IPython Notebook Example for Data Visualization and Analysis

gistfile1.txt

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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "def formatter(x):\n",
      "    return '{:.3e}'.format(x)\n",
      "np.set_printoptions(formatter={'float':formatter})\n",
      "\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "plt.rc('savefig', dpi=100)\n",
      "\n",
      "import gcms"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Open the GCMS files. In this case, `data` is the data for H6-phenol + H2 + D2O. This is a sample that was run by Ryan on his Aug. 2014 trip to Orono. The catalyst for this reaction was rcn1016, which is 1% RuCl3/TiO2. `ref` is the natural-abudance reference data the first reaction run with rcn1016 as the catalyst, which was H6-phenol + H2 + H2O. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ref = gcms.AIAFile('../gcms_rna3/data/rcn1016_001.CDF')\n",
      "data = gcms.AIAFile('RNA15323.CDF')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's take a look at the TIC for these two runs over the region that corresponds to benzene/cyclohexane. The red line is the D2O spectra. The blue line is the H2O spectra."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(ref.times, ref.tic, 'b')\n",
      "plt.plot(data.times, data.tic, 'r')\n",
      "\n",
      "plt.xlim(2.5, 3.5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "(2.5, 3.5)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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TeAa4HOvN8GQAE4G7gdeBhcCFWPA4y63pBVwK3Ai8j/VUXAIcgwUZsEAy1j3+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\nP5PMZ9mhpd66AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f43a9e15a50>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we are going to set time masks for extracting the data that corresponds to the benzene/cyclohexane region."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "start = 2.8\n",
      "stop = 3.3\n",
      "\n",
      "for i in (ref, data):\n",
      "    i.mask = (i.times > start) & (i.times < stop)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, check to see that these regions are relatively pure for one compound. We can do this by plotting the MS intensities for the selected times.\n",
      "\n",
      "In both cases, there were some masses that \"streaked\" through the data set, which correspond to background noise. Subtration of the first MS of this region from all other slices provides a simple background subtraction."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(14,5))\n",
      "start = 1\n",
      "for i in (ref, data):\n",
      "    plt.subplot(1, 2, start)\n",
      "    i.region = i.intensity[i.mask]\n",
      "    i.region = i.region - i.region[0]\n",
      "    plt.pcolormesh(i.masses, i.times[i.mask], i.region, \n",
      "                   vmax=i.region.max()*0.01)\n",
      "    plt.xlim(30,110)\n",
      "    plt.xlabel('m/z')\n",
      "    plt.ylabel('Time (min)')\n",
      "    plt.title(i.filename)\n",
      "    start += 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f43a6e3c7d0>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Rather than selecting a single slice to represent the MS of these peaks, we'll generate a MS by summing all the data along the mass axis and then normalizing based off the largest peak."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in (ref, data):\n",
      "    i.ms = i.region.sum(axis=0)\n",
      "    i.ms = i.ms/i.ms.max()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the parent ion region for benzene/cyclohexane. The important m/z values are 78-85, which represent H6- to D6-benzene, repectively, and the m/z >= 84 which are for cyclohexane. The blue bars are the H2O data; the red bars are the D2O data.\n",
      "\n",
      "The D2O sample clearly has some deuterium incorporation into the benzene and cyclohexane. Unfortunately, there is some overlap between the heavily deuterated benzene and undeuterated cyclohexane mass regions (m/z 84~87)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "width = 0.3\n",
      "plt.bar(ref.masses, ref.ms, width=width, color='b')\n",
      "plt.bar(data.masses+width, data.ms, width=width, color='r')\n",
      "\n",
      "plt.xlim(75, 98)\n",
      "plt.grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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WMXY3cAmTTzyAYsWG9+3bx7Jlky9w/PrXv87zn//8KQufzS7FXrsjT3eZ8215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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f43a9e15850>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we'll select out the important data from each spectrum that we'll use for the subsequent fitting steps.\n",
      "\n",
      "The m/z=84,85,86 from the H2O sample are reference values for the isotopic distribution expected a C6 compound with natural abundance C13 incorporation. (`ref.ms[ref.mass_mask]`) We can assumes the same distribution for the other isotopologues of benezene, but there is some inaccuracies because of the small amount of natural abundance deuterium (which is only ~0.01%).\n",
      "\n",
