supp_mat_figures.ipynb 406 KB
Newer Older
Florent Chatelain's avatar
Florent Chatelain committed
1
2
{
 "cells": [
Florent Chatelain's avatar
Florent Chatelain committed
3
4
5
6
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
Florent Chatelain's avatar
up nb    
Florent Chatelain committed
7
    "# \n",
Florent Chatelain's avatar
up nb    
Florent Chatelain committed
8
9
10
    "# <center>*\"Two-way kernel matrix puncturing: towards resource-efficient PCA and spectral clustering\"*</center>\n",
    "## <center>-- Supplementary Material -- </center>\n",
    "## <center>-- Python Codes of main article figures --</center>\n",
Florent Chatelain's avatar
Florent Chatelain committed
11
12
13
14
    "\n",
    "## Preamble: useful packages and functions"
   ]
  },
Florent Chatelain's avatar
Florent Chatelain committed
15
16
  {
   "cell_type": "code",
Florent Chatelain's avatar
Florent Chatelain committed
17
   "execution_count": 1,
Florent Chatelain's avatar
Florent Chatelain committed
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.linalg as lin\n",
    "import scipy.stats as stats\n",
    "import scipy.sparse.linalg\n",
    "import scipy.special\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "\n",
    "from numpy.random import default_rng\n",
Florent Chatelain's avatar
Florent Chatelain committed
33
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
34
35
    "rng = default_rng(0)\n",
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
36
37
38
39
    "%load_ext autoreload\n",
    "\n",
    "%autoreload 2\n",
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
40
    "# user's functions from the local .py file\n",
Florent Chatelain's avatar
Florent Chatelain committed
41
    "from punctutils import *\n",
Florent Chatelain's avatar
Florent Chatelain committed
42
43
44
45
    "\n",
    "%matplotlib inline\n",
    "\n",
    "plt.rcParams.update({\"font.size\": 12})"
Florent Chatelain's avatar
Florent Chatelain committed
46
47
48
49
50
51
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
Florent Chatelain's avatar
Florent Chatelain committed
52
    "## Two-way puncturing of the kernel matrix\n",
Florent Chatelain's avatar
Florent Chatelain committed
53
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
54
    "The data matrix is $X\\in \\mathbb{C}^{p \\times n}$ where $p$ and $n$ are the feature and sample size resp.\n",
Florent Chatelain's avatar
Florent Chatelain committed
55
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
56
    "Then \n",
Florent Chatelain's avatar
up nb    
Florent Chatelain committed
57
    "\n",
Florent Chatelain's avatar
up nb    
Florent Chatelain committed
58
    "$$K = \\left[ \\frac 1p (X \\circ S)' (X \\circ S) \\right]  \\circ B$$\n",
Florent Chatelain's avatar
up nb    
Florent Chatelain committed
59
    "\n",
Florent Chatelain's avatar
up nb    
Florent Chatelain committed
60
    "is the $n\\times n$ *two-way punctured* kernel matrix where $ \\circ$ is the Hadamard (elementwise) product and\n",
Florent Chatelain's avatar
up nb    
Florent Chatelain committed
61
62
    " * &nbsp; $S$ is the Bernoulli iid $(p \\times n)$ random matrix to select the **data** entries with rate `eS`\n",
    " * &nbsp; $B$ is the Bernoulli iid $(n \\times n)$ random matrix to select the **kernel** entries with rate `eB`"
Florent Chatelain's avatar
Florent Chatelain committed
63
64
65
66
67
68
69
70
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulations\n",
    "\n",
Florent Chatelain's avatar
up nb    
Florent Chatelain committed
71
    "bal\n",
Florent Chatelain's avatar
up nb    
Florent Chatelain committed
72
    "$$[\\mu_1^T,\\mu_2^T]^T \\sim \\mathcal{N}(0, \\frac1p {\\tiny \\left[\\begin{matrix} 10 & 5.5 \\\\ 5.5 & 15\\end{matrix}\\right] } )$$\n",
Florent Chatelain's avatar
up nb    
Florent Chatelain committed
73
    "bla $\\otimes$\n",
Florent Chatelain's avatar
up nb    
Florent Chatelain committed
74
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
75
    "#### Figure 1.\n",
Florent Chatelain's avatar
up nb    
Florent Chatelain committed
76
    "Eigenvalue distribution $\\nu_n$ of $K$ versus limit measure $\\nu$, for $p=200$, $n=4\\,000$, $x_i\\sim .4 \\mathcal N(\\mu_1,I_p)+.6\\mathcal N(\\mu_2,I_p)$ for \n",
Florent Chatelain's avatar
up nb    
Florent Chatelain committed
77
    "$[\\mu_1^T,\\mu_2^T]^T \\sim \\mathcal{N}\\left(0, \\frac1p {\\tiny \\left[\\begin{matrix} 10 & 5.5 \\\\ 5.5 & 15\\end{matrix}\\right]}\\otimes I_p\\right)$; \n",
Florent Chatelain's avatar
up nb    
Florent Chatelain committed
78
    "$\\varepsilon_S=.2$, $\\varepsilon_B=.4$. Sample vs theoretical spikes in blue vs red circles. <b>The two \"humps\" remind the semi-circular and Marcenko-Pastur laws.</b>"
Florent Chatelain's avatar
Florent Chatelain committed
79
80
81
82
   ]
  },
  {
   "cell_type": "code",
Florent Chatelain's avatar
Florent Chatelain committed
83
   "execution_count": 2,
Florent Chatelain's avatar
Florent Chatelain committed
84
85
86
87
   "metadata": {},
   "outputs": [
    {
     "data": {
Florent Chatelain's avatar
Florent Chatelain committed
88
      "image/png": "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\n",
Florent Chatelain's avatar
Florent Chatelain committed
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generation of the mean vectors for each sample\n",
    "\n",
    "p = 200  # dimension size\n",
    "n = 4000  # sample size\n",
Florent Chatelain's avatar
Florent Chatelain committed
104
    "c0 = p / n  # dimension/sample size ratio\n",
Florent Chatelain's avatar
Florent Chatelain committed
105
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
106
    "# Set the covariance for the two mean vectorss\n",
Florent Chatelain's avatar
Florent Chatelain committed
107
108
109
    "cov_mu = np.array([[10, 5.5], [5.5, 15]]) / p\n",
    "mus = gen_synth_mus(p=p, n=n, cov_mu=cov_mu)\n",
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
110
111
    "# Set the proportion for each of the two classes\n",
    "cs = [0.4, 0.6]\n",
Florent Chatelain's avatar
Florent Chatelain committed
112
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
113
114
    "# Generate the noisy data matrix and the spikes matrices\n",
    "X, ells, vM = gen_synth_X(p, n, mus, cs)\n",
Florent Chatelain's avatar
Florent Chatelain committed
115
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
116
    "# Puncturing settings\n",
Florent Chatelain's avatar
Florent Chatelain committed
117
118
    "eS = 0.2  # data puncturing ratio\n",
    "eB = 0.4  # kernel puncturing ratio\n",
Florent Chatelain's avatar
Florent Chatelain committed
119
120
121
    "b = 1  # kernel matrix diagonal entry\n",
    "\n",
    "#  Empirical Spectrum\n",
Florent Chatelain's avatar
Florent Chatelain committed
122
    "lambdas = puncture_eigs(X, eB, eS, b)[0]\n",
Florent Chatelain's avatar
Florent Chatelain committed
123
124
    "xmin = min(np.min(lambdas) * 0.8, np.min(lambdas) * 1.2)  # accounting negative min\n",
    "xmax = np.max(lambdas) * 1.2\n",
Florent Chatelain's avatar
Florent Chatelain committed
125
    "xs, density = lsd(eB, eS, c0, b, xmin=xmin, xmax=xmax, nsamples=200)\n",
Florent Chatelain's avatar
Florent Chatelain committed
126
127
128
129
130
    "\n",
    "isolated_eig_0 = spike(eB, eS, c0, ells[0], b=1)[0]\n",
    "isolated_eig_1 = spike(eB, eS, c0, ells[1], b=1)[0]\n",
    "\n",
    "f, ax = plt.subplots(1, 1)\n",
Florent Chatelain's avatar
Florent Chatelain committed
131
132
133
134
135
136
137
138
139
140
141
142
    "sns.histplot(\n",
    "    lambdas.flatten(),  # color=\"blue\", cbar_kws={'edgecolor': 'darkblue'},\n",
    "    stat=\"density\",\n",
    "    ax=ax,\n",
    ")\n",
    "plt.plot(xs, density, \"r\", label=\"Limiting density\")\n",
    "plt.plot(\n",
    "    isolated_eig_0, 0.002, \"og\", fillstyle=\"none\", label=r\"limiting spikes $\\rho_{1,2}$\"\n",
    ")\n",
    "plt.plot(isolated_eig_1, 0.002, \"og\", fillstyle=\"none\")\n",
    "plt.plot(lambdas[-1], 0.002, \"ob\", label=r\"Largest eigvals\")\n",
    "plt.plot(lambdas[-2], 0.002, \"ob\")\n",
Florent Chatelain's avatar
Florent Chatelain committed
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
    "\n",
    "plt.legend()\n",
    "plt.xlim([-2, 5])\n",
    "_ = plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Figure 2.\n",
    "Illustration of Theorem 2: asymptotic sample-population eigenvector alignment for $\\mathcal L=\\ell \\in\\mathbb R$, as a function of the ``information strength'' $\\ell$. Various values of $(\\varepsilon_S,\\varepsilon_B,c_0)$ indicated in legend. Black dashed lines indicate the limiting (small $\\varepsilon_S,\\varepsilon_B$) phase transition threshold $\\Gamma=(\\varepsilon_S^2\\varepsilon_Bc_0^{-1})^{-\\frac12}$. <b>As $\\varepsilon_S,\\varepsilon_B\\to 0$, performance curves coincide when $\\varepsilon_B\\varepsilon_S^2c_0^{-1}$ is constant (plain versus dashed set of curves).</b>"
   ]
  },
  {
   "cell_type": "code",
Florent Chatelain's avatar
Florent Chatelain committed
159
   "execution_count": 3,
Florent Chatelain's avatar
Florent Chatelain committed
160
161
162
163
   "metadata": {},
   "outputs": [
    {
     "data": {
Florent Chatelain's avatar
Florent Chatelain committed
164
      "image/png": "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\n",
Florent Chatelain's avatar
Florent Chatelain committed
165
166
167
168
169
170
171
172
173
174
175
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
Florent Chatelain's avatar
Florent Chatelain committed
176
177
178
179
180
181
182
183
    "eSeBc0s = [\n",
    "    (0.1, 0.1, 1),\n",
    "    (0.2, 0.025, 1),\n",
    "    (0.1, 0.2, 2),\n",
    "    (0.05, 0.05, 1),\n",
    "    (0.1, 0.0125, 1),\n",
    "    (0.05, 0.1, 2),\n",
    "]\n",
Florent Chatelain's avatar
Florent Chatelain committed
184
    "ells = np.linspace(1, 400, 100)\n",
Florent Chatelain's avatar
