{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4ec3fe9c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "89131220",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.17483199]\n",
      " [ 1.65422612]\n",
      " [ 1.63731591]\n",
      " ...\n",
      " [ 0.16791458]\n",
      " [-1.18443056]\n",
      " [-0.79847463]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1.9767812449587734"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n1 =10000\n",
    "n2 = 15000\n",
    "x1 = np.random.randn(n1)+2\n",
    "x2 = np.random.randn(n2)-1\n",
    "Y = np.vstack([x1.reshape(-1,1),x2.reshape(-1,1)])\n",
    "print(Y)\n",
    "np.mean(x1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "13209cfb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.0083336004715935"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "cd5f1d43",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.]\n",
      " [0.]\n",
      " [0.]\n",
      " ...\n",
      " [1.]\n",
      " [1.]\n",
      " [1.]]\n"
     ]
    }
   ],
   "source": [
    "X = np.vstack([np.zeros((n1,1)),np.ones((n2,1))])\n",
    "print(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "939c74e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  1.17483199],\n",
       "       [ 0.        ,  1.65422612],\n",
       "       [ 0.        ,  1.63731591],\n",
       "       ...,\n",
       "       [ 1.        ,  0.16791458],\n",
       "       [ 1.        , -1.18443056],\n",
       "       [ 1.        , -0.79847463]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = np.hstack([X,Y])\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "ac40c294",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  49.,  710., 3320., 6036., 4490., 3518., 4036., 2306.,  489.,\n",
       "          46.]),\n",
       " array([-4.74525979, -3.70209036, -2.65892094, -1.61575151, -0.57258208,\n",
       "         0.47058734,  1.51375677,  2.5569262 ,  3.60009562,  4.64326505,\n",
       "         5.68643447]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "5c6388c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  20.,  202., 1034., 2907., 4525., 3852., 1863.,  513.,   77.,\n",
       "           7.]),\n",
       " array([-4.74525979, -3.95884655, -3.17243331, -2.38602007, -1.59960683,\n",
       "        -0.81319359, -0.02678035,  0.75963289,  1.54604612,  2.33245936,\n",
       "         3.1188726 ]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(2,1,1)\n",
