experiments_paper.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "23f186bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "import PSILOGIT\n",
    "import numpy as np\n",
    "from PSILOGIT.tools import *\n",
    "from sklearn.linear_model import LogisticRegression, LogisticRegressionCV\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba774be9",
   "metadata": {},
   "source": [
    "# Experiments for Section 6.1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b5bef8f",
   "metadata": {},
   "source": [
    "### First example with a small selection event. $p=20, \\lambda=1.5, n=10$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "33f249ce",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    }
   ],
   "source": [
    "model = PSILOGIT.PSILOGIT(truetheta=np.ones(20), regularization=1.5,  n=10, p=20)\n",
    "print('Size of the set of active variables: ', len(model.M))\n",
    "nbM_admissibles, ls_states_admissibles = model.compute_selection_event(compare_with_energy=True)\n",
    "print('Size of the selection event: ', len(ls_states_admissibles))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "198723e6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear_temperature(t):\n",
    "    return 0.2/np.log(t+1)\n",
    "\n",
    "states, ls_FNR, energies = model.SEI_SLR(total_length_SEISLR_path=50000, backup_start_time=2000, temperature=linear_temperature, repulsing_force=True, random_start=True, conditioning_signs=False, seed=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "445c72db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.last_visited_states(states, ls_states_admissibles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "521c5a73",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.histo_time_in_selection_event(states, ls_states_admissibles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "b38d4d8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "q = len(ls_states_admissibles)\n",
    "cov = np.zeros((q,q))\n",
    "for i in range(q):\n",
    "    for j in range(q):\n",
    "        cov[i,j] = np.sum(np.array(ls_states_admissibles[i])!=np.array(ls_states_admissibles[j])) / model.X.shape[0]\n",
    "fig, ax = plt.subplots()\n",
    "heatmap = ax.pcolor(cov)\n",
    "\n",
    "#legend\n",
    "cbar = plt.colorbar(heatmap)\n",
    "\n",
    "# put the major ticks at the middle of each cell\n",
    "ax.set_xticks(np.arange(cov.shape[1]) + 0.5, minor=False)\n",
    "ax.set_yticks(np.arange(cov.shape[0]) + 0.5, minor=False)\n",
    "ax.invert_yaxis()\n",
    "\n",
    "#labels\n",
    "column_labels = [int(fy) for fy in nbM_admissibles]\n",
    "row_labels = column_labels\n",
    "ax.set_xticklabels(column_labels, minor=False)\n",
    "ax.set_yticklabels(row_labels, minor=False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4be1a9a4",
   "metadata": {},
   "source": [
    "### Second example with a larger selection event. $p=15, \\lambda=2, n=10$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4ceb4d54",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of the set of active variables:  2\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "835748990c9e44369faf04b8d6803d28",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/100000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of the selection event:  22\n"
     ]
    }
   ],
   "source": [
    "model = PSILOGIT.PSILOGIT(truetheta=np.zeros(15), regularization=2,  n=10, p=15)\n",
    "print('Size of the set of active variables: ', len(model.M))\n",
    "\n",
    "def linear_temperature(t):\n",
    "    return 0.2/np.log(t+1)\n",
    "\n",
    "states, ls_FNR, energies = model.SEI_SLR(total_length_SEISLR_path=100000, backup_start_time=2000, temperature=linear_temperature, repulsing_force=True, random_start=True, conditioning_signs=False, seed=0)\n",
    "nbM_admissibles, ls_states_admissibles = model.compute_selection_event(compare_with_energy=True)\n",
    "print('Size of the selection event: ', len(ls_states_admissibles))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c8ebcf42",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.last_visited_states(states, ls_states_admissibles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f3ef60c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.histo_time_in_selection_event(states, ls_states_admissibles, rotation_angle=80)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea55eef9",
   "metadata": {},
   "source": [
    "# Experiments of Section 6.2.2: Calibration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "276c9bed",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of the set of active variables:  8\n"
     ]
    },
    {
     "data": {
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       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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       "version_minor": 0
      },
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       "model_id": "83c4353dd4094aebb2414b1398896283",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/287 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## CHOOSE THE REGULARIZATION PARAMETER\n",
    "lamb = 0.5\n",
    "\n",
    "model = PSILOGIT.PSILOGIT(truetheta=np.zeros(10), regularization=lamb, n=100, p=10)\n",
    "print('Size of the set of active variables: ', len(model.M))\n",
    "states = model.SEI_by_sampling(model.sig, nb_ite=100000)\n",
    "thetanull = np.zeros(model.X.shape[1])\n",
    "signull = sigmoid(model.X @ thetanull)\n",
    "if np.max(np.abs(signull-model.sig))<1e-3:\n",
    "    statesnull = np.copy(states)\n",
    "else:\n",
    "    statesnull = model.SEI_by_sampling(signull, nb_ite=100000)\n",
    "tildeGN12, barpi = model.params_saturated(signull, statesnull)\n",
    "lspvals_selec, lspvals_sat, gaps = model.pval_SIGLE(states, barpi, l2_regularization=100000, grad_descent={'lr':0.01,'return_gaps':True,'max_ite':10000}, \n",
    "                                                    calibrated_from_samples=False, statesnull=statesnull)\n",
    "gamma = np.zeros(len(model.M))\n",
    "gamma[0] = 1\n",
    "lspvals_tay_1 = model.pval_taylor(states, thetanull=thetanull, gamma=gamma)\n",
    "lspvals_tay_Bon = model.pval_taylor(states, thetanull=thetanull, mode='Bonferroni')\n",
    "lspvals_naive = model.pval_weak_learner(statesnull, states, barpi, signull=signull)\n",
    "lists_pvalues = [lspvals_naive, lspvals_tay_1, lspvals_tay_Bon, lspvals_selec, lspvals_sat]\n",
    "names = ['Weak learner', \"TT-1\", 'TT-Bonferroni', 'SIGLE Selected', 'SIGLE Saturated']\n",
    "model.plot_cdf_pvalues(lists_pvalues, names, states = states, sigalt=model.sig)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54c40c76",
   "metadata": {},
   "source": [
    "# Experiments of Section 6.2.3\n",
    "\n",
    "\n",
    "## Power analysis: Setting 1\n",
    "### Localized and Disseminated alternatives"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f88ae106",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of the set of active variables:  5\n"
     ]
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      "text/plain": [
       "  0%|          | 0/100000 [00:00<?, ?it/s]"
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       "  0%|          | 0/100000 [00:00<?, ?it/s]"
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## CHOOSE THE SIGNAL STRENGTH\n",
    "nu = 0.04\n",
    "\n",
    "## CHOOSE THE MODE (LOCALIZED OR DISSEMINATED)\n",
    "modes = ['disseminated-signal' ,'localized-signal']\n",
    "mode = modes[0]\n",
    "\n",
    "## CHOOSE THE NUMBER OF STEP FOR THE REJECTION SAMPLING METHOD \n",
    "## (for the results presented in the paper, we used nb_ite=3 000 000)\n",
    "nb_ite = 100000\n",
    "\n",
    "\n",
    "if mode=='localized-signal':\n",
    "    vartheta = np.zeros(10)\n",
    "    vartheta[0] = nu\n",
    "else:\n",
    "    vartheta = nu*np.ones(10)\n",
    "\n",
    "model = PSILOGIT.PSILOGIT(truetheta=vartheta, regularization=5, n=100, p=10)\n",
