ch2/Untitled.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c64b780c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "s1 = np.random.normal(0, 0.1, 1000)\n",
    "s2 = np.random.normal(2, 0.5, 1000)\n",
    "s3 = np.random.normal(-1, 0.8, 1000)\n",
    "x = np.array([s1, s2, s3]).T  # concatenate the 3 sources of gaussians\n",
    "S = np.exp(x) # raise it exponentialy\n",
    "rng = np.random.default_rng()\n",
    "M = rng.standard_normal(size=(3,3)) # generate random mixing matrix to record the 4 sources using 3 sensors\n",
    "X = np.dot(S,M) # mix the four sources"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "d666f590",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "data": {
      "image/png": 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jLsY6fnBOIKMqFD8WpdHHcud9Ph9tbW14PB6tM05l86Ph9JiNpw4OYnP7qCvN5dbmJYz2B8KCO6/ezlNHRug1j+DxSXRx3oNGJ6xbF6jXq5JaX18fVquVvLw8bRFIJJG2EFBknVWrVgGBRUBRhnt6ehBCaItELMqw3++f4fVkVIUSw6Iy+tDaezh3WXXG1dXVsWzZslnZ+0iw2D08ub+fglw9dfm5DJptfPO51/nbS+tZt24dQgg+eEkDl6ys4KmDA/zPiWFMVi++OK57bMpBZVHerJKayqZ3dXXhcDi0RFp5eXmyH9EsJLvThztO8OdtMBioqKjQEqJer3cGZVh5CmVlZbNCm1jXFEtVCBb3IrBojD5W33uszjidThfV6E02Nz6/pCDbgM1mwzMxij+vlLply88q1+h1bFhSxIbr1/PxK5bz6d3H+WvPRMxr/85L3fzrjRtm/C1cNl0l0k6ePInNZuPUqVNaLiKRGDodiGWooZRht9uNxWLBaAyENgaDYUZSMFHKcLRFwGg0UltbS05OzqJQFVoURh9Lxkp1xul0uoidcUKIqO59QbYen18yYjTicbspr1mKx8+M2D4YxbkGbmms4Y3eCXwxMnp7j47xrzdGf05oIm3//v1UV1djNps5c+YMUkpKS0spLy+npKQk7o67VO70iRwnOzub6upqjenocrm0pODExARer5fe3t4ZlOF4EboIDAwMUFVVhcPh0J5zIasKXdBGH4+MVbydcbHc+9IcWCLGOeUwUFpSgd3j585t9VFvlnajneIcHeYYRfvZ809jI7ijDs66zyaTia6uLq3Zpry8nKKiorRXBua6eOTk5FBbW0ttbS02m42uri6ys7NnUIbV+y0oKEjoXFLKGQv9ha4qdMEafTzufG9vL0NDQ2E740IR7UseHR2lvb2d2996MW59Pja3j4qCbErzo7vUk04P7jgy+KlAOPdZ7ZxTU1Pk5ORoi0Cw0SzUTh/rWAaDYUZ+w+FwaElBm81GQUGBVhlIhDIMF76q0AVp9F6vl76+PnQ6HTU1NbO+ELfbzfHjx8nLy+OSSy5JepdTApaTk5Ns27YtoRr+0KSLfosTVzx1O+A3R/u5sbE+qesMh+zs7BnNNspoent7sVqtmtEEC2nOBak0+nDZ+/z8fPLz86mrq5uR5Dx9+jQOh0N7P0plOBFcaIvABWX0we58pPp7rM64eOF0OjXSztatWxP+kl88YaS2KIcsg8AbqqYRBg/+5nRKjT4UeXl55OXlsXTp0hkUW5vNxpEjR7Saenl5eULsOgXlcaUCoUYfinBJTqvVitlsDiswmijCLQKhqkIvvPAC73jHO+Z0j6ULF4zRh9bedTrdjF1KdcaZTKaonXHxwGQy0dbWlhAHPxQWuweX309+lgGX1xO1zRbAB3giaOelGsEU2/HxcdatW6cl0lpbW/F6vZSUlGiVgXiINaElu7kgltGHQghBUVERRUVFmsCo1WrVNgCbzUZbW1tSlGF1/FBBkSeffJJt27ZljD4diDRCKljfLbgzbvv27UnffFJKOjo6sFgsCbvzwRgfH4eJIboGfJRlg9ke3+v+enqct62pTOqcc4EQYpYgZzhiTXl5eUQZrlTH9HM5lk6n0yodUkreeOMNamtrMZvNDAwM4PP5ZrAFEy13CiGw2WwUFhYmfY3pxHlt9NFGSCmlFpVkm8uuDIGSkd0esM5t27YlddNJKenu7mZ0dJR7rtmC5aVeXu4cRye8MXd6gB+/1jXvRh/OwIK1+GC2DJeqqavKQCIKPPEg0Z0+nmMpJuDKlStnLGrB5U71E49nkzH6NCBW7V0Iwejo6Jx3ZTjrzufk5LBmzZqkjuHxeDRZre3bt+P3+/noW5fTOepg0mHFG6tYD7w54Erq3OlGOBmuUAWevLw8vF5vSow/1UYf6pmELmqRKMOKLRjOs3E6nXMKIdOJ887o46m92+122tvbycrKSirJFnwupZCzdetWDh48mNRxJicnOX78OKtWraK2thYI3GwleQbW1hTQO27H5YhNyPUBR9u6WLG0KmFCSrJIxkiDa+qqnDYwMMDU1BT79++fQRdOpO9eIR07fTSEUoaVZzM2NjaD81BaWjqDMpzoNQoh3g38J6AHvi+l/ErI42L68fcAduAeKWXCN+V5ZfSxau9wtjOuoaEBq9WatGG4XC6OHTtGcXFxTIWcaOjv76evry8sFyAvS8+1F1dxoGcCcxAbLBqOjLgx+PuZmpoiPz9f25HStavMdWdW5TTFD1i9erWWST916hQul4vi4mItKRhPEi2VoYLP50toHgDM9myCKcMdHR18+ctfxuPx8Prrr7Nt27a4wgEhhB74DnAN0A+8IYR4Tkp5Iuhp1wFrpn8uAb47/W9COG+MPtYIKdUZ53a72bFjBw6Hg8nJ2JJU4aCyumvXrtW+WCCh2NTn83HixAmklGzfvj3iF3/JijI+e+1F/NNTJ7DHUbP/fa+dD759q1aLHh8fp6OjA6fTqRlPMmWodCN4oQ7NpAdP6fH7/VploKSkJOznNt87fSyEUoa/+c1vctttt/H973+ff/3Xf+XFF1+M5zA7gE4p5WkAIcQvgZ1AsNHvBH4iA9TQvwohSoUQS6SUQ4lc7zlv9PG48+E641wuFz5fPD1sM891+vRpTCYTW7duneV6Kv59rJ3Bbrdz5MiRsDPswqGqMJvty0s51D/BpDP6Nb/ZZ9OuRdWily1bNsN4+vr6sNlsdHZ2Jsy1D0W6uuwUQpNowfFzcLedqgwogdJE++8jIZULiEJDQwO5ubl8//vfT+RldUBf0O/9zN7Fwz2nDrhwjD5W33u0zrhg9dp4oPTrCwsLI7rzsTrtAEZGRujs7GTTpk2UlMQnapmfrackL4u6klwcbltMcY0/nzZx2aqZlYhQ49m/fz+lpaVa3GkwGLRQYL4EOIIR7+IRLn42m82MjIxo2vwAZWVlKVmQknHvY8HpdJKfn5/oy8K9kdCbLZ7nxMQ5afTxyFjF6oxLxOjVFNhQdz4U0TrtlIST1Wpl+/btMWPT4PdTX5rL5avLmHB4aB+xxbze7/3pzCyjD3f8YK69y+VifHycvr4+pqamNFpqrHzAQnPvs7KyZrjOTqeT9vZ2TCYTw8PDWl5D0WsTPUc6dnqr1ZqM0fcDwSqo9cBgEs+JiXPO6KPV3hXi6YyLx+iD6+bxsPQi7fQul4sjR45QUVFBS0tLwjeeEIJ3X1yF3e3lcN84EzEqc8f6pxI6PgQy6sENKopmq2ipwfmAdPTep2rxyM3NpaCgQHP5Fcc+WJFXvY94yrTpMvokavRvAGuEECuBAeAO4AMhz3kOuG863r8EmEg0nodzzOhj1d4T6YzT6/VRY3rlzhcUFMTN0gu306uk31zJP2a7h1/sH8QTRxoiPi3dyAim2QbnA5QnIKXUKKmp4syng5wTSUhkfHycEydO4PV6Z1QGwi1m6XDv7XZ7zK7NUEgpvUKI+4AXCZTsfiilbBVCfGz68ceB3xIo13USKNn9bTLXd04YfTwyVol2xkXb6S0WC62trQk33QTv9FJKenp6MBqNYZN+iWLPkWEsTm/YoC0cxu0uyvOTJxwFI5yIpdlsZmxsDLvdzuHDh6moqKCsrCzpfEAqG24iJQWDhUQUXVgtZpGERNKx06vW3kQhpfwtAcMO/tvjQf+XwD/M9foW3OillIyOjpKbm0t2dnbYG0PF3IkYabjjBBtqMk03aqf3eDwcP36c3NzcpLn8DocDh8NBcXExQgi6Ru2U52fhdHkQyJjZmQefO8l37mhO+LzxwGAwaHXoiYkJLr74Yo2Sqtpug+PoeJDqhpt4FpDgqbxwVkgkmFSj1+spLCxMqfEn6d7PGxbU6JU739fXR11d3awYTJXQxsbG5twZp2iweXl5SRuqEAKr1crRo0dnsOsShcrw5+XlaRztXHwUZQv8MaoDCq90JcdBSAahgpw2m43x8XEtHxDccRcpH7CQXXYK4YRE2tvbmZiY4MCBA+Tk5GiLWaLqO8E4l3n3sEBGH1p7V25WMFLVGQdn3fnVq1fPGjWdCBwOBx0dHWzZsiWpL1V16U1NTbF161b8UnJ8cIp24wSVuRP8udsKMlCDiTHfEoCTQ1NcvKQoxrNSi+B8gCLXBDenADNc6GAxynOt4SY7O5uCggJqamo0jbxQ9Z1EPRrIGP0shKu9GwyGGUm3VHXGKXd+eHiYLVu2JFNGAQLJnpMnT+Jyudi4cWNSX6jb7ebo0aOUlJTQ0tKCz+fjqYMDvNplJtugY9QKhQX5COHA65Q44xCs2X1ogAeXrE/iHaUOOp1uhguteOmKkpqdnU15eTkulytlhpCuBSSSkEiw8IZaBKKVZJON6ecL82b00WrvKummat1TU1Nz7ozzeDw4HA7sdjs7duxIemdQ7Lq6urqkZZAmJiY4fvz4jJzElMvLX7ot1JXmotMJdAI6jFacbomUIq64/nCvOYl3lF6E8tKdTifj4+MMDw9jNBoZHx+fU7MNpLbMFil7H67CoSoDqudeddqFttvabLY5bVbpxrwYfawRUnq9HrvdzhtvvEFVVdWcOuPgbB0/KyuLDRs2xH5BBKjdSrHrTp06FZORFwrVcBPqaQRaaSXqbeYYdLi9fvwSZBwGD9A17qGjo0OLp1NdekoFcnNzWbp0KW63Wxt9PT4+rvVJqHxAWVlZ3NTaheDe63Q6TUgkuOd+fHx8RrutKn/OZacXQnwNuJFAdbYL+FsppSXM83qAKQINmF4p5bZ4jp92o49FpYXAyjg6Okpzc7NWNkoGUkrOnDnD0NAQzc3NHD58OClXMBK7LhojL9wxTpw4gc/nY8eOHbMMsqwgmxXlefSMOynNz2J40kVNUQ65wkPHeHxilD4gp7CE8fFxTp8+PYNqm+jilG4o4wqXD1AlNUALFaIN7Ez1Tp/MsSIJifz85z/nV7/6Ffv27aOjo4O7776bJUuWJHr4/wU+P127/3fg88DnIjz3KinlWCIHT5vRx1N7V51xk5OT1NfXz8ngPR4Pra2tZGdns337dvR6vRY2JLIDulwuTfAylF2nuuxiwel0cuTIEWpra2loaAi76OiE4K5L6nnx5BhnzA62LCumIFvHmMVGjsGPz+OPOQQDoHtS8PZ1a7RrVwZkt9tpbW3Vbsy5hEqpQLjsfax8QCRZ7lSLbKbCQ1Jhzac+9Sl6enq48cYbmZqa0sLZRCCl/J+gX/8KvG/OFxiEtBh9PH3vwZ1xFRUVWK3WpM+nRCpWrlw5Y1VVrLx4v1TFrlu3bp1W1glGPNRepbKzYcOGmC2u+dl63rvl7PU+fXiIx14yI5HodYJcvQ6Xx4c3ivF/9089vH1dIH4Optru37+fhoaGGew0lVVfiFAgHo8rNB8Qmk1XFNtzrbU2FDabjZUrV9LU1JSKw30I+FWExyTwP0IICTwhpfxePAdMudHHQ6VVnXGbNm2iuLiYsbGxhNtg1bH6+voYGBgIS8uNt+kmXnZdtC67VDD06krzWFuRg8Ul6Ta7ARlzt28dCS++Edy3vnz5cnw+nzYgMjQUmI+uu2TCrNBsulKwdTqdvPHGG5p4ZSL5gFCki4YbOgsxFFdffTXDw8MAtLa2Hg966AEp5bMAQogHAC/w8wiHeauUclAIUQ38rxCiTUr5SqzrS5nRx9P37vV6OXHiBEKIGZ1xsXjy4eD1ejl+/DgGgyFszAzxGX0i7LpIMb26FhVaJLtzVBRkoROC6gIDJodkzOpKvG8yAvR6/YyW1eBQQDHI0hkKpEKBRy1iilGp+AG9vb0IIbRQQPXdx4OFouHu27cv+NdNoY8LIe4GbgDeKSPsNFLKwel/jUKIpwkIccyf0QNR3XnlgofrjEvU6Kempjh27FjM+XOxjF4dJ152XbiYXjH0Yl1LPFhVmc/ly/P5S7+TbINAxkXRgQmHm5K8xLTaQ7vu1C4aGgqkKiGYyto6hE+kmc1mhoeHaW9vj5tdl+rrgsA9EWunj4ZprbzPAW+XUoYVSBdCFAA6KeXU9P+vBf4tnuOnzOjV7h5qZCqjPjg4GLEzLl6jl1LS399Pf38/jY2NMcke0YxehRjxHCfS8UZGRujq6tLClLlCCMFblxeyY3kJh8YEuw4N0zVqwxXDx//Izw6z66M75nTeSKGA3W7n0KFDcw4F0mFcwQjtu3c4HFo5zWazaRNtwnkyqb4ul8s1V2/pMSCHgMsO8Fcp5ceEEEsJCGa+B6gBnp5+3AD8Qkr5u3gOntaSneqMy83NjdoZF4/Rq9BAiWbEE4eFO65i1/n9/qjadeGg3PtgOu327duT6j8fHh5mbGxM614Lvo6CbD3ZBphweinKNeCyRc8AtxmTmWsbGcGhgMViYcOGDXMOBVKZcY8HeXl51NXVabPtQj0ZxQ9IR2kzUngbL6SUqyP8fZBAay3TWnpJZQrTZvSqMy4evnsso1du+PLly6mrq4v7GkJ3ZrvdztGjR1m6dKmmpZcIdDodDoeDN998k9LS0qQEM6SUtLe3Y7VaWbp0KRaLhd7eXnQ6HeXl5Xg8HgwGAz3jLrJ1YMjRB6bbxnCEphxuihJ08eNFvKFAtKpAKhtuEkU4T0bxA+x2OwcPHkzZ2G4p5TnHkQhFyo0+mc64aEavGG2JuOEKwUYfyq5LBg6Hg/7+fjZt2hRVVisSFP++tLSU5uZmPB6Pllhzu92Mj48zOjqK0WikfyiLdRVZuDFQXZTDwTMTUTP5X3yhna/eOisflHIkWxVIpezWXBGcDzCbzWzatAmLxcLQ0BCnTp3SZt2Xl5cnPOZaYb41CBNBSo3e5XJx+PBhSkpKEspihyuFKXceSNgNDz6uz+ejvb1dc8WTmbgKgcVnYGCA2trapAx+amqKo0ePavz7UHc3Ozub2tparfqxPdvLvpNGivUOiv2S0lyByRH5hn/p1HhS72uuiLcqoN7XXJHK3IC650IlrFU+QI25TkSCKx3VgFQjpUY/PDzMypUrwxJbEoEi7ixbtoz6+uTHM0sp6ezsZMmSJUm54jCTTrt27VqmphLXpxsaGqK7u5umpqaY3oq6xptbluHXZfHmmQnyBNxYLfnJm2NEqkU4/AHJrbL81OvbJYJwWnzj4+Paoqd22GQJQqk0qkgLSGg+IFSCK1KjDQQWjHN1nJVCSo1eSRTNBQMDA/T29s6StE4UanjCkiVLuOiii5I6hsPh4OjRoxqd1mQyJSSrreJ3m82WcMIvS6/j/VuXclvLEgRwuG+SXUdN2KLMsj9jslKWf+4MugjuVDObzaxZs0brukuWIDQfHXah7yFUgiu40UZRiVU+QCkLJQshxBeAjwKj03/6P9MyWqHPizoCKxpSavRzcbuklBw/flxrUEmWYRXMjFu+fHnSxwlHp42Xew8z++e3bNkS92cTSgDSCYHJ5ubJNwdwRuPjAoda2/CNBurTPp8v7WWyRCClnGHkMFuWO56qwEKLcYTyA9xuN2azmcHBQbq6uvj2t7+t9ZSsW7cu2Wv9Dynlo5EeFPGNwIqIBdfIg4A7b7PZaGhoiGsiTCR4vV6OHTumseuGhoYSbnhQi8bo6OgsOm28tF5VbbjooovmpNSj8EKrkQmHF4NO4IuSzcsqq2PTplrGx8dxu93asMjy8nIqKiqSzmekAuEMLFIocPLkSTweT9iqwLnGu8/OzqampoaamhrWrVuHlJLHHnuMBx54gPXr1/Pwww+n5FpDEM8IrIhYcKMfHBykp6eH/Px86urqkjZ4ZWjBTTeJTrlRdNqcnJywU27i2emHh4c5ffp0zGpDpPcZ7hxme6Beb9DrcEUJn3YdGuZ9W+upra2lr6+Pbdu2YbVaMZlMHD9+HL/fT2lpKRUVFVFbV9OBWDt0qAxXsButQoGysrKks+nhkGrevU6no7KyksbGRh5//PHYL4iM+4QQdwEHgH+SUoaqpcQzAisiFsy9VyQZr9fLjh07OHToEF6vN6ndKBK7Lpz2XiTEQ6eNtoikgrATCRuWFNJutFJXmkOX0U4ksx+ccPL88RFubQ4sesHltRUrVmjS1qp8mZubq7mqyUqJxYtE3fJQN1rNvB8aGtJEUs4lBR6FeJRwg5ttYEbDzQMEJtF+kQD/+ovA1wl02gVjTuOtFmSnt9lsHD16dMbAyUR3ZTi7cPh8vrBlPSFEXIlFRaeNlTyMtNN7PB6OHj1KcXFx0lWCaOe4ck0Fkw4PTx8eJi9bj83tC/sNe3zQYYw8FitY2hrQpt6q6TChKjapJJnMNRZXM+/z8/MZGBhg2bJlmgKPCgVUx128u3eyAhrREI8oZkizDYRpuAEQQvwXsDfMQ3MabzXvRq/KV6F8db1ej9cbn2IMxMeui7XTB7Pj4tmdwy1MqY7fw0GvE2xtKOX37SauWV+ByebmlS7LrOd5JZwZt+Pyxrd45ufnk5+fT319vaZiYzKZZjAEFe04FS51Ko6hRC8ihQI9PT2a3n1FRUXUqkCqBDSCMVclXDFz9PQtwPEwT4tnBFZEzJt77/P5OHXqlDY/PnRXTsQVj5ddF817cLvdHDlyhLKysrh359BdON74PRyklFpNNx51nn5LoG8+N9tAXbYBgSXsbj8w4WJ/j5lEHd5QFRuXy4XJZJqREKyoqKC8vPycSwhGCgWCh3Wqx4NDgXNpuk0QviqEaCbgrvcA9wIEN9tEGoEV7wnmZadXu/KSJUu4+OKLI+7KsVxxFTdPTk7Gxa6LZPRKnTbWlNpIx5tr/O7xeDhy5IimP1BSUqI13kQy+oIcQ0ATf3rX1QvCKup0jzkYnnCxIqErmo2cnBxqamoYGhqipaVFI6iohKCKp+c7IRiPoapQoLa2dkZVQIUCKozxeDxp2enn4vFJKT8Y4e9as83077NGYMWLtBu92g03btwYdVeOZfRKu66srCxutdxwRh9JnTYeqBzBwYMHk47fgyfkqBnryq3u7u7G7/eTk5ODzWabkanetKSIpvpijgxMohNQnGdg3D47HPIDZ8YdrChN6LKiIpSgcj4lBKNVBYxGo8aLUOSauYYgdrv9nB50AWl07/1+P21tbbhcrrh2w2hGrzr2ImnXRUKw0Ss6rd/vj7s1NxR2u52JiQk2b96c1Eir0dFROjo62Lx5M4WFhbjd7llu9eDgIGNjYxrvu7i4WPMCPnzZMjqMNlxePzokd/74SNjzvNxp4opt6eO5BycEVZgyPj5OR0eHNuaqoqIiLE11rpirSx4cCuTm5uL3+8nOzqa/vz9qKBAvzvVBF5CmnV6587W1tRHd+VCEM3o5PZp6ZGQkqVl26pgOh4MjR46wZMmSiOq0saDmzxUUFCRs8FJKuru7MZlMbNu2jezs7IiZ8ezsbIqKili5cqWmoR6cXKuoqKCuooKCggKKs2EyzNzqMasTmB/+txBiVkJQdd2ppFoqGYKpJueoRqdYoUC8VYFzfXglpMHolcu3cePGhCStQ40+lF2XzBet0+lwuVwcPHgwLnXacFBNO5OTk2zbto2DBw8m9Hqfz8fx48fJyspi69atcb0PtSCEjpBWtNWenh6ODkziiFDscMVfBIl5HcloDoSj2qqEoBoNlWxCMJ3c+2ihgOLZq2uPFAqc63PsIMVGL6XEYrGwY8eOhJNber1eo8yGY9clcy1nzpzB4XBw+eWXJ+Wqqfp7UVERLS0t2nHjhdPp5PDhwxofIR5EY/3l5OTgySnlqd4pXu7UEaky5/UT9/TbdENRbfv7+9m2bducE4KpFOOItYCE49mPj49HDQXiUcKNBCHEr4B107+WAhYpZXOY5/WQxGQbhZTH9Ip/nCj0ej1Op1PrskumDKagvIScnBzy8vKSMvi5jqRWeYhkPYxwGLe5+dq+LiYcXnz+yJ+xQYDd7mR4eJiKioqk2YGpbtiJlBAcGRnREoKqLBgplPP7/SnLEyRKzokVCrzyyitYrdakSU1Syver/wshvg5MRHl6wpNtFFLu3ifSiRb6uuHhYQoLC+fUZRdKp/3zn/+c8DHiZehFghLvTCYPEe3z6xqz4/T6qSjIottkj8i7XFqWg1X6tdZgQGu6STRDnc4uvXAJQZPJpE2JDW64UfdDqmP6ZEt24UIBk8nEr3/9a26//XaKi4v57W9/m5RApgh86LcD70jq4mJgwRtuIOASqbHGjY2NSd9oqjyYrLGq+H1iYiKp+rvf7+fUqVNaxSLVNeAsvQ4pA8KZBl3kz2jK6WV3p6SpqZatK1fi8XhmuKXxdt7Np9ZbcEJQTYlVCcHu7m6tLdfpdKYsO57KBUSv1/Pud7+bL3/5y+zfvx+TyTQXRdy3ASNSyo4Ijyc12UZhwY1eJf5WrFiBxWJJWt0meOBkMu6sx+Ph2LFjFBYWJjU1V/XPl5WVsX79+qQXrmg7/YbaQi6qzKdz1IZBLzDowOef3Wkx6fThzRe81GHirkvqycrK0to/lbBlcOedikvDDYlYKF27SAnBoaEhTUtwLglBSM90G/VeI5WWQ5ttQGu40SbbAHcCT0Y5TVKTbRTS4t7Hg1B2ndvtxmQyJXy+ZOi0oZhr/K5ev3r1ak1nLR3INuj4x3esZH+PhZPDU/z64BATTi+uEGqexw/dExKLY7aWQLjOO2VMp06d0pJTFRUV59SgC5UQtFqtVFRUYDAYZixcimu/kNNt4vm8wjTbQFDDjRDCANwKbI1ynqQm2ygsyE4fjl3n8/kSltpKlk4bDKPRSGdnZ9IhgXr9XBKPwYiVE8nN0nPFmgquWFPB1oZS/s9zbQyFKdZPeeDVznHu2LqU6qLIbqbBYNBEIVVyymQyceLECW0IqdlsnhPdNtVqN3q9XksIrly5UksIquk2eXl5mhcQLaeSLhHLOb7Xq4E2KWV/hGMnPdlGYd6NXmW1Qw010dFWc6HTQuBG7OrqwmKxaISZRF9/+vRpzGZzUq9X7Lxg9pper0/ohtnaUMLamkImHeaw2nkDE07+69VeHrhubVzHC05OLV++HKvVSltbmxaCKWOqqKhIqCKSbomr0ISgahkOTQiGEmxS7d6n6Hh3EOLaixRNtlGYN6OPxa6L1+gTpdMqbnXwjeL1ejl69CgFBQVJxe8+n08rCba0tCS0W6jPwWg0snnzZux2OyaTia6uLnJzc8nPz49b4svtkzg9fnKy9Ng8sxk5Lo+PP3ebkzY6nU5Hbm6uVoZVxqRKVKrGXlpaGvUzSLVsdSwFnoKCAgoKCli2bNkMgk1wQrCioiLlU3fsdvucew+klPeE+VtKJtsozEtMH89U13hENJKh06rjqnOq+DtZ4o/f72f//v1JyXOrBQtg69ateL1erVkFAjfNwMAAFouFN954Q4tTI7nW2XpBfWkuRwcmw57P5QOr04vXL8nSJ59YVP+GGpPZbGZsbIzOzk7tfVRUVMxa0BdSzDJc261i2Nntdk6ePKlxA+aqdjRXJdz5Qtp3+njZdbFuinDqtPEg3JSbxsbGpOJ3s9mM3W5n+/btCRNu3G43hw8fprq6muXLl4d9Tn5+PjU1Nfh8PtasWTOjky0vL08bKqFKQUIIPn7Fcv7SbcYx4Qp7TLvHF7W8Fw3Rcgt6vZ7KykotSx3qUgd7AfPJoouFYDHO/fv3U19fj8lkYmBgIGYlIxbOBwoupNnolejlXJJcqlllbGxsljptPFBTbjo7O7FYLElPuenr62NgYICCgoKEx2KpQQ/BeQw18yzUIFQiL9iolGutEmw+n0/zAiqLi/nZPc3c8H/fwO6Z7Sl5fTAy5aK2OHFWYiI7dHDTTeioK6WKlCL3N2ULSDBDcOU0nyGZhKDCojV6FUMrGeO5sOuCm27CqdPGez3Hjx/X+t8TPYZqEfZ4PGzfvp0DBw4ktNuo7H7wdBspJX6/XxPk8Pl8mk5guOx9sGvd0NAwI1utymzb63J5uWf2KHOdDjwxRl2nGqGjrsbHx+nq6pqhxafahRNNfKVz+m3wuOvgHIZSfFJKwpGm81it1rTrCaQCKTd6h8PBgQMH5tTGCvGp08aCzWbDbDazcuVKVq1alfDrFQegoqJCaxGOV8AzWD8/OLuvjFxKqbXY+nw+/H4/Pp8Pl8ul/V+dLxSh2WqbzcYtrv6wRp+lF9QUJUdeSVUsnpOTQ35+Phs3bpzFtMvKytJyAfHIW6eqzBarph4pIWgymTRJbpULKCgoQAiR8E6/a9cuvvCFL3DixAk/sENKeSDo/J8HPkygqeb/lVK+GOYay4FfASsISGvdHkYuexZSbvQ6nY7169cn1FYbDCklIyMjc6LTwtn4XbnBiULlItasWTOjtBhPb4Hf76e1tRUhxAwPJdjghRDaj3rcYrHQ1dXF2rVrtYUl2PjD3exjVjffemmA02MOcgxiFlHHALT3DrGuoSalstyJIHjxCGXaBY+5ChUNCechptLo5yrJbTKZ6Onp0TaXP/3pTwkZ/aZNm9izZw/r16+fQawRQmwgULrbCCwF9gkh1kopQ8tb9wO/l1J+RQhx//Tvn4t13pQbfW5ubtJfik6no62tTUuWJXOTqvr5+Pg427dvp7OzM2FpbdVwEy4XEWunD03YqRtL7d7qGOHO2dPTQ3NzsxY/qteoxUKpBat6vhCCr/+hm8EJJ9VF2QxMGJDSi3vanRdAdpaeJ/46xN3mYYQQmtsdz+y4VO300Y6Tm5vL0qVLWbp0qabIOz4+Tm9vr2ZoFdOiIcGVhLlirvLXOTk52nVLKTlx4gQDAwMcOnSIl19+mS996UtcddVVUY9x8cUXR3poJ/BLKaUL6BZCdBJg3f0lzPOunP7/fwMvsRBGnyzcbjc2m43S0tKk6bQqB5CXl6cJViSipx9M2Im06ETb6SMl7FT8rgw19Jw9PT2YzWZaWlpmnDN4dw+O/9X7sbl89JvtVBXmIIRgZUU+xwen0AuJlAHX3uOHDotkQ2MLBnwzxkirXbW8vDxi3iVVRh+PgYVT5FXlNZvNRnFxMR6PB6/XO+f22lTKXwsh2LhxI5deeinXXnstt99++1wHudYBfw36vX/6b6GoUXLZUsqhaS5+TJwTRq/otCpRlcyNZrPZOHLkyKwcQLzS2qELRqRrUInKUMRK2IUzeJXw1Ol0NDc3RzUM9VjwTDeEF4NOh9PjI8egoyhbR3l+FqM2Fzk6KMg14PFJJhwefH4/+bkz+8GVFNeZM2c0Ka7gXXWhuffB5TW/38/U1BQmk4nDhw9rYUK8Xkso0iV/XVdXN6OcG67BBuDhhx9m586dkQ41pwk2sbBgDTcKfX199Pf3s2XLFjo7O5NaIUdHR2lvb2fz5s0zBmjA2ZJdNDgcDg4fPkxDQwN1deEW1JnHCzYGtVOPjY3NSthFM3jVlVddXU1DQ0Mib1e7jtycbP7hypV8+4/d2Nx+fH7J29eU8UrnOGarm1GrB78M3EGP/6mXz1x90QwXuaSkhJKSElatWjWLtFJcXExeXl5KDD8VGXedTkdJSYk2Z1Cp2CivpaioKCGSTTqm24RTwo3QYBML8U6wGRHTwzGEEEsAYzwHX7CdXo2kCqbTJsq/D43fw9XfY7n3akpqvJp+oQq7ra2t6HS6Gfp34RJ2wbDZbNpUnGQbhRQuXVnOsrI8+sxOSvOyWFaazZnhMYxTECyu8+SbQ2xeWsi1F1eHvdlDd9XJyUkGBgYYHx/H4XBoXkAyAyRTrcADs1VslBfQ3x/oU4klGpKu6TYpYuQ9B/xCCPENAom8NcD+CM+7G/jK9L/PhnnOLKTF6GO5hpHotIkYfbj4PRyiGf2ZM2cYGhpKiPSj3pvL5eLw4cPU1tbOeA9SSi3hFu6aFGtt48aNSVcmQlFXmkddaZ5WYvzE25Zx164eQCIAnQCvT/LzN4Z459oKbZeLVBJUgpyqrLhs2TKtVOVwOGLWq0ORDqMPRjiSTahoSOh0nnS594lk759++mk+8YlPALwFeF4IcVhK+S4pZasQ4tcERk97gX9QmXshxPeBx6fLe18Bfi2E+DBwBrgtnvPO+04fjU4br9GrAZjLly+PWcMPZ/Qqlvb5fGzbti2hFV8IgdVqpbW1dYYOfyx3HgKdgUNDQ2zZsmUuqiphobyHNWvWUFJWRpauV8vi+2UgIBy3e8jKyppRSYhVEoRAhr2uro66ujqtzq4WgezsbM0LiMRaS7fRhyIe0RCDwbDgRn/LLbdwyy23AMy6GaSUDwOzhttLKT8S9H8T8M5Er3Neu+wUnXbbtm1hb/p4jF7F77Hm2AUf0+0+22+uSmpVVVWsWLEi4ZvR6XQyNjZGS0tL3Ak7JRjidDppaWlJuVtpsVhoa2ub4T1UFGZjMzu17I8OKM3P0sKoYONX/waXFJVHE/peQuvswbp2oay14HBnoRR4QkVDFNV2YGAAq9WK0+nUvIC5LsQ2my1l3ls6MS/ufbx02mhGrxYNk8mUEH8+OJE3OTnJsWPHkhLdUOefnJxk3bp1cRu86jAsKipi8+bNKd/xhoeHOXPmDM3NzTNCFCHAoBP4/AEXHwHbGmYukrFKgh6PR3t/kb6zvLw86uvrZ3DugzvvlAJPKt53KhKCimqrhDgrKytn9TQkO6PvfJhuA/Ow0ydCp41k9MpwcnJy4h4YoaDceyWa2dzcnPAX4/f7OX78OHq9nqVLl2o7dayEndPp5OjRoyxbtixp/f5IUH354+PjtLS0zKpbCwR5WYEd2+eX+KWkoSIyLzy0JGiz2ejt7WX16tWaF6AagSLlAkI596pJaHBwUBvWGa1VOJ73nMpBFwaDYYZoSKgkt+psjHfE1aJtuAlGouq0oa44BG6cI0eOxFVOCwchBCaTSdPiS5TlF5ywW758OV1dXdquGC1hNzk5SWtrKxdffHHSlORIUKq7UsqI9f3lFfnodYJJpxenx4dep+OMyYHPL9HHaLVV175x40aKi4vDegFer1fzFCIZouq8MxgMuN1uCgoKorYKx/O+09miG06BR+Wg4hEN8fl8CzrGO16kxeillJw6dSphddrQnT7R+D0UXq+X06dP4/f7k2L5KYZd6OBMRYmNlLALR6lNFVSoVFpaGjUn8eHLlvHvL3Yy4vHh80vys3X8pdtMzRv9fPCSyNN2TCYTHR0dNDU1aR1j4YhB0XIBoQYRT6uwKrEVFxdHfE+pNvporL7QzsZwoiGhgzkSzTlEargRQlxDIDOfDbiBz0op/xDmGr8AfBQYnf7T/5GBEdZRkRajb29vR6/XJ2xoyuiTjd+DoTyEqqoqXC5XwgYfiWGn1+sZGhrSZJeCjxuNUpsKuFwujhw5Ele4sG15GbdvW8r3Xz1DWUEWZfnZ+KXkhVYj/8+O+rCfx9DQkDakI9pnHisXEFoSDI3pw7UKj4+PMzg4SFtbW9gSmzpXqnIiierZhRMNCR7MsXv3bvR6PS6XK+7yb6SGG2AMuFEGZK43AS8SnoYL8B9SykfjfiOkyejXrVuXcJMLBG4mr9fLkSNHkorfFZRLtmnTJnQ6Hd3d3XG/NnjBCcewW7JkCfn5+YyNjdHR0UF+fj6VlZVUVFTQ1dUVF6U2GVitVk35V2XOY6GuJI/S/CzK87Mx2z2Y7W5AYnN7KcyZuSCpxWrLli0J8dqDvYBgo1fJTeUVRTtmqCJvcIlNSql5AdFCiUQxV68heDCH1+tlYGCAF154gbe+9a1s27aNJ554IuYxIjXcSCkPBf3aCuQKIXKmG3DmjLQYfSJNLsHwer2MjIywfv36pOJ3KQNDK4eHhzXCjc1mi/taVMLOYDBEZNgFJ6tUL/vw8DB/+ctfMBgM1NXVaQmdVO1KitCzadOmhBJFTfXFFOYY+Gv3OM7pllu9gDu+/ya/+PBWinOzkFLS3t6Ox+OhqalpToagXhvsBTgcDoxGIxdddJEm+BmNGBSuxKaINhMTgdFuIyMjc9a0S2WoYDAYuOGGG/jWt77FgQMHsFgsKTnuNN4LHIpi8PcJIe4CDgD/tCD99MlibGyMtrY2iouLkzJ4JToppZwhvhnvAqQSdoolqBAtYadi+rGxMS3vYDKZ6O7u1joGq6qqklKIUVAudzKEHoM+kLn3TPNxddPXPGBx8h+/P82D162htbWV3NxcNm7cmPJyotPp5NixY6xbt46SkhLNW0qEGBRMtLFYLPT19WG32+nv70cIQXl5OZWVlTNab+NBquWvbTablgMJTtwm2XADgBBiI/DvBLTtw+G7wBcJcK++CHwd+FCsa11wow9WmGlqaqKjI9L4rshQsW5oDzvEZ/Sqfh8uYReNYReOUhvMX7dYLIyOjtLZ2UleXp4WE8ZjvMG8gGQJPUMTLmxuL3ohQEh0QuBHotMJTo1McfjwYSorK5Nq+ImFqakpjh8/rlUAFEKJQcqLiqckKKUkJyeHlStXsnLlSq3ppre3V2sVrqysjCjAEYxU03CtVmtYLyzJhhuEEPXA08BdUsqucM+RUo4EPf+/gL3xHDtt5Jx4ECyNvW3btqSm3EQyWIVYrbVKMCO4fp8KSm0wc01lq0dHRzl27Bh+v5/KykqqqqrChgGKJqzX62lqakp6By7I0SMlFOboMdu9yGl+npBQ6LdTV7eOmpqapI4dDYoh2NjYGJETEU8yMNQLCK3TBzfdqNbbsbExTYAjWpNQqrvswnXYJQshRCnwPPB5KeVrUZ63RPXTA7cAx+M5/oLt9Cq7Hqofn4jRDw0N0d3dHZVwE6m1NrRDT8WHwS6oij1DX5copTY4W63i1LGxsbBhgJSSo0ePUl5ePstrSRRVhTnc3FzL7oND2Nw+XF6JToBfSlbUllNeObcOv3AYGxvTFtF4s9iRSoLBXgCglUkjHUO1CsNZOSvVJBQqxpnqLrtkNO8jNdwA9wGrgQeFEA9OP/1aGZhdF9xw81UhRDMB974HuDee84oYtcWkmqn9fn/UKS1jY2OcOnUqbP39z3/+M5dddlnU4yvDs1qtNDY2RnXlpJT85S9/mXFMn89Ha2srBoOB9evXx90SqzyTwsJCLrroopTEwMFhgMlkwuVyUVtby6pVq1LSlCOl5NjgFK93j/Oz1/vwe72UFOSi0+u4betSPrgjcs0+UQwPD9PX10dTU1PKSCrBRCgVJi1ZsiRqGBDuGErU0mw2k5WVhcPhmBV6zAWvvPIKL7zwAo899lgyL5+/biTmeacPjt8jNd3EghpJVVhYyJYtW2IaXujj0RJ2C0GpVWFAVlYWJpOJ9evX43K54goD4oEQgsa6Yv7Y2s+kw4tfCMxmJwJ46uBgyoy+v7+fkZGRhEt+saDq/D09PQghWL58uRZ6heoORmsVDpbhcjqdHDx4kO7ubm3WXSKtwuFwvlBwYR5jep/Px/Hjx8nKykpaw16FBCtWrEjK8FT8v379+hkKucEJu/mm1MJMFpxyESOFAZWVlZSXlyd0cw4ODvJm9xheqTrewO+HHpODN3rMbF+R2LSeYCiDnJycpLm5OS3z3lV+Q8mQB4cBwT9qwY62AECgVTgrK4vGxkaklDNahXNycmYx7eJBKmP6dGNedvpI8XsiiBYSxINkE3aKUhtMS00lBgYGGBwcDMuCy8rKClsNUMMuq6qqolYDlEFaLBaW1VZyaHQEJKiILtug4/UeS9JGr8Isj8fD5s2bU05IUmXY3NzcsOFUuGRgqBcQrSSovvPgVuHg8VxutzvmPEGF86XDDubB6BU7Ll45KpjZf626yYxGY1IhgVK56evrC5uwS0alNhWQ08q7NpstroRgaB+7zWabVQ2orKzU5KFU/4PP56OpqYkzOiO/P2XC4faiEyCEjvxsHSV5yd0CqsKQlZXFhg0bUl7j9/v9HDt2TFPDiYVwycDg3oDQMCASQsdzxZonqGC1WpOar7AQSGs/fTLxu6qrqwxruKER8UKFFFLKGSOtYsXviajUJgP1vrKzs2lsbEzKYMJVA1S9uqSkBJvNRklJCevWrUMIwbs3VvHkgX6ODUwBkJclWVGWx/WbEi/Zqc+1uLg4KSGSeI4fXMFIBmp3NxgMM7wAtQD4/f4ZnYLhEO88weLiYux2e0LXqpptTp48iZRyW1CzzQrgJHBq+ql/lVJ+LPT1IsnpNpAmo/f7/Rw9ejSp+F013Xi93rAadPEiOGFns9lmeA7RDN7tdnPs2DGqqqpYtmxZym9oj8fD0aNHqaqqShkpJjgMcLlcHDp0iKysLMbHxzly5AiVlZX8sc/LpNPL+tpCrC4vLq+f926to7wgsSy76o2oqalJOlSb7+MHewE6nY7W1lbq6wNNR/ESg8I1Cal5gl//+td57bXXmJqa4qqrroqL+6Cabe69915efvnl0Ie7pJTNMQ6R1HQbSONOv2zZsrgbQ4Kh1+uxWCx0dHTMSrjFi9CE3cDAwCx3PtwXm0qV2nBwOBwcPXqUlStXUl0d11yChKAqDCtXrtRuPJvNxtjYGH843off7UOny6YiPwur20/bsJUbN8d/fCW8uWzZMmpra1N+/R6Ph8OHD1NfX59y0REIeBBqI1CCLvESg0IR3Hv/0EMPcd9992G1Wrnjjjv4zne+w4YNG6JeS5TpNvEiqek2kEajVw0picLtdtPe3k5LS0tSibNwCjk6nQ6Px6PFc/FSalOJiYkJTpw4wYYNG5JKRMaCWrDWrVs3Q3BU7U6rl7kYPT2OTh9YHKwOHz6rmdHR0biqAU6nkyNHjnDRRReFZT7OFUq7cPny5WlhCYYzeJi7VkDwYx/96EfZvn17Ki53pRDiEDAJ/IuU8k9hnpPUdBs4B7j3Cqrby+l00tjYmLDBK4ad2WyelbDT6XQMDw9TUxN+iKPKoKdDpRbQMu7pENWAAO315MmTbN68OWLZ6J5LGzg2MIXN5QWRzfLqbO64pA6z2UxXVxc5OTlaNSCUSacWlLkMJo0GFYqla0FRoWJdXV1MDyJRrQCFcHX6JJtthoAGKaVJCLEVeEYIsVFKORnv+42FtBl9qDhmNKg4t7i4OCm3VyWWsrOzwybs1q5dy/DwMAcPHiQrK0tzy3JyctKqUguBCT5Go5GtW7emZWrs6Ogop0+fZsuWLVFpr3WluXz3zs0c6Z9EJwRbG0ooyDEAgc9bhQGtra34fD4qKio02agTJ06wadOmtHhATqeTw4cPJ6QTkAiUwdfX1ycckkTzAoKJQXq9PqzRJ9NsM91C65r+/5tCiC5gLYHW2WAkNd0GzoGdXs2gW7VqFbW1tVqZKV4ot3Pp0qUsW3aWXRacsCsoKGD16tWsXr0ah8PB6Ogox48fZ2pqiqKiItatW5fyDL2qYbtcLrZs2ZLy40PAQxkaGoq7pFiWn82Va8PvpCoMWL58OR6PRyMMWSwWqqqqcDqd5Ofnp3RhtNvtHD16NG0ehNfr5dChQynLQYR6AepHDW9JRdJXCFEFjEspfUKIVQSm25wO89SkptvAAhu9ItwEz6AzGAxxG30khl20Hvi8vDyqq6sZHh7moosuIisri9OnT2O32ykvL6e6ujpptVYFxe3Pz89n06ZNKa8AqLbbqakptmzZknIPJSsroI/v9Xp561vfqi2UscKARKAGlqSS/x4MlRRsaGhIS45ALQBut5t7772Xj3/84zHVnoOhmm1GR0dhZrPNFcC/CSG8gA/4mJRyHFIz3QbS1HADgVU2moa9quE3NzfPYKJ1d3drs7+jQSXsgqmr8TDsFKV2/fr1MxJePl9gjPPo6CgTExMUFRVRXV1NRUVFQkalBlPW1tampaQlpaStrQ0ppUZLTTWUcEdzc/MsD0K1CI+Njc0IAyLNjAsH1WsfLQcxFyiDX758eVqqJMHn+dCHPsSOHTv453/+57l8F/PacDPvRq92QcWlDt1Rz5w5o5X8wl6QPDtDvqmpKW6GHQTELk+fPh0zUSilZGJiQut8y8nJobq6mqqqqqjdY8pdXb16dVoSUip3UVRUxMqVK9Ni8GfOnGFsbIympqaYi50KA0ZHRzVSUFVVVdRqgKpiROu1nwvmy+C9Xi9/93d/x8aNG/mXf/mXuX4XF67Rq/g7tMMtGAMDA3g8HlasWDHrMZ/Px7Fjx8jJyZkRh8dDqVWDITZv3pxwQk1RXsfGxpBSaonA4JtWZdDTlfDyeDwcOXIkJR6E3e3j96dGmXR4aaovZtPSYq36YbPZNEHRRKDaV0dHRxkfHw8bBpjNZk6dOkVTU1Naqhgej4dDhw6xcuXKtPAsFHw+H//wD/9AQ0MDX/ziF1Ox+F4YRq9YdQoWi0XrVIuWpR0eHsZms3HRRRfN+LvK8tbV1UVM2MWi1KYiYed2uxkdHWV0dFSbg6bX6zEajQkJRyQCtVimgtTj9Pi471fH6DHZ8cvA6KuPvrWBKmmmMk/Hxg2pCRlCw4C8vDympqZoaWlJy2ek6vzpNni/38+nPvUpysvL+cpXvpKqBO2FZ/QDAwOcOXMmrk610dFRzGYza9eu1f42MTHB8ePHZy0Y0RJ2MJPymg5Krdfr5dSpU5hMJgwGg6aAk2jrazQo6etUZbj3tY3y1f/ppCBHj0AwYHHgcPuoLjRwUXUx/37rBkrzUltaHBoaoquri6KiIux2OyUlJZpseCo+J2Xwq1atSktYpeD3+/nsZz9LdnY2//Ef/5HKisyFI6KhOr0cDgfbt2+PS1whdMqNStht2bJFWzDiid/TTamVUtLZ2QnA5ZdfjhBiRutrXl6e5t4mqyKjtOYSlb6OBrv7rFc04fBgd/nQ6aC0IJduk53vvtLD59+1JiXngsD319/fzyWXXEJWVpbWvz42Nqb1ryuhkGQ8ALfbzaFDh9JG7FHw+/088MADAKk2+HlH2oze6/Xy5ptvUlpaSnNzc9y7bPCUm66uLiYmJhJqiYUApVb13qcjvla5BVXjV9eg1FmUHv7o6CiHDx9Gp9NpeYB4mYZGo1HT/0ulO9xcX4JBr8Pm8jJldyEFFOZmIYQg16Cjw2hL2bkGBgYYHh6eoaYjhNA+pzVr1mC322eRgiorK6OOt1JQTL7Vq1enta1VSslDDz2E1Wrlv/7rv85rg4c0uvfj4+NYrdaEa6RWq1XbQXNzc2cYVTwGryi1jY2NaaHUulwujh49Sl1dXdx1WTXT3mg04vF4tDJXpBtbSU81NjamhcX3xukx/v23rZjcOqxuybKyXHQiMOzyijUV/Mt1a2MfJAYSqQIoqMEWo6OjTE1NRQ0DlMGvWbMmLUw+BSkljzzyCL29vfz4xz9OC2uTCyWmjyWOGQkWi4U333yTdevWzchSx0rYBavUbty4MS1fjgoZ1qxZk/TO4vV6tTLX1NQUpaWlVFdXU1ZWhhCC06dPY7Va2bRpU1reg2KPrV27lqKSUr7423b295gRQrC0JJev3boh4XbbUPT09DAxMTEnNZ1wZVMVBggh5s3gv/71r3Py5El++tOfplT7LwQXhtFLKWeNnY6FiYkJjh07hk6nm6FeGythp+rXBQUFKVOpDYXZbKatrS2lhBIlgWU0GjGbzVqWO107vNVq5dixYzM6/fxS0m924vb5aSjPI1ufvOuqyn52u52NGzemXFd+bGyMkZERJicnqampYdmyZXGFAclASsm3v/1t3njjDX75y1+m5fsIwuI0eqVhv3nzZlpbW7n00kuB2FNmVA95fX19QjTIRDA8PMyZM2dobGxMS7lJKcXk5eVpqrh6vV4jBKXinIoUky4WnPK0vF5v2piCqmy7evVqfD6f5i0VFxdTVVWVsmqAlJInnniCl156id27d8