arokem/gist:4253775a276d63852c7d Secret

## gistfile1.txt
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   "language": "python",
   "name": "python2"
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Is demeaning the signal a good idea? "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import nibabel as ni\n",
      "import numpy as np\n",
      "import osmosis.model.analysis as oza\n",
      "import osmosis.model.sparse_deconvolution as ssd\n",
      "import osmosis.model.dti as dti\n",
      "import osmosis.viz.mpl as mpl\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We set the data-path to point to the installation-specific location of the data-files"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import os\n",
      "import osmosis as oz\n",
      "import osmosis.io as oio\n",
      "oio.data_path = os.path.join(oz.__path__[0], 'data')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We generate strings pointing to all of the data-files for this subject:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "subject = 'SUB1'\n",
      "data_1k_1, data_1k_2 = oio.get_dwi_data(1000, subject)\n",
      "data_2k_1, data_2k_2 = oio.get_dwi_data(2000, subject)\n",
      "data_4k_1, data_4k_2 = oio.get_dwi_data(4000, subject)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Wewill only look at white-matter voxels. This loads the white-matter mask:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wm_mask = np.zeros(ni.load(data_1k_1[0]).shape[:3])\n",
      "wm_nifti = ni.load(oio.data_path + '/%s/%s_wm_mask.nii.gz'%(subject, subject)).get_data()\n",
      "wm_mask[np.where(wm_nifti==1)] = 1\n",
      "\n",
      "# Start working on a small chunk:\n",
      "#wm_mask = np.zeros(wm_mask.shape)\n",
      "#wm_mask[40:42, 40:42, 40:42] = 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The following are the parameters defining the performance of the Elastic Net solver , based on the calculations in AppendixA\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Initialize the class instances of the SFM objects, using AD/RD derived from the corpus callosum. Parameters are not saved (hence `temp`"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ad_rd = oio.get_ad_rd(subject, 2000)\n",
      "\n",
      "SD_2k_1_nnls_demean = ssd.SparseDeconvolutionModel(*data_2k_1, mask=wm_mask,  params_file ='temp', \n",
      "                                       axial_diffusivity=ad_rd[0]['AD'], radial_diffusivity=ad_rd[0]['RD'], \n",
      "                                       solver='nnls')\n",
      "\n",
      "SD_2k_2_nnls_demean = ssd.SparseDeconvolutionModel(*data_2k_2, mask=wm_mask,  params_file ='temp', \n",
      "                                       axial_diffusivity=ad_rd[1]['AD'], radial_diffusivity=ad_rd[1]['RD'], \n",
      "                                       solver='nnls')\n",
      "\n",
      "SD_2k_1_nnls = ssd.SparseDeconvolutionModel(*data_2k_1, mask=wm_mask,  params_file ='temp', \n",
      "                                       axial_diffusivity=ad_rd[0]['AD'], radial_diffusivity=ad_rd[0]['RD'], \n",
      "                                       solver='nnls', demean=False)\n",
      "\n",
      "SD_2k_2_nnls = ssd.SparseDeconvolutionModel(*data_2k_2, mask=wm_mask,  params_file ='temp', \n",
      "                                       axial_diffusivity=ad_rd[1]['AD'], radial_diffusivity=ad_rd[1]['RD'], \n",
      "                                       solver='nnls', demean=False)\n",
      "\n",
      "SD_2k_1_EN_demean = ssd.SparseDeconvolutionModel(*data_2k_1, mask=wm_mask,  params_file ='temp', \n",
      "                                       axial_diffusivity=ad_rd[0]['AD'], radial_diffusivity=ad_rd[0]['RD'])\n",
      "\n",
      "SD_2k_2_EN_demean = ssd.SparseDeconvolutionModel(*data_2k_2, mask=wm_mask,  params_file ='temp', \n",
      "                                       axial_diffusivity=ad_rd[1]['AD'], radial_diffusivity=ad_rd[1]['RD'])\n",
      "\n",
      "SD_2k_1_EN = ssd.SparseDeconvolutionModel(*data_2k_1, mask=wm_mask,  params_file ='temp', \n",
      "                                       axial_diffusivity=ad_rd[0]['AD'], radial_diffusivity=ad_rd[0]['RD'],\n",
      "                                       demean=False)\n",
      "\n",
      "SD_2k_2_EN = ssd.SparseDeconvolutionModel(*data_2k_2, mask=wm_mask,  params_file ='temp', \n",
      "                                       axial_diffusivity=ad_rd[1]['AD'], radial_diffusivity=ad_rd[1]['RD'],\n",
      "                                       demean=False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.bvals\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.nii.gz\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.bvecs\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.bvals\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.nii.gz\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.bvecs\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.bvals\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.nii.gz\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.bvecs\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.bvals\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.nii.gz\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.bvecs\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.bvals\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.nii.gz\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.bvecs\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.bvals\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.nii.gz\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.bvecs\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.bvals\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.nii.gz\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.bvecs\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.bvals\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.nii.gz\n",
        "Loading from file: /home/arokem/usr/local/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.bvecs\n"
       ]
      }
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Calculate rRMSEfor each b value , from a cross-prediction: fit the model to one data-set in each b value and predict the other data set. Calculations average across both directions (1=>2)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rrmse_2k_nnls = oza.cross_predict(SD_2k_1_nnls, SD_2k_2_nnls)\n",
      "rrmse_2k_nnls_demean = oza.cross_predict(SD_2k_1_nnls_demean, SD_2k_2_nnls_demean)\n",
      "rrmse_2k_EN = oza.cross_predict(SD_2k_1_EN, SD_2k_2_EN)\n",
      "rrmse_2k_EN_demean = oza.cross_predict(SD_2k_1_EN, SD_2k_2_EN_demean)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " \r",
        "SparseDeconvolutionModel.model_params [********         22%                  ]  14910 of 68694 complete "
       ]
      }
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#print(rrmse_2k_nnls[np.where(wm_mask==1)])\n",
      "#print(rrmse_2k_nnls_demean[np.where(wm_mask==1)])\n",
      "#print(rrmse_2k_EN_demean[np.where(wm_mask==1)])\n",
      "#print(rrmse_2k_EN[np.where(wm_mask==1)])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rrmse_2k_nnls_demean[np.isfinite(rrmse_2k_nnls_demean)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "array([ 0.91143276,  0.82941019,  0.89216963, ...,  0.93824783,\n",
        "        0.85796653,  0.96076982])"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = mpl.probability_hist(rrmse_2k_nnls[np.isfinite(rrmse_2k_nnls)], label='NNLS')\n",
      "fig = mpl.probability_hist(rrmse_2k_nnls_demean[np.isfinite(rrmse_2k_nnls_demean)], fig=fig, label='NNLS (demean)')\n",
      "\n",
      "fig.axes[0].plot([1,1], fig.axes[0].get_ylim(), '--k')\n",
      "fig.axes[0].plot([1/np.sqrt(2),1/np.sqrt(2)], fig.axes[0].get_ylim(), '--k')\n",
      "fig.axes[0].set_xlim([0.6,1.4])\n",
      "plt.legend()\n",
      "\n",
      "fig = mpl.probability_hist(rrmse_2k_EN[np.isfinite(rrmse_2k_EN)], label='Elastic Net')\n",
      "fig = mpl.probability_hist(rrmse_2k_EN_demean[np.isfinite(rrmse_2k_EN_demean)], fig=fig, label='Elastic Net (demean)')\n",
      "fig.axes[0].plot([1,1], fig.axes[0].get_ylim(), '--k')\n",
      "fig.axes[0].plot([1/np.sqrt(2),1/np.sqrt(2)], fig.axes[0].get_ylim(), '--k')\n",
      "fig.axes[0].set_xlim([0.6,1.4])\n",
      "plt.legend()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "<matplotlib.legend.Legend at 0x108dbd90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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X8+nTxOyXXiLOMRXT/v3EmmXLiMN09yuVSbn8T/itLW0tBkx97+vOrtv3zYNv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\nyr8sNElKAsGQIZCo+Brbl6w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       "text": [
        "<matplotlib.figure.Figure at 0x1d0f9850>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZU5HVYCO7N3jmERpl7/s8i5sMJ0GlRPQ4A6BKoJj3oLqzyIhhaZeJdw6EEJru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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x104a7750>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "whos"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = mpl.probability_hist(rrmse_2k_nnls[np.isfinite(rrmse_2k_nnls)], label='NNLS')\n",
      "fig = mpl.probability_hist(rrmse_2k_EN[np.isfinite(rrmse_2k_EN)], fig=fig, label='Elastic Net ')\n",
      "fig.axes[0].plot([1,1], fig.axes[0].get_ylim(), '--k')\n",
      "fig.axes[0].plot([1/np.sqrt(2),1/np.sqrt(2)], fig.axes[0].get_ylim(), '--k')\n",
      "fig.axes[0].set_xlim([0.6,1.4])\n",
      "plt.legend()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "<matplotlib.legend.Legend at 0x10556850>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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s8x64fK6jTptjm7KcLwcAoFKoYi8Lr2w7VmZJejr4kZ0HIaR8sMx74NZzHSl8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\nfTZK8tisWXApPBzurVsHh8j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Ti5UxZ3x8/FgPD48cT0/P7Hnz5l2QjHJQ5LJw4cKz1tbW\nZZqamgI7O7viI0eOrOy5z999993vXF1d8/z9/VOTkpKCyPhZDpSzvLzcys7OrtjIyIhvYmJSZ29v\nX9TY2GigbDlXrVr1q5mZWU1gYGBKYGBgyqhRo54q48/ziy++2OTj4/MiMDAwZcKECXFPnz4dpWwZ\nuy/Lly8/9scff8wdzHrl8uEUCCGEFEvq0ywIIYSUB5Y5QgipACxzhBBSAVjmCCGkArDMEUJIBWCZ\nI4SQCvg/CRn7o1pXKqMAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1cd80310>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}