    "print('Size of the set of active variables: ', len(model.M))\n",
    "states = model.SEI_by_sampling(model.sig, nb_ite=nb_ite)\n",
    "thetanull = np.zeros(model.X.shape[1])\n",
    "signull = sigmoid(model.X @ thetanull)\n",
    "if np.max(np.abs(signull-model.sig))<1e-3:\n",
    "    statesnull = np.copy(states)\n",
    "else:\n",
    "    statesnull = model.SEI_by_sampling(signull, nb_ite=nb_ite)\n",
    "tildeGN12, barpi = model.params_saturated(signull, statesnull)\n",
    "lspvals_selec, lspvals_sat, gaps = model.pval_SIGLE(states, barpi, l2_regularization=100000, grad_descent={'lr':0.01,'return_gaps':True,'max_ite':10000}, calibrated_from_samples=True, statesnull=statesnull)\n",
    "gamma = np.zeros(len(model.M))\n",
    "gamma[0] = 1\n",
    "lspvals_tay_1 = model.pval_taylor(states, thetanull=thetanull, gamma=gamma)\n",
    "lspvals_tay_Bon = model.pval_taylor(states, thetanull=thetanull, mode='Bonferroni')\n",
    "lspvals_naive = model.pval_weak_learner(statesnull, states, barpi, signull=signull)\n",
    "lists_pvalues = [lspvals_naive, lspvals_tay_1, lspvals_tay_Bon, lspvals_selec, lspvals_sat]\n",
    "names = ['Weak learner', \"TT-1\", 'TT-Bonferroni', 'SIGLE Selected', 'SIGLE Saturated']\n",
    "model.plot_cdf_pvalues(lists_pvalues, names, states = states, sigalt=model.sig)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb4b2f4c",
   "metadata": {},
   "source": [
    "### Code to reproduce the figure of the paper presenting the power with respect to the signal strength $\\nu$: To run on a cluster !"
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     "text": [
      "Size of the set of active variables:  7\n",
      "nu:  0.28\n"
     ]
    },
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      "Size of the set of active variables:  7\n",
      "nu:  0.3\n"
     ]
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   "source": [
    "assert False, 'Comment the first assertion if we are aware that this portion of code will take several hours to be completely executed. Create beforehand a folder \"data\" at the root.'\n",
    "modes = ['disseminated-signal' ,'localized-signal']\n",
    "mode = modes[0]\n",
    "\n",
    "if mode=='localized-signal':\n",
    "    lsnu = [round(0.1*i,2) for i in range(0,11)]\n",
    "else:\n",
    "    lsnu =  [round(0.02*i,2) for i in range(0,16)]\n",
    "    \n",
    "    \n",
    "for nu in lsnu:\n",
    "    theta = nu * np.ones(10)\n",
    "    model = PSILOGIT.PSILOGIT(truetheta=theta, regularization=5, n=100, p=len(theta))\n",
    "    print('Size of the set of active variables: ', len(model.M))\n",
    "    print('nu: ', nu)\n",
    "    states = model.SEI_by_sampling(model.sig, nb_ite=3000000)\n",
    "    np.save('data/states-n100-p10-lamb5-nu'+str(nu)+'.npy',states)\n",
    "\n",
    "names = ['Weak learner', \"TT-1\", 'TT-Bonferroni', 'SIGLE Selected', 'SIGLE Saturated']\n",
    "\n",
    "power = np.zeros((len(lsnu),len(names)))\n",
    "for idxnu, nu in enumerate(lsnu):\n",
    "    if mode=='localized-signal':\n",
    "        vartheta = np.zeros(10)\n",
    "        vartheta[0]=nu\n",
    "    else:\n",
    "        vartheta = nu*np.ones(10)\n",
    "    model = PSILOGIT.PSILOGIT(truetheta=vartheta, regularization=5, n=100, p=len(vartheta))\n",
    "    print('Size of the set of active variables: ', len(model.M))\n",
    "    print('nu: ', nu)\n",
    "    if mode == 'localized-signal':\n",
    "        states = np.load('data/states-1coor-n100-p10-lamb5-nu'+str(nu)+'.npy')\n",
    "    else:\n",
    "        states = np.load('data/states-n100-p10-lamb5-nu'+str(nu)+'.npy')\n",
    "    states = states\n",
    "    thetanull = np.zeros(model.X.shape[1])\n",
    "    signull = sigmoid(model.X @ thetanull)\n",
    "    if mode == 'localized-signal':\n",
    "        statesnull = np.load('data/states-1coor-n100-p10-lamb5-nu0.0.npy')\n",
    "    else:\n",
    "        statesnull = np.load('data/states-n100-p10-lamb5-nu0.0.npy')\n",
    "    tildeGN12, barpi = model.params_saturated(signull, statesnull)\n",
    "\n",
    "    lspvals_selec, lspvals_sat, gaps = model.pval_SIGLE(states, barpi, l2_regularization=100000, grad_descent={'lr':0.01,'return_gaps':True,'max_ite':10000}, calibrated_from_samples=True, statesnull=statesnull)\n",
    "\n",
    "    gamma = np.zeros(len(model.M))\n",
    "    gamma[0] = 1\n",
    "    lspvals_tay_1 = model.pval_taylor(states, thetanull=thetanull, gamma=gamma)\n",
    "    lspvals_tay_Bon = model.pval_taylor(states, thetanull=thetanull, mode='Bonferroni')\n",
    "    lspvals_naive = model.pval_weak_learner(statesnull, states, barpi, signull=signull)\n",
    "\n",
    "    lists_pvalues = [lspvals_naive, lspvals_tay_1, lspvals_tay_Bon, lspvals_selec, lspvals_sat]\n",
    "    power[idxnu,:] = model.compute_power(lists_pvalues, names, states = states, sigalt=model.sig)\n",
    "\n",
    "if mode == 'localized-signal':\n",
    "    np.save('data/1coor-n100-p10-lamb5-power-nu.npy',power)\n",
    "else:\n",
    "    np.save('data/n100-p10-lamb5-power-nu.npy',power)\n",
    "\n",
    "for j,name in enumerate(np.array(names)):\n",
    "    plt.plot(lsnu, power[:,j], label=name)\n",
    "if mode=='localized-signal':\n",
    "    plt.xlabel('$\\\\nu$ such that $\\\\vartheta^*=[\\\\nu,0, ..., 0]$', fontsize=14)\n",
    "else:\n",
    "    plt.xlabel('$\\\\nu$ such that $\\\\vartheta^*=[\\\\nu, ..., \\\\nu]$', fontsize=14)\n",
    "plt.ylabel('Power', fontsize=14)\n",
    "plt.legend()\n",
    "plt.savefig('data/n100-p10-lamb5-power_nu.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0316b297",
   "metadata": {},
   "source": [
    "## Power analysis: Setting 2\n",
    "### Code to generate states from the SEI-SLR algorithm in the Setting 2: Running this cell will take 50 minutes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1e0e512d",
   "metadata": {},
   "outputs": [],
   "source": [
    "### Theta\n",
    "vartheta = np.zeros(20)\n",
    "\n",
    "model = PSILOGIT.PSILOGIT(truetheta=vartheta, regularization=3,  n=15, p=len(vartheta))\n",
    "def linear_temperature(t):\n",
    "    return 0.2/np.log(t+1)**2\n",
    "\n",
    "states, ls_FNR, energiesnull = model.SEI_SLR(total_length_SEISLR_path=1000000, backup_start_time=2000, temperature=linear_temperature, repulsing_force=True, random_start=True, conditioning_signs=False, seed=0)\n",
    "idxs = np.where(energiesnull<1e-3)[0]\n",
    "fy_EM = list(set([binary_encoding(statesnull[i]) for i in idxs]))\n",
    "states = np.array([binary_encoding_inv(fy, model.X.shape[0]) for fy in fy_EM])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e7d42cf",
   "metadata": {},
   "source": [
    "### A fast way to reproduce the results of the paper"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c12eb491",
   "metadata": {},
   "source": [
    "###### --> Calibration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "27af48ea",
   "metadata": {},
   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = PSILOGIT.PSILOGIT(truetheta=np.zeros(20), regularization=3,  n=15, p=20)\n",
    "model.sampling_algorithm = 'SA'\n",
    "nbM_admissibles, ls_states_admissibles = model.compute_selection_event(compare_with_energy=True)\n",
    "thetanull = np.zeros(model.X.shape[1])\n",
    "signull = sigmoid(model.X @ thetanull)\n",
    "tildeGN12, barpi = model.params_saturated(signull, ls_states_admissibles)\n",
    "lspvals_selec, lspvals_sat, gaps = model.pval_SIGLE(ls_states_admissibles, barpi, l2_regularization=100000, grad_descent={'lr':0.01,'return_gaps':True,'max_ite':10000}, calibrated_from_samples=True, signull=signull, statesnull=ls_states_admissibles)\n",
    "gamma = np.zeros(len(model.M))\n",
    "gamma[0] = 1\n",
    "lspvals_tay_1 = model.pval_taylor(ls_states_admissibles, thetanull=thetanull, gamma=gamma)\n",
    "lspvals_tay_Bon = model.pval_taylor(ls_states_admissibles, thetanull=thetanull, mode='Bonferroni')\n",