/HzPkLJ3sfD4ITdjt27NBksuZCqU3ltSlhyZaWlrS4d4pBFpwjuOiiizS+e3CCq7q6OikpbNU8k67WXkUNFkKk3eCDS5c1NTUzwoDu7u4ZXZTJLJZSSn74wx+yb98+9uzZMx8GP+9Y0J1eZcFDE3avvfYal156aUootcnC7/fT1tYGMGMgRiqhlHRWrVoVtayoNPBGR0ex2WyUl5dTVVVFaWlpzOsaGRmht7d3Vo9DqqAUa3Nycli9enVaDF7lIeLhKqjFcmxsLK6kaSh+8pOf8NRTT/Hcc8+lZYGMgAvDvYdAhjUS1MpdX18/K2H3pz/9SWNWhcZSc6XUxgOv18uxY8coLS1Ni/AjnG06SVRJx+/3axlui8VCUVGR5tqGeiKqZNbU1JQWL0WN9la9AOmAMviLL744YcWh0KSpCgPKy8vDfh5PPvkkP//5z/nNb34z33LWF47Ru93usEIa0Rh2Pp8Pq9WK0WhkbGyM7OxsLbY1GAycPHkSIUTadl+VI2hoaEiLDhyclebavHnznG4uKSWTk5Nahjs7O1tzbYeGhrBYLGzevDktVYBUKNbGwlwMPhTBYcD4+LgWBqgBl0899RTf//732bt3b1q4HTFwYRv90NBQ2OERkRJ2drsdo9HIyMgIdrudsrIy1q1blxbXS2W305UjgLPudlNTU8p5BOqz6uvrw+fz0dDQQHV1dcKz22NB6c2lSxEXznYsbtiwIS399ioM+M1vfsP3vvc93G43P/jBD3jHO96xEOSbCzORp2irk5OTMyi5sRJ2+fn5VFVVMTw8zNq1a7UY0ufzUVVVpd3Uc4VKdqWr5RMChJXR0dG0JQXz8vKw2+1UV1ezYsUKTCYTXV1dOByOGXmAuSwAqtsvHr25ZKEmIqVLYAMCn1VDQ4PG17/33nv52c9+hs1mi6Zfd0EgrTu9x+PRtMSOHTtGXl4ea9euncWwizQWGiKr1Lrdbo3l5nQ6qayspLq6OiExB4XBwUEGBgbSxuJTFQq73Z5U22o8UPF1YWHhrF57JRBiNBqZnJxMusSVbsVaOKuoky4KdTD27dvHl770JX7729+mlbcfBy4c997j8WC32yMm7KIx7CB+Sq1K2IyMjGjZ7ZqaGkpKSqIuAIpMMjU1lbbYV7X2GgyGGQteKqEm+apuwmgIZbqpmXixBEIU7TVWpWEumE+Df/nll3nwwQd5/vnn07aAJYALx+jVrLUNGzbMiJHjodR2dnZqO2Mixuj3+zGZTNquFkxzDd5hlTHq9foZ5cJUQiW7ysrKWL58eVrOMdcBETabTUuaCiE0jyk435JuxVo4m09JF3koGK+99hqf+9zn2Lt3b9oIXQniwjH69vb2WZ1lsRh2qaTUhtJcle5dcXExJ06coKKiIm2ZZzUNJl3TWuCsuEaqdl+Xy6UJhLhcLm1O2+nTp9M2phvm1+Bff/11Pv3pT/Pcc8/F9IrmEReO0QdLZsXDsEsnpVaVtwYHBxkcHKSwsJCGhgYqKytTXutXpaa5NObEgspuh060SRW8Xi+Dg4N0dXWRlZWlKQWXl5enNCcxnwb/5ptv8olPfIJnnnkmrBzbAuLCy96fC5RadV5Fqc3KysJoNHLo0CEMBoPGBZhrIk+9j3RmnhWxJ52xr8PhYGBggO3bt5Ofn68JhHR0dJCfn091dfWcF0z1PtJZMVE4cuQI9913H0899dS5ZvDzjrTv9Gq3j5awSzelFgIa+52dnWHP4XA4MBqNGI1GhBBaKTBRLkBw2S9d70Op6aTzHNEUa6WUWK1Wjeqq1+u1RGAin9d8Gnxraysf/vCH2bVrF+vWrUvruZLEhePe22w2jZyTDpXaeNHf38/w8DCNjY0x+ecqrjUajXi9Xi2xFcv1VJ146eK4w9kRVk1NTWnp9oPEFWudTqeWB/B4PFrPe7TSqfKG4tFMnCva2tq45557ePLJJ9m4cWNazzUHXDhGf9ddd9HX18dNN93Ezp07qamp0W4ElT1PJ6VWVQEcDkdSwhqq0cVoNOJwOLROt9Dmjd7eXkwmE42NjWkTWlADKJqamtK2qJhMJjo7O5NeVEJ18MvKyqiqqppROZlPg+/o6OCDH/wgP/3pT2lqakrrueaIC8fo1U6+Z88enn76aQBuvPFG3va2t7Fr1y4++tGP0tDQkJZSlt/vp7W1lZycHNasWTPnc/h8Pm0BsFqtGsNN7XAbNmxIG32zr6+P0dHRtC4qRqORnp6elHkqfr8fs9msqRsXFhZSUFDAyMjIvBh8T08Pd955Jz/60Y9oaWlJ67lSgAvH6GccSEqGhob47ne/y3e+8x2ampq45ppr2LlzZ8o72RRVVKmrpBqKC9De3o7H46GqqoqampqUZ7aDZ9bNRXoqFoaHh+nr6ws7xioVUN99R0cH2dnZ2iCMVAmEhKKvr4/3v//9PPHEE1xyySUpP34acOFl7yEQ0y9ZsoTDhw/zhz/8gSVLlvD000/zj//4j1gsFq6//np27tw5511ZlbLSJX0NAaPv6+ujvr6ehoYGjQvQ0dFBYWGhNgNvLruylJL29na8Xi+NjY1p8YYgvGJtqjExMcGZM2fYsWMHeXl5swRCVN4kFY1Bg4OD3HHHHTz22GPni8HPO+Ztp9cOOJ3FD4bJZOKZZ57hqaeewmg08u53v5ubb745YRUWlXVOZ7nM5XJx5MiRsK23UkqmpqY0hltubq5WCkxkB50PYQo4GzYkolibKFS1IZKUd3DeRE0OjlcgJBTDw8PcdtttfP3rX+fKK69M0TuYiV27dvGFL3yBkydPsn//frZt26Y99sgjj/CDH/wAvV7Pt771Ld71rnfFe9gL072PFxaLheeee449e/bQ29vLNddcwy233BLTvVU68Y2NjWlTPFFeRLx0VEVxHR0d1TTvqquro3IBVHOSEvBIF1KhWBsLqhIQr3b/XCYHj46Ocuutt/KVr3yFa665JlVvYRbUiLR7772XRx99VDP6EydOcOedd7J//34GBwe5+uqraW9vj3cxXdxGH4zJyUmef/559uzZQ3t7O+985zu5+eabaWlpmXGjqpbVdKnIqmtpbW1NmhCjXFqj0agNwQzluHu9Xi0Xka4+9XQq1gYjUYMPhWJQGo1GTQJb5QFCF02TycR73/tevvCFL/Ce97wnVW8hKq688soZRv/II48A8PnPfx6Ad73rXXzhC1/gLW95SzyHuzBj+mRQXFzMnXfeyZ133ondbueFF17gu9/9LsePH+fKK6/khhtu4Le//S0333wz27dvT9sNnAphSdW/3dDQgNvtxmg0curUKdxuN5WVlZSXl9Pe3s6KFSvS1vWlFGs9Hg+bNm1KW9ig2qG3bNmSNMNRCEFJSQklJSWsWbNGmxh09OhRAC1kKigo4LbbbuOBBx6YN4MPh4GBAU3BGaC+vp6BgYEFu55oOKeNPhj5+fm8973v5b3vfS9Op5O9e/dy7733UlZWhtPpxOVycdlll6U8GaXq4y0tLSmrj2dnZ2utxh6Ph6GhIQ4fPkxWVhaTk5Pk5uamXM89WLF2w4YNaTX4jo6OORl8OBQUFFBQUMCKFSu0ycH333+/JqJaXV2N3+9PycJ/9dVXMzw8POvvDz/8cESBjXAec7o+47nivDH6YOTm5tLW1saDDz7IBz/4Qf7whz+we/duPvOZz3DppZeyc+dOrrjiijm5+opjYDabaWlpSVuiy+12MzAwQEtLC4WFhZhMJvr6+piamqKsrIzq6uqkklrBmK/EoCL3NDc3p0WMRCE7O5uSkhJGR0f5yle+QllZGT/+8Y/ZunVrShbmffv2Jfya+vp6+vr6tN/7+/vPlbbdWTinY/poCFcF8Hq9vPzyy+zatYtXX32VrVu3snPnTq666qqEbsLgctnFF1+ctrAh2gAKRW4xGo1YLBaKi4u1LrdE9QWUos6qVatS/RY0KIPfsmVL2rXi7XY7t99+O/fccw933XVXWs8VCaExfWtrKx/4wAe0RN473/lOOjo6Mom8+YTP5+PVV1/lqaee4o9//CObNm3i5ptv5uqrr44alysjyc/PT9uILDgb98bDcVdqNyqpVVBQoHW5RQtn5kOxFtDGTqez70DB4XBwxx138P73v5+PfOQjaT1XODz99NN84hOfYHR0VJvI/OKLLwIB9/+HP/whBoOBb37zm1x33XXxHjZj9KmG3+/nr3/9K0899RT79u1jzZo13HLLLVxzzTUzdliVPa+urk6rwIKivCajiKu63MJJhAcbnM/n095LuioBgDZZZj4M3uVy8Td/8zfccMMN/P3f//05GzMngYzRpxN+v59Dhw6xa9cufve737FixQpuuukmGhsbee655/jbv/3btGqmKRGPpqamlJQXVVZ7dHQUnU6nDXNoa2tLq2ItnDX4LVu2pHvAI263m7vuuot3vOMdfPKTn7yQDB4yRj9/UK78448/zpNPPslll13GTTfdxA033JAWIQ/VRtzY2JiWxKDT6WR4eJjTp0+Tk5PD0qVLUyYRHgrlrcyHwXs8Hj70oQ9xySWX8NnPfvZCM3jI1OnnDzqdjosvvphjx47x0ksvkZWVxe7du7n11lspLS3VFoC5cviVBLbD4aCpqSltiUEhBCMjI2zevJmSkhLGxsZob2/H7XZTUVFBTU1NUgMwQ2E0Gunt7Z0Xg/d6vdx77700NzdfqAY/71jUO72Cz+ebsfOqPvzdu3fzm9/8htzcXG666SZuuummGZoA8SC4Pp4u1V2Irljr9Xo1frvNZtN0AWJJhIfDyMiIJhaSboP3+Xx8/OMfZ8WKFfzbv/3bhWzwGff+XIKq1z/11FM8/fTT6HQ6brzxRm6++WaWLl0a9Uacr0qA6gmIZ6pr6OCLSBLh4aBacNPZkafg9/v55Cc/SUVFBV/5ylcWYtTUfCJj9OcqpJQMDg5qC4DL5eLGG29k586ds3TtVbmsoqKChoaGtF2TGhCRTGdhJInwcA0uw8PD9Pf309zcPC8G/5nPfIbc3Fy+8Y1vXOgGDxeC0f/ud7/jk5/8JD6fj4985CPcf//9yV3dOQwpJUajkT179rBnzx4mJyd5z3vew80330xJSQl/+MMfuOKKK9LKylLikqmQjw5tcMnLy9O4AGNjYwwMDMybwT/wwAN4PB4ee+yxxWDwcL4bvc/nY+3atfzv//4v9fX1bN++nSeffJINGzYkf5XnAcbGxnjmmWf4xS9+QWtrq1ZLTlQTIF5EU6ydK6SUWlvw4OAgXq+XVatWUVtbm9ZavN/v56GHHsJsNvO9731vsRg8zLPRp/xT3b9/P6tXr2bVqlVkZ2dzxx138Oyzz6b6NOccKisrueOOO7BYLPzgBz/giiuu4Itf/CJve9vbeOihhzh69Ch+vz8l5zKbzZw8eZLm5ua0lOOEEBQWFpKbm0teXh7btm1DSsmRI0c4cOAAZ86cweFwpPScUkoeeeQRRkZGeOKJJxaTwc87Uu6rDQwMzGCz1dfX8/rrr6f6NOckCgsLeeGFFzRyz913383k5CR79+7l0UcfpbOzU9ME2LJlS1I3dnBTS7pksOGsjFZzczN6vZ7CwkKWL1+Oy+XCaDRy8uRJvF6v1uM+l/BCSsmjjz7K6dOn+elPf5q25qbPfvaz/OY3vyE7O5uLLrqIH/3oR1ricw6qN+cdUr6cnk8thulAKJuvuLiYD3zgA+zevZvXXnuNt7zlLXznO9/hsssu4/777+cvf/mLNvorFkZHR+nq6mLLli1pNfj+/n5GRkY0gw9GTk4Oy5Yto6WlRWuf7ezs5K9//SudnZ1MTk6GvQciQUrJt7/9bY4ePcpPfvKTtOYMrrnmGo4fP66pHynhixMnTvDLX/6S1tZWfve73/Hxj3887u/kfETKP+HzqcVwvlFQUMD73vc+3ve+9+F0Ovmf//kffvzjH/OpT32Kyy+/nJ07d0bUBAgul6WzPt7f34/RaIyom+fw+Pjfk6NYXV7esrKclUuXsnTpUk0ivLe3V5MIV23BkRZ9KSVPPPEEf/7zn9m9e3fa6/7XXnut9v9LL72U3bt3A/Dss89yxx13kJOTw8qVK1m9ejX79++PV/XmvEPKjX779u10dHTQ3d1NXV0dv/zlL/nFL36R8HE+9KEPsXfvXqqrqzl+/HiqL3PBEUz4cbvd/P73v+fXv/41n/nMZ3jLW97Czp07edvb3kZWVhanTp3CarWmvT7e19fH2NhYRIO3u33c9l8HGJ504p9ubf7uHY1csrIMvV5PTU0NNTU1+P1+xsfHGRoaoq2tjZKSklnDL6WU/OAHP2Dfvn3s2bMn7c06ofjhD3/I+9//fuD8Ur1JBVJ+BxkMBh577DHe9a534fP5+NCHPpTUOKF77rmH++67b8H6pecT2dnZXHfddVx33XV4PB5efvlldu/ezf33309tbS0+n49du3bNm8FHyjXsPjjI4IQDl1e575J/3XuK333i0hnP0+l0VFZWUllZiZRyhkR4Xl4ex44dw+VysXfvXp599tmUhirxqN48/PDDGAwG/uZv/ibwLhZZSJqWu+g973nPnPXKrrjiCnp6elJzQecRsrKyuPrqq7n66qv52te+xrPPPktTUxNXXXUVmzdv5uabb+ad73xnShV/z5w5w/j4eMy+gDGbO8jgA7A4PFGPLYSgrKyMsrIypJSMjIzw1a9+lT/96U9cdtll7N27l9tuuy0l7wNiq97893//N3v37uX3v/+9ZtiLLSRd1A035zqWL1/OH//4R7KysvD5fJomwJe+9CXWrVvHzTffzLXXXjunsl1vby8Wi4XGxsaY1YS3rCzjZ/v7cXoCpcdsveDSlfF3IwohePXVVzGbzfT29tLX10dbW1vS154ofve73/Hv//7vvPzyyzNUiG+66SY+8IEP8OlPf5rBwUE6OjrYsWPHvF3XfOOcpuH29PRwww03XJAx/Vzg9/s5ePAgu3bt4sUXX2TlypXcdNNNXHfddQlRcZPRvv/lgX4e3Xcal9fPZavK+MZ7N1KQE9/e8dxzz/HYY4/x/PPPU1JSEvd1pgqrV6/G5XJRUVEBBJJ5jz/+ODAn1ZtU4Pxm5KUSGaOPDb/fz7Fjx9i1axcvvPACS5Ys4aabbuL666+PqgmgZuRt2rQpKb5AOI3CaHjhhRd49NFHef755+MaFLLIkDF6hVQZfV9fH3fddRfDw8PodDr+7u/+jk9+8pMpuspzB1JKTpw4we7du3n++ecpKytj586d3HDDDVRWVmrPm6vBJ4p9+/bx8MMP8/zzz8+4jgw0ZIwe4M477+Sll15ibGyMmpoaHnroIT784Q8ndayhoSGGhoZoaWlhamqKrVu38swzz1zQ/QBqsIXSBMjLy2Pnzp2cOnWKt7zlLdxyyy3zYvAvv/wyDz74IL/97W+prq5O+/nOU2SMPt3YuXMn9913X1pnnp1LkFLS09PDvffeS1dXF/X19ZomwJIlS9JWnnr11Ve5//77ef7559Oq1XcB4PxuuDnX0dPTw6FDhxbVGGMhBJOTk9TX13Pq1Cl+/vOfk5WVxUc+8hGuvfZavvWtb9HT05MQfTYWXn/9dT73uc/x3HPPZQz+HMOi2umtVitvf/vbeeCBB7j11lsX+nIWHKpurjQBpqamuP7669m5c+ecJuG8+eabfOITn+DZZ59Nq97+BYSMe58OeDwebrjhBt71rnfx6U9/eqEv55zE6OgozzzzDHv27GFsbIzrrruOnTt3sn79+rgXgCNHjvCxj32Mp556itWrV6f5ii8YZIw+1ZBScvfdd1NeXs43v/nNOR3L6XRyxRVX4HK58Hq9vO997+Ohhx5KzYWeQxgfH+e5555jz5499Pf3c+2113LLLbdEHW/d2trKhz/8YXbt2sW6devm+YrPa2SMPtV49dVXedvb3jaDhPLlL385KaqwUpUpLCzE4/Fw+eWX85//+Z8zGjYuNExMTLB371727NlDV1cXV199NTfffDPNzc3a59nW1sY999zDk08+mVSvxSJHxujPF9jtdi6//HK++93vLprEoNVq5YUXXmD37t2cPHmSq666im3btvG1r32Nn/3sZzQ2Ni70JZ6PmN/uHilltJ8MwsDr9cqmpiZZUFAg//mf/3mhL2fBYLfb5TPPPCO3bNkin3/++YW+nPMZsewwpT+LrmSXCuj1eg4fPkx/fz/79+9ftDRhRfg5ePDgnLsqo+HBBx+ksbGR5uZmrr32WgYHB7XHHnnkEVavXs26deu06bEZREfGvZ8jHnroIQoKCvjMZz6z0JdywWJyclJrJPrWt77FiRMnePzxxzlx4gR33nmnNhP+6quvpr29PW0ae2lEhpxzLmN0dBSLxQIEZqXv27eP9evXL+xFXeAI7hy02Wxa+TCSzFUG0ZHpp08QQ0ND3H333fh8Pvx+P7fffjs33HDDnI7p8/nYtm0bdXV17N27N0VXemHhgQce4Cc/+QklJSX88Y9/BBafzFWqkDH6BNHY2MihQ4dSesz//M//5OKLL2ZycjKlxz2fEEvm6uGHH+bhhx/mkUce4bHHHuOhhx5adDJXqULG6BcY/f39PP/88zzwwAN84xvfWOjLWTDEkrlS+MAHPsD111/PQw89tOhkrlKFTEy/wPjUpz7FV7/61cxElyjo6OjQ/v/cc89pOZSbbrqJX/7yl7hcLrq7uy94matUIbPTLyCUxPfWrVt56aWXFvpyzlncf//9nDp1Cp1Ox/LlyzWJq40bN3L77bezYcMGDAYD3/nOd87HzP28I1OyW0B8/vOf56c//SkGgwGn08nk5CS33norP/vZzxb60jKYX2RouIsRL730Eo8++uics/crVqygqKgIvV6PwWDgwIEDKbrCDNKIeTX6jHt/AeKPf/xjRosug4jI7PQXGFasWMGBAwcyRn9+IcPIyyB5CCG49tpr2bp1K9/73vcW+nIyOAcRa6fP4DyDEGKplHJQCFEN/C/wCSnlKwt9XRmcO8js9BcYpJSD0/8agaeBTOE6gxnIGP0FBCFEgRCiSP0fuBZYnH2/GUREJnt/YaEGeHqaf24AfiGl/N3CXlIG5xoyMX0GGSwyZNz7DDJYZMgYfQYZLDJkjD6DDBYZMkafQQaLDBmjzyCDRYaM0WeQwSJDxugzyGCRIWP0GWSwyPD/AyS9thZkJNP+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(projection='3d')\n",
