GPR.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# GPR\n",
    " * Implement multiple kernels\n",
    "     * linear\n",
    "     * periodic\n",
    " * Use HXDY to do log marginal likelihood optimization\n",
    "#### Imports and Function Defs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import numba as nb\n",
    "import scipy.sparse.linalg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kernel Defs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#@nb.njit(cache=True)\n",
    "def rbf(xp, xq, sf, l):\n",
    "    return sf*sf*np.exp(-.5 * np.power((xp-xq)/l, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.vectorize\n",
    "def periodic(xp, xq, sf, p, l, mu):\n",
    "    return sf*sf*np.exp(-2.*np.power(np.sin(np.pi*(xp-xq)/p - mu)/l,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def kernel(xp, xq, params):\n",
    "    return rbf(xp, xq, params[0], params[1]) + \\\n",
    "        periodic(xp, xq, params[2], params[3], params[4], params[5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kernel Derivative Defs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#@nb.njit(cache=True)\n",
    "def rbf_prime(xp, xq, sf, l):\n",
    "    x_diff = xp-xq # this is a vector\n",
    "    result = np.empty(2)\n",
    "\n",
    "    result[0] = 2.*sf*np.exp(-.5 * np.power(x_diff/l, 2))\n",
    "    \n",
    "    result[1] = sf*sf*np.exp(-.5 * np.power(x_diff/l, 2)) * x_diff * x_diff * np.power(l, -3)\n",
    "    \n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def periodic_prime(xp, xq, sf, p, l, mu):\n",
    "    result = np.empty(4)\n",
    "    sin_arg = mu + np.pi*(-xp+xq)/p\n",
    "    exp_arg = -2*np.power(np.sin(sin_arg)/l, 2)\n",
    "    \n",
    "    # derivative w.r.t. sf\n",
    "    result[0] = 2.*sf*exp_arg\n",
    "    # derivative w.r.t. p\n",
    "    result[1] = 2*exp_arg*np.pi*sf*sf*(-xp+xq)*np.sin(2*sin_arg)*np.power(l*p,-2)\n",
    "    # derivative w.r.t. l\n",
    "    result[2] = 4*exp_arg*sf*sf*np.sin(sin_arg)*np.power(l,-3)\n",
    "    \n",
    "    # derivative w.r.t. mu\n",
    "    result[3] = -2*exp_arg*sf*sf*np.sin(2*sin_arg)*np.power(l,-2)\n",
    "    \n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def kernel_prime(xp, xq, params):\n",
    "    return np.append(rbf_prime(xp, xq, params[0], params[1]),\n",
