examples/nlopt_optimizers.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "6a7a0c24",
   "metadata": {},
   "source": [
    "# Using NLopt optimizers"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f24ebd0",
   "metadata": {},
   "source": [
    "We have an interface to [NLopt](https://nlopt.readthedocs.io/en/latest/).\n",
    "\n",
    "NLopt is a free open-source library that provides a lot of optimizers of different kinds.\n",
    "There are global and local optimizers, gradient or gradient-free.\n",
    "For a full list, see [here](https://nlopt.readthedocs.io/en/latest/NLopt_Algorithms/)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27a95aef",
   "metadata": {},
   "source": [
    "To illustrate the interface, we import the usual example on GPR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ea0d0123",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "\n",
    "os.environ[\"CUDA_VISIBLE_DEVICES\"] = str(0)\n",
    "\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "\n",
    "from gpx.models import GPR\n",
    "from gpx.kernels import SquaredExponential\n",
    "from gpx.parameters import Parameter\n",
    "from gpx.priors import NormalPrior\n",
    "from gpx.bijectors import Softplus, Identity\n",
    "\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.style.use(\"dark_background\")\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "63dd79de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jax.config.x64_enabled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7c4b3e1a",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
     ]
    }
   ],
   "source": [
    "train_x = jnp.linspace(0, 1, 100)\n",
    "key = jax.random.PRNGKey(0)\n",
    "train_y = jnp.sin(train_x * (2 * jnp.pi)) + jax.random.normal(\n",
    "    key, shape=train_x.shape\n",
    ") * jnp.sqrt(0.04)\n",
    "test_x = jnp.linspace(-0.5, 1.5, 51)\n",
    "test_f = jnp.sin(test_x * (2 * jnp.pi))\n",
    "\n",
    "train_x = train_x.reshape(-1, 1)\n",
    "train_y = train_y.reshape(-1, 1)\n",
    "test_x = test_x.reshape(-1, 1)\n",
    "test_f = test_f.reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "899d4ee3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2b27309a97b0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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vaNq0KS3YJRbP2toK/+36DOHhwcjNLcSpiw9h16E7HhdbIavMGgzSOXjZDqWNs+ch5dw5rFr1Bqa+NgQAcP36Q0yJXIVz524rdLCm5ouEaGbkyF7Ytv0TCAQCxMffwNEjiTh16jri42/iyRPl23+ff7431q57F56eLqisrMJXX27FV1/9RWthatHm81uvyYuDgwPatm0LALh06RJmzZqFuLg4ZGdn4+HDh1iyZAmaN28ur+XSunVrJCUl4ccff8T69esxaNAgfP/99xg+fLjGW6UpeSHmiMfjYcPGWXj11YEoKirFoEGfIuKrFWpbAHwV8QKYRILhw3ti3S/vwdu7KSorqxC99RzSvHpCWGOksyg3D8c3b8WhXzZSEkOIEiEh/jgU+yWaNLHFb78ewLRpP2h8X1dXEX6Megfjx/cDAFy8mIwpkauQlJSir3BNjtEkL6GhoThy5Eid6zds2ICpU6ciOjoarVu3xsCBAxXus2rVKnTq1AmPHj3CF198gY0bN2r8nJS8EHNQe1Rk2ouB+PjjF1BRUYnnR36BO08YpkdHqX2cqKnT5QuAmzYV4vsf3sLLL4cCADJLBIhJFSKzVHH2uCgnF38vWkbbswmpQbZ2xdVVhF27zmLsmK9QVaV9kj9+fD/8GPUOXF1FKC+vwOcL/8DXX29r0GOZG6NJXrhAyQsxdbXrvQS5lmCAdxEAYErkKmzadBhBw4Zg0orFah9r88cLFJo58vh8/J6wDc93soK9FUOVBPj7nhPSSqzlxzDGAAZqI0BINW/vpjgV/zV8fDxw+vQNDA6b36gdfJ6ezvh57bsYNeoZAMAffxzFpFe+0VW4Jkubz2/qbUSIEQkIC0XkyqVw8nAHALQXlSHUS5q4HE+zR0KqdI68of2QfIMDkcb3xKbbLrhfYA0BHxjSvBAC3tPvMLL6FaPmzFQ6JUWIJXFycsC+/Z/Dx8cDN28+wsgRXzS69IBYnIsxo7/ClMhVqKioxMsvh2Ls2D46itgy0DsTIUaCx+dj9NxZABh4fD5aOJQjvEUBeDwg4YkdzmXayhOKhvZDknWmLqniY+9DIYoqeHC1q0Jv9+JasfDg4u0F3+BAvZwrIabAxsYK27Z/gq5d2yAtLRsR4QtVLsptiE2bDmP5sn8AAGt+fFtlyQNSFyUvhBgJ3+BAOHt5gsfnw82uEs+3KoAVH7iVZ4OjaQ7g8QXyhELWDwng1UlgZLuNzvz7H7qFh8GvR5B8BKXmSEyZhI/Yx9I3y57uJXC3q1t/QpbsEGJpeDweNv3v/zBwYFfk5xfjuWGfIyUlQ+fP8+WXW3Ht2gN4ebng25Vv6PzxzRUlL4QYCVmiILKuwhiffNgKGB4WWWH/I6F8GzQAdB7YH4C0ncDG2fOQl6HYI6QoLw/FeXmIeO9NTFqxGNOjozA/ZhsCwkLrjNgkF9jiVp4N+DxgaPMC8GstgdN0eooQc7Nq1RsYP74fyssrMGb0V7h8+Z5enqe8vBJvvP49JBIJpkwJw9ChQXp5HnNDC3YJ4UjtHUU8Ph+zNnyPCb55aGpbhaxSAf6664QyieJ3DMYYNs56upi25uO4tWqB8OnTIJt6kt+nRu0XAIhcuRTgSb9d2gskmNwuB02sGE6k2+Ncln2drdaEWJKPPhqL5SumAgBemrgCW7ce1/tzrlr1BmbMHIWUlAwEdHkPhYUlen9OY0O7jSh5IUZOWQfp3HQxIrtbwdeFIb+cjy13nVBUKahzX1WJBY/Px/yYbRrVfukysD9eXDgXDi7OAICOzqWIaFGISgnwv9tOyCmzot1GxCINHRqE/THSnXyzZ/2K1atVF1bVJXt7W1xJXANfXy/8uGY33n9/rUGe15jQbiNCjFjtHUXy632d4evCUCkBtqeIlCYugDRJUbaYtuaaGXX3S4w9ioUDhmP/mnUoys3D9Vxb3CuwhhUfCPPMxab/o8SFWB4ej4ely6RFU3/+aa/BEhcAKC4uw5vVRe/efW8E+vXrZLDnNkWUvBBiQLV3FD3F0NdLOkycIBYgu0x927Hai2k1XVwrO45JJDi4NhoLQ59D1NR38d57a1FYVIZWzjw860/d2YnleeGFPggK8kN+fjHmz99s8Oc/fPgKfvtVWk3+l1/fh52djcFjMBWUvBBiQKpGR3yF5fC2r0SFBLiY66TRY9VeTNvQ2i9MIkHy+QTs27QdH3/4GwBgydLJ8PHx0OjxeHw+/HoEIWjYEIWdTYSYEj6fj0WLXwEArFq5A9nZ3Cw7+PDD9UhNfYIOHVpgwYKJnMRgCuhdhhADUj46whDiIa2zkvCkCYqr+CjKzdO6hktDa7/UtHbtfhw9mgRHxyZYu+49tecTEBaK+THbMD06qs7OJkJMycsvh6Jjx5Z48iQfq1YZbrqotry8Ikx/R9r648OPxiIoyI+zWIwZJS+EGJCy0ZH2onJ4NKlCWRUP57OaAACOb96K+mq47Fy+Wult6mq/KLufwnGMYdob36OkpAxDhwZhypQwlceqWrvj5OGOyJVLKYEhJsPKSoCFn78EAPh6xTbk5xeruYd+7dp1Flu2HIOVlQC/rf8AVlbK179ZMkpeCDGg2qMjPDCEeErfKC9kNUFpBZCTlo5Dv2xUWsMlV5xR7y4gVbVfcsUZiIn6BVY2Nmqndu7cScPCBb8DAL5d+Qa8vFzqHKN67Q6qf2bUXoCYjKlTB8PPzxvp6TlYs2Y31+EAAGZ8sA5ZWfno1s0XH3/8AtfhGB3aKk2IgclGLACGzk3LEd6iECWVPPx2wxnlEr5CclK7Fszdi5c1qrtSu/bLM+NG1dmWvWPZKpVJkEDAR/zpb9CjRzts23YK415YqnC7X48grbtaE2KMbG2tcev2WrRs6Y4ZH6zDDz/s4jokuZdfDsXm3z9EWVkFgoNm4Pr1h1yHpFe0VZoQIyYbHSnMzMQz1Wtdzmc1QUZaZp1RFdli2oR9B5F8PkHjgnGy+1WWlyN8+jStp3aqqiR4/bXvUVFRibFj+9Sp+qntziZCjNVbb0WgZUt3PHyYiXXr9nMdjoI//jiK3bvPwdbWGqu/m8Z1OEaFkhdCOJAYexRp/6yFk40EWdlFmD5uHr6KeEGntVUaO7WTmHgfUT/uAQDMnDVK4baG7mwixJjY29ti3icvAgC+WLwFZWUVHEdU1/vv/YzKyioMGRKELl18uA7HaFDyQggHbG2t8emn4wEAixduxtWTZ3Vehl+bonWqfPfdLlRVVSEiojv8/VvIr9fFziZCuPb++yPh6emC5OQ0bNgQy3U4SqWkZGDbtngAwIwZz3McjfGg5IUQDrz99jC0aOGGBw/0N1Sti6md+/fF+O+/swCADz4YKb9eFzubCOGSSGSPjz4eCwBY9PmfqKys4jgi1b7/7j8AwMuvhMLVVcRxNMaBkhdCDMxRaI/5C6TbMn/edBIVlfr5gNfV1I7sjfPVyYPg4uIov76+nU3UF4kYu9mzR6NpUyGuXXuAP/4w7t/VU6eu4/z522jSxBZvvhnOdThGgXYbEaKhhuz8qX0fexdnfBs1E4Pb8pFbxsfG2y7ITs+od+dPY+LVtFGjuvNIuPQ9AgPbYM7H0fj66231nqOmO6II4YqrqwjJd3+BSGSPF8ctxb//nuI6JLUmTRqITf+bjdTUJ2jT+nWjHilqKOoqTckL0TFVXaDrSzqU3ceGV4XX/XNhJ2DY99ARN/Ls5NMs+hitqLktu2YCo+1zTpkShvXRM/HgQSb8fN9AVRUlJ8R0LVsWiY/njMPFi8no2WMWGDP+j0EbGyvcu/8bvL2b4uWXvsaWLce4DknnaKs0ITrUkEqyqu7T3a0UdgKGJ6UC3MyzBaDfom66mtr5889jyMjIRatW7hgztg/1MiImy8vLBe+9L12/teCzzSaRuABAeXklfv5pHwDggxkj1Rxt/mjkhZB6NGTqRdV97AQSvN4+BzYChl0PhLiTb1vn8fRV1E0XUzuLF7+C+Z9NREoOw7bUp0lZfSNQNKVEjM13372J9z8Yifj4G+jb5yOuw9GKh4czUh6sh62tNUKe+RBnztzkOiSdopEXQnSkIduNVd2np1sJbAQM4hIB7uQrb3Wvr6JuDS12V9ORpBxUMcDHhQcPu0r59apGoKhpIzE2LVu64823IgAA8z/9H8fRaC8jIxd//imdLrL00RdKXgipR0O2Gyu7jxWPIaBpKQAgXuwA6aBnXcZa1I3H56PvtDdxK1eadAW5lijcVnvai5o2EmP0zjvDYGtrjbi4K4iLu8J1OA0i2/03blxfNGvWlONouEPJCyH1aMh2Y2X3aedUBlsBQ245H/cKrevcbuxF3fx6BMHZyxMJ2dKu1x2cymBv9XT0puYIFDVtJMZIIOBjcuQgAMCaH4yj+WJDXLp0F0ePJsHa2grTpw/nOhzO0LsHIfVoSCVZZffp5FwGALiWY4fa6wONvahbQFgoJn/7FQBAXGKNx8VWEPCBwKYldY4VubvppLIvIbo2dGgQmjVzRWZmHnbvPsd1OI0iG315860I2Nkpn4I2d5S8EFKPhlSSrX0fkXUVWjlWgDHganbdURdjLuomm/6xFwnl1yVkSUdfApqWQsBTzMTyM7OoaSMxSlOmDgYA/PH7EVRUVKo52rjt3HkG9++L4eYmwiuvDOA6HE5Q8kKIGg3ZblzzPp1dpGtdHhRZ4+GjJ9g0+xNETZ2OzR8vQNTU6TpvyKgrqqZ/7uTboKCCDwcrhg5O0hGlmiNQ1LSRGBtXVxFGjeoNAIiOPsRxNI0nkUjkU1+WunDXiusACDEFibFHkRR3XKttv4mxR3H1yAlMexANwAWrl/6B75dtNsqpIWVk0z+1ScDD5Sd26OdVjG6uJbiabYOaI1CyaTN128uNdX0PMT8vvxwKGxtrXLhwB1eu3Oc6HJ347beD+HzRywgIaI2BA7ua7ALkhqKRF0I01JDtxgNCO6NFMxfk5hZi7cotJpO4APVP6yTm2KFCAng2qYIby1MYgaKmjcTYTJkaBgDYYAajLjJ5eUXYtPEwAGDGTMvrNk3JCyF6NPW1IQCALX8eQ2lpOcfRaKe+aZ3SKj5u5EqL7Hk+Sawz7UVNG4mx6NbNF0FBfigrqzD6Boza+v77XQCAESN6wtfXi+NoDIumjQjREycnB4wdGwIAWL/e9L7xqZv+uZhpi4CmZRgc2gE+Ph5ISclQuL0hU22E6NrU6oW6O3eeQU5OIcfR6NatW6nYu/c8nnuuB95/fwRmzfqV65AMhkZeCNGTCRP6o0kTWyQlpeD8+dsqj+Px+UbZK0jd9M+TMmtcvC6GQCDAp1++pnJ9S2Mr+xLSUDY2Vnj5FWlBxOj1BzmORj9k26anvjYEQmETjqMxHON4lyTEDE19TfqNr755dmMvoa9q+qcoLw/FeXl4YN8OADDppX5YfMh44iYEAEaO7AVXVxEePcrCwYOXuA5HLw4cSMD16w8hEtnLR5ksASUvhCjR2NGQjh1bonfvDqioqMTmzUeUHmMqJfQTY4/iy/Cx8u3d+9esg4OTM+ydRLhXYI2cMj7sBAw92oo0ittYR5qI+ZGtOfvfpsOQmPGo3w/Va19kfZssAa15IaSWgLBQjJ47S2GbcH2dk5WRfQPas+c8MjJy69yuroQ+k0gwas5MJMUdN4qpFtn0j6xjds24r+Xaoa9nMTo4l+Nqjm29cevi35YQTTRr1hTh4UEAzKO2S33++OMoVq2ehk6dWqFLFx8kJaVwHZLe0VceQmrQxWiIlZUAr04eCED1lJGpltBXFvfNPOmuo1aOFbC3hsq4TWWkiZiHV18dBIFAgOPHr+LOnTSuw9Gr/Pxi7N17HgAwceKzHEdjGJS8EFJNVw0Fhw3rDk9PF4jFOfI3lNpMtYS+snjyygUQl1iBz5M2oFR2HDVrJIamyZozc/LX1uMAgAkT+3MciWHQOwUh1XQ1GiLrobL5f0dQWVml9BhTLaGvKp6budLmcLJ2AbWPM9WRJmKa+vTpiPbtm6OoqBR//32S63AMYteusygqKoWfnzd69GjHdTh6R8kLIdV0MRri7u6EESN6Aqh/nr0h3aqNgaq4b+VLp46a21eiMrtu3KY60kRMk2zN2V9/nUBhYd3u5+aouLgMu3adBSAt02DuKHkhpJouRkMmvToQ1tZWSLqZjjJ7V5UjDaZaQl9V3AUVAqQWWYHHA1jSsTpxm+pIEzE99va2GD+hHwDLmTKS2bpFOnU0fkI/8Hg8jqPRL0peCKnW2NGQgLBQfLzoNQCA2NFPbc0WUy2hryruSw+lU0bPBjercx9THWkipmfcuL4QCu1x585jHD9+letwDGr//gvIyytCy5bu6NOnI9fh6BVtlSakmmxUIXLlUjCJRGHUpL7REB6fj8HTIjH5w6nwdMxDpeTpDhzZThpVyYipltBXFndRagoePlyPZ57xR+vWnrh/Xyw/vqH/toRoS7bmbOOGWI4jMbyysgrs2HEakZFhmDChH06evMZ1SHpDIy+E1KDtaIisQm7Ee2+ii4t05OF2vi3KJNI/LU120phqCf3acaenZePIkSQAwPjx/eocb6ojTcR0+Pp6YcCAAEgkEmys7rhsaWRTRy+O7weBwHw/4mnkhZBaNB0NkdUtARgEPIYOztLk5VqOrcJxNXfSJJ9PMNRpGByPz0fcmfsICwvE5NfC8fU32+v8m5nqSBMxDVOmhAEADh68hEePLHP91KFDl/DkST48PV0QGtoFhw9f4TokvTDftIyQRlA3GlK7bklbUTnsBAz55Xw8KLJW+pjmvJNGNgLVfMxUVDGgUwdvrDqufL2PqY40EePG5/MxOVKavFjaQt2aKiursO3fUwDMe9cRJS+ENEDtuiWdnEsBANdybQEoX+VvrjtpalbOLa3i40GhNHnr4etIlXOJwQwcGIBWrdyRk1OIHTtOcx0Op7ZUTx2NfaEPrK3Nc4KFkhdCGqDmKIqdQIJWjhUApH1+ajPnnTTKKufeql6s3MG5HICEKucSg5Cts/pr63GUlVVwHA23jh5NQnp6DlxdRRg82DwLP9I7CiENUHMUxVdYDj4PyCgRIK9coHAckzAYcieNoTs2K6uceyffBpUSwNWuCm5NGFXOJXrH5/Px/KjeAIB/q6dMLJlEIsE/f58AAIw306kjSl4IaYCadUvaisoBAMn5tnWOM+ROGtm6k+nRUZi0YrHaOjO6oGwdT7mEj/uFiu0CzHm9D+FeSIg/PD1dkJNTiCNHErkOxyjIpo7GjAmBra3ydXimjJIXQuqhaiRDVrfEigf4OEqTlzv5NvLbmIRh/5p1+CpirMESFy46NqvsdSSfOioDwMx2vQ8xDmPGPAMA2L37nMp+YpYmPv4GHj7MhEhkj2HDunMdjs5R8kKICupGMhJjj+L+tmhY8YHccj6yyqRTRrLRloNrow02VcRVx2ZVlXPv5tugQgI420jQpEhslut9iPEYPSYEALBjezzHkRgPxhj+2mq+U0eUvBCihKYjGcF+IgDAv38fx+aPFyJq6nR8FfGCQQuucdmxWVWvo0rGQ3L1SFSTFNoOTfSna9fW8PX1QklJGWJiLnIdjlHZsuUYAGDkyF6wt687rW3KKHkhpBZNRzJsbG3kHaQ3/PQfZ3VLuO7YrKpy7sX70m6+g0Jam32TOMKdMdWjLjExCSguLuM4GuNy4cId3LnzGA4Odhg5shfX4eiUQZKX6dOn4969eygpKcHp06fRs2dPlcdGRkaCMaZwKSmxjJbmxDhoOpLx0hvPw9nZEWJxDuLjbxg4yqeMoWNzYuxRfBk+FlFTp2PzxwsQNXU63ugzQd4kLiTEX2/PTSwbTRnVz1ynjvSevIwfPx4rV67EokWLEBwcjMuXLyMmJgbu7u4q75OXlwcvLy/5xcfHR99hEiKn6QjF8GFBAID/dp6BhMNpEWPp2Fy7cm5pSZm8WNjEieb1xkmMQ5s2nggMbIPKyirs3n2O63CMkmzq6LnnekAksuc4Gt3Re/Iye/Zs/PLLL9iwYQOuX7+Ot99+G8XFxXjttddU3ocxBrFYLL9kZGToO0xC5DQboWDo36s1AGD7dm6reapadyK7jcuOzZbSJI5wQzZldOxYErKzCziOxjglJaXg6tUHsLW1xujRz3Adjs7o9d3E2toa3bt3x6FDT/tMMMZw6NAhhISEqLyfo6Mj7t+/jwcPHmDHjh3o1KmTymNtbGwgFAoVLoQ0hiYjGY7FYni6i5CfX4zDh7nfSWOsHZtrN4kjRJeeThlZdjsAdf7aKv0SMWHisxxHojt6TV7c3NxgZWUFsViscL1YLIaXl5fS+9y8eROvvfYaRo0ahUmTJoHP5+PUqVNo3ry50uPnzZuH/Px8+SU1NVXn50EsiyYjGVb3pLsa9uw5h/LySsMHqYSydSeG3vlUm6U0iSOG5+HhjD59pGupLL2XkTpbq5OXwYMD4eoq4jga3TC6cdzTp0/jf//7Hy5fvoxjx45h7NixyMzMxFtvvaX0+KVLl0IkEskvqpIcQrShbiSjX3ALAMb3jc8YOzZbQpM4YnijRvUGn8/HuXO38egRFUGsz61bqbh4MRnW1lYYO1b1rIcp0es7SVZWFiorK+Hp6alwvaenJ9LT0zV6jMrKSiQkJKBt27ZKby8vL0d5eXmjYyWktsTYo0iKOw7f4ECI3N2Qn5mFuxcvo6N/C7Rr1wylpeW4Ka5A0LAh8tuMIVkwNrImcV5eLggLC8T+/Re4DomYgVHV6zdol5Fm/tp6HMHBfhg/oT9++SWG63AaTa8jLxUVFbhw4QLCwsLk1/F4PISFhSE+XrNfOD6fj4CAAKSlpekrTEJUUjaSIStFnlJgjcgfVxusj5Cpkkgk8g8Yc6s1QbghFDZBWJi06OJ2Sl408s8/JwEAzz7bGU5ODhxH03h6nzZauXIlpk2bhsmTJ8Pf3x8//fQTHBwcEB0dDQDYuHEjlixZIj/+s88+w5AhQ9CmTRsEBQVh8+bN8PHxwa+//qrvUAnRyEuThwAAUkodFa7Xdx8hU7Zr11kAwPARqms8EaKp557rAVtba9y48Qg3bjziOhyTcPduOq5dewBrayuEhwdxHU6j6T15+euvv/Dhhx9i8eLFuHTpErp164aIiAj59udWrVrB29tbfryLiwt++eUXXL9+HXv37oVIJEKfPn1w/fp1fYdKiFo+rT3Rqb0XJAy4W6hYblvffYRMWVxcIoqLy9CqlTu6dm3NdTjExFFhuobZU10LZ/gI0x8B5QFgXAehS0KhEPn5+RCJRCgooH3/RLcWf/MO5v/fc3hUZIW/7zmrPC5q6nQkn08wXGAmYMfO+Xj++d6Y/+n/sGTJX1yHQ0yUra01MjI3Qyi0R+9es3Hu3G2uQzIZ/ft3xtFjy6TlCzxe5bS4pjLafH7T10NCtBAxpCsA4E5+/U3O9NVHyFTw+Hz49QhC0LAh8OsRBB6fj900dUR0ICwsEEKhPR49ysL583e4DseknDp1HdnZBXB1FZl8yw7at0iIhtzcRAjq3AwA5B2TVSnIegK/HkEKu5QsZSdSQFgoRs+dBWevp7sMc9PFOPXLLwCA3r3bw93dCZmZeVyFSEyYrKruzh2nwZhZTRzoXVWVBPv2XcArrwzAiBE9cfLkNa5DajBKXgjR0MiRvSAQ8JFWwJBXxgNPybglk0hQlJeHl5YsqPPhvXP5ahTl5pl1QhMQForIlUtRezbaycMdwz79FNduXUWn9l547rke2Lgxlpsgicni8/kY+bx0vQbtMmqYPbvP4ZVXBmD4iJ6YN28j1+E0GCUvhGhItkhw+7+ngODnwSQShYW5suq7Ds7OAKv74T155RLweDz5dbnpYuxYtorTCri6xOPzMXruLACszoJlHp8PJpFALPBAJ0injih5Idrq27cjPDyckZ1dgGPHrnIdjknav/8CKiur0KWLD1q39sT9+2L1dzJCtOaFEA04OjbBkCHdAAA/f/unyuq7xXl5AFP+4V2buW2t9g0OhLOXp8qdVjw+H2nMBQAQHh5E1XaJ1mRTRrt2nUVlZRXH0Zim3NwinDghnS4aYcLrz+jdgxANREQEw87OBnfuPEZSUgqQlFKn+i6Pz8c7v61R+Rg1R12Ap6MRo+bMRFLccZOfQtJkkbK41ApZ2UVwa+qA0NAuOHTokv4DI2Zj9BhZVV3jasthavbsPocBAwIwfERPrFmzm+twGoRGXgjRgLLutbWr7wpdm2r9uDw+Hy7eXvANDtRZrFzJz9SkvwwPh4/dAGDa3/qI4XXr5ovWrT1RXFyGAweoDEFj7K6u9zJgQAAcHZtwHE3DUPJCiBrW1lYYPrwHgPoXCWr24a2cOWytvnvxMnLTxSpHkJhEgpy0dGzZJO2rMoJaBRAtyKaM9u+/gJKSMo6jMW03bz7CnTuPYWtrLZ8ONzWUvBCixqBBXeHk5IC0tGycPn1T5XHqPrzr05jEx1gwiQQ7lq0CwKvzbyBbzLxz+WocPJCA0tJy+Pp6wd+/hdLHUlYnhlg2mjLSrd27pKMvpjoCSu8IhKgh+8b3384z9daVqPfDW8X9ZKMRdy9e1lm8XEqMPapyMfPG2fOQGHsURUWliItLBKC8UWNAWCjmx2zD9OgoanpJAAB+ft4ICGiNiopK7N59lutwzILs3/G54T3qrMczBZS8EKKGNnUlVH14A3UTmJqjEca6WLchIyCJsUfxZfhYRE2djs0fL0DU1On4KuIFhS3he3Yrr7YrqxPj5OGucL257cwi2nm++m/wyJFE5OYWcRyNeTh+/Bry8org6emCHj3ach2O1mi3ESH16NbNF97eTVFYWIIjRxI1uk9i7NE6O5HsXZwx+uMZioXrxBnYuXy10dZ5UVUpV5PaNLLFzKrs3n0Oa358B337doSLiyNycgo1qhNjLjuziHaGPSddcyZrLEgar6KiEjExCRg/vh9Gjuxlcj2iKHkhpB7PVb9pxsZeRnl5pcb3U/bhnRR7VCGhMeYKu/VVyo1cuVQ+BdRQDx5k4sqVe+jatQ0iIrrjzz+PyuvEqFJzZxY1vbQcjo5N8OyznQEAe/ee5zga87Jn91mMH98Pw0f0xIIFv3MdjlZo2oiQekQM6w4A2L/vQqMfq/bWamNNXNSNgAAMo+bMbPQiWtm36BEjpVNHmu64MoedWURzgwZ1hY2NNe7ceYw7d9K4Dses7Nt3ARKJBEFBfmje3JXrcLRCyQuxeKrWdTg7OyAkpAMA6R+5pdCkUq4uatPIak1ERHSHlZVA4x1X5rAzi2humA6/QBBFWVn58h2UprbriKaNiEWrb12Hf9MqCAQCXLv2AA8e1F2Aa64MNQJy5swtZGbmwd3dCS++9jxuPipCYXYOHJydlCZOTCJBrjjDbHZmEc3IRj8t6QuEIe3edRZ9+nTE8BG9sHbtfq7D0RiNvBCLpW5ny8uvDQcA7NtrWW+ahhoBkUgkiE94BACY9eW7eGX