    "ax.scatter(X[:,0], X[:,1], X[:,2])\n",
    "\n",
    "\n",
    "plt.legend(loc=\"best\", shadow=False, scatterpoints=1)\n",
    "plt.title(\"PCA of 3D dataset\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "144c3f50",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components=3)\n",
    "pipe = Pipeline([('scaler', StandardScaler()), ('pca', pca)])\n",
    "X_PCA = pipe.fit_transform(X)\n",
    "\n",
    "total_var = pca.explained_variance_ratio_.sum() * 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "c77d7136",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.71299086e-15,  1.76081372e-15, -5.52030643e-16])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.mean_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "ce1d8c0f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_vector(v0, v1, ax=None):\n",
    "    ax = ax or plt.gca()\n",
    "    arrowprops=dict(arrowstyle='->',\n",
    "                    linewidth=4,\n",
    "                    shrinkA=0, shrinkB=0, color='black')\n",
    "    for i, j in zip(v1, v0):\n",
    "        ax.annotate('', (i, j), arrowprops=arrowprops)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "73b814c3",
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "'\\nfig.savefig(\\'figures/05.09-PCA-rotation.png\\')\\n\\n\\n#ax = fig.add_subplot(projection=\\'3d\\')\\nax.scatter(X_PCA[:,0], X_PCA[:,1])\\n\\n\\nplt.legend(loc=\"best\", shadow=False, scatterpoints=1)\\nplt.title(\"PCA of 3D dataset\")\\n\\nfor length, vector in zip(pca.explained_variance_, pca.components_):\\n    v = vector * 3 * np.sqrt(length)\\n    print(v)\\n    draw_vector(pca.mean_, pca.mean_ + v)\\nplt.axis(\\'equal\\');\\n\\n'"
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     "execution_count": 69,
     "metadata": {},
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\n",
      "text/plain": [
       "<Figure size 1152x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "import plotly.express as px\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "\n",
    "    \n",
    "fig = px.scatter_matrix(\n",
    "    X_PCA,\n",
    "    dimensions=range(3),\n",
    "    title=f'Total Explained Variance: {total_var:.2f}%',\n",
    ")\n",
    "\n",
    "fig.update_traces(diagonal_visible=False)\n",
    "fig.show()\n",
    "\n",
    "fig, ax = plt.subplots(1, 2, figsize=(16, 6))\n",
    "fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)\n",
    "\n",
    "\n",
    "# plot data\n",
    "ax[0].scatter(X[:, 0], X[:, 1], alpha=0.2)\n",
    "for length, vector in zip(pca.explained_variance_, pca.components_):\n",
    "    v = vector * 3 * np.sqrt(length)\n",
    "    draw_vector(pca.mean_, pca.mean_ + v, ax=ax[0])\n",
    "ax[0].axis('equal');\n",
    "ax[0].set(xlabel='x', ylabel='y', title='input')\n",
    "\n",
    "# plot principal components\n",
    "\n",
    "ax[1].scatter(X_PCA[:, 0], X_PCA[:, 1], alpha=0.2)\n",
    "draw_vector([0, 0], [0, 3], ax=ax[1])\n",
    "draw_vector([0, 0], [3, 0], ax=ax[1])\n",
    "ax[1].axis('equal')\n",
    "ax[1].set(xlabel='component 1', ylabel='component 2',\n",
    "          title='principal components',\n",
    "          xlim=(-5, 5), ylim=(-3, 3.1))\n",
    "'''\n",
    "fig.savefig('figures/05.09-PCA-rotation.png')\n",
    "\n",
    "\n",
    "#ax = fig.add_subplot(projection='3d')\n",
    "ax.scatter(X_PCA[:,0], X_PCA[:,1])\n",
    "\n",
    "\n",
    "plt.legend(loc=\"best\", shadow=False, scatterpoints=1)\n",
    "plt.title(\"PCA of 3D dataset\")\n",
    "\n",
    "for length, vector in zip(pca.explained_variance_, pca.components_):\n",
    "    v = vector * 3 * np.sqrt(length)\n",
    "    print(v)\n",
    "    draw_vector(pca.mean_, pca.mean_ + v)\n",
    "plt.axis('equal');\n",
    "\n",
    "'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "21f61510",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(projection='3d')\n",
    "ax.scatter(X_PCA[:,0],X_PCA[:,1], X_PCA[:,2])\n",
    "\n",
    "\n",
    "plt.legend(loc=\"best\", shadow=False, scatterpoints=1)\n",
    "plt.title(\"PCA of 3D dataset\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "90d9dfc5",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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