    "plt.hist(x1)\n",
    "plt.subplot(2,1,2)\n",
    "plt.hist(x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "7b49bef3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.18571233770055337"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "2ddadb24",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9767812449587734"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(x1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "a7215a35",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.0083336004715935"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "50ce1a0f",
   "metadata": {},
   "outputs": [],
   "source": [
    "var_totale = np.var(Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "05e5ccae",
   "metadata": {},
   "outputs": [],
   "source": [
    "var_intra = np.var(x1)+np.var(x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "7819a9bd",
   "metadata": {},
   "outputs": [],
   "source": [
    "var_inter = var_totale - var_intra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "71f1e14a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1267110400866756"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var_inter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "cab7c75e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3577307336966838"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var_inter/var_totale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "c199e006",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_diabetes\n",
    "X,y = load_diabetes(return_X_y=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "496bfc1a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X.shape = (442, 10), y.shape =(442,)\n"
     ]
    }
   ],
   "source": [
    "print(f\"{X.shape = }, {y.shape =}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "3d7463b0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([38., 80., 68., 62., 50., 41., 38., 42., 17.,  6.]),\n",
       " array([ 25. ,  57.1,  89.2, 121.3, 153.4, 185.5, 217.6, 249.7, 281.8,\n",
       "        313.9, 346. ]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "3a6a62bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(442, 10)"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.[]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "a35ca41a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(150, 4)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "X,y = load_iris(return_X_y=True)\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "84479b80",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.1, 3.5, 1.4, 0.2])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[0,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "ae26668b",