      "The m/z values from 78-91 in the D2O spectrum are the ones that we would like to fit to determine the isotopic distribution. (`data.ms[data.mass_mask]`) Values above m/z 91 are all zero, presumably because they were below the detection threshold on the instrument."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ref.mass_mask = (ref.masses >= 78) & (ref.masses <= 80)\n",
      "data.mass_mask = (data.masses >= 78) & (data.masses <= 91)\n",
      "\n",
      "ref.vals = ref.ms[ref.mass_mask]\n",
      "data.vals = data.ms[data.mass_mask]\n",
      "\n",
      "print ref.vals\n",
      "print data.vals"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[1.000e+00 6.672e-02 1.939e-03]\n",
        "[1.000e+00 5.775e-01 1.538e-01 2.553e-02 7.440e-03 9.631e-03 7.537e-02\n",
        " 8.318e-02 4.688e-02 1.626e-02 3.713e-03 6.378e-04 1.896e-05 5.883e-05]\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This part is tricky...\n",
      "\n",
      "We can fit the D2O distribution data using least squares techniques. The observed isotopic distribution is simply a linear combination of the fractional contribution from each isotopologue of benzene and cyclohexane.\n",
      "\n",
      "$$ MS_{obs} = \\sum_{i=0}^{6} m_i*MS_{C_{6} H_{6-i} D_{i}} +  \n",
      "\\sum_{i=0}^{12} n_i*MS_{C_{6} H_{12-i} D_{i}}  $$\n",
      "\n",
      "Where $MS_{obs}$ is the observed mass spectrum, $MS_{C_{6} H_{6-i} D_{i}}$ / $MS_{C_{6} H_{12-i} D_{i}}$ are the mass spectra for the isotopologues of benzene and cyclohexane, and $m_i$ / $n_i$ are coefficients that are related to the relative contributions of each spectra to the observed data. These $m$ and $n$ values are then related to the concentration of each of these components.\n",
      "\n",
      "In order to perform a least squares regression analysis, a 2D array of mass distributions for each isotopologue of benzene and cyclhexane is necessary. In this case, we will use the isotopic values from the benzene standard run (`ref.vals` from above) but simply shift the values by an appropriate mass adjustment each additional isomer. H0-Benzene is not used in the fitting. This is because the masses directly overlap with H12-cyclohexane, which makes a unique fit impossible. This most likely isn't a problem, though, because the lighter isotopologues of benzene (H1 and H2) appear to only have very small contributions to the overall intensity.\n",
      "\n",
      "The array construction is complicated, so comments are added in the code below. The final array is saved into a csv file so you can check it in Excel (filename is the same as the GCMS file). In the final array, rows represent the masses in increasing order; columns represent the various isotopologues. The first columns are benzene; the final columns are cyclohexane. You can determine the number of columns for each by looking at the `comps` array below. The values in the array are the isotopic distributions for the different masses (which are all going to be equal to the standard in this case)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Size and start of components as well as the number of D atoms in the \n",
      "# lightest compound.\n",
      "# The inner tuple is such:\n",
      "# (# components to fit, starting mass, # D atoms in lightest isomer)\n",
      "comps = np.array( [(6, 78, 0), (6, 84, 0)] )\n",
      "# Total number of components\n",
      "total_comps = comps[:,0].sum()\n",
      "\n",
      "# Construct a 2D array of zeros that has the number of rows equal to the\n",
      "# total number of components and the number of columns equal to the number of\n",
      "# masses selected from our data spectrum.\n",
      "iso_dist = np.zeros((total_comps, data.vals.size))\n",
      "\n",
      "# Make an array of masses that correspond to our extracted data\n",
      "mass_min = comps[:,1].min()\n",
      "sim_mass = np.arange(mass_min, mass_min+data.vals.size)\n",
      "\n",
      "# This is the magic code that sets the isotope data for each isotopologue.\n",
      "# It is effectively moving the mass distribution by one mass unit for \n",
      "# each isomer.\n",
      "start = 0\n",
      "for comp in comps:\n",
      "    num = comp[0]\n",
      "    mass = comp[1]\n",
      "    \n",
      "    for n in range(num):\n",
      "        rng = np.where((sim_mass>=mass+n)  \n",
      "                       & (sim_mass<mass+ref.vals.size+n)\n",
      "                       )[0]\n",
      "        if rng.size >= ref.vals.size:\n",
      "            iso_dist[n+start,rng] = ref.vals\n",
      "        elif rng.size > 0:\n",
      "            iso_dist[n+start,rng] = ref.vals[:rng.size]\n",
      "            \n",
      "    start += num\n",
      "\n",
      "# Transpose the data so that the columns are isotopologes and rows are\n",
      "# masses. This is necessary for the least squares routine.\n",
      "iso_dist = iso_dist.T\n",
      "\n",
      "# Save the 2D array into a csv file that has the same prefix as the CDF file.\n",
      "np.savetxt(data.filename[:-3]+\"csv\", iso_dist, delimiter=\",\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we will perform the least squares fitting of the data (`data.vals`) with the 2D isomer array from above (`iso_dist`).\n",
