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  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8ad9fe94",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Walker:\n",
    "    # ...\n",
    "    \n",
    "    def sample_next_step(self, current_i, current_j, random_state=np.random):\n",
    "        \"\"\" Sample a new position for the walker. \"\"\"\n",
    "        # Combine the next-step proposal with the context map to get a\n",
    "        # next-step probability map\n",
    "        next_step_map = self._next_step_proposal(current_i, current_j)\n",
    "        selection_map = self._compute_next_step_probability(next_step_map)\n",
    "\n",
    "        # Draw a new position from the next-step probability map\n",
    "        r = random_state.rand()\n",
    "        cumulative_map = np.cumsum(selection_map)\n",
    "        cumulative_map = cumulative_map.reshape(selection_map.shape)\n",
    "        i_next, j_next = np.argwhere(cumulative_map >= r)[0]\n",
    "\n",
    "        return i_next, j_next\n",
    "\n",
    "    def _next_step_proposal(self, current_i, current_j):\n",
    "        \"\"\" Create the 2D proposal map for the next step of the walker. \"\"\"\n",
    "        # 2D Gaussian distribution , centered at current position,\n",
    "        # and with different standard deviations for i and j\n",
    "        grid_ii, grid_jj = self._grid_ii, self._grid_jj\n",
    "        sigma_i, sigma_j = self.sigma_i, self.sigma_j\n",
    "\n",
    "        rad = (\n",
    "            (((grid_ii - current_i) ** 2) / (sigma_i ** 2))\n",
    "            + (((grid_jj - current_j) ** 2) / (sigma_j ** 2))\n",
    "        )\n",
    "\n",
    "        p_next_step = np.exp(-(rad / 2.0)) / (2.0 * np.pi * sigma_i * sigma_j)\n",
    "        return p_next_step / p_next_step.sum()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "95148e45",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Walker:\n",
    "    # ...\n",
    "\n",
    "    def _next_step_proposal(self, current_i, current_j):\n",
    "        \"\"\" Create the 2D proposal map for the next step of the walker. \"\"\"\n",
    "        raise NotImplementedError(\"`_next_step_proposal` not implemented\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "da34226f",
   "metadata": {},
   "outputs": [],
   "source": [
    "class GaussianWalker(Walker):\n",
    "    # ...\n",
    "\n",
    "    def _next_step_proposal(self, current_i, current_j):\n",
    " \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "class RectangularWalker(Walker):\n",
    "    # ...\n",
    "\n",
    "    def _next_step_proposal(self, current_i, current_j):\n",
    "\n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "class JumpingWalker(Walker):\n",
    "    # ...\n",
    "\n",
    "    def _next_step_proposal(self, current_i, current_j):\n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cfd90d16",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Walker:\n",
    "    # ...\n",
    "\n",
    "\n",
    "    def _compute_next_step_probability(self, next_step_map):\n",
    "        \"\"\" Compute the next step probability map from next step proposal and\n",
    "        context map. \"\"\"\n",
    "        next_step_probability = next_step_map * self.context_map\n",
    "        next_step_probability /= next_step_probability.sum()\n",
    "        return next_step_probability\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "72041675",
   "metadata": {},
   "outputs": [],
   "source": [
    "class GaussianWalkerWithProductInteraction(Walker):\n",
    "    def _next_step_proposal(self, current_i, current_j):\n",
    "        # ...\n",
    "    def _compute_next_step_probability(self, next_step_map):\n",
    "        # ...\n",
    "\n",
    "        \n",
    "class GaussianWalkerWithSumInteraction(Walker):\n",
    "    def _next_step_proposal(self, current_i, current_j):\n",
    "        # ...\n",
    "    def _compute_next_step_probability(self, next_step_map):\n",
    "        # ...\n",
    "\n",
    "        \n",
    "class RectangularWalkerWithProductInteraction(Walker):\n",
    "    def _next_step_proposal(self, current_i, current_j):\n",
    "        # ...\n",
    "    def _compute_next_step_probability(self, next_step_map):\n",
    "        # ...\n",
    "\n",
    "        \n",
    "class RectangularWalkerWithSumInteraction(Walker):\n",
    "    def _next_step_proposal(self, current_i, current_j):\n",
    "        # ...\n",
    "    def _compute_next_step_probability(self, next_step_map):\n",
    "        # ...\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5ee2e200",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Walker:\n",
    "    def __init__(self, size, context_map, next_step_proposal, next_step_proposal_arguments):\n",
    "        self.next_step_proposal = next_step_proposal\n",
    "        # ...\n",
    "\n",
    "    \n",
    "    def sample_next_step(self, current_i, current_j, random_state=np.random):\n",
    "        \"\"\" Sample a new position for the walker. \"\"\"\n",
    "        # Combine the next-step proposal with the context map to get a\n",
    "        # next-step probability map\n",
    "        next_step_map = self.next_step_proposal(current_i, current_j, **next_step_proposal_arguments)\n",
    "        selection_map = self._compute_next_step_probability(next_step_map)\n",
    "\n",
    "        # Draw a new position from the next-step probability map\n",
    "        r = random_state.rand()\n",
    "        cumulative_map = np.cumsum(selection_map)\n",
    "        cumulative_map = cumulative_map.reshape(selection_map.shape)\n",
    "        i_next, j_next = np.argwhere(cumulative_map >= r)[0]\n",
    "\n",
    "        return i_next, j_next\n"
   ]
  }
 ],
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