   "metadata": {},
   "outputs": [],
   "source": [
    "moy_par_var = np.mean(X,axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "397395be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.12502600e-15, -7.60872846e-16, -2.55203266e-15, -4.48530102e-16])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(X-moy_par_var,axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "d87d312f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(150, 4)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(X-moy_par_var).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "e248b9bd",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_wine\n",
    "X,y = load_wine(return_X_y=True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "3dd7607a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.boxplot(X);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "5315e326",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_cr = (X-np.mean(X,axis=0))/np.std(X,axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "f1eb7327",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 7.84141790e-15  2.44498554e-16 -4.05917497e-15 -7.11041712e-17\n",
      " -2.49488320e-17 -1.95536471e-16  9.44313292e-16 -4.17892936e-16\n",
      " -1.54059038e-15 -4.12903170e-16  1.39838203e-15  2.12688793e-15\n",
      " -6.98567296e-17]\n"
     ]
    }
   ],
   "source": [
    "print(np.mean(X_cr,axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "6411c4d3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n"
     ]
    }
   ],
   "source": [
    "print(np.std(X_cr,axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "66ef9f6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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OfdpafX29EhMTVVdXp27dupkup1McO3ZMVVVVvvfHjx9XTU2NUlNTFR8f77dvRkaGunTpEuwSHe3EiRN69tln9eWXX2rQoEG66667jLWEeDwepaenKzMzs8XBqm63W5WVlaqurmacSAu2bt2qkSNHqry8XCNGjDBdDjqAxxuEl878mwzk+s2smSCrqqrSyJEj27UvJ+jmYmNjNXv2bNNlSPr7gmZr164944JmWVlZKi0tDdrsqJ8GXYmwC3s0tQZOmjRJ8+bNU3x8vI4fP65169YpLy+PMVJoN4JIkGVkZKi8vNz3fseOHZo2bZpefvllDRkypNm+cC4nLmgWSNCVCLvoGI/Ho7lz52rkyJGqrKz0m9GWmpqqkSNH6t5779W1115LayDaRBAJsi5durR44h8yZAgXhBBz+oJmo0ePbva5iQXNfhp0JcIuOl9Ta+BXX32lyZMna+3atRo6dKgqKyu1ePFilZSUyLKsoLYGInQRRIAOcuKCZmcKuhJhF51