Florent Chatelain committed
185
    "plt.figure(figsize=(8, 4))\n",
Florent Chatelain's avatar
Florent Chatelain committed
186
    "for eS, eB, c0 in eSeBc0s:\n",
Florent Chatelain's avatar
Florent Chatelain committed
187
188
189
190
191
192
193
194
    "    plt.plot(\n",
    "        ells,\n",
    "        [spike(eB, eS, c0, ell)[1] for ell in ells],\n",
    "        label=\"({},{},{})\".format(eS, eB, c0),\n",
    "    )\n",
    "plt.xlabel(r\"$\\ell$\")\n",
    "plt.ylabel(r\"$\\zeta$\")\n",
    "plt.grid(\"On\")\n",
Florent Chatelain's avatar
Florent Chatelain committed
195
196
197
198
199
200
201
202
203
204
205
206
207
208
    "_ = plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Figure 3.\n",
    "\n",
    "Phase transition curves $F(\\ell)=0$ for $\\mathcal L=\\ell\\in\\mathbb R$ and varying values of $\\ell$, for $c_0=.05$. Above each phase transition curve, a spike eigenvalue is found away from the support of $\\nu$. <b>For large $\\ell$, a wide range of $\\varepsilon_B$'s (resp., $\\varepsilon_S$) is admissible at virtually no performance loss. Here, also, sparser $B$ matrices are more effective than sparser $S$ matrices.</b>"
   ]
  },
  {
   "cell_type": "code",
Florent Chatelain's avatar
Florent Chatelain committed
209
   "execution_count": 4,
Florent Chatelain's avatar
Florent Chatelain committed
210
211
212
213
   "metadata": {},
   "outputs": [
    {
     "data": {
Florent Chatelain's avatar
Florent Chatelain committed
214
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt4AAAERCAYAAABMwqCjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAgAElEQVR4nOzdeXzU1b3/8deZJeskIQkkLCHs+y5xRSBtrRWVqtW2KrUbra3We3tvW7pctdJeW21vF29/LtVr7Sa1tC64UqvVKODGIossAQXCTghL9pBJ5vz++CYYspCZZLYk7+fjMY9JvvP9nvM5wzDzyZmzGGstIiIiIiISWa5YByAiIiIi0hco8RYRERERiQIl3iIiIiIiUaDEW0REREQkCpR4i4iIiIhEgRJvEREREZEoUOItIiIiIhIFUUu8jTFZxpinjDHVxpgSY8z1HZz3H8aYncaYCmPMAWPMr40xnhaPDzfGvGqMqTHGbDPGXBStNoiIiIiIdFU0e7zvA+qBXGAB8IAxZlI75z0LnGWtTQcmA9OAf2/x+GPAu0A2cCvwuDFmQCQDFxERERHpLhONnSuNManAcWCytXZ707E/A/uttd8/w3XZwFJgu7X2ZmPMWGAT0N9aW9l0zgpgibX2t5Fuh4iIiIhIV3k6PyUsxgKNzUl3kw3A3PZObhqG8lsgDSgDvt300CRgZ3PS3aKc9nrOMcbcCNwIkJycPHPo0KEhBR0IBPAbP4f9h8nx5JDkSsLTUE1y7UGqU4cScCWe8Xp/APZXBeifbPB5TUh1R0MgEMDl6p3D/Htz26B3t09ta2v79u1l1tpe/81e6/fsIUOGhPR8VTZWcrzxOHkJebjC8IWuK+AntbqEuuRc/J60bpfXkc5eF8frLBX1lmHpPfv/RW/+v91SX2hnX2gjROg921ob8RswGzjU6thXgaJOrhsD/DcwsOn3G4C3Wp3zE+APncUwc+ZMG6pXX33Vrj201k7+w2S7av8q52Dxi9bekW7t3jWdXt/QGLDn/OQl+7U/dX5uLLz66quxDiFienPbrO3d7VPb2gLW2Ci8V8fTbebMmSE/X49uedRO/sNke7z2eEjXdajsfef9fsPS8JTXgc7a+dMXttixt74Q0RiioTf/326pL7SzL7TR2si8Z0frz5UqIL3VsXSgsp1zT7HW7gA2A/d3p5zucBnnKQrYgHPA09TL3VDX6bVul+GCUf1Zv/dEpMITERERkR4iWon3dsBjjBnT4tg0nKS6Mx5gVNPPm4GRxpiW3/kFW06XeFzOaJyuJN4AM4dlcqiijm2HKiIRnoiIiIj0EFFJvK211cCTwI+NManGmFnAFcCfW59rjPmKMSan6eeJwA+AfzWVsx1YD9xhjEkyxlwFTAWeiFTszT3eDYEG58CpxPtkUNd/ZHwOAKt3Hw97bCIi0vt5XIaGgKWmviHWoYhIN0VzZPzNQDJQirMk4E3W2s3GmNnGmKoW580CNhljqoEXmm7/1eLxa4ECnFVS7gausdYeiVTQbuMGWvZ4Jzn3jcEl3oMzkhiQlsiqHWWRCE9ERHq5mcMyaQxYNu4rj3UoItJN0VrVBGvtMeDKdo6vAHwtfv9SJ+XsBgrDHF6Hmnu8G22jcyDEHm9jDB8bn8MLmw5ircWY+FvdRERE4ldKQvOQx8gv/ysSDLfbzfvvv4/f7491KBGVkZHB1q1b230sNTWVvLy8kFc9iVri3VO5XU6Pd2OgKfF2hzbGG2BqXj/+unov2w9XMW5g5JakEhEREYmkiooK0tPTGTx4MMnJyb26Q7GyspK0tLZ5WyAQYP/+/ZSVlZGTkxNSmb1/EcZuah5q8mGPd9NQkyB7vAEunpSLx2V4Yt2+cIcnIiIiEjWlpaUMGTKElJSUXp10n4nL5SI3N5fy8tCHfynx7kTHywkGn3j39yXysQk5PLluH/7GQLhDFBEREYkKv99PQkJCrMOIOa/XS0ND6BOelXh3wmNaLycYeo83wKfOyqOsqp41Wt1EREREerC+2tPdUlefAyXenTi1nKBt+qvG7QHjCmmMNziz0gE27tNmOiIiIiJ9kRLvTjRPrgwEWgwR8SSFnHj39yUyYVA6z208GM7wRERERKSHUOLdiTbLCYIzzruxPuSyPlOQx6b95Ww5oF0sRURERCJl0aJFTJw4kdLS0pCuu/feeykoKCAxMZGvf/3rYY9LiXcn2qxqAl3q8Qa4cvoQEtwu/r52b7jCExEREZEWiouLee2115g4cSJlZaFtYDh48GBuu+02vvzlL0ckNiXenWizcyU4Pd7+0BPvzNQEPj4xl2Xv7qe+QaubiIiIiITbsmXLuO666yguLmbMmDEhXfupT32KK6+8kuzs7IjEpg10OtHuUBNvCvhrulTepwvyeH7TQe58fgs/vmJyOEIUERERiYkfPbs54kNoJw5O5475k4I+/5VXXmHBggVMmjQJr9cLwOWXX87KlSvbPf/CCy/kueeeC0usnVHi3QmPy3mKTu1cCd1KvGePGcDw7BSeXLef788bf2orYBERERHpvo0bNzJmzBhuvvnmU8eilVh3RllfJ5qHmpxaThAgIQXqu5Z4u12Gn18zjc88+CbLNx3i6pl54QhTRETCzZvi3JfHdl5OalMHzYEToQ9xFIm0UHqio6GqqgprLSUlJcyZMyfW4bShMd6dcLvcGAwNgRaJtzcF/NVdLvPs4ZkMz07h23/fQHmtPwxRiohI2KUPgn7D4PCWmIYxeUg6iR4XxYe0IpZIZyoqKigrK+POO+887fi8efPw+Xzt3ubNmxe1+JR4B8Hj8rRNvLvY4w3Obke3fNQZ7P/MhgPdDU9ERCLFFfsvho0xuF3aKVAkGGvWrGHQoEFMnTqVl156CWstAMuXL6eqqqrd2/Lly09d39DQQF1dHY2NjTQ2NlJXV9elreE7osQ7CB6X5/Qx3gldH+Pd7OqzhjBhUDqLn9nM8erQ1wQXERERkQ/5/X6WLl3KwoULmTt3LsXFxSFv7X7nnXeSnJzM3XffzdKlS0lOTm7Te94dSryD4DGe08d4e1O71eMNTg/G1+eOpDFg+dVL27sZoYiIiEjf5vV6WbJkCYsXL+b111/nlltuCbmMxYsXY63FWktFRQXWWhYvXhy2GJV4B6HNUJOE7o3xbnbF9CFMGZLBn98qoag4tJ2VRERERKRnUeIdhLZjvFMh0ACN3Z8Y+avPTAPg7uXbTo1DEhEREZHeR4l3EDwuD/5AiyQ7oWmJqfru93qPyU3j1ksnsO1QJT98enO3yxMRERGR+KTEOwjtrmoC3Z5g2eyG84eR6HHx57dKeH37kbCUKSIiIiLxRYl3ENzGffqW8Qmpzn03J1g2S/K6eek/5wLw+Ufe4cCJ2rCUKyIiIiLxQ4l3ENr2eCc792GYYNksPzuFX3/WGe99yT2vs1/Jt4iIiEivosQ7CF6Xt/2hJmHq8W521Yw8FpybT0VdA1fcu4r6hkBYyxcRERGR2FHiHYS2ywk2DTUJY493s59cNYWFF46grOok03/8T2rrGzu/SEREcBnnI62usS7GkYSfyxhq/fo8EOnplHgHocPJlWHu8W72X5dO4LKpg6ipb2T+vSuprOv+soUiIr3d1AFTAVh3eF2MIwm/6UP7sWb38ViHISLdpMQ7CB5Xq50rT/V4RybxdrsM9143g8JxA3i/tIqzf/Iyu8rC37suItKbpCekA5z+ft1LZCR7aQhorweRYC1atIiJEydSWhr8BoUnT55k4cKFDBs2jLS0NC688EKWL18e1riilngbY7KMMU8ZY6qNMSXGmOs7OG+RMeY9Y0ylMWaXMWZRq8d3G2NqjTFVTbd/Rjp2t3FHdDnB9hhj+MOXzuH6c/Op8wf4yC+K+O1rH0SsPhEREZHeoLi4mNdee42JEydSVlYW9HUNDQ0MHTqU1157jfLycm699VY+85nPsHv37rDFFs0e7/uAeiAXWAA8YIyZ1M55Bvg8kAlcAtxijLm21TnzrbW+ptvFkQwaOtgyHiI21KSln141hXuvnwE4u1t+9U9rqNM4PxEREZF2LVu2jOuuu47i4mLGjBkT9HWpqaksXryY4cOH43K5mDdvHiNGjGDt2rVhi80TtpLOwBiTClwNTLbWVgErjTHPADcA3295rrX25y1+LTbGPA3MAv4ajVjbE+kNdDpz+dTBnJWfyfX/9xYvbTnMpDte5C9fOZeC4Vm4XSYqMYiIiIi0sfz7cGhTZOsYOAXm3R306a+88goLFixg0qRJeL1eAC6//HJWrlzZ7vkXXnghzz33XJvjpaWlbN++nUmT2usn7pqoJN7AWKDRWru9xbENwNwzXWSMMcBs4MFWDy0xxriAd4FF1toNHVx/I3AjQG5uLkVFRSEFXVVVRVFRESeOnqDcX37a9XOMh33vb2WnDa3M7rijAB7e5GHVgQY++9BbjOnn4uvTEslO7toXF83t6416c9ugd7dPbeu7Wr9nh/p8lfmdr5S3bt1K+t70sMR0Tm0tlaWlbI3gv1sw7Sw9UkdNdaBHv376yuu/t7czIyODxsZGKisrAUj01+NqjOy8ioC/npNN9QVjw4YNDBs2jC9+8Yun4nzsscfOeE1lq/L9fj8LFy7k+uuvZ8iQIW0eB6irqwv53zpaibcPKG91rBxI6+S6xTjDYX7f4tgCYB3OkJRvAi8aY8Zba0+0vtha+xDwEEBBQYEtLCwMKeiioiIKCwt54bUXOH7sOKdd/1Yq+YP6kx9imd1VWGjZsK+cb/9tPTuOVPPt12pZcG4+/3XpBFITQ/vnbG5fb9Sb2wa9u31qW9/V+j3b5/OF9HztrdwLT8KECRMoHBX8dWe0MZmUnBxyI/jvFszr4u/713E8UElh4Rn7q+JaX3n99/Z2bt26FbfbTVpaUwr3yV9Fpd6EIM+rqqoC4ODBg1xyySVdqisQCHD99deTkJDAgw8+eKrXvLWkpCRmzJgRUtnRGuNdBbTufkgHOvzzxRhzC85Y78ustSebj1trV1lra621Ndbau4ATOL3iEeN2tZpcCeBNjcoY79aMMUwf2o9/fbuQuz41hfQkD0ve3sOkO17k5//YRmlF71u/VkRERCQYFRUVlJWVceedd552fN68efh8vnZv8+bNO3WetZaFCxdy+PBhHn300Q6T7q6KVo/3dsBjjBljrd3RdGwasLm9k40xX8YZ+z3HWruvk7ItTu93xLQZ4w3OBMsIbKATiuvOyWf+tME89vYefvLCVu4v+oCHV+7impl5LLp4HJmpwf59KCIiItLzrVmzhkGDBjF16lReeuklLrroIowxQS8LeNNNN7F161ZefvllrA3/Ep5R6fG21lYDTwI/NsakGmNmAVcAf259rjFmAfBT4OPW2p2tHss3xswyxiQYY5KalhrsD6yKZPztJt7elJj0eLfmS/Tw1Tkjeff2j/ONj4wiI9nLX97ew4z/folZd7/CS1sOs+947OMUERERiSS/38/SpUtZuHAhc+fOpbi4GGe6YHBKSkp48MEHWb9+PQMHDmTQoEH4fD6WLFkSthij1eMNcDPwCFAKHAVustZuNsbMBpZba31N590JZAOrWzxZj1prv44zJvwBYBRQB6wH5llrj0YycI/xtN2QISE1aquaBCMzNYFFnxjPok+M5w+rdrFuzwme2XCAr/5pDQALzs1n1AAfV8/MIyM5vF+biIj0Wi4P1LWZQhR1bpehotZPIGBxaTUrkXZ5vd5TSfLixYtDvn7YsGGn9XJXVlZ+OJY9TKKWeFtrjwFXtnN8Bc7ky+bfR5yhjM3A1IgEeAbt9ngnpkHV4WiHEpQvzhrBF2fBwgtHsPVgBbcue48lb+8B4Jf/LOasYZnccN4wvNZirQ3pr0ERkT4l/1zY8kyso6BgeCbPbDjAwYo6hvRLjnU4ItJF0ezx7rG8Li+NgVab1iSmQ9mO9i+IE9OG9mPa0H5cPTOP+oYA//uvHazZfYwVO8pYscNZdsv90nK+MnsEF4zqT0ayl+lD+8U4ahGROOJNhQiM8wxVstcNQEDbxov0aEq8g9DuqiZJ6XAy+DUlY8nrduF1u/ivSycAsO1QBf947xC7du3m6Q/8PPjaTh58zRlOf/HEXPKzUnC5DAvOzWdYdmosQxcRERHpNZR4B8HjcsZ4nzYsIzENTlbENrAuGj8wnfED0ykqOsCt185h77FaKuv8LHp8I6veL2MVUF3fyEOv72RsrjMKKCPZyy8+PY2kpl6XJI+bjBSNFRcREREJlhLvIHiM8zQ12Aa8pinZTEyHxnrw14E3KYbRdU9OWhI5aU78q2+96NTxJ9bu4+Wtzhj2vcdrWL37OHP/p+i0a788awTjB3046WBE/1TOHp4V+aBFREREeiAl3kHwuJoS70ADXldT4p2U4dyfrOzRiXdHrp6Zx9Uz8wBnMfnl7x3iRI0fgJr6Bu58fiuPrNrV5rqLJ+aS2NQrDpCa4ObWyyaQlqTecREREenblHgHoWXifUpiU0/vyQrwDYhBVNFjjOHSKYNOO/bZs4dSXus/9XvJ0Rp+/OwW3i+tOnWs8mQDRypP8tfVe9tdwnD+tEF8pmBou3VmpiQwNCslTC0QERERiT0l3kFoTrxPW9kkMd2576HjvLsrLcl7Wi92XmYKL/7nnDbn/W7lLvYea7ve+eNr9/HoW3t49K09HdbxxQuG09/X8e6bKQkePnfeMBI8UdkHSkRERKRblHgHoeUY71OSmhLvur6ZeAdr4YXtL8v+7x8bw7t7jrf72MHyOhY/s5k/vLG70/Lve/V9RuX42hwvP1HL/cVvnvp9YHoSd189BXeIG08ketydnyQiEiVxsLKhiHSDEu8gdDrUREKWlZrAxybkdvj4defkEzjDJ4y1cNuyTexppzcdwBhozrFLjtbwzq5jPLPhQMhxzhqdzRcv6HBPp6B43IZZo/qrZ15EumxEf2dp1/X7TpCfrWF4Ip1ZtGgRzz//PEVFReTk5AR9XWFhIW+99RYej5P7DRkyhOLi4rDFpcQ7CM2Jtz/w4ZjmD4ea9Iy1vHsat8vg5sy90z+/ZlqHjxUVFVFYeD4AjQHLX94uoaKuocPz2/PX1XtY9f5RVr1/NKTr2jMmx8f5o7K7XU6z/ftP8kr5ewBcOmUQ540MX9kiEn+GNyXe5TX1MY5EJP4VFxfz2muvMXHiRMrKykJKvAHuvfdevvKVr/TsLeN7snZ7vJtXNdFQk7jndhluOH94yNctvHDEaZNFu+rHz25hR2klz3ahx70jfn8D3rIDHK/x86c3Sxgewx4wX5KHX3x6GqkJ4Xk7OVITaHdeQCQNykjC49Y3EiIivcGyZcu47rrreOSRRxgzZkyswzmNEu8gtD+5UkNNerskr5vJQzK6Xc7fvn5+GKI5ndOjX8ia3cd49K0SYjXsc//xWtaUHOeSe1aEt+DXXw1veZ0Ym+vj81344yxUH+z1UxjxWkREoudn7/yMbce2RbSO8Vnj+d453wv6/FdeeYUFCxYwadIkvF5nIYjLL7+clStXtnv+hRdeyHPPPXfq9x/84Ad8//vfZ/To0dx9990UFhZ2K/6WlHgHod3JlW4veJKVeEtMFQzPoiDGmxa9su0wx6r9nZ8YpG3btjJ+/ISwldeZP725m437yrlt2XsRryvRDXdEvBYRkb5t48aNjBkzhptvvvnUsZaJ9Zn87Gc/Y+LEiSQkJPD73/+e+fPns379ekaNGhWW2JR4B6HdoSYAyf2gtv2VOUT6io+O73iSbFcUVb5PYdPmTdFw9VlDOFJ1Mip1vfnGm52fJCLSg4TSEx0NVVVVWGspKSlhzpy2yxx35txzzz3184IFC1i2bBkvvPAC//Zv/xaW+JR4B6HDxDulP1R3f+KdiMSOMYactOjsPpuRGNpyliIiEpqKigrKysq48847Tzs+b948Vqxof1jk7NmzWb58ebuPGWOwYVzHU7OJgtDuqiYAqf2h+kgMIhIRERGR1tasWcOgQYOYOnUqL7300qmkefny5VRVVbV7a066T5w4wYsvvkhdXR0NDQ0sXbqU119/nU984hNhi0+JdxA67PFO7Q81ZTGISEREosK4oLEeGsM3j6ErXMb5tqSmvrGTM0X6Lr/fz9KlS1m4cCFz586luLgYY4L/ptHv93PbbbcxYMAA+vfvz4MPPsiyZcsYN25c2GLUUJMguI2ze2GjbfWGp6EmIiK9W95MeOs+OLjR+TlGMlO85GelsKbkOF+LWRQi8c3r9bJkyRIAFi9eHPL1AwYMYPXq1ad+j8Q63urxDoLX5SxF026Pd30l+OtiEJWIiERcUj/nvvX7f5QZY8hI9tIY0J7xIj2ZEu8geN1O4l3f2GrHsNT+zr2Gm4iIiIhIJ5R4ByHBlQBAfaBV4p3SlHhXK/EWERERkTNT4h2EBLeTePtbT65JVeItIiIifUs4l9frqbr