    "        periodic_prime(xp, xq, params[2], params[3], params[4], params[5]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Covariance Matrix Calculations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#@nb.njit(cache=True)\n",
    "def K_XX(X, params):\n",
    "    cov = np.empty((len(X),len(X)))\n",
    "    for i in range(len(X)):\n",
    "        for j in range(i+1):\n",
    "            cov[i,j] = cov[j,i] = kernel(X[i], X[j], params)\n",
    "    return cov"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#@nb.njit(cache=True)\n",
    "def K_XY(X, Y, params):\n",
    "    cov = np.empty((len(Y),len(X)))\n",
    "    for i in range(len(Y)):\n",
    "        for j in range(len(X)):\n",
    "            cov[i,j] = kernel(Y[i], X[j], params)\n",
    "    return cov"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prediction Tools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#@nb.njit(cache=True)\n",
    "def predict(X, X_s, params, k_xx_i_y, y_mean):\n",
    "    return np.dot(K_XY(X, X_s, params), k_xx_i_y) + y_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fitPredict(X_train, y_train, X_test, params):\n",
    "\n",
    "    k_xx = K_XX(X_train, params)\n",
    "    y_mean = np.mean(y_train)\n",
    "    k_xx_i_y = scipy.sparse.linalg.minres(k_xx, y_train-y_mean)[0] \n",
    "    pred = predict(X_train, X_test, params, k_xx_i_y, y_mean)\n",
    "    \n",
    "    return pred"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $\\theta$ Optimization Tools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "#@nb.njit(cache=True)\n",
    "def log_marginal_likelihood(x, y, params):\n",
    "    K = K_XX(x, params)\n",
    "    K_inv = np.linalg.pinv(K)\n",
    "    \n",
    "    term1 = -.5*np.log(np.linalg.det(K))\n",
    "    term2 = -.5*((y.T @ K_inv @ y))\n",
    "    term3 = -(len(x)/2)*np.log(2.*np.pi)\n",
    "    return -(term1 + term2 + term3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def log_marginal_likelihood_prime(x, y, params):\n",
    "    \n",
    "    K = K_XX(x, params)\n",
    "    K_inv = np.linalg.pinv(K)\n",
    "\n",
    "    alpha = y.T @ K_inv\n",
    "\n",
    "    kernel_der = np.empty((len(x), len(x), len(params)))\n",
    "\n",
    "    for i in range(len(x)):\n",
    "        for j in range(len(x)):\n",
    "            kernel_der[i,j] = kernel_prime(x[i], x[j], params)\n",
