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   "source": [
    "EEG parametric leadfield sensitivity analysis\n",
    "=============================================\n",
    "\n",
    "As for the surrogate model in the previous example, we have to build a simple model from the parametric solution generated before. Since the goal of this example is to compute the Sobol sensitivity indices, we have to produce a scalar value representing the full matrix and then build the surrogate model.\n",
    "\n",
    "The first steps are the same as before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from shamo.eeg import SolParamEEGLeadfield\n",
    "\n",
    "solution = SolParamEEGLeadfield.load(\"../../derivatives/eeg_leadfield/parametric_ssp-grid/parametric_ssp-grid.json\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from shamo.eeg import SolEEGLeadfield\n",
    "\n",
    "reference = SolEEGLeadfield.load(\"../../derivatives/eeg_leadfield/single_ssp-grid/single_ssp-grid.json\")"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "We then define the metric function that takes both a reference matrix and another matrix to compare to. This function must return a single scalar value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def metric(ref, mat):\n",
    "    return np.linalg.norm(ref - mat, \"fro\")"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "Next, we use the :py:class:`~shamo.eeg.leadfield.surrogate.SurrEEGLeadfieldToRef` class to build such model and fit it with the metric function as a parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from shamo.eeg import SurrEEGLeadfieldToRef\n",
    "\n",
    "surrogate = SurrEEGLeadfieldToRef.fit(\"eeg_param_leadfield_ssp-dist_surr-toref\", \"../../derivatives/eeg_leadfield/\", solution, ref=reference, metric=metric)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "In the end, we simply have to compute the Sobol indices for this model. They are both returned as a dictionary and stored as a JSON file in the directory of the object.\n",
    "\n",
    ".. note::\n",
    "\n",
    "   This method computes the first, second and total Sobol sensitivity indices for the surrogate model with regard to all the varying parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "s_i = surrogate.gen_sobol()"
   ]
  }
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