",
        "origen_280590000_4     0.000476  \n",
        "origen_461090001_3     0.000377  \n",
        "origen_812040000_2     0.000647  \n",
        "...                         ...  \n",
        "origen_802040000_2     0.000000  \n",
        "origen_802040000_3     0.000000  \n",
        "origen_802040000_4     0.000000  \n",
        "origen_802040000_5     0.000000  \n",
        "origen_812030000_1     0.000000  \n",
        "origen_812030000_2     0.000000  \n",
        "origen_812030000_3     0.000000  \n",
        "origen_812030000_4     0.000000  \n",
        "origen_812030000_5     0.000000  \n",
        "origen_812050000_1     0.000000  \n",
        "origen_812050000_2     0.000000  \n",
        "origen_812050000_3     0.000000  \n",
        "origen_812050000_4     0.000000  \n",
        "origen_812050000_5     0.000000  \n",
        "origen_822060000_1     0.000000  \n",
        "origen_822060000_2     0.000000  \n",
        "origen_822060000_3     0.000000  \n",
        "origen_822060000_4     0.000000  \n",
        "origen_822060000_5     0.000000  \n",
        "origen_822070000_1     0.000000  \n",
        "origen_822070000_2     0.000000  \n",
        "origen_822070000_3     0.000000  \n",
        "origen_822070000_4     0.000000  \n",
        "origen_822070000_5     0.000000  \n",
        "origen_822080000_1     0.000000  \n",
        "origen_822080000_2     0.000000  \n",
        "origen_822080000_3     0.000000  \n",
        "origen_822080000_4     0.000000  \n",
        "origen_822080000_5     0.000000  \n",
        "origen_721780001_3     0.000000  \n",
        "\n",
        "[2802 rows x 6 columns]"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Relative Error Fraction\n",
      "-------------------------\n",
      "The fraction of the data with a relative error greater than 50%"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(df.relerr > 0.5).sum() / len(df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "0.0067808708065667384"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Weighted Error Fraction\n",
      "-------------------------\n",
      "The fraction of the data with a mass-weighted relative error greater than 50%"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(df.weightederr > 0.5).sum() / len(df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "0.0"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Relative and Weighted Error Fraction\n",
      "-------------------------------------\n",
      "The fraction of the data with both relative and mass-weighted relative error greater than 50%"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "((df.relerr > 0.5) & (df.weightederr > 0.5)).sum() / len(df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "0.0"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Length\n",
      "--------\n",
      "The number of decay calculations compared"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "len(df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "2802"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plot\n",
      "-----\n",
      "The relative errors, grouped by nuclide"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 20\n",
      "plt.figure(figsize=(10, 6))\n",
      "for i, (key, grp) in enumerate(df.groupby(['nuc'])):\n",
      "    if i > N:\n",
      "        break\n",
      "    nn = nucname.name(int(key))\n",
      "    p = grp.plot(x='t', y='relerr', logx=True, label=nn)\n",
      "    plt.xlabel('t [sec]')\n",
      "    plt.ylabel('Relative Error')\n",
      "    p.legend(p.lines, (nn,), loc=0)\n",