6HCjxDkJz4n2ysdUmG6kDnHsNNREREZE+wOv1Ul9f3/mJvZzf78fjCX2NEiXeQWhOvNuM8U7Jdu7V4y0iIlGgyZUSazk5Oezfv5+ampo+2/MdCAQ4fPgwGRkZIV+r5QSD0OEY76QMcHm1iY6IiETc6BwfL289HOswpI9LT0+noqKCAwcO4PfHdn37SKurqyMpqf2djVNTU+nfv3/IZSrxDkKHPd7GOL3eGmoiIiIRNjQzmaqTsV3WUASgsbGR0aNHxzqMiCsqKmLGjBlhLVNDTYLgMi48Lk/bxBuccd7aREdEREREOhG1xNsYk2WMecoYU22MKTHGXN/BeYuMMe8ZYyqNMbuMMYtaPT7cGPOqMabGGLPNGHNRNOJPcCW0HWoCkJqtoSYiIiIi0qlo9njfB9QDucAC4AFjzKR2zjPA54FM4BLgFmPMtS0efwx4F8gGbgUeN8YMiGTgAInuxPZ7vFP6a6iJiIiIiHQqKom3MSYVuBq43VpbZa1dCTwD3ND6XGvtz62166y1DdbaYuBpYFZTOWOBs4A7rLW11tongE1NZUeU1+09w1ATJd4iIiIicmbRmlw5Fmi01m5vcWwDMPdMFxljDDAbeLDp0CRgp7W2slU57fWcY4y5EbgRIDc3l6KiopCCrqqqOnVNoD7A3oN725Qx9Eg1o+qrWPHycho9ySGVH2st29fb9Oa2Qe9un9rWd7V+zw71+SrzO50gW7duJX1velhiyjy2kWnAunfXUbGzNixlthZsO3eX1IOlx76G+srrvy+0sy+0ESLTzmgl3j6gvNWxciCtk+sW4/TK/76Tcoa0d7G19iHgIYCCggJbWFgYdMDgvLk1X3PPsnvI7JdJmzI2HIKdf2L29NHQf0xI5cday/b1Nr25bdC726e29V2t37N9Pl9Iz1f5yXJ+svQneAd5KZwZ/HVndCgbNi7mrLxkCFeZrQT7utiTuJtnPtjMkAkzGZPb2cdn/Okrr/++0M6+0EaITDujNca7Cmjd/ZAOVLZzLgDGmFtwxnpfZq1t3jIy5HLCJcGd0P5Qk7RBzn3lwUiHICIiZ5CRmEFeWh4Hq8L4fpw7GYwLTuwNX5ldNHmIs1nHvhOR6XkXkciLVuK9HfAYY1p2CU8DNrd3sjHmy8D3gY9Za/e1eGgzMNIY0/JP/Q7LCacOE+/0wc59hRJvEZFexxicOf+xFx9RiEh3RCXxttZWA08CPzbGpBpjZgFXAH9ufa4xZgHwU+Dj1tqdrcrZDqwH7jDGJBljrgKmAk9Eug0J7gRONp5s+0DaQOe+8kCkQxARERGRHiyaywneDCQDpThLAt5krd1sjJltjKlqcd6dOEsFrjbGVDXdftvi8WuBAuA4cDdwjbU24gtpJ7gS8Afa2Ro1MQ0S0qDyUKRDEBEREZEeLGpbxltrjwFXtnN8Bc6kyebfR3RSzm6gMMzhdarDHm+A9EFQoR5vERGJPGttrEMQkS7SlvFB6nCMNzgTLJV4i4hIBA3NSsHtMqzfcyLWoYhIFynxDlKHQ00AMofBiZLoBiQiIn1Kf18iaUkeyms7+CwSkbinxDtIZxxqkjUSqo/AyYivaigiIiIiPZQS7yCdcahJZtOw9GO7oheQiIiIiPQoSryDdMahJlkjnftjO9t/XERERET6PCXeQTrzUJPmHm8l3iIivY4x0NH7fwzUNwZiHYKIdJES7yAluBMI2AANgYa2DyamQeoAOK6hJiIivc6g6bDn7VhHAcCUIRms2X081mGISBcp8Q5SgjsBoONx3lkjNcZbRKQ3Sh0ADXWxjgJwVjY52aAeb5GeSol3kBLdiUAniffRD6IYkYiIiIj0JEq8g+R1eQGoD3SQeOdMgMoDUHMsilGJiIiISE+hxDtIzUNNOpxgOXCqc39wQ5QiEhGRvqhBkytFeiwl3kFK8iQBcLKhg8R70DTn/tDGKEUkIiJ9zYRBaRwor+PAidpYhyIiXaDEO0jJ7mQA6ho7mGCTkgXpeXBQibeIiERGbrrTCVTrb4xxJCLSFUq8g5TscRLv2oYz9DIMmqoebxERERFplxLvIDUPNTlj4j1wKpTtgPrqKEUlIiIiIj2FEu8gBd3jjYVDm6ITlIiIRIeNrwmNgYCNdQgi0gVKvIPU3ONdd6ZNFPLPB5cXipdHKSoREYm4AeOgdAvUVcQ6EsbkpAGwbo92rxTpiZR4BymoHu+ULBg4BfavjVJUIiIScf3ynR5vf+xXEsnLcj6LKusaYhyJiHSFEu8gNSfeZ+zxhg8nWFp9DSgiIiIiH1LiHaQkdxCTKwEGTYe6cjiyLQpRiYiIiEhPocQ7SG6XmwRXArWNnSTe4y4F44YNj0UnMBEROSU9MZ09lXtiHUbEJHpcJHpc7D6q1bNEeiIl3iFI9iZT29kYv7RcZ5Ll7pXRCUpERE6Z2n8qJRUlsQ4jYhI9biYOTmd3WU2sQxGRLlDiHYIkd1LHO1e2NGSGs6Rg7YnIByUiIqcYY2IdQsS5+kAbRXorJd4hSPYkdz7GG2DSp6CxHt57IvJBiYhIdNj42aa9Uet4i/RISrxDkOxJ7nxVE4DBMyBnErz7aOSDEhGRyMqZ6NzveSu2cTQZm5vGuj3HlXyL9EBBJd6mL3x3F4Sge7yNgRmfgwPr4PCWyAcmIhKHjDEJxpgCY0x6rGPpln5DnY/YxewAACAASURBVPv6qtjG0SQvM5mTDQEl3iI9ULA93iuMMRkAxphJxpiHjDHfNsZ4gq3IGJNljHnKGFNtjCkxxlzfwXkfMca8aowpN8bsbufx3caYWmNMVdPtn8HG0F1JnqTgerwBpn7G2cVy/ZLIBiUiEr9eAG4FXjTGfM4Ys8UY84YxZmqsAxMRiYVgE++Atba86ec/AOuBROD/hVDXfUA9kAssAB4wxkxq57xq4BFg0RnKmm+t9TXdLg4hhm5J9iRT0xDkTPLU/jBuHmz4KzTURzYwEZH4lGStvQr4OPAz4DzgeuB/YhpVD+d1O19CH6/RZ4tITxNs4t1ojPEYY0YBHmvt/dbanwLjgrnYGJMKXA3cbq2tstauBJ4Bbmh9rrX2HWvtn4GdQcYWNSH1eAPMuAFqymDHi5ELSkQkflljjLHWVgHF1toKa+1uwB3juHq0mcOyANiwVytnifQ0wQ4V+TnwJpAK/KbF8eQgrx8LNFprt7c4tgGYG+T1rS0xxriAd4FF1toN7Z1kjLkRuBEgNzeXoqKikCqpqqo67ZoTR09QXlMedDkm4Oa8hCwanv0Bqw+lgomvuayt29eb9Oa2Qe9un9rWqxwE1hlj3MBAY8xinG9MM9o7ufV7dleer33H9tHY0BjW5zmx7gjnA9uKizlUEb5ym4XazpIKZ3WVTe+9R0IP2iW5r7z++0I7+0IbITLtDCrxttYuN8asAAZaa98HMMaMAXYHWY8PKG91rBxIC/L6lhYA6wADfBNn7OB4a22bP/2ttQ8BDwEUFBTYwsLCkCoqKiqi5TVvv/M2699fT0jlNH6exFX3UJhd5oz7jiOt29eb9Oa2Qe9un9rWe1hrPwNgjPECE4DJwDnAgQ7OP+092+fzhfx8vbP6Hdw73OF9nsv3wVswftw4xp8VxnKbhPq62HygHN5YyeTJkymcNDDs8URKX3n994V29oU2QmTaecYuWGPMOmPMRICmISLvG2MyjDHZ1tod1trrgqynCmg9qz0dqAw1YGvtKmttrbW2xlp7F3ACmB1qOV2R4k2hxl9DwAaCv+ijt0FyFrx5L1jNQBeR3q/lZweAtdYPlAAvWmv/y1p7Reyi64KkDHAnwuHNsY4EgAG+RIyBbQdD/ggVkRjrbOzDaGvtFgBjzFebjqUDy0OsZzvgaeolbzYNCMe7mMXp/Y64NG8aFkuNP4Stet1eOP9mOLgBXrw1csGJiMSPcH12xIfENMgaCRX7Yx0JADnpSfT3JXKoIojlbUUkrnSWeJ80xiQ1/fxrAGvtXmBMx5e0Za2tBp4EfmyMSTXGzAKuAP7c+lxjjKupTq/zq0kyxiQ0PZZvjJnVtDZskjFmEdAfWBVKPF3lS/ABUOUPcS3X829xxne//VuoOhKByERE4kpYPjviSpxtZ2HQl6giPVFnifdLwEPGmNuBgDFmpDEmja71MN+MMxmzFHgMuMlau9kYM9sY0zKTnQPU4qz/mt/0c/Na3WnAA8BxYD9wCTDPWnu0C/GErDnxrqwP8es9bzJ87XVnu+FHPgGBEIaqiIj0POH87JB2DM1KYeO+1lOnRCTedZZ4fx1nXe0BwPeB54An6EIPs7X2mLX2SmttqrU231r7l6bjK6y1vhbnFVlrTatbYdNjm621U5vKyLbWfsxauybUWLoqzevMBQ25xxtg4BQYczEc+wBe/EGYIxMRiSth++yQ9o0e4ONYtdbxFulpzriqibW2Arip+XdjzD5gEvD7CMcVl7rc493ss4/CXXnOkJPUATDnO2GMTkQkPuizQ0SkfSEtLG2tfcZae5e19lCkAopnp3q867vQ4w3gSYRbVkOCD175b1j1v2GMTkQkPkXzs8OFC3+jH3+jP7wFGxfUhzCxPsJcLqj1NxIIaKC3SE8SXzu6xLkuT65sKXM43PSG8/NLP4R3H+1+YCIiAsDUAVOpD9Sz5diW8BacVwB73w5vmd0wY2gm5bV+PjjSjc8jEYk6Jd4h8Hm7OdSkWeYw+GbTZptPfwNW/BIaTnYzOhERSUtwvplsDDSGt+CkDAg0hLfMbkhPdkaK1vk1WV+kJ1HiHYJkTzJu4+5ej3ezzOHw1Vecn//1Y/jtbKg51v1yRUSk15s4KAOANSX63BDpSZR4h8AYgy/B1/0e72ZDZsJ/bIL8C6CsGH49CXYWhadsERHptXLSEwFnnLeI9BxKvEPk8/rC0+PdrF8+fOkFmLMI/DXwpyvg0WviZmtiEREBMM5Qk3BP2uyi5v18TmqoiUiPosQ7RGkJaV1f1aQjxsBHb3OGnvTLh/dfggcugGf+HcrjY4tiEZE+bchZTuK9f22sIwEg0eNm/MA0Vu/WUBORnkSJd4h83jAONWltyEy4+W24+neQnAXr/gi/ngiPXALHdkF9dWTqFRGRM0vJdu4b42fTmqzUBOo01ESkR1HiHSJfQpiHmrSWkAJTroHv7YLLfgWDpsGeN+E30+Gng+GtB6DkjcjVLyIiPcKYHB/v7a/gZIOSb5Ge4ow7V0pb6QnpbK/fHp3Kzl4IBV+GLU/Dnrfg7QfgH993Hht3GST6YNY3IXdSdOIREZG4kZeZQn1jAH+jJVGf5iI9gv6rhsjn9VHpj9BQk/YYA5OudG5zvuNMulz+PTiyDY59ABuXQnImuBPgkrsgayR4kmHAuA9n34iISHjE0VCTZv6GACTGOgoRCYYS7xD5EnxU+6ux1mKindim9oeRc+Ebbzm/Fy+HD15xxn6vXwKPf/nDc8dd6owZB2fjh4KFzh7DIiISupyJzrbxe96G0RfFOhoAJg1OB2BNyXE+PjE3xtGISDCUeIcozZtGwAaoaagh1Zsa22DGzXNuAOfdBOX7nFn3T38Dil9wbs1W3uNs2tOs4EuYQMbpO2YaN7j1khCRni9gw7zMXkoWeJKgoTa85XZD81reNfXxs6OmiJyZsqwQZSQ6u4WdOHki9ol3SwOnODdwxn83b20c8MMz/waVhz88t2QllKxkLsDrLcpweeCSuyEjr235qTmQNzNCwYuIhEd+ej4A75W9R8HAghhHE1kDM5JJ9LjYsLecK6YPiXU4IhIEJd4hyk52lpQ6WnuUIb44faNzucCV0PRLAlzzyOmPl26D4ufZuXMXI0eOcI5VHXEmb77wnY7LnXiFk4B3JGc8nP2VboUuItIdQ3xD8Lg8lNeXxzqUiPMlehiQlsiJ2vgbdy4i7VPiHaLspA8T7x4rZzzkjGdPYxEjZxd+ePy8m6C2nc0Yqo7As9+EXSs6LrP5uhW/Bk+Qs3ymXwdTPhN02G14U8A3oOvXi4iEwpcDh7fEOorTDEhLpPhQFCf8i0i3KPEOUVZSFgDH6nrhbmGZw5xbe7699czXVh+Fl38I/rrg6tr8FLxyp3PrjrO/0u5yioMObIc1O7tXNsCoj3X8nIhI3zJwKpRFaTnZIE3L68fS1XupbwiQ4NEEepF4p8Q7RFnJTuJ9tK4H93hHQmo2XHFf8Od//Eew87Wu1+evcYbFrH643YfHAYTr83HC/DAVFD6TjpTB4aa2T70WJlwe24BE+oI4XKJ15rBM/vDGbooPVTIlLyPW4YhIJ5R4hyjRnUiaN61nDzWJBxl5MGNB98qYfj2cbP8r1jfeeIMLLrige+VvetxZpvHoB90rJwKSa6vhaDmUboGtz0I8TfTtptmNjbDKHd1KJ8x3NquKsPTyYqAw4vVIpJjTV4KKA76mnXNqtXW8SI+gxLsLspKzeudQk54mIdW5taM+MQvSBnav/AtucW5xaE1REYWFhc6GShseA2tjHVLYHNi7j6FD21lZJ1LW/wU2/tW5Rdg0VxJc8bWI1yMRMng6bFnmrBKVFh/rZk8e4vRyryk5xjkjsmIcjYh0Rol3F2QnZWuoicSH3ElwcTfHyceZD4qKGFpYGL0K5yyC/WujUtWmTe8xPSo1SUQ0r+rUEORcligYkJZIvxQvWw5UxDoUEQmCEu8uyE7O5oMT8Tf8QES6ILkfjP5YVKo6sS/KQ2ikT5iW14+9x2piHYaIBEFToLsgKymLstqyWIchIiLtSHYnU1pTGv6CvcnOfeXB8JfdDSkJbkorTxII9J4hZyK9lRLvLshJyaGivoK6OPq6UUREHNNzplN8rDj8Beef59wf2hT+srth5rBMDpbXUVYVXxM/RaQtJd5dkJPijPM7UnskxpGIiEhrHleERlG6vJEpt5uaJ1iuLTke40hEpDNRS7yNMVnGmKeMMdXGmBJjzPUdnPcRY8yrxphyY8zudh4f3vR4jTFmmzHmoogH30pOspN4R+SrTBERiU/eZHB54PjuWEdymjE5PoyBrdrBUiTuRbPH+z6gHsgFFgAPGGPabjkI1cAjwKIOynkMeBfIBm4FHjfGRHXf8OYebyXeIiJ9SKIPciZC2Y5YR3KabF8iw7NTtbKJSA8QlcTbGJMKXA3cbq2tstauBJ4Bbmh9rrX2HWvtn4E2+30bY8YCZwF3WGtrrbVPAJuayo6anFQl3iIifZKJzxGa0/IyWFui/SVE4l20lhMcCzRaa1tu4r0BmBtiOZOAndbalt+nbWg63oYx5kbgRoDc3FyKiopCqqyqqqrda6y1JJgE1havZdiRYSGVGU86al9v0JvbBr27fWpb39X6Pburz1dZWRlVDZF5rqecdJFyfANvh7HscLwuPDX1HK/x88TyV8hOjs8/DvrK678vtLMvtBEi085oJd4+oLzVsXIgLUzlDGnvZGvtQ8BDAAUFBbYwxE05ipp3B2zHwCcHkpidSOHc0MqMJ2dqX0/Xm9sGvbt9alvf1fo92+fzden5WvbqMk4cPxGZ5zqwEl7/RVjLDsfrIiGvjMe3v03WiMkUjs8JT2Bh1lde/32hnX2hjRCZdkbrz+IqIL3VsXQg1Jkg4Sqn2walDmJ/1f5oVysiIp2YNmAaeyv3Rma/hYRUwELFgfCX3Q3ThvbDl+jhuY3xtca4iJwuWon3dsBjjBnT4tg0YHOI5WwGRhpjWvaUd6WcbhuTOYYdx3fQGGiMdtUiInIGaQnOR0RE3p+HNq3lfXhL+MvuhtRED+eOyGL9Xi0pKBLPopJ4W2urgSeBHxtjUo0xs4ArgD+3PtcY4zLGJAFe51eTZIxJaCpnO7AeuKPp+FXAVOCJaLSjpVH9RlHXWMehmkPRrlpERGIlUmuEh8HkIRl8cKSa49X1sQ5FRDoQzRkYNwPJQCnOkoA3WWs3G2NmG2OqWpw3B6gFXgDym37+Z4vHrwUKgOPA3cA11tqo72STn5YPwJ6KPdGuWkREYiW5n3N/rM3CWzE3bqDT07/1oJYVFIlXUfvT3Vp7DLiyneMrcCZNNv9eBJgzlLMbKAx7gCHKT/8w8T5/8PkxjkZERKKi/xhIzICj78c6kjY+Mi6HtEQPy9bv54LR/WMdjoi0Iz7XHOoBclJySHInUVJZEutQRESkhUR3IgBldRGYXAnODpZVhyNTdjckJ7gZleNj++Gqzk8WkZhQ4t1FLuNiaPpQ9lbsjXUoIiLSwoycGQBsPbo1MhXknwv710Wm7G66ZPJA1u89wfulSr5F4pES724YljaM3RW7Yx2GiIi04HV5I1vBoOlQvgcq4m/pvmtm5mEMPLMhvpY7FBGHEu9uGJM5hpKKEmr8NbEORUREoqWfM8eHk1HfQqJT/X2J5KQlUnxIEyxF4pES724YnzUei2X78e2xDkVERFrxB/yRKTi9abPkQxsjU343zZ86mH9tLeVI5clYhyIirSjx7oaJ2RMBeLf03RhHIiIizfon96d/cv/IvTcPmurcl8bXJjrNrj0nn4aA5fG1+2Idioi0osS7GwamDmR81nhW7l8Z61BERKSJ2+UmKymLkw0R6vFNSIWBU+N2guXoHB/jctN4c+fRWIciIq0o8e6mKf2nsPXoVvyNEfpKU0RE4k9CKsTx/J6Jg9N5d89xausbYx2KiLSgxLubZg+ZTaW/krWla2MdioiIRMvgs2DfamhsiHUk7frs2UOprGvguY1a3UQknijx7qbm9WLfK3svxpGIiEizAckD2HFiR+QqyBkPNgCHN0Wujm44d0QWIwek8tg7e2Idioi0oMS7m/ol9WNC1gT+ufufsQ5FRESajMsax6HqQ5GrYPBZzn1phDbp6SZjDNefk8+6PSfYpqUFReKGEu8wuHL0lWw9tpVtx7bFOhQREQEMBovFWhuZCnImQGI67H07MuWHwdVn5ZHgdvHHN0piHYqINFHiHQaXjbwMr8vLsveXxToUEREBBvsG0xBoiNxwE5cbBoyHPW9BpJL7bspMTeCzZw/lsXf2sHr3sViHIyIo8Q6LjMQMPpb/MZ7b+Rz1jfWxDkdEpM8b1W8UAMfqIphwTv0MHNkGRz+IXB3ddOtlE+iX4uUPq3bHOhQRQYl32Fw1+irKT5bz6t5XYx2KiIhEQ46ziVq87mAJkOR1c/VZeby4+ZB2shSJA0q8w+TcQecyMHUg9757L40BrZsqIhJLLuN8vNX6ayNXyZCZzv3hzZGrIwyua9rJ8oGi+O2ZF+krlHiHidvl5pOjPsnuit08u/PZWIcjItKnjc8aj8fl4d0jEdo2HsCbBEPPgy3L4nacNzg7WS44N59HVu1i++HKWIcj0qcp8Q6jm6fdTHZSNrevup0jNUdiHY6ISJ+V7EkmwZUQuW3jm838Ahx9P65XNwH4z4+PJT3Jw3f+viFyK72ISKeUeIeR2+XmWwXfAuDa56+lIRCfO5qJiPQF47LG8W5pBHu8AfLOce7jfLhJf18it142gY37ynly3f5YhyPSZynxDrNPjvokF+VfRGlNKXe9fVeswxER6bNyU3KpbYjgGG+ArJHObdPjka0nDD51Vh4FwzK5a/lWqk+qY0gkFpR4R8AvC39Jbkouf9v+N5ZsXRLrcERE+qS8tDz2Vu6l/GR55CpxueCsL8CeN6A0vjdR87pdfH/eeI5V17PocQ05EYkFJd4R4DIuHr30UQDufudufrH6FzGOSESk7xmRMYJG20hFfYS3TJ++AFxeWPfHyNYTBgXDs/jeJeN5YdMhHnhNq5yIRJsS7wgZmDqQp698GoA/bvkj3339u1TWaza5iEi0ZCZmArDzxM7IVuQbABMuh/V/AX9dZOsKgxvnjGT+tMH8z4vFFBWXxjockT5FiXcEjcwYyarrVjEodRDLdy3ngscu4L719+Fv9Mc6NBGRXm9K/ykAkds