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  "name": ""
 },
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 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import nibabel as ni\n",
      "\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": 1
    },
    {
     "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": "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": "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"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "l1_ratio = 0.8\n",
      "alpha = 0.0005 \n",
      "solver_params = dict(l1_ratio=l1_ratio, alpha=alpha, fit_intercept=False, positive=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ad_rd = oio.get_ad_rd(subject, 1000)\n",
      "SD_1k_1 = ssd.SparseDeconvolutionModel(*data_1k_1, mask=wm_mask,  params_file = 'temp', axial_diffusivity=ad_rd[0]['AD'], radial_diffusivity=ad_rd[0]['RD'], solver_params=solver_params)\n",
      "SD_1k_2 = ssd.SparseDeconvolutionModel(*data_1k_2, mask=wm_mask,  params_file = 'temp', axial_diffusivity=ad_rd[1]['AD'], radial_diffusivity=ad_rd[1]['RD'], solver_params=solver_params)\n",
      "ad_rd = oio.get_ad_rd(subject, 2000)\n",
      "SD_2k_1 = ssd.SparseDeconvolutionModel(*data_2k_1, mask=wm_mask,  params_file = 'temp', axial_diffusivity=ad_rd[0]['AD'], radial_diffusivity=ad_rd[0]['RD'], solver_params=solver_params)\n",
      "SD_2k_2 = ssd.SparseDeconvolutionModel(*data_2k_2, mask=wm_mask,  params_file = 'temp', axial_diffusivity=ad_rd[1]['AD'], radial_diffusivity=ad_rd[1]['RD'], solver_params=solver_params)\n",
      "ad_rd = oio.get_ad_rd(subject, 4000)\n",
      "SD_4k_1 = ssd.SparseDeconvolutionModel(*data_4k_1, mask=wm_mask,  params_file = 'temp', axial_diffusivity=ad_rd[0]['AD'], radial_diffusivity=ad_rd[0]['RD'], solver_params=solver_params)\n",
      "SD_4k_2 = ssd.SparseDeconvolutionModel(*data_4k_2, mask=wm_mask,  params_file = 'temp', axial_diffusivity=ad_rd[1]['AD'], radial_diffusivity=ad_rd[1]['RD'], solver_params=solver_params)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_1.bvals\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_1.bvecs\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_2.bvals\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_2.bvecs\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.bvals\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.bvecs\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.bvals\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.bvecs\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_1.bvals\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_1.bvecs\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_2.bvals\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_2.bvecs\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#pred_1k_1 = np.concatenate([SD_1k_1.S0[...,np.newaxis], SD_1k_1.fit], -1)\n",
      "#pred_1k_2 = np.concatenate([SD_1k_2.S0[...,np.newaxis], SD_1k_2.fit], -1)\n",
      "#new_bvecs1 = np.concatenate([np.array([[0,0,0]]).T, SD_1k_1.bvecs[:, SD_1k_1.b_idx]], -1)\n",
      "#new_bvecs2 = np.concatenate([np.array([[0,0,0]]).T, SD_1k_2.bvecs[:, SD_1k_2.b_idx]], -1)\n",
      "#new_bvals = np.hstack([0, SD_1k_1.bvals[:,SD_1k_1.b_idx]])\n",
      "#TM_1k_1 = dti.TensorModel(pred_1k_1, new_bvecs1, new_bvals, mask=wm_mask, params_file='temp')\n",
      "#TM_1k_2 = dti.TensorModel(pred_1k_2, new_bvecs2, new_bvals, mask=wm_mask, params_file='temp')\n",
      "\n",
      "#pred_2k_1 = np.concatenate([SD_2k_1.S0[...,np.newaxis], SD_2k_1.fit], -1)\n",
      "#pred_2k_2 = np.concatenate([SD_2k_2.S0[...,np.newaxis], SD_2k_2.fit], -1)\n",