      "    plt.savefig('decay-relative-error-{0}.eps'.format(nn))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<matplotlib.figure.Figure at 0x7f34d7a2a208>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f34d7a2ac88>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f34d79bfa20>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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k7iwRKbr6ehg0CCZPTjoSKRUVkYSkvZ+01JTPeHUkn5Mnw1VXwSuvxBdPJUv7\nd1NFRERi1a8fnHZaGGiX9NOYiIjE7v33YeBAuPVW+NrXko5G4qAxEREpmS23hKuvDoPsjY1JRyPF\npCKSkLT3k5aa8hmvOPJ5yCHQuzdcf33H46lkaf9uqoiISFGYwZQpcOmlYdp4SSeNiYhIUf3Xf8Eb\nb4TxEalcmjsroiIiUlrvvgu77QZ33gn77JN0NFKoRAbWzazezJab2YtmNq6VNlOi158zs9q2tjWz\nnmY218xWmNkjZtYjWl9jZh+Y2aLoMa2Yn62j0t5PWmrKZ7zizOdWW8EVV8CYMfDJJ7HttmKk/btZ\ntCJiZp2AqUA9MBA4xswGNGszCtjF3fsDJwM35LHteGCuu+8KzIuWm6x099roMbpYn01E2ufYY8MZ\nWzNmJB2JxK1o3Vlmtg9wgbvXR8vjAdz9sqw2NwLz3f3X0fJyoA7o29q2UZsR7v66me0AZNx9NzOr\nAe53993biEvdWSIJeO452H9/WLoUPv3ppKOR9kqiO2tHIHvig9XRunza9M6xbS93bzrX43WgV1a7\nvlFXVsbMvtLB+EUkRnvuCUccEe7LLunRuYj7zvfP/U0qWyttNtmfu7uZNa3/B7CTu79tZkOA35rZ\nIHd/t/l2DQ0N1NTUANCjRw8GDx5MXV0dsKH/stjLTetK9X5pX25aVy7xVPpy07q497///hkaGuD7\n36+jtrZ8Pm8xlxcvXsyZZ55ZNvHku5zJZJg5cybA+t/LFrl7UR7AcOChrOUJwLhmbW4Ejs5aXk44\nsmh126jNDtHzzwLLW3n/+cCQFtZ7OZg/f37SIaSK8hmvYuZz+nT3L33Jfd26or1FWUnLdzP67dzk\nt7aYYyKdgReA/QhHCQuBY9x9WVabUcAYdx9lZsOBa9x9eK5tzewK4E13vzwaK+nh7uPNbDvgbXf/\nxMz6AY8DX3D3Nc3i8mJ9ZhFp27p1sPfeMHYsHHdc0tFIvhK5TsTMRgLXAJ2AGe4+0cxOAXD3m6I2\nTWdhvQec4O7PtrZttL4ncAfwOWAVcKS7rzGzw4CLgUZgHXC+uz/YQkwqIiIJW7AADj003Alx662T\njkbyoYsNI+VSRDKZzPp+SOk45TNepcjnSSfBttvCpElFfZvEpeW7qVl8RaSsTJwIs2aFU36lculI\nREQSM2UK3HcfzJ0bJmyU8qUjEREpO6NHhxl+77476UikUCoiCck+H186TvmMV6ny2bkzTJ0KZ58d\n7oaYRmkBa/QQAAAJsklEQVT/bqqIiEiiRoyAL385jJFI5dGYiIgk7tVXw7QoCxbAzjsnHY20RGMi\nIlK2dtwRfvQjOOuspCOR9lIRSUja+0lLTfmMVxL5PPNMeOEFeHCTS4QrW9q/myoiIlIWunaFa68N\nxeSjj5KORvKlMRERKSuHHBLm1powIelIJJumPYmoiIiUt5dfhr32gkWLYKedko5GmmhgvcykvZ+0\n1JTPeCWZz759w/3YzzknsRBilfbvpoqIiJSdcePC6b6//33SkUhb1J0lImXpnnvCrXQXLYIuXZKO\nRtSdJSIV5ZBDwvUj11+fdCSSi4pIQtLeT1pqyme8yiGfZuGU30svDZM0VqpyyGUxqYiISNnabTc4\n4QQYPz7pSKQ1GhMRkbL27rswYAD85jewzz5JR1O9NCYiIhVpq63giivCab+ffJJ0NNKcikhC0t5P\nWmrKZ7zKLZ/HHAPdu8PNNycdSfuVWy7jpiIiImXPDK67Ds4/H958M+loJJvGRESkYpx+eujSmjYt\n6Uiqj+bOiqiIiFSut98Og+y/+x3U1iYdTXXRwHqZSXs/aakpn/Eq13xuuy1cckkYZK+UvwXLNZdx\nURERkYpy4onQ2Ai33550JALqzhKRCrRwYZgWZfly2HrrpKOpDhoTiaiIiKTDSSdBjx5w1VVJR1Id\nNCZSZtLeT1pqyme8KiGfEyfCbbfB0qVJR5JbJeSyI1RERKQibb99uG5k7NjKGWRPI3VniUjF+vhj\nGDIkFJPDD086mnTTmEhERUQkXR57DL73PVi2DLbcMulo0ktjImUm7f2kpaZ8xquS8jliBHz5y2GM\npBxVUi4LoSIiIhXvyivhhhtg5cqkI6k+6s4SkVS44gp44gm4//6kI0kndWeJSKqdeSasWAEPPph0\nJNWlqEXEzOrNbLmZvWhm41ppMyV6/Tkzq21rWzPraWZzzWyFmT1iZj2yXpsQtV9uZvsX87N1VNr7\nSUtN+YxXJeZz881hyhQ44wz48MOko9mgEnPZHkUrImbWCZgK1AMDgWPMbECzNqOAXdy9P3AycEMe\n244H5rr7rsC8aBkzGwgcFbWvB6aZWdkeaS1evDjpEFJF+YxXpebzm9+E3XeHyZOTjmSDSs1lvor5\nIzsMWOnuq9y9EZgNHNyszUHALAB3XwD0MLMd2th2/TbRv4dEzw8GfuXuje6+ClgZ7acsrVmzJukQ\nUkX5jFcl53Py5PBYsQLeey8clTQ2wrp1ycRTybnMR+ci7ntH4JWs5dXA3nm02RHonWPbXu7+evT8\ndaBX9Lw38FQL+9pEJpOhrq6u1cBzvd7Sa/msa+s9i6Ej79mebQvNZ3vWV0s+4/5utrY+zfns2xfG\nj4ehQ2Ht2gxQxyefhCLiDpttBp06hQdk2Hzzuo3WNT3Wrs3QvXvdRuvefz/DNttsWLfZZvDvf2fo\n2XPjdWvWZNh++7BuxQpYsmTT/bf0nh1Z9+KLGQYOrGv3ts8/n2Ho0Lo227WmmEUk31OgNhntb6XN\nJvtzdzezXO/T4mvlUERWrVqVI+x4VFMRSUs+y6WIVHo+zzknPC68MMOFF25o5x7ujNj0uOSSDOPG\n1W20bt268O9VV2U4/fS6jdZNnZrh5JM3Xjd9eobjj9943W23ZTj66LDu2mtXcdRRtPge7Vm3dm3u\ndgsXZnj77bp2v8fLL2fo06flHGQ/WuXuRXkAw4GHspYnAOOatbkRODpreTnhyKLVbaM2O0TPPwss\nj56PB8ZnbfMQsHcLcbkeeuihhx7tf7T0W1/MI5FngP5mVgP8gzDofUyzNvcBY4DZZjYcWOPur5vZ\nmzm2vQ84Hrg8+ve3Wet/aWaTCd1Y/YGFzYNq6TxnEREpTNGKiLt/bGZjgIeBTsAMd19mZqdEr9/k\n7nPMbJSZrQTeA07ItW2068uAO8zsJGAVcGS0zVIzuwNYCnwMjNZVhSIixVV1V6yLiEh8yvY6ChER\nKX8qIiIiUrBiDqxLO5jZV4DvEP6bDHT3LyccUkUzsz7AFOBtYIW7X55wSBUrmg3iAuBNYJ6735Vw\nSBXJzPoC5wLbuPsR0bruwDTgIyDj7r9MMMSC6EikTLj7k+5+KvAAMDPhcNJgd+Audz8JqG2rseRU\nD1zn7qOB7yUdTKVy95fd/T+brT4MuMPdTybMxlFxVESKyMxuMbPXzewvzdbnmpjyWKDi/hophXbm\n84/AyWY2j3DNkGRpZy5/DhxtZlcAny55sGWswP/Hs2XP2pHrkr6ypSJSXLcS/opbL9fkkmb2OeD/\n3P29UgdaIdqTzxOA89x9P+BbpQ60AuSdS3d/w93HEC76/VfJIy1v7fp/vAWrgZ2i5xX5e1yRQVcK\nd3+C0CefLdfkkicCt5QwxIrSznz+HjjDzG4AXi5tpOWvPbk0s/9nZjcRJjy9osShlrV25rGnmd0I\nDM46Orkb+LaZTSNcMF1xNLBeeq1OTOnuFyYRUIVrMZ/u/jxweDIhVazWcvl34JRkQqpIreXxLeAH\n2Q3d/X3CH48VS0cipaerO+OlfMZHuYxHVeVRRaT0XmVDHyjR89UJxZIGymd8lMt4VFUeVURKb/3E\nlGa2OWFyyYrsCy0Tymd8lMt4VFUeVUSKyMx+RTjVdFcze8XMTnD3jwkzFz9MmCzy11mTS0oOymd8\nlMt4KI+agFFERDpARyIiIlIwFRERESmYioiIiBRMRURERAqmIiIiIgVTERERkYKpiIiISMFURERE\npGAqIiIxMrNtzOzUVl6rMbMPzOzZGN+vn5ktNrN349qnSHuoiIjEa1tgdI7XV7r7kLjezN1fcvfB\nce1PpL1URETidRmws5ktMrPLczU0s+5m9mB0JPEXMzsyWj/UzDJm9oyZPWRmO0TrdzGzR6P2fzaz\nfiX4PCI56aZUIvEaBwxy99o82tYDr7r7twDMbGsz6wJcBxzo7m+a2VHApcBJwC+An7r7vdHssJ2K\n8xFE8qciIhIva0fb54FJZnYZ8IC7P2lmXwAGAY+aGYRC8Q8z+xTQ293vBXD3tTHHLVIQFRGRhLj7\ni2ZWC3wLuMTM5gH3AH919y9ltzWzrZKIUaQtGhMRide7QF4/+Gb2WeBDd/8FMAmoBV4APmNmw6M2\nXcxsoLu/C6w2s4Oj9V3NbIuifAKRdlAREYmRu78J/CEaKM85sA7sDiwws0XA+cAl7t4IHA5cbmaL\ngUXAPlH744CxZvYc8Adgh6J8CJF20E2pRErEzGqA+9199yLs+113V5eXlJyORERK52Ngm2JcbAi8\nFtc+RdpDRyIiIlIwHYmIiEjBVERERKRgKiIiIlIwFRERESmYioiIiBTs/wOyNUjpugU9tQAAAABJ\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f34d79bafd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f34d87ad160>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f34d7d8b0f0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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R9eyxB7RvD088kXQk0pQyukNiKWnojKS6uprKysqmC6jEKZ/xKZZc3nxzuOHV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\nEhERycn/B9nuesuCpQ/fAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f34d7a83400>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f34eb4dd668>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f34de7fb470>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f34d8b59908>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f34f30f6cf8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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cSmLOwswGmNksM3vHzM5PU2dM+Pw0M+uba9twRdyVZrZBnJ9BRJrXrl1wo94v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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f34f2805ba8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f34f4e6fe80>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f34f3603470>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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qljsLkdb88pdwzz0wd27akUihBg2Cf/u3sIR5qRU7z2Ind1/UtBH9Bt4UV3Ai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\nEclJlYWIiOT0/wNHCmK4CtR3LQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f34f6ea32e8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f34f3def198>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f34f23f7b38>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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szMKYzf3+97BunZs40ITv3XfhvPPcZbRRmZcr1ZhFqiflbUcdEwgaYwrPd9/B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\nxqRljYUxxpi0/h+GNkCGQPDGhQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f34edc93358>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GzQYC44EK4DZ3H5tjmQnA4YQmuEp3fy3futHIzvcD2wKLCP1BK81sCPCTGpvu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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f34f3803f98>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f34f12d5278>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f34ed2e5b00>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f34f6144320>"