5Ijg2dQF4PJPcmUV0r2PHlvDx8UBJSRmOHEniOhyzJBsBDQvriiZNbDmORnOUvBCLpH5dhwSDBkoXCe7bZ1mLBDWtlNvYEZCAsFDwOvQGAPiKyms8Qd2aODXrxBDLIVswf+RIElXV1ZOkpBSkpGSgSRNbDBrUletwNEbJC7FI6tZ1eNozCG15KCouk3dgtRSaVsptzAiILHlMKbBCFQOa2lbB2aZKfhsYQ8GTbGyes1BpnRhiGXS5YJ6oJls8r6xopLGi5IVYJHXrNVoLpSMB5y6narVF2lxoUim3MWTJYwWskFpkDQBoI3w6+sLj8yF0bYr8jEyj3plF9MfRsQn69+8EwPJGPw1t1y7lRSONGS3YJRaHx+dL11bUo7Wj9IM0Ns5y59mVFdvTVW2amsnj3QIbtHKsgK+wHAlPmqg8jlgW2Rbp27dpi7S+HTmSiKKiUjRv7opu3Xxx6dJdrkNSi5IXYlGU7S6qzVYggbe9dLTlf+t2Gio0o6SuUm5D1Vzse7fABgO8i9DcoQI2fAnKJXylxxHLIlvvQlNG+ldWVoGDBy9h9OhnMHJkL5NIXmjaiFgMVbuLau9saWVfBj4PSL6fhQcpGXUehzoeN17NRcF55QI8KRVAwAN8HCsAmF/DSqI92iJtWLtNbOqIRl6IRah3d1GtjqrNrQsA8LHjn+N1Hqcx/X7IU7JFwZErl4JJJLhXYANXuxL4CstxK9catC3asnXq1AqtWrlXb5HWrKcYaRxZ64VevdrD09MZYnEutwGpQV8ZiUVQt7tIZufyVfDm5wGou0iQOh7rVs1FwXcLbABIF0rn0bZoiyerqnvkSBJKS8vVHE10IT09R96cUTZlZ8woeSEWQdOFn81drODl5YKCgmKFLdKG6vdjaRJjj+LL8LFY+PIs5BeUwt6KIXbRp5S4WLhhz1VPGVEjRoPas1s6dTTCBLZM0zstsQiaLvzs0dEDABAbe0Vhi7Sh+v1YIiaR4OaZC9iz+wwAICI8iOOISEPoai2Yo2MT9Osn2yJN610MSVZtd/DgQFhbG/eqEkpeiEXQtGpsr67NANTd4UAdj/UvZv9FAMDQ8GCOIyHaCggLxfyYbZgeHYVJKxZjenQU5sdsa9BUalhYoHyLdHIybZE2pISEu8jIyIVQaI+QEH+uw6kXJS/EImhSNTYu6mc880x7AHW/8VHHY/07cEC6JbtHj7ZwcxNxHA3RlK7XglEXae4wxuR/hxERxv0lgpIXYjHUVY1tblMEgUCAW8liuHXppjD0bah+P5YsPT0Hly7dBZ/Px5AhNHVkCvSxFky2RXovrXfhhKmMgBr3pBYhOlZf1dgvYpYBAPJFrTFpxWIAituga27trflmTB2PdedAzEV06+aLoeFB+PNPWrRr7GRrwVSpuRZMk2KHnTs/3SJ99KjlVrfmkmzkJTjYDx4ezsjIyOU2IBVo5IVYHFnV2IR9B+V9c7oODkXYwC4AgPuF1vJjaw5967vfDwH2V3/rCw8PrlN/hxgfXa8Fk00ZxcUl0hZpjmRm5uHChTsAgKFDjXcElEZeiMXj8fl4+8tZcLBmKK/iIbXYWuE2JpFg1JyZSIo7rtd+PwQ4efI6CgtL4OXlgq5dW+Py5Xtch0Tqoeu1YNRF2jgciLmI7t3bIjwiGJs3x3EdjlI08kIsnm9wIAJaCwEAD4qsIWGK3/hrb4NWNnJDdKOiohKHD18BAEREdOc4GqKOLteCCYW0RdpYyEZAhw4NMtoRUEpeiMUTubuhjVA6RH2/utKrquOI/h2IkS0YNN4hayKlyS4+TdeCybZI37qVSlukORYffwP5+cVwd3dCcLAf1+EoRckLsXi8siJ4NZEWpLtXY71LbbQN2jBk3/r69esER8cmHEdD1NHVWjDaIm08KiurEBsrHS0LN9JdR7TmhVi89p7W4POArFIBCisEdW5nEglyxRm0DdpA7t5Nx507j9G2bTMMHBiAXdXdbonx0sVaMOoibVwOxFzEmDEhCI8IxpIlf3EdTh2UvBCLF149PXG/wJq2QesJj8/X6oMtZv9FtH2vGSIiulPyYiJka8GUUff6d+7cCi1b0hZpYxITI30tQ0L8IRLZIz+/mOOIFFHyQiwaj8eTD1f/vGwjmg8bp1C3IlecgZ3LV9M26EYICAvF6LmzFP9da9TPUSYm5iLefW8Ewo28yidRT5PXX9bF+PDhK7RF2kjcvy/GzZuP0KFDC4SFBWL79niuQ1JAyQuxaLJCTAUFxfjfD1tQufoP2gatQ7LS8QBTuF5WP0fVmoi4uESUl1fA19cLbdt6I/mumF4XE6Tp609bpI1TzP6L6NChBcLDgyl5IcSYyEZdDh26jIoK6aJdTSqBEvXUlY5nEgle+OxjWNnaIj8jUyEhKSoqxYkT1zBoUCCmfjABpR0HaDVyQ7gjmyJy8nDHqDkzUd/rP2rOTKScP09bpI1UTMxFfDDjeaMcAaXkhVg0+sanP5qUjhe6NsWk5YsA1E1IYvZfxKBBgZgQGYEd94UK91U3ckO4oWyKSBVZ/aSXp42CtbUVbt1Kxd276QaIkmjq6NEklJaWw8fHAx06tMDNm4+4DkmOtkoTi+Xs7IDevaVdpGXbc4nuaFsXp3YX4gMHLwEAWjpWwEpQt3BgQ5r+Ef1R1V1aHVlbDvoCYXyKi8tw/PhVAMbXZZr+6onFGjy4GwQCAa5de4CHDzPV34FoRdu6OLUTkkIrJxRV8GDNB5rZVyg9vmblY8Kd+qYI68fQu1sLANIpCmJ8jLXLNCUvxGLJii8diKE1LvqgrnS8MjUTEpG7G+4XSiset3asm7zIUOVj7smmCLVJXJhEAn6eGC2auaCsrIK2SBspWVI5YEAX2NmprkBuaJS8EIsl+yZxJxvw6xFE0w86Vl/peHVku4pkyYuPUPX2Wap8zD1tE0hZ/aTSBOl6pePHr6K4uEwPkZHGunr1AR49ykKTJrbo378z1+HI0bs1sUijpo5Fy5ZuqJQAHSa+hunRUZgfs02+3oLohqrS8erItkMn3s0FY4C7XRUcrKoUjtGm6R/RL20TSFnrgC5tRACe9rMixkn2+hjTuhdKXojFCQgLxYwv3wUApBZbo7K6i3TtBaNENxJjj+LL8LGImjodv89ZiMLsHI26EDOJBH9+sQrpJdJNkT41po6o8rFx0aS7dMGTbGyesxBRU6fjq4gXcPP4SQwYEADgaTVXYpz2G+G6F0peiEWRLSxsLZR+EN4vsFa4jXaw6IesdPzFvQfwz+Ll0LQLcWLsUfz373EAQGvHp1NH2jb9I/qlSXfpf79YgYS9B5B8PgFMIkG/fp3g4GCHx4+fIDHxPhdhEw0dOnQJVVVV6Ny5FVq0MI41ZvQOTSyKb3AgXL090MJBmrykFCouQKMdLPqnbRfiTT9tAwB48nLxx9yn39wpcTEu2r6u8gXzBy4ZKkTSQLm5RThz5hYA4+kyTUXqiEURubuhuX0FrPhAQQUfT8rqdpGWHUf0R5suxGfP3kJubiGcnR1hlZWC5PM3OYiYaEKb13WofLcfrXcxBQdiLqJPn44IjwjGb78d4DocGnkhliU/Mws+QtmoizUAnsrjiH7JppIS9h2UTyUoU1UlwcHqgnWyDuDEeGnyunp5uSAwsA0kkqevLTFusnUvgwcHQiDgPnXgPgJCDOjuxctoaSdt7Z5SULdmAe1gMU6yWjzhEd05joTowtCh0iT0woVkPHmSz3E0RBPnz9/Bkyf5cHZ2RO/eHbgOh5IXYlm8vZzh6cgDY0BKgeKUEe1gMV6yQlm9erWDi4sjx9GQxqIpI9NTc5TMGNa9GCR5mT59Ou7du4eSkhKcPn0aPXv2rPf4cePG4fr16ygpKcGVK1cwbNgwQ4RJLIDsG1/SjTSI054o3EY7WIzXo0dZuHr1AQQCAQYP7sZ1OKQReDwehgzpBoBaApgaWbJpLF2mmT4v48ePZ6WlpWzKlCmsY8eObO3atSw7O5u5u7srPT4kJIRVVFSwDz/8kPn7+7PFixezsrIy1rlzZ42eTygUMsYYEwqFej0vupjm5Y8/P2IStostWvQK4/H5zK9HEAsaNoT59QhiPD6f8/joovryzTevMQnbxX799X3OY6FLwy/BwX5Mwnax3LytzMpKwHk8dNH84u3dlEnYLlZZtZO5uop0/vhafn7r92RPnz7NfvjhB/nPPB6PPXr0iM2ZM0fp8Vu2bGG7du1SuC4+Pp799NNP+jh5uljQhc/ns8ys35mE7WJ9+nTkPB66aHcZMiSISdgu9vDRBs5joUvDL/PmvcgkbBf7d9snnMdCF+0vly5/zyRsF5s48VmdP7Y2n996nTaytrZG9+7dcejQIfl1jDEcOnQIISEhSu8TEhKicDwAxMTEqDzexsYGQqFQ4aIPrVt74ttvX8ePP76jl8cn+te9ux9cXUXIyyvC2bO3uA6H1MLj8+HXIwhBw4Yo7TV17FgSiovL0Ly5Kzp3bsVRlKSxZOtdDh5I4DgS0hDG0mVar8mLm5sbrKysIBaLFa4Xi8Xw8vJSeh8vLy+tjp83bx7y8/Pll9TUVN0EX4u9vS1mzR6NKVPDjKqzJtGcbJFZbOxlVFZWqTmaGFJAWCjmx2zD9OgoTFqxWGmvqZqdhyNo15FJEgqboE8ffwC03sVUyV43rssWmPxuo6VLl0IkEskvzZs318vzXLv2tLPms88aT2dNormnOxzoG58xCQgLReTKpXDycFe4XlmvKdmCwaFU78UkDRzYFdbWVrh9+zHu3ROrvwMxOidOXMOaH3bh7bd+BJ/DNip6feasrCxUVlbC09NT4XpPT0+kp6crvU96erpWx5eXl6OgoEDhoi+y4TJj2CZGtCMS2eOZZ6S1Cegbn/GQ9ZoCWJ1pImW9pmSFsp59tgvs7W0NHC1prHDaIm3yyssr8cEH67Br11lIOCwpodfkpaKiAhcuXEBYWJj8Oh6Ph7CwMMTHxyu9T3x8vMLxADBkyBCVxxtSjJFtEyOaGzSoK6ysBLh58xFSUjK4DodU8w0OhLOXp8pGmLV7TcleP1tba4SGdjFkqEQHZCNm9AWCNJbex3xWrlyJadOmYfLkyfD398dPP/0EBwcHREdHAwA2btyIJUuWyI//7rvvEBERgdmzZ6NDhw5YuHAhevTogTVr1ug7VLVknTU7dWqFli3d1d+BGI1wmjIySpr2kKp5nGwElNa9mBY/P2/4+XmjvLwCcXGJXIdDTJzek5e//voLH374IRYvXoxLly6hW7duiIiIQEaG9Ntvq1at4O3tLT8+Pj4eL7/8Mt58801cvnwZ48aNw+jRo3H16lV9h6qWYmdNmnM3JbL1LvSNz7ho2kOq5nExtda9qNulRIyD7D3z5MnrKCoq5TgaYuoM0lX6xx9/xI8//qj0toEDB9a57p9//sE///yj77AaJGa/tLPm0PBg/Por9501iXrt2jVDmzaeKCurwJEj9I3PmNy9eBm56WI4ebgrTTqYRIJccYZCrynZbrEOHVpg0ifvov2wkXBwdpLfnpsuxo5lq6hSspGhBfNEl+gripZk3/qMpbMmUU82ZXTixDUUF5dxHA2piUkk2LFsFQBenX5SqnpN5ecX48r1NABA5PQXFBIXQPkuJcIta2srDBwYAIBGP4lu0KevloytsyZRj5rAGbfE2KPYOHse8jIyFa5X1WsqICwUxe7tAAA+woo6j6dslxLhVp8+/hAK7SEW5+Dy5Xtch0PMgEGmjcyJrLPmxInPIjw8GKdOXec6JFIPGxv6xmcKEmOPIinuOHyDAyFyd0N+ZhbuXrxcZzRGtrU6pcAa/bxK0NKhAnweg4Tx6hwn26WUfJ6mKbgmXzB/4BIYYxxHQ8wBfS1pAHm9F9oybfT69u0EBwc7pKVl48qV+1yHQ+rBJBIkn09Awr6DSD6fUCdxAZ5urc4os0ZxJQ+2AgbvJpUqH1PT3UxEv2j0k+gaJS8NcKC6J0ePHm3h6iriOBpSH9kOhwPUR8UsPE1GeEgplLbpaC0sV3m8pruZiP54eDgjONgPAP0dEt2h5KUB0tKycfnyPfD5fAwZ0o3rcEg9aIeDeamZjKQUWgMAfBzrJi9MwpCTlq6wS4lwQ/YeefFiMjIz87gNhpgNSl4a6GmPFZo6Mlaens7o1s23ep0SJS/mQLa1mkkkSCmQjrx4NqmCveDpFJNsTUXtXUqEGzRlRPSBkpcG2r/fODprEtWGDpW+NhcvJiMrK5/jaIgu1NxaXVQBiEsEAACfGlNHRbl5SncpEcPj8XjykRdaME90iZKXBjp58hqKikrh7d0UXbu25jocosSQ6uSFpozMS82t1bJ1Lz6OFSjMycX+Nevw+YDhlLgYia5dW8PLywWFhSU4deoG1+EQM0LJSwOVl1fi8OErAKjHijHi8XjykRdaJGh+EmOP4svwsfhuvrRytyfLxqKBI3BwbTRNFRkR2XtjXFwiKipU7wojRFuUvDTCgVo9Vojx6N69LTw8nJGXV0S1eMwUk0jwT/QuFBQUo6mLA7oFtuY6JFJLxDBp8rJ/3wWOIyHmhpKXRpCte+nXT1pLhBiPYdVvmocOSfvgEPNUUVGJ2FgaATVGIpE9+vbtCADYR8kL0TFKXhohOTkNyclpsLGxlldxJcaBvvFZDhoBNU6DB3eDlZUAN248wv37Yq7DIWaGkpdGklXbpW99xsPVVYTevdsDAPbvp+TF3Ml2sYSE+EMksuc4GiIzjL5AED2i5KWRYuhbn9EZOjQIfD4fly/fQ2rqE67DIXp2754Yt26lwtraCoMGdeU6HFJNNvq5d+95jiMh5oiSl0aKi0tEeXkF2rZtBj8/b67DIaApI0sk7zdGRSONQteurdG8uSuKikpx7FgS1+EQM0TJSyMVFpbg5EnpbhYqWMc9Ho8nfx1okaDp4/H58OsRhKBhQ+DXIwg8vvK3LNkIKDVLNQ7DhvUAABw+fAXl5bRFmuieFdcBmIOY/RcxcGBXhEd0R1TUXq7DsWi0Rdp8BISFYvTcWXD28pRfl5suxo5lq+oUoTtyJBFlZRVo3doT7ds3x61bqYYOl9RAo59E32jkRQdk3/oGDgyAjQ3lg1x67jnpm+bBg5doi7QJCwgLReTKpXDycFe43snDHZErlyIgLFTh+uLiMhw/fhUAEEGjL5yiLdLEECh50YHLl+8hLS0bjo5N0LdvJ67DsWj0jc/08fh8jJ47CwCrM00k/Zlh1JyZdW6TrXup2SxV02knojtDhki3SF+//pC2SBO9ob9kHZGVoKd1L9xxdRWhVy/aIm3qfIMD4ezlqTLR4PH5cPH2gm9woML1shHQAQMCYGtrjYCwUMyP2Ybp0VGYtGIxpkdHYX7MtjqjNkS3aIs0MQRKXnRE2bc+Ylg1t0g/fpzNdTikgUTubg06LikpBampT2Bvb4vJH7yk1bQT0Z3w6ppXNGVE9ImSFx05ePASJBIJunXzhZeXC9fhWKRh1etd9lFdCZOWn5nV4ONk1XYj330B2k47kcajLdLEUOivV0eePMnH+fN3AEDezZgYjnSLtHTUi77xmba7Fy8jN12ssjs0k0iQk5aOuxcv17lN1m+svae11tNOpPGee066RTo29jJtkSZ6RcmLDh2gWhOc6dGjLdzdnZCXV4T4+Btch0MagUkk2LFsFQBenQRG+jMPO5evVprcHDp0CVVVErjZVcHRuv7dZppOTxHN0YJ5YiiUvOiQ7FufbO0FMRzZIkHaIm0eEmOPYuPsecjLyFS4PlecgY2z59Wp8yKTk1OIK1elNV5aO1bU+xyaTk8RzTg5OaBPH9oiTQyDipLo0JkzN5GdXQBXVxGeeaYDFUkzoGHVw9X0jc98JMYeRVLccfgGB0Lk7ob8zCzcvXhZ5XSSzPZ/jiGo6yto41iGpBy7OrcziQS54gyl006k4QYPDpRvkU5JyeA6HGLmaHhAh6qqJPJvHCNG9OQ4Gsvh5iZCz57tANA3PnPDJBIkn09Awr6DSD6foDZxAYDdu84CAHyEFeAzxVE4ddNOpOFko5+0YJ4YAiUvOrZn9zkAwIiRvTiOxHLIpukuXbqLtDTaIm3pLl26i9TUJ7DmA00rFaeG1E07EUXaFPmTrXehLxDEEGjaSMf277+AysoqdOnig9atPanCpAHQIkFS257d5/DmWxEoiI9BVPRpraadiJQ2vaUCA9ugWTNXFBaWyNs0EKJPNPKiY7m5RThx4hoAYPjwHhxHY/74fD4iqCgWqWVX9dTR8OE91E47UQuBurTtLSWbMqIu0sRQaORFD/bsPocBAwIwYmQv/PjjHq7DMWs9erSFm5sIubmFtEWayB0+fAUlJWXw8fFAly4+SEpKUXqcNqMLlkJdbykmkWDUnJlIijsuTwYjaL0LMTD6iqEHu6vXvQwYEABHxyYcR2PeaIs0UaakpAyxsVcAACNVrD/TdnTBUmjaW6rfS+MQNGwIug0I0XiLNI1yEV2hkRc9uHnzEW7ffox27Zph8OBA7NhxmuuQzBatdyGq7N51FiNG9MTwET2xdOnfCrc1ZHTBUmhavE/67we0E5XByqoAySlP8OBBpsrjaZSL6BKlvXoi33VEW6b1puYWaVmBQEJk9uyR/g0+80wHuLmJFG5raOdqS6Bt8b7WwnIAQI59c5WjVTTKRXSNkhc92b1bumDwueE9wePxOI7GPIWHB4PP5yMhIZm2SJM6UlOfICEhGXw+Xz69KNPQztWWQG1vKcZq/iSvZHyvwFppw0t1o1zUKJM0BP226Mnx49eQl1cELy8X9OjRlutwzBJNGRF1VNVdakznanNXX28pAApfxtztquBoLUF5FZBWYqN0tIpGuYg+UPKiJxUVlYiJSQAAjBhBBet0TbpFmrpIk/rJtkyHhwfD2vrpEr/GdK62BKp6S9UmmzJ6WGSDKiZNamqPVtEoF9EHSl70aE/11NGIkbTuRdd69mwHV1faIk3qd/78HYjFORCJ7NG/fyf59Y3pXG0pEmOP4svwsYiaOh2bP15Q/e+lqI2jNHm5X2Atv672aBWNchF9oORFj/btuwCJRIKgID80b+7KdThmRbaG4cCBS6iqstwPGFI/xhj27pHWHqm9ZbqhnastSc3eUif+/EdhtMqWL4G3vbQg3b1CGzCJBAVPsnHvUqLCY9AoF9EHSl70KCsrXz4qMHw4jb7o0tP1LlQUi9RPNnWkrN9Y7dGFqKnT8VXEC5S4KFF7tKqVYwX4POBJqQAFFQLw+HwIXZvi033/KOweolEuog+UvOgZNWrUPW/vpujVqz0A2iJN1Dt06DLKyirg5+eNDh1a1Lm9IZ2rLVXN0So/kXTK6F6BjcIxNbc/y4rSWdnYICbqFxrlIjpDRer0bPfuc1iyNBJhYV3RpIktSkrKuA7J5I0a1RsAEB9/A+npORxHQ4xdYWEJjhxJRHh4MEaM6ImbNx+pvQ+Pz4dvcCA1dFQiMfYobp48jbn5/wAAkmslL7Iif+MWzlFalG7/mnXIevCI/l1Jo9DIi54lJaXg/n0xmjSxxaBBXbkOxyyMHhMCANixPZ7jSIgxqa/0/O56po5qCwgLxfyYbZgeHYVJKxZjenQU5sdso0JqNUx8bSSaWANFFTw8Lq77HZjH58PRxQVOnh4K1zt5uCN8+jRUlpfTKBdpFEpeDEA2daSqxwrRnLOzAwYODAAAbKfkhVRTl3DsqV6027dvR7i4ONb7OFQJVr3hw4IAAMkFtgBUF+GsXaCTitIRXaHfHgOQNWocTq0CGm348J6wtrZCUlIK7txJ4zocYmDKRlc0STju3xcjKSkFVlYChIcHK31svpUVxi2YA/BAlWDrwePx8Gzv1gCAO/k29R+s7P5UlI7oAK15MYAjRxJRWFiC5s1d0a2bLy5dust1SCZLNmW0k5pdWhxVjf2sbW2hSYPFPbvPoUsXHwwf0RNbthyr89jjFnwMx6YuKp+/5odu8vkEnZ6bKenVqz083UUorWR4WCCob+ClXlSUjjSGZX+FMJCysgocPHgJAE0dNYadnY28qi5NGVmW+kZXHFycNSo9L9syPWxYdwgET4+XPbaDs7NGsVj6h+6YMc8AAOKO3UAV46vY/qweFaUjjUHJi4HsoamjRhs6NAgODnZIScnAxYvJXIdDDER9Yz/1RO5uOH36Jp48yUfTpkL06dNR7WOrYukfurLRzw0//6eyyF9RTi4VpSN6RdNGBrJ3r3TBYK9e7eHp6QyxOJfbgEwQTRlZJlljv8bIz8yCRCLB3r0X8OqrAzFiRE8cP35Vq8dmEglyxRkW/aHbqVMrtG/fHKWl5di37wIKC0uQFHe8zrbyLgP7I3LlUjCJRCEppKJ0RFdo5MVA0tNzcPbsLQDAc8/14Dga0yMQ8DGyukcUTRlZlsZM09T+ll97y7Smj80YA33oPp0yOnToMgoLSwAoL/JHrReIvtHIiwHt2X0OvXq1x4iRvRAdfYjrcEzKs892gaurCFlZ+Thx4hrX4RAD0nSahkkYeHxejZ/rfss/cCABFRWV6NixJfz8vDV+7MLsHPz7xQqT/9BtbPE9bWosJcYeVToqY8nJH9EdSl4MaPfuc1i0+BUMGdINtrbWKCur4DokkzF6tPQb367/zlAjRgsja+zn5OGudF0Kk0hQlJeHyrJyxZ1I4gzsXL5aIeHIyyvC8eNXMWhQIIYP74Ef1uxR+9iFOblYPHgUJJWV+jlBA1G1W2vHslUaJWWtWrmje/e2qKqqwn//ndHoOWWjMoToGk0bGVBCQjJSU5/A0bEJQkO7cB2OSRlVnbzQlJHl0aSx3z+LlmvcYHH3rqeL5zV57H+/WGEWiUtji+/JvkCcOHEdWVn5eomTEE3pNXlxcXHB5s2bkZeXh5ycHPz6669wcHCo9z5xcXFgjClcfvrpJ32GaVBUbVd73bu3RatW7igsLJFvOW+I+srHE+OmyRoKTRss7t4tXfcSGtoFQmETs1+foX63lmbF96gtBzEmep02+v333+Ht7Y0hQ4bA2toa0dHRWLduHV555ZV677du3TosWLBA/nNxcbE+wzSo3bvP4s23IjBiZC+8//5arsMxCWOq3zT37bvQ4Km2xg6ZE+7pag3FnTtpuHnzETp0aIHw8GD8889Js16foW5HlSbF99zcROjfvxMAYAft9iNGQG9fPf39/TFs2DC88cYbOHv2LE6ePIn3338fEydOhLe3d733LS4uhlgsll8KCgr0FabBxcZeQWFhCXx8PNCzZzuuwzEJo6t3OOzY3rA3TepXYz40HV1R57+d0jUb417sp/PHNjaa7qiq77iRI3tBIBDg4sVkpKRk6Co0QhpMb8lLSEgIcnJycOHCBfl1hw4dgkQiQe/eveu97yuvvILMzEwkJiZiyZIlaNKkicpjbWxsIBQKFS7GrKSkDP/9Jx22njjxWY6jMX7t2zdHp06tUF5egT17zml9f10NmRPzsmXLcQDAiBE94eBgx3E0+qXpjqr6jqMpI2Js9PaO7eXlhYwMxQy9qqoK2dnZ8PLyUnm/P/74A5MmTcLAgQOxdOlSvPrqq9i8ebPK4+fNm4f8/Hz5JTU1VWfnoC9/bZW+cb44vl+drqtEkWzK6PDhK8jP1376UDZkrkn5eGI5EhKScfv2Y9jb25r9+jPZbq2GVrx1dGyCIUO6AaAF88R4aJ28LF26tM6C2tqXDh06NDigX375BQcOHEBSUhL++OMPTJ48GWPHjoWvr6/KeEQikfzSvHnzBj+3oezffwG5uYVo0cINfft25Doco9bYKSNdDJkT87S1ujnjhIn9OY5EvzTZUVVf8b2IiGDY2dng/oMnsGnVgRa7E6Og9W/gt99+C39//3ovd+/eRXp6Ojw8PBTuKxAI0LRpU6Snp2v8fGfOSOem27Ztq/T28vJyFBQUKFyMXXl5JbZXfxjT1JFqzZo1Re/eHSCRSLBzZ8OSF10MmRPzJJs6GjasO5yc6t8Faeoas6NqyjujAABZTVpg0orFmB4dhfkx22itGOGU1ruNsrKykJWl/o0+Pj4eLi4uCA4OxsWLFwEAgwYNAp/PlyckmujWrRsAIC0tTdtQjdpfW49j6tTBeGFcH8yYsY4Krykhqytx+vTNBveC0qTAmaX3q7FU1649QFJSCrp08cHo0c9g48ZYrkPSq4bsqAoKH4iw0E4AGO7k28ivly12N4et5MQ06W3s78aNG9i3bx9++eUX9OzZE3369MGaNWuwZcsWeSLSrFkzXL9+HT17SnvW+Pr6Yv78+QgODoaPjw9GjhyJTZs24ejRo0hMTNRXqJyIjb2MrKx8eHq6YMCAAK7DMUq6WCTY2CFzYt4sZepIRpsdVTw+HzOXzoCtgKGogoe0EiuF22ixO+GSXn/rXnnlFdy4cQOxsbHYu3cvTpw4gTfffFN+u7W1Nfz9/WFvbw9AOgU0ePBgHDhwADdu3MC3336Lf//9FyNHjtRnmJyorKzCv/+cBEBTR8q4uDjKk7rtDVzvImPuRchIw22tXjw/eHA3uLmJ1B5vSYUOfYMDEegjnU5LLrAFoLi5QLbYffC0SA6iI5aOB4BxHYQuCYVC5OfnQyQSGf36lwEDAnA4bgmyswvg7TUZFRWmXYJcl159dSA2bpqNxMT7COz6vk4es7FN6Yh5Ond+Fbp3b4t33v4Ra9fuV3mcpRU67D58KI5s/wAO1gzb7ouQUmij9DjGGDbOoi8BpPG0+fw2368NJuDYsatIS8tG06ZC+VZEIvV0ykh31TzNtQgZaRzZ1NH4Caqnjiyx0KGvZxM4WDOUVvHwsMha9YEMNH1EDI5+2zgkkUjw918nAAATaOpIrkkTW4SHBwOguhJE//6q/hsMDe0Cb++mdW631EKHvTq5AgDu5VtDwlTXo+LxeVQriRicef21mSDZnPuoUb1hZ6d8WNbShIcHwd7eFvfvi3Hp0l2uwyFm7sGDTJw6dR18Ph8vvti3zu2WWuhQttuv5i6j+lCtJGJIlLxw7PTpm0hJyYBIZI9hw7pzHY5R0MeUESH12Vpd80XZ1JElFjoMCGgNPz9vlJaW49eVv2t0H6qVRAyJkheOMcbk7QLqm3O3FDY2VvJy7TRlRAzl779PQCKRoE+fjvDxUSyuaYmFDl94oQ8A4MCBBOxes766vYDyvR3q2gsQog+UvBgB2dTRyJG9zL5JnDrPP98bLi6OePQoCydPXuc6HGIh0tNzcPRoEgBg/Ph+Crc1tjeQqeHxeJgcOQiAdETqaa0kUK0kYjQoeTECFy9aTpM4daa+NgQAsGnjYUjozZAYkKqpI20LHZp6LZiBAwPQurUncnML5aOfVCuJGBut2wMQ/di65RjmfzYR4yf0x5bqrZuWplmzphg6tBsAYMOGQ9wGQyzOv/+ewpof30b37m3Rrl0z3L79WH6b7MO7Tp0XcQZ2Ll8t//A2h1owU6YOBiBN5kpLy+XXN6S9ACH6QkXqjETnzq2QmPQjysoq4OX5KvLyirgOyeDmzh2HJUsjcexYEgaEzuM6HGKB9u77HBER3bHgs8348sutdW6vr9ChrBZM7S3VstEZUxihEInskZa+CU2a2KJ3r9k4d+421yERC0JF6kzQ1avSJnG2ttbyLYqWRvaNb0M0jboQbtS36whQXejQXGrBTJjQH02a2OLq1QeUuBCjZtx/SRZGk0qf5qpv305o3745CgtL8PffJ7kOh5g4TdadKDtmx47TKCurQJcuPujcuZXGz2estWC0XX8z9TX6AkFMA615MSJbtx7HF1++iiFDusHVVYQnT/K5Dslgpk4NAwD8/dcJFBWVchwNMWWarDup75j9+y9g1KhnMHHis/jss80aPacx1oLRdv2Nv38LPPOMPyorq/C//8UZLE5CGoJGXozInTtpuHDhDqysBPI6C5bAwcEOL1ZvT42mb3ykETTpQaTumFNJ0notEyZqPgJqbLVgGtKLaWr1tO2ePeeQkZFriDAJaTBKXozM06mjfmqONB/jxvWFUGiP27cf48SJa1yHQ0yUputO1B0jDIlAcXEZ2rZthuBgP42e+2ktGO4LuTVk/Y2VlQCvTpbWdtkQHav3GAlpLEpejIysSdyAAQHw8nLhOBrDkC3U3biB3jRJw2m67kTdMQ4eXog7eQsAMFHDhqldBvaHta0tePy6DQwNXcjNr0eQ1utvIiKC4eXlgoyMXOzZc07vMRLSWJS8GBnFJnHmP/ri6+uF0NAukEgk2LiRkhfScLpcTxJ35gEA6eJ5Hk91R2Xg6RSNvZNI6e1FefkG2yYdEBaKyd9+pdGxnQc+nRaTfYHY/L84VFZW6SU2QnSJkhcjJNuuqc2cu6maMkW6UPfAgQSkpj7hOBpiynS5nmT//gvIzy9Gq1buCAnxV3lcfVM0gHTUpaK0FElxx3UWmyryJEok1Oj4Z1+diICwULi5ieSVvWnNGTEVlLwYob//PoGqqir06dNRq+2apobP5yOyOnmhrZmksTTtQaTJMdfjL8hL478xLVzlcxrLFml1SZRSTLr2ZdKrg2BtbYVz527j6tUHeo2TEF2h5MUIpafnYPv20wCADz4YyXE0+hMWFoiWLd2RnV2AnTvPcB0OMXGa9iDStE/Rzz/tAwC89NKz8PBwVvqcxrJFWl0SpYw0sfLEm+8MBwBErz8ov96UezMRy0C/lUbqu9X/AQAmvToQTZtqNgxsaqZU13b584+jKCur4DgaYg40aSCoaZPBM2du4vTpG7C1tcZbb0UofT5j2SLd0OTIw64K/u28UFpaji1bjiEgLBTzY7ZhenQUJq1YjOnRUZgfs03p1mpCuES9jYzYufOr0L17W3wybyOWLfuH63B0ytnZAY/TNsHOzgY9us/ExYvJXIdEzEjtHkT3LiWiTbcAOHm4w8HFGYU5uSjIzAJ4PAhdm6psMjhx4rP448+PkJ6eg9Y+r6G8vLLO88yP2QYnD3eVa15yxRn4KuIFve408usRhOnRUVrfb6B3Ibq5liIxXYJPVsRg4JRJMOXeTMS0afP5TcmLEXv11YHYuGk2Hj3Kgm+bN8xqF8A77zyHH6PewZUr99At8AOuwyFmTFmlWRl1HZ+trAS4d/83NG/uismvrsTmzXUrz+qzIWN9jSBrH1dfEqWMgMfwpn827AQM/94VIqXIRvpYSnZXGSoJI5aNGjOaia1bjyM9PQctWrhh7NgQrsPRKdnWzOj1tFCX6I+qSrMyTp4eKivOAkBlZRWiftwDAPhghvL1Z5pOQzUkdk2ncOpd78MYGKv7HdVPWA47AUN+OR8Pi23A4/FUbgvnqjcTIarQyIuRW7BgIj5f9Ari42+gb5+PuA5HJ7p08cGVxDWoqKhE82aRyMqynB5OxHA0HY1QN6rg6irCg4fr0aSJLfr1/RinTl1X+XyajJJooqGjOcpGmQpzcsADDw4uzgrHjvHJQ2thBU5nNEF8hoNGcW3+eAES9h1syCkRopY2n9/UmNHI/fzzfsz7ZDxCQvzRs2c7s2hTL+uhsmvXWUpciN7IduCoU3NUIfl8Qp3bnzzJxx+/H8XrbwzFjJnPq0xemESi9P7aUlfen0kkGDVnJpLijtdJjhJjjyIp7nidJAoAhr7zOoa+/RoAwNG6Cj6O0kXy13LtNI7NUL2ZCFGHpo2MXEZGLrZU9zv6YMbzHEfTeFZWArwyaQAAmjIi+qXtDpz6jv/uO+nuvzFjQtCypfIpKF1pbO0YWRKVsO8gks8ngEkkYBIJ7pw5Lz+mk3MZeDzgYZEV8soFamMyZG8mQjRByYsJ+P67XQCA8eP7wdu7KcfRNM7w4T3h4eGMtLRs7N9/getwiBnTdpSgvuOTklIQG3sZVlYCvPvuc40NrV76qh3ztIhfFTo5lwIAruXUHXWpvT7G0L2ZCNEEJS8mICEhGceOJcHa2grTp+v3jVPfZLVdNv8vDlVV9EZI9EddxV0ZTUcVvq8efXljWjjs7W11Fmdt+qodI1vU29y+Ci62EpRX8XArr+551F6029iFx4ToAyUvJkI2+vLmWxGwtbXmOJqGad++OUaM6AmAeqgQ/atvB478GMag6ajCnj3nkZychqZNhXj11YG6D7iapm0OGjKFkxh7FO7p0hHPW/k2qGT1N53csWwVvop4gRIXYnQoeTERO3eexv37Yri7O+Hll02z2uXCz1+CQCDAzp2ncePGI67DIRZA1TZmmdx0scajChKJBD98L/0S8b4e23Zo2uagIVM43bu3xaB+7VBVJcGFrCZqjy/MzqGpImKUaKu0Cfm//xuDr795zSQLuwUEtMblKz8AAAK7vo/ExPvcBkQsimwbc80Ku/kZmVpvZxYKm+Dhow0QiewRPnQBDh5s/O4iVZRte85JS8fO5asbPBKyZ+/nGDasO7btTkBK6yFqj4+aOl0nO6gI0QRV2DXT5MXZ2QEPH22Ag4MdBg38BEeOJHIdksa2bf8Uo0c/gy1bjuHll77mOhxCGmz16mn4YMbz2LPnHEaOWKzX59Jl7Zi+fTvh+InlqKioRKdO7+Lln6I4b2tASE1UYddM5eYWYdPGwwBMa9t0jx7tMHr0M6iqqsKiz//kOhxCNKasw/IPP+yGRCLB8OE90b59c70+v7Jtzw315VevApCWKEi+81hvU1OEGAIlLybm++o59+ef7wVfXy+Oo9HMF19OAgBs2hSHmzdprQsxDarK89u3bo/du88BAN5/f4RBY1KWTGli8OBuCA3tgtLScnzxxRYAqtcDFeXlIybqFyTFHdd5/IToCk0bmSDZvPXqVTsxe/avXIdTr/79O+PosWWoqKhEh/Zv4/59MdchEaKWuvL81//3E375ejwKC0vQssVU5OUVGSSm2mtg1DWWlIk//Q169+6A71bvxKxZiu8ZPD4fg6dFov+kCXBwdtL6sQnRFZo2MnOyehNTXxsMR0f1Owa4JBt1+e3XA5S4EJOgrjw/wOA9dCwSE+/D0bEJXnttsN5jUtVg0snDvd7GkgAwYkRP9O7dAUVFpVi69J86t3cZ2B/h06fBXiTU+rEJ4QolLybowIEE3LjxCE5ODpgyJYzrcFQaMiQIzz4rHar+8sutXIdDiEY0Lc+/5T9pnZX33h8JvobTNw2hSTI1as5MpfHyeDx88aV0rcsP3+9CRkauzh6bEC7Rb6QJYozJR19mzHweNjbG2V9TNuryU9RePH6czXE0hGhG07L7ceceISsrH23aeGLcuD56i0fTZMqve7c662HGjeuLwMA2yMsrwtdfb2vwY6vqo0QIV4zzU4+otWnTYSz8/CX4+Xlj3rwXsWiRce3iGTmyF3r1ao/CwhIsW1Z3qJoQY6Vp2f3MVDF+XLMbCz9/Gd+ufAMxMQl6WfuiaTI1eeUShTUr+WIxJrfLBQCs/HYHcnIKG/zY2vZRIkTfaOTFRBUXl+GD99cBAD75dDy6dPHhOKKneDweFn8hHXX5/rtdyMzM4zgiQjSnTXn+5cv/xa1bqWje3BVffz1VL/FomkzZO4kUfu7dXoQ2rVyRk1eM1at3Nuqxte2jRIi+UfJiwv7++wS2b4+HtbUVfls/AwKBcbycL74oHarOzS3EN9/UHaomxJhpUp7/vxXfgUkkKC0txxuvfw9A2rBx0KCuOo9HbTLFGBhjCg0V+TyGEM8SAMBZsS0Ki8oa9tiN6KNEiD4Zx6cdabD33v0ZubmF6NmzHWbOHMV1OBAI+Fi0+BUA0qHq3Fz9byElRNdU1UDh8fng8XkYNWemfBfOiRPXEPXjHgDAul/e13nHaXXJFI/Hq9MJuotzKZxsJCiq4OFWhYfKNSv67KNEiD5R8mLi0tKy8X+zfwMALP7iFbRt681pPJMmDUSHDi2QlZWP1av/4zQWQhojMfYodqz4Tj6yUVPtbcRz525ESkoGfH298GX17h5dx6KqoFxtAh5Db4/qUZdMe1QyXr1rVlQ9dq44Q+OmlYQYGhWpMxMxBxZjyJAgHDmSiLBBn9Z5szUEa2sr3Lj5M9q08cRHH67Ht99uN3gMhOgKj8/H/JhtGvf/CQ8Pxr79iyCRSNC3z8c4c+amXmKq2euIx+fjnd/WKBwT5FqCAd5FyC/nY8NtF1QxnkYNFnXZR4mQhtDm85t2G5mJt978EYlJazBgQADefDMca9fuN3gMr78+BG3aeCItLRtRUXsN/vyE6JJsG7EqNbcRJ59PQEzMRWzcGIvIyDD8tv4DBAfNQHl5ZZ37yBKEgqwnAI8HoWtTjZMFWa+jmo+Xmy6WJ1jWfIZe7sUAgDOZ9qisYsgVizVas1L7sQkxZpS8mIn798X49JNNWP3dm1i+Yir27DmPR48Mt0OgRQs3LFj4EgDgqy+3oqRE+QJBQkxFQ7YRz571KyIigtGpUyt8+ukELFz4u/w2ZeX9a2pIOX7ZmpXIlUvBJBL08SqGvRVDbhkfV59Yg9asEHNFa17MyJo1e3Dq1HWIRPb46efpBnteZ2cH7Nu/CF5eLkhKSsGvvx4w2HMToi8N2Uack1OI9979GQAwd944dO3aGoDq8v41NbQcv2zNSie7LAS7lQIAjqU7IFucSWtWiNmi5MWMSCQSvPH69ygrq8Dw4T3x8sv670liZ2eDnf99hs6dW+HRoywMf25RnaFyQkxRQ7cR//vvKfz77ylYW1vh198+gJW1lbQEPw/1ltlvTDn+zu4MEe2l9/lu/Qn837hZ+CriBUpciNmi5MXM3LjxCF8slra8X/3dm3B3d1Jzj4bj8/n4/Y8P0b9/Z+TmFmJYxEI8fJip/o6EmABNthGf+fc/dAsPk5fjl3nv3Z+Qk1OIHj3aIWrLYmkJ/lrbmZVpSDn+QYO6YsPGmQCkTVtnvb4cyecTaKqImDVKXszQihX/4tKlu3BzE+H7H97S2/OsWfMWxowJQWlpOUaP+gpXrz7Q23MRwgXVW5TzUJyXh4j33sSkFYsxPToK82O2yad8xOJczJ71KwBgyugAONtUafW8mq63CQxsg23bP4WNjTUOHLuFNb9foCaKxCLQVmkzFRTkhzNnv4WVlQBjRn+FnTtP6/TxP/10PL748lVIJBKMf3E5tm07pdPHJ8SY1Nwl5NaqBcKnT0PtTsyy0RjZOhMen48b4h1o58bDoyIr/H3PCdK3XPU02drcurUnzpxfDXdXRzwstMb2FBGqGK9BC38JMQbafH5Tim6mEhKS8U11F9nf1n+AF17QXdfbqVMH44vqQlwzPlhHiQsxe7JtxJdiYvHMuFGonbgAddes+AYH4uiTpiivAlo4VCKiRSFs+eq3QmtSjt/VVYS44yvg7uqIzBIB/nsgRBWTJkYNXfhLiCmh5MWMLV68BWfP3kLTpkL8/c88bP79QzRtKmzUYw4f3hNr170HAFi65C/8WF0WnRBLIKv9ompqpuaaFZG7GwoqBIhLc4SEAR2dyzC5XS58HMuV3lfTcvz29rbYtXsBfFo0RX45H9tTRCiXPI2nMQt/CTEV9JttxkpLy9G/3xx89eVWVFZW4eWXQ5GYtAbDh/ds0OP17t0BW/+aAysrATZsiMWnn/5PxxETYty0qf0i20J9LdcOW+86IbtMAEdrCca2zsfgZgWwqTUKo0k5foGAjy1b5+CZZzqgpJKHbfdFKKoU1DmuIQt/CTElektePvnkE5w8eRJFRUXIycnR+H6LFi3C48ePUVxcjIMHD6Jt27b6CtEiVFRU4rPPNqNPyEe4du0BvL2bYtfuBfht/QyIRPYaP0779s2xa/cC2NvbYu/e83hz2g96jJoQ46RN7RcHZydIqqQLddNLrPH7HWdczLIDY0BA0zK82jYXrlVPsHnOQkRNna7R1ua1a9/FiBE9UVpagZ0pIuSU119nVNNkixBTo7fkxcbGBn///Td++uknje/z8ccf44MPPsDbb7+N3r17o6ioCDExMbC11W2XVkt0/vxtdA+eiW++3gaJRIKpUwcjMWkNhgwJUnq8h4czRo16BsuXT8Gx48tx6fL3cHMT4ezZW5gwfjkqK7XbPUGIOdC09ou9izMmf7tEYXt0JePhaLoj/r7nhNxyPkQ2EkwOZHhtWBukXbtW5zGtrATo0aMdPvhgJP7c8jFSHqzHa68PRVVVFWZ88hfSSqzVxqtpskWIqdH7bqPIyEisXr0aLi4uao99/Pgxvv32W3z77bcAAJFIBLFYjClTpmDr1q0aPR/tNlKvT5+OiN4wE+3aNQMArP15H375JQY9erRDSB9/9O3bEW3bNqtzv4SEZIQPXYCsrLqdbAmxFLJquap2G236v08was5MlQ0dAUDAKuF1/yjGj5RO69y58xjvvfszbGys0KdPR4T06YiePdvB3l7xi1tpaTneeTsKm/4Xp1XTSEJMgTaf30aTvLRp0wZ3795Ft27dcPny05X2R44cwaVLlzBz5kyl97OxsVEYmREKhUhNTaXkRQ17e1ssWxaJ994fqfR2iUSCq1cfIP7UDZw6dR2nTl3HnTtpBo6SEOOkrE9RTlo6di5fjeK8fEyPjlL7GFFTp6ONM8Nv6z9Ay5bK2wbk5hXj5ImrOHXyOk6evI7z52+juLhMHkN9SRS1BiCmxiS7Snt5eQEAxGKxwvVisVh+mzLz5s3D559/rs/QzFJxcRk++GAdtm2Lx49R76BFC1ecOXML8adu4OTJazhz5hby8oq4DpMQo5QYexRJccflu4pqdoUOGjZEo8cQubvh0L6DCOjyHlaufB0vvRyKxxmFyLVywRMmwuNiK+SUuyLX1ha7zx5F4rGkOjFsnD2vThKVK87AzuWrKXEhZk2r5GXp0qWYO3duvcf4+/vj5s2bjQpKG0uXLsXKlSvlP8tGXohmjhxJROdOhmviSIi5kNV+qU3bho75+cV4440f8N2fV5SOpMjqtigbSakviSLEnGmVvHz77bfYsGFDvcfcvXu3QYGkp6cDADw9PeX/L/v50qVLKu9XXl6O8nLldRMIIcTQZIt61a1HqVmIjsfnP23eyKtb/I5JJBg1ZyaS4o4r7bOkrhovIeZGq+QlKysLWVn6Wb1+7949pKWlISwsTL7mRSgUonfv3lrtWCKEEC7JGjpGrlwKJpEoXY9SuxDd4GmRClM/tdWs20KJCiF63CrdsmVLBAYGolWrVhAIBAgMDERgYCAcHBzkx1y/fh2jR4+W/7x69WrMnz8fI0eORJcuXbBp0yY8fvwYO3bs0FeYhBCic6oaOiorRBcQFlrdK0k9qttCiJTeFuwuXrwYU6ZMkf8sm/oZMGAAjh6V/uH6+/vDyclJfsyKFSvg4OCAdevWwdnZGSdOnEBERATKysr0FSYhhOiFJutR5NNFYNCkaSPVbSFEirpKE0IIR/x6BGm0rZpJGHLFYqrbQswadZUmhBAToPE0EA9qGzYSYkkoeSGEEI5oOg0U8+MvVLeFkBooeSGEEI5o2ivp0C8bDRwZIcaNkhdCCOGIbFs1wFNav0XZtmpCCCUvhBDCKW22VRNCpIymtxEhhFgiHp+P4rx87FkVBQcXZxTm5CI/I5PK/BNSD0peCCGEI8q6U+emi7Fj2SpKXAipB00bEUIIBwLCQhG5cimcPNwVrpc1YgwIC+UoMkKMHyUvhBBiYDUr69Zu3ij9mWHUnJlKGzsSQih5IYQQg/MNDoSzl6fK5KRmI0ZCSF2UvBBCiIFpWlmXGjESohwlL4QQYmCaVtalRoyEKEfJCyGEGJimlXXvXrxs4MgIMQ2UvBBCSCPw+Hz49QhC0LAh8OsRpNEiW6qsS0jj8AAwroPQJW1aahNCSGPUV6dFk8q4yu6fk5aOnctXU2VdYnG0+fym5IUQQhpAVqel9nZn2ciJpqX9eXw+fIMDIXJ3Q35mFlXWJRZLm89vqrBLCCFaUlenhUkkGDVnJpLijqtNRJhEguTzCXqMlhDzQ2teCCFES1SnhRBuUfJCCCFaojothHCLkhdCCNES1WkhhFuUvBBCiJaoTgsh3KLkhRBCtER1WgjhFiUvhBDSAImxR7Fx9jzkZWQqXJ8rztB4mzQhpGGozgshhDSCIeq0UC0YYgmozgshhBiIvuu0NLaKLyHmiEZeCCHESKmr4hsT9QuyHjyi0RhiFmjkhRBCTJzaKr6MIeK9N+XX0WgMsSS0YJcQQoyQ2iq+PJ7Cz04e7ohcuRQBYaGGCI8QTlHyQgghRkjb6rzSJIdh1JyZKhMeQswF/YYTQogRakh1XuqpRCwFJS+EEGKE1FXxrQ/1VCLmjpIXQggxQvVV8VWHeioRc0fJCyGEGClVVXwZU17hgnoqEUtBW6UJIcSIJcYeRVLccXmFXbdWLRA+fRoYkyit/UI9lYgloOSFEEKMXO0qvul37tatuivOwM7lq6nOC7EIVGGXEEJMEPU7IuaGKuwSQoiZ03dPJUKMGS3YJYQQQohJoeSFEEIIISaFkhdCCCGEmBRKXgghhBBiUih5IYQQQohJoeSFEEIIISaFkhdCCCGEmBRKXgghhBBiUih5IYQQQohJMdsKu0KhkOsQCCGEEKIhbT63zS55kZ18amoqx5EQQgghRFtCoVBtbyOza8wIAM2aNdNLU0ahUIjU1FQ0b97cLJs+mvv5AeZ/jnR+ps/cz5HOz/Tp8xyFQiEeP36s9jizG3kBoNGJN0ZBQYHZ/lIC5n9+gPmfI52f6TP3c6TzM336OEdNH48W7BJCCCHEpFDyQgghhBCTQsmLFsrKyvD555+jrKyM61D0wtzPDzD/c6TzM33mfo50fqbPGM7RLBfsEkIIIcR80cgLIYQQQkwKJS+EEEIIMSmUvBBCCCHEpFDyQgghhBCTQslLDS4uLti8eTPy8vKQk5ODX3/9FQ4ODvXeJy4uDowxhctPP/2kcEzLli2xe/duFBUVQSwWY8WKFRAIBPo8FZW0PUcXFxd8//33uHHjBoqLi5GSkoLvvvsOIpFI4bja/waMMUyYMEHfp4Pp06fj3r17KCkpwenTp9GzZ896jx83bhyuX7+OkpISXLlyBcOGDatzzKJFi/D48WMUFxfj4MGDaNu2rb7C14g25/jGG2/g2LFjyM7ORnZ2Ng4ePFjn+Ojo6Dqv1b59+/R9Gippc36RkZF1Yi8pKalznDG9htqcn7L3E8YYdu/eLT/GmF6//v3747///kNqaioYYxg1apTa+4SGhuLChQsoLS3F7du3ERkZWecYbf+u9UnbcxwzZgwOHDiAjIwM5OXl4dSpUxg6dKjCMQsXLqzzGl6/fl2fp6GStucXGhqq9HfU09NT4ThDvIaMLtLL3r17WUJCAuvVqxfr27cvu3XrFvv999/rvU9cXBxbu3Yt8/T0lF+EQqH8dj6fz65cucIOHDjAAgMDWUREBMvIyGBfffWVSZxj586d2T///MNGjBjBfH192cCBA9nNmzfZ33//rXAcY4xFRkYq/DvY2trq9VzGjx/PSktL2ZQpU1jHjh3Z2rVrWXZ2NnN3d1d6fEhICKuoqGAffvgh8/f3Z4sXL2ZlZWWsc+fO8mM+/vhjlpOTw55//nkWEBDAduzYwZKTk/V+Lro6x82bN7N33nmHBQYGsg4dOrD169eznJwc1qxZM/kx0dHRbO/evQqvlbOzs0mcX2RkJMvNzVWI3cPDQ+EYY3oNtT0/FxcXhXPr1KkTq6ioYJGRkUb5+kVERLAvvviCjR49mjHG2KhRo+o9vnXr1qywsJB98803zN/fn7377rusoqKCDR06tMH/ZsZ2jqtWrWIfffQR69GjB2vbti376quvWFlZGevWrZv8mIULF7LExESF19DV1dUkzi80NJQxxli7du0U4ufxeIZ+DQ3/j2WMF39/f8YYY927d5dfFx4ezqqqqpi3t7fK+8XFxbFVq1bV+4tRWVmp8Ab71ltvsdzcXGZtbW0S51j7Mm7cOFZaWsoEAoH8Ok1+6XV9OX36NPvhhx/kP/N4PPbo0SM2Z84cpcdv2bKF7dq1S+G6+Ph49tNPP8l/fvz4Mfu///s/+c8ikYiVlJSwCRMmcPJ7qe051r7w+XyWl5fHXn31Vfl10dHRbPv27ZycT2PPLzIykuXk5NT7mMb0Gjb29ZsxYwbLy8tj9vb2Rvn61bxo8h6wbNkylpiYqHDdn3/+yfbt26ezfzOuz1HZJSkpiX322WfynxcuXMgSEhI4P5+GnJ8seXFyclJ5jCFeQ5o2qhYSEoKcnBxcuHBBft2hQ4cgkUjQu3fveu/7yiuvIDMzE4mJiViyZAmaNGmi8LiJiYnIyMiQXxcTEwMnJyd07txZ9ydSj8acY01OTk7Iz89HVVWVwvU//vgjMjMzcebMGUydOlVncStjbW2N7t2749ChQ/LrGGM4dOgQQkJClN4nJCRE4XhA+lrIjm/Tpg28vb0VjsnPz8eZM2dUPqY+NeQca7O3t4e1tTWys7MVrh8wYADEYjFu3LiBqKgoNG3aVKexa6Kh5+fo6Ij79+/jwYMH2LFjBzp16iS/zZheQ128fq+//jq2bNmC4uJiheuN4fVrCHV/g7r4NzM2PB4PQqGwzt9gu3btkJqaiuTkZGzevBktW7bkKMKGuXTpEh4/fowDBw6gT58+8usN9RqaZWPGhvDy8lJIMACgqqoK2dnZ8PLyUnm/P/74AykpKXj8+DG6du2K5cuXo0OHDnjhhRfkjysWixXuI/u5vsfVh4aeY02urq747LPPsG7dOoXrP/vsMxw+fBjFxcUYOnQooqKi4OjoiB9++EFn8dfk5uYGKysrpf+2/v7+Su+j6rWQnbvsv/UdY0gNOcfali9fjsePHyu8kezfvx/btm3DvXv34OfnhyVLlmDfvn0ICQmBRCLR6TnUpyHnd/PmTbz22mu4cuUKnJyc8OGHH+LUqVPo3LkzUlNTjeo1bOzr17NnTwQEBOD1119XuN5YXr+GUPU36OTkBDs7O7i4uDT6d97YfPjhh3B0dMRff/0lv+7MmTOYMmUKbt68CW9vbyxcuBDHjx9Hly5dUFhYyGG06qWlpeGtt97C+fPnYWtrizfeeANHjhxB7969kZCQoJP3LU2YffKydOlSzJ07t95jGvMP+ssvv8j/PykpCWlpaTh8+DB8fX1x9+7dBj+uNvR9jjJCoRB79uzBtWvX8Pnnnyvc9uWXX8r//9KlS3BwcMBHH32kt+SFqDdnzhxMnDgRAwYMUCjjvXXrVvn/JyUl4cqVK7h79y4GDBiAw4cPcxGqxk6fPo3Tp0/Lfz516hSuX7+Ot956CwsWLOAwMt17/fXXceXKFZw7d07helN+/SzNSy+9hIULF2LUqFHIzMyUX79//375/ycmJuLMmTNISUnB+PHjsX79ei5C1ditW7dw69Yt+c/x8fHw8/PDrFmzMHnyZIPFYfbJy7fffosNGzbUe8zdu3eRnp4ODw8PhesFAgGaNm2K9PR0jZ/vzJkzAIC2bdvKH7dXr14Kx8hWZWvzuPUxxDk6Ojpi//79KCgowJgxY1BZWVnv8WfOnMGCBQtgY2OD8vJyjc5DG1lZWaisrKyzwt3T01PluaSnp9d7vOy/tR/D09MTly5d0mH0mmnIOcr83//9H+bOnYvBgwcjMTGx3mPv3buHzMxMtG3b1qAffo05P5nKykokJCTIdxMZ02vYmPOzt7fHxIkTNUrIuHr9GkLV32BeXh5KS0t18jthLCZMmIBff/0VL774ImJjY+s9Ni8vD7du3eJ8Z2NDnT17Fv369QOgm79rTZj9mpesrCzcvHmz3ktFRQXi4+Ph4uKC4OBg+X0HDRoEPp8vT0g00a1bNwDSoTVAmpUGBATA3d1dfsyQIUOQl5eHa9eumcQ5CoVCHDhwAOXl5Xj++ec1asbVrVs3ZGdn6yVxAYCKigpcuHABYWFh8ut4PB7CwsIQHx+v9D7x8fEKxwPS10J2/L1795CWlqZwjFAoRO/evVU+pj415BwB4KOPPsJnn32GiIgIhfVNqjRv3hyurq7y31lDaej51cTn8xEQECCP3Zhew8ac34svvghbW1ts3rxZ7fNw9fo1hLq/QV38ThiDiRMnIjo6Gi+99BL27t2r9ngHBwf4+fmZxGuoTLdu3eSxG/I15HyFs7Fc9u7dyy5cuMB69uzJ+vTpw27evKmwjbhZs2bs+vXrrGfPngwA8/X1ZfPnz2fBwcHMx8eHjRw5kt25c4cdOXLk6Yro6q3S+/fvZ127dmVDhw5lYrGY063S2pyjUChk8fHx7PLly8zX11dhaxyfz2cA2IgRI9jrr7/OOnfuzPz8/Njbb7/NCgsL2eeff67Xcxk/fjwrKSlhkydPZv7+/uznn39m2dnZ8p1dGzduZEuWLJEfHxISwsrLy9ns2bNZhw4d2MKFC5Vulc7OzmYjR45kXbp0Ydu3b+d8q7Q25/jxxx+z0tJSNnbsWIXXysHBgQFgDg4ObMWKFax3797Mx8eHDRo0iJ0/f57dvHmT2djYGP35ffbZZ2zIkCGsTZs2LCgoiP3xxx+suLiYdezY0ShfQ23PT3Y5duwY+/PPP+tcb2yvn4ODAwsMDGSBgYGMMcZmzpzJAgMDWcuWLRkAtmTJErZx40b58bKt0suXL2cdOnRg77zzjtKt0vX9mxn7Ob700kusvLycvfPOOwp/gyKRSH7M119/zZ599lnm4+PDQkJC2IEDB1hGRgZzc3Mz+vObMWMGe/7555mfnx/r3LkzW7VqFausrGSDBg0y9Gto+F8GY724uLiw33//neXn57Pc3Fz222+/yd/0ATAfHx/GGGOhoaEMAGvRogU7cuQIy8rKYiUlJezWrVts+fLlCnVeALBWrVqxPXv2sKKiIpaRkcG+/vprhW3GxnyOsm1xyvj4+DBAut364sWLLD8/nxUUFLCEhAT25ptvKuz719fl3XffZffv32elpaXs9OnTrFevXvLb4uLiWHR0tMLx48aNYzdu3GClpaUsMTGRDRs2rM5jLlq0iKWlpbGSkhJ28OBB1q5dO05/L7U5x3v37il9rRYuXMgAMDs7O7Z//34mFotZWVkZu3fvHlu7di1nHwzant/KlSvlx6alpbHdu3cr1M8wxtdQ29/R9u3bM8YYGzx4cJ3HMrbXT9X7g+ycoqOjWVxcXJ37XLx4kZWWlrI7d+4o1LDR5N/M2M8xLi6u3uMB6fbw1NRUVlpayh4+fMj+/PNP5uvraxLn99FHH7Hbt2+z4uJilpWVxQ4fPswGDBhg8NeQV/0/hBBCCCEmwezXvBBCCCHEvFDyQgghhBCTQskLIYQQQkwKJS+EEEIIMSmUvBBCCCHEpFDyQgghhBCTQskLIYQQQkwKJS+EEEIIMSmUvBBCCCHEpFDyQgghhBCTQskLIYQQQkwKJS+EEEIIMSn/D8s1eL4hiDYvAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(train_x, train_y, \"o\", label=\"Train\")\n",
    "plt.plot(test_x, test_f, label=\"True\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e20647b8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌────────────────────┬─────────────┬────────────┬──────────────────┬─────────┬─────────┬─────────┐\n",
