Implementacion GA polinomial.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hasta aquí pudo correr\n",
      "Start of evolution\n",
      "  Evaluated 500 individuals\n",
      "-- End of (successful) evolution --\n",
      "Time Elapsed: \n",
      "93.560901\n",
      "\n",
      "-- Punto final generado --\n",
      "[ 0.96701899  0.99082247  2.05708292]\n",
      "-- Punto final real --\n",
      "[ 1.  1.  2.]\n",
      "-- Error --\n",
      "0.0044304338242\n",
      "-- Energia --\n",
      "3786.79736401\n"
     ]
    },
    {
     "data": {
      "image/png": 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acC1msrYozGRt11EVhq4D9gIXAF+eQi0iUkdlZaYVY9++2peDB00oqdS2rQkY\nffrAFVdUBY6kJNPZVESan/oEkhhqnpX1r0AHYDjwRMX9UwkkJ9IJiOfYUFGKmZRtMCaQpAAB1fY5\nCGys2EeBROQUlZTA/v21B429e81oFsuhPTMsDNq1M6Gje3e44AKz3rat6ePRqRMEB7vvPYmIZ6pP\nIEnF/PhX9yGwGtPHYyZwbwPqqi6h4jat2vZ0oL3DPqWYEUGO0jBhRkQqlJRAeroJE2lpZv3gweMD\nR+VIlUpRUVVho29fGDWqKmxULpGROq0iIqeuPoGkBHMhvZ3Vtg8CiivW/RzWG1uDhhpPmTKF6Gpt\nxKmpqaSmpjaoKBFXsiwzzXlluHAMGjVty60e24EWLarCxsCB5lSKY9Bo00ZXpRVpjmbOnMnMmTOP\n2Zbj2PHLSeoTSP4JvIppJVlVsW0gcDPw/yruX4jpoOoshypu4x3Wq98/BARi+pI4/rlNAJbXduBp\n06aRnJzsvEpFnMCyzAReWVnmSrKZmaa1oragkZ4OxdX+C+DnB3FxZomPN6dKzjzTrFduq1yPjYXA\nQPe8VxHxbDX9J33NmjWkpNR0sqT+6hNI/g/4DbgD02kUYBvmVM0HFfdfBV5pcHVVfsMEjhHALxXb\nAoFzMUOFwZwuKqvYZ07FttaYTrb3ObEWkVNSVGQCRWW4qOm2pm2lpccfKySkKkjEx5vTJjUFjPh4\nM+Oor6/r36+ISH3Ud9T++xVLbYrqccwwoKvD/c7AGUAmZqTMNOBhzJDfnRXr+VSFoFzMkOGpFc/J\nxsxJsh4z6kekXizLTM6Vk2NOdVS/zc2F7OzaA0f1lgswfSxiYswQ1xYtzG2HDpCcXHXf8bZFCxM0\nwsNd//5FRFyhIdMIBQJxmKv9OtpTz+MNoGq4rgW8ULH+FmY473OYyc5ewYz0WYlpDSlwOMYUwAbM\nrtj3a2ACmtK+WSsrOz5A1BYuatvHcciqI19f09EzOtqEh5YtoXVrM0toTcGi8jY6Wq0XIiKO6hNI\nugHTMUNpq7MwHVrr4zuODzfVPVGx1KYUuLNiES9lWeY0x5EjpqOm41KfbSUltb9WWFhVoKi8jY+H\n0047dnv1fSpvw8I0okRExBnqE0hmYFohRmH6daj1oRkrLzenM/LzzVJQUPd1x23VQ4X9BPPq+viY\n0R4REWaIaeV6RAS0anX8toiImgNFZCQEBLjusxIRkdrVJ5CcAfQHtji5FmkElmVaCAoKTHAoLKxa\nP9lt5fp0SPcYAAAgAElEQVSJwkRRHXoLBQSYvg/h4aZFwXG9VSvo2PH4AFFTqKjcFhqqVgkRkaam\nPoFkC9DK2YU0R2Vl5ke/qKgqANS2frLHThQqTtTaUMnHx/zQh4UdexsaasJDq1am02VtwaK29bAw\nDScVEZGTq08geQD4O/AIZgRLWbXHjzS0KHcpLzc/9HVdKoNBXfarKVBUXja9LkJDzZDPypBQuR4S\nYn70W7euOVDU9TY4WK0OIiLiPvUJJJVDaL+p4bGGdGp1i+HDTTAoKjItFqciJKTmxTEotGp1fIio\nvn6ix0JCFBZERKTpq08gGVbLdgvwuilPx40zVxitLVzUtgQFKSSIiEjztK+mCZYaqD6B5Ltq96OB\n8Zip4/sCLzawJpeaNMlMRiUiIiIntyYvjxu3bnX6cRsyNdP5mFlSD2Cmkf8UM/pGREREmqCvs7I4\nd9067KWZTj/2qbaQtAVurFhaALMwM7aOBTY5tzQRERHxFB+kpTFx61Y6k822X/7q9OOfSgvJ58Bu\nzJV8n8BcuO5WTN8RTY4mIiLSRE3du5fxW7YwOLCIbUuu5I9nTHD6a5xKIBmBuaLuY8Db1O8CeiIi\nIuIl7JbFvTt3ct+uXUyI9mPFN2O4ttfV3Nr/Vqe/1qkEkrOBDcB8zBV3/4JpJREREZEmpsRu57ot\nW3hx3z7+1iaGz74ay8A2A3hz9Jv4NMIw01MJJCuAPwKJwP8DLgF+x8w7MgKIcHp1IiIi4nJHbDZG\nrV/PRxkZTO/SgVlfXE1UcBTzrp5HsH9wo7xmfUbZ5GOu9ns20Bt4HngIyAAWOq80ERERcbVDJSWc\nu24dP+flsbhXD97+5iYyCjP49NpPaRXaeFeOaciwX4BtmKnk2wLXoM6tIiIiXmt7YSGD1q4lo7SU\npWecwXvf38/yvcuZf/V8urbs2qiv3dBAUsmG6Vsy2knHExERERf68cgRzl67lhBfX5YnJ/PJ2pd4\n+5e3mT56OkM6DGn013dWIBEREREvtTgzk2Hr1tEtJIRl/fqxbMfHPPq/R3nivCcY32e8S2pQIBER\nEWnGZhw8yGUbNjA8Joav+/Zl88EfuXHBjUzoO4FHhz7qsjoUSERERJohy7J4+vffuWnbNv7YujVz\ne/ZkX86vjJk1hsHtBvPGpW80yvDe2tTn4noiIiLixcotizt37OCVAwd4smNH/tqhA1lFWYz6YBSt\nQlvx0biPCPQLdGlNCiQiIiLNSHF5OeO3bGH+4cO80a0bf0xMpMRWwuUfXk52cTYrb15Ji5AWLq9L\ngURERKSZyC4r47KNG/k5L4/5vXpxaatWWJbFzZ/czKr9q/j2hm9JapHkltoUSERERJqBfcXFXLR+\nPQdLS/mmb18GRUUB8MSSJ3h/w/vMGjuLwe0Gu60+BRIREZEmblNBARetX48f8EO/fnQPCwPgnV/e\n4YklT/DMsGe4utfVbq1Ro2xERESasGU5OZyzdi0t/P1Znpx8NIws2b2EP37yR2464yYeOuchN1ep\nQCIiItJkzcvIYPj69fQLD2dpv34kBgUBsO3wNi7/8HKGdhjKa5e85tLhvbVRIBEREWmCXtu/nys3\nbWJ0y5Z81qcPUf6ml0ZGQQYjPxhJQngCc8fNJcAvwM2VGgokIiIiTYjNbucvv/7KbTt2cEebNszs\n0YMgX/NzX2wr5rJZl5Ffms/iaxcTHRzt5mqrqFOriIhIE7GrqIjxmzfzc14ezyclcU/btkdPx9gt\nOxPnT2TtobV8d8N3dIrp5OZqj6VAIiIi4uUsy+LtQ4e4Y+dO4gICWNavH2dVDOut9Oi