      "\n",
      "The raw fit parameters (first) and the relative percents (second) are printed for both benzene and cyclohexane. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fit, resid, rank, sglr = np.linalg.lstsq(iso_dist, data.vals)\n",
      "\n",
      "start = 0\n",
      "fits_pers = []\n",
      "for comp in comps:\n",
      "    f = fit[start:comp[0]+start]\n",
      "    per = f*100/f.sum()\n",
      "    fits_pers.append([f,per])\n",
      "    print \n",
      "    print \"Compound starting at {:d}\".format(comp[1])\n",
      "    print f\n",
      "    print per\n",
      "    \n",
      "    # Save a file for Pandas\n",
      "    fname = data.filename[:-4] + '-{:d}-per.csv'\n",
      "    d = np.vstack( (np.arange(comp[1],comp[1]+comp[0]), per) )\n",
      "    np.savetxt(fname.format(comp[1]-comp[2]), d, delimiter=',')\n",
      "    \n",
      "    start += comp[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Compound starting at 78\n",
        "[1.000e+00 5.107e-01 1.178e-01 1.668e-02 6.099e-03 9.192e-03]\n",
        "[6.022e+01 3.076e+01 7.092e+00 1.005e+00 3.673e-01 5.536e-01]\n",
        "\n",
        "Compound starting at 84\n",
        "[7.474e-02 7.818e-02 4.152e-02 1.334e-02 2.743e-03 4.281e-04]\n",
        "[3.543e+01 3.706e+01 1.968e+01 6.324e+00 1.300e+00 2.029e-01]\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A bar graph of the percentages of each isotopologue is useful to visulally compare the relative levels of deuterium in benzene (red) versus cyclohexane (blue)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "width = 1./(comps.shape[0]+1.)\n",
      "\n",
      "start = 0\n",
      "cs = ['b', 'r', 'g']\n",
      "for comp, fit_per in zip(comps, fits_pers):\n",
      "    plt.bar(np.arange(comp[2],comp[2]+comp[0])+start*width, \n",
      "            fit_per[1], width=width, color=cs[start%len(cs)])\n",
      "    start += 1\n",
      "\n",
      "plt.xlabel('# D atoms')\n",
      "plt.ylabel('% Composition')\n",
      "plt.grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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BU6dUjUqzZs2askuoJHOLZ2ZpzC2emRUjppF4EXBC/v0L8p+HHy8m3A307inW8y7gCUbf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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f43a6e0b690>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To check the fit, we can construct a simulated MS using the isotopic distribution matrix and the fit parameters. Multiply the 2D array by the fits to get the contribution to the observed MS from each isotopologue. Then sum these values along the mass axis to get the simulated MS intensities."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sim = (iso_dist*fit).sum(axis=1)\n",
      "\n",
      "print \"Real Data:\"\n",
      "print data.vals\n",
      "print \"Simulated Data:\"\n",
      "print sim\n",
      "print \"Residuals:\"\n",
      "print data.vals - sim"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Real Data:\n",
        "[1.000e+00 5.775e-01 1.538e-01 2.553e-02 7.440e-03 9.631e-03 7.537e-02\n",
        " 8.318e-02 4.688e-02 1.626e-02 3.713e-03 6.378e-04 1.896e-05 5.883e-05]\n",
        "Simulated Data:\n",
        "[1.000e+00 5.775e-01 1.538e-01 2.553e-02 7.440e-03 9.631e-03 7.537e-02\n",
        " 8.318e-02 4.688e-02 1.626e-02 3.713e-03 6.370e-04 3.388e-05 8.299e-07]\n",
        "Residuals:\n",
        "[0.000e+00 1.110e-16 2.498e-16 9.714e-17 4.415e-16 -2.411e-15 1.349e-13\n",
        " -3.153e-12 3.882e-11 2.902e-10 -3.002e-08 8.835e-07 -1.493e-05 5.800e-05]\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A graphical way to compare the real data with the simulated data is with a loglog plot. It looks like there is only one data point that is very poorly fit, and that corresponds to the last mass value."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(data.vals, sim, 'o')\n",
      "plt.loglog()\n",
      "\n",
      "plt.xlabel('log(Real Data)')\n",
      "plt.ylabel('log(Sim data)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "<matplotlib.text.Text at 0x7f43a6dcd5d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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uZixJUgLuZixJkhqKCYokScocExRJkpQ59ZygvB24G3gQ+CkwpbrhSJKkYtXz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\nWn74gMoHAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f43a6deb850>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A bar graph is another way to compare the real data (blue) to the simulated data (red)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "width = 0.3\n",
      "plt.bar(sim_mass, data.vals, width=width, color='b')\n",
      "plt.bar(sim_mass+width, sim, width=width, color='r')\n",
      "\n",
      "plt.xlim(sim_mass[0]-1, sim_mass[-1]+1)\n",
      "plt.ylim(ymax=sim.max())\n",
      "plt.grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3/Z+77cXa9rFjx7I3wHfccQcrV65c0NhHH32U8fHxOceceuqpPPvss/M+1vnn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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f43a5c15490>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    }
   ],
   "metadata": {}
  }
 ]
}