n7969kqSrr77a73d/9OjRKi4u1uTJk7Vu3TrffkBrmDUDdBALmiFSHTp0SNKP6+i0ND7K7Xb77Qe0hiACnIWmBc22b9/ut6BZZWUlg/UQtnr27CnpxwGrXq/X7zOv16vi4mK//YDW0DUDdMDps1NSU1P1+uuv69NPP1VVVZUyMjI0evRouVwubd26VRKzU5zMqVPqA5kBFezfr759+0qS1q1bJ7fbrfz8fN8YkYKCAq1bt85vP6A1BBGgA5idEj6cOqXeqXUdO3ZMXbt2VXJyss477zxt2bJFWVlZvs+Tk5N18cUXq66uLqC/EUQuggjQAcxOCR9OnVIfyO9YMOuqqqrSZZddJknat29fs8/37dvn215dXU0AR5sIIkAHMDslfDh1Sr1Tf8dOD0gfffSRnnzySb9A0rdvX82ePVu//OUvCeBoF4IIAKDdTg9II0aM0D333KPVq1frzjvv1MqVK3XbbbcxUwwBYdYMAKDDXC6XRo0aJUkaNWoUIQQBC9sWEaeOhEdgeHYKAIS3sA0iTh1xjsAwOwUAwlvYBhGnjoRHYJidAgDhLWyDiFNHwiMwTp05AADoHGEbRAAAkYPxZKGLIAIACHmMJwtdBBEAQMhjPFnosjWIFBQUqKioSFVVVYqPj1dWVpYef/xxDR482M7DAgAiDOPJQpetC5pt2rRJM2fO1Keffqr169fr5MmTuvLKK3X06FE7DwsAAEKErS0i7777rt/7F198Ub169VJ5ebn+4R/+wc5DI0BOfuQ4ACB8BXWMSF1dnSSpe/fuLX7e2NioxsZG3/v6+vqg1AUWgAMAmBG0IOL1ejV79myNHTtWQ4cObXGfgoICLVq0KFgl4TROfeQ4ACC8BS2IzJw5U5WVlfrkk0/OuE9+fr7mzJnje19fX6+UlJRglBfxGOgFAJ2P9U3aFpQgMmvWLJWUlOjjjz9Wv379zrhfXFyc4uLiglESAAC2Y32TttkaRCzL0m9/+1u9+eab2rhxo9LS0uw8HAAAjsL6Jm2zNYjMnDlTa9as0VtvvaWEhAQdOHBAkpSYmNisOQoAgHBDt3fbbF1HZMWKFaqrq9O4ceOUlJTke7322mt2HhYAAIQI27tmAAAAzsTWFhEAAIDWEEQAAIAxBBEAAGAMQQQAABhDEAEAAMYQRAAAgDEEEQAAYAxBBAAAGEMQAQAAxhBEAACAMQQRAABgDEEEAAAYQxABAADGEEQAAIAxBBEAAGAMQQQAABhDEAEAAMYQRAAAgDEEEQAAYAxBBAAAGEMQAQAAxhBEAACAMQQRAABgDEEEAAAYQxABAADGEEQAAIAxBBEAAGAMQQQAABhDEAEAAMYQRAAAgDEEEQAAYIytQeTjjz/WlClTlJycrKioKBUXF9t5OAAAEGJsDSJHjx7V8OHDtXz5cjsPAwAAQlSMnV8+ceJETZw40c5DAACAEGZrEAlUY2OjGhsbfe/r6+sNVgMAAOzmqMGqBQUFSkxM9L1SUlJMlwQAAGzkqCCSn5+vuro636u2ttZ0SQAAwEaO6pqJi4tTXFyc6TIAAECQOKpFBAAARBZbW0SOHDmiXbt2+d7v3r1bFRUV6t69u/r372/noQEAQAiwNYhs2bJFOTk5vvdz5syRJE2fPl0vvviinYcGYFh1dbUaGhrO+PmOHTv8/rc1CQkJuvDCCzutNgDOYWsQGTdunCzLsvMQPpz0AOeorq7WRRdd1K59p02b1q79vvjiC/4ugTDkqMGqHcVJD5HMiSG8qZ6XX35ZQ4YMaXGf48ePq6amRqmpqYqPjz/jd+3YsUPTpk1r9d8RQOgKiyDCSQ+RyukhfMiQIRoxYsQZPx87dmynHAdwirZuDCRa6H8qLIJIE056iDSEcMA5ArkxkIJ/c+DE1lMpzIIIEKkI4YB57bkxkMzcHDi59ZQgAgAIOZ3ZBdLZ3R9t3RhIwb85cHLrKUEkQjn5jxgAWmNHF0ikTFBwYuspQcRmTuyT448YQCjrzC4QxkaZRxCxkVP75PgjBhAOnNgFgsARRGzk5D45iT9iRCYntlK2p65AaqO7FKGEIBIETuyTcypOxrCTU1sp6S5FJCOIwDE4GcNuTm2lpLsUkYwgAsfgZIxgcWorJd2liEQEETgOJ2MAiBwEEaAdGLuCSMXvPuxGEAHawNgVRCp+9xEMBBGgDYxdQaTidx/BQBAB2omxK4hU/O7DTtGmCwAAAJGLIAIAAIwhiAAAAGMIIgAAwBiCCAAAMIYgAgAAjCGIAAAAY1hHBACAThB16gdd2ida8Ye/kPad/X1+/OEvdGmfaEWd+qETqnMugggAAJ3gnCN7tPXOc6WP75Q+PvvvGyJp653naseRPZKyzv4LHYogAgBAJ/jh3P4asfKIXnnlFQ3JyDjr79tRVaWpU6dq9f/r3wnVORdBBACATmDFnKNtB7w6ft5FUvLPz/r7jh/watsBr6yYc86+OAdjsCoAADCGFhEAna4zB+1FyoA9IFIRRIAQ5tQLfmcO2ouUAXtApApKEFm+fLmWLFmiAwcOaPjw4Xr66ad12WWXddr3O/VkDNjNqRf8zhy0FykD9oBIZXsQee211zRnzhw999xzuvzyy/XUU0/pqquu0s6dO9WrV69OOYZTT8aA3Zx6we/MQXuRMmAPiFS2B5Hf/e53uuOOO3TLLbdIkp577jm98847+uMf/6j58+d3yjGcejIG7MYFH5GIVvDwYmsQOXHihMrLy5Wfn+/bFh0drQkTJqisrKzZ/o2NjWpsbPS9r6+vb9dxOBmHB04uANqDVvDwYmsQ+fbbb+XxeNS7d2+/7b1791ZVVVWz/QsKCrRo0SI7S4Kce8Hn5AKgPWgFDy+OmjWTn5+vOXPm+N7X19crJSXFYEXhyakXfE4uANqDVvDwYmsQueCCC+RyuXTw4EG/7QcPHlSfPn2a7R8XF6e4uDg7S4Kce8Hn5IJI5dRWSiAYbA0isbGxGjlypD788EO53W5Jktfr1YcffqhZs2bZeWi0ggs+4CxObaUEgsH2rpk5c+Zo+vTpGjVqlC677DI99dRTOnr0qG8WDeB03K3Cbk5tpQSCwfYgcsMNN+jQoUN68MEHdeDAAf385z/Xu+++22wAK+BU3K3CbrRSIpIFZbDqrFmz6IpByOJuNXzQuhUYfl4IBkfNmgGciLvV8EHrVmD4eSEYCCIAIgatW4Hh54VgIIgAiBi0bgWGn1f4cHI3G0EEAIAw5+RuNoIIAABhzsndbAQRAADCnJO72c6uowgAAOAsEEQAAIAxBBEAAGAMQQQAABjDYFUbOXneNgAATkAQsZGT520DAOAEBBEbOXneNgAATkAQsZGT520DAOAEDFYFAADGEEQAAIAxdM1EoGPHjkmStm7d2up+x48fV01NjVJTUxUfH9/iPjt27Oj0+gAAkYMgEoGqqqokSXfccUenfWdCQkKnfRcQabg5QCQjiEQgt9stScrIyFCXLl3OuN+OHTs0bdo0vfzyyxoyZMgZ90tISNCFF17Y2WUCEYObA0QygoiN2nOX0547HKlz73IuuOAC3X777e3ef8iQIRoxYkSnHR+AP24OEMkIIjbiLgdAe3BzgEhGELFRe+5y2nuHI4X/XQ795AAQeQgiNgrkLoc7HFqQACASEUTgGPSTw25OHbcFRDKCCByDfnLYjVa38EA3bngJiyDCXQ6A9mDcVmCcesEnUAbOydfJsAgi/FLCTk49GTuZU096jNsKjFPPrXTjBs6p/y2lMAki3OXATk7+A3YqfmbhwakXfLpxA+fk62RYBBHucmAnp56MnczJJz20Hxf88OHk62RYBBHATk4+GdMFAiDU2RZEHn30Ub3zzjuqqKhQbGysDh8+bNehgIhFFwiAUGdbEDlx4oSuu+46jRkzRqtXr7brMEBEowsEQKizLYgsWrRIkvTiiy/adQgg4tEFAjhHZ86wkyJnlh1jRAAA6AR2dJVK4d9d6qgg0tjYqMbGRt/7+vp6g9UAANB+nT3DToqM7tKAgsj8+fP1+OOPt7rPjh07lJGR0aFiCgoKfF06AACEEifPsHOygILI3LlzNWPGjFb3GThwYIeLyc/P15w5c3zv6+vrlZKS0uHvAwAAzhZQEOnZs6d69uxpVy2Ki4tTXFycbd8PAACcxbYxInv27NH333+vPXv2yOPxqKKiQpKUnp6uc889167DAgCAEGJbEHnwwQf10ksv+d5feumlkqQNGzZo3Lhxdh0WAACEkGi7vvjFF1+UZVnNXoQQAADQxLYgAgAA0BaCCAAAMIYgAgAAjCGIAAAAYwgiAADAGIIIAAAwhiACAACMIYgAAABjCCIAAMAYgggAADCGIAIAAIyx7aF3aNmxY8dUVVXle79jxw6//z1dRkaGunTpErTaAAAINoJIkFVVVWnkyJHNtk+bNq3ZtvLyco0YMSIYZQEAYARBJMgyMjJUXl7ue3/8+HHV1NQoNTVV8fHxzfYFAKCz/bR1XjLXQk8QCbIuXbo0a+UYO3asoWoAAJHoTK3zUvBb6AkiAABEmJ+2zkvmWugJIgAARJiWWuclMy30TN8FAADGEEQAAIAxdM0AANotkNkWrIWE9iCIAADaLZDZFqyFhPYgiAAA2i2Q2RashYT2IIgAsJ2TFk/C2XHSbAuEB4IIANs5afEkAM5CEAFgOyctngTAWQgiAGxHcz6AM2EdEQAAYAxBBAAAGEMQAQAAxjBGBEBE++nUYqYVA8FFEAEQ0c40tZhpxegMrKHTNtuCSE1NjR5++GF99NFHOnDggJKTkzVt2jQ98MADio2NteuwABCQn04tZloxOhNr6LTNtiBSVVUlr9erlStXKj09XZWVlbrjjjt09OhRLV261K7DAkBAWppazLRidBbW0GmbbUHk6quv1tVXX+17P3DgQO3cuVMrVqwgiAAAIgJr6LQtqGNE6urq1L179zN+3tjYqMbGRt/7