3jzJ702zm\nXDWHM9ue6aZKa6dAIiIi4sWyysq4Zft25mZkcGNCAi916UKE/7E/79PXTueZZc/wj+H/YGyPsW6q\n9MQUSERERLzUt9nZTNiyhUK7nTk9enBlXNxx+3zz6zfcsugWbkm5hXsH3euGKutGgURERMTLlNjt\n/PW333h+716GRUfzdvfutA0OPm6/zRmbGTt7LOd3Op+XR77sEcN7a6NAIiIi4kU2FxQwfssWNhUU\n8I/OnbmnXTt8awgaaflpjPpgFO2j2jP7qtn4+3r2T75nVyciIiKA6bj6yoED3LdrF52Cg1mVnMwZ\nERE17ltYVsjoWaMpthWzZOISIoMiXVztqVMgERER8XBppaXctHUrn2ZlcXtiIs8lJRHq51fjvkVl\nRVwz9xo2pm9k6cSltI9q7+Jq60eBRERExIMtOnyYm7ZtwwdY1Ls3o1q2rHXfw4WHGT1zNOsOreOj\ncR+RkpjiukIbSIFERETEAxWWl3Pfrl28euAAo1q04M3u3YkPDKx1/51ZO7n4/Ys5UnKE7yZ+x8A2\nA11YbcMpkIiIiHiYtXl5XLtlC7uLi3mla1duTUw84QiZFXtXMHrWaFqGtGTFzSvoHNPZhdU6h65l\nIyIi4iHslsVze/Zw5po1BPv6siYlhdvatDlhGPl4y8cMe2cY3Vt1Z/nNy70yjIBaSERERDzC3uJi\nbti6le9ycrivXTue6tTp6EXxajNt5TTu+eIexvUcx1tj3iLY//i5SLyFN7WQPA7Yqy0HathnP1AI\n/A/o4bryRERE6mdOejp9fv6Z7YWFfNO3L88lJZ0wjJTby5ny+RTu/uJu7h98Px+M/cCrwwh4XwvJ\nRuACh/vlDusPAlOAicAO4K/AV8BpQL6L6hMREamzIzYbd+7YwdtpaVwVG8tr3brRIiDghM8pKivi\nunnXMX/rfF4Z+Qq3DbjNRdU2Lm8LJOVAeg3bfTBh5GlgfsW2G4A04FrgPy6pTkREpI5W5OYyfssW\nMsrKeKt7dybEx590aveMggxGzxrN+rT1LLhmAZd0u8RF1TY+bzplA9AVc0rmV2Am0KlieycgHvjS\nYd9SYAkw2JUFioiInEip3c7jv/3GkLVriQ8MZF3//tyQkHDSMLIjcweD3hzEr9m/smTikiYVRsC7\nWkhWAtcD24EEzCmZ5UDPivtgWkQcpQPeMUWdiIg0aZZl8UlmJvfv2sWuoiIe69iRR9q3x/8kHVcB\nlu9dzuiZo4kNi2XlzSvpFNPppM/xNt4USD53WN8ErAB2YU7N/HiC51knOuiUKVOIjo4+Zltqaiqp\nqan1LFNERORYa/PyuGfXLr7LyeGCmBjm9uxJn/DwOj33o80fMf7j8ZzZ9kzmXT2PFiEtGrnaY82c\nOZOZM2cesy0nJ8fpr+O51yGumy8xHVifx4STfsAvDo8vALKAG2t4bjKwevXq1SQnJzd2nSIi0gwd\nKCnhkd9+4+1DhzgtNJSpSUlc3KLFSU/PgGlRmbZyGvd+eS9X97qaty57iyD/IBdUfXJr1qwhJSUF\nIAVY44xjelMLSXVBmGG9S4HfgEPACKoCSSBwLnC/W6oTEZFmq6C8nKl79/L3PXsI8fXl5a5dmdS6\nNQF1OD0DZljvPV/cwz9X/ZOHzn6Ip89/Gl8fb+v2eWq8KZA8D3wC7AXiMH1IwoG3Kx6fBjyMaTHZ\nWbGeD3zg8kpFRKRZslsW76Wl8fCvv5JRVsZdbdvycPv2RJ9kKK+jwrJCxn88nk+2fcJro17jlv63\nNGLF9WSzOf2Q3hRI2mBG1rQCMjB9SM7CBBSA54AQ4BUgBtMJdgRQ4PJKRUSk2Vmak8PdO3eyJj+f\nK2NjebZzZ5JCQk7pGOkF6YyeOZqN6Rv55JpPGNVtVCNVWw92OyxbBrNmQbU+Jc7gTYGkLr1Mn6hY\nREREXGJnYSEP/vorHx8+TP+ICL4/4wzOqTZYoi62Z27n4vcvprCskCUTl5CSmNII1Z4iy4KffzYh\n5MMPYf9+aNcORo+Gd95x6kt5UyARERHxGNllZfzf77/zr/37iQ8M5L3TTyc1Lg7fOnRYre6HPT8w\netZo4sPi+XbCt3SI7tAIFZ+CjRtNCJk1C3btgrg4GDcOUlPhrLNg3ToFEhEREXcqs9t57cABHt+9\nmxK7nb917MjdbdsS6udXr+PN2TSH6+ddz6B2g/h43MfEhMQ4ueI62rWrKoRs3AjR0TB2LLz2Gpx3\nHvg3bmRQIBEREakDy7JYnJnJfbt2sb2oiJtbt+bJjh1pHVS/obiWZfHCihe476v7uLb3tUwfPd31\nw3r374fZs02fkJ9+grAwuOwyeOYZuPBCCAx0WSkKJCIiIifxS34+9+7cyTc5OQyLjubDnj3pW8eJ\nzWpSebXel396mUeGPMJTf3iqTnOTOEVGBnz0kQkh338PAQEwciTcdx+MGmVCiRsokIiIiNTiYEkJ\nj/72G9MPHaJbSAgLe/ViVMuWDQoPR0qOMGHeBBZtX8R/LvkPk1ImObHiWuTmwvz5JoR8/bXZdsEF\nMGMGjBkDUVGNX8NJKJCIiIhUU1hezgt79/Lsnj0E+fryzy5duCUxsc4Tm9Xmi51fMGnhJLKLs1mY\nupCLu17spIprUFgIixaZPiGffgqlpTBkCLz8sukbEhvbeK9dDwokIiIiFUrsdj5IS+Ox3btJKy3l\nzjZteKRDB2JOYWKzmmQXZXPvl/cyY90MhncezhuXvuH8kTSlpbB2LSxfbuYL+eILKCiAAQNMn5Bx\n46BtW+e+phMpkIiISLOXVVbG6wcO8K/9+zlYWsrYVq34e1LSKU9sVpOF2xZyy6JbKCgr4L+X/peb\n+t3knP4i6emwYoUJIMuXm/lCioshOBgGDoS//AWuuQaSkhr+Wi6gQCIiIs3WrqIipu3bx/SDBym3\nLCYkJHB327ac7oSOnZmFmdz5+Z18sOEDRnYdyeuXvE7byHq2UNjtsHlzVfhYvhx27DCPtWkDZ58N\nzz4LgwdD374uHR3jLAokIiLS7KzIzeX5vXuZd/gwLQMCuK9dO25v04Y4J/2Qf7T5IyZ/Opmy8jLe\nGfMO1/W57tRaRfLyYNUq+OEHEz5WrjQdU/384Iwz4KKL4MknTQBp394pNbubAomIiDQL5ZbF/MOH\nmbp3LyuOHKFbSAivduvGhPh4Quo5qVl16QXp3P7p7czdPJcx3cfwyshXaB3R+sRPsizYvfvY1o/1\n602rSEyMCR0PPGBuBwxw27DcxqZAIiIiTVpBeTkzDh7kxX37+LW4mKFRUXxSMXy3PtO818SyLGZt\nnMUdn92Bj48Ps8bOYlzPcTW3iuTmmtMvK1ZUtYAcOmQe697dBI8//9mchunWDRo4ssdbKJCIiEiT\ndLCkhH/t389rBw5wxGbjqrg4PuzRg/6Rkc59nbyD3Lb4NhZsW8DVPa/mXxf/i1hC4ZdfTD+PymX7\ndnObkWGeGBICZ54JN91kQshZZ0HLlk6tzZsokIiISJOyIT+fF/bt4/20NIJ9fflj69bc1bYtHYKD\nnfo6VlERn3z6IrMXPE1yli/TQi6g4/8OwV1nwIEDVTu2aAFdu5rloovM7WmnQa9eZpZUARRIzOQw\nkZHmSxEQYHomN3T9RNsCA2veVttjTjqvKSLSlFmWxVfZ2Uzdu5cvs7NpGxTEM506MSkxkaiGXBSu\nrAx+++3YFo4dO7Bt24rvvn1cZsFlgD0iHN+uWSZsDB1aFUC6dm3WrR6nQoHk7LNNei0tNV+8srKq\n9dJSyM8/fltN+zluKy11Xn2+vnULNNW31/d+Xfep7TkBAeCq6zGISLNXarczMz2dqXv3sqGggH7h\n4bx3+umMi4098ayqlmX+vqelVS3p6VXru3ebALJ7N5SXm+eEhGB16cLuVv583Dmd/YOiufKyhxh8\n/kR84+L0t6+BFEjuuQeSk517TMsyX+DqIaWmEON429B9HJfiYjhy5PjnnOi+zeac919bgKlLsHHl\n4u+vPyAiXqr6RGajWrTgpaQkzvPxwSc9HbZtOzZs1LQUFR17UD8/iIuD+Hho185c46WylaNbN3aH\nlvLHRX/im9++4eZ+N/P8iOeJDo52zwfQBCmQNAYfH/Nj5+9vOi15C7v9+JBTUlJzGDrRcrJ9qj9e\nUmKuuZCTc/JjOy7OcLIWn/osdWl1qs82nb6T5sJmM/NwVC5Hjhxd/6W4mP8GBTE9JoZy4PpNm7jn\niy84fcMG08JRUnLssQICTMCoXHr0gD/84dhtlUuLFjWOaLFbdl796VUe/PpBWoa25IvrvmBE0gjX\nfBbNiAKJVPH1haAgs3g6yzJ/tOoSkKqHqoYuBQWQnX3y13AMdc5Q0+k7Z91WrgcEmCBduX6ipa77\nOe7r56dWqaakvNx8v0tKqr7rlf/BqCFMHLN+oseqtVzsb9WK9y+4gPcuuIANSUnE5uRw76JF3L5+\nPfFhYZCYCP361RwyoqMb9J3bmbWTmz+5maW/L+W2/rfx7AXPEhnk3FE6YiiQiHfy8an6sQsNdXc1\nJ1Z5Cq+21qNT3Xaqt6Wl5g98XZ/juDSGytbD6ktlcKnrUtP+fn5Vi6/vydfrs1/lj5uPT9XieL+2\n9bruZ1mmtdJuN9+byvXq9xvymGN4qB4maluv6bHKvhV1ER4OERFmEEFERNXSvn3VusNjeZGRfBwV\nxbsBAXxrWQT6+HBZZCTPtGnDha1aETBmTMO+hydRbi/npR9f4q/f/pWE8AS+nfAtf+j0h0Z9zeZO\ngUSksTmewvM2jn2h6rtUtmRVrtdlqeu+RUXHb6v88S0vP/H6qeznqXx8qoKSr2/d14OCTKtYZYuo\n43pkZNX6ifarbT0oyJyqdgwe4eF1mtzLZrfzVXY276alMf/wYYrsds6LiuKN+HiujI1t2GiZU7Ap\nfROTFk5i5b6V3DHwDp45/xnCApvm7KiexAv/QoqIy1S2Djh5/gavU9nKVV5u1iu3VV9v6P1KdQkV\nvr5N4vSXZVmszc/n3bQ0ZqalkVZWxumhoTzaoQPj4+Np78Lv3tbDW3lq6VPM3DCTLi26sPTGpZzT\n/hyXvX5zp0AiInIy3tzK5aH2FBfzfloa76WlsbmwkLiAAFLj4rg+IYHk8PBTuxBdAzkGkTaRbfj3\nyH9zU7+bCPL3gv50TYj+dYmIiEscsdmYm5HBu2lpLMnJIdjXlzGtWvF8UhLDY2Lwd/E1W7ZkbOGp\npU8xa+Ms2ka25ZVRr3DjGTcqiLiJAomIiDSaMrudL7KyeC8tjQWZmZTY7QyLjmb6aadxRWwskW5o\nddqcsZmnlj7Fhxs/VBDxIAokIiLiVJZl8XNeHu+mpTErPZ2MsjJ6hYXxRMeOXBsXR1s39UmqHkRe\nHfUqE8+YqCDiIRRIRESkweyWxeq8PBZnZjIrPZ1tRUUkBAZyfXw818fH09fF/UIcbUrfxFNLn2L2\nptm0i2rHa5e8xsQzJhLoF+iWeqRmCiQiIlIveTYbX2Vnsygzk08zM0krKyPa359LWrbkn127cn5M\nDH5uHAmkIOJdFEhERKTOdhQWsjgzk0WZmSzNzaXMsugRGsqEhARGtWzJ4MjIE1/UzgU2pm/kqaVP\nMWfTHNpHtef1S17nhjNuUBDxcAokIiJSq1K7nWW5uSzKzGRxZibbi4oI9PHhD9HRvJCUxKiWLenk\nIdfs2pi+kSeXPMmczXPoENWB/1z6Hyb0naAg4iUUSERE5BhppaV8VtEK8mV2Nnnl5SQGBjKqZUue\nS0ri/Ohowj1oThbHINIxuiNvXPqGgogX8pxvlIiIuIW9YrbUxRWtIKvy8vABBkZE8EC7doxq2ZIz\n3NgptTYb0jbw5NInmbt5Lh2jO/LfS//LhL4TCPALcHdpUg8KJCIizVC+zcbXlR1Ss7I4WFpKpJ8f\nF7ZoweQ2bbi4RQviAj2zhcExiHSK7sSbo9/k+j7XK4h4OQUSEZFmwG5ZbCwo4H85OXyamcl3OTmU\nWhanhYRwbVwco1q25JyoKLd3SK1Nfmk+czfPZfra6Xy/53sFkSZIgUREpAkqs9tZk5/P0pwcvs/N\n5fvcXHJsNgJ8fDgvOprnkpIY1aIFXUJD3V1qrSzLYtmeZcxYN4PZm2ZTUFbA+Z3O5/0r3ueqHlcp\niDQxCiQiIk1AUXk5q/LyWJqTw9LcXJbn5lJotxPi68vgyEjubtuWoVFRDIyMJNTPz93lntC+I/t4\n55d3eGvdW+zI2kHH6I48cPYD3ND3BjpEd3B3edJIFEhERLzQEZuN5bm5LM3NZWlODj/l5VFqWUT5\n+TEkOprHO3ZkSFQUyRERBHroaRhHJbYSFmxbwIx1M/hy15cE+QVxZY8ref2S1zm347n4+nj+e5CG\nUSAREfECGaWlLHMIIOvy87ED8QEBDImO5vm4OIZGR9MrLMyts6OeCsuyWHtoLTPWzuD9De+TXZzN\noLaDeG3Ua4zrOY6o4Ch3lygupEAiIuKB9hUXHw0f3+fmsrmwEIAOQUEMjY7mtsREhkZH0zUkxOOG\n457M4cLDvL/+faavm876tPUkhCcwKXkSN/a7ke6turu7PHETBRIRETcrsdvZkJ/P6vx8VlS0gvxW\nXAxA99BQhkZF8XCHDgyJiqK9m66U21A2u40vdn7B9HXTWbhtIQCjTxvNM8Oe4cIuF+Lvq5+j5q6p\nfgMmA/cDCcAmYAqwzK0ViYhgwsf6/HxW5+WxuuJ2Y0EBZZaFH9A7PJxLW7ZkaHQ0Q6KiPHYukLra\nengrM9bO4N3173Iw/yB94vvwj+H/YHyf8bQKbeXu8sSDNMVAcjXwInAb8ANwK/AZ0APY68a6RKSZ\nKS4vZ0NBwTHhY0NBAbaK8NEzLIyUiAhubt2alPBw+oaHE+LhI2Dq4kjJET7c+CEz1s1gxb4VxATH\nML73eG7sdyP9Evp53SkmcY2mGEjuAf4LTK+4fzdwISagPOyuokSkaSsuL2d9ZfioCCAbawkf/SMi\n6BMW1iTCR6WMggw+2/kZi3csZuG2hZSUlzAiaQSzr5zN6NNGE+Qf5O4SxcM1tUASCCQDz1Tb/iUw\n2PXliEhTdKLw4e/jQ8/QUFIiIpjUujUpTTB8ANgtO2sPrmXxjsUs3rGYn/b/hIXFgMQBPDr0USb0\nnUCbyDbuLlO8SFMLJK0APyCt2vZ0TH8SEZE6syyLfSUlbC4sZFNBARsLCliTl8emwsKj4aNXWBgp\n4eH8ySF8BDex8FHpSMkRvtr1FYt3LOaznZ9xKP8QkUGRXJh0IZP7T+aiLhcRHx7v7jLFSzW1QCIi\ncsosy2JvSQmbCgqOho/NFet55eUAhPj6cnpoKP0jIrglMZH+ERH0bsLhA8znsvXwVj7d8SmLdyzm\n+z3fY7Pb6BHbg+v7XM+orqMY3G6wpnAXp2hqgeQwUA5Uj+jxwMGanjBlyhSio6OP2Zaamkpqamqj\nFCgi7mN3DB4FBWwqLDwaPPIrgkeory89wsLoERrKFbGx9AgNpUdYGB2Dg/FtBp0xi8qK+G73d0dD\nyG85vxHsH8ywTsN46aKXGNl1JB2jO7q7THGhmTNnMnPmzGO25eTkOP11muK/rpXAauB2h22bgXnA\nIw7bkoHVq1evJjk52YXliUhjs1sWe4qLjwaOypaPzQUFFNjtAIQ5BI+eYWH0CAujZ2go7ZtJ8HC0\nJ3fP0QDyza/fUGQrokNUB0Z1HcXIriP5Q6c/EBrguRfhE9dbs2YNKSkpACnAGmccs6m1kAC8ALwL\n/IwJJ38C2gKvubMoEXG+XJuNnUVF7CoqYmdREdsKC9lcWMgWh+AR7udHj9BQeoWFMS429mj4aBcU\n1OyCRyWb3cbyvcuPhpCN6Rvx8/HjnPbn8Ph5jzOq6yh6xPbQ8FxxqaYYSGYDLYHHgNbABmAkmoNE\nxOtYlkVGWdkxocNxPdNmO7pvC39/uoaE0CcsjGvi4uhZcaqlXVBQs/9htdltrE9bz/K9y/l+z/d8\nuetLcopziA2NZWTXkTw69FFGJI0gOjj65AcTaSRNMZAAvFqxiIiHs1eMZNlVLWzsKi5mZ1HR0b4d\nAK0DA+kSEsLpYWFc2qoVScHBdAkJISkkhJgAdayslFWUxcp9K1m+dznL9y7nx/0/UlhWSIBvACmJ\nKdw58E5GdRtF/8T+uoqueIymGkhExIMUl5ezp6SEXx1bOSoCx29FRZRYFgC+QPuKkHFmRATj4+JI\nCgmhS0gInUNCCGvCI1rqy27Z2XZ429HwsWLfCrYc3gJAXFgcg9sN5vFzH2dwu8GkJKYQ7O+d18KR\npk+BREQaxG5ZpJeWsqekhD3Fxcfc7q1YTy8rO7p/gI8PnStCx4iYGLokJh4NHR2Dgwn01f/YTyS/\nNJ+f9v9kAsi+5azYu4Ls4mx88KF3fG/O7XAufznnLwxuN5jOMZ2b/ekq8R4KJCJyQvk2mwkW1QLH\nXofb0ooWDjDDZtsHB9M+KIgzwsMZ3bIl7YODaRcURFJICG2DgvDTj2SdWJbF77m/H9P68cuhXyi3\nyokMimRQ20FMOWsKg9sNZmCbgUQGRbq7ZJF6UyARacYKyss5WFLCwdJS9juEDscAkuXQcdQHSAwM\nPBo4+kdE0D4o6Oj99sHBxPj763/l9VRsK2bdoXVHA8jyvcs5mG+mUOraoiuD2w3mlpRbGNxuMD1i\ne6j/hzQpCiQiTYxlWRxxCBoHS0s54LB+sLSUgyUlHCgtPToLaaUIPz86VISLsyIjGRcbezRstAsK\nok1QEAE6pdJgdsvO7zm/sz5tPRvSN7AhfQPr09azI3MH5VY5wf7BDGwzkBv63sDgdoM5q+1ZxIbF\nurtskUalQCLiJSzLIstmOxo0DlQEC8egURk8iirm4KgU7udH68BAEgMDaR0URL/wcFoHBpolKIjE\nwEASg4KI8tefBGfLKspiQ5oJHRvSNrA+fT0b0zeSX5oPQExwDL3je3N+p/O5+6y76ZfQj74JfQn0\nC3Rz5SKupb8+Im5iWRb55eWkl5WRUVpKRlnZ0SXd8X7F+qHS0mP6agDE+PsfDRYdg4MZFBlpgkdQ\nUFXgCAwkXEGj0ZXYSth6eOsxwWND2gb25+0HIMA3gNNjT6dPfB8u7345veN60ye+D4kRiTrFJYIC\niYjTVJ4qqSlMHBcyKh4rqRYwwISM2IAAswQGkhIRQWxAAAkVrRmVISMhMLDJXdLeG1iWxZ7cPccF\nj8YmIHIAAA6mSURBVG2Z27DZTX+b9lHt6RPfhwl9JxwNHt1adtNF6EROQIFEpBrLssgrLyerrIws\nm42ssjKybbaj61k2G9kOj2XZbGRWhIyyagHDBzODaGxgILEBAcQFBNA5JKQqcFSEjsrHWgYEqI+G\nh8gpzmFn1s5jlh1ZO9iUvoncklwAooKi6B3fm6EdhvLngX+md1xvesX1Iio4ys3Vi3gfBRJpkizL\noshuJ9dmI9dmOxooqgeJ2sJGeQ3H9AVaBAQQ4+9PC39/WgQE0DYoiD7h4ceEjtiAAOIq1lv4++Ov\ngOGRLMvicOFhdmbtZFf2ruPCR2ZR5tF9W4W2okuLLiTFJHFpt0vpHdeb3vG9aRfZTqdbRJxEgUQ8\nTmXfilybjdzK28qlvJwjDuvVH8u12czj5eXYajgdAhDi62tCRUVgaBEQQI/Q0OO2tfD3J8bhfoSf\nX7O9GJu3siyLQ/mHjg0b2VXrR0qOHN23dXhrklokcXrs6Vza7VK6tOhiQkiLJF3jRcQFFEikwSzL\nothuJ6+8nPyK5Zh12/9v785jJLkOOo5/p8+5jz08650Z78GCtRjF6/WV2ItjgmzF/xhjwBuCBLYR\nGCOIyCFAQSEOAiIUJXEkDkeCxERKDAlKiAAlGCkJAmFx2IjYyWLEYbJrvOP1XnN3z3Q3f7yanuqe\n7pnp3pnunZ7vRypV1auqmTdPra7fvHpVtVReXrUtmuLBYrpQoFjnd3UBg8kkQ6nUypRMMpbN8r2p\nVM1tQ6lUOWyMpFKOu+gwM/kZTl8+zemp07xy6ZVVPR5zi3MAdNHF+OA4R3Yd4eZrb+bkDSfLoePw\nyGH6M/1t/kuknc1AskMUo0sYc4UCc8Uis4VCebnWfDa2PlMnXMSDRb0AsSzT1cVAMkl/NA2kUuXl\nPel0RXgYjC1XB4s+eyl2lLnFOc5MnSkHjtOXT4f1qZX15fEcAImuBAeHD3Jk1xFOTJzg4RsfLoeO\nQyOHfI+LdBUzkLRBqVQiVyyyEE3zseW1ymqVz28wVCwU14sMQRfh0d+9ySS9iQQ9yWRFkBjLZldC\nRZ2AUVGeTNKXTPp+Eq2ysLRQDhvlkBEFj+X1C/MXKo65pu8axgfHmRic4O4DdzMxNFFenxiaYGxg\nzDtZpG1qxweSf5ueZuriRXKlEvlikVyxSD4KDOV5sbih7bX2zUWXM5bDw0JU1qh0Vxc9iQTdNaa+\nKDwMp1Lsz2TojUJAPFisNe+LrWcTCQfp6YrML84zOTvJ5Mwkk7OTnJ05y+RMmJ+ZXgkg5+bOVRy3\nq2dXOVjcMXEHE4NR2BiaYGJwgrHBMXs4pA624wPJoy+/DHUCQgLIJhJkurrCPJEg29UV5vHyaJ5N\nJBhIJstlmUSiZoioWZZM1t0nm0j4MjK1VXXIWA4Yk7OVoWNydrJioCiEsRt7+/Yy2jfK+OA4t+6/\nlQePPljRszE+OE5vurdNf52kq8GODyRfuOEGjt10U83AYQhQp1osLHJh/gLn589zfu485+fPc272\n3Eq4qAoda4WMff37ODh8kNvHbi+vj/aPMto3ymj/KHt695BK7PivGknr2PHfEod7ejjS639m2p5K\npRIz+ZmKYLFqXqOsOmBAZcgY7R/lwPABbhu7zZAhqSX8RpHarFQqsbC0wKWFS1xauMTl3OXycnyq\n7tFYnucL+VU/M51Is6d3D7t7d7O7Zze7e3dz3dB15eVa85GeEUOGpLbx20e6Qsu9FLWCxOWFyrKa\n++Qu1wwVEG5jHe4eZig7VA4OY4NjvGn0TWuGi/5Mv4OTJW0rBhLtSIuFRabz00znppnOTzOVmyov\nx+dTuamwXK88N81MfoYStQdGpxNpRnpGGMoOMdw9XJ4ODB2oWB/uHmaou3KfoeyQwULSjmEg0VWr\nVCqRL+SZXZxlJj/DbH6W2cXZjc9jx83kZyqCR66QW/N3d6e6GcgMMJAdYDA7WF7e27uXw8OHQ1l2\noGKf6jAx3D1Md6rbQCFJG2AgUcOWg8Lc4hzzS/Nhvjjf8PLcUjRfnKsbLAqlWq+5q5ROpOnL9NGX\n7ls178/0M9o3Wg4O8Xl1qFgu68/0+3AtSWoxA8k2tVRcIl/Ik1vKsbC0sOaUK6y/T73jlkNEdZio\nd4milp5UD73pXnrSPTWXh7qH2D+wv2ag6MuEUFFvW1+6z/AgSR3AQFJDqVRisbhIvpAnX8izWFhZ\nLpcVa5TV2C9fyJMr5Mgt5cgVcuUQkSvUWF/Krb1/bHuxtLFHwcelEim6U92rpmwyW7Hen+lnT++e\n8ra1wsRay73pXrLJrJcsJEnr2vGB5L7P3gdfoyJALBWXNuVnJ7uSZJIZsqks2WS2PK8uyyQzZJNZ\nhrqHQtka+9Qq60n31AwWFaEjlfWWTknSVWvHn6E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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3e81fd7650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3e56ecb090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KVkpAmQIcBvytwmWRJEkCSpsH5c/AFpUuiCRJUs5ga1C2T/1+EXAuMAl4mN6jeR6uQLkk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\nc94ArEuEs/fQXdORX943U7/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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3e56e72690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3e56e19350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#GA con ajuste polinomial de grado 10 por cada angulo. 4x10-> 40 genes reales.\n",
    "#Inicio aleatoria entre -20 y 20\n",
    "from __future__ import division\n",
    "from ThePablos import *\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "from deap import base, creator, tools, algorithms\n",
    "import time\n",
    "%matplotlib inline\n",
    "\n",
    "####---------------------- PARAMETROS ---------------------- #####\n",
    "\n",
    "#Arreglos para iterar\n",
    "lam = [0.5, 0.1, 0.05, 0.01, 0.005, 0.001]\n",
    "Pmc = [0.5, 0.4, 0.3, 0.2, 0.1, 0.05]\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "#Posiciones en que se discretizan los caminos\n",
    "Npos = 20\n",
    "#Numero de generaciones\n",
    "Ng = 100\n",
    "#Numero de individuos en la poblacion\n",
    "Npop = 500\n",
    "#Duracion del movimiento\n",
    "t_mov = 1\n",
    "#Ponderacion de la energia en el fitness\n",
    "lam = 0.01\n",
    "\n",
    "n_coef = 10 #ind_size = 4*n_coef, grado 10\n",
    "\n",
    "#Probabilidades de recombinacion y mutacion\n",
    "Pci = 0.9 #cada individuo\n",
    "Pcc = 0.9 #cada atributo\n",
    "Pmi = 0.5\n",
    "Pmc = 0.1\n",
    "\n",
    "cotainf = np.array([-180,-90,-90,-90])*np.pi/180\n",
    "cotamax = np.array([180,90,90,90])*np.pi/180\n",
    "l1 = 1\n",
    "l2 = 1\n",
    "l3 = 1\n",
    "l4 = 1\n",
    "r = 1e-2\n",
    "\n",
    "#configuracion inicial de angulos\n",
    "condborde=np.array([90, -30, 30, -20])*np.pi/180\n",
    "\n",
    "#Posicion target\n",
    "#x,y,z plano cartesiano\n",
    "#finalpos=np.array([1.93, 1.93, 1.0])\n",
    "finalpos = np.array([1.0, 1.0, 2.0])\n",
    "#finalpos=np.array([0, 0, 0])\n",
    "\n",
    "#Crossover y MUt\n",
    "eta_cx = 2 #SimulatedBinary\n",
    "alpha_cx = 0.5 #Blend BLX-0.5\n",
    "sigmaMut = 0.1\n",
    "\n",
    "\n",
    "#Simulador de robot\n",
    "robotArm = ThePablos(l1, l2, l3, l4, r, t_mov)\n",
    "\n",
    "\n",
    "#FUNCIONES AUXILIARES\n",
    "def checkBoundis(individual):\n",
    "    global cotainf\n",
    "    global cotamax\n",
    "    thetaAux = getPathFromInd(individual) - condborde.reshape((4,1))\n",
    "    cotainfAux = cotainf - condborde\n",
    "    cotamaxAux = cotamax - condborde\n",
    "    for i in range(4):\n",
    "        factor = 1\n",
    "        for k in range(Npos): \n",
    "            \n",
    "            if thetaAux[i,k] > cotamaxAux[i]:\n",
    "                factorTemp = cotamaxAux[i]/thetaAux[i,k]\n",
    "                if factorTemp < factor: factor = factorTemp\n",
    "                    \n",
    "            elif thetaAux[i,k] < cotainfAux[i]:\n",
    "                factorTemp = cotainfAux[i]/thetaAux[i,k]\n",
    "                if factorTemp < factor: factor = factorTemp \n",