    "lspvals_naive = model.pval_weak_learner(ls_states_admissibles, ls_states_admissibles, barpi, signull=signull)\n",
    "lists_pvalues = [lspvals_naive, lspvals_tay_1, lspvals_tay_Bon, lspvals_selec, lspvals_sat]\n",
    "names = [\"Weak learner\",  \"TT-1\", 'TT-Bonferroni', 'SIGLE Selected', 'SIGLE Saturated']\n",
    "model.plot_cdf_pvalues(lists_pvalues, names, states = ls_states_admissibles, sigalt=model.sig)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40fdf942",
   "metadata": {},
   "source": [
    "###### --> Alternative"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "8de80add",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of the set of active variables:  2\n"
     ]
    },
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "modes = ['disseminated-signal' ,'localized-signal']\n",
    "mode = modes[1]\n",
    "\n",
    "if mode=='localized-signal':\n",
    "    theta = np.zeros(20)\n",
    "    theta[0] = 3\n",
    "else:\n",
    "    theta = 1.5 * np.ones(20)\n",
    "    \n",
    "model = PSILOGIT.PSILOGIT(truetheta=theta, regularization=3,  n=15, p=len(theta))\n",
    "print('Size of the set of active variables: ', len(model.M))\n",
    "nbM_admissibles, ls_states_admissibles = model.compute_selection_event(compare_with_energy=True)\n",
    "model.sampling_algorithm = 'SA'\n",
    "thetanull = np.zeros(model.X.shape[1])\n",
    "signull = sigmoid(model.X @ thetanull)\n",
    "tildeGN12, barpi = model.params_saturated(signull, ls_states_admissibles)\n",
    "lspvals_selec, lspvals_sat, gaps = model.pval_SIGLE(ls_states_admissibles, barpi, l2_regularization=100000, grad_descent={'lr':0.01,'return_gaps':True,'max_ite':10000}, calibrated_from_samples=True, signull=signull, statesnull=ls_states_admissibles)\n",
    "gamma = np.zeros(len(model.M))\n",
    "gamma[0] = 1\n",
    "lspvals_tay_1 = model.pval_taylor(ls_states_admissibles, thetanull=thetanull, gamma=gamma)\n",
    "lspvals_tay_Bon = model.pval_taylor(ls_states_admissibles, thetanull=thetanull, mode='Bonferroni')\n",
    "lspvals_naive = model.pval_weak_learner(ls_states_admissibles, ls_states_admissibles, barpi, signull=signull)\n",
    "lists_pvalues = [lspvals_naive, lspvals_tay_1, lspvals_tay_Bon, lspvals_selec, lspvals_sat]\n",
    "names = [\"Weak learner\",  \"TT-1\", 'TT-Bonferroni', 'SIGLE Selected', 'SIGLE Saturated']\n",
    "model.plot_cdf_pvalues(lists_pvalues, names, states = ls_states_admissibles, sigalt=model.sig, figname='alt1p5-n15-p20-lamb.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc00225b",
   "metadata": {},
   "source": [
    "# Experiments for Section 6.3.5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9272fbcb",
   "metadata": {},
   "source": [
    "#### a) Under the null"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "42072367",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of the selection event:  2\n"
     ]
    }
   ],
   "source": [
    "model_size2 = PSILOGIT.PSILOGIT(truetheta=0*np.ones(5), regularization=7, n=100, p=5)\n",
    "print('Size of the selection event: ', len(model_size2.M))\n",
    "\n",
    "signull = 0.5 * np.ones(model_size2.X.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "c37b2f32",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2a7479d0a5f64a5e9668942984b903eb",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/100000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1662\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d9b610621ecc49afb65c01ab050d6ade",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/100000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "74d49bfba4d349efa37c12bb2f331748",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/1662 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "states2 = model_size2.SEI_by_sampling(model_size2.sig, nb_ite=100000)\n",
    "print(len(states2))\n",
    "statesnull = model_size2.SEI_by_sampling(signull, nb_ite=100000)\n",
    "tildeGN12, barpi = model_size2.params_saturated(signull, statesnull)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "ded98e30",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Proportion in the ellipse :  0.9494584837545126\n",
      "Proportion outside of the ellipse :  0.05054151624548736\n"
     ]
    },
    {
     "data": {
      "image/png": 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TrbDTlGOUMJS6SheVArC0ZikADptD2SCEty5XHfq2D77tgvJRk8ns7eDVA86DVS9Dw/88+3Ztg5+eUT72XNjvMthvJiSb4+XT0dERlXGVzCxHy0Ds7JgV/MtfgpXBHMtQaVkNvy5WPs0BnN4yD4CxJ0HRScqgcrQEkrMwHW1LQkv5jHLAY1DUZQD2v4pzn5rCMZ0buTgxQQl9ouKsh//NhS/vUsYp9r9KGYsa6MN8kOMqDTWWgdAhLy9vqCXooqvLzOBfYQ7keekKVU9rFfz6qmIUmlbqnzhuGOQfA0Unw5gTYfjokPTo6ooiLF398X3wawmmS2ssGmKH8VxSIRdfuERxZPjlBVj1imfMqq8bVr2kfDIPgP2vholnGx+rkJK8554b9LhK4WBmOVoGQgen0zn0gfF06KcrQsG/QtYVTM+825Wuox+fhg1f6J8sbpjSdTTxbMUoxCcNXFeUYenqj9YwqAPVaitC1aU1BF4tB9cxpYtK3V1Upc8e6d6Xkr/Dmjfhuweh4XPPQZu+hQ8vgk9vhMnXKa2KhOH9s9L5Lrv+OidMwDbIea/DwcxytAyEDlu2bIlsqOgQ3UL76YpQcvZg+ty69PTMnw+2ekgth8dy9MNZxNoUYzDxd0oXUoK9/z5hEPFyDBFLV398jUJbZxtLa5ZSuqiUm/a8iRPTT3TvV7qolPIZ5aTMS3Hvqz1HP2ITYI9zlM/Gb6HiIaUF0ePqq9+xGZbdCt/8HdomwftboSdOmZmtvuSowQB/8xu3N96WQw4hffr0gXfLmoyZ5WgZiKFmoG6qZo0dmKVP1eNcDz89qwwQZrpCaGmnKsTEK+6IE38HRaeAzTdKi8XugNoqUB/yy2qX0asJw1HRWEH7uHav1oFqJHwpzi6morGC4uzifi0MN1kHwPFPwRH3wA9PKcZim8sLoqMFbEvgeKACWLxcCRG+UtMFOmVK//tNyy4y9qBiGQgdMjJ0JtoMBgbdQv3qGqxKGqI+ty7ZBzUfwbf307vufWL1zjlyX9jnYthzuv6EJhOJWDkaxNLlwe9bP4onU3F2Mf9r/p/Xfm2dbV6GRPV4Kp9Rrms4dBmWDgffBJOvhZ+fh+V/hTZXxJ8k4DDXh5WwDtiKJ6SH6/7aHcrR1FAbQ41ZoTa2b99OcnJ4gdgMYyDERUR1GdC3fUsjydWvw3cPKPkSfLE5YI9zFcOQNTlib1lDcr1CwNLlwde9taSgpF93U5G9iCpnFRWNFe6WhsPm8PoO0DqnNXwhva7B6y/vUqLS+vI88G2vVyiYXakc/YXasPwEdVDzCkQE7biBip8uoojq0uJP35ZKWHINw54bB59c3c84fNQDd9j35LjkfeGYhyH7wIDGoXRRaehvgCEwZNcrCJau4Gi7iX6b91vKZ5RTnF1MrIh1tyzU761zWr2MQ1j1KDYe9r4QZvwM2yb1334+8Lc8aFzhXmXa9fJ9SR/gS7uZ5Wh1MQ01EchRGzZlZeBKyuPFqXvBjCIlFhLS6y3DKWL5wJbNLc3rqZJQYssM+jOh3sy6vu8WuyRar6Qriq4g7g7lUdUre726mNo62wzXC7/7SwnX3QD3r4RYlDRkRZrtiQ3wwoGwz0VwxLwB/HcaIpBhbiBYBkIHu90cL5qgGHRTjZguVduWLZ7Y+7OuhmFrYcd7kL8K1q3y3j91IhwwC/te53NWwnAeWlRKLqHdtGqXgtplULqoNPhgYwhE9HoZwNLlQW/iW9wdcV4D1V9s7O8S7TuQXZxd3K+7yrDhePZIZtRUM0PNKxE/hZMcXzN/5fdMyG+HGKkkHfjpGah6h5GT/wq+0VyNMEh5UMwsR8tA6BCxwSeDbqoRHRQTQhmQ++pL6PwK4h+Afj8vYOyJ9E76I7Fjjted2RzoJvX1YPFlWe0yUualuPuijd74u8MgopkMtS611aB9+MeKWJ769SmvdVrU7ia9AWrtwHbKvBScXU6m5k8NWI8WnVbIjAuXuLZVsLT2C95Lh/NSD+TK9rUc2q2k9qSjmZTPL4dNHyndp0nBW8r9GEhomgCu52aWozUGoYOaczoilJV5Vwa10ug0LyOqq6cTfngSLmmG6YA2g2GsDSZdCRevhtP/xbq+8f2Mg95kpmA4bA5iheL71NbZRq/sxdnlDOjpEoiIXi8DWLr6Uz6jHGeXk2W1y9zr1G6kJ494st/+7lhNrmNT5qW4jy0pKKGkoMT9YqEaB3+oYxZLa5Yqcy+ePZKKjSs19yS8u3kNJ7T3cvPwfZSUsipr3qD10VwlKkA4GBiDdFNWprQ01LEKtSfC9cwwsxytFkQ0EE2+1L3d8MMTsPxuZS6Dlg6gazLc+C7YA+e8HUhzX/uQ0PY5W+x+qC8M2u9T86cC+K0Tvl2WvttiRSxT86e666I64U6LtlWidmEBLAf4/TJYeoPyAgWkyG7419mw+nU49nFI7H8+vxgdgwylW8pELAOh01SLi4vOyzKoumSfEkX1f39W4iRp6bXB1DnweiMseIzXvziIB39fRPlFS03Vpd6EWndG8H5IGGG3LMcBMJS61BcIe4LdXfZ214z6LZ2Ko0Sv7CVWxLof2OrLg7jdc/+qLyT+6oxeS8I3MKB2XESti+p5AUpfPpWKxgr+ue8tjP35b+SpjefVrynhO055Uwk/H4xwQuWE0C1lZjnu3vMgotyDICJIqSRa+ewW2PSd97a+ZNi6P9z2njLT2XV9FlW/zaLTCkNqDQRrOZQuKmVZ7TLsCXavmbDaG1J1ZVTf9Abk724RdWgfxFpKCkoA5YXB2eV0j0OoD39/4xKg1BntMdpz+g6M+4YYb53T6tVy0NZF9Rzqtu9qlvJ3G1wWr9khbpjSktjrPIIS7jMo3PS8fohIylEhRBrwFHAcsBm4RUr5ks5+M1z77dCsPklKWW7kPAMiQFOt7u23yYuC3LK+1NXVmRtxc8Nyvn31NxzQ0+q9PjEVDr4Fiq+CuET3dSh99kiYJFmaWgM1Ne4b7Pmjnw9Ll3oTqm+C6oPAl7bONlLmpbgfIOrAdTADZfr1MglLlwd/xgE8hmHeQfO48asbDZ/bronp5exyYk+we9UZ37Et35aEv8Fv9Rx1dXWc//H5vAhcdugflcB/3duhZwd8cD5s+BJK5yuxoPwRTqicIN1SZpaj2W3Kh4AuIAsoBt4TQqyUUuoF+f9CSjnVhPOER4CmWufee0edcQDo7Ow050Rba5U+1NWvcYBmdQcxvJE4mumXfO+/H1VzXdQbzJ8u3/5bvW3aB0OgoGv+PJ0CYdr1MhlLl0Kgt3QtefbwHnbaLku9MQe9etkvKmyAOux1vSaepeQ9f+cMaHG5gFc8BBtXwGn/DOzlFGgM0vdFta8PrrsuYLeUmeVomoEQQiQDvwX2kVI6gWVCiHdQ5iDOifR5Qvwx/eQ2VVX+j9mZ6emAb/6hxJ3p8TTeeiQ815fAbR1dbHDW8cQrpwH9u4UCxezXEsp23wdDrIgN2GWgRTtfwpo0t/OifRHQlr/a1ePvpUCvnsSKWHeLwTttabn7u1ov1Vaqb9eSvyRF/loSvucnfU+Y/hV8eLEyYA1KK+Llw+HM/4BjjO75/aLX/XTddVBRMfgRnF2Y2YKYAPRKKbXxFlYCJX72318IsRloQYl08jcpZY/R8wghZqLMeSQ3N5fKSiWOSnp6OjabjYaGBgCSk5PJzs6myvXwj4mJYeyYMdS/9RYdr7wCQN5NN+F88klkaSmVlZVkZGQQFxfnnrput9vJyMhwu5HFxcVRWFhIXV2d22rn5+fT1tZGW5tSuTMzMxFCsHHjRgBGjBhBWloa1dXVAMTHx1NQUEBNTQ3d3UrO5cLCQlpaWti6dSsAWVlZSCmRUlJZWYnD4cDhcFBbq0ShtNls5OXlUV1dTU+PEjJ1zJgxNDU14XQqN0Nu10riP7+R2K3eLnC1aYfwQ+7ZbO7pYsNXN/PMEc+Q6XrbkVLS2NjI9u3bAcjJyaGzs5Orxl0FwOK1i1nZvJIfN/3Iig0raOlu4YqjruAPY/9AjIihV/YyvWY609Km8fqy10mKT+KoSUdx+MjDuWnPm5iQPoEn0p/g/XXvc9v+twHw7eZveXL1k7xylFImO3p2cNGnF3HX5LsY5xgHwE1f3cS4xHGcMeaMgOWkXq9Il9OmTZsA/JZTTEyMu576ltOoUaPo6emhqUlJcJOamordbqeurg6AxMREcnNzWbt2LX19fQAUFRXpllNzczMAaWlpJCUlUV9fD0BSUhI5OTlUVVUhpUQIQVFRETabza0rNzeX9vZ2WloUv/+Q7qexY6mvr3envMzLy8PpdLLFNRtfLaelPyoP5hnjZvD4qse5ougKrii6gi2dW7ji8yv406Q/kW/PB2D2F7P5YuMX7vrw6C+P0tPXw1V7K3WwfEM5i6sW88jUR4gVsWzq2MSr9a9yWdFlpCakUllZ6S6nK4quAKBrRxe2WBuX73k5AEsbl/Lf9f9VthdBh+ygorGCx6c9zgFZShu7t7eXU0afwh4j9uD95e/zRt0b3HPkPe7r5SmnjbDH3Ywctgcp39+tOH+0VtLz/CHE/u4jGnszQi+nvfcm53e/o+qUU5D5+YjaWooWLqTh1Vdp339/qKrylNNVyvVI37KFjIwMt65Qy8kfpg1SCyGmAa9JKbM16y4DpkspS332HQtIoAbYG1gMPC+l/JuR8/hiaJA6gAdB01NPkXHRRVHXzdTU1GR8EkxrFSy5RkniriWjmKs64YXmdf3ekAINKGtR38Cu2OsKHv/lcfcbnN6bn/qWph04VAf71Dc63zdI33Opg5PqgHaw1kNY1ysC7O66fPM4+EMt7wvGX8Azq59xr1frjd6gtm/LVG+d7/ntCXbdeul7X/i2ONZcsibw9VrzFrz3e+h1dfnYUuC0dyHXX8+6DwYCeWoJpxwjEazPCfgG9R8BbPPdUUq5Vkq5TkrZJ6X8AbgDONPoeQaEv1nMs2fTNm5c1BkHwP22GxK9XfC/Mli0t7dxsKWwIHkcR/WO4KGGCvfgsJHgZuokOHViW0l2iXugWe+BXlJQQuuc1n5N+KU1S90T4rTdBup5irOLcdgc7t9R99Mmkwmk29D1iiC7u67i7GK/3TngPWES4Pjc4wFPfVLrjS9GJ1ROzZ/qfqmxJ9jddQ0UTyZ/LyBq/fx67deB75vxp8Nv/61kqQPobIU3joW174UWoC+cSXSYW45mdjGtBuKEEOOllGq28ElAKAPLEiXKyUDPYwx/HgTRNAYRYrY5Lxq/UTwqNv+oWSlg30th6l/556tnee2u3qzBWg6+k95CQb2p1bfGUMcZwPgNb7Fz4Nufrw3dDcbGHlTUeuY7wU1dB94tD3V/PVdY33rnO7jtqy9gyzuvFH63FN78DbRvUsYB3zwVmk6Fea8Hdm2NgkCeprUgpJTbgTeBO4QQyUKIw4FTUcYXvBBCnCCEyHJ93wP4M/BPo+cxBR0Pgkzf5tlQzRXxmVKfmZHhNaW+Hz2d8Nmt8NIh3sYh+2CYvhyOexySMtwtgJKCEq9kKyqhhktundNKz196eHzV47rbp+ZPpecvPe4wCkY9kdRj9G5iUG7kQN1MmZlhxMeJAJYuBW1YlUA8+suj7v213Y/a80zNn+qeR5MyL6XfQ76isYJltcvcv9Ure1las1S3XqkRYn3vAbXlo7ZwPmj4IDQniaz94ZzPPYPUohdGvAk3nevdjdTa2j98htoF3ten/F240DvMhg5mlqPZbq5XAk8Dm4Bm4Aop5U9CiHzgZ2AvKWUtcDSwSAhhBzYCLwB3BzuPyVr1KStDJCfDDTcM7eQ5nXka4vHH/Ud63PCV0mpo/tmzLi4Jpv1NScauE0hPRZvnVw+9iJva5a6eLq/9VY8S7fnUfl4IvRWh7mek1aFFRGE3IezeugLNe/BHp6sPX+1e9MWeYO+XqlRFO+7gO7va13MuVE86VcOKxhVekWcDtiRSx8FZH8MrU8HZAImA/RXIegWa6D+2EGogT50eBjPL0dRgfVLKFinlaVLKZCllvjq5TUpZK6W0u4wDUsobpJRZrv3GSin/IqXsDnaeQcf1UN6Yn++x0nrWPRJoxkRYuBBiYhRdvhWppwM+vRlePtTbOOSVwoXfwwGzAkZZVftT1Tcvr6BlIbQkKhormL3PbK916iBy6aJS9znVsQaVcMNnaNGGeNZD9UiKNixdxvCtX3qE8mCfmj/VPc7gsDncMZ2053DYHO4Z3HpoWyaz95lt7OXFMQZ++6EyERXAjuJ/6UC/2yhYIE8/Qfs2fucTEWEAWNFctagFkJnpfih7eTlF+s0v2CBVy69Kd9LX9yjudADxyXD0Q8rbSkoRgfDN8xsscqpvhFY1yxd4ex5pByB9z2lPsJtiHMAao9gZKZ9RbnqolFBbI2rLRe261JucFyjqqzarnS+xIja0CMYj94HT/gV9rs6bVOAS4Lqr/A9U6y1rexh8X2Z7e017mY3OqGFDiRCM2Gsv73VDld3NZ5BqRHk5fPGFoufn5+HjK5Wp/Sr5R8NxT4KjMOiptQN56g3m+0YVqLJrB673TNoT8MTmV9G7AcOZEe2PQDczKHMZopHdWVc4KWXLN5Sb9vvqeIVvfCeVXtnr1V3l222khhZv62xz61K7pgJ107rPc+ESuPdV+KAHLosB0Qc5wFcPw7XxoT9rAkSCGLHXXqY9r6wWhC9Skub71h5kUGiwdPgOUqU5HPDIQrhzb/j3hW7j0IXgvuRxcOZHIRkHFbUyx4pYdxCzYEZB/Wjf3hdXLfYyDBWNFV7btdtiRaxpLYhe2RuwFZGWlmbK75jN7qxLHSw2wuKqxab8ttrNubRmqTs2kx7Buo1a57TisDlYXLUYh83h3j8kd3F1bOGE2XDsw571BwMj1xl7sPvpYUhLTw/9HEGwDIQW10O5ev/9DXsOmI7OIFXDWYfD7amQ/It7t9qYYRzVnczbiaPDemsozi7ud6MECqmhvcFVT6gXjnrB3XWgNsO1cxi0D3HfOQ9m4O+mVGdBRxu7uy6j5f/I1EcGRYNeC1Q7RqH30qS+ILV1tvHI1Ef6uef6Gol+yYgWlVJaWK7c0/vNhL0u8Pz48P/AporQ/wk/brBmlqPVxaRFfShnZkYkzklQtPM0vn+S3E//CPEej6F/27K4xLmDhs6t4Kp8EFpSHt+5Deo632iX2squ3bets83twXHVuKu8WhXhdCMZicWkJdCEK4voonRRadBuwUiiV9+0Af4geLh637DiIddH9VlyzMNKDonNPyoOJ++eCeetAB13Xi8C5ZI49dSB5crWYBkIX8rKiK+pMRZ+dyAEmwgne2HJ9fDd/Z7mXnwyf7Xlce+WDbR1bnXv6i/qpEqgfApqTgZfwxGoC0e9KTrl0EQnddgcAY1hfHy8321DiaXLGBt3DJ53lW+4DfB+EfK9p7St6x56+uWOCBbgsl99jU+Gk1+HFw6EbqcSGuezW+GYhwILD+AGG9/VZdrzavdOGDTUBEsW0rFFSWVY85HnmIz94KRXKX3nD4B3fJhg8Yn0DITaCtAOMPv6qevFUYoGYkUsPX/pGWoZFgbQ5vUYTNQWqb/EQf6SDmlndWu/q66vweYEBR2k9nd//vISvD/dtSDg3C9h1MGB/0kIL9KCDpGIxbTLUFNTM/g/onVTu+Ya7ybjli3QvEpxYdUYh+2jT4Df/w/SJvabDe1rHLRzGFLmpbhvTDVFo7hdkDIvxX2DqG5//loM6liF3gDzwkMXmnRRjNEre73STfoSkXIMg91ZVzhdTP7ql+rwoOf4oK3XRl5qtGNngVrj5TPKefbIZ72WA72cBXWB3eP3MOYE14KEj/4AfSG8/Oi4wZpZjlYXkw5qOOdBQbXwapPwiy/g/vuVD8CsWZBYA88Ug9B03Rw6lw0Z5zIuPrnfKUOJbKqH3s3q690RK2Ldcxn8tSCyhmUZ/u1IMKjlOAB2Z13anNOh4q9+BYvNpNc6AO/7RS9bnPZtP9Cbv6nXSwhl/tKivZVcLU0V8O39cOB1hk9lpi7LQEQSvS6lLu8wFST/BKkfe0IXxg2D3zyrZKxyxXjX4ltxjQTW02t2+3o0ad/EohGHzUHKvBQrT/VOQOmi0qDZ44yg1ldtl5Czy+nOHhfo4R+IIUtC5RgDh/wFlt2iLP/vLzDxbBg+emj0YBkIXQoLC80/qb8c2BUVnn1KgPSPPcv2XCVdoStpyaDo0hDu+MIVy67QXR+uZ5IRAhmuwb5e4WLp8o+2q0gN2fJ8zfNeg8ngvxUQbHa9v0HkUPfXMijX68Dr4ZcXoPknZZ7T1/fAUca6cM3UZRkIHVpaWsyPbOlv5iPA1VdB5YNKCEOVzAPgjPcg2Z03KSRd6luSXtKdkoIS9xwGf0HK1H5Xf8HP9Di76Gx3xE0tkRrQ9jfxblDK0QR2V13+unW0dU31JlKNA8DTxz3N797/nXt/f0bA6MN/oAzK9YqNh5J74c0TleUfHocpt0Jy6N24ZuqyDIQOW7duHZwbRS8H9tV/hLSl3sahaTj88RNI9PaF1tMVyHXVF39Ne99cvhWNFYYe7qWjSnUNRCRaEIDfMAeDVo4DxNKlEOoDvLKyMugA8FAwaNer8DeQNRk2rvDkkS+5Z0h0WQYikvjOfIyFbR2PMny45yHasCmRnPnboGOu4fkXeqkRfd+2/Ln3aTFrMlM0ucRaRA9D1se/syAETLkN3jldWV75MBx8MwwzL4RGqFhurjpkZQ2CV47vzMeeLtZfl8jwiZqH6J7TOX/igbx+5GjdmdtaXb6uqynzUnRj3Pj20euFulAjXKqo6RdDZeGPQ+PmqkXvoTMo5WgCli5j7Ja6xp2iRH4FZSziuwdCPtRMXZaB0GFQJg9qZj4eud+3fPhwHqOzOtybH+9N4MiNdXxSt4yzDltPaWF/j4tb/3trQC8MNUlPSUGJOw+0kcB4apA939zSwbDF2kLed7BQu9q0ROskUEuXMXZLXSIGpvzJs/zTIk9I/yCYqcsyEDps2rRpcE5cVgbz5zOrvYrjuzzhAxYn5nJTXyLSHd5D//ATck5wf2+d0+qOKumwOdzLvvT8pcc9C1SN2lpSUKI7scioYVC5fM/LDR9jNnq6B60cB4ilyxi7ra7xZ0CiK8Lu1hpY/3lIh5mpy1QDIYRIE0K8JYTYLoSoEUKc62e/C4UQK4QQW4UQ9UKIe4QQcZrt5UKIDiGE0/X51UydQ4aUsOxWTu9scK961zaKs6+spTh7f7+HqbOit3VtCynTm15iH6Mhts0KyR0pdja9FhZBiU2AiR7vLX55IeISzB6kfgjoArKAYuA9IcRKnXzSScA1wHIgA3gHuAGYp9nnKinlkybrCwmHI/T+d0N89Tf4+v/ci/9NyGRB8nhODnEg+sP6D/utC3WCmG/MIt8BbXXSkZr4HUKLvRQrYvmo/qOA+0QCvdj+g1aOA8TSZYzdWtce02Gly0Pw11fhyPshLnCXrpm6TAvWJ4RIBrYA+0gpV7vWPQ+sl1LOCXLsdcCRUsqTXcvlwAtGDYRZwfq6urpISEgY8Hm8+PEZ+PBiz3LRKUoUx1jvCJqBpvaf9uJptHa3muoFog3T7Rt7JtTk8lnDsgY14mYoqN1sWgalHE3A0mWM3VqX7IMni2BrtbJ8ylsw/jTTdUUiWN8EoFc1Di5WAnuHcOwRgG8r429CiM1CiM+FEKXmSAyN2tpac0+4/nMl+JZK/tFw0uJ+xiEYM8fNNFeXi+LsYneyH+2ndU6rOxigmkBF/a7isDmGLFifFj3XXNPL0SQsXcbYrXWJGNjjHM9yTfDWupm6zGxBTANek1Jma9ZdBkyXUpYGOO4i4E6gWEq52bVuCvAzSnfVOcCDru1VOsfPBGYC5ObmTl6yZAkA6enp2Gw2GhqU/v7k5GSys7OpqlJOERMTw9ixY6mvr6ejQ/EmysvLw+l00tjYiM1mIyMjg7i4ODZs2ACA3W4nIyODdevWARAXF0dhYSF1dXV0diqB9fLz82lra6OtTXnzzhrWQfI/jyJmRxMA3al7Ic5ZRnVDM6DE4C8oKKCmpsYdZKuwsJCWlha2blVyPWRlZSGlpK6uDpvNhsPhwOFwuCuCzWYjLy+P6upqenqUrqQxY8bQ1NSE06k8OEeNGkVPTw9NTYqO1NRU7HY7dXV1ACQmJpKbm8vatWvp61O8JYqKinjgkwcYZx8HwOLaxWQnZlOSqQx6f970OX8+5s/89OtPbOzYSM32GhbXLubKoiuRSJLjk/n7qr9z9MijmeCYAMCfv/kzk9InceaYMwF4qfIl1m5by2373wbAt5u/5R8//IMXj3wRgB09O7jo04u4a/JdjHMoOm766iamZk3llIJTAHh29bNs793OU0c95VVOq1atwmazhVROmZmZCCHYuFFpCY0YMYK0tDR3di4j5aQOEvorp59//tn9hmdWOTU2NrJ9u5KCNicnh87OTpqblTqWlpZGUlIS9fX1ACQlJZGTk0NVVRVSSoQQFBUV8csvv7hzQuTm5tLe3k5LSwswsPtpy5YtAGHfT2vXriUuLi7i5RTsfqqvryc2NnbQy6nhi2fJ+d8MlIu4Hw3HfEB7e7vfcmpqaiImJsZQOSUmJuq2IMw0EPsDn0spkzTrrgdK1a4jnWNOAx4DjpFS/hDg3P8G3pNSBnQGNquLqa6ujry8vAGfhy4nvDIVmlYqy8NGwvSvDeWNHhRdJqDtCnv202d5Zu0z7m16UTDVvBPqYPLU/KmA9xiIut1IxM9AOSGi6XppsXQZY7fX1eWEB1OU5GEI+GMLJKaYqstfF9NgjEHsLaVc41r3HNCgNwYhhPgN8Dzw/6SUXwU59wfAB1LK+wPtF1UJg2QfvHsWrHlTWY6Jh7M+htxpQ6triPCXdctf4hUV35hQsSLWbVzULHhWJFeLXZ4XDoKNrmfb6f+Csf/P1NP7MxBIKU37AK8ALwPJwOFAG4rB8N3vKKAZOEJnWwpwPJCI4mU1HdgOTAz2+5MnT5ZmsG7duoGf5Mu7pfw7ns/3T0aHrkHA0mUMS5cxLF1Syk+u8TxLlt4ccNdwdAHfSJ1nqtkT5a4EhgGbXIbiCinlT0KIfNd8hnzXfn8GHMD7mrkOH7i2xQN3AU3AZuBq4DQpZcTmQqj9jmGz4SsllrvKAbNh30sGdk5M0DVIWLqMYekyhqULyDnM832z3954wFxdps6DkFK2AKfprK8F7JrlIwOcowk4yExdEaXLqeSWVdMF5hwGJX8fWk0WFhY7NyljPd+3Rc6rywq1ocOYMWPCP7j8Wmh1ZX5LGA4nvgAx5tjhAekaRCxdxrB0GcPSBQwv8HzfWqNEZfCDmbqscN86NDU1kZ2dHXxHX9a8CT9o5vYd/ZCSRnAQdXV3d3u5rA0Fvb29bne/aMLSZYzdXVdsbCwpKSmMHDnS7SYaiLCfE+EwLF1JP9yzA7q2QWcrJKYOui7LQOig+jobYvtG+M9lnuWJZ8Oe55knCn1d9fX1DB8+nMLCQoSB3BFm0tHRQWJi4pD8diAsXcbYnXVJKenu7mbjxo3U19eTn58f9JiwnhPhIgSMKICWVcry1lq/BsJMXVYXk1l8djN0KJNVGJ4HxzxiKNlPuHR0dJCenj5kxsHCYldACEFCQgKjR492T2SLOuyjPd+3b4jIT1oGQodRo0YZO2D9/+CnZz3Lxz3h17oPBH+6hto4qLNvow