    "    #print('kernel_der', kernel_der.shape)\n",
    "    #print(np.around(kernel_der[:,:,0], 2))\n",
    "    \n",
    "    der = np.empty(len(params))\n",
    "    \n",
    "    for i in range(len(der)):\n",
    "        idx = tuple([slice(None)]*(kernel_der.ndim-1) + [i])\n",
    "        #print(np.around(kernel_der[idx], 2))\n",
    "        der[i] = (.5 * alpha @ kernel_der[idx] @ alpha.T)\n",
    "        der[i] -= .5*np.trace(K_inv @ kernel_der[idx])\n",
    "        #print((.5 * alpha @ kernel_der[idx] @ alpha.T)[0,0], -.5*np.trace(K_inv @ kernel_der[idx]))\n",
    "    return -der"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 300"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(0, np.pi, 1e-3)\n",
    "y = np.sin(x*np.pi) #+ .01*np.random.normal(size=len(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fd9b6321860>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sf, p, l, mu\n",
    "params = np.array([0., 1, 1., 2, 10, np.pi/4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/david/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:6: RuntimeWarning: divide by zero encountered in log\n",
      "  \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-inf, array([-0.        , -0.        , -0.00968906,  0.08543339,  0.18091834,\n",
       "        -0.04741994]))"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "func_wrapper(params, x[::n], y[::n])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = fitPredict(x[::n], y[::n], x, params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.plot(x, y, label='truth')\n",
    "plt.plot(x, p, label='prediction');\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sf, p, l, mu\n",
    "params = np.array([0., 1, 1., 2, 10, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = fitPredict(x[::n], y[::n], x, params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.plot(x, y, label='truth')\n",
    "plt.plot(x, p, label='prediction');\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.optimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "def func_wrapper(p, x, y):\n",
    "    return log_marginal_likelihood(x, y, p), log_marginal_likelihood_prime(x, y, p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "      fun: -18.69490548051146\n",