    "        individual[ i*n_coef:(i*n_coef+Npos)] = individual[i*n_coef:(i*n_coef+Npos)] *factor       \n",
    "    return individual\n",
    "    \n",
    "\n",
    "def kernel(X,Y,sigma):\n",
    "    return  np.exp( -sum((X-Y)**2) / (2*sigma**2) )\n",
    "\n",
    "\n",
    "#CONVERTIR INDIVIDUO A TRAYECTORIA\n",
    "def getPathFromInd(individual):\n",
    "    global Npos\n",
    "    global t_mov\n",
    "    global condborde\n",
    "    global n_coef    \n",
    "    \n",
    "    t1 = np.ones(Npos)*condborde[0]\n",
    "    t2 = np.ones(Npos)*condborde[1]\n",
    "    t3 = np.ones(Npos)*condborde[2]\n",
    "    t4 = np.ones(Npos)*condborde[3]\n",
    "    theta = np.vstack([t1,t2,t3,t4])\n",
    "    for i in range(4):    \n",
    "        for k in range(Npos):\n",
    "            for j in range(0,n_coef):\n",
    "                theta[i,k] += individual[i*n_coef+j]*((k*t_mov/Npos)**(j+1))\n",
    "    return theta    \n",
    "\n",
    "#Calculo del fitness a partir del path\n",
    "def evaluatePath(theta):\n",
    "    global finalpos\n",
    "    global robotArm\n",
    "    global lam\n",
    "    global en_scale\n",
    "    \n",
    "    robotArm.setPath(theta[0], theta[1], theta[2], theta[3])\n",
    "    robotArm.angularCons()\n",
    "    finalGenerado = robotArm.endPoint()\n",
    "    energia = robotArm.getEnergySim()\n",
    "    \n",
    "    fitness1 = mse(finalGenerado, finalpos)\n",
    "    #fitness1 = 1/(1+mse(finalGenerado, finalpos))\n",
    "    #fitness1 = kernel(finalGenerado, finalpos,5)\n",
    "    \n",
    "    fitness2 = energia\n",
    "    #fitness2 = 1/(1+energia)\n",
    "    #fitness2 = kernel(np.array([energia]), np.zeros(1),sigmaEnergy)\n",
    "    \n",
    "    return fitness,\n",
    "\n",
    "\n",
    "#EVALUAR INDIVIDUO\n",
    "def evaluate(individual):\n",
    "    theta = getPathFromInd(individual)\n",
    "    return evaluatePath(theta)\n",
    "\n",
    "def kernel(X,Y,sigma):\n",
    "    k =  np.exp(-sum((X-Y)**2) / 2*sigma**2)\n",
    "    return k\n",
    "\n",
    "def mse(x,y):\n",
    "    return sum(abs((x-y)**2))\n",
    " \n",
    "\n",
    "#Registro de fitness\n",
    "#creator.create(\"FitnessMulti\", base.Fitness, weights=(1.0,)) #maximizar\n",
    "creator.create(\"FitnessMulti\", base.Fitness, weights=(-1.0,)) #minimizar\n",
    "creator.create(\"Individual\", np.ndarray, fitness=creator.FitnessMulti)\n",
    "\n",
    "#Asignacion de funciones para crear individuos\n",
    "toolbox = base.Toolbox()\n",
    "toolbox.register(\"attr_real\", random.uniform, 0, 1)\n",
    "toolbox.register(\"individual\", tools.initRepeat, creator.Individual, toolbox.attr_real, n=4*n_coef)\n",
    "#Un individuo es un arreglo de coeficientes\n",
    "\n",
    "#Asignacion de funciones para crear la poblacion\n",
    "toolbox.register(\"population\", tools.initRepeat, list, toolbox.individual)    \n",
    "    \n",
    "#Asignacion de operadores    \n",
    "toolbox.register(\"evaluate\", evaluate)\n",
    "#toolbox.register(\"mate\", tools.cxBlend, alpha=alpha_cx)\n",
    "toolbox.register(\"mate\", tools.cxSimulatedBinary, eta=eta_cx)\n",
    "toolbox.register(\"mutate\", tools.mutGaussian, mu=0, sigma=sigmaMut, indpb=Pmc)\n",
    "toolbox.register(\"select\", tools.selTournament, tournsize=3)\n",
    "toolbox.register(\"checki\", checkBoundis)\n",
    "\n",
    "print \"Hasta aquí pudo correr\"\n",
    "\n",
    "####---------------------- ALGORITMO GENETICO ----------------------- #####\n",
    "\n",
    "\n",
    "def main():\n",
    "    startToooodo = time.clock()\n",
    "    pop = toolbox.population(n=Npop)\n",
    "    for ind in pop:\n",
    "        toolbox.checki(ind)\n",
    "    print(\"Start of evolution\")\n",
    "     # Evaluate the entire population\n",