+vr6YJQFAAAMCdr03V27dunpp5/WnXfeecZ9CgoKlJiY6HulpKQEqzwAAGBAwEFk/vz5ioqKavX10xHCe/fu1dVXX63rrrtOd9xxxxm/Oz8/X3V1db5XbW1t4P9GAAAgZATcNTN37lzNmDGj1X0GDhzo+//79u1TTk6OsrKytGrVqlb/ubi4OMXFxQVaEgCEnUCmfUbilE+Ej4CDSM+ePdWzZ8927bt3717l5ORo5MiReuGFFxQdzUKuCA+sDQC7BTLtMxKnfP4Uf5Ohy7bBqnv37tW4ceM0YMAALV26VIcOHfJ91qdPH7sOCwSFU9cG4GQcPgKZ9hmJUz5/yql/k2ibbUFk/fr12rVrl3bt2qV+/fr5fWZZll2HBYLCqWsDcDIOH0z7DIxT/ybRNtuCyIwZM9ocSwKEKqdeJDgZI1I59W8SbeNZM0AY4WQMINQwehQAABhDEAEAAMYQRAAAgDEEEQAAYAxBBAAAGEMQAQAAxhBEAACAMQQRAABgDEEEAAAYQxABAADGhO0S7z99CilPIG1dIE9t5ecFAOgsYRtEzvQUUp5A2rJAntrKzwsA0FnCNoj89CmkPIG0dYE8tTWYP69AWmokWmsAINREWZZlmS7iTOrr65WYmKi6ujp169bNdDkwYOvWrWdsqWkJrTUAYF4g1++wbRFBeAikpaZpfwBA6CCIwNG6dOni18Lh8XhUWlqq6OhonTx5UqNHj5bL5TJYIQDgbDB9FyGjqKhI6enpysnJ0U033aScnBylp6erqKjIdGkAgA4iiCAkFBUVKS8vT5mZmSorK1NDQ4PKysqUmZmpvLw8wggAhCgGq8LxPB6P0tPTlZmZqeLiYkVH/z0/e71eud1uVVZWqrq6mm4aAHCAQK7ftIjA8UpLS1VTU6MFCxb4hRBJio6OVn5+vnbv3q3S0lJDFQIAOoogAsfbv3+/JGno0KEtft60vWk/AEDoIIjA8ZKSkiRJlZWVLX7etL1pPwBA6CCIwPGys7OVmpqqxYsXy+v1+n3m9XpVUFCgtLQ0ZWdnG6oQANBRBBE4nsvl0rJly1RSUiK32+03a8btdqukpERLly5loCoAhCAWNENIyM3NVWFhoebOnausrCzf9rS0NBUWFio3N9dgdQCAjmL6LkJK08qq+/fvV1JSkrKzs2kJAQCH4VkzCFsul0vjxo0zXQYAoJMwRgQAABhDEAEAAMYQRAAAgDG2BpFrrrlG/fv31znnnKOkpCT95je/0b59++w8JAAACCG2BpGcnBy9/vrr2rlzp9544w19+eWXysvLs/OQAAAghAR1+u6f//xnud1uNTY26mc/+1mb+zN9FwCA0OPI6bvff/+9XnnlFWVlZZ0xhDQ2NqqxsdH3vr6+PljlAQAAA2wfrHr//fera9eu6tGjh/bs2aO33nrrjPsWFBQoMTHR90pJSbG7PAAAYFDAQWT+/PmKiopq9VVVVeXbf968edq2bZvef/99uVwu3XzzzTpTb1B+fr7q6up8r9ra2o7/mwEAAMcLeIzIoUOH9N1337W6z8CBAxUbG9ts+9dff62UlBT95S9/0ZgxY9o8FmNEAAAIPbaOEenZs6d69uzZocKaHuF++jgQAAAQuWwbrPrZZ59p8+bNuuKKK3T++efryy+/1MKFCzVo0KB2tYYAAIDwZ9tg1S5duqioqEjjx4/X4MGDddttt2nYsGHatGmT4uLi7DosAAAIIba1iGRmZuqjjz6y6+sBAEAY4FkzAADAGIIIAAAwhiACAACMIYgAAABjCCIAAMAYgggAADCGIAIAAIwhiAAAAGMIIgAAwBiCCAAAMIYgAgAAjCGIAAAAYwgiAADAGIIIAAAwhiACAACMIYgAAABjYkwXAGfyeDwqLS3V/v37lZSUpOzsbLlcLtNlAQDCDC0iaKaoqEjp6enKycnRTTfdpJycHKWnp6uoqMh0aQCAMEMQgZ+ioiLl5eUpMzNTZWVlamhoUFlZmTIzM5WXl0cYAQB0qijLsizTRZxJfX29EhMTVVdXp27dupkuJ+x5PB6lp6crMzNTxcXFio7+e071er1yu92qrKxUdXU13TQAgDMK5PpNiwh8SktLVVNTowULFviFEEmKjo5Wfn6+du/erdLSUkMVAgDCDUEEPvv375ckDR06tMXPm7Y37QcAwNkiiMAnKSlJklRZWdni503bm/YDAOBsEUTgk52drdTUVC1evFher9fvM6/Xq4KCAqWlpSk7O9tQhQCAcEMQgY/L5dKyZctUUlIit9vtN2vG7XarpKRES5cuZaAqAKDTsKAZ/OTm5qqwsFBz585VVlaWb3taWpoKCwuVm5trsDoAQLhh+i5axMqqAICOCuT6TYsIWuRyuTRu3DjTZQAAwhxjRAAAgDEEEQAAYAxBBAAAGBOUINLY2Kif//znioqKUkVFRTAOCQAAQkBQgsh9992n5OTkYBwKAACEENuDyLp16/T+++9r