       ]
      }
     ],
     "prompt_number": 57
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Drill Down into Problem Sepcies\n",
      "--------------------------------\n",
      "Should explain the issue with remaining high relative error"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Mo-99\n",
      "-------\n",
      "Origen seems to have the wrong branch ratios"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nucsummary(420990000, 1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Nulcide: Mo99\n",
        "origen half life: 237600.0\n",
        "data.half_life(): 237513.6\n",
        "relerr half life: 0.000363702491362\n",
        "\n",
        "Material:\n",
        "mass = 0.9939597000001054\n",
        "density = -1.0\n",
        "atoms per molecule = -1.0\n",
        "decay_time = 2375.136\n",
        "name = origen_420990000_1\n",
        "-------------------------\n",
        "Mo99   0.9991350755970234\n",
        "Tc99   0.000864924402870568\n",
        "Ru99   1.0604051653199704e-13"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "Material:\n",
        "mass = 0.9999999336058844\n",
        "density = -1.0\n",
        "atoms per molecule = 1.0000000354067466\n",
        "---------------------------------------\n",
        "Mo99   0.9930925617347804\n",
        "Tc99   0.006907402611982175\n",
        "Ru99   3.565323735891612e-08\n",
        "\n",
        "420990000    0.000008\n",
        "430990000    1.557261\n",
        "440990000    1.999988\n",
        "dtype: float64\n"
       ]
      },
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>nuc</th>\n",
        "      <th>t</th>\n",
        "      <th>relerr</th>\n",
        "      <th>child</th>\n",
        "      <th>childmass</th>\n",
        "      <th>weightederr</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>origen_420990000_1</th>\n",
        "      <td> 420990000</td>\n",
        "      <td> 2375.136</td>\n",
        "      <td> 1.557261</td>\n",
        "      <td> 430990000</td>\n",
        "      <td> 0.006907</td>\n",
        "      <td> 0.010757</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "                          nuc         t    relerr      child  childmass  \\\n",
        "origen_420990000_1  420990000  2375.136  1.557261  430990000   0.006907   \n",
        "\n",
        "                    weightederr  \n",
        "origen_420990000_1     0.010757  "
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<matplotlib.figure.Figure at 0x7f34e1ff8780>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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XAHs1ey08XFVLm3UGSdImMNEawl501w9e2Py5zuN0b07bKFX1+Kj330jymSQvorvvwjFJ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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f34e2014630>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In-114\n",
      "-------\n",
      "Origen just seems to have the wrong branch ratios"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nucsummary(491140000, 3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Nulcide: In114\n",
        "origen half life: 71.9\n",
        "data.half_life(): 71.9\n",
        "relerr half life: 0.0\n",
        "\n",
        "Material:\n",
        "mass = 0.9999699999999999\n",
        "density = -1.0\n",
        "atoms per molecule = -1.0\n",
        "decay_time = 71.9\n",
        "name = origen_491140000_3\n",
        "-------------------------\n",
        "Cd114  0.016870506115183457\n",
