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   "source": [
    "EEG parametric leadfield computation - On all ROI elements\n",
    "==========================================================\n",
    "\n",
    "The computation of a parametric solution for the EEG leadfield matrix takes almost the same parameters as the single problem.\n",
    "\n",
    "The first step is to load the finite element model created before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from shamo import FEM\n",
    "\n",
    "model = FEM.load(\"../../derivatives/fem_from_labels/fem_from_labels.json\")"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
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   "source": [
    "Next, we import the :py:class:`~shamo.eeg.leadfield.parametric.problem.ProbParamEEGLeadfield` class and create an instance of it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from shamo.eeg import ProbParamEEGLeadfield\n",
    "\n",
    "problem = ProbParamEEGLeadfield()"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "As for the single problem, we must set the electrical conductivity of the tissues but this time, we must provide probability distributions. If a parameter is fixed, the :py:class:`~shamo.core.distributions.constant.DistConstant` can be used. Otherwise, we can pick from the following probability laws:\n",
    "\n",
    "* :py:class:`~shamo.core.distributions.uniform.DistUniform`\n",
    "* :py:class:`~shamo.core.distributions.normal.DistNormal`\n",
    "* :py:class:`~shamo.core.distributions.normal.DistTruncNormal`\n",
    "\n",
    "For the sake of this example, we only use uniform distributions and define the ranges with the values reported in :footcite:`mccann_variation_2019`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from shamo import DistUniform\n",
    "\n",
    "problem.sigmas.set(\"scalp\", DistUniform(0.137, 2.1))\n",
    "problem.sigmas.set(\"gm\", DistUniform(0.06, 2.47))\n",
    "problem.sigmas.set(\"wm\", DistUniform(0.0646, 0.81))"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "The electrodes and the regions of interest are set as for the :py:class:`~shamo.eeg.leadfield.single.problem.ProbEEGLeadfield`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "problem.reference.add(\"IZ\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "problem.markers.adds([\"NZ\", \"LeftEar\", \"RightEar\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "problem.rois.add(\"gm\")"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "Finally, we can solve the problem to generate `n_evals` sub-solutions. The `method` parameter determines how the solutions are solved:\n",
    "\n",
    "* `\"sequential\"` means each solution is computed one at a time.\n",
    "* `\"multiprocessing\"` means `n_proc` solutions are computed in parallel on the same computing node.\n",
    "* `\"jobs\"` means a python script is generated for every sub-solution. Those scripts can be run in any way we like, on a HPC unit or on the computer. If this solution is chosen, the :py:func:`~shamo.eeg.leadfield.parametric.problem.ProbParamEEGLeadfield.finalize` method must be called after all the sub-solutions are generated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "solution = problem.solve(\"parametric_ssp-elems\", \"../../derivatives/eeg_leadfield\", model, n_evals=4, method=\"multiprocessing\", n_proc=4)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "We now have multiple sub-solutions accessible with a single parametric solution. To really use the power of those results, we still have to generate a surrogate model.\n",
    "\n",
    ".. footbibliography::"
   ]
  }
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