1LlzEsXYTUtaRi+DkxUGI18ZUCBNE0U5dlIHQw5CbW1wufXOVZHnc6FB5vviii191P7o4JXQaApcsY0aor4vej0DyuAyQPMlOXZSB0UOPghMT3j8Om75TvcYlw5ILBEYVBXREkWg2XpcsYli5jRP5+1BoI/0bTTF2WgRgI7Zvhc01awINvVQaSLHYKLr/8cq666qrgOxpg0aJFjBs3ztRzBmPGjBlceuml7uXCwkJeeEFJLlNbW4vdbncH2bPYiQmxBWEmloHQITU1xPGDb+6FDiVSJY6xcNCNgycKA7oijBppMxDNzc1ceOGFZGdn43A4OPfcc91RPn25+eabEUK4H3J6bN++ndNOOw2Hw0FpaSmNjY3ubWvXrmXPPfdkx44dATU9+uijPPjgg0G1+6OsrIxjjjnG8HGhXC+zyM/Px+l0kpOTE3TfSOoyQrTqivz9qG01+DcQZuqyDIQOdnv/7GT92NEMFQ97lo+4R+liGkRC0hUGwVKYBiOUgb0LLrgAp9PJmjVrWLduHc3NzZx//vn99vvqq6/44IMPgg60PfbYYyQkJNDc3ExxcTF33303oPRXX3bZZcyfPz9qM5EZGQiNJJYuYwzW/eiXdk3X0bCRfnczU1d0XvkhRo3pHpBv74dul7/xyH1g/OmDK4oQdQ0BXV1dAbdv376dDz74gL/85S8MHz6ctLQ0br31Vt577z1qamrc+3V2dnLJJZe4H/6BqKys5OijjyYuLo7f/OY3VFYqs9efeOIJcnNzOeGEE4Lq8u2aEULw8MMPc9BBBzF8+HAOOeQQVq1apXvs4sWLufvuuykvL8dut2O321m7dq17+/33309ubi6pqan84Q9/oLfX43VSWVnJmWeeyahRoxg1ahQzZ85k27ZtfnW2t7dzww03MGbMGNLS0rz+32BUV1cjhHDnGCgrK+Poo4/m2muvJT09ndzcXObNUzL9dnV1sWXLFs466yzS09NxOBzss88+fPbZZ+7zvf3220yePJmUlBT23HNPXnzxxZB0DIRg5ThURPx+dK73fE/23yI0U5dlIMKhsw2+00Qen/In7/7BnQS15bC0ZilLa5YOuCXhD+kdrRfAnURl5cqV7nVlZWUcddRRHHrooUHPud9++/HRRx/R1dXFBx98wH777cf69ev5xz/+wYIF4TsKLFq0iDfeeIPNmzeTl5fH1Vdfrbvf2Wefza233kppaSlOpxOn08nYsUq8nJqaGjZu3EhVVRVff/01r732Gq+88gqgzFs54YQT2GuvvVi7di0///wz9fX1zJ4926+mSy+9lFWrVvHll1/S2NjIlClTOOmkk9wJcYzy6aefkpWVxYYNG/jnP//J/PnzefnllwG49957aW9vp6amhtbWVt58801yc3MB+Oijj7jkkku47777aGlp4dlnn+Wqq67i008/DUuHhQFkn/fcB+2ciEFk53uqRYCgszYrHlamugOkjocJZw26JghB1xARrAvAbrdTWlpKWVkZra2tNDU1ubuE1Cxf33zzDa+99hp//etfQ/rNiy++mJycHCZPnsyWLVu45ZZbuPzyy7n77rtZtWoVxxxzDMcffzzvvvuuof/lxhtvJD8/H5vNxowZMwgnv8iwYcO44447sNlsjBs3jqOPPtp9nn/9619IKbnjjjsYNmwYqamp3Hnnnbz44oterQyVzZs38/LLL/Pwww+TlZVFQkICc+fOZcOGDSxfvtywNlD85G+++WYSEhKYPHkyM2fO5JlnniEmJsbdbffrr78ipWTChAnu2D4LFy5k9uzZTJs2jZiYGA4++GDOO+88nnvuubB0hEq0djFF9H7csRn6XC8EiakQP8zvrmbqis7RnyFGfWPSpbcLVmjeUA++FWIiE78moK4w8E3So03kY4RQEqS/8MILXHfddey5554kJiZy/fXX89///peRI0fS1dXFRRddxEMPPRRy/2lCQgL33+9pxb344ovYbDbOOOMMCgoK+Pjjj3E4HBxwwAFMmzaNlJSUkM6rHftITk4O2PXjj8zMTK/YQdrzrFu3jrq6un56hBA0NjYyerT3m6GajnO//fbzWt/d3R12V0JBQYHX5MrCwkLefPNNEhISuPHGG+nu7ubCCy9kw4YNnHTSSdxzzz1kZWWxbt06lixZwvz5893H9vb2Mm3a4CbBCqV+DQVm348B2RZa9xKYqys6TfMQo+1L7r/xPXDll8Y+GvacHhlRBNE1hKj5gwMxevRoFi9ezIYNG1i3bh1jxowhMTGRQw45hIaGBn766SemT5/OyJEjGTlyJHV1dVxxxRVMnx78+m7atInbb7+dhx56iKamJrq7uxk/fjwOh4Pc3FxWr15txr/Zj3DebAsKChg/fjytra1en46Ojn7GQd0fYM2aNV77t7e38/vf/z4s3TU1NV7dfdXV1eTm5tLZ2UlycjJ//etf+fHHH/npp59Yv349N954o1uL2gpUP9u2beP9998PS0eohFK/hoKI3o9NFZ7vKYHdqM3UZRkIHdT+cV1+WuT5vvcMiI1cGICAugZA+YzysFsPENpM119//ZWWlhb6+vr4+uuvueaaa5gzZw4pKSnk5eVRW1tLRUWF+5OTk8Pdd9/t1Urwx9VXX81tt91GVlYW6enpdHZ28u2331JdXc3q1avdD1mzyc7Opra21tAgqjp2cPfdd7Nt2zaklKxfv5633npLd//MzEzOPfdcrrzyStavV94iW1tbeeutt8IOyrZhwwbuvfdeuru7+e6773jiiSe48MILkVLy7rvv8ssvv9Db24vdbicxMdHtZnrNNddw33338dlnn9Hb20tXVxcrVqwIqxvOCNE6k3qw7kddGjVZmUcdHHBXM3VZBsII2zcqLQiVvS8cOi07GZ9++il77703drudc889l6uuuoq5c+cCSpjl3Nxcr09sbCypqamkp6cHPO/bb7/N1q1bueCCC9zneuKJJzjllFM44ogj+Otf/0pWVtag/E9nnXUWeXl5ZGdnk5KS4u4OCkRSUhLvv/8+P//8M3vssQcOh4Ojjz6aiooKv8c88cQTTJw4kdLSUoYPH86+++7La6+9FnYMrmnTprFhwways7M56aSTmD17Nueeey4AVVVVnHzyyYwYMYLCwkKGDRvm9nI67rjjePzxx7nxxhsZOXIko0aN4tprr41sVNPdlQ2a8abswAbCTISZ1lkIkQY8BRyHki70FinlS372vRa4GSVF6Rso6Uk7jZ5Hy4EHHijNeJuRUurffCsWQPl1yvecw+H3ywb8WwPV9csvv7DnnntGVIcvfq/XEGPp6k9ZWRnLli3jv//9b79t1vVSCPWeipiu7nZ4YIQnQN8ft0Biiqm6hBArpJQH+q43uwXxENAFZAHTgUeEEHvriDkemAMcDRQCY4HbjZ5nsNDOyvVCG7F17xkR0aLFr64hJlx3y8HG0mUMS5cxInY/bvrOYxzS9ghoHMBcXaYZCCFEMvBb4M9SSqeUchnwDtB/uixcCDwlpfxJSrkFuBOYEcZ5BgXdePBb66DJ5bMfa4OJkXFt1RKtceoj2hdrAEuXMSxdxojY/Vj9b8/3UVOC7m6mLjPdXCcAvVJKrcvISqBEZ9+9gX/67JclhEgH8g2cJ3LUaprko6eBLTrDOFhYBKKsrGyoJVgYZc2bnu9jT47oT5tpIOxAm8+6NmB4CPuq34cbPA9CiJnATFD8f9UQBOnp6dhsNncUy+TkZLKzs6mqqgIUF8WxY8d65XPOy8vD6XTS19dHZWUlGRkZxMXFsWHDBrJ+esstYLN9f1orK4mLi6OwsJC6ujq3K15+fj5tbW20tSn/QmZmJkIINm7cCMCIESNIS0ujuroaUJKhFBQUUFNT425KFxYW0tLS4p5ElpWVhZTSrcvhcOBwOKitraW7u5uuri4SEhLo7Ox0e3zYbDZ6enrck6/i4+ORUrpDJ8fFxRETE+P2wFEnSfmeo7u72/0G5+8coMwQVs+hzY+dmJhIV1eX+xwJCQn09fV5nUMI4f7fY2JiiI+Pd19PIQQ2m83QOWJjY92eNx0dHX7P0dvb63V9gH7n8NUR7Br7niM2NrbfNVZ1RbqcfM/hW05CCPe6SJZTsHPExMS4dUWinFS91dXV7u9jxoyhqanJPSA/atQoRowY4X7epKamYrfb3XNTEhMTyc3NZe3ate7/paioiMbGRvcbfk5ODp2dnTQ3NwOQlpZGUlKSOyxKUlISObat0PwzAH2xicSM+Q0NDQ20t7cDyjOvvb2dlhYlm2V6ejppaWluXaE+9/xh2iC1EGJ/4HMpZZJm3fVAqZTyZJ99VwJ/lVK+6lpORxmMHonSggjpPL6YNUi9ZcsW74iIUsKj2dC+SVk+bwVkHTDg3xmwLqJjkLqnpycqI25auoxh6VII9Z7Sux9NZ/nfYNmtyvdxp8OpbwbeP0xdkRikXg3ECSHGa9ZNAn7S2fcn1zbtfhullM0GzzMoqBbdzeYfPMYhMR0yiyMlxYt+uqKEaE3oYukyhqXLGBG5H7XdS+PPCOkQM3WZZiCklNuBN4E7hBDJQojDgVOB53V2fw64RAixlxAiFbgNWBTGeSLDeo07a/5RO2VgPgsLi52MzT/BRlePSEw8jD0p4hLMftJdiTKvYRPwMsrchp+EEPlCCKcQIh9ASvlv4B5gCVDj+swNdh6TtfolLS3Ne0XzL57vWZMjJaMf/XRFCdHYLQGWLqNYuowx6Pfjdw94vhedHNS9VcVMXaYaCClli5TyNCllspQyX53cJqWslVLapZS1mn3nSymzpJQjpJQXqZPkAp0nUiQlJXmvaNEYiLSh6+/vpytKiNZom5HWFSyF6bJlyxBCDKquefPmkZWVhd1u5+uvvw7pGDUzXiSvV2lpKXfddZd7WQjBsmVKS/2zzz7zCmYYrfVrUO/Hji3wsyZK7gH+w8H7Yqau6LzyQ4zqReCmRZM0Jm2PyIrR0E9XlBBKLKIZM2YQHx/vTq5jt9t5+OGH/e6/atUqDjjgAFJTU7nkkku8fOFfeeUVTjvtNFN0BdOsTSgUjFBTmA5WApz6+npuvfVWlixZgtPp5KCDDuq3T6D/KVoS80ybNo3W1lb3crTo8mVQ78cfnoIeV8rcjEmKa32ImKnLMhDB6NzqyeQUEw8pY4dWj9n4erENYmC0Cy+80J1cx+l0cuWVV/rd96abbuKiiy5yR3p9++23ASU/wty5c3nkkUcGTefOSnV1NTExMey1115DLcViIPT1QoXmRWP/WTBEIVAsA6GDVxNti2a+Xup4iBm6/lDTm7RlZXDttR6jIKWybHAy1WB0AVRWVnLccccxbNgwSktL3X7ds2bNYs6cOUFzVoOSevHUU09l5MiR5OXlcc0117Bjxw73dm23BkB5ebm7v/uee+7hxRdf5Nlnn3W3eHp7e/nuu++YOnUqDoeDtLQ0DjvsMLZs2QL0fztfs2aNO8DepEmT3FFP1evV09PD3XffzYQJE0hJSeHwww9nxYoVAf+nRx55hIkTJ+JwODjkkEPc6UAXL17Mscce647CWlRU1O9Yf/8TKPF75s6dS2ZmJpmZme5Aiio//vgjxx9/PCNHjiQ/P59bbrklYAiM5uZmLrnkEvLy8sjIyOB3v/udey5QMLTlADBz5kymT5/O+eefz4gRIygqKmLRokXu7dXV1Rx//PGkpKSQmprK5MmT+fXXX93bn3jiCfbZZx8cDgf7778///nPf0LSEYxB62Ja/RpsdaXiTUyHPYyFdTdVlzYd5M7+mTx5sjSdtR9I+XeUz6vHmH/+AfLzzz+Hd2Bfn5SzZ0sJyl+9ZRO58MILZUpKikxNTZXjx4+XN9xwg9y2bZvf/c8++2y5YMEC6XQ65cEHHyw/+OAD+c4778hjjz02pN/r7u6We++9t5w5c6Z0Op2yvr5eHnjggfLKK6907wPIzz77zL28ZMkSGRsb66X5kksu8TrvoYceKm+//XbZ09Mju7q65BdffCGdTme//bu7u+XEiRPllVdeKdvb2+Xq1avlxIkTpXLLKdxyyy3y4IMPllVVVbKnp0c++eSTMj09Xba0tOj+Ty+99JJMT0+XX375pezu7pZPPvmkTEpKktXV1br69dD7n+bOnSvj4uLkI488Iru7u+WXX34p4+Li5LJly6SUUm7cuFGmpaXJRx99VHZ2dsr6+no5efJkefvtt+v+Rl9fn5w6daq85JJLZGtrq9y+fbu8+OKL5VFHHeXep6SkRN55553uZW1Z6JVDXFycfP7552V3d7f8z3/+IxMTE+Xnn38upZTy97//vbz00ktlR0eH7OnpkStXrpSNjY1SSikfe+wxWVRUJCsqKmRvb6987733ZHJyslyzZo3faxT2PWUGPZ1SPlnkeeZ89qeI/CzwjdR5pg75Q93Mj1kGorKy0rPw62uewnr7dFPOHy5eulwMqDJrjYL6CcM47NixI+g+33zzjWxsbJS9vb3yxx9/lAcddJA855xz/O5fV1cnTzvtNLnffvvJsrIy2draKidOnCirq6vlY489Jo844gh54oknylWrVuke//nnn8uEhAT3w1tKKf/973/LxMRE2ef6/8IxECUlJfKSSy6R69at6/eb2v2XLVsmExIS5Pbt293bH3/8cQnIHTt2yL6+Pmm32+XSpUu9zrHPPvvI559/Xvd/OvbYY+Wtt97qte6QQw6Rd999t65+PfwZiL322surHA888EB53333SSmlvPfee+WRRx7pdczrr78ui4qKdH/j66+/lsOGDZMdHR3udZs3b5aArKurk1IaMxDnnXeenDp1qtdvTJ8+XV522WXu/+mkk07SvRf23ntv+eyzz3qtO+mkk7x+25dQ7ym9+3HAfPug53nzYKqUO7YYPkU4uvwZCKuLSQep7Yfv0sS6T9CN9hExvHSZgRCwYIH3ugULBqW/c/LkyWRlZRETE8Pee+/NggULeP311/1mC8vNzeWtt95i5cqVzJ07lxtuuIGrrrqKHTt2cN999/Hvf/+b2bNnc/HFF+seX1dXR0ZGBsnJye51RUVFdHR00NTUFPb/8cwzz9DX18fUqVMZM2YMf/7zn3UnctXX15OZmenV3FdzO4MyluJ0Ojn55JNJSUlxf9auXet3kLGuro6xY73HwIqKisJOParFt8vON03q559/7qXz4osv9hs1dN26dXR2dpKVleXev6ioiMTERGpra3WPCUZhYWG/ZfU63XvvvYwZM4aTTz6ZUaNGcfXVV7tDYqxbt44//vGPXtqXLFniTr40EEy/H7u2wZd3eJan/Clk11YtZuqyDIQOXrHUuzQ5ieNDy5c8WJgee166xhy0aMckBhG1Hz6Uyvzxxx/z66+/8sc//pHvv/+eSZMmMWzYMI444gi+++473WPy8vJoampyx6wBJRVjYmIiI0eOBJSHoDbypRq3y1ejljFjxvD0009TX1/PO++8w5NPPslzzz3Xb7/Ro0ezadMmr9/XJhQaOXIkycnJ/Pe///VK4bl9+3bmzJnj93/yTUq0du3agLF0fAk3TeoxxxzjpbOtrc1voqCCggKSk5NpaWnxOmbHjh0cdthhhn8fcMcu0y6ruZczMjK4//77qays5PPPP6e8vJx77rnHreXpp5/20uF0Ok1xcjD9fvxmvidiw/B8KP5jWKcxU5dlIHTwGuDrjp4WhN7AY9ioxmHhQpg9G/r6lL8LFxo2EomJiUH3eeWVV9yui2vWrOH666/nlFNOCXrs9u3bmTVrFk8++SRCCIqKili+fDlbtmzh/fffZ9w4/fy8Bx98MOPGjeP666+nvb2dhoYG/vznP3PRRRe5H5IHHnggzz77LF1dXVRXVzN//nyvc2RnZ3sFWwN49tln3YYkJSWFuLg43YlchxxyCAUFBcyZM4cdO3ZQVVXFAldrTQ2MN3v2bG644QbWrFkDgNPp5MMPP+xnqFRmzJjBY489xldffUVPTw+LFi2ioqLCUG5qvf9JxV9ZXHDBBXzzzTc8/fTTdHR00NfXx9q1a/n3v/