      "#new_bvecs1 = np.concatenate([np.array([[0,0,0]]).T, SD_2k_1.bvecs[:, SD_2k_1.b_idx]], -1)\n",
      "#new_bvecs2 = np.concatenate([np.array([[0,0,0]]).T, SD_2k_2.bvecs[:, SD_2k_2.b_idx]], -1)\n",
      "#new_bvals = np.hstack([0, SD_2k_1.bvals[:,SD_2k_1.b_idx]])\n",
      "#TM_2k_1 = dti.TensorModel(pred_2k_1, new_bvecs1, new_bvals, mask=wm_mask, params_file='temp')\n",
      "#TM_2k_2 = dti.TensorModel(pred_2k_2, new_bvecs2, new_bvals, mask=wm_mask, params_file='temp')\n",
      "\n",
      "#pred_4k_1 = np.concatenate([SD_4k_1.S0[...,np.newaxis], SD_4k_1.fit], -1)\n",
      "#pred_4k_2 = np.concatenate([SD_4k_2.S0[...,np.newaxis], SD_4k_2.fit], -1)\n",
      "#new_bvecs1 = np.concatenate([np.array([[0,0,0]]).T, SD_4k_1.bvecs[:, SD_4k_1.b_idx]], -1)\n",
      "#new_bvecs2 = np.concatenate([np.array([[0,0,0]]).T, SD_4k_2.bvecs[:, SD_4k_2.b_idx]], -1)\n",
      "#new_bvals = np.hstack([0, SD_4k_1.bvals[:,SD_4k_1.b_idx]])\n",
      "#TM_4k_1 = dti.TensorModel(pred_4k_1, new_bvecs1, new_bvals, mask=wm_mask, params_file='temp')\n",
      "#TM_4k_2 = dti.TensorModel(pred_4k_2, new_bvecs2, new_bvals, mask=wm_mask, params_file='temp')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "TM_1k_1 = dti.TensorModel(*data_1k_1, mask=wm_mask, params_file='temp')\n",
      "TM_1k_2 = dti.TensorModel(*data_1k_2, mask=wm_mask, params_file='temp')\n",
      "TM_2k_1 = dti.TensorModel(*data_2k_1, mask=wm_mask, params_file='temp')\n",
      "TM_2k_2 = dti.TensorModel(*data_2k_2, mask=wm_mask, params_file='temp')\n",
      "TM_4k_1 = dti.TensorModel(*data_4k_1, mask=wm_mask, params_file='temp')\n",
      "TM_4k_2 = dti.TensorModel(*data_4k_2, mask=wm_mask, params_file='temp')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_1.bvals\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_1.bvecs\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_2.bvals\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_2.bvecs\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.bvals\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.bvecs\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.bvals\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.bvecs\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_1.bvals\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_1.bvecs\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_2.bvals\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_2.bvecs\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Reliability estimated via the tensor model: \n",
      "pdd_rel_1k = oza.pdd_reliability(TM_1k_1, TM_1k_2)\n",
      "pdd_rel_2k = oza.pdd_reliability(TM_2k_1, TM_2k_2)\n",
      "pdd_rel_4k = oza.pdd_reliability(TM_4k_1, TM_4k_2)\n",
      "\n",
      "# Or directly on the SD model:\n",
      "#pdd_rel_1k = oza.pdd_reliability(SD_1k_1, SD_1k_2)\n",
      "#pdd_rel_2k = oza.pdd_reliability(SD_2k_1, SD_2k_2)\n",
      "#pdd_rel_4k = oza.pdd_reliability(SD_4k_1, SD_4k_2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_1.nii.gz\n",
        "Fitting TensorModel params using dipy"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b1000_2.nii.gz"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Fitting TensorModel params using dipy"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_1.nii.gz"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Fitting TensorModel params using dipy"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b2000_2.nii.gz"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Fitting TensorModel params using dipy"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_1.nii.gz"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Fitting TensorModel params using dipy"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Loading from file: /Users/arokem/usr/lib/python2.7/site-packages/osmosis/data/SUB1/SUB1_b4000_2.nii.gz"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Fitting TensorModel params using dipy"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = mpl.probability_hist(pdd_rel_1k[np.isfinite(pdd_rel_1k)], label='b=%s'%str(1000), color=[0.8, 0.8, 0.8])\n",