      "│ \u001b[1;35mname\u001b[0m               │ \u001b[1;35mtrainable\u001b[0m   │ \u001b[1;35mbijector\u001b[0m   │ \u001b[1;35mprior\u001b[0m            │ \u001b[1;35mdtype\u001b[0m   │ \u001b[1;35mshape\u001b[0m   │   \u001b[1;35mvalue\u001b[0m │\n",
      "├────────────────────┼─────────────┼────────────┼──────────────────┼─────────┼─────────┼─────────┤\n",
      "│ kernel lengthscale │ True        │ Softplus   │ Normal(0.0, 1.0) │ float64 │ ()      │       1 │\n",
      "├────────────────────┼─────────────┼────────────┼──────────────────┼─────────┼─────────┼─────────┤\n",
      "│ sigma              │ True        │ Softplus   │ Normal(0.0, 1.0) │ float64 │ ()      │       1 │\n",
      "└────────────────────┴─────────────┴────────────┴──────────────────┴─────────┴─────────┴─────────┘\n"
     ]
    }
   ],
   "source": [
    "# create a model with default parameters\n",
    "model = GPR(\n",
    "    kernel=SquaredExponential(),\n",
    ")\n",
    "\n",
    "model.print()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4764c1e0",
   "metadata": {},
   "source": [
    "### NLoptWrapper"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28fe1b8c",
   "metadata": {},
   "source": [
    "The NLopt optimizers can be used in GPX via the `NLoptWrapper` that you find in `gpx.optimizers`.\n",
    "This wrapper is needed to have an interface that is very similar to the original NLopt one.\n",
    "\n",
    "For example, the original interface from the [tutorial](https://nlopt.readthedocs.io/en/latest/NLopt_Tutorial/#example-in-python):\n",
    "\n",
    "```python\n",
    "# [...]\n",
    "\n",
    "opt = nlopt.opt(nlopt.LD_MMA, 2)\n",
    "opt.set_lower_bounds([-float('inf'), 0])\n",
    "opt.set_min_objective(myfunc)\n",
    "opt.add_inequality_constraint(lambda x,grad: myconstraint(x,grad,2,0), 1e-8)\n",
    "opt.add_inequality_constraint(lambda x,grad: myconstraint(x,grad,-1,1), 1e-8)\n",
    "opt.set_xtol_rel(1e-4)\n",
    "x = opt.optimize([1.234, 5.678])\n",
    "minf = opt.last_optimum_value()\n",
    "\n",
    "# [...]\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c39ce29",
   "metadata": {},
   "source": [
    "In GPX it's pretty much the same, except that we work with a `ModelState`, and that we have bounds for the parameters in the form of `forward_transform` and `backward_transform`. The wrapper takes into account everything automatically.\n",
    "You can access the NLopt optimizer from the `.opt` attribute of the wrapper, put bounds, constraints, etc.\n",
    "Here we just set the relative tolerance, as e.g. the bounds are imposed by the transformations associated with our parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "980aa154",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌────────────────────┬─────────────┬────────────┬──────────────────┬─────────┬─────────┬──────────┐\n",
      "│ \u001b[1;35mname\u001b[0m               │ \u001b[1;35mtrainable\u001b[0m   │ \u001b[1;35mbijector\u001b[0m   │ \u001b[1;35mprior\u001b[0m            │ \u001b[1;35mdtype\u001b[0m   │ \u001b[1;35mshape\u001b[0m   │    \u001b[1;35mvalue\u001b[0m │\n",
      "├────────────────────┼─────────────┼────────────┼──────────────────┼─────────┼─────────┼──────────┤\n",
      "│ kernel lengthscale │ True        │ Softplus   │ Normal(0.0, 1.0) │ float64 │ ()      │ 0.411055 │\n",
      "├────────────────────┼─────────────┼────────────┼──────────────────┼─────────┼─────────┼──────────┤\n",
      "│ sigma              │ True        │ Softplus   │ Normal(0.0, 1.0) │ float64 │ ()      │ 0.217112 │\n",
      "└────────────────────┴─────────────┴────────────┴──────────────────┴─────────┴─────────┴──────────┘\n"
     ]
    }
   ],
   "source": [
    "import nlopt\n",
    "from gpx.optimizers import NLoptWrapper\n",
    "\n",
    "optim = NLoptWrapper(model.state, nlopt.LD_MMA)\n",
    "optim.opt.set_xtol_rel(1e-4)\n",
    "\n",
    "optim_state, optim_result = optim.optimize(model.state, train_x, train_y, model.state.loss_fn)\n",
    "\n",
    "optim_state.print_params()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "532f2438",
   "metadata": {},
   "source": [
    "### Calling `model.fit_nlopt`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c59a1ae9",
   "metadata": {},
   "source": [
    "To make the optimization easier, models have an utility function `fit_nlopt`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "dc918f67",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌────────────────────┬─────────────┬────────────┬──────────────────┬─────────┬─────────┬──────────┐\n",
      "│ \u001b[1;35mname\u001b[0m               │ \u001b[1;35mtrainable\u001b[0m   │ \u001b[1;35mbijector\u001b[0m   │ \u001b[1;35mprior\u001b[0m            │ \u001b[1;35mdtype\u001b[0m   │ \u001b[1;35mshape\u001b[0m   │    \u001b[1;35mvalue\u001b[0m │\n",
      "├────────────────────┼─────────────┼────────────┼──────────────────┼─────────┼─────────┼──────────┤\n",
      "│ kernel lengthscale │ True        │ Softplus   │ Normal(0.0, 1.0) │ float64 │ ()      │ 0.814884 │\n",
      "├────────────────────┼─────────────┼────────────┼──────────────────┼─────────┼─────────┼──────────┤\n",
      "│ sigma              │ True        │ Softplus   │ Normal(0.0, 1.0) │ float64 │ ()      │ 0.304    │\n",
      "└────────────────────┴─────────────┴────────────┴──────────────────┴─────────┴─────────┴──────────┘\n"
     ]
    }
   ],
   "source": [
    "# new starting point\n",
    "model = model.randomize(jax.random.PRNGKey(2023))\n",
    "model.print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5980c4e5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌────────────────────┬─────────────┬────────────┬──────────────────┬─────────┬─────────┬──────────┐\n",
      "│ \u001b[1;35mname\u001b[0m               │ \u001b[1;35mtrainable\u001b[0m   │ \u001b[1;35mbijector\u001b[0m   │ \u001b[1;35mprior\u001b[0m            │ \u001b[1;35mdtype\u001b[0m   │ \u001b[1;35mshape\u001b[0m   │    \u001b[1;35mvalue\u001b[0m │\n",
      "├────────────────────┼─────────────┼────────────┼──────────────────┼─────────┼─────────┼──────────┤\n",
      "│ kernel lengthscale │ True        │ Softplus   │ Normal(0.0, 1.0) │ float64 │ ()      │ 0.411059 │\n",
      "├────────────────────┼─────────────┼────────────┼──────────────────┼─────────┼─────────┼──────────┤\n",
      "│ sigma              │ True        │ Softplus   │ Normal(0.0, 1.0) │ float64 │ ()      │ 0.217114 │\n",
      "└────────────────────┴─────────────┴────────────┴──────────────────┴─────────┴─────────┴──────────┘\n",
      "is fitted: True\n"
     ]
    }
   ],
   "source": [
    "optim = NLoptWrapper(model.state, nlopt.LD_MMA)\n",
    "optim.opt.set_xtol_rel(1e-4)\n",
    "\n",
    "model.fit_nlopt(train_x, train_y, opt=optim, minimize=True)\n",