2vqWZX4S6E7Dl6cjX1U3GGH529RTG5abx74+9S8nR6liHJNJnKPGOsPSEdJ664ikWFSwC4Lcbfsv8ZfO5f/39Gl8nIhJB/ZL6MSx9GOtL10e+suFznEmWa/8Q+brCICXBw0M3FGCM4cY/reVYdX2sQxLpE5R4R0GqN5XPT/o8K69dyewhs9lftZ8HNjzAOUvO4Y437mDbsW0crzse6zBFRHqd0f1G817Ze5GvqOUkyyPFka8vDPKzU7jv+rPYdbSaq+5fxdEqbSkvEmlRS7yNMVnGmKeMMdXGmBJjzPUdnGeMMT8zxhxtuv3cGGNaPG6byqhquj0crTZ0V0ZiBvdfdD9vX/82X5r0JRI9iTy540k+/eynmbN0Dv+38f/43abf8f7x92MdqohIrzAxeyJH645GdmWTZtMXgDsBXl4c1ztZtnThmP489tVzOVhex4KH32bvsZpYhyTSq3miWNd9QD2QC0wHnjfGbLDWtt514EbgSmAaYIGXgJ3Ab1ucM81a22Oz0xRvCt8q+BYLpyxk7eG1rD60miVbl/Cbd38DwD3r7uHcgecCkOhJ5Pbzbqd/cv9T17uNmxZ/i4iISAemD5gOwIYjG5iTNyeylfkGwEdvg5d+CLtXwojZka0vTGYOy+KRL5zNTUvWcuV9q1jy1XMZPzA91mGJ9EpRSbyNManA1cBka20VsNIY8wxwA/D9Vqd/AfiltXZf07W/BL7K6Yl3r5CRmMFH8z/KR/M/yrdmfotG20jR3iIe2/YY/oCf2oZath7ayscf//hp16V507jzwjvxuNr+800bMI2MxIxoNUFEJK6N6jcKl3Gx8cjGyCfeAOfcCCt+6dyGzXKGoPQAF47pz7JvzOK6h97iy79fzcNfOJuJg5V8i4SbicYEP2PMDOANa21yi2PfAeZaa+e3OrccuNha+3bT7wXAq9batKbfLXAQZ5jMG8C3rLW7O6j3RpwedHJzc2f+9a9/DSnuqqoqfD5fSNeE27rqdZT6P1zuaW/9XjbWbuzw/GSTzDm+czot9+zUs8n2Z8e8fZESD/92kdSb26e2tfWRj3xkrbW2IAIhxZXW79kPP/xwWF4Lt++7nfyEfL6a89VulxWMwftfYOyOB9k97Fp2j7iu0/Pj6TVfUtHIr9eepLLe8slRXuaP8uIK0zes8dTOSOoL7ewLbYTIvGdHa6iJD2g9wK4cSAvi3HLAZ4wx1vkrYS7wFpAC3Ak8Z4yZbq1ts/+ttfYh4CGAgoICW1hYGFLQRUVFhHpNuBXStv4dx3dQ19B2rdgndjzBP0v+ybqT685YZmV9Ja9VvkauJ5eUhpQuxeV1ebn13FsZlDqoS9eHQ5InicykzHYfi4d/u0jqze1T2/qu1u/ZPp8vLM/XZe9cxtLipcw4f0Z0vhG0c+HxIwwvXsbwT/0QMoac8fR4e11c9tGT/PjZLTy14QBHXf346VWTycvs2mdFS/HWzkjpC+3sC22EyLQzWol3FdD6O6t0oL0dZVqfmw5UNSXdWGtfbzpeb4z5JlABTAA2hTXiODYmc0y7x6cMmMLiCxZ3ev2q/at46v2nKC0tJSczJ+T6a/w1rNi/gi/84wshXxtuCyYsYEy/ts9HcWUxR7cfjUFE0RFP7ctOzqZwaGGswxDp0IycGSzZuoSSihKmDpga+QqNccZ67/gnLP0cfGk5eJMiX2+Y9Pcl8r/XTuecEVn85PmtXHLPCn7x6Wl8YlKu5heJdFO0Eu/tgMcYM8Za27yTwTSg9cRKmo5NA97p5LxmFtA7QQhmDZnFrCGznL/k5hZ2qYx3Dr7D/qr94Q0sBDUNNdz9zt0s2bqk45PejF48MRFH7ZuRM4MByQPCUtaRI0d4tujZsJQVb46XHW/3WyyJrLMHno3X5WX5ruXRSbwBskfBVQ/C0gXw/LfhinudhLyHMMbwufOGMXfsAL7+6Fq+/uhazsrvxw/nT2L60H6xDk+kx4pK4m2trTbGPAn82BjzFZxVTa4ALmjn9D8B3zLGvICTVH8b+H8AxphJgBendzsZZ6jJfmBrxBshpzlnUOfjyCPtqtFXUVFf0e5jb775Jueff36UI4qeeGlfVX0Vt6+6nfKT5WFbrq3GX0P5iSgs/RYDfr92rY2FrKQsLsq/iGc+eIZvnvVNkjxR6n2ecDnM+S68/nMYPB3Oic4Y83AampXCkzdfwONr9/Gbf+3gqvtX8YXzh/Oti8eSnuSNdXgiPU40lxO8GXgEKAWOAjdZazcbY2YDy621zaPXHwRG8uHQkYebjoGzFOEDQB5QjTO58nJrrT7N+qAUbwop3vbHHWZ6MhmYOjDKEUVP3LQvFR67/LGwFtmbxw4WFRXFOoQ+65qx17B893JeKnmJ+aPmd35BuBT+AA5thOXfhUAjnPu1HtXzDZDocbPg3GF8ctpgfvnP7fzxzd089e5+vjxrBAvOy6e/LzHWIYr0GFFb58hae8xae6W1NtVam2+t/UvT8RUtkm6s47vW2qym23dbjO9+xVo7rqmMnKbydnRUp4iICDjDTfLT8nl8++PRrdjlgqt/B2PnwT++By/eGt36wygtycviT07i2VsupGBYJr9+eTsX3PUK3/n7BnaXVcc6PJEeoWcsMCoiItINxhiuGXsN60rX8cGJD6JbeaIPPvuos8b3W/fByz+CQCC6MYTR5CEZ/O6LZ/Pyt+Zw3TlDeW7jAT76yyJu/NMaVuw4QiDQM3btFIkFJd4iItInXDH6CjwuD38r/lv0K3e54JK74azPw8pfwd9ugOr4WJmoq0bnpPGjKybz+nc/wtfmjmJNyXFu+N07XPSr13ig6ANKjqoXXKQ1Jd4iItInZCVl8clRn+SvxX9l45GONyKLGJcb5v8GPnEXbP8H3FsA7y6BKGxkF0k5aUl875LxvPmDj/Lrz06jX4qXn/1jG3P/p4hL7nmd/315B9sPVxKNDftE4p0SbxER6TO+e/Z38Xl9/HLNL2kItNl3LfKMgfNvhq+vhP5j4embmbbhNijr+dOVEj1urpqRx5M3z2Ll9z7CbZdNIC3Jwz3/2s7Fv36dH6yo5ef/2MamfeVKwqXPUuItIiJ9Rqo3le8UfId1petYvmt57ALJmeBsrDP/f/FV7YIHLoCXF0PNsdjFFEZ5mSl8ZfZI/v71C3j7Bx/jv6+cTHay4cHXdzL/3pVc+LNXuX3Ze7yw6SBHq07GOlyRqInmcoIiIiIxd8XoK3hs22Pc9c5dTBswjfz0/NgE4nLBzC/yztF+zKp6AVbeA+/8n7Pk4Pm3QEpWbOIKs5z0JG44bxhD63Yx7ewLeHnrYf7x3iGeWLePP79VAsDoHB9nD8/inBGZnD08Kyxb1IvEIyXeIiLSp7iMi18V/oprn7+WL7/4Ze6/6H7GZo6NWTz+hH7wqYdg1n84m+2s+BW8/aCz4c7ML0Lm8JjFFm6ZqQl8umAony4Yir8xwKb95by18yjv7DrGcxsO8Ng7ewAYnJHE2SOyOCs/k8lDMpg4KJ3kBHeMoxfpPiXeIiLS5+Sl5fG7i3/HzS/fzDf+9Q0evvhhhqUPi21QuRPh03+AOVucBHzlPbDy1zBiDsz4vLMTpjc5tjGGkdft4qz8TM7Kz+TmQmgMWLYdqmD1rmOs3n2cNz44ytPrDwDgdhlGD/AxeUgGU/MylIxLj6XEW0RE+qRxWeO492P38rWXvsbnXvgcf7n0LwxNHxrrsD5MwC/eB+v/Au/+GZ78CiT4YOwlMPGTMPrjubLnYAAAGCFJREFUkNC7hmO4XYZJgzOYNDiDL84agbWWQxV1bNxXznv7y9m0v5zXtpfyxLp9gDNPdWhmCmNzfYzJTXPuc9IYneMjyauEXOKTEm8REemzJmRP4E/z/sT1L1zPp5/7NN89+7t8asynYh2WIyMP5n4XZn8Hdq+A9x6Hbc87994UGH0RTLwCxn4CEtNiHW3YGWMYlJHMoIxkPjFpIMBpyfjWgxXsKK1ix+FKXtt+BH+jbboO8rNSGJOTxqgBqeRnpzA8O5X8rBQG90vG7TKxbJb0cUq8RUSkTxueMZylly/lR2/+iDveuIO1h9eyqGAR/ZL6xTo0h8sFI+c6t8t+DSWrYMvTsO052PoMuBMh/zwYPhtGzIbBM8CTGOuoI6K9ZBzA3xhgd1k1O0qr2H64kh2Hq9hRWsnrO45Q3/DhLqFet2FoVgrDslIYlp3KsKakfGhWCkP6JWvoikScEm8REenzhqYN5cGLHuT+DffzyKZHWLFvBd85+zvMHzkfY+Koh9Tt+TAJv/R/YO/bsPVZ2PU6vHonvAp4kmDITMg/H4adD0PP7ZU94i153S7G5KYxJjeNS6cMOnU8EHB6yHcfrWbP0Rp2H/3/7d17cFzVfcDx72/fLz2sB5INtsFgg1/YmCSldmgc05YEQkPbGaZ5lZmmJXQKyTQNbV5/pEwmTZgwzYQk0NBAJrSQTgIJyWTIQJu6eRjCI+FhYiwTwMa2ZGI9V7va9+kf5672rrRCWrHalXZ/n5kz995zz+6enyUd//bsuXeTHBtJ8MrpJI+/PEIiky97nlURP2s6w6zpDHNmZ5g1nSFWd5SOe9uCOmOu3hBNvJVSSinA6/Fy40U3cvnZl3PzozfzqZ9/iu+/+H0+fNGH2XnGzkZ3bzaPF9bvtgXsPcCP/gKOPgrHDtgLM3/2RRAP9G+HNbvstn87nLEFgrHG9r8OPB6ZTqR3n1t+zhjDcCLD0eEEx0aSnBxLcXJsipNjUxwbTvLYb4eJp8u/ZMnnEfo7QqzpCNPXEaI3FqS3zVViQcbThnzBaIKuKtLEWymllHLZtGoT33rnt/juwHf5yq+/wgce+gC7ztjFey54D/vW7SPgDTS6i5VFumDzVbYApCfh+ONOIv4oPP8APHW301igawP0b4O+7Xbbez50rrcJfQsQEXpiQXpiQS5eX/me6ROpLINOQn7CScptSXHwxDivTaRmzZoDfPT/HqI7GihLyN0Jek8sSFc0wKpIgM6IH79Xv8+wVWjirZRSSs3gEQ/XnH8N79rwLr4z8B3ue+E+bvrpTXQEO7jinCt493nvZkvXluW1DGWmYAzO3WcLgDEwfhyGnoNTB2HoWRh81q4XL/IGofs86Nlov9K+Z5OzvxEC0cbE0UDtIT/t/X7O7597qU4ineP0ZJrfxW35xa8O0tm/zh479S8Mxjk9mSZXMHO8js8m4tEAXRFn6yTmXVG/sy2d7wj78eiM+oqkibdSSik1h4g/wrVbr+X9m9/PY4OP8eCLD3L/wP3c98J9nNd5HlefdzVXbriSnnBPo7s6PxHoXGvLBVeU6lMT8NohOH0YTg/A6SM2KT/0AzClCxNpPwu6zoFV6+3MeOf60n6sz14E2oKiQR/RoI/13faNSXj4MHv3nj+rXaFgGJvKTifoo8kMo8kMI4kMo4kMI8kso4kMg+MpfjM4wXAiU3ZhqJtHoDMSYFXET0fYlvaw375RCPtoD81d1xby4dMZ9obRxFsppZSah9fjZc+Ze9hz5h4mMhP8+OUf8+BvH+SLT36RW5+8lS3dW9i9Zje71+xmR+8O/F5/o7u8cKF2WPd7trjl0jDykpOMOwn5yMtw5BGYPFXe1ht0knpXMt65FmL90OaUFufxCF3OTPbrzaAXGWOYyuadxDzLSNJJ0BOuhD2ZYWIqx+nJDC+dTjAxlWUilSM/x8x6UTTgpb2YsLsS8/bpZN1He9hPzHlTEQt67RuMgI9Y0DfnzL2anybeSimlVBXaA+1cc/41XHP+Nbw0/hIPv/IwB04e4K6Dd3Hnc3cS9oXZ1beLS/ov4ZI1l7Bp1SY8sgJnGH1BOGOzLTNlp2DsVRg7CqOvONujdnvyVzA1Oushb/VG4OBZNgmfTshXQ1uf3cacbZN9MdBiiQiRgI9IwMdZqxb+OGMMiUzeScKzTEzlGJ/Kzj5OlepOjKU4NBVnIpUlnsrN/yJA4H8eIhL0TifjUSc5LyXrM+oCs+ujQR+xgD1ulVl4TbyVUkqpRdrQsYHrd1zP9TuuZyIzwZNDT/LY4GP8cvCX3PrUrfAUdAQ72NazjW3d29jes53N3ZvpDfcu7/Xh8/GHoXeTLZWkxmH8BEwOQdyWoRee5KwOnz1+9TGIn4J8evZjg+0Q7YFID0S6Idrt2nfqo932ONJj156v5H/LGhMRYk6Cu4Zw1Y/PFwyT6RwTU1km0zkS6ZyzzU/vHzx8hDPWrCPhPp/JMZHKMTiecj0mx0Inx4M+D7Ggj5DfSzjgJRLw2n2nRAJeQoHScTiwwK2zH/R5lsXfnCbeSimlVA20B9rZt24f+9bZixlPJU7x+NDjPDH0BAeHD3LnyTspOGumO4OdbFy1kU2rNmHihp7TPZzbeS5hX/WJ0rIU6rClb8t01Yv5/Zy1d2+pjTF2ZnzyFMQHbSIeH7SJefI0JIftxaCDT0PiNBSylV/LF3KS8GJi7krUw52lvgTbS/uhDk3Y5+D1yPS68bnszx1l794L5n0uYwypbKEsgU9m8mWJ+XRSn7HHU9k8qWyeZCbPVCbPWDLDoHOcytq6ZDaPqXK1iwjTiXjISeTD8yT346ey/EHB1PRCVk28lVJKqSXQF+3jqnOv4qpz7e39ktkkh0YOcXjkMAOjAxwZPcIDRx5gKjfFvT+6F0FY176ODR0bWNe2jrVta1nbvpa1bWtZHV2Nz9Nk/2WL2FsgRroqL2dxMwbScZuQJ4ZtUp48bRPypHNc3B95ybbJxOd5fa9d3+5OxoPtEOosr6vYpsN+KVGL3HpxsUTEzjwHvPS21e7bVI0xpHMFm4gXk/FiYu4cl22L+zOPs6Xk/qRzPDO5f99rcS7ob69Z35vsr1gppZRaniL+CBf3XczFfRdP1xVMgfv/+366NnUxMDbAwMgAr0y8woGTB0i7lmF4xcsZkTPoj/bTH+1ndXQ1q6Orp/f7o/20B9qXxUfpS0LESYDb7f3HFyKXtndsSY3bkh4v7U+XifLjyd9C2qnLTM7/Gr6wnTkPRCEQg0CUCxMZGDrLVV86RyAK/jnqAzG7vt0X0pn4eYgIIWfmunOJXuPh54e47p6nyOVreyGpJt5KKaVUg3jEQ6+/l73r93LZ+sum6wumwO+Sv+NY/BjH48d5Nf4qQ4khhpJDPPe753jk6CPkCuUXwUV8kbJEvCfcQ3e4m+5Qd9k25o81b4Lu5gtCrNeWxcjnnCR8bHaCnhq3M/DZBGTcZRLvxLi9+0tmslSfm1r464pnRkLuJOX+SHmC7g/bxN8fmrF1ii9Uvp1Z1wq/A8uQJt5KKaXUMuMRD33RPvqifby5/82zzhdMgeGpYYYSQwwmBhlMDNrE3Dk+NHKI0dQohtmzdQFPgK5wF6uCq+gIdtAZ7JzeztzvDHYSC8SIBWL4PSvoFom14PWVlsJU4df797PXvZYdoJAvJeHZZHlSXrafqFyfTdqlNWNHS+eyqcoXpy6UL+Qk4hEnaQ+BN+DUB2YcB23x2u3ZxwfB+9T0sS0VHj/9GKfOWyx+u/X4W+7+75p4K6WUUiuMRzz0RnrpjfSyvXd7xTa5Qo6x9BjDU8MMp4YZnhpmJDUyfTyaGmU8M85gYpCx9BgT6YmKiXpR2Bcm5rdJeFugjTZ/m03K/c5xoI2YP0bUHyXijxD2hYn4ItP747lxEtkEIW8Ib6utjfZ4S0tlaqlQgFzKlmzSJuO5qfJtNumcn5qxndk+BfmM83wZO8vvPnadPzufgaM1isHjK0/GZxV/hfML3PcFnW3YfpNrIAqBNmc/ZtfpB2L2TUGdaOKtlFJKNSGfx0dPuGfB36qZL+SJZ+KMpcdsIp6ZYCw9RjwTJ56JM5mZJJ4t7U9kJjgxecIeZyfL1qTP5dP3fhqAkDc0nZCHfWEi/ggRnz0OeUMEfUGC3lIJ+UJlx0FvsKxNyBsi4A1UbNfUSb7HY5edBCJAdTPzb8T+//0Je9+6286451wln66YqE8fF7KQz9r6fMbWF/en67MV6pz97PgcbdPlbavl8TvJeCkp35UNcIvPi+TeBHTU7N9OE2+llFJK4fV46Qx10hla3OVqmXyGeCZOMpckmU0ylZsimUsylbXbZ37zDGs3rCWZTdr63FRZu2Q2yUhqhHQ+bUsuTSqfIp1PT9+GcTF8Hh9BbxC/x18q3tK+z+Mr7Xt95e2ctj7xlT1m5nO4n2cgMQCvUtbOK1684sUjHrye0r5PfHg8nvLz4i1r495fNsRjl6f4Q43uyWzGQCFXntznpiA9aZfoFLfT+3Fn6yzhScchM0l4/CjX+F7mxbEXYX1fzbpXt8RbRLqAbwB/DJwGPmGMubdCOwE+D/y1U/UN4J+MsXdsFJGdTt1m4BDwQWPM00sfgVJKKaXmEvAG7EWcdFc83/ZqG3u37l3Uc2cLWdK59HRSnsqnyOQzpHKpUqKeT5PKOfX5VFkCn86nyRVyZAvZ6ZIr5MjmS8eZQoZkLmmPXfXTxVU3r58sKszXJUjl5N3jwyOeUiI/4/ysRN45nqv9Qt4MnBw9yTO/emZBrzmzz7V4A1Kx386/w/Rz+CNIILrof++Bh/+Diw78XQ1/glY9Z7y/CmSAPmAn8CMRecYY8/yMdtcBVwM7AAM8ArwE3CEiAeBB4EvA14APAQ+KyEZjzCI+W1BKKaXUcuf3+PEH/MSINborGGPIm3zFhDxbyPLoLx9l58U7S/X5LHmTny4FUyBfKO3nCjlbZ+aoK+TLzudNnkLhddrPOD/Xa2ZNlqRJznqOufpU7Eve5Mnlc+w/uJ+8yb/udQGNVpaIV5nsp+KjtK3u47rUKc6rYZ/qkniLSBT4c2CbMWYS+LmI/AD4APDxGc2vBW41xhx3Hnsr8DfAHcBep89fcmbAvywiHwP2AT+uRyxKKaWUal0igk98+Dw+whW+kv1Y4Bhbu7c2oGf1s99155ZiUj7vG4oFvBmYlewX8vO+wciZud8wzHzTspA3GMW6ibQhY04TjtRufTfUb8Z7E5A3xgy46p4B3lah7VbnnLvdVte5Z4vLThzPOvWzEm8RuQ47gw4wKSKHq+x3D3ZZTLNq5viaOTZo7vg0ttnW17ojy9HMMfvtb3/7MM37u+DWzL/zbhpn82iFGAF6/os/rOmYXa/EOwaMz6gbB9oW0HYciDlrv6t5HowxXwe+vpgOA4jIk8aYNy328ctdM8fXzLFBc8ensbWumWN2q/x7aZzNpRXibIUYYWnirNclspPAzJtXtgPxBbRtByadWe5qnkcppZRSSqllo16J9wDgE5GNrrodwMwLK3HqdszR7nngQin/rtsL53gepZRSSimllo26JN7GmATwAHCziERFZA/wbuCeCs2/BXxURM4UkTXAPwDfdM7tB/LAh0UkKCI3OPVLcOMe4A0sU1khmjm+Zo4Nmjs+jU0Vtcq/l8bZXFohzlaIEZYgTim/TnHpOPfxvgv4I2AY+Lgx5l4RuRR4yBgTc9oJ8AVK9/H+d8rv432RU7eF0n28f12XIJRSSimllFqkuiXeSimllFJKtbJl9P2jSimllFJKNS9NvJVSSimllKqDlk+8RaRLRL4nIgkROSoi752jnYjIF0Rk2Cm3zLi7yrJTRWw3ichBEYmLyMsiclO9+7oYC43P1T4gIi+IyPF69XGxqolNRHaJyE9FZFJETonIR+rZ12pV8XsZFJE7nJhGROSHInJmvftbDRG5QUSeFJG0iHxznrZ/LyJDIjIuIneJSLBO3Vw2mnn8dWv2sbiomcdkt2Yen92aeawuasSY3fKJN/BVIAP0Ae8DbheRSt/1eh1wNfb2hhcC7wI+VK9OLtJCYxPgL4FVwDuAG0TkL+rWy8VbaHxFNwGv1aNjNbCg2ESkB/utrf8GdAPnAQ/XsZ+LsdCf20eA38f+va0BxoDb6tXJRToJfBZ7IfmcRORy4OPAZcDZwAbgn5e6c8tQM4+/bs0+Fhc185js1szjs1szj9VF9R+zjTEtW4Ao9pdqk6vuHuDzFdoeAK5zHX8QeKzRMdQitgqP/TJwW6NjqGV8wDnYu+C8Ezje6P7XKjbgc8A9je7zEsV2O3CL6/hK4HCjY1hgnJ8Fvvk65+8FPuc6vgwYanS/l/HvwooafxcbZ4XHLvuxeLFxrqQxebFxrrTx+Q3EuWLHalef6zZmt/qM9yYgb4wZcNU9A1R6R7fVOTdfu+WimtimOR/fXsry/1KiauO7DfgkMLXUHauBamK7BBgRkQMi8przEd+6uvRycaqJ7RvAHhFZIyIR7IzLQ3XoYz1UGk/6RKS7Qf1phGYef92afSwuauYx2a2Zx2c3HavL1WzMbvXEOwaMz6gbB9oW0HYciC3jdYbVxOb2Gezvxd1L0KdaWnB8IvKngM8Y8716dKwGqvnZnQVci/2obx3wMnDfkvbujakmtgHgGHACmAA2Azcvae/qp9J4AvP/fTaTZh5/3Zp9LC5q5jHZrZnHZzcdq8vVbMxu9cR7EmifUdcOxBfQth2YNM5nDstQNbEB9iID7PrCK40x6SXsWy0sKD4RiQK3ADfWqV+1UM3Pbgr4njHmCWNMCrvmbLeIdCxxHxermthuB0LYtZFR7LffNsssSqXxBF7n77MJNfP469bsY3FRM4/Jbs08PrvpWF2uZmN2qyfeA4BPRDa66nZQ+aO9551z87VbLqqJDRH5K5wLB4wxK+EK84XGtxF7IcTPRGQIOyCsdq5MPrsO/VyMan52zwLu5KO4v1xnAquJbQd2zd2Ik3zcBrzFuWBppas0npwyxgw3qD+N0Mzjr1uzj8VFzTwmuzXz+OymY3W52o3ZjV7Q3ugCfBv70U8U2IP9+GBrhXbXYy8EORN71e7zwPWN7n+NYnsfMARsbnSfax0f4AP6XeXPsFcx9wPeRsdQg5/dPmAU2An4gX8Fftbo/tcotruB+4EOJ7ZPAica3f95YvNhZ37+BXshUgj7kfrMdu9w/ua2YO9g8RMWcLFds5VmHn8XGeeKHIuriXOljsmL/HmuuPF5kXGuuLHa1fe6j9kND7rRBegCvg8ksGuU3uvUX4r9KLPYTrAfj4045RZAGt3/GsX2MpDFfpRSLHc0uv+1im/GY/ayAq6gryY24G+xa+tGgR8Caxvd/1rEhv3Y8j+xtxsbA34OvKXR/Z8nts9gZ7Xc5TPY9Z2TwDpX248Cp7BrIu8Ggo3u/zL+XVhx4+8i41yRY3G1cc54zIoYkxcb50obnxcT50ocq119r/uYLc6TKaWUUkoppZZQq6/xVkoppZRSqi408VZKKaWUUqoONPFWSimllFKqDjTxVkoppZRSqg408VZKKaWUUqoONPFWSimllFKqDjTxVkoppZRSqg408VaqSiLSISL3ichpEYmLyNMion9LSim1DOmYrZYTX6M7oNQK9AUgD6wHpoAtxphCY7uklFJqDjpmq2VDE2+lqpcFjgBJY7/69SCAiHwHWOO0SQNXGGNSjemiUkopx1xj9hXAPwJep1xqjMk3rJeqJehHLUpV7wXgY0BCRD7kqt8EvM0YsweYAC5sROeUUkqVmTVmi0gbcDNwuTHmUuBKTbpVPeiMt1JVEJE/AW4AdhljjrjqA4DHGJMTkRiwGhhoUDeVUkox95gN9AMxYC3wojFmtBH9U61HZ7yVqs424ARwCkBE1onIKmAz0C8i+7EfaX7VGDPWsF4qpZSCOcZsJwn/MvBdEXlKRLY3spOqdWjirVR17gYywKsiMg48gP3kaBtwuzFmL3AB8ImG9VAppVTRXGM2xpivGWN2AncBH2lcF1Ur0aUmSlXBGDMIXDGzXkS2AU84h6uA8Xr2Syml1GyvM2ZvMsYUlwN2Aofr2jHVssRe4KuUeiNE5AfAmcAYUABuMsY83dheKaWUqkREvg2cg7294GHgRmNMprG9Uq1AE2+llFJKKaXqQNd4K6WUUkopVQeaeCullFJKKVUHmngrpZRSSilVB5p4K6WUUkopVQeaeCullFJKKVUHmngrpZRSSilVB5p4K6WUUkopVQeaeCullFJKKVUH/w/ExO+TPPMS6wAAAABJRU5ErkJggg==\n",
Florent Chatelain's avatar
Florent Chatelain committed
215
216
217
218
219
220
221
222
223
224
225
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
Florent Chatelain's avatar
Florent Chatelain committed
226
227
    "ells = [1, 2, 5]  # spike powers\n",
    "c0 = 0.05\n",
Florent Chatelain's avatar
Florent Chatelain committed
228
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
229
    "f, ax = plt.subplots(1, 2, figsize=(12, 4), sharey=True)\n",
Florent Chatelain's avatar
Florent Chatelain committed
230
231
232
    "\n",
    "for ell in ells:\n",
    "    eBs, eSs = phase_transition(c0, ell, res=1e-3)\n",
Florent Chatelain's avatar
Florent Chatelain committed
233
234
235
236
237
238
239
240
241
242
    "    ax[0].axes.plot(eBs, eSs, label=r\"$\\ell$={}\".format(ell))\n",
    "    ax[1].axes.plot(eSs, eBs, label=r\"$\\ell$={}\".format(ell))\n",
    "\n",
    "ax[0].axes.set_xlabel(r\"$\\varepsilon_B$\")\n",
    "ax[0].axes.set_ylabel(r\"$\\varepsilon_S$\")\n",
    "ax[0].axes.grid(\"On\")\n",
    "ax[1].axes.set_xlabel(r\"$\\varepsilon_S$\")\n",
    "ax[1].axes.set_ylabel(r\"$\\varepsilon_B$\")\n",
    "ax[1].axes.set_ylim([0, 0.3])\n",
    "ax[1].axes.grid(\"On\")\n",
Florent Chatelain's avatar
Florent Chatelain committed
243
244
245
246
247
248
249
250
251
    "ax[1].axes.legend()\n",
    "_ = plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Figure 4: \n",
Florent Chatelain's avatar
Florent Chatelain committed
252
    "Two-way punctured matrices $K$ for **(left)** $(\\varepsilon_S,\\varepsilon_B)=(.2,1)$ or **(right)** $(\\varepsilon_S,\\varepsilon_B)=(1,.04)$, with $c_0=\\frac12$, $n=4\\,000$, $p=2\\,000$, $b=0$. Clustering setting with $x_i\\sim .4\\mathcal N(\\mu_1,I_p)+.6\\mathcal N(\\mu_2,I_p)$ for $[\\mu_1^T,\\mu_2^T]^T\\sim \\mathcal N(0,\\frac1p[\\begin{smallmatrix} 20 & 12 \\\\ 12 & 30\\end{smallmatrix}]\\otimes I_p)$. **(Top)** first $100\\times 100$ absolute entries of $K$ (white for zero); **(Middle)** spectrum of $K$, theoretical limit, and isolated eigenvalues; **(Bottom)** second dominant eigenvector $\\hat v_2$ of $K$ against theoretical average in red. **As confirmed by theory, although (top) $K$ is dense for $\\varepsilon_B=1$ and sparse for $\\varepsilon_B=.04$ ($96\\%$ empty) and (middle) the spectra strikingly differ, (bottom) since $\\varepsilon_S^2\\varepsilon_Bc_0^{-1}$ is constant, the eigenvector alignment $|\\hat v_2^T v_2|^2$ is the same in both cases.**"
Florent Chatelain's avatar
Florent Chatelain committed
253
254
255
256
   ]
  },
  {
   "cell_type": "code",
Florent Chatelain's avatar
Florent Chatelain committed
257
   "execution_count": 5,
Florent Chatelain's avatar
Florent Chatelain committed
258
   "metadata": {},
Florent Chatelain's avatar
Florent Chatelain committed
259
260
261
262
263
264
265
266
267
268
269
270
271
272
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
Florent Chatelain's avatar
Florent Chatelain committed
273
274
275
276
277
   "source": [
    "# Generation of the mean vectors for each sample\n",
    "\n",
    "p = 2000  # dimension size\n",
    "n = 4000  # sample size\n",
Florent Chatelain's avatar
Florent Chatelain committed
278
    "c0 = p / n  # dimension/sample size ratio\n",
Florent Chatelain's avatar
Florent Chatelain committed
279
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
280
    "# Set the covariance for the two mean vectorss\n",
Florent Chatelain's avatar
Florent Chatelain committed
281
282
283
    "cov_mu = np.array([[20, 12], [12, 30]]) / p\n",
    "mus = gen_synth_mus(p=p, n=n, cov_mu=cov_mu)\n",
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
284
285
286
    "# Set the proportion for each of the two classes\n",
    "cs = [0.4, 0.6]\n",
    "n0 = int(n * cs[0])\n",
Florent Chatelain's avatar
Florent Chatelain committed
287
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
288
289
    "# Generate the noisy data matrix and the spikes matrices\n",
    "X, ells, vM = gen_synth_X(p, n, mus, cs)\n",
Florent Chatelain's avatar
Florent Chatelain committed
290
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
291
    "# Puncturing settings\n",
Florent Chatelain's avatar
Florent Chatelain committed
292
293
    "eS = 0.2  # data puncturing ratio\n",
    "eB = 0.04  # kernel puncturing ratio\n",
Florent Chatelain's avatar
Florent Chatelain committed
294
295
    "b = 0  # kernel matrix diagonal entry\n",
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
296
    "f, ax = plt.subplots(3, 2, figsize=(12, 8))\n",
Florent Chatelain's avatar
Florent Chatelain committed
297
298
    "\n",
    "# S-punctured spectrum\n",
Florent Chatelain's avatar
Florent Chatelain committed
299
    "B, _, _ = mask_B(n, 1, is_diag=b)  # mask for diag entries\n",
Florent Chatelain's avatar
Florent Chatelain committed
300
301
302
303
304
    "X_S = puncture_X(X, eS)  # punctured data mat\n",
    "K_S = puncture_K_vanilla(X_S, B)  # remove diag entries\n",
    "l, u_S = sp.sparse.linalg.eigsh(K_S, k=2, which=\"LA\", tol=0, return_eigenvectors=True)\n",
    "u_S = u_S[:, 1].ravel()  #  second principal eigvect\n",
    "u_S = u_S * np.sign(u_S[:n0].mean() - u_S[n0:].mean())\n",
Florent Chatelain's avatar
Florent Chatelain committed
305
306
    "lambdas_S = np.linalg.eigvalsh(K_S.todense())\n",
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
307
    "#  B-punctured spectrum\n",
Florent Chatelain's avatar
Florent Chatelain committed
308
    "B, _, _ = mask_B(n, eB, is_diag=b)\n",
Florent Chatelain's avatar
Florent Chatelain committed
309
310
311
312
    "K_B = puncture_K_vanilla(X, B)  #  punctured kernel mat\n",
    "l, u_B = sp.sparse.linalg.eigsh(K_B, k=2, which=\"LA\", tol=0, return_eigenvectors=True)\n",
    "u_B = u_B[:, 1].ravel()  # second principal eigvect\n",
    "u_B = u_B * np.sign(u_B[:n0].mean() - u_B[n0:].mean())\n",
Florent Chatelain's avatar
Florent Chatelain committed
313
314
315
316
317
    "lambdas_B = np.linalg.eigvalsh(K_B.todense())\n",
    "\n",
    "\n",
    "# S-punctured figs\n",
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
318
319
    "ax[0, 0].imshow(\n",
    "    np.abs(K_S[:100, :100].todense()), interpolation=\"nearest\", cmap=\"gray_r\"\n",
Florent Chatelain's avatar
Florent Chatelain committed
320
    ")\n",
Florent Chatelain's avatar
Florent Chatelain committed
321
322
    "ax[0, 0].axis(\"off\")\n",
    "disp_eigs(ax[1:, 0], lambdas_S, u_S, 1, eS, c0, n0, ells, b, vM)\n",
Florent Chatelain's avatar
Florent Chatelain committed
323
    "ax[1, 0].axes.set_ylim([0, 2])\n",
Florent Chatelain's avatar
Florent Chatelain committed
324
325
326
    "\n",
    "# B-punctured figs\n",
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
327
328
    "ax[0, 1].imshow(\n",
    "    np.abs(K_B[:100, :100].todense()), interpolation=\"nearest\", cmap=\"gray_r\"\n",
Florent Chatelain's avatar
Florent Chatelain committed
329
    ")\n",
Florent Chatelain's avatar
Florent Chatelain committed
330
331
    "ax[0, 1].axis(\"off\")\n",
    "disp_eigs(ax[1:, 1], lambdas_B, u_B, eB, 1, c0, n0, ells, b, vM)"
Florent Chatelain's avatar
Florent Chatelain committed
332
333
334
335
336
337
338
339
340
341
342
343
344
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Figure 5.\n",
    "\n",
    "Limiting probability of error of spectral clustering of $\\mathcal N(\\pm\\mu,I_p)$ with equal class sizes on $K$: as a function of $\\varepsilon_B$ for fixed $\\ell=\\|\\mu\\|^2=50$ <b>(top)</b>, and $\\varepsilon_S$ for fixed $\\ell=50$ <b>(bottom)</b>. Simulations (single realization) in markers for $p=n=4\\,000$ ($\\color{blue}\\times$) and $p=n=8\\,000$ ($\\color{blue}+$). <b> Very good fit between theory and practice for not too small $\\varepsilon_S,\\varepsilon_B$ </b>."