6dKldh8KAACEGFun7x48eFB33HGHiouL1aVLlzb3b2xsVGNjo+99fX29neUBAADDbGsRsSxLM2bM0L/8y79o1KhR7fpnCgoKlJiY6HulpKTYVR4AAHCAgIPI/PnzFRUV1eqrqqpKTz/9tBoaGpSfn9/u787Pz1ddXZ3vVVtbG2h5AAAghAS8xPuhQ4f03XfftbrPwIEDdf311+vtt99WVFSUb7vH45HL5dLUqVP10ksvtXmsuro6nXfeeaqtrWWJdwAAQkR9fb1SUlJ0+PBhJSYmtrqvbc+a2bNnj98Yj3379umqq65SYWGhLr/8cvXr16/N7/j666/pngEAIETV1ta2eb23bbBq//79/d6fe+65kqRBgwa1K4RIUnJysmpra5WQkODXstIRTenMaa0rTq1Lcm5t1BUY6gqMU+uSnFsbdQUmEuqyLEsNDQ3tWrrD0Q+9i46Obndoaa9u3bo56j98E6fWJTm3NuoKDHUFxql1Sc6tjboCE+51tdUl0yRoQSQ1NVU29QIBAIAQxbNmAACAMRETROLi4vTQQw8pLi7OdCl+nFqX5NzaqCsw1BUYp9YlObc26goMdfmzbdYMAABAWyKmRQQAADgPQQQAABhDEAEAAMYQRAAAgDFhH0Q+/vhjTZkyRcnJyYqKilJxcbHpkiT9+KThX/ziF0pISFCvXr3kdru1c+dO02VpxYoVGjZsmG9BmzFjxmjdunWmy2rmscceU1RUlGbPnm26FP37v/97swc/ZmRkmC5LkrR3715NmzZNPXr0UHx8vDIzM7VlyxajNaWmprb4sMyZM2carcvj8WjhwoVKS0tTfHy8Bg0apIcfftgR6x81NDRo9uzZGjBggOLj45WVlaXNmzcHtYa2zqWWZenBBx9UUlKS4uPjNWHCBFVXVzuitqKiIl155ZXq0aOHoqKiVFFRYbyukydP6v7771dmZqa6du2q5ORk3Xzzzdq3b5/RuqQfz2kZGRnq2rWrzj//fE2YMEGfffaZbfWEfRA5evSohg8fruXLl5suxc+mTZs0c+ZMffrpp1q/fr1OnjypK6+8UkePHjVaV79+/fTYY4+pvLxcW7Zs0S9/+Utde+21+utf/2q0rtNt3rxZK1eu1LBhw0yX4nPJJZdo//79vtcnn3xiuiT97W9/09ixY/Wzn/1M69at0//+7/9q2bJlOv/8843WtXnzZr+f1fr16yVJ1113ndG6Hn/8ca1YsULPPPOMduzYoccff1xPPPGEnn76aaN1SdLtt9+u9evX609/+pO2b9+uK6+8UhMmTNDevXuDVkNb59InnnhCf/jDH/Tcc8/ps88+U9euXXXVVVfphx9+MF7b0aNHdcUVV+jxxx+3vZb21nXs2DFt3bpVCxcu1NatW1VUVKSdO3fqmmuuMVqXJF100UV65plntH37dn3yySdKTU3VlVdeqUOHDtlTkBVBJFlvvvmm6TJa9M0331iSrE2bNpkupZnzzz/f+s///E/TZViWZVkNDQ3WhRdeaK1fv976x3/8R+vuu+82XZL10EMPWcOHDzddRjP333+/dcUVV5guo0133323NWjQIMvr9RqtY9KkSdatt97qty03N9eaOnWqoYp+dOzYMcvlclklJSV+20eMGGE98MADRmr66bnU6/Vaffr0sZYsWeLbdvjwYSsuLs5au3at0dpOt3v3bkuStW3btqDWZFntu/58/vnnliTrq6++Ck5RVvvqqqursyRZH3zwgS01hH2LSKioq6uTJHXv3t1wJX/n8Xj06quv6ujRoxozZozpciRJM2fO1KRJkzRhwgTTpfiprq5WcnKyBg4cqKlTp2rPnj2mS9Kf//xnjRo1Stddd5169eqlSy+9VM8//7zpsvycOHFCL7/8sm699dazfrDl2crKytKHH36oL774QpL03//93/rkk080ceJEo3WdOnVKHo9H55xzjt/2+Ph4R7S8SdLu3bt14MABv7/LxMREXX755SorKzNYWWipq6tTVFSUzjvvPNOl+Jw4cUKrVq1SYmKihg8fbssxHP3Qu0jh9Xo1e/ZsjR07VkOHDjVdjrZv364xY8bohx9+0Lnnnqs333xTF198semy9Oqrr2rr1q1B7xtvy+WXX64XX3xRgwcP1v79+7Vo0SJlZ2ersrJSCQkJxur6v//7P61YsUJz5szRggULtHnzZv3rv/6rYmNjNX36dGN1na64uFiHDx/WjBkzTJei+fPnq76+XhkZGXK5XPJ4PHr00Uc1depUo3UlJCRozJgxevjhhzVkyBD17t1ba9euVVlZmdLT043W1uTAgQOSpN69e/tt7927t+8ztO6HH37Q/fffrxtvvNERD8IrKSnRr3/9ax07dkxJSUlav369LrjgAluORRBxgJkzZ6qystIxdzeDBw9WRUWF6urqVFhYqOnTp2vTpk1Gw0htba3uvvturV+/vtmdoWmn3zEPGzZMl19+uQYMGKDXX