    "\n",
    "model.print()\n",
    "print('is fitted:', model.state.is_fitted)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77a1ba10",
   "metadata": {},
   "source": [
    "It is also possible to perform multiple restarts by providing `num_restarts` to the function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "bec3e87d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌────────────────────┬─────────────┬────────────┬──────────────────┬─────────┬─────────┬──────────┐\n",
      "│ \u001b[1;35mname\u001b[0m               │ \u001b[1;35mtrainable\u001b[0m   │ \u001b[1;35mbijector\u001b[0m   │ \u001b[1;35mprior\u001b[0m            │ \u001b[1;35mdtype\u001b[0m   │ \u001b[1;35mshape\u001b[0m   │    \u001b[1;35mvalue\u001b[0m │\n",
      "├────────────────────┼─────────────┼────────────┼──────────────────┼─────────┼─────────┼──────────┤\n",
      "│ kernel lengthscale │ True        │ Softplus   │ Normal(0.0, 1.0) │ float64 │ ()      │ 0.411059 │\n",
      "├────────────────────┼─────────────┼────────────┼──────────────────┼─────────┼─────────┼──────────┤\n",
      "│ sigma              │ True        │ Softplus   │ Normal(0.0, 1.0) │ float64 │ ()      │ 0.217113 │\n",
      "└────────────────────┴─────────────┴────────────┴──────────────────┴─────────┴─────────┴──────────┘\n",
      "is fitted: True\n"
     ]
    }
   ],
   "source": [
    "model.fit_nlopt(train_x, train_y, opt=optim, minimize=True, num_restarts=5, key=jax.random.PRNGKey(3))\n",
    "\n",
    "model.print()\n",
    "print('is fitted:', model.state.is_fitted)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f86bc3b",
   "metadata": {},
   "source": [
    "**Take home message**: you can fit your models using `fit_nlopt` and providing a `NLoptWrapper` to it, similarly to what you do with `fit`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d139990",
   "metadata": {},
   "source": [
    "### Using boundaries/constraints from NLopt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17f0a32b",
   "metadata": {},
   "source": [
    "An important caveat to keep in mind: if bounds/constraints are specified in NLopt, then the parameters should have \"null\" forward and backward transforms, because the mixing of these transformations and the additional ones specified with NLopt will likely not do what you want.\n",
    "\n",
    "For example, if we use the `GN_ESCH` optimizer, we must provide a finite boundary for the parameters.\n",
    "If we enforce them to be positive with a nonlinear transformation like softplus, we will obtain strange results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3c51fe69",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌────────────────────┬─────────────┬────────────┬──────────────────┬─────────┬─────────┬──────────┐\n",
      "│ \u001b[1;35mname\u001b[0m               │ \u001b[1;35mtrainable\u001b[0m   │ \u001b[1;35mbijector\u001b[0m   │ \u001b[1;35mprior\u001b[0m            │ \u001b[1;35mdtype\u001b[0m   │ \u001b[1;35mshape\u001b[0m   │    \u001b[1;35mvalue\u001b[0m │\n",
      "├────────────────────┼─────────────┼────────────┼──────────────────┼─────────┼─────────┼──────────┤\n",
      "│ kernel lengthscale │ True        │ Softplus   │ Normal(0.0, 1.0) │ float64 │ ()      │ 0.706873 │\n",
      "├────────────────────┼─────────────┼────────────┼──────────────────┼─────────┼─────────┼──────────┤\n",
      "│ sigma              │ True        │ Softplus   │ Normal(0.0, 1.0) │ float64 │ ()      │ 0.73211  │\n",
      "└────────────────────┴─────────────┴────────────┴──────────────────┴─────────┴─────────┴──────────┘\n",
      "is fitted: True\n"
     ]
    }
   ],
   "source": [
    "# create a model with default parameters\n",
    "model = GPR(\n",
    "    kernel=SquaredExponential(),\n",
    ")\n",
    "\n",
    "optim = NLoptWrapper(model.state, nlopt.GN_ESCH)\n",
    "optim.opt.set_lower_bounds([0., 0.])\n",
    "optim.opt.set_upper_bounds([10., 10.])\n",
    "optim.opt.set_maxeval(500) # run for 500 steps\n",
    "\n",
    "model.fit_nlopt(train_x, train_y, opt=optim, minimize=True)\n",
    "\n",
    "model.print()\n",
    "print('is fitted:', model.state.is_fitted)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5bc34329",
   "metadata": {},
   "source": [
    "You see that it is going in the wrong direction. Instead, if we want to impose constraints with NLopt, it's better to not impose them in GPX by using the `identity` (null) transformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5cff8f2d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌────────────────────┬─────────────┬────────────┬──────────────────┬─────────┬─────────┬──────────┐\n",
      "│ \u001b[1;35mname\u001b[0m               │ \u001b[1;35mtrainable\u001b[0m   │ \u001b[1;35mbijector\u001b[0m   │ \u001b[1;35mprior\u001b[0m            │ \u001b[1;35mdtype\u001b[0m   │ \u001b[1;35mshape\u001b[0m   │    \u001b[1;35mvalue\u001b[0m │\n",
      "├────────────────────┼─────────────┼────────────┼──────────────────┼─────────┼─────────┼──────────┤\n",
      "│ kernel lengthscale │ True        │ Identity   │ Normal(0.0, 1.0) │ float64 │ ()      │ 0.242172 │\n",
      "├────────────────────┼─────────────┼────────────┼──────────────────┼─────────┼─────────┼──────────┤\n",
      "│ sigma              │ True        │ Identity   │ Normal(0.0, 1.0) │ float64 │ ()      │ 0.280894 │\n",
      "└────────────────────┴─────────────┴────────────┴──────────────────┴─────────┴─────────┴──────────┘\n",
      "is fitted: True\n"
     ]
    }
   ],
   "source": [
    "# create a model with default parameters\n",
    "model = GPR(\n",
    "    kernel=SquaredExponential(),\n",
    "    sigma=Parameter(1.0, True, Identity(), NormalPrior()),\n",
    "    kernel_params=dict(lengthscale=Parameter(1.0, True, Identity(), NormalPrior()))\n",
    ")\n",
    "\n",
    "optim = NLoptWrapper(model.state, nlopt.GN_ESCH)\n",
    "optim.opt.set_lower_bounds([0., 0.])\n",
    "optim.opt.set_upper_bounds([10., 10.])\n",
    "optim.opt.set_maxeval(500) # run for 500 steps\n",
    "\n",
    "model.fit_nlopt(train_x, train_y, opt=optim, minimize=True)\n",
    "\n",
    "model.print()\n",
    "print('is fitted:', model.state.is_fitted)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2d1f9ee",
   "metadata": {},
   "source": [
    "And you see that everything is going in the right direction."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e3a9d01",
   "metadata": {},
   "source": [
    "**Take home message**: if you impose constraints with NLopt, then use the `identity` transformation for you parameters. If you don't want to impose constraints with NLopt, use the transformations to impose boundaries (e.g., using `softplus`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0b7976c4",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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