       " hess_inv: array([[ 1.00000000e+00,  0.00000000e+00,  0.00000000e+00,\n",
       "         0.00000000e+00,  0.00000000e+00,  0.00000000e+00],\n",
       "       [ 0.00000000e+00,  1.00000000e+00,  0.00000000e+00,\n",
       "         0.00000000e+00,  0.00000000e+00,  0.00000000e+00],\n",
       "       [ 0.00000000e+00,  0.00000000e+00,  1.00000000e+00,\n",
       "         2.32377100e-12,  8.45908722e-10,  1.01854013e-19],\n",
       "       [ 0.00000000e+00,  0.00000000e+00,  2.32377100e-12,\n",
       "         1.00000000e+00,  4.22452055e-09,  1.19749109e-21],\n",
       "       [ 0.00000000e+00,  0.00000000e+00,  8.45908722e-10,\n",
       "         4.22452055e-09,  2.67308015e-15, -1.08241515e-14],\n",
       "       [ 0.00000000e+00,  0.00000000e+00,  1.01854013e-19,\n",
       "         1.19749109e-21, -1.08241515e-14,  1.00000000e+00]])\n",
       "      jac: array([-0.00000000e+00, -0.00000000e+00, -1.00012094e+02, -1.15607961e+00,\n",
       "        4.42859702e+05, -4.47581174e-08])\n",
       "  message: 'Desired error not necessarily achieved due to precision loss.'\n",
       "     nfev: 47\n",
       "      nit: 1\n",
       "     njev: 36\n",
       "   status: 2\n",
       "  success: False\n",
       "        x: array([0.00000000e+00, 1.00000000e+00, 1.00000000e+00, 2.00000000e+00,\n",
       "       1.00000000e+01, 3.53006361e-22])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best = scipy.optimize.minimize(func_wrapper, x0=params, args=(x[::n], y[::n]), jac=True, method='BFGS')\n",
    "best"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = fitPredict(x[::n], y[::n], x, best.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.plot(x, y, label='truth')\n",
    "plt.plot(x, p, label='prediction');\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sf, p, l, mu\n",
    "params = np.array([0., 1, 1., 1.8, 1, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = fitPredict(x[::n], y[::n], x, params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gQkp5UkrZDbwMrDWQfwB4yQnf67GsK6yi7nIXX1ua4dgJJ9+Hii0q2iIs3rXKXYUQgi8vmUh9SxdvHTp3rcAtP1DheDt+7Fa9NF6AuU9Fl40er2bhV/HMjkoC/Ew8sciNq4F+0m+GrDXwwS9VT2Q7hAb58y8LJ7CjtIFj1b4XQeQMQ5AMDPQrVFuOXYMQIhUYD7w34HCwEKJQCLFXCHG7rS8RQjxhkStsaLD/hx0u+sySP+46xYxxUY6tBqSErd+HiLEw5wnXK2iFGyfGMjkpgj/srMRsvmqDLXqC2rg++Ddo8O3ICs1VHH0F6otg6X9e0/q0vqWTNw7VcE/eWPeuBgZyyw9UIcVdP3dI/OEbxhEe5M8fd510qVqeiDMMgbVwGFvb9fcDr0kpB/ogxllapz0I/FIIYXX6IKV8VkqZJ6XMi4tzsHzzMLC5qJazTe08sXCCY5FCxW+qmiw3f+fj6ozuRgjB526aQGVDG9tK6q8VWPRNCAwbVP13zQinpxPeewrGzIDJ187fnt99mh6zmcdvnGDlZDcRmwEzHob9f3IoJyY8OIAH5o5j47HzVF9sd71+HoQzDEE1kDLg/VjAio8BUIbgCreQlPKc5fkksAOY4QSdho0/7jrJuOhRLM9xIG+grwe2/TfEZcO0+12vnAGrpySRHBXCszsrrx0MjVFN70s3qcY4Gs1Hz8LlarVBfFXSY1tXL3/fe5YVkxNJc2XegCMsflJF4L33lEPin16QhgD+/MFpl6rlaTjDEOwHMoQQ44UQgaib/TXRP0KIScBoYM+AY6OFEEGW17HAAqDYCToNCwfOXOTg2WY+syDNsVoqh16Apkq45ftuCRc1wt/PxOMLx7P/9EUOnGm6VuCGf4WwRIcvKM0IpqNZ5Q1MXAbjF10z/GphFZc6eviXRcO4GugnYoz63z22TmUd2yEpMoTbpo3h5f1nfaq/8ZANgZSyF/gSUACcAF6VUhYJIX4ohBgYBfQA8LKUV2R5ZAOFQogjwHbgJ1JKrzUEz+06SUSwP/fkpdgX7u2C93+mKn5m5rteOQe4b3YKkSEB/OkDK9VHA0LUquDMB6pHgsZ32fcH6GyGJd+7Zqi3z8yfPjhFXupoZqWOHgblrLDgaxAc6fAk5vGFE2jv7uMfH51xsWKeg1PyCKSUm6SUmVLKdCnlU5Zj/ymlXD9A5gdSyievOm+3lHKKlHKa5dlrK52dvdBOQVEtD92QSmiQv/0TDv4NWs6p5Jch9hlwFqMC/bl/dgoFRXXUXrISfz3rMQhPgu0/drhxuGaE0XkJ9v4WJq2CMdOvGd56oo7qix08vnD8MChng5AomPdFKHsHzh+xKz55TAQ3TozlhT1n6O3zjSq8OrPYSbyw9zQmIXjUkTrrvV3wwdNqNTD+JpfrNhgeviEVs5S8uM/KbCggWNWRObsbTjnWHlAzwtj3rDIGNrrlvbD3DGMig7klO8Hq+LAx93MQFKnqEDnAp+alcv5SJ1tP+EYXM20InEBnTx/rDlSzPCfBsa5Lh/8Bl2vUxeQhq4F+UqJHsTQrnhc/Onttghmo6qQRybD9/+pVga/ReRn2/C9krlTRQldRUd/KhxUXeOiGVPz9POzWEhyp9gpKNkDtcbviS7MTSI4K4YW9vuEe8rC/lney8eh5mtt7eHiuA/0Gerth1//A2NmQvsT1yl0Hn5qXRmNrN+8et5JN7B+kVgVV++DkDrfrphlGPnpW7Q0s/pbV4b/vPUOAn+BeR/bIhoMbPg9BEbDT/qrAzyR4cO44Pqy4QEV9qxuUG160IXACL+w9w4S4UMcSyI68pKo03vQtj1sN9HPjxFgmxIby/O7T1gVmPKz2Cj74H7fqpRlGulrUaiBjhdXVQHt3L/88UM3K3KThSyCzR8ho5SIqfgvq7Mek3Dc7hUA/E3/3gVWBNgRD5HjNJQ5XNfPw3FT7CWR9vSrsbswMmHiLexS8DkwmwSPzUjl4ttl6ur1/kNp8O7UTqg+4X0GN+znwV+i4qCYwVnjz0Dlaunr51DwHu/ANFzd8QSVH7vqFXdHYsCBWTUnknweqaesa2U3utSEYIv/Yd4bgABN3zRprX7j4TWg+Awu/4bGrgX7umjWW4AATL3501rrArMeU3/XDp92ql2YY6O2GPb9TrVPHzrpmWErJ3/acJisx3HNCRm0xKhryPg1FbziUbfzIvDRaunp583CN63UbRrQhGAKXO3t489A5bps2hsiQAGNhKVXN9piJKvTOw4kIDmD1lDG8feQc7d1WZkNB4ao20okN0KB7vo5ojr+mQp1v/JrV4UNVzZTUtvDIPAdWxZ7A3H8FYVLGzQ4zx0WRlRjOyx9V2ZX1ZrQhGAJvHaqho6fPsab0p3aqGOb5X3ZJH2JXcP+cFFq7etl49Lx1gbmfV3Xodb+CkYvZrP6+Cbmql7UV1hVWERLgx23TxrhZueskMhmm3qsy+9utZNEPQAjBfbNTOFZzieJzl92koPvxjjuSh7LuQDXZSRFMHRtlX3j3ryE0XnVx8hLyUkczIS702qY1/YTGqnDSoy/DpWrrMhrvpnwzNJTAgq9adWe2d/fy9pHzrJ6aRHiwnVWxJzH/y9DTDvufsyt6+/RkAv1MvFo4clcF2hBcJyW1lzlafYl78xzYG6g9rpp3zP3csFUYvR6EENyXl0LhmYtU1LdYF5r/JeX22