    "    fitnesses = list(map(toolbox.evaluate, pop))\n",
    "    for ind, fit in zip(pop, fitnesses):\n",
    "        ind.fitness.values = fit\n",
    "    print(\"  Evaluated %i individuals\" % len(pop))\n",
    "    \n",
    "    max1 = np.zeros(Ng)\n",
    "    min1 = np.zeros(Ng)\n",
    "    prom1 = np.zeros(Ng)\n",
    "    max2 = np.zeros(Ng)\n",
    "    min2 = np.zeros(Ng)\n",
    "    prom2 = np.zeros(Ng)\n",
    "    \n",
    "    # Begin the evolution\n",
    "    for g in range(Ng):\n",
    "        \n",
    "        #print(\"-- Generation %i --\" % g)\n",
    "        #start = time.clock()\n",
    "        \n",
    "        # Select the next generation individuals\n",
    "        offspring = toolbox.select(pop, len(pop))\n",
    "        # Clone the selected individuals\n",
    "        offspring = list(map(toolbox.clone, offspring))\n",
    "        besties = tools.selBest(pop, 1)\n",
    "        best1 = besties[0]\n",
    "        # Apply crossover and mutation on the offspring\n",
    "        for child1, child2 in zip(offspring[::2], offspring[1::2]):\n",
    "            # cross two individuals with probability CXPB\n",
    "            if random.random() < Pci:\n",
    "                toolbox.mate(child1, child2)\n",
    "                # fitness values of the children\n",
    "                # must be recalculated later\n",
    "                toolbox.checki(child1)\n",
    "                toolbox.checki(child1)\n",
    "                del child1.fitness.values\n",
    "                del child2.fitness.values\n",
    "        \n",
    "        for mutant in offspring:\n",
    "            #    mutate an individual with probability MUTPB\n",
    "            if random.random() < Pmi:\n",
    "                toolbox.mutate(mutant)\n",
    "                toolbox.checki(mutant)\n",
    "                del mutant.fitness.values\n",
    "                \n",
    "        # Evaluate the individuals with an invalid fitness\n",
    "        invalid_ind = [ind for ind in offspring if not ind.fitness.valid]\n",
    "        fitnesses = map(toolbox.evaluate, invalid_ind)\n",
    "        for ind, fit in zip(invalid_ind, fitnesses):\n",
    "            ind.fitness.values = fit \n",
    "        \n",
    "        #print(\"  Evaluated %i individuals\" % len(invalid_ind))\n",
    "         # The population is entirely replaced by the offspring\n",
    "        pop[:] = offspring\n",
    "        indaux = np.random.randint(0, len(pop))\n",
    "        pop[indaux] = best1 #Elitismo\n",
    "        \n",
    "        fits1 = [ind.fitness.values[0] for ind in pop]\n",
    "        #fits2 = [ind.fitness.values[1] for ind in pop]\n",
    "        length = len(pop)\n",
    "        max1[g]= np.max(fits1)\n",
    "        #max2[g] = np.max(fits2)\n",
    "        min1[g] = np.min(fits1)\n",
    "        #min2[g] = np.min(fits2)\n",
    "        prom1[g] = np.sum(fits1) /length\n",
    "        #prom2[g] = np.sum(fits2)/ length\n",
    "        \n",
    "        #end = time.clock()\n",
    "        #print \"Time Elapsed: \"\n",
    "        #print(end-start)\n",
    "        #print \"\"\n",
    "    print(\"-- End of (successful) evolution --\")\n",
    "    \n",
    "    best_ind = tools.selBest(pop, 1)[0]\n",
    "    #print(\"Best individual is %s, %s\" % (best_ind, best_ind.fitness.values))\n",
    "    endToooodo = time.clock()\n",
    "    print \"Time Elapsed: \"\n",
    "    print(endToooodo-startToooodo)\n",
    "    print \"\"\n",
    "    #return best_ind, max1, max2, min1, min2, prom1, prom2\n",
    "    return best_ind, max1, min1, prom1\n",
    "    \n",
    "\n",
    "####---------------------- VISUALIZACION DE RESULTADOS ----------------------- #####    \n",
    "    \n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    #best, max1, max2, min1, min2, prom1, prom2 = main()\n",