+tu/+BBx5IcXExs2fPdod9aGpq4pVXXglZp5bY2Fi+/PJLXn75ZXp7e/nkk09444033FkEFy9ezLp165BS4nA4SEhIcJfJtddeS1lZGRUVFUgp2bFjB8uWLWPVqlWBfjIkTL0ft9XDN3/3LB9+J8QFv6/0MFOXZSB08LpBZfTEovf34AgLISAlRTEKarfSggXKckqKoW6mUPzUH330UcaOHUtycjLHHXcchxxyCM8880zQ4/70pz9xwQUXMGHCBEDpqjr77LMZN24cc+bM8fsmGBcXx5tvvkl9fT35+fkcfPDBTJkyhb//3XMTPvjgg1RWVpKWlsbvfvc7ZsyY4XWOSy+9lO3bt5Oenk5KSor74TR58mTsdjuHHnoo5557LtOnT9f9/XfeeYeVK1eSmZnJGWecwcyZM72u1+23386pp57KqaeeyogRIxg/fjyPPvqo3/wH5557LnPnzuW8884jPT2dhx9+mPfff79f90sg9P4nFX/lmJ2dzZIlS3j77bcpLCwkNTWV008/nbVr1+ruHxMTw9tvv01fXx+TJ09m+PDhTJkyhfLy8pB1aunr6+N3v/sd77//vntezEMPPcTUqVMB+O677ygpKcFut7P33ntzwAEHcMMNNwBw2WWXuV2mU1NTyc/P58477zQlCZFp96OU8N/LPS+jI/eFPfvXqYjrwuSUo0ONWdFcKysrPW+m3z0En7hmx066HI4ZOv97L10uBhzNVUpvY+C7HAIdHR0htSIijaXLGNGq6/zzz8dms/Hkk09G5PdCvaf07sfwfvBFeP8814KAsz+F3Klhny4cXZFKObrrkagJm9uxZeh0DBa+xiAKcxJbWOyytG+CTzRhNIr/OCDjYDaWgdBBHfwCwJbi+d7ZGmkpXnjpiiLUJDjRhqXLGNGqK1pjMZlyP358NXS4wnMPz4dpdw/4lGY+J6IzTOIQ097e7mlqR5GB8NIVRfT19UXlTWzpMka06nrqqaeiMqLrgO/H1W/A6lc9y8c9YYojjJnPieirDVGAmr4PgGEjPd+3Ddx3eiB46YoiojWhi6XLGJYuYwzofmytgg81c3j2ngGFxw1YE5j7nLAMRDAcYyDW1fR21kflOMSu5GhgYTGURORe6t4B75wJXUrOeUYUQOn8wMcMEZaB0CE9Pd2zEBsPaZromJt/iLwgF166XMTGxprisjcQorH5D5Yuo1i6YMeOHcTHx4e0r979GBJLZkFThfI9NgFOft3bGWaAhK1LB8tA6GCz2bxXZOzn+d70fWTFaOinC2Wy1saNG/36zkcC02eUmoSlyxi7sy4pJe3t7axfv57MzMyQjtG7H4Py4yL4QeOuW3ofZPfzLh0QYenygymmWQiRBjwFHAdsBm6RfrLACSEuBGYB44GtwEvArVLKHtf2cuAQQO14XC+lnGiGzlBpaGjw9iMeua/n+xC2IPrpQgnZUF9f7xXeONJ0d3eH/NYVSSxdxgikq7bNE0PJtxtGCIGU0utBnu/Idx+T78gfNF1mEh8fT1ZWFiNGjAhpf737MSAbv4OPNTlQ9pyuzK0yGcO6AmBW2+0hoAvIAoqB94QQK6V+Hukk4BpgOZABvAPcAMzT7HOVlDIys2JCIWOS5/v6z4dOhw4xMTHk5w/sBhwopk0YMhlLlzH86Yq7I45e2atzhDexIta9n8PmoK2zzf1dS3F2MeUzykmZl0JbZxuxIhZ7gt29HqB0USkVjRU4u5y8ctQrPFjpnalP3W+nYWsNvHWiJ0tc+l5wzKNRP+9owAZCCJEM/BbYR0rpBJYJId4Bzgf6RR2TUmqnIq8XQrwIHDlQHWaijQAKQM6hEGuD3k5o/gnaqsFROPS6ogRLlzF2Jl0p81JCMg6A136qcdB+Vw0BKAbA6YqU3Ct7aetso6KxgtJFpQBu49Are/mm6RsqGisAxbgsq11GyrwUWue0us8FitHQfvdHKPuEQsjluKMF3vgNbHdFv7U5lHGHhMEJ/mlm/TKjBTEB6JVSalKvsRIoCfH4IwDflsbfhBDzgF+BP0kpywes0gDZ2dneKxLskHckVLuCk619D/YPL9KiqbqiBEuXMXYWXaG2HEJFNQRLa5bqbve37e8//N2tQ93e1tlG3B1xTM2f6jYeoeK7fzgGo3RRKTHE8MmMTwLv2NMB/zzVk9c+NgFO/Sek7xlWWJtQMLN+mWEg7ECbz7o2IOiMDyHERcCBgDaL+s3AzyhdVucA7wohiqWUVX7OMROYCcoMQjU1ZXp6OjabzR24Kjk5mezsbKqqlNPExMQwduxY6uvr6ejoAJRwyk6nk8bGRmw2GxkZGcTFxbFhwwYcw6eQgWIgtv/4GhuGH09cXByFhYXU1dW58xrk5+fT1tZGW5tySTIzMxFCuNMtjhgxgrS0NHf44vj4eAoKCqipqXF7IxUWFtLS0sLWrYobXFZWFlJK6urqsNlsOBwOHA6HO7a+zWYjLy+P6upqt8/4mDFjaGpqcodkHjVqFD09Pe5cCKmpqdjtdncugcTERHJzc70ifRYVFdHY2OgOiZ2Tk0NnZ6c7QmdaWhpJSUlUVVVhs9lISkoiJyeHqqoqd590UVERDQ0N7rDXubm5tLe3u321B1JOaqpPbTkB2O12MjIyWLVqFTabLeLltGmTErLZXzn98ssv7lnLkSwnNX+Cv3JatWqVu68/NzeX0wtP58wxZwLwUuVLrN22ltv2vw2Abzd/yz9++AcvHvkiADt6dnDRpxdx1+S7GOdQuqlu+uompmZN5ZSCUwB4ZvUzbO7YzI373QjAFxu/4PFVj/NMiRK0cUvnFq74/AruOfge8u1Kt+nsL2bzQukLNHcq/8ujvzxKZ28ns/dRwlOUbyjne/k9j0x9hNeXvc4ZOWcw+4vZvPjZi9iEMli7qHoRTx/3NN+sU+K07eXYC1usjfeXvw/AMdnH8Nyq53h/+ftMSJ8Q0v1UZC/i/MLz3c8b3XIanYPztdOxN3jS2m6Zch/NnaOhspKcxYvpzMmhedo0Q+UU7H5qampyT3gM9X7yR9Bgfa5BY3+tgc+Bq4HPpZRJmmOuB0qllCcHOO9pwGPAMVJKvyO/Qoh/A+9JKR8IKJRBCtan0lYNT7oSvsTa4I/NEB/ZroKdre96qLF0GcNXl9ktiHB55ahXOOeTc4Lupx0DKSko8eqWUsc8wLvLC/AaN9GOg+ihtjaW1izllaNe4ZEqpce83zF9fbBkNlRoxk7eBYpd0ZO1ofZNTtIV0WB9UspSKaXw85kKrAbihBDjNYdNon+3kVbMb4AngJMDGQdVAhDRkRzdcAOOQhi5j/K9txNWvx5JSUD0xqSxdBljZ9E1NT86gsbtUAd2g2DX9OkvrVlKW2ebu9tKNQ7+9gf6jYNoKV1U2m+9X11lc+GOA7yNw9Zi6DhYMQoxMYNmHMDc+jXgM0kptwNvAncIIZKFEIcDpwLP6+0vhDgKeBH4rZTyK59tKUKI44UQiUKIOCHEdJQxig8HqtMIvmkd3ex5nuf7dw9EJPOaFr+6hhhLlzF2Jl0lBaEOJQ4eF316kSnnKc4upji7mFgRi8PmoHVOK1Pzp3p5WRVnF/s1EqC0FMpnlFNSUMKimkXuZTd9fcDbMHylZ137BLizAqYc4n0yX+Pg+zwJ8/liZv0yy9RcCQwDNgEvA1eoLq5CiHwhhFMIofpi/hlwAO+71juFEB+4tsUDdwFNKPMprgZOk1JG1MnfX05g9rlE6V4C2LgCGr/S32+Q8KtriLF0GWNn0RUtrqR3Tb7L0P5q15GK2nUESstC7VJSWxXF2cU4bA5KCkoon1Hu3hc8LYelNUtZWrPUqyVxXqHmhRGU5GKfXAXDNZNpvwPKVsPVs/oL1WZuLCvzXlYzPpaVGfrfwdz6ZYqBkFK2SClPk1ImSynztZPkpJS1Ukq7lLLWtXyklDLOtU79nODa1iSlPEhKOVxKmSKlPERK+ZEZGo2gDt70I2kk7KFJ7/jdg/r7DRJ+dQ0xli5jWLqMoQ56B0MdW/AdN1HdabVojYBqFNSWg9YY+Ho8VTRWUNFYobjU5pZ6Nsg++O8VsFLjxf8tyuuyGuTg/vv10/v29UFrq3e6X3WMorXVcEvCzHKMzuAr0cz+V8FPi5Tvq1+FknshOTrdFi0sLBQqGisozi72GrxWxyfUFoHWaKiog9b+upwA6O2Gj2Z6ngsA2yfCK796jMPy5TBrlnd6X1DS+8bEeJYXLlQ+MGhjFEawUo7q0NnZGTieyUuHwoYvle/Ff4SjI9OSCKpriLB0GWNn0iVuH/qZvvn2fGqdtcF3ROlOUifYadeBxwCoxkKdU6Fub53T6m41+Hoz+XpAlRSUkGHL4LUznoJ3z4Ka/3hEbN8DylbBLB+PpVmz4L77PA98vXS/2gHmvr6wjEM49cufF5PVgtDB6XQGvsBTboW3Fd9uvn8M9p8FaROGXtcgEWym6t0f383STUt137S0roa+xw02Q3W9grEz6dK6jg4VU7Om8pJTN7Qb4K1R7U7SrlMf6ktrllJSUBJaq8AH7RiGypSkPFh8BDRpBqT3uQS+yIFZW2H+fO/WgsPh/cD3NQ7XXuv9o9deG1YLwsz6FZ3+dkOMOgHLL2NPgrxS5XtfD3zWL6LIoBBUlwH03PbU9SnzUoi7I87LNdA3DIL22H1H7EtFYwUp81JYWrPU3U+7rHYZzi4nbZ1tLKtdRqQx83qZyc6kq+cvPf1iKUUadaKdHmr4jpKCEkoKSrAn2LEn2EMyamo9Vccc1PqrGhS9+0P9nfKTHmT2+le8jcOhc5WscGV3KMZAHU8QQjEWbW36g87aMQe9MQqDvTxm1i+rBREOQkDJ3+EFV4us8i2o/wxypw36Tw80jow2CBqg6x+uNtGdXU73oB3Astpl7htvWe0yd6iDK4qu0I29o6VX9nr190aLh4xFYEoXleqWpxEGsxWiBvnTjiuEil6rIBT2794Cr0wlXv2tmDjY/v/g1VY4FOWB3tqqDEovXw5ffAHXXecxAL5dS0IoYxHaMQftGMUQjkFYBkKHjIyM4DtlTVbC9f6ihBqg/Fo490ulsgyAQA9QX13hPGy1QdDA28PD9yZWH+p627WxcRJ7Q89/u6x2WcQmYIVUjkPAzqTLaJwjPXzHA3zHCPTQGpVnVj/jdbw2Sqx2YFk7ruA7S1oPbeRYddn3ntLOnAa4L3Mcf2yvQpm/i5JD+qTXYOEHnsFl9eEOioFQxxUCDTqXlXkbDtVIhGEczKxfloHQIWgGK7Ugp/5VmVHd26nMi1h+Nxz6l0HRVLqoFNkl+XTDp+5ldTAt1OMrGiv6vWGZ8Wa3uWOzof0j1XqwMqQZQ0+Xs8tpagsgFOMA3vVSrV+xItbdWnB2Ob3GEoJ1Y6oGI9y6lwQ8ZoPz2ivd6/qSRhHz2w8gcxIscOWT1nohzZqltCJUgj3wfbeF2XIws35ZYxA6qEHfdNFOaBlRAIeWebZ9cQc0fh3WbwaakKNy9V5Xu7+rD3t/+6pjCdr1ev7gwQil/1kNvhYKvbKXuDsi84AMWI5DyM6kS+3TNwt7gr3fRDYtetvU+qVt9WrDhqtv91qj4qu7V/bSK3t17xXtbGjfmdHlM8opP/VJvnckc542Z1HWZGqnLlaMA3h3C/kj1PGEAc6oNrN+WQbCCGrfonbw6OUGWKtu74X3z4fudkOnDTQhR90Onhsg0A2mvQGcXU6v84Zzow+0/9mXQNotoo/WOa0ht1KDoZZ9oHoYrHVR0VjhlT9Cb/xAbWmYorvyHXjxQIp6t3vW7XspnLOMnmGjPOv0vJDuv19pRRgZdDZxRrUZRGdbd4ix2/1UYO1bgrYped0MiH8dup2w5Vf49GY4OmjwWS9Ccb37YuMXij7XDaYXfdJ3jEGNmw/mdCdB//5dVVeomPlGGvB3/JXjELMz6dK+oQ8U9cFuhFgRS8n4EkqqSrycK8B7zEG7P/QfQ1AJpYupdFEpsbKPj8dPU7qN3Se3wVEPwn5KdgL39fL1QlqwAA49VBl/UAll0Fn7Aqoeoz1viPkjzKxf1kQ5HXp7e4mNDfCmqzeh5cen4T+atBYnPA97ndf/WA2+A2AlBSUsq12GPcHuNSEHlIp93HPH0dXX5TYkvnMM9MYYVMzsR/Y1EMNih7GjN7SImypy7uDXu6DlOETsTLpKF5V6ea9FAm1Lozi7mI/P/5ijnz8a8LwAqdvA412nBuDz1e8b9jsY5z11MH/atoo9e7d5Vo4ogFPeUJxTXHhdr7Iy5eGujjNICddcA6mpnrf/UB7wWmOjYnBGdTj1K+xw37sj69at87/R34SWvS+Ccad51v3nkrDyV2srvi/XTLzGnW5R66+9rHZZvy4qbVdOSUEJU/On6gYxU/c14uuu9ueqqAlfQsHobw2EgOU4hOxMuspnlNPzl56IRnXVtn6X1izlw28+dNfxts42r8x02uB7bZ1t7pcutatVjbMUinEofaaE+Y9O4PEtX3sbh4Lj4LwVXsYBfK5XWZn3Q1wIZda0tmsolAe83liGQW8mM+uX1cVkBL2mpNbaz1sEWw5X8lb3dsE/T4Nzl0OKfvhdPTc7Fb11E9KV2draZrZqJHy9Q7TfVe8ObWIU1QtEvcHMHmvwx9T8qdYciJ0UdVJaqJ5IgdC6q2rPr55X24o2ck4t2uB7EMQtfHsjf9v2I4d2t7izz3QjeCqpkMvPeB9iQngjN8MLycQZ1WZgtSB08Osm5m9Cy+zZyvpEB5z+Lgxz+SHv2AxvnwwhVPRAMehBqdzfbvzW/fbu2xrwvWGDDQb3yl7TZjdv6Qx95mYkjcPO5E4aDQTSVT6j3D1/xYzuJr2Hv3ZsShuCe6+svej5Sw+tc1qJFbF+67ZvRFZ1IDsolf+EZ/dVjIOLdbFJxJ+3gsuvWOvXOJhejibNqDZTlzUGEQ56Qba0y+s/h9eOUloRoITlOP1fAVOUBhtM00uXqPa76t1s2vWhpl+MRD+zdkzFYuciZV6KKa0Hf+ilDNV2DanjIdrZ01o92mO043p6wfcA2L5RmeC66mWv1a8ljuaJYWP4z/eTlRe/SHoQ6Y1lXHvtoOuwgvUZoK6uLmAi76BNydGHw3FPwQfnu05YDm+dpGskfAeq/fXPF2cXc9HYi5ixZAbgnQ5Sz8tE2w2lHdhTxzACTZgLZRaqlnsOvoebvroppH2NTO4bKEHLcYjY2XSpdTQS3ZCxIrZfN2RdXR3nf3w+FY0V7m3qC4622xRwD1LrzY52I/vgh6fg05ugs9WzvhXoOp2z5r3BWSF4Dw1KOZowo9pMXZaB0KGzszO8A7UFu9d5sK0elt2iLNeVw5v/D854D+KTKX2mRLfQfQOFaW+UDFuG+0bQrvd1Y1XdX7Vugeo4Q6yIDThhTm15aFsgwVoX+fZ8v9v0iFTrIexyHGQsXfpjEGrXqbZbqHRRKVeNu6rfxFDQd3PVw6u+Nf8MH/0B1vt0r+4xHT62w4LH4J4QQmNg8vXyNQq+ywYwU5cpBkIIkQY8BRyHkir0Fm1WOZ99Z7j21fpFniSlLDd6rqhCr2n4ciNkHg22j5V96pfCGyfC6f/iqpercCbFMeOtdSBEyM1333SI4P9NXz2f9kb0t686ANk6p9X9dqbexGrfsNbYhNMlZU2S2zlRH7D+5tOEUhdCrS++c2QqGivoLfKuw9pWqN5cIK1mN907YPlf4et7oK/bsz6lCI5+BAqPhROlYiBUIjUwPETdSqFgVgviIaALyAKKgfeEECvVvNQ6fCGl9Bexzei5TCc/39gbccAJLrNmwfAOSHW5vK7/lM13juTMz7u4b194/bhcnMnxFJ9WrOuvre2CWrVpFXtk7hGSJHXGqZZAN6lqSPS6n7TLqtHQnmf2F7ND0hSpIH0qhssxQuxsuvy9iGjnKwTrftK6b/uOE6hoXWm13Vra+qU1CCHlc5ASKt+GT2+E1irP+pg4OOgmmHIbxA9TBoSvu8772CDeQ6aUo0mT40zX5WLAXkxCiGTgt8CfpZROKeUy4B3g/