        "In114  0.5000150004500135\n",
        "Sn114  0.48311449343480306"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "Material:\n",
        "mass = 0.999990639989361\n",
        "density = -1.0\n",
        "atoms per molecule = 1.0\n",
        "------------------------\n",
        "Cd114  0.002499989836490059\n",
        "In114  0.500004576422662\n",
        "Sn114  0.4974954337408478\n",
        "\n",
        "481140000    1.483744\n",
        "491140000    0.000000\n",
        "501140000    0.029351\n",
        "dtype: float64\n",
        "\\begin{tabular}{lrrrrrr}\n",
        "\\toprule\n",
        "{} &        nuc &         t &    relerr &      child &  childmass &  weightederr \\\\\n",
        "\\midrule\n",
        "origen\\_491140000\\_1 &  491140000 &     0.719 &  0.029356 &  501140000 &   0.006873 &     0.000202 \\\\\n",
        "origen\\_491140000\\_2 &  491140000 &     7.190 &  1.483651 &  481140000 &   0.002259 &     0.003352 \\\\\n",
        "origen\\_491140000\\_3 &  491140000 &    71.900 &  1.483744 &  481140000 &   0.016870 &     0.025031 \\\\\n",
        "origen\\_491140000\\_4 &  491140000 &   719.000 &  1.483783 &  481140000 &   0.033710 &     0.050018 \\\\\n",
        "origen\\_491140000\\_5 &  491140000 &  7190.000 &  1.483744 &  481140000 &   0.033740 &     0.050062 \\\\\n",
        "\\bottomrule\n",
        "\\end{tabular}\n",
        "\n"
       ]
      },
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>nuc</th>\n",
        "      <th>t</th>\n",
        "      <th>relerr</th>\n",
        "      <th>child</th>\n",
        "      <th>childmass</th>\n",
        "      <th>weightederr</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>origen_491140000_1</th>\n",
        "      <td> 491140000</td>\n",
        "      <td>    0.719</td>\n",
        "      <td> 0.029356</td>\n",
        "      <td> 501140000</td>\n",
        "      <td> 0.006873</td>\n",
        "      <td> 0.000202</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_491140000_2</th>\n",
        "      <td> 491140000</td>\n",
        "      <td>    7.190</td>\n",
        "      <td> 1.483651</td>\n",
        "      <td> 481140000</td>\n",
        "      <td> 0.002259</td>\n",
        "      <td> 0.003352</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_491140000_3</th>\n",
        "      <td> 491140000</td>\n",
        "      <td>   71.900</td>\n",
        "      <td> 1.483744</td>\n",
        "      <td> 481140000</td>\n",
        "      <td> 0.016870</td>\n",
        "      <td> 0.025031</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_491140000_4</th>\n",
        "      <td> 491140000</td>\n",
        "      <td>  719.000</td>\n",
        "      <td> 1.483783</td>\n",
        "      <td> 481140000</td>\n",
        "      <td> 0.033710</td>\n",
        "      <td> 0.050018</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>origen_491140000_5</th>\n",
        "      <td> 491140000</td>\n",
        "      <td> 7190.000</td>\n",
        "      <td> 1.483744</td>\n",
        "      <td> 481140000</td>\n",
        "      <td> 0.033740</td>\n",
        "      <td> 0.050062</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 59,
       "text": [
        "                          nuc         t    relerr      child  childmass  \\\n",
        "origen_491140000_1  491140000     0.719  0.029356  501140000   0.006873   \n",
        "origen_491140000_2  491140000     7.190  1.483651  481140000   0.002259   \n",
        "origen_491140000_3  491140000    71.900  1.483744  481140000   0.016870   \n",
        "origen_491140000_4  491140000   719.000  1.483783  481140000   0.033710   \n",