    "    best, max1, min1, prom1 = main()\n",
    "    tiempo = np.linspace(0.0,t_mov,num=Npos)\n",
    "    thetaWin = getPathFromInd(best)\n",
    "    thetaWinA = thetaWin[0]\n",
    "    thetaWinB = thetaWin[1]\n",
    "    thetaWinC = thetaWin[2]\n",
    "    thetaWinD = thetaWin[3]\n",
    "    robotArm.setPath(thetaWinA, thetaWinB, thetaWinC, thetaWinD)\n",
    "    robotArm.angularCons()\n",
    "    \n",
    "    #Trayectoria\n",
    "    \n",
    "    plt.figure(1)\n",
    "    plt.plot(tiempo, thetaWinA*180/np.pi, label=\"theta1\")\n",
    "    plt.plot(tiempo, thetaWinB*180/np.pi, label=\"theta2\")\n",
    "    plt.plot(tiempo, thetaWinC*180/np.pi, label=\"theta3\")\n",
    "    plt.plot(tiempo, thetaWinD*180/np.pi, label=\"theta4\")\n",
    "    plt.xlabel(\"Time\")\n",
    "    plt.ylabel(\"Angle\")\n",
    "    plt.legend(loc='upper center', bbox_to_anchor=(0.5, 1.05),\n",
    "          ncol=4, fancybox=True, shadow=True, prop={'size':8})\n",
    "    \n",
    "    #Evolucion fitness\n",
    "    \n",
    "    lablox = range(Ng)\n",
    "    plt.figure(2)\n",
    "    #plt.subplot(211)\n",
    "    plt.plot(lablox,max1, label = \"Maximo\")\n",
    "    #plt.plot(lablox,min1, label = \"Minimo\")\n",
    "    #plt.plot(lablox,prom1, label = \"Promedio\")\n",
    "    plt.xlabel(\"Time\")\n",
    "    plt.ylabel(\"Fitness\")\n",
    "    plt.title(\"Fitness Evolution\")\n",
    "    #plt.legend(loc=\"lower left\")\n",
    "    \n",
    "    #plt.subplot(212)\n",
    "    #plt.plot(lablox,max2, label = \"Maximo\")\n",
    "    #plt.plot(lablox,min2, label = \"Minimo\")\n",
    "    #plt.plot(lablox,prom2, label = \"Promedio\")\n",
    "    #plt.xlabel(\"Time\")\n",
    "    #plt.ylabel(\"Fitness2\")\n",
    "    #plt.title(\"Fitness Evolution\")\n",
    "    #plt.legend(loc=\"lower left\")\n",
    "    \n",
    "    \n",
    "    finalGenerado = robotArm.endPoint()\n",
    "    energia = robotArm.getEnergySim()\n",
    "    print(\"-- Punto final generado --\")\n",
    "    print finalGenerado\n",
    "    print(\"-- Punto final real --\")\n",
    "    print finalpos\n",
    "    print(\"-- Error --\")\n",
    "    print mse(finalGenerado,finalpos)\n",
    "    print(\"-- Energia --\")\n",
    "    print energia\n",
    "    \n",
    "    #Posicion inicial robot\n",
    "    plt.figure(3)\n",
    "    puntitos = robotArm.getExtremos(0)\n",
    "    dataR = puntitos[0]\n",
    "    dataZ = puntitos[1]\n",
    "    plots = [ plt.plot(dataR[i:i+2],dataZ[i:i+2]) for i in range(3)  ]\n",
    "    plt.plot(dataR[-1],dataZ[-1],'o',alpha=0.5)\n",
    "    plt.xlim([0,3])\n",
    "    plt.ylim([-1,3])\n",
    "    plt.xlabel(\"Radial Distance\")\n",
    "    plt.ylabel(\"Height\")\n",
    "    plt.title(\"Initial Position\")\n",
    "    \n",
    "    #Posicion final robot\n",
    "    plt.figure(4)\n",
    "    puntitos = robotArm.getExtremos(-1)\n",
    "    dataR = puntitos[0]\n",
    "    dataZ = puntitos[1]\n",
    "    plots = [ plt.plot(dataR[i:i+2],dataZ[i:i+2]) for i in range(3)  ]\n",
    "    rDeseado = np.sqrt(finalpos[0]**2+finalpos[1]**2)\n",
    "    zDeseado = finalpos[2]\n",
    "    plt.plot(dataR[-1],dataZ[-1],'o',alpha=0.5)\n",
    "    plt.plot(rDeseado,zDeseado,'s',alpha=0.5)\n",
    "    plt.xlim([0,3])\n",
    "    plt.ylim([-1,3])\n",
    "    plt.xlabel(\"Radial Distance\")\n",
    "    plt.ylabel(\"Height\")\n",
    "    plt.title(\"Final Position\")\n",
    "    \n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "file = open(\"newfile.txt\", \"a\")\n",
    "\n",
    "file.write(\"This is a test\\n\")\n",
    "\n",
    "file.write(\"And here is another line\\n\")\n",
    "\n",
    "file.close()"
   ]
  }
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