vt79yqncQ8f/goiUyDnDqvDm47V0trV67kho7aIz1YRUPueUaWqDRgdGsjynATePFxjPbdmBKANwXWyrrCaAD/B2ulWWy9cye7fQECoyxvSu4I7Z47F3yRsrwqixqkuZgdfUCGGmpFD1Ucqi3zeF69pSN/Pq4VVpMWMYnaah28SW2PBV6H9gkrwtMN9s1Nobu9hc9HIzDTWhuA66O418+ahGm7JTiA6NNBY+FK12myb+SkVx+xlxIUHcUt2Aq8frKG710bdlXlfhK5LcPhF9yqncS27fw3BUTDjEavDpxrb+OhUE/fkpXjHJvHVpM6H5DzY/b+q25oBC9JjSY4KGbHuIW0IroP3Suq50Nbt2HJ43x+U62TeF1yvmIu4b3YKF9q62War7srYPJUpvff3anNR4/1cPAMlG1WoZVCYVZHXDlRhEnDXTAfco56IEGoSc/GU2gsxwGQS3D1rLB9UNI7IpjXaEFwHrx2oIj48iIUZscaC3W1w8HnIvlW5ULyURZlxJEQE8c+DBhvCN3xBXVBl77pPMY3r2P8cIKz2IgbVkvW1A9UsnhTvWH0tTyX7VlU7y4E9rnss+4HrCkdeYIQ2BIOkvqWT7aUNyndur7DW0VdVpca5n3ePci7Cz6T2QnaUNnChtcu6UPZtqu/yXvux2RoPp38CM/k2iLQ+299Z3kDd5S7HgiU8Gb8AtXd36n2oP2EoOnb0KBakx/L6oWrkCCu46BRDIITIF0KUCiEqhBBPWhl/TAjRIIQ4bHk8PmDsUSFEueXxqDP0cSVvHqqhzyw/nh3YREpVpCtxCoy7wT3KuZA7ZiTTa5ZssJVT4OcPc5+A07sc6gSl8WCOvmJ3AvP6wRpGjwpgSZaHlZu+HmY+pvJh9j1jV/T2GclUNXVw8OxF1+vlRoZsCIQQfsBvgZXAZOABIcRkK6KvSCmnWx7PWc6NBr4PzAXmAN8XQnj0jurrB2uYMS6K9DjrftOPOf0B1BfDnM95fDkJR8hOiiArMZzXDxmk2s/8FASM0qGk3oyUal8raRqkzLUq0trVy5biWlZPTSLQfwQ4FUJjYMo9cOQVuwlm+bmJBAeYeMPoOvBCnPFXnANUSClPSim7gZeBtQ6euwLYIqVsklJeBLYAntG30QoltZcpqW3hjhkOhIzuewZComHK3a5XzE3cOTOZI1XNVDbYKMsbMhqmP6j6w7Y2uFc5jXM49b5KIJv7eZsTmILjtXT2mB27DryFuZ+H3g7VOdCAsCB/lk9OZMPR87aj6LwQZxiCZGBgTFW15djV3CWEOCqEeE0I0R9u4+i5HsFbh8/hZxKsnpJkLNh8Fko3waxHVa/fEcLa6cmYhHKP2WTOE9DXrdL3Nd7Hvj9AaBzk3mVT5M3DNaREhzBznEcv3gdHYq4qqrf/OVUl2IA7ZiTT3N7D+2UjZ7LjDENgbdpw9U7K20CalHIqsBV4fhDnKkEhnhBCFAohChsa3P8HMJsl6w+fY2FGLDFhduqt96et53lfApkRCRHBLJgYyxuHamxvlsVNUhfUgb/Yjc3WeBhNp6D0HZj1aVVq3Ar1LZ18WNHI2mnJ3pk7YMTcz6leIaUbDcVuzIglJjSQNw6NnOghZxiCamBgQP1Y4NxAASnlBSllf7jJH4FZjp474DOelVLmSSnz4uLinKD24Cg8c5Ga5g5ut5dJ3GNZXmatgSgvS7t3gDtmJFN9sYPCMwabZbM/q1ZFFVvdp5hm6Ox/Dkx+kPcZmyJvHzmPWcLtM7ykwNxgmLRKldMo/LOhWICfiVunjWHriXoudfS4STnX4gxDsB/IEEKMF0IEAvcD6wcKCCEG+lJuA/rjtAqA5UKI0ZZN4uWWYx7HW4drCAnwY9lkO1ESx15TDTzmfs49irmZFTmJhAT48fpBA/dQ1hoIS3CooJfGQ+jpVKUWslZDhG3X51uHa8hNjmBifLgblXMTJj+Y+ahqwXqh0lD0jhnJdPeaefe4jSg6L2PIhkBK2Qt8CXUDPwG8KqUsEkL8UAhxm0XsK0KIIiHEEeArwGOWc5uA/0YZk/3ADy3HPIruXjMbj51n2eQEQoP8jYUP/AXisiB1gXuUczOhQf7k5yay8eg525tlfgGqcU35Foeaf2g8gBPr1QTGYDVQ2dDK0epL9lfF3syMh0H4qevYgKljI5kQGzpiooecEvslpdwkpcyUUqZLKZ+yHPtPKeV6y+tvSylzpJTTpJQ3SylLBpz7ZynlRMvD+Lc/TOwsa6C5vcf+cvj8Uag5oG6CI81/OoBbpyVxubOXDyoM9mpmPqqafxR65J9UczWFf4HoCZC2yKbIW4dqEAJu9Za+A9dDRBJkrYJD