        "origen_491140000_5  491140000  7190.000  1.483744  481140000   0.033740   \n",
        "\n",
        "                    weightederr  \n",
        "origen_491140000_1     0.000202  \n",
        "origen_491140000_2     0.003352  \n",
        "origen_491140000_3     0.025031  \n",
        "origen_491140000_4     0.050018  \n",
        "origen_491140000_5     0.050062  "
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<matplotlib.figure.Figure at 0x7f34f08eaf60>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f34f33849e8>"
       ]
      }
     ],
     "prompt_number": 59
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Sr-91\n",
      "------\n",
      "Relative error is high for Y-91, but the mass weighted relative error is low"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nucsummary(380910000, 1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Nulcide: Sr91\n",
        "origen half life: 34200.0\n",
        "data.half_life(): 34740.0\n",
        "relerr half life: 0.0156657963446\n",
        "\n",
        "Material:\n",
        "mass = 0.9959470702700001\n",
        "density = -1.0\n",
        "atoms per molecule = -1.0\n",
        "decay_time = 347.4\n",
        "name = origen_380910000_1\n",
        "-------------------------\n",
        "Sr91   0.9970409368550067\n",
        "Y91    0.0029589925890349494\n",
        "Zr91   7.055595834118967e-08"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "Material:\n",
        "mass = 0.9999996178756235\n",
        "density = -1.0\n",
        "atoms per molecule = 0.9999998380652019\n",
        "---------------------------------------\n",
        "Sr91   0.9930928753873625\n",
        "Y91    0.006907124612637552\n",
        "\n",
        "380910000    0.000093\n",
        "390910000    0.803749\n",
        "400910000         NaN\n",
        "dtype: float64\n"
       ]
      },
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>nuc</th>\n",
        "      <th>t</th>\n",
        "      <th>relerr</th>\n",
        "      <th>child</th>\n",
        "      <th>childmass</th>\n",
        "      <th>weightederr</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>origen_380910000_1</th>\n",
        "      <td> 380910000</td>\n",
        "      <td> 347.4</td>\n",
        "      <td> 0.803749</td>\n",
        "      <td> 390910000</td>\n",
        "      <td> 0.006907</td>\n",
        "      <td> 0.005552</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "                          nuc      t    relerr      child  childmass  \\\n",
        "origen_380910000_1  380910000  347.4  0.803749  390910000   0.006907   \n",
        "\n",
        "                    weightederr  \n",
        "origen_380910000_1     0.005552  "
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<matplotlib.figure.Figure at 0x7f34e1fd5e10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f34e2a0c710>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "... and so on"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df.relerr.plot(kind='hist', bins=10000, loglog=True, figsize=(10, 6))\n",
      "plt.xlabel('Relative Error, on range [0, 2]')\n",
      "plt.ylabel('Number of Calculations, Total = {0}'.format(len(df)))\n",
      "plt.savefig('decay-relative-error-histogram.eps')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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fLSQpIv68yAC2z5d0qKRH275V0psj4hzbr5H0efVu3fGRiLhhRZGrq17PT2dl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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f34f28299b0>"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}