{
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  "name": ""
 },
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 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Appendix A: A fast version\n",
      "\n",
      "This takes a (very long) while to run unless the tools in osmosis.parallel are used to parallelize the computation of all the model params and the rRMSE values.\n",
      "\n",
      "For completeness, the notebook AppendixA will do that for you, but god only knows how long that might take. This here, on the other hand, works FAST!\n",
      "\n",
      "We import the needed modules: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import nibabel as ni\n",
      "import os\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"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The following points the data-path variable to where the data is stored, relative to the install location"
     ]
    },
    {
     "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": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Set ht subject to be analyzed:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "subject = 'SUB1'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We sweep through particular regularization parameter combinations in each b value: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "alphas = [0.0001,0.0005, 0.001, 0.0025, 0.005, 0.0075, 0.01, 0.025, 0.05]\n",
      "l1_ratios = [0.0, 0.2, 0.4, 0.6, 0.8, 1.0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the following loop, we collect the median value of the rRMSE from pre-computed rRMSE files for each combination of regularization parameters: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rmse_matrix = {}\n",
      "rel_matrix = {}\n",
      "for b in [1000, 2000, 4000]: # \n",
      "    ad_rd = oio.get_ad_rd(subject, b)\n",
      "    rmse_matrix[b] = np.zeros((len(l1_ratios), len(alphas)))\n",
      "    rel_matrix[b] = np.zeros((len(l1_ratios), len(alphas)))\n",
      "    for l1_idx, l1_ratio in enumerate(l1_ratios):\n",
      "        for alpha_idx, this_alpha in enumerate(alphas):\n",
      "            \n",
      "            rrmse_fname = \"%s/%s/RMSE_b%s_l1ratio%s_alpha%s.nii.gz\"%(oio.data_path,\n",
      "                                                             subject,\n",
      "                                                             b,\n",
      "                                                             l1_ratio,\n",
      "                                                             this_alpha)\n",
      "            \n",
      "            rrmse_fname = \"%s/%s/PDD_angle_b%s_l1ratio%s_alpha%s.nii.gz\"%(oio.data_path,\n",
      "                                                             subject,\n",
      "                                                             b,\n",
      "                                                             l1_ratio,\n",
      "                                                             this_alpha)\n",
      "            \n",
      "            rrmse = ni.load(oio.data_path + '/%s/'%subject + 'RMSE_b%s_l1ratio%s_alpha%s.nii.gz'%(b, l1_ratio, this_alpha)).get_data() \n",
      "            median_rmse = np.median(rrmse[np.isfinite(rrmse)])\n",
      "            rmse_matrix[b][l1_idx, alpha_idx] = median_rmse\n",
      "            rel = ni.load(oio.data_path + '/%s/'%subject + 'PDD_angle_b%s_l1ratio%s_alpha%s.nii.gz'%(b, l1_ratio, this_alpha)).get_data() \n",
      "            median_rel = np.median(rel[np.isfinite(rel)])\n",
      "            rel_matrix[b][l1_idx, alpha_idx] = median_rel\n",
      "            \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The results are visualized: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "vmax = 1.5\n",
      "vmin = 0.5\n",
      "for b in [1000, 2000, 4000]:\n",
      "    fig, ax = plt.subplots(1)\n",
      "    cax = ax.imshow(rmse_matrix[b], interpolation='nearest', cmap=cm.RdYlGn_r, vmax=vmax, vmin=vmin)\n",
      "    cbar = fig.colorbar(cax, ticks=[0.5, 1., 1.5])\n",
      "    cax.axes.set_xticks([0,1,2,3,4,5,6,7,8])\n",
      "    cax.axes.set_xticklabels([str('%1.4f'%this) for this in alphas])\n",
      "    cax.axes.set_xlabel(r'$\\lambda$')\n",
      "    cax.axes.set_yticks([0,1,2,3,4,5])\n",
      "    cax.axes.set_yticklabels([str('%1.1f'%(1-this)) for this in l1_ratios])\n",
      "\n",
      "    cax.axes.set_ylabel(r'$\\alpha$')\n",
      "    im = ax.matshow(rmse_matrix[b], cmap=matplotlib.cm.RdYlGn_r, vmax=vmax, vmin=vmin)\n",
      "    fig.set_size_inches([8,6])\n",
      "    fig.savefig('figures/AppendixA_acc_b%s.svg'%b)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ImgAA+ORK0mQhEAAAPlFpAgCsc+U2eiRNAIB1DM8CAOCT6TdpvQYTj8dVWlqq\nWCymhoaGk36+efNmTZ48WRUVFaqoqNCdd945ZJxUmgCAUSmZTGrlypXatGmTIpGI5s6dq+rqapWV\nlQ1od9lll2nDhg2+jkmlCQCwLohKs62tTSUlJSoqKlJOTo5qamrU0tJy8rlPYz6VShMAYJ357ba0\n9j/77LNP+l53d7cKCwtT29FoVNu3bx/QxvM8bd26VeXl5YpEIvrlL3+pGTNmDHoekiYAwKqgVs56\nnjdsmzlz5iiRSCg3N1cbN27U1Vdfrb179w7anuFZAMCoFIlElEgkUtuJRELRaHRAm0mTJik3N1eS\nVFVVpb6+Ph06dGjQY5I0AQCjUmVlpTo6OtTZ2ane3l6tW7dO1dXVA9r09PSkKt22tjYZY5SXlzfo\nMRmeBQCMStnZ2WpsbNTChQuVTCZVW1ursrIyNTU1SZLq6urU3NysNWvWKDs7W7m5uXrssceGPKZn\nXLkNAwAAljE8CwCATyRNAAB8ImkCAOATSRMAAJ9ImgAA+ETSBADAp/8PR6MROeJLXt4AAAAASUVO\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5422e10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x54ceb90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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A4BOVJgDAOlcqTZImAMA6kiYAAD65chs95jQBAPCJShMAYB3DswAA+ETSBADA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\n+v+KsByIkoEVMwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5a1e3d0>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We also visualize the reliability of the PDD predicted from the SFM model parameters in each combination of regularization parameters:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for b in [1000, 2000, 4000]:\n",
      "    fig, ax = plt.subplots(1)\n",
      "    cax = ax.imshow(rel_matrix[b], interpolation='nearest', cmap=cm.OrRd, vmax=90, vmin=0)\n",
      "    cbar = fig.colorbar(cax)\n",
      "    cax.axes.set_xticks([0,1,2,3,4,5,6,7,8])\n",
      "    cax.axes.set_xticklabels([str('%1.4f'%this) for this in alphas])\n",
      "    cax.axes.set_xlabel(r'$\\lambda$')\n",
      "    cax.axes.set_yticks([0,1,2,3,4,5])\n",
      "    cax.axes.set_yticklabels([str('%1.1f'%(1-this)) for this in l1_ratios])\n",
      "\n",
      "    cax.axes.set_ylabel(r'$\\alpha$')\n",
      "    #ax.matshow(rmse_matrix[b], cmap=matplotlib.cm.hot)\n",
      "    fig.set_size_inches([8,6])\n",
      "    fig.savefig('figures/AppendixA_rel_b%s.svg'%b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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qqkotLS26/fbb9f777ysQCKi0tFTDhw/vtg9XKsqqqiqlpaUpEAgoISFBhYWFKisr69Dm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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x62bf190>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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AAPflJAxRTsKQ6P6zn5xx780G203Rp0yZourqatXW1qq1tVUbNmxQQUFBhzYF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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x54be050>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x8fab590>"
       ]
      }
     ],
     "prompt_number": 17
    }
   ],
   "metadata": {}
  }
 ]
}