KE810BoazPY16r1Zlq4UJlEpxbwfffBnZ8p7q8uRqZ20XoTpNrhzP82sKNpA0hJW2eb2/NCr/KfmHei17IaN8Zhc7g9PtSEKNqWhsPmcPftqvuq+L7VB4vXpHZT+eoKFl8nVsT2i3Mz2Bguxwixs+tS61DPX3rcbq/B9m2d0+oue/UBX1JQ4t6udi2pcxu0oWZOzDvRvY9ar7WeSupyPzaugFdL4Z0zvI1DzmFwfoUSbDN+GMydC5Mne+7Z3l4oLg7qPWRKOQZ6doTZgjGzfpnRgpgA9EopV2vWrQQCzazZXwixGWgBngf+JqXsCfNcptPW1mY8ZK5a0NoZkNom452fQUkMnKpsSrHDhaXw6ch0bpnUTbGmImgf7tr+2ONzj+eRKk9SdN/BQ3Vf34E6Fe3gnko4Him+xxyfezxv1rwZ8C0yUuE1tIRVjhFgZ9Olbc1qW7m+LQtfB4tAzgh6M7R9w2ionDn2TNZ2rnVrCdpy2LYePv8T/PQc7rDcALYUmDYP9rsMhOvdWEolkU9FhWIU5s9XWhLqsm8WOA2mlWOgZ0cYmFm/BuzmKoSYBrwmpczWrLsMmC6lLNXZfyxKqdUAewOLgeellH8zei7X9pnATIDc3NzJS5YsASA9PR2bzUZDQwMAycnJZGdnU1WlvEnExMQwduxY6uvr6ejoACAvLw+n00ljYyM2m42MjAzi4uLc0RHtdjsZGRnumYpxcXEUFhZSV1tLZ1cX1NWR//vf03biibQdfzxkZpL566+IrVvZeNBBsGkTI79+Bkf6h4gERX8fMSxILuLMEz7ip0alF+24ycfR0tLC1q1bqWis4LFVj9HT18M9B99DU2cT/6r9Fw1dDcwcNxOAn1p+4qavbmLxMYuxx9mZkD6BMWPGsPCThewxQumSeqPuDeYfO5/PVyldXS+ueZFlG5dxz8H3AFDZVsltK27jmSOeYVjcMACmL5nO9ftezwEjDwDgru/uYuzwsZw77lwAXl/3OiubV/LikS+ydttaftzyI3d9dxcvHvmiuztr+pLp3DH5DiZnTGZC+gRyc3Npb2+npaVlwOWkZs7yV06rVq3CZrN5yqmuzj2Al5+fT1tbm/ttKzMzEyEEGzduBGDEiBGkpaVRXV0NQHx8PAUFBdTU1NDdrfRhFxYWussJICsrCyklmzZtAsDhcOBwOKitVfIp22w28vLy+Pnnn0lIUCrAmDFjaGpqwulUHo6jRo2ip6eHpqYmAFJTU7Hb7dTV1QGQmJhIbm4ua9eupa+vD4CioiIaGxvZvl0JKJeTk0NnZyfNzc0ApKWlkZSURH19PQBJSUnk5ORQVVWFlBIhBEVFRfzyyy/ExyshS/XK6Zr/XsPJo04mKT6JSmclt39zOw8f9jAAO3p2cNGnF/F/B/8f+6TtA8Aza5/h0eMe9Sqn6z66jt/m/RaApRuW8sCPD7hn4ju7nVz/1fUsPGwhh+coLe4blt/A9Xtez6gRo/qV0+rm1fzQ+gPXH3091dXViJ520tc+TcqaJ6DHEzBTxsSxY8IMGsfMpC8hVSmnvj42ua6xw+HAsWABtZMmKeVUW0ve+vVUz55NT2+v33Kqr693h7QYcDnV1ZH28MMkrVxJ/Z13QmYmSRMmkDN6dL9yamhooL293W85NTU1EeMKBRTq/ZSYmKjr5hrUQAghyvH/Bv85cDXwuZQySXPM9UCplPLkgCdX9j0HuFFKOVkIsf9AzmXWPIitW7cyYsQIzwrtINLtt4Oa0i81VWmeXnONEphr+fL+M6yLi5W3EYCrr4bPPoOmCrgY0LxwvW3L4XKnkz2y9/d6S9K6vx6edTjvXfSe36Qmet03eknYfXNDaH3F/cVzUh/4ei6wpaNK+a7lO78tCF8XxEjRrxyjhJ1Rlz93bG2Zx4pYev7SE9Lx2rk50D9YpbYu+9NVuqgUpKT8/P/Aj08pg9DOBu+dik6BI+6BtImedf7iJmlzN/T1BX2DN6UcA0VnCLObKRxdYc+D8PfmrjlxMhAnhBgvpVzjWj0JCHVQWeKe3M7qAZ7LFITvJDh1EEk1pmpFmjXLU7GmTFGWfVMGOhxgsynG4wFXhNfiYv61YgNH79PEsEzl7eK0zgb2S0xm7EkP+tW1tXOrbugAf2gNgdY9UA81NLg/I6EaBHWgWfugmDhyIktmLvHriRWpeQ++iEh4oITBrqDLN1Ae4M63AP6jqapo5+Zo0XvJ8aervHoadP8Pnh4P2+q8N2ZMgpJ/QMHR3uv1BoV9jQN4D1D7GSg2pRwHId2omfXLlJnUQohXUB70l6J4Hr0PHKbneSSEOAH4Vkq5UQixB/A6SrfS7UbP5YtZLYjKykrGjRvnWaEXYVGLWrigP8PaN/prb6+yvns7dX/KJC9b4/Eba1MqdvGVAKT8XyqgvH2/v/x97vnlHq+3MAjccvD1QNLzkPLt19UzEKobrNYTxdnlZGr+VK4adxWXLrvUKzcweBK7RLrloNKvHKOEnVmXNqe5nveS1l1a3R/0xzF8Ixar+Nbnfrp6u+GnRfDB9RC3zWtftgI9x8AdH0Csn/dff/fzrFnKQ/mdd5RW/+zZnjEJHZdTU8sxWHQGA4Sja7CjuV4JDAM2AS8DV6gPdCFEvhDCKYRQfa+OBr4XQmxHefi/CdwdyrmGjGDZolTLrzfDWi/4lupOl2Dn/D0P5O/J40G6KnNvJ3xyFbx9Klx/OXP+2+E+bEL6BLf3R0lBSVCvIF9PJq0HiIo2do3qPeLscvbzdJqaP9XrQV+cXazrs656YmmjbobkjmixS6C+RPjLkKjWL995DSHR1wM/PgPPTISPZnobh23AP4Gtf4S7/uPfOID+/ay2/rUD1g6Hcq8uXKi0OgYzLJFJ6UbNxpR5EFLKFuA0P9tqAbtm+QbghnDOFSn69d/pPeS1+POXDhb9dcECyi/+VNnvxgtAvgA5rmPXvgsjYFIatHV0UrqolBNGncDN424Oqt+3ZaAdg9A+rPU8QvTmPGjPq229qHmA90zaM2AeiqEiGvv5YefV5dsq9XV51k7K9BdSRV2nF1rGX9RVx7AYWHEffHsfbK3xPuGwkfDqZvgCZfbU0gdCz7ngi29CMHXsUG1J+Jx3Zy1HI1ihNnRIS0vzLGgf8ldfrVQStb9SXdb2Z2orkb/+RSn79y/e+xxc64BPH4IjXOuGwwlT4KMeWNTbzmdNn3EzN1N+4RJKnz3SHe8eAg9U+/qO6+3vG7xPRdvy0L7pqd97ZS+LqxbrXkd1u9pKiXSAPq9yjCJ2RV2+3U2BBp3B23miH2r3irMBvr2fkSsfhS6fF5DENDjwRnilFpZ6XL+DhsYO9NKm3p8Ob3ddf91Mu2I5+mKF+9ZBdW0EPA/5KVM832fNUozDV18plUkN9612KWnxTSRy++3K37lzlb9qhb39dljwgDIt8EmUwGEujomDF7at5LmUsUrIgGuvZcbbGo0uKhor3MmEtIPSoT6YffNMqF0B2hmv6sQm7Y39yNRHiEa8yjGK2Fl1lc8op3VOq3uCW0lBCT1/6XGH4lbXq/sGQzUi6qekoIRnviug/KdcyrMK4YlC+Pr/EFrjMGykMsHt0nVKKJv7HjEWGjtYyH4plTEILeokOp9upp21HI1gtSBCYe5cxbX1/vu93zqWL4fOTvjmG4iN9R9DRTUOqgfF/fd7KqY2JMc11yj7rQLuBW4uRg6vUA7v7SLt1wfY9u3DDP9PL60jYGl1jW7Ybj2CtTQCubiC98C1b0A1f/gOWFrsfvgzFP3W9/VySOdmziyoh1Evwc8+B2xLhNMXwF4XKrOfIXzvH38RU0G5H9UxCLWLSTuJLkrGBiKF1YLQ4no7UCcLud8W1PSB6htKbKzykFcr0fXXezdd/Q1o+ZtWP2uWsl01QH19cPlsuKMC0XgOdGa5TzE8uRcugQNOh0Nj+4fG8J3VGmrrQX07VEMaqG+H6luhtsXgOzjd3NnsPk59s3TYHAHTp0YCdzlGGTu7LrWu6GVA1LpUB3VOkBKcG+DLv8KTY5nn/Al7vs/M/rWwKfZS2HIZ7PcHj3EA/TSfCxaEFuBOb1BY27pYscJ7+ymneHsisvOXYyhYCYNUQomoqOeuqno5qIQyucX3PH19SheTv9//820wLR5ORPHv0vB+XxyvpRbz1mZl2oj6lu8vymUw1LkMatx9PVdYX5dF3yBsKlZSoN0HvYlw4KcOyD64awbwBdirFe8kr+3AD0A5UIvyAnXffZF7e1cD9xm9r3dirIRBgfCZPFNz7bUUqLFR1IiKoO+uOn9+6DFU/J1HHVgD/83eL6Du7DvJK/8zvYdBrMu+nBjTw29av+HY2HjeSdufxljFghh9OOslhQk0sKz1aDkj5wyu+/I6emUvS2uWRjTBfSBqamooKCgYahn92BV1heIswfaN8PPz8P1jkFSprOvTbgd6DwDnPvDccx5dxx5LxK6WlB7j4MfzUL1Hd8Vy9MUyENDPva370EO9Kwj493xYutT7XP68KMrKPCE67r/f0620fLl35fNF87ud/+8cePlfxM5bzurzYhiX10eMgBgB54puzm37hk/i03llmJJNyuggdTD0xi2W1iwla1iW1+zpSGaNC4QaMyna2K10dW9Xcj7/8gJU/wf0gkOuRXFTnXYlENdvVnP39u3K+FwkWhEGZjbvDuVoGQiVYBEVfSvN/PmKcVBnXAZ40/AanFZDcoDHUEyZoj+w5ltZq6qUfZcvp+dfyRxxWR+vtfYwKsOVQUr2cVRXE0d1NcGrR3FwVzNfxQd3eQvUjeQPdV+90OHhdG1Z7JykzEsBKWm9RWl5ls8oh94exRj88gKseVMxEr7YHLDXBXDuA7DRte6bB+Cww5TvareS6rixfPng/iNaTEj7uatgjUGoaAaZe1JTiduypX+/o+/097lzlZmXoWSC0pve7y9Eh542Iejp6SEuNrZ/7JibzoSD2qDmo36H/tAL/xoxgSW2LP5z0ae6pw82zqBd9j1uWe0yRsSPYEvXFq9tAfugI0RPTw9xcdH3DrQr6Zp3TCKOHZIrPm2Hpu9g1Uvw1WMQ265/wOhpsPcMmHg23PSn/veDw6G0tNV5CVLSM2cOccOGDXl2NV92pXL0NwZhGQjoN3lm0y23kPm3v4UWUdFIDBW9wWkDbyWbNm0iMzPT/3k2fgfPXEhf7A++Dhd0dsdgO/iPsO+lMHJfEMIzsFi9FIT+Qz1Yi6J0USn7D9+f+368z2t9NBgI9/WKMnYFXSnzUoiRfTz2+TbOioOuSZDgbwJv2h6w1/mwx7ngKPS+36ZMUT7gaVFLCWlp7jf5TZs2kZnl8uQbQIwis9kVylFlsGMx7dz4dOVs3bbNe/JMoAoZagwVven9gSb06LB169bA58kshsajiPkbsK2YHZritcX3wXcPwHOT4G/ZsPIxkvp6QEoWfABzl3if0l8sHV/KZ5RzbO6xXhntQokTFQnUPA3Rxk6tq6cT1r7H/bHtrI53ctaRwDQd47AV2FYM07+GGT/DlFsV4wDeE06nTPGOjqxGPW5tVVro116r3I/gqftR0pLYqcsxRKKvfTRUBOp3HOhbSwgxmUI+f7DzqF1Wty9k2DDgEOCIBBje5TmHbRP893Lej0uC1gJohZ9b7JRduCSs/3NC+oSoGJS2GCS2NypjCuveVz5d27hA79WyHWWC23fAb66GBQv91yf1fgPvcDXgHUV14UI49VQoKhpwruYBoddTsBtgdTH5UlbGtuRkht9wQ/BxBYPnDTrPIgjbtm1j+D/+YXy+hgBuPB2mJcDPr0Js/zLv7BLYDrgIJpwF+UdDrDLZRi9tqYq67d3fvsvw4cND+h8iybZt2yxdBnDr6umEhs+h+kPl07TS7zEbpKB5nWCfj/qgCo/bam9vv4llfvHXZeqq29u++orhX3yhbBuK+Qh+7t1tEycy/IorIqcjRMKpX9Y8iFBweRvJpUth/fr+2Z0G8tYSimdEkPEMKWXw8+h1QU0qhnvegnuAJODk0ZC3HrI9u9gSJPz4tPJJTIWi02DiWcTLPrpF4Bs9Wl8yLF0hIiVsWU38qn9C41KoK/dK2dmPlHEw7nQYdxqj7l3MqIddUQX6Kjz7TJ6szEYOZiT8dZlqXEzlUUd5tkXaOOglGHI9E+Q//hFVYyIqptYvKeUu85k8ebIcMH19cs0nn0ipFL3ymT1byr6+gZ87EHPnev9OX5+yPHeue5c1a9YEPod6jFazuqz9XH218jcfKU9Bynl2Kf+O7qf97zHyfwvT5FV/RY6/HVny9BHS8TeHLHmmRFKGpAz53pfvyZJnSgbhogyMoNdriBhyXb09UjaukHLFfVL+87dSPpzlt/zl35FyfpyUr5RI+eXdUjb94H0v/OUvUhYXe+pcb6/3cqD7JlB9Vc81e7Zc88orkb0XA+nU6BjycvRDOLqAb6TOM9VqQfgiBOTlea8b7LeWAG8phlouepN8tPM1VNTUp7Wuz7tOuP4sOHE0rHnDK33jMPo4tLuFQ22ADTa0fsUHMX2s7dzMdyhjkRZRTk8HNH4F9Z/B+s+g4X/QtS3wMSnjoPB4KDgO8o+EBD9dFmp04pIST51bscITHjuYg4e/SWnaZD2nnqp0O4U7bjdQ/M2RqqqKzO8PIdYYhC9S0vTMM2RccolnXST6PbUD2X5+t6mpiYyMjNDOpR2fUA3N/PkwejQ0NipdAitWKNvVCXxffAFIaPwafn0Nqt6GVv83QS9QFWsnb9zvGFZ0NIw+HIbnR02TO+TrFWEGVVdPJ2z+ATau8Hw2/wB9QWbX2lLozDwE24RTFMOQMtbY7xpx9w71WFfff9Of/qRcL7PGA43i595064oywqlfgzoPQgiRBjwFHAdsBm6RUr7kZ99HgfM0q+KBLinlcNf2chTfGzWC13op5cRQdAzYQLgqQtcrr5Bwzjn93+QjYSQCzJPo6uoiISHB2Dl9B9jmzlXi3Z9yivL2J6Uy8S41Vf+ma62C6g9Z9ulfOKC7lSR0QiVosedAzmHKZ9ShkLEvxCcb02wSYV2vCGCaru7t0PyLcWMAYB+tTFobPRVyp8HIfejq7om+6yUlXd3dHl1D4b3kx3Ow69ZbSbjrrqh5IVIJp34NtoF4GWVOxSVAMfAecJgMIZe0EGIR0CelvNi1XA68IKV80qgOs7yYKktKGFdaaq4XUzBCaEGEnSTd96bq6/M2RKHedL1d0PAFPH8btH8LKe2Kh1RABKSOh4z9IGMSjNwPMidFpKVhalJ5EzGsq3MrtPwCzT97f7ZWh36O1ImKIRg9Tfk7orDf9d9lrpfZ+PFiqjzjDMYdcUSwoyNOONdr0LyYhBDJwG+BfaSUTmCZEOId4HxgTojHnjRQHaZRVgaVlZGNwxLgLQUY+O/7HuvrWRLquWMTIPcI2HgA3L8MEoFZp9Kyn4O0pc9BAco6LxQPGbashtWve1YnjFCMRupESClyfcYpfzXxnXYLpIQdm6FtnfLQV/+2ViktBGe9sfOlFEHmZMiaDNkHQuYBkJgyCMJ3E/x5Du4GYxBmDFJPAHqllKs161YCJSEc+1ugCfANEvQ3IcQ84FfgT1LKchN0hozNZvNeESURJPvpGgpUrWqypHv+yfZ77iHtCWDKQfDO40oro+Fzpctjy2ol/r8vXVth/TLl40tiusdoOMZA8ihIznb9dX2PTwoqNSquV28XtG+C9o1KuOvtjYzc8CvUtMPWddBWrRgDvYB2wRCxyjXKmARZByoGIesAxU05DKLieukQFbp0IiZEhS4dzNQ14C4mIcQ04DUpZbZm3WXAdCllaZBjPwY+k1KWadZNQZmP2QWcAzwIFEspdc21EGImMBMgNzd38pIlSwBIT0/HZrPR0NAAQHJyMtnZ2VS5rH5MTAxjx46lvr6ejo4OAPLy8nA6nWxxheXOyMggLi6ODRs2AGC328nIyGDdunUAxMXFUVhYSF1dHZ2dSkTV/Px82traaGtrAyAzMxMhBBs3KiErR4wYQVpamjtvbHx8PAUFBdTU1LjD9BYWFtLS0uKeMp+VlYWUSkwaAIfDgcPhoLa2FlAqRF5eHtXV1fT0KEM3Y8aMoampCadTyTg3atQoenp6aGpqAiA1NRW73U5dneKxlJiYSG5uLmvXrqWvT3mgFxUV0djYyPbtysMrJyeHzs5OmisqYNMm0l5/naSVK6m/804AkoQg56yzqFq7FiklQgiK8nNoWlVO36YKbFtXMbyzGtH0PTFdrQFqRnD64ofTY8ug1zaSuOFZYEthe3csffF24pLTsaflsLG1k754OzG2FEbljaFx02Y6u/uQMXHk5BawdfsOtjp3IEUcGVk5CCRNGxugr5sRycNIGWGnvm4doq+H+FhBTlYGjfVV9HW0EtPtJMNho711I93OzcT0OEmO64XurXRv20RcRxNxXS3E+AQxDAcZE09X8hi6ho9Dpk5kxJhDqNsxnM5h+RBr819Ozc2AksQ+KSmJ+nqlJZKUlEROTg5VVVWecioqoqGhgfZ2Zf5Dbm4u7e3ttLS0ANb9NKj3UxSUU2JiYnhjEK4xAX+tgc+Bq4HPpZRJmmOuB0qllCcHOG8esA6YIKVcG2C/fwPvSSkfCCgUk8YgUJJ+FxYWDvg8ZhM1uvr6lIlQLtfZ6kceofCKK+Dqqz1ROAMhJTgblAHV1iporVT+tlUpf3s7B/9/iDYSRiitpRGFyl9HofI9bQ+llRAz+B7pUVO/fLB0GSMcXWGPQYTQCkgG4oQQ46WUa1yrJwHBBqgvAP4XyDioEghhKNRM1LeGaCMqdKnjJZp5FT2pri6NBx5QjEOwxC5CwPDRyqff+fsU46Eajm31sH2D69Po+RuKp040IGJgWIbSLZaUBclZbOmykTp6T48RcIwBW8qQe8NERf3SwdJlDDN1Dfi1REq5XQjxJnCHEOJSFC+mU4HDghx6AfB/2hVCiBRgCrAUxc31bOAI4JqB6rQIQqh+7OoYRHa2Mp9CpbgYEhIUd9kBDajHwPBc5ZPnp+Eq+6Bji2IsnBugsxU626CrTfH4cf11tqzHHt+rjHf0dkJvt2JY+npcf10fdb2IVd7UY+KVWFQiTvkbE+9ZH5cEthHKG3/CCO/v6rItFZKzFKOQmA4xsV7ymysrSY1CbyELi37oTa82+gHSgLdRssrWAudqtuUDTiBfs+5Q177Dfc6TAXwNbANagS+BY0PVYUqoDSllT0+PKecxm0HTFUKYDzfasAOzZknZ1yd7rr/eazla2O3KcYBYuoyxK+nCT6gNU/JBSClbpJSnSSmTpZT5UjNJTkpZK6W0SylrNeu+cO27zec8TVLKg6SUw6WUKVLKQ6SU/dOkDTLqwFO0MSi6tGE+1LwSqotta2v/sMZajytXV1LTDTcoywNtPZjMblWOJmDpMsbuoMuKxaSD6qkQbQyKLq1L7cKFnrkXgWaO+/iFO53OqMzZu1uVowlYuoyxO+iyMspZeBsJlWAP/FAz6VlY+OLbKt2F4sHtalgGQodRo0YNtQRdBk2X2q2kxUA61N3ueg2Q3VpXWZl33VLrXoAwNrv19QoDM3VZBkKH3cF9zY1vmI++PuWvdkxiKHSZgKXLGIOuy+h4V6R0hcnuoMsag9ChqakJhyP64gGZqksdQ9AmkA8Q5iNiukzE0mWMQdcVznhXJHSFye6gy2pB7I74NvPnzlX+qslf1Bs5kjH3LXYPwhnvshgyLAOhQ6o6MzjKMEWXv2b+/fd7N/MN3LC79PUaBHZrXWGMd+3W1ysMzNRlGQgd7Hb7UEvQxRRd6hucOs4QEzPghEi79PUaBHZbXWGOd+221ytMzNRlGQgd1IiM0YZpukxu5u/y18tkdltd/sLaz54dcLxrt71eYWKmLmuQenfEXzN//vzwMs1ZWISKv+Q7Vj2LSqwWhA6Jif3SokUFpugK1MyfPFlZ1u4XwkD1Ln29BoHdXpfBSZa7/fUyiJm6LAOhQ25u7lBL0MUUXXrN/PnzPRnirrsuZP90U3UNApYuY1i6jLE76LIMhA5r1wZLUTE0mKarrMy7WR8TAytWhD1wvctfL5OxdBnD0mUMM3VZBkIHNUVgtGGqLt+HfkxM2APXu8X1MhFLlzEsXcYwU5dlICwUBhiPycLCYtcjaE7qnQmzclJLV4LwaGPQdPkOXC9Y0H85wO/udtdrgFi6jGHpMkY4uvzlpLZaEDo0alNpRhGDpitM//RB1zVALF3GsHQZY3fQZYqBEEJcJYT4RgjRKYRYFML+1wohGoUQbUKIp4UQNs22NCHEW0KI7UKIGiHEuWZoNML27dsj/ZMhMai6fAeuDcRj2i2v1wCwdBnD0mUMM3WZ1YJoAO4Cng62oxDieGAOcDRQCIwFbtfs8hDQBWQB04FHhBB7m6TTIhBWEiALCwsNZuWkflNK+TbQHMLuFwJPSSl/klJuAe4EZgAIIZKB3wJ/llI6pZTLgHeA883QGSo5OTmR/LmQsXQZw9JlDEuXMXYHXUMxBrE3sFKzvBLIEkKkAxOAXinlap/tEW1BdHZ2RvLnQsbSZQxLlzEsXcbYHXQNRSwmO9CmWVa/D9fZpm4f7u9kQoiZwExQZhBWVlYCkJ6ejs1mo6GhAYDk5GSys7OpqqoCICYmhrFjx1JfX09HRwcAeXl5OJ1OGhsbaW5uJiMjg7i4ODZs2KAIt9vJyMhg3bp1AMTFxVFYWEhdXZ27UPLz82lra6OtTfk3MjMzEUKwceNGAEaMGEFaWhrV1dUAxMfHU1BQQE1NDd3d3QAUFhbS0tLC1q1bAcjKykJKSUNDA83NzTgcDhwOB7W1tQDYbDby8vKorq52Z5MaM2YMTU1N7gTmo0aNoqenh6amJkAJCWy3292BvRITE8nNzWXt2rVuP+qioiIaGxvdfZo5OTl0dnbS3Kw0FNPS0khKSnLrSkpKIicnh6qqKrcnRVFREQ0NDbS3t6OWUXt7Oy0tLQMupy1btgD4LSdVV6TLadOmTQB+y2nDhg3uaxjJcqqvrwfwW05qvY90OQW7nzZu3OjWFclyCnY/bdq0ya0rkuUU7H5qampynzPUcvKLlDLgBygHpJ/PMp997wIWBTnfSuB3muV017nSgf2Bdp/9rwfeDaZTSsnkyZOlGaxZs8aU85iNpcsYli5jWLqMsSvpAr6ROs/UoC0IKWVpsH0M8hMwCXjVtTwJ2CilbBZCdABxQojxUso1mu0/hXLiFStWbBZC1JigcSSw2YTzmI2lyxiWLmNYuoyxK+kq0FtpSheTECLOda5YIFYIkQj0SCn1smc/BywSQrwIbABuAxYBSCm3CyHeBO4QQlwKFAOnAoeFokNKmTHAfwUAIcQ3UmfSyFBj6TKGpcsYli5j7A66zBqkvg3YgeK+ep7r+20AQoh8IYRTCJEPIKX8N3APsASocX3mas51JTAM2AS8DFwhpQypBWFhYWFhYR6mtCCklGVAmZ9ttSiDz9p184H5fvZvAU4zQ5eFhYWFRfhYoTb0eXyoBfjB0mUMS5cxLF3G2OV17VLB+iwsLCwszMNqQVhYWFhY6GIZCAsLCwsLXSwDYWFhYWGhi2UgMBZiXCjcJYRY7wpXXj5Y0WaNhj4XQowVQvxLCLFNCLFZCHFPNOjSHPeJEEK65s0MqS4hxIVCiBVCiK1CiHohxD1m6TKow2/oe7MJVddgXpuB6PI5ZlDrklFdkbr3jOgy5VmlN716d/ugzLdYjOKOOxUl/tPefvb9HUp487EoEwP/BnwbBboSgCrgOiAZSAT2G2pdmmOmA5+ihFWJG2pdwBXANNd1Gw2sAOZEUgdwPLARJRhlKkpYm3lDXc8H89qYUZ8iUZcMXq+I3XsGdQ34WTUo/8DO9HEVaBcwQbPueX83KnAz8KpmeW+gIwp0zQQ+i7br5druAFYDhwzWTR2OLp/jryPEmF9m6QBeAu7WLB8NNEZLuZl9bczQFYm6FEY5RuTeC0PXgJ9VVheT8RDjrwDjhBAThBDxKPkt/h0Fug4BqoUQH7iauOVCiH2jQBfA3cAjwGDmaBxoqPgjCDHml4k6AoW+N5uBXB+zro0eRnVFoi4Z1RWpe8+orgE/q4Yi3He0YTTE+AbgM+BXoBeoA46KAl25wJHAKcDHwGzgn0KIPaSUXUOlSwhxIHC4S0+uiToGpEuLEOIi4EDg0gjrCBT6PpTkW4Oly43J12ZAuiJYlwzpInL3nlFdA35W7fItCJc1l34+ywAnMMLnsBHANj+nnAscBOSh9DXeDnwihEgaYl07UMKvf+CqlH9HCaG+51DpEkLEAA8Ds6V+4MYh0eVz3tOAecAJUkozInMa0eG7r/o9oOYI6AIG5dqErcvMumSmLhem3HuDoGvAz6pd3kBIKUullMLPZypKf2acEGK85rBAIcYnAYullPVSyh4p5SKUAca9hljX9yh9sgPCZF0jUN4+FwshGoGvXevrhRDThlAXAEKI3wBPACdLKX8woicARnSooe+1+22UUprdejCqa7CuzUB0mVaXTNYFJt17IWJE18CfVZEYWIn2D0pf3csoA0CHE9j7ZS6wDMhCMbDnA9uBlCHWNRFoB45B8Vi4FsWzImGodAECyNZ8DkK5kUYPpS7XvkehdOMcMYTX5zcofel7uW7cTxhcL6ZQdQ3atQlXV6TrksHrFbF7z6CuAT+rBr3wd4YPkAa87bp4tcC5mm35KM26fNdyIvAQSv/eVuBb4DdDrcu17gyg0qWr3N/DMdK6NNsKGVzPEyPluAToca1TPx8Mpg4/ZXYdiqvrVuAZwBbpeh7JazPQ6xWpuhRGOUbk3jNYjgN+VlnB+iwsLCwsdNnlxyAsLCwsLMLDMhAWFhYWFrpYBsLCwsLCQhfLQFhYWFhY6GIZCAsLCwsLXSwDYWFhYWGhi2UgLCwsLCx0sQyEhYWFhYUu/x+dWlbsL72r+AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_size2.ellipse_testing(states2, barpi, alpha=0.05, figname='data/null-ellipse.png', grad_descent={'lr':0.01,'return_gaps':True,'max_ite':5000}, calibrated_from_samples=True, statesnull=statesnull, l2_regularization=100000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6303c539",
   "metadata": {},
   "source": [
    "#### b) Under the alternative"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "6f9eb902",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of the selection event:  2\n"
     ]
    }
   ],
   "source": [
    "theta = np.zeros(10)\n",
    "theta[0] = 0.5\n",
    "model_size2 = PSILOGIT.PSILOGIT(truetheta=theta, regularization=8, n=100, p=len(theta))\n",
    "print('Size of the selection event: ', len(model_size2.M))\n",
    "\n",
    "signull = 0.5 * np.ones(model_size2.X.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "cd2b3a4d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "74e5540b8d694558a5ed0ffedad4648b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/100000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3210\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "610533e370714795b9d4558c87447b5e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/100000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "950f851a80034f7897fdb1c79bf87b06",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/435 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "states2 = model_size2.SEI_by_sampling(model_size2.sig, nb_ite=100000)\n",
    "print(len(states2))\n",
    "statesnull = model_size2.SEI_by_sampling(signull, nb_ite=100000)\n",
    "tildeGN12, barpi = model_size2.params_saturated(signull, statesnull)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "e9567fb2",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Proportion in the ellipse :  0.7514018691588785\n",
      "Proportion outside of the ellipse :  0.2485981308411215\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_size2.ellipse_testing(states2, barpi, alpha=0.05, figname='data/alt-ellipse-1p5-lamb8.png', grad_descent={'lr':0.01,'return_gaps':True,'max_ite':5000}, calibrated_from_samples=True, statesnull=statesnull, l2_regularization=100000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c73da108",
   "metadata": {},
   "outputs": [],
   "source": [
    "# probas = [compute_proba(ls_states_admissibles[i], model.sig) for i in range(len(ls_states_admissibles))]\n",
    "# probas /= np.sum(probas)\n",
    "\n",
    "# idxs = np.random.choice([i for i in range(len(ls_states_admissibles))], size=3000, p=probas)\n",
    "# states = np.array([ls_states_admissibles[i] for i in idxs])\n",
    "\n",
    "# idxs = np.random.choice([i for i in range(len(ls_states_admissibles))], size=3000)\n",
    "# statesnull = np.array([ls_states_admissibles[i] for i in idxs])\n",
    "\n",
    "# thetanull = np.zeros(model.X.shape[1])\n",
    "# signull = sigmoid(model.X @ thetanull)\n",
    "# tildeGN12, barpi = model.params_saturated(signull, statesnull)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}