/4BeG8mTqMq8t89IZu/JJs41G1cv9QZGQBCw63nzsEqeWZhhZ2/iwF9VYsrU+9yi13Bx48Q4IkMCePuIwbI4MhkmrVTRQz2d7lNOM3jqS1SV0VmP2WyaJKXkzcPnWJAeS0KEF5eUcIS8z0BHExSvNxTrb8Sz6Zj3u4e0IbBDa1cvW0/UsXpqEgFGJSW621RJicm3q76oI5hAfxP5OYlsLqqls8cgMmj246rMb/Fb7lNOM3gO/AX8AmH6QzZFDlU1c7apnbXTR/BqoJ/xi2H0eLubxmmxoeQmR/C2rWx7L0IbAjtsKVbJM3b9osf/Cd0tqlqjD3DrtDG0dfexo7TettD4myA63a6/VTOM9HTAkZdU8bVQ20UUNx49T6CfiRW5iW5UbpgwmdR1fHa33fpDa6aO4UhVM1VN3l2RVBsCO2w4cp4xkcH2k2cO/FVtEttIyx9p3DAhmpjQQGP3kMkEMx+Bs3ugsdx9ymkcp+gNVVdolu0JjNks2XTsPIsyY4nwpnaUQ2H6Q2qVZGePqz+51GYNLi9BGwIDLnX0sKu8kVVTkjCZDDZ/fWSTeCD+fiZWTUliW0kdbV0GmZjTHlRRGDrT2DMp/AvEZEDajTZFDlVd5PylTlZPtZNRP5IIjVUVdY+8DN22Z/sp0aOYnhLFhqNW05+8Bm0IDNhaXEd3n5lV9i4AH9kkvpo1U5Po7DGz1VbDGoDwBMjMV93L+kZG8s2IofY4VH+k3CAGE5iNR2sJ9DdxS/YIqDQ6GPI+rTrv2dnjWjM1iaJzlznV2OYmxZyPNgQGbDp2nuSoEGakRNkW8qFN4quZnRZNQkSQ/WXxzEegrQHKPDJX0Hc59IJyf0x7wKZIv1vopsw4wn3FLdRP6gK1aWynp3H/SmmjF68KtCGwQb9baGVuonFNlaI31SbxrMfcppunYDIJVk8Zw/ulDcap9hOXQVii3cqOGjfS260mMJNWGU5gDp69SO3lTtb4kluoHyFgxkOqx0bTKZtiSZEh5KWO9up9Am0IbOCwW+jwiyoyZgQ0n7ke1kxLorvPzOaiWttCfv6qPHXFFrjsvbOmEUXZOypWfsbDhmIbjlcoSooAACAASURBVJ4n0N/EUl9zC/Uz7QFAqOvcgDVTkyipbaGivsU9ejkZbQhs4JBbqOkUnPlA3eR8ZJP4amakRDF2dIj92dCMh0Ga7V5QGjdx6B8QngTpS2yKmM2Sd46fZ3FmHGH2SquMVCLHqt/RkZfAbLv/wKopSQiBcRSdB6MNgRUcdgsdeRkQMO1+t+nmaQghWDUlid2VjVxqN3APxaRD6o3KL21wQWncQEutWp1Nu18VWrPBgbMXqbvc5VvRQtaY8ZAqT33qfZsi8RHBzB0fzYaj57yyn7E2BFZwyC1kNsORF2HCYpsNvn2F/NxEevqkcfQQqFaWF0+rVZRm+DjyslqdTTd2C208ep4gX3YL9TNpNQRHwaG/G4qtmTqGyoY2Suu8zz2kDYEVHHILnflQ1dw3SMv3FaaPjSIxIph3jhvsEwBMvg2CIuDwS+5RTHMtUir3XMpciJ1oU6zPEi1086R433UL9RMQrHoal2yAjmabYstzEhAC3rV3HXgg2hBchcNuocMvqpta1mr3KeehmEyC/NxEdpY30GqUXBYQoozBifUq7FbjfmoOQGOp2tcyoPB0E/Ut2i30MTMegt5OVUrGBvHhwcxOjdaGYCTgkFuoq1UlmeTcAYGj3KecB7MyN5HuXjPbSwxqD4GKwuhuhRLjdoAaF3Ho7+AfAjl3GoptOqbcQkuy4t2kmIeTNB0Scu26h/JzEympbfG65DJtCK7CIbdQ8VvQ06bdQgPIS4smNizQ/mxo3HzVDvDIy+5RTPMJPR1w/HW1KguOsClmNkveLapl8aQ4+42YfAUh1PV+7iA0lNoU6y/K522rAqcYAiFEvhCiVAhRIYR40sr414UQxUKIo0KIbUKI1AFjfUKIw5aHcQFwF3O5cxBuoeh0SJnjPuU8HD+TYHlOIttL6+noNihNbTKpUhwnt6voFY37KH1HlUyw4xY6XN1M3eUu8n2h0uhgyL1LNVs6+qpNkeSoEKaNjfS6FpZDNgRCCD/gt8BKYDLwgBBi8lVih4A8KeVU4DXg/w0Y65BSTrc8bmMY2V5ST3ef2fgC6I968eHcAVuszE2kvbuP98sMOpeBCluUZji2zj2KaRTH1qkM77SFhmIFRbX4mwRLsnw8WuhqwhNgws1w7FW16W6D/NwkjlRfosaLOpc5Y0UwB6iQUp6UUnYDLwNrBwpIKbdLKftL+O0FPDLecnNRHbFhQcYlp4+9pp6n3usepbyIGybEEDUqwP5sKDYDxsyEI6+4RzENtDepHtJT7jbMHZBSUnC8lnnpMUSG+FhtIUeYeq+KFqzaZ1OkfyJZ4EXuIWcYgmSgasD7assxW3wWeGfA+2AhRKEQYq8Q4nZbJwkhnrDIFTY02JlxXgedParJyrLJCbZLTkupZlXj5kHUOKfr4O0E+JlYlp3AthP1dPUauIdAbRrXHVMVMDWup/hNMPeoMEgDyupaOX2hXbuFbJG1Wm22H7U9iRkfG0pWYrhX7RM4wxBYu2taXTcJIR4G8oCfDTg8TkqZBzwI/FIIkW7tXCnls1LKPCllXlycnd7B18GHFY20dfexIsdgOVxXBA0lalalscrKKYm0dPWyu+KCsWDuXWDyh6N609gtHF0HsZmQNM1Q7N3jtQgByyZrt5BVgsKVMSh6QxXus0F+biL7zzRR3+Id/bqdYQiqgZQB78cC11QWE0LcAnwXuE1K2dV/XEp5zvJ8EtgBzHCCToOmoKiW8CB/5qfbbtfHsXXq5jX5Dvcp5mUsmBhLeJA/79hzD4XGQMZy5Woz21k9aIZG81nVdnHKvXb3tQqKapk1bjTx4SO8Qf1QmHovdFyEym02RfJzE5ESthTbybb3EJxhCPYDGUKI8UKIQOB+4IroHyHEDOAPKCNQP+D4aCFEkOV1LLAAKHaCToOit8/M1hP13JwVT6C/jV+J2aySSdKXqJuYxipB/n4syY5nc3EdPX12agpNvQ9azsOpne5Rzlfp39eys5Ktamqn+PxlVuRot5Ah6UtgVIyhe2hSQjjjY0O9xj00ZEMgpewFvgQUACeAV6WURUKIHwoh+qOAfgaEAeuuChPNBgqFEEeA7cBPpJRuNwSFZy7S1NZtfAFU7VOFp+z4WDWwMjeJ5vYe9p1sMhbMXAGBYVD0unsU81WOrYOxcyB6vKFYgaWUuDYEdvALUAl5pe9A52WrIkKobPs9lRdobrftQvIUnJJHIKXcJKXMlFKmSymfshz7TynlesvrW6SUCVeHiUopd0spp0gpp1me/+QMfQbL5qI6Av1NLJ5ksPdwbJ3aJJq0yn2KeSk3ZcYREuDHu0V23EMBlt/nibcN/a2aIVB7HOqLHYpye/d4LdlJEYyL0dnydpl6ryo5ceJtmyL5OYn0mqVXuId8PrNYSklBUS0LJ8bazqLs61GbQ1mrICjMvQp6ISGBftyUGceW4jrMZjsleXPvUv7WkzvcopvPcexVEH6qlaoB9S2dHDh70ThYQvMJY2fD6DT1+7XB1LGRjIkM/nil5cn4vCEoOneZmuYO4+Vw5XbVzUm7hRxmeU4CdZe7OFpzyVgwfQkER2r3kCswm+GYZV8rzDjSbktxHVKiw0YdRQjIvVvtb7VaD2cXQrAiN5Gd5Y3GxRg9AJ83BJuLajEJWJptUFzr2DpVjzx9qfsU83KWZMXjZxLGLSwB/AMh+1Y4sQF6vCPUzmuoKYTL1WrVZYeCojpSY0YxKSHcDYqNEHLuUBnyJ2xXxlmZm0R3r5kdpXaKMQ4zPm8ICorqmJ0WTUxYkHWB7nZVKXPyWnXT0jhE1KhAbpgQ7diyOOdO6G6Biq2uV8yXKHoD/AKVS9OASx097K5oJD/HTo0tzZUk5EBMhvo922BW6mhiQh0oxjjM+LQhON2ougkZuoUqtqpKo7nGZXs117J8ciKVDW1U1LcaC46/SYXjGdR61wwSs1lVyU1fqlxvBmwvqafXLFmuo4UGhxBqVXDmQ2i1PuNXxRgT2F5ST2eP5+bL+LQh6J+tLjfaICt+U92kUm90k1Yjh/7sVLtRE37+ajOz7F3dsMZZ1BTC5RrIMd4kBhUtFB8eZFx6XWMdB9xDK3ISaevuY3dloxsVGxw+bwhykyMYO9pGuFxPB5QVQNYadbPSDIoxUSFMHRvpmHso907oaVfGQDN0+t1Ck1YainVYqsUuzzGosaWxTXw2xE6CojdtisxPV9n2nuwe8llDUH+5k4Nnm1kx2cgttE1103JgVqWxzvLJCRyuaqbusp2N4HHzIDxJNU7RDI1BuIV2ljfQ0dNHfo5uSXld9LuHTn8ALdZXvoH+JpZkx7OluI5ee9n2w4TPGoLNFnfFCqNwueK3IGS03frtGtv0+53tuodMllj38i3Q1eIGzUYwH7uF7NfEKiiqJTIkgLkTot2g2Agl53ZAGrqH8nMSudjew/7TF92n1yDwWUNQUFTL+NhQMuJtJIj1dqkU8qw1KqVcc11kxIcxPjbUMffQ5LXQ1wXlm12v2EjmY7dQvqFYT5+ZrcV1LM2KJ8DPZ28FQyc+G+KyDKOHbpoUR5C/yWOTy3zyr3+po4c9lRdYnpNgO1yu8j0V0mgnI1NjjBCC