   ]
  },
  {
   "cell_type": "code",
Florent Chatelain's avatar
Florent Chatelain committed
345
   "execution_count": 6,
Florent Chatelain's avatar
Florent Chatelain committed
346
   "metadata": {},
Florent Chatelain's avatar
Florent Chatelain committed
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f19b73fa890>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
Florent Chatelain's avatar
Florent Chatelain committed
371
   "source": [
Florent Chatelain's avatar
Florent Chatelain committed
372
    "p = 4000\n",
Florent Chatelain's avatar
Florent Chatelain committed
373
374
375
    "\n",
    "ns = np.array([2000, 2000])\n",
    "n0 = ns[0]\n",
Florent Chatelain's avatar
Florent Chatelain committed
376
    "n = np.sum(ns)\n",
Florent Chatelain's avatar
Florent Chatelain committed
377
378
    "cs = ns / n\n",
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
379
    "c0 = p / n\n",
Florent Chatelain's avatar
Florent Chatelain committed
380
381
382
    "\n",
    "power = 50\n",
    "mu = rng.normal(size=(p,))\n",
Florent Chatelain's avatar
Florent Chatelain committed
383
384
    "mu = mu / np.linalg.norm(mu) * np.sqrt(power)\n",
    "mus = np.array([mu, -mu]).T\n",
Florent Chatelain's avatar
Florent Chatelain committed
385
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
386
387
    "X, ells, _ = gen_synth_X(p, n, mus, cs)\n",
    "ell = np.max(ells)\n",
Florent Chatelain's avatar
Florent Chatelain committed
388
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
389
    "f, ax = plt.subplots(2, 1, figsize=(8, 8), sharex=True)\n",
Florent Chatelain's avatar
Florent Chatelain committed
390
391
392
393
    "\n",
    "## Perf vs epsilon_B (fixed epsilon_S)\n",
    "\n",
    "res = 1e-1\n",
Florent Chatelain's avatar
Florent Chatelain committed
394
395
    "eSs = [1 / 10, 1 / 20]\n",
    "eBs = np.linspace(res, 1, int(1 / res))\n",
Florent Chatelain's avatar
Florent Chatelain committed
396
397
    "\n",
    "res_thin = 1e-2\n",
Florent Chatelain's avatar
Florent Chatelain committed
398
399
    "eSs_thin = [1 / 10, 1 / 20]\n",
    "eBs_thin = np.linspace(res_thin, 1, int(1 / res_thin))\n",
Florent Chatelain's avatar
Florent Chatelain committed
400
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
401
402
    "perf_sim = np.zeros((len(eBs), len(eSs)))\n",
    "perf_th = np.zeros((len(eBs_thin), len(eSs_thin)))\n",
Florent Chatelain's avatar
Florent Chatelain committed
403
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
404
405
    "for iS, eS in enumerate(eSs):\n",
    "    for iB, eB in enumerate(eBs):\n",
Florent Chatelain's avatar
Florent Chatelain committed
406
    "        u = puncture_eigs(X, eB, eS, b=1, sparsity=1)[1]\n",
Florent Chatelain's avatar
Florent Chatelain committed
407
    "        overlap = 1 / n * (np.sum(u[:n0] > 0) + np.sum(u[n0:] < 0))\n",
Florent Chatelain's avatar
Florent Chatelain committed
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
    "        perf_sim[iB, iS] = np.min([overlap, 1 - overlap])\n",
    "\n",
    "    ax[0].axes.plot(\n",
    "        eBs, perf_sim[:, iS], \"xb\", label=r\"Simulation, $\\varepsilon_S=${}\".format(eS)\n",
    "    )\n",
    "\n",
    "for iS, eS in enumerate(eSs_thin):\n",
    "    for iB, eB in enumerate(eBs_thin):\n",
    "        zeta = spike(eB, eS, c0, ell, b=1)[1]\n",
    "        perf_th[iB, iS] = qfunc(np.sqrt(zeta / (1 - zeta)))\n",
    "\n",
    "    ax[0].axes.plot(\n",
    "        eBs_thin, perf_th[:, iS], \"r\", label=r\"Theory, $\\varepsilon_S=${}\".format(eS)\n",
    "    )\n",
    "\n",
    "ax[0].axes.set_xlabel(r\"$\\varepsilon_B$\")\n",
    "ax[0].axes.set_ylabel(r\"$P_e$\")\n",
    "ax[0].axes.grid(\"On\")\n",
Florent Chatelain's avatar
Florent Chatelain committed
426
427
    "ax[0].axes.legend()\n",
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
428
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
429
430
    "## Perf vs epsilon_S (fixed epsilon_B)\n",
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
431
432
    "eBs = [1 / 100, 1 / 400]\n",
    "eSs = np.linspace(res, 1, int(1 / res))\n",
Florent Chatelain's avatar
Florent Chatelain committed
433
434
    "\n",
    "res_thin = 1e-2\n",
Florent Chatelain's avatar
Florent Chatelain committed
435
436
    "eBs_thin = [1 / 100, 1 / 400]\n",
    "eSs_thin = np.linspace(res_thin, 1, int(1 / res_thin))\n",
Florent Chatelain's avatar
Florent Chatelain committed
437
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
438
439
    "perf_sim = np.zeros((len(eSs), len(eBs)))\n",
    "perf_th = np.zeros((len(eSs_thin), len(eBs_thin)))\n",
Florent Chatelain's avatar
Florent Chatelain committed
440
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
441
442
    "for iB, eB in enumerate(eBs):\n",
    "    for iS, eS in enumerate(eSs):\n",
Florent Chatelain's avatar
Florent Chatelain committed
443
    "        u = puncture_eigs(X, eB, eS, b=1, sparsity=1)[1]\n",
Florent Chatelain's avatar
Florent Chatelain committed
444
    "        overlap = 1 / n * (np.sum(u[:n0] > 0) + np.sum(u[n0:] < 0))\n",
Florent Chatelain's avatar
Florent Chatelain committed
445
446
447
448
449
    "        perf_sim[iS, iB] = np.min([overlap, 1 - overlap])\n",
    "\n",
    "    ax[1].axes.plot(\n",
    "        eSs, perf_sim[:, iB], \"xb\", label=r\"Simulation, $\\varepsilon_B=${}\".format(eB)\n",
    "    )\n",
Florent Chatelain's avatar
Florent Chatelain committed
450
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
451
452
453
454
    "for iB, eB in enumerate(eBs_thin):\n",
    "    for iS, eS in enumerate(eSs_thin):\n",
    "        zeta = spike(eB, eS, c0, ell, b=1)[1]\n",
    "        perf_th[iS, iB] = qfunc(np.sqrt(zeta / (1 - zeta)))\n",
Florent Chatelain's avatar
Florent Chatelain committed
455
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
456
457
458
    "    ax[1].axes.plot(\n",
    "        eSs_thin, perf_th[:, iB], \"r\", label=r\"Theory, $\\varepsilon_B=${}\".format(eB)\n",
    "    )\n",
Florent Chatelain's avatar
Florent Chatelain committed
459
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
460
461
462
463
    "\n",
    "ax[1].axes.set_xlabel(r\"$\\varepsilon_S$\")\n",
    "ax[1].axes.set_ylabel(r\"$P_e$\")\n",
    "ax[1].axes.grid(\"On\")\n",
Florent Chatelain's avatar
Florent Chatelain committed
464
465
466
467
468
469
470
    "ax[1].axes.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
Florent Chatelain's avatar
Florent Chatelain committed
471
    "#### Figure 6\n",
Florent Chatelain's avatar
Florent Chatelain committed
472
    "Examples of **MNIST-fashion images**, `trouser` instances **(top row)**, `pullover` instances **(bottom row)**.\n",
Florent Chatelain's avatar
Florent Chatelain committed
473
474
    "\n",
    "**Note:** the GAN data we generated and used in the submitted paper are too voluminous to be included in the supplementary material and is not publicly and anonymously available. For this reason, we are using below the smaller, publicly available, MNIST-fashion real word data set. However **the conclusions obtained for this dataset are very similar to those drawn in the paper for the GAN data.**"
Florent Chatelain's avatar
Florent Chatelain committed
475
476
477
478
   ]
  },
  {
   "cell_type": "code",
Florent Chatelain's avatar
Florent Chatelain committed
479
   "execution_count": 7,
Florent Chatelain's avatar
Florent Chatelain committed
480
   "metadata": {},
Florent Chatelain's avatar
Florent Chatelain committed
481
482
483
484
485
486
487
488
489
490
491
492
493
494
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjwAAADlCAYAAABXoS1UAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAgAElEQVR4nO2dV7BeVfn/F9JrSEISSC8EUoCEEgkBfhGQasAJQhR0xHGG4UKUGS9QM1xYZhALFgYFBXRkRtRxhAg6IoI0AQk1gZBAQk5oSSCEErq0/83fxXd9yX7yvue855yd7edz9exZ++y2yrvOU7d4//33EwAAAECT+Uh/PwAAAABAb8OGBwAAABoPGx4AAABoPGx4AAAAoPGw4QEAAIDGw4YHAAAAGs9Wm2jvt5j1e+65pzi+8sorszx48OCibeedd87yVlt98ErPP/98cd4WW2yR5dGjRxdtDz74YJafe+65om3dunVZvvnmmzf57B1mi02f0jJ92p9vvPFGlrfffvu+vHXIO++8k2UdL31Ep/qz3+bmK6+8UhzPnz8/yyNHjiza3n333Sx/5CMf/H+lfZBSSmvXrs3y1ltvXbRtt912Gz0vpZQuuuiiLOs60EdstnMz4pJLLslyq+vdTjvtVHm85ZZbFm2HHHJIlufNm9edR+wtNvu56Rx99NFZ1rmYUkrbbLPNRv9mv/32K44ffvjhLL/66qtF2957751ln7dnn312lqdMmdLiE3eMjfYlGh4AAABoPH3+722r3HLLLcWx7jJVU5NSSl1dXVnWHahreAYOHJjlAQMGFG277rprlnfbbbeibdWqVa09NBSoVuc///lP0ab/qY8YMaJoq0qGqRqjlFJ68803K9vWr1+f5UGDBhVtY8aMiR4bNsHll19eHF988cVtX0O1PSml9N5771Weq/85vv3220Xb7Nmzs/yFL3yh7eeAlF577bXieMGCBVl27Yyeu2HDhiyPGjWqOE/nt2vzFi9enOWaaXg2e5599tnieOHChVmeOXNm0aZr8ssvv5zlG2+8sThPf2932WWXom2HHXbIsmt+dQz0g4Zno6DhAQAAgMbDhgcAAAAaDxseAAAAaDy19eFxu/K4ceOy/MILLxRtaj9WXwD1IE8ppbfeemuj56VU+vC4z4f+nfvzjB07dmOPD8ZZZ51VHF9//fVZ1m+fUunDs+2222bZ/Te0D92vS+3J3terV69u9bFhI7itXr+9zzmdx9p/7qelESTqF5BSGaWl/noppfTiiy+2+thQgUelvv7661l23wtdC9WHx307FI/eWbp0aZYfeuihom3fffdt4Ymhirvvvrs4PvDAA7Ps66f6PWok8vDhw4vzdH7r2EgppUcffTTL7pfnv9N1AA0PAAAANB42PAAAANB4amvSeuyxx4pjVbl58iNVm6s8dOjQ4jwNj3T1nqrpXd2uf3fbbbcVbZi0WkPTCqSU0u677155rqrN16xZk2Xvdw0vd5W6mkHqlPSwCaxYsaKyTcNbUyr7UufVjjvuWJynbWoqSamcq548TVXq0D006WpKZUI6XyfV/KX95KHnakb2NB9qpl62bFnRhkmrZ9x3333Fsa6fUSoWnbd77bVXcZ4mE73rrruKNu1nn7eafuCUU07Z5LP3BWh4AAAAoPGw4QEAAIDGw4YHAAAAGk9tfXi8LIT62HjIutofNaTc7f3qJ+DX0NA79TtIqbRPEwbbPbzoo/aT+3Oof88zzzyT5fHjxxfnqW+OF8LT4zvuuKMbTwxVuH+dhpG7/1tVwVCfm4r6X/k11P8jJVIMdILHH3+8ONa542HI2hcaduypBPTY13IdI94GPWP58uXFsfaD+1Kp/40We33yySeL89R/Vsv5pFTOVffLjMrF9BdoeAAAAKDxsOEBAACAxlNbk5aHt+6xxx5Z9oyOjzzySJbV5OSqcaWqIndKH1bP6rl6L2gdr5auVZjdhKgq9WHDhm30b1IqTSQ+JrTvPQvzE088kWUqp7ePV2RWdbh/az3WjLuuGve/U7ba6oNlyk2XmER6joeUa3/uvPPORZvOM52b+jcpxWuvuid42Dv0DDdpqQnYTUw6B3X+ubuHuhV4Vny9hmfU9jW/DqDhAQAAgMbDhgcAAAAaDxseAAAAaDy18uGpqsSbUkpTp07Nstvx1f740ksvZVltjymVpQm8FEEUvqe2ak3VDTFq3/WKzKNHj86y++aoXV9D1r1EhNqnveyEMnjw4OJYQ5nx4Wkf98/Q/nI/Ae3bqIK9HnsKfJ3f7iviYerQPr4Wqg+H+2zoHLz33nuzrH5WKaV08sknV97P01BA59A5llLp++opBqrm45AhQ4rzdL67z5X67bjPTrQm9xdoeAAAAKDxsOEBAACAxlMrk5Zm7vRwSFWzaebHlEpVmqrtPNT1jTfeyPKhhx5atGm4pZtYVKUXhbNDifanq7wHDhyYZVfDKpHJQvvFTaB6P88A6ikPoD18fug88/6qCltdtWpVcZ72kavN1cTl5mxMWj1HzcsplSYtNyNrFt4zzzwzy74ma/qOffbZp2jT+T5ixIhuPDEoXV1dWXYzkq6DHm6u81jnkWfF1zHgZjFdg90U7XO1DqDhAQAAgMbDhgcAAAAaDxseAAAAaDy18uHRshBu/1MfG7fx67lahdnLQAwfPjzLXhF27NixWXa7tYZtevpsqEZ9ePybRinlqyppu/+U+o54m97Pw2ApR9AzPFRZfaLcp0Z9CqLQc/X18bB3LX3gIdR+DO3jPjxVJQdSKn2vvvjFL2bZy40sWrQoy56CQH0uNd0IdI+VK1dm2ddV/d10v1hdMzVVh6+P6m/pv8vqB+RrcFRepL9AwwMAAACNhw0PAAAANJ5ambRUlRpl43S1narNNUuyq2NVFe/qNlXVemZeDe2rYwXYzZGoyq6i2be9qrNmx3Z1qqpa/e/ow54xdOjQ4njx4sVZ1j5JqTRnRGGqOle1z1MqVfEe/oxJpOf4Wqjf31M4aPoHNZdoyg//O2/T+YeLQM9ZsWJFlqMKAlE6Dq1K8Mtf/rJoO/fcc7Psc1jXXQ+Jx6QFAAAA0A+w4QEAAIDGw4YHAAAAGk+tfHjUju9hzIqHOWqIq4eiKxpe51WXJ06cmGUPWVd/Ew/tg2rUVq/2/pRKvyjvC/3e6ne19957F+ctXLgwy2671rHk9/bSCNAekyZNKo4XLFiQZf/W6m+n88/REgNPP/105Xma6iCllCZMmBA/LGwS96PRtBDen+oPF1XijvzkNHWB+3xB+6j/ja+D+lvpv13qDzdu3Lgsn3rqqcV58+bNy/L06dOLNu1LLxGkaWDqAhoeAAAAaDxseAAAAKDx1MqkpSFurkpVvE3DKD00Ttlzzz2zrJlAUypNWq5m1XA+zCGto30RhST7N1W1uapM3ZSpanTP/qtqeh8vVZmcoTW8+rXOW/+22pdetV5Rc5ebtHR8eMi6zlvoHm7q8