39dt912m7G6vF6vRo0apcWLF0uSLr30UlVWVuq5555zTBBZvXq1Jk6c2K5Hhdvt9ddf1yuvvKI1a9bokksuUUVFhWbPnq3k5GTjP68//elPuvXWW9W3b1+5XC6NGDFCN954o8rLy43Whc5x8uRJXX/99bIsSytWrDBdjiQpJydHFRUV+vbbb/X888/r+uuv12effaZevXp1+rHomjFs1qxZKikp0YYNG9SvXz/T5UiSYmNjlZ6erpEjR6qgoEDDhw/X73//e6M1lZeX65tvvtGIESMUExOjmJgYbdq0SX/4wx8UExMjj8djtL7TnXfeebrooou0a9cuo3UkJSU1C49DhgxxRLeRJH311Vf64IMPdPvtt5suRZI0b948zZ8/X7/+9a+VmZmp3/zmN7rnnntUUFBgujQNGjRImzZt0pEjR1RbW6vPP/9cJ0+e1MCBA02XJknq06ePJOngwYN+2w8ePOj7DC1rCiFfffWV1q9f74jWEEnq2rWr0tPTNXr0aK1evVoxMTFavXq1LcciiBhiWZZmzZqlN998Ux999JHS0tJMl3RGXq9XjY2NRmsYP368tm/froqKCt9r1KhRmjp1qioqKuRyuYzWd7ojR47oyy+/VFJSktE6xo4d22xK+BdffKEBAwYYqsjfCy+8oF69emnSpEmmS5H04yyG6Gj/U6LL5ZLX6zVUUXNdu3ZVUlKS/va3v+m9997Ttddea7okSVJaWpr69OmjDz/80Letvr5en332mWPGlzlRUwiprq7WBx98oB49epgu6YzsvA6EfdfMkSNH/O5Md+/erYqKCnXv3l39+/c3VtfMmTO1Zs0avfXWW0pISPD1oyYmJio+Pt5YXfn5+Zo4caL69++vhoYGrVmzRhs3btR7771nrCbpx37yn46f6dq1q3r06GF8XM29996rKVOmaMCAAdq3b58eeughuVwu3XjjjUbruueee5SVlaXFixfr+uuv1+eff65Vq1Zp1apVRuuSfjypvfDCC5o+fbpiYpxxGpoyZYoeffRR9e/fX5dccom2bdum3/3ud7r11ltNl6b33ntPlmVp8ODB2rVrl+bNm6eMjAzdcsstQauhrXPp7Nmz9cgjj+jCCy9UWlqaFi5cqOTkZLndbuO1ff/999qzZ49vjY6mgN6nTx9bW2xaqyspKUl5eXnaunWrSkpK5PF4fNeB7t27KzY21khdPXr00KOPPqprrrlGSUlJ+vbbb7V8+XLt3bvXvin2tszFcZANGzZYkpq9pk+fbrSulmqSZL3wwgtG67r11lutAQMGWLGxsVbPnj2t8ePHW++//77Rms7EKdN3b7jhBispKcmKjY21+vbta91www3Wrl27TJdlWZZlvf3229bQoUOtuLg4KyMjw1q1apXpkizLsqz33nvPkmTt3LnTdCk+9fX11t13323179/fOuecc6yBAwdaDzzwgNXY2Gi6NOu1116zBg4caMXGxlp9+vSxZs6caR0+fDioNbR1LvV6vdbChQut3r17W3Fxcdb48eOD9t+3rdpeeOGFFj9/6KGHjNXVNJW4pdeGDRuM1XX8+HHrV7/6lZWcnGzFxsZaSUlJ1jXXXGN9/vnnttUTZVkOWDYQAABEJMaIAAAAYwgiAADAGIIIAAAwhiACAACMIYgAAABjCCIAAMAYgggAADCGIAIAAIwhiAAAAGMIIgAAwBiCCAAAMIYgAgAAjPn/NgoetIE7upUAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.boxplot(X_cr);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "98002d4e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "178 13\n"
     ]
    }
   ],
   "source": [
    "n,p = X.shape\n",
    "print(n,p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "1f70db66",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7fd0d672fdc0>"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 480x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow((X_cr.T@X_cr))\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7557fee8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "mlenv",
   "language": "python",
   "name": "mlenv"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}