      "print(\"For b=1000, the median PDD reliability is %2.2f\"%np.median(pdd_rel_1k[np.isfinite(pdd_rel_1k)]))\n",
      "fig = mpl.probability_hist(pdd_rel_2k[np.isfinite(pdd_rel_2k)], fig=fig, label='b=%s'%str(2000), color=[0.59, 0.59, 0.59])\n",
      "print(\"For b=2000, the median PDD reliability is %2.2f\"%np.median(pdd_rel_2k[np.isfinite(pdd_rel_2k)]))\n",
      "fig = mpl.probability_hist(pdd_rel_4k[np.isfinite(pdd_rel_4k)], fig=fig, label='b=%s'%str(4000), color=[0.32, 0.32, 0.32])\n",
      "print(\"For b=4000, the median PDD reliability is %2.2f\"%np.median(pdd_rel_4k[np.isfinite(pdd_rel_4k)]))\n",
      "ax = fig.axes[0]\n",
      "ax.set_xlim([0,90])\n",
      "plt.legend()\n",
      "fig.savefig('figures/tensor_pdd_reliability.svg')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "For b=1000, the median PDD reliability is 3.62\n",
        "For b=2000, the median PDD reliability is 3.80\n",
        "For b=4000, the median PDD reliability is 5.01\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PaG5uxjfffIOvvvoqoDV9/vnniI6ORmZm5pCX9wbq9/fd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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x100741e10>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pdd_rel_1k = oza.pdd_reliability(SD_1k_1, SD_1k_2)\n",
      "pdd_rel_2k = oza.pdd_reliability(SD_2k_1, SD_2k_2)\n",
      "pdd_rel_4k = oza.pdd_reliability(SD_4k_1, SD_4k_2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " \r",
        "SparseDeconvolutionModel.model_params [****************100%******************]  64463 of 64464 complete "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = mpl.probability_hist(pdd_rel_1k[np.isfinite(pdd_rel_1k)], label='b=%s'%str(1000), color=[0.8, 0.8, 0.8])\n",
      "print(\"For b=1000, the median PDD reliability is %2.2f\"%np.median(pdd_rel_1k[np.isfinite(pdd_rel_1k)]))\n",
      "fig = mpl.probability_hist(pdd_rel_2k[np.isfinite(pdd_rel_2k)], fig=fig, label='b=%s'%str(2000), color=[0.59, 0.59, 0.59])\n",
      "print(\"For b=2000, the median PDD reliability is %2.2f\"%np.median(pdd_rel_2k[np.isfinite(pdd_rel_2k)]))\n",
      "fig = mpl.probability_hist(pdd_rel_4k[np.isfinite(pdd_rel_4k)], fig=fig, label='b=%s'%str(4000), color=[0.32, 0.32, 0.32])\n",
      "print(\"For b=4000, the median PDD reliability is %2.2f\"%np.median(pdd_rel_4k[np.isfinite(pdd_rel_4k)]))\n",
      "ax = fig.axes[0]\n",
      "ax.set_xlim([0,90])\n",
      "plt.legend()\n",
      "fig.savefig('figures/sfm_pdd_reliability.svg')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "For b=1000, the median PDD reliability is 31.08\n",
        "For b=2000, the median PDD reliability is 35.90"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "For b=4000, the median PDD reliability is 37.80\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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DUVNTgxs3bqCurg5lZWWmLocQ8hASbNiLRCJoNBpTl/FAFBcX4/bt29DpdJ2u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\nAMV9Bto8jkU2AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1090371d0>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    }
   ],
   "metadata": {}
  }
 ]
}