HQeioaY6zo5aNCg4jztd5/fas4mU3bP0VQB7gqifemmS62yftlll7V0r+i319dnX5PrABoeAAAAaDxseAAAAKDxsOEBAACAxlMrHx61N6qdN6XSXux2Sg2vi8LZ99prryzfcccdRZumwXZfgzVr1mQZ/4/W0fBy70+1BUc+PFoqJApzjKqv+709hBbaY//9969si/pyyJAhlX+n5Vy8knqUon7atGmVbdAaOsdSKn2yXnrppaJNfeq0n3z+vfbaa1nWdSCl0pckKiEEraE+PI72l5eW0Pk4Z86cymv4fFS0L/36dUw5gIYHAAAAGg8bHgAAAGg8tTJpKR4aqapxV3FrWxQKN2XKlMq29evXZ9krb6vqLwrZhJJWq5J7uKR+fw1n90y9kfmyE88FG2fy5MnFsfafqtBTKuejh60q2s8+x7TNr49Jq/NEFczVpK+h6J4uQNdk78/IRALtU5XGI6XS1Bj9rkXouuvX0PtFbgV1AQ0PAAAANB42PAAAANB4amXSUnWZmx3U09+z9mrET1Tcc8aMGVl29XqUGVTVtXX0PK8rqv52lbfiKm/t+8hcon3m0XPah65qjZ4F2kcLeHpfaj9o5I6jc9+j6hQvXAqdR+eZr4U6H9W1QAuJplT2p87TlFhDe5PI5OTFPTVqOUILi7744otFm853HytDhw5t6fp9CRoeAAAAaDxseAAAAKDxsOEBAACAxlMrHx71w3BbpPphuB1Rz41Cz6OQdfUDcpuzQlh662h/us+U9llUgVdDIj0DdpWvj1/f2RzCJzcnNPPy4sWLiza160cZrtWvw8eDzrkDDjig288JraG+Oe4bV5VaIEoV4v6YkZ8ltE/02xX5OY4dO7al6+t5zz//fOV5PgaGDRvW0vX7EjQ8AAAA0HjY8AAAAEDjqZVJS00Nb7zxRtGmBe60mGdKpQlk1KhRlddXVaqbQFT152pbVct7SDy0hn9vNVO4CePVV1/N8ogRI7K85557FuepqtyvEYVARyZLaB+dV9G3jdp0XrkJRMfKLrvs0p1HhDaIMutG86oKX8tJC9FZdO3zb61zKTLzR2hY+r333lt5npu06jhX0fAAAABA42HDAwAAAI2HDQ8AAAA0nlr58Cjr1q0rjnfccccsuw1Y7ZTu51HFTjvtVBzrNb0Kt5a18L+DavSbeji/lg9wvyj19Rg+fHiWPVW5+hO4j5D6XXkbYemdRfvWQ8/1W3tpEEXHgPv66Pzz0FroPNoX+u1Tist+KDrn3CeSPuws6t/6wgsvFG3qA+nfvdV1UH1xohQi3s+tjpW+BA0PAAAANB42PAAAANB4aqVzUjOEh9c9/fTTWXaVt6rmWq0AO3jw4OL4pZdeyrJnAlWVPZmWW0fVnR4Sqceuan355ZezrH3hJi3td7++9pOPlyjjL7SPfk8PW9ZvP3PmzMprTJ06NcsLFiwo2nRuasoC6B2izL1u7q9C13LWzN7lsMMOy/JvfvObok37z/uh1XVQ+9LXWTVjdXV1Vf5dXUDDAwAAAI2HDQ8AAAA0HjY8AAAA0Hhq5cMTEaU0V7vioEGDWrreyJEji+OlS5dmOar86yHOUI32i4dARmUG1E8jquir4ZIePqvVtwmL7V2eeuqpLEf9OmvWrMq2adOmZdl9DfSa6ssHvY+X+Wh1/dM11NMRsIZ2lmOPPTbLmr4lpfJ30312vERTFeq3tWHDhqJNQ+K9n9evX59lXY/7EzQ8AAAA0HjY8AAAAEDjqa1Jy80QUeirqki10m+EhzgvW7YsyxoG68eauRJax81IaqbwzNmaoXP8+PGV11TzpYcr77rrrt16TmifVatWZdkzsapZU7NmOxqWHmVoXb58eTeeENphwIABWVZzZUqthxprtmafm2Sr7yxqShoyZEjRpvPP5+a//vWvlq6vKVzc3KwmLjVvpUS1dAAAAIB+gQ0PAAAANB42PAAAANB4auvD47Zi9enx8Dq1FXrl7Sq8tIT+nfsQaGhmHSvA1hX1rfJwZbU7v/LKK0WbfmMPs1TUT8f9BNRnyEPi3ZYNPcNTAijqQxDNzaiSuvoN+FiBzqNrr8+VqJ8Unfs+/9xnDzrHjBkziuPbbrsty+5Dp/28aNGiLGuKiJRKnyv3xdRr+G9jHdN/sPIDAABA42HDAwAAAI2nVvYZVY176KKqxr2SehTuWoVn8FWzlWdaVjBptY5m1/Qqu2qW9FBHrZAehcHuscceWda0AimVqQv83vRhZ9F+dnOzmkSiqtmR+ltNIpGJEzqDzjnvl1azJKv50k1YkQkUesanPvWp4vjGG2/MspsWtW9vuummLLtJS9N/RGunjw2qpQMAAAD0A2x4AAAAoPGw4QEAAIDGUytnBrUxuv1PfWzcJtydMgJeWkL9C9zXQO9dR7vk5sC4ceOKY+1r98mKykkoWuZjyZIlRZv2odudIx8taB/tB6/ArL54EydOrLzG7rvvnmX3BVC/oNGjR3f7OaE11OfN/T7cH64KDV/3lBR+TegcRxxxRHGsKVv8u6uf1S233JLlr371q8V56ivpc1N99Py3sY6/lWh4AAAAoPGw4QEAAIDGU1uTVhT+6GpVDYuNzlMzh5s1VAXr2UVVLYg5pHW6urqyvH79+qJNQx29Ov2sWbNaur6aNzx8VkNfPTuvVveGnqPmKO8HnZuR6VnV3x56/vzzz2d5zJgx3X5OaA1de9283x2Tlqcq8Kzo0HtoRYG1a9cWbTrPHnroocprRCYtrYAQpZ2oC2h4AAAAoPGw4QEAAIDGw4YHAAAAGk+tfHiUgQMHVra5z87222+/0fPUvphS6Sfg1dI1dNl9eCLfH6hm7733zrKHpavfx8qVK4u26dOnt3T9/fbbL8s+XgYMGJBl9ys59thjW7o+tEaURsBLxLSC96X6XE2ePLnt60F7aBi5pwBpdf3TOeelJEaNGtWDpwNHf+f8t2vevHlZ/v73v1+06RqpflWeWkJ9eKKST+q3lVI9fyvR8AAAAEDjYcMDAAAAjadWJq1169Zl+bnnnivadttttyy7irRKdRaZtDy8TlW3Hl6n4fKEVLbOnDlzNip3itmzZ2dZM4WmVM8sn01F54RmJU+prFrfKh7GrHgKA+g8ao5yk5ZnTa5CXQQ8k7qbPqBnRCatuXPnZvmiiy4q2tQcpb+vV1xxRXHeeeedl+WFCxcWbQcddFCW3XVA57GmdulP0PAAAABA42HDAwAAAI2HDQ8AAAA0nlr58Oy7775ZPvHEE4s2tR1rWYKUPlwh9r+4PVPRsOiUUtpzzz2z7H4CQ4YMyfLUqVMrrwkl6s+hlXnbQf21vOq5Hkc+O25b1rGEP0HP+dKXvpTl1atXF23qQ9Aq559/fnF85ZVXZvnTn/5029eD9tD11dfaqDyIoiVA3I9Lw5yh50Rrn/bXIYccUrTdfffdWdZ5eu6551Zez+eflqvwkkB18dtR0PAAAABA42HDAwAAAI1ni1ar3wIAAABsrqDhAQAAgMbDhgcAAAAaDxseAAAAaDxseAAAAKDxsOEBAACAxsOGBwAAABoPGx4AAABoPGx4AAAAoPGw4QEAAIDGw4YHAAAAGg8bHgAAAGg8bHgAAACg8bDhAQAAgMbDhgcAAAAaDxseAAAAaDxseAAAAKDxsOEBAACAxsOGBwAAABoPGx4AAABoPGx4AAAAoPGw4QEAAIDGw4YHAAAAGs9Wm2h/vzsXff/9D/5siy226M4l0nPPPVcc//Of/8zyZZddVrTtuuuuWZ48eXKWt9122+K8F198Mct33XVX0TZz5swsn3/++UXb9ttv39Iz63un1P13Nzpykf9Pt/qzuMD71Zfo7vveeuutxfGECROyPHLkyJau0dXVVRzfe++9WT711FO79Vy9RKf6s6W+7I0xecMNNxTHl156aZaffvrpom3cuHFZfu211yqf4913383y8uXLi7ZJkyZl+dxzzy3aDj/88FYfuzfok7nZ6pzrVF+vXLkyy7fffnvRdsYZZ7R9PZ2LKaX0wgsvZPmYY45p+Trvvfdelv3dOvQdNvu5qX2XUko/+tGPsrxw4cKi7fOf/3yWd9999yxfe+21xXk6H7/85S8XbR/72MeyPHz48PYfuPfY6MdEwwMAAACNZ4vov4fUCzvV559/Pss//elPi7Ybb7wxy2+++WbRtuOOO2b5P//5T9G2bNmyLL/yyiuV9956662zPGLEiKJtjz32yPIbb7xRtA0aNCjLs2fPLtp0xztw4MDKe/eAWml49L+slFL6yEeq98z63/6vfvWrou3CCy/M8oYNG3r6WB9Cn0v7PaWUvve972X5nHPOafma+u7Re2+CPv0vsh1WrVqV5bPPPrtou/POO7P8+uuvF22qYfXxsW7durafY7fddiuOdT3x6+nc3G+//Yq2X//611keO3Zs28/RAn0+N7urYVXtWkopPfDAA1m+7777ijbtw3/84x9F284775xl1ZI/9dRTxXlHHnlklnfZZZfKaxxyyCFFm/b9Rz/60aJtzJgxqRU2Fw1PO+i4/8Mf/lC06dz0+adz85577inaVBukv3k77LBDcd706dM3KqeU0ooVK7Ls8/awww7L8ty5c4u2XvqtVNDwAAAAwP8mbHgAAACg8bDhAQAAgMbT6z48jz/+eNE2Z86cLKtneEopbbfddll2v4stt9wyyx59pXb8V199daN/43/nfkBqI33nnXeKtrfeeivLb7/9dtGm9s6zzjqraDv55JNTB+h3H55WfVf233//4li9+/UbplR+N7cZq/+W2nrVHp1SSmvWrMmy+11pZJ37g+kY0bGTUkpHHXVUlq+66qpURTu+TEaf+gn4WN5qqw8CMxctWlS0nXTSSRs9L6WUBg8enGWfV9tss02WX3755aJN+0/b3Ifu0UcfzbLP71GjRmVZfQBTKv2J3BdM5+of//jHok39C2rg85FSi1Fa0bM988wzxfFtt92W5ccee6zy73baaafiWH1uBgwYULTpuqzf28eEjh+f3/p3zz77bNGm67BG7qVU+v7MmDGjaDvuuOOy3INop9pEad19991F2/z587PsfjTRWqrrkvfRk08+mWVdEz3aSuew+9Cpb+1LL71UtOkaqfM7pZS+853vZPnAAw9MvQA+PAAAAPC/CRseAAAAaDwdMWlFzJs3rzhWlbSHpqn63dWSqkp184GqwKvklEozlqveVf0dfRM3Zeg13Uz25z//OcuuNm6Dfg99jVTEGlbqCcaGDRuWZf82ek03u2j/ajitP5eardwEo/2pplLH763j85Of/GTRtmDBgsrrtJFsszahr0cffXRxrCYuV2tH5mA1gXgCSFWVq0lC00CkVIbEuzlbn0WTh6ZUmtPcBKJzXM1iKX3YZNBN+t3crOHlmtYjpXJOuOlWx6h/Nx3LPj/079REov2QUjn/3JytY8mvr3Pan0tNJj4ONCWBh0BvjmHpp512WnGsCTyHDBlStOm3iNwxPIGu/z7+F5/fek2fm9rmJjN1QXBTtKYsueKKK4o2H0vdBJMWAAAA/G/ChgcAAAAaDxseAAAAaDybKh7aLTRceO3atUWb2vs9xFttzp6+Xn053LartkOV3ddHw5P9+lEpAr2m++Kof4inb9cibKeffnraXIhs3tdcc01x/O9//zvL7ieh/k7e13qPqBCgjhf34dHre5v2p4el6/W9r0ePHp3lv//970Xb3/72tywff/zxldesMxoGvGTJkqJNQ8X9u6hdPZpX48ePL9rUr0tTz3saAR0ffn3193EfIX1m90lQnyH3IdBSCD5u64wW3kypLP3gaRs8RLkK72vtC/en0OPID0jnZuS/6H2tPiful6f9OXTo0KLt4YcfzvKsWbOKNk9/Ule0RISmgXD8d0b9aLy/dF3076lzUNuivvS1VH///N7qQ+fro47Vv/zlL0WbpnPpdIFVNDwAAADQeNjwAAAAQOPpFZOWhsm5SUvNQx6uqGYmD3HTUDlXg6raS9Vvrv7ykD1Fz3U1mqr7PNOkquk9nE/DROtu0lI1pn97xbNH6/t7pXpVW0Zq86iftK2dCuXRudrmfa196CaCE044Ictqtk2pVJtH2Y37m4svvjjLPjdVPe0ZdnXcu4lAs6162gY1Oa1evTrL++yzT3He4sWLs7zXXnsVbZoR1p9L7+cmLe1bNwNoKOw3v/nNtLnwyCOPFMdqlvDxqnPa55ibLRQdB76m6bGOa59vOt/9Xrrue1tkJotcHvR+bvbcXExaGqrt6Fx1c5fOCV9r9Bt6X2qf6ZrlplD91u2YILUtclvQlBROp10F0PAAAABA42HDAwAAAI2HDQ8AAAA0nl5xLlB7vPszqC3S7f167OUANL38hAkTiraxY8dmWe2PnkpbfQ3cp0TtjQ899FDRdt1111VeU9Odaxr9lD7sN1BnIr8dLbHgfgIacuq2WD03svE7kX9Bd/B7V6XHT6kcg27L1jF5yy23FG2f+cxnKq9ZJ26++eYsuy+A+sB42Rf1v9FUBCmVPjca1p9SWdJAffs0LNzx764h5V4iIUpDoSH4XpV74cKFlfevM48//nhxrOuR+2ioT4WvW/qNfR1WPNRY52ZUTiUKc9ZxFs0Vv6b6K3laA32fZcuWFW1a/qbO6Bzz765t7sem39NLbmg/RH2pY8D9o6JSD9pH6s+ZUkq33357lidOnFi0ab9Ha0GnQcMDAAAAjYcNDwAAADSeXjFpqXr/8MMPL9p++9vfZlmzY6aU0vz587M8adKklu+nKrhI7akmJs8YqeYuDyH/7ne/m+UZM2YUbWqic1X8ypUrN/nsmwN33XVXZZunFlCi0PAo07ISVa5vlSgkMsrQ7Nmhdczcc889RZuO+TpnXda5EplnPcRb56OPcw0b9/Gg5i41S2tl9pTKb6bPkVJKe++990bvlVJpUvW+1KzEGh6fUkorVqxImyP+bXRMuklLTRZRSg53H9A5EKVUaDWVRZS519F3iMKo/Zo6ljds2FB5/Trz3HPPZdl/u3Q+uqtE9O11fETpVnT+eZ9rf0WZnD0tiWZy33fffYs27T9P9dKboOEBAACAxsOGBwAAABoPGx4AAABoPL3iw3Puuedm2f04jjjiiCzvv//+RZvaXt2HR22FWkE7pTK8NipnEPluaGVX9y3ac889s6w+SCmVPgRRmO/mTKuhr45+46i0RJQOXYlCyCNfn8jG7b4N6s/g/ijq53XVVVcVbRdeeGHlPepEZC/Xd3c/JJ2bnqpfQ8WXL19etKmv07Rp0yqvEfne3XfffVmOwm6nTJlStOna43PTq45vLvhY1m/v301D2D0sXyuK+3zTquRRmRQdL36eHvsz69hyvw+9pqe50NBsr4iu64unB9lc0PUs8nvyb63v7t9TfW4i3xztk+j7eV+qP5/7PI4aNarymbWffdzqGjVkyJDKZ+kOaHgAAACg8bDhAQAAgMbTKyatY489Nss33XRT0fanP/0pyzfccEPRdsYZZ2T55z//edGmJicPKVUVnKrmXI2mKjcPr1P19+c+97miTVW8F1xwQdEWZae9+uqrs3znnXcWbZ4xtk54yLCqGD3Lp4Y9+jfVNg99jUJaVdWqbe2El0dten1X8+q5bj7Rvq5TBfR20IrMI0eOLNrUhOfq6UkzBUMAABN9SURBVMg8q2bOYcOGFW2aJfn+++/PspqCUyrN1Go6TKkcO6omT6k0tXkWYp23nj02qkxdN3RM+nvod/N5pGYsDe1PqUwREIUrR1nP9e/cdSGaH7ouax+lVM7NyZMnF23r16+vvKaOXf9GOpajDO/9jZp2/LdLv4uvS9rmc0evGbl4aD/7eTq/3cyv93azsf4euil9zJgxWfZxq2ZxTFoAAAAAbcKGBwAAABoPGx4AAABoPL3iiPD1r3/9gxuYLVdtx26jvfbaa7P87W9/u/L6bmOsqr4bVfCN/Hs8dbeGuh988MFFm4bXash9SmU4e519dpzIfuyo/5Tb8dXG79fUNr++tqlt2a8fhaVHoeh6rp8X2bL1/puTD4gydOjQLLs9XueLpx9Q3wD3kdAqyWvWrCnatEryo48+mmWfD3oNv7fOR7+3+qZ4uRgdc+6TVGdfDkfHpL+j+jh42YkTTzwxy+77tHTp0izrmEgpLkOhc0DnTjslYKJ0FeqrOX78+KLtyCOPzLI+f0plCRP/DlqywUuM1Akd974uqf+S+9Opn47/5kUpBpSoqrrez6+hPmRdXV1Fm/qCnnDCCUWbPqe/q68hnQQNDwAAADQeNjwAAADQeHrFpDV37twse1i6Zk09/vjji7aTTjopy6qGTCml0aNHZ9lDJVVdreq9KKTSTW2aMdLVrJq98oknnijafvzjH1e23XLLLVn2rNJ+XCc0fDilUtXqKlNVT7sqVDM0u5kwMinoPVSF7veOqidH6QmicaFtngFUzQceVn333Xdn2c2e/YmH8kYhwWq6dbOSmr/cnKcZcb0qsoaj6hzz8HU1Q7j5Sb+194me6xlitb987Pg96oz2hZt19djNSuo+4OHKuqbpeSmVY8TvpykC1LzoZukoLF3b3JyhaQZ0vKRUZtK+/fbbizZ1H/D57mbQuhBl+/f0H5oZfNy4cUWbfs8obNzXZ50vOvd9fdTx599W55WbC9Xd45FHHina9P18bvZmFnQ0PAAAANB42PAAAABA42HDAwAAAI2nV3x4NGTQ7bBq15s5c2bRdscdd2T5oYceKtrUzheFSet5kb+JE4U/6zOffvrpRdv06dOz7LZVDQX11O51xr9TFMbdanivX1P/zkNt9R7aL+30p+J/p3Zut5WrXTuqSuy28p/85CdZ/t3vftfSc/UFTz75ZHGs9nGfm2vXrs2yhyqr74xXJX/ssceyrHM4pTKkVX26tOSEP4v7m6j/l/vw6L2jdBWRH4f6TqT04THR30SVx3V++Hvo37lvlY5RDelOqVxf3ZdL76/94j5tOjd9rmi/+FqrZRO89Ine2/tT39V9UPz+dcH9yKKUGDqPvdyCfnufO3oP9Y9KqXqdjXwcdQ6nVK4n+juZUpl2xtMI6Dx2fy/C0gEAAAB6ABseAAAAaDy9YtLSqsWuHnvqqaey7CqwKDRc1XatVvd1dWlUQVtVpH5vDZF3M4CaQJ555pmiTUNt1VyQ0oeziNYJV08r3p/6rTzssSpj8qaITJatEoXLa7+4uUtV+Bqq6c8VVYavE15BXHHziIabe2ZeNQt4iKlmW3X071T2bLiKq+XVtOHfXdX0Psb0/aIxtXr16uK4biYtHZP+/nrsJgtdXz07r35jNxMqGr6eUvlNNUTd0WtGKQB8DOr7ePXtyDSlz+nfqK54f6mJ0H9ntP88LUS0zuq393lVlSnb10T9jfO5HqU30DB1N/OrO4ubtLyyeidBwwMAAACNhw0PAAAANJ5eMWmpeszVnqq+8kyvalaKCkW62q6qEGVUzDK6vkcmaJsWOXQ8Q6RGDrjavM4mrfPPP784VrOVm/tUzezvryrpdooLdgIdI67iVlWuq8lVBeymPR2frnJesGBBlv1dXUXcl0TmBDfZeabwquu4alxNQJ5BvCqKyiPg9NhV46rOHzNmTNGm88pV4aqKd7W59ombbeqGmjois51H0HjUqDJw4MAsa2RUSuWa7Wu0jgOdV24W0/XV11p9B59/Og68z/S5oshLp66FYn3c6bt71mI1JUX96uuS9ou36f0is5j+nZsgtU98/k2aNCnLvgbrmPZ+9t/KToKGBwAAABoPGx4AAABoPGx4AAAAoPH0ig+P+ry4P4Pac9WOnFJpb4x8bCKfiFYzLUe+KO5foPf2Ks9qw3T7pl6n7n4CysqVK4tj9aFwW7n6O7l/hfq89LUPjxJlefZ+UR8FHz+RH9nYsWMr/64/8Sr16m/jc0zxOaB2fH/3ZcuWZdnt8epvoPP9/vvvL87TrKxe9Xzx4sWVz6mV2t33R30KfK2pyhhcR/T5PLxe38NDz92np+rvPKWC9qGvk1V+WH6eXjPKDu1oW6sV11Mq55z7rUUpEPqTqMK8fyN9B8/ar/3gGaj1Hp6Ju+r7Rr9j3qZ49nT9PZg6dWrRpmuyP0d0j56ChgcAAAAaDxseAAAAaDy9YtJSXDWuqkfPtBwV+FMiM5nez1WGehyphiOVq6uNq0LiU4pVlHVDs0R7iKmG4nsfqSo7Cj+NUgS4CUj7wlMEVOHXr8oimlLZh67m1fBJT6mg5i9Xw3qRzrrgIcdRplx9JzcDDBo0KMuevVnNUf53ao5RE5OHO+uxh8/qO3h/aeoAV6lH40/NPXU3aem481QCSmS2c/Sb+jX127h5SNc47SfPGqzzyNe+qNBnVCRa+9ALaOr48feuqzuBuwfot3CzrvaRm261L/176pz2366q+eEmzshNRNcQ/zt9Pw1RT6nsE5/veg8fV1FW91ZAwwMAAACNhw0PAAAANB42PAAAANB4esWHp9WwXLc5u7+PojbGqFp6FL4ePVfkb6P3c/8Wta1G6c3rWk37v9x+++2VbZFPjfrwuE+Ilprw1OLaF25zr+qnToV7qy3byyToOHM7uo5Pf9dOVHjvC/RbR35PXjFc/W8mTpxYtKnvjPqCpVQd+urfq6urK8vun7F+/fosR6UI/H1aHWPRvK0D7rekqP+Rl0KJ5ktUeiXyN9S1MErhoNfwb6/95OtJVK5C56qPEb2Hv0+UfqE/8XfXNeXZZ58t2nTNcp8rnUvuY9lqJXX9fv47rGu8r4nq3+njT/thwoQJRdtNN92UZV9r1G/HyxXhwwMAAACwCdjwAAAAQOPp9bD0doiyc0bh31XmhEilG2Vy9vA9DbV1Nauq9x988MGiTVV6/ZlpuBWiisL6Pfxb63t5SHKUNTWqal+VPsCfMfqmem8fB5EZTts8pLvVLLB1InpON5Xo9zzttNOKtksvvTTL/s10Trh6Ws0QqopftGhRcZ6qrr2fNbv50KFDizZdJ5YsWVK0tWrKqPvcVNNHZFKO0nr4O0ZpISJzlLapSSRKSRGZtDzsvdV55SYtrbAdrTV1wt0cNB2Ar6VRJfU1a9Zk2d9V7+Hztsq87aavKPRcx6ObEteuXZtlN0XpuPWxqWHqnTY3o+EBAACAxsOGBwAAABoPGx4AAABoPL3iiKBpvj2MLbKnqi+A2/GjcFpF7dGR3ToKgXdbZOQ/NHr06Czfe++9RZv6vtS9tMTs2bMr2/Sb+revSgmQUtmH7hcVpQ/QvlHZqz9XhVWmVH7vKMzS+yXyL+jNKr69hc+BKBxbz/2///u/ou2HP/xhltU2n1Jcgf2xxx7LsvqY7LfffsV5WhF95cqVRZv6EIwaNapo01DYqAyJj7Eo1UTdUD8oH5NK5LPoKfrVF6OdcH4l8gNS2vGhicpOKF6aJPJVifwT+5MoLN19ZbQUg4d4RylF1HfGr1lVBd3X6igdh85pb1NfnL322qtou+aaa7IcpXqJxnt3QMMDAAAAjYcNDwAAADSejpi0XDUXmZWiTImqvorCE119WmXaaDVs2f8uUvG6eWTs2LEbfQ6/TqdVc53mr3/9a2Wbmvjc3KcZeDV82M/1vohCWqvUq64a137x/mzVZBZlTI7GyOZi3vLQ+ki9r+Yhz+aqJhH/ZmpmcjNZVT94SLxew6snq4lr+fLlRdu0adOyPH369KItqmCvZiIN660j2hc+JnXt9cz1ioc5K77W6tz0davK3BWZn7xN1wUfSzp+vF/0tyMKnXY8m3pdaKeKvGYbd3QMuDlK8d9evZ/OUzcxaZuPlei7qzvLlClTijY1hfm6ruNDM4l3AjQ8AAAA0HjY8AAAAEDjYcMDAAAAjacjPjxRVXK3AXtabCUqBxCFoqt/SJXs14jKGfi91W6p4YEplaUlIh+euqevv/766yvb9P3dRqzf45JLLinaPvvZz2bZv436i3hfqA03SnneaukQD8fUY/cl0fD8J554omhzv5YqvNKx+zb1Jf7dBw8enGV/d/WBcTt+5Cui1dL93TUcVdP/Dxo0qDhvjz32yLLb7Q8++OCNPoff+4ADDijaNFx+xYoVRZv6Mq1atSrVGX1W98HSORH5Z/k76vzwdA/qe+HrlvrYtOrD434feg3311J/m8jvyIlKHNQ1LN393XS8qm9kSmV/uS9OVBE9+t3R71SVCsTvHaV6icqLeD9Hfr7a5mltegoaHgAAAGg8bHgAAACg8fRKpmVVSXnI2fDhwyv/TlVgrh5T1XwUgtyq6cvNIa2Gs7sZYOrUqRt9Dj+uu0lL1auexVRDCKPvO3fu3OL4K1/5Spavuuqqok1NYVopO6XSvBFVy9U+iyqiu1pU/07NJSmldM4552T51ltvLdpazUB77bXXFsdnnnlm5bm9TRTK76Guc+bMyXJkBnB1u87HSZMmFW1qatAUDl1dXcV5qkZXc2dKpQnSzS86jjz8WNcaz96s57oJpM64iVLXlWhM+vuredbNhFFmeUXHUpRGxM3gOqd9Ldf+dfcBJXpXb6trCgn/ZtoPbtbVNjdp6feNUrY4Oq/0PJ8POgb0tyCl8h3cbKVrSJQFPUpdE/1dd0DDAwAAAI2HDQ8AAAA0HjY8AAAA0Hh63YfH7XNjxoyp/Du1RQ4ZMqRoU7+SyCYbVe+O7NH6nO43orZO9weJwuz1OaPq7HVA+8xt562GYzsXXHDBRuVNod9bnyUKX3Tbtdqho3Im7aD3d9u4pli/7rrrirb+9OFxP4EolF/n5r777lu06XzU0PaUSr8unzvqo6HzQf15UirD4L2foxIl+n6zZs0q2pYuXZrl2267rWjTMeZ+CXVDv6+vYbqu7LbbbpXX8BIj6m8RVYuPfA9bXdPc7y+qVK/zfe3atZXX9N+AyNejnWrtfYn7NkU+nzqP/DdIw/d9buq65P5S2i/qN+ffUo/dT07nuz+z9qVfU31ho7Q2nf7dRMMDAAAAjYcNDwAAADSejpi0ouyLjoc8K6oe8+y4GuLm4bSq1m41vNxRdaKbQDRE0Cv4qsrQ1fmqjut0eF2nueKKK7J89dVXF236/q4ejsLUu4t+06gab2/jZhcNx3Yzn47XQw89tFefqx18Dujc8YzJmg7A0Xf381RVHmVp1Tng40bDkX2u6DXdRKfh1iNHjizaNLuwz0010UWpMupAq6HhUXi9Z5rWd27HpFVloozcDPz6rWaHjqrYuzlIf1cis2qd0JQmKcW/JR//+Mez7KZLzW4erc9uOqrqS0fPi76tt6nZavz48UWbZmCP9g+e5qKnoOEBAACAxsOGBwAAABoPGx4AAABoPB3x4XEbqdqS3TYY+dWccsopWd6wYUPRpjZ3v1+V/TGqHBtVUnc/Aa1ie9BBB230Xil92B7dajXhOqA+KV4lXMN9vV9OP/30Ht87Sh8QVbFXWq2c7sdRqPtxxx1XtF1++eVZ9tDQT3ziE1n+2te+VvksfY2nTdCwUvet8JBWZcmSJVl2H4Lo23enpEp0PZ+b6lukfgEppfTAAw9UXlOPZ86c2fYz9iXq0xT5WkQlIhwdv1EFdkfno/6df9/o3tH76JiMQpLdX0SP3b+nrmV9Bg0aVBzrd/dyO9/61rey7N9s2bJlWXafx6iSelUppyiNQPRb799d00L4vNUyNr///e+LtmHDhmV54sSJqZOg4QEAAIDGw4YHAAAAGk9HTFquGq8ySaRUZoV0vvGNb3TicfoNV+vqu0fvXTdGjx5dHKsK2rMwP/3005XX0XB2z9CpRCan3sZVtKp6nT59emWbm7TOPvvsXni6nuPmJ80q7NmiDznkkMrrTJkypbMP1iE8tF6ZPXt2lufPn1+0aXj+7rvv3vkH6yAa3qvmi5RKM8I+++xTtOl69LOf/ayyrZ20Ip0gureumZFJy8eujms3d0VV1+uEpgrwkPUJEyZk2X9TDz/88CyPGjWqaNPv4n+n67qOIzeZ6d/5d9djX7ePOeaYVMXkyZOz7O/qVdc7CRoeAAAAaDxseAAAAKDxsOEBAACAxtMRHx4Pr9PwULcpHnzwwZXXiWzHUahqXfAQ7a6uriwfeOCBff043cb74Qc/+EGWva+jcgQeplhHonGlqRBSKssf+Lv1pd9ROxxwwAHF8dy5c7Ps7+DlMhT1p4jCVvt6nkZlCjSk1eem+pS5r1bd0LVDU2SkVPowaTiv005Kh77sQ79XlB5EUb+VlEr/F/czcR+RunLeeed16+9+8YtfdPhJep+jjjpqo3JvU89VGgAAAKCDsOEBAACAxrNFXbNQAgAAAHQKNDwAAADQeNjwAAAAQONhwwMAAACNhw0PAAAANB42PAAAANB42PAAAABA4/l/b3gafA75Z44AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x288 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
Florent Chatelain's avatar
Florent Chatelain committed
495
496
497
   "source": [
    "from tensorflow.keras.datasets import fashion_mnist\n",
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
    "(X, y), _ = fashion_mnist.load_data()\n",
    "selected_labels = [1, 2]\n",
    "nb_im = 5  # number of images to display for each class\n",
    "im0 = X[y == selected_labels[0]]\n",
    "im1 = X[y == selected_labels[1]]\n",
    "f, ax = plt.subplots(2, 5, figsize=(10, 4), sharex=True, sharey=True)\n",
    "for i in range(nb_im):\n",
    "    ax[0, i].axes.imshow(im0[i, :, :].squeeze(), interpolation=\"nearest\", cmap=\"gray_r\")\n",
    "    ax[0, i].axes.axis(\"off\")\n",
    "    ax[1, i].axes.imshow(im1[i, :, :].squeeze(), interpolation=\"nearest\", cmap=\"gray_r\")\n",
    "    ax[1, i].axes.axis(\"off\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Figure 7\n",
    "Empirical classification errors for $2$-class (balanced) MNIST-fashion images (`trouser` vs `pullover`), with $n=512$ (**top**) and $n=2048$ (**bottom**). **Theoretically predicted ``plateau''-behavior observed for all $\\varepsilon_B$ not too small**. "
   ]
  },
  {
   "cell_type": "code",
Florent Chatelain's avatar
Florent Chatelain committed
521
   "execution_count": 8,
Florent Chatelain's avatar
Florent Chatelain committed
522
   "metadata": {},
Florent Chatelain's avatar
Florent Chatelain committed
523
524
525
526
527
528
529
530
531
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[progression 40/40]"
     ]
    }
   ],
Florent Chatelain's avatar
Florent Chatelain committed
532
533
534
535
536
537
538
539
   "source": [
    "nbMC = 40\n",
    "df_1, _ = get_perf_clustering(n0=256, nbMC=nbMC)\n",
    "df_2, _ = get_perf_clustering(n0=1024, nbMC=nbMC)"
   ]
  },
  {
   "cell_type": "code",
Florent Chatelain's avatar
Florent Chatelain committed
540
   "execution_count": 9,
Florent Chatelain's avatar
Florent Chatelain committed
541
   "metadata": {},
Florent Chatelain's avatar
Florent Chatelain committed
542
543
544
545
546
547
548
549
550
551
552
553
554
555
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
Florent Chatelain's avatar
Florent Chatelain committed
556
   "source": [
Florent Chatelain's avatar
Florent Chatelain committed
557
    "f, ax = plt.subplots(2, 1, figsize=(8, 8), sharex=True)\n",
Florent Chatelain's avatar
Florent Chatelain committed
558
559
560
561
    "plot_perf_clustering(df_1, n0, ax[0])\n",
    "plot_perf_clustering(df_2, n0, ax[1])"
   ]
  },
Florent Chatelain's avatar
Florent Chatelain committed
562
563
564
565
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
Florent Chatelain's avatar
Florent Chatelain committed
566
567
    "#### Figure 8\n",
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
568
    "Sample vs limiting spectra and dominant eigenvector of $K$ for 2-class MNIST-fashion images (`trouser` vs `pullover`); **(left)** $\\varepsilon_S=\\varepsilon_B=1$ (error rate: $\\mathbb P_e=.09$); **(right)** $\\varepsilon_S=0.02$, $\\varepsilon_B=0.2$ ($\\mathbb P_e=.12$). **Surprisingly good fit between sample and predicted isolated eigenvalue/eigenvector in all cases; as for spectral measure, significant prediction improvement as $\\varepsilon_S,\\varepsilon_B\\to 0$**"
Florent Chatelain's avatar
Florent Chatelain committed
569
570
571
572
   ]
  },
  {
   "cell_type": "code",
Florent Chatelain's avatar
Florent Chatelain committed
573
   "execution_count": 6,
Florent Chatelain's avatar
Florent Chatelain committed
574
   "metadata": {},
Florent Chatelain's avatar
Florent Chatelain committed
575
576
577
578
579
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
Florent Chatelain's avatar
Florent Chatelain committed
580
      "Punctured (right) error rate == 0.12\n",
Florent Chatelain's avatar
Florent Chatelain committed
581
582
583
      "Full (left) error rate == 0.10\n",
      "Full (left): ratio of eigenvalues < 15 == 4083/4096\n",
      "Full case: largest sample eigval == 981.74, lagest limiting spike == 783.62\n"
Florent Chatelain's avatar
Florent Chatelain committed
584
585
586
587
     ]
    },
    {
     "data": {
Florent Chatelain's avatar
Florent Chatelain committed
588
      "image/png": "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\n",
Florent Chatelain's avatar
Florent Chatelain committed
589
590
591
592
593
594
595
596
597
598
      "text/plain": [
       "<Figure size 864x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
Florent Chatelain's avatar
Florent Chatelain committed
599
600
   "source": [
    "eB = 0.2\n",
Florent Chatelain's avatar
Florent Chatelain committed
601
602
603
    "eS = 0.02\n",
    "\n",
    "X, n0, n1, ell = gen_MNIST_vectors(n0=2048)\n",
Florent Chatelain's avatar
Florent Chatelain committed
604
605
606
    "\n",
    "(p, n) = X.shape\n",
    "c0 = p / n\n",
Florent Chatelain's avatar
Florent Chatelain committed
607
608
609
    "eigvals_punct = puncture_eigs(X, eB, eS, b=1, sparsity=0)[0]\n",
    "u_punct = puncture_eigs(X, eB, eS, b=1, sparsity=1)[1]\n",
    "u_punct = np.sign(u_punct[:n0].mean() - u_punct[n0:].mean()) * u_punct\n",
Florent Chatelain's avatar
Florent Chatelain committed
610
    "overlap = 1 / n * (np.sum(u_punct[:n0] > 0) + np.sum(u_punct[n0:] < 0))\n",
Florent Chatelain's avatar
Florent Chatelain committed
611
    "print(\"Punctured (right) error rate == {:.2f}\".format(1 - overlap))\n",
Florent Chatelain's avatar
Florent Chatelain committed
612
    "\n",
Florent Chatelain's avatar
Florent Chatelain committed
613
614
    "eigvals_full = puncture_eigs(X, eB=1, eS=1, b=1, sparsity=0)[0]\n",
    "u_full = puncture_eigs(X, eB=1, eS=1, b=1, sparsity=1)[1]\n",
Florent Chatelain's avatar
Florent Chatelain committed
615
    "u_full = np.sign(u_full[:n0].mean() - u_full[n0:].mean()) * u_full\n",
Florent Chatelain's avatar
Florent Chatelain committed
616
    "overlap = 1 / n * (np.sum(u_full[:n0] > 0) + np.sum(u_full[n0:] < 0))\n",
Florent Chatelain's avatar
Florent Chatelain committed
617
    "print(\"Full (left) error rate == {:.2f}\".format(1 - overlap))\n",
Florent Chatelain's avatar
Florent Chatelain committed
618
619
620
    "\n",
    "# Truncate the eigvals dist to show the histrogram\n",
    "lmax = 15\n",
Florent Chatelain's avatar
Florent Chatelain committed
621
622
623
624
625
    "print(\n",
    "    \"Full (left): ratio of eigenvalues < {:d} == {:d}/{:d}\".format(\n",
    "        lmax, np.sum(eigvals_full < lmax), n\n",
    "    )\n",
    ")\n",
Florent Chatelain's avatar
Florent Chatelain committed
626
627
628
    "\n",
    "f, axes = plt.subplots(2, 2, figsize=(12, 10))\n",
    "# Puncturing\n",
Florent Chatelain's avatar
Florent Chatelain committed
629
    "disp_eigs(axes[:, 1], eigvals_punct, u_punct, eB, eS, c0, n0, ell, b=1, vM=None)\n",
Florent Chatelain's avatar
Florent Chatelain committed
630
    "# Full\n",
Florent Chatelain's avatar
Florent Chatelain committed
631
    "disp_eigs_full(axes[:, 0], eigvals_full, u_full, c0, ell, lmax=lmax, b=1)\n",
Florent Chatelain's avatar
Florent Chatelain committed
632
633
634
    "\n",
    "plt.show()"
   ]
Florent Chatelain's avatar
Florent Chatelain committed
635
636
637
638
639
640
641
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
Florent Chatelain's avatar
Florent Chatelain committed
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:tensorflow2]",
   "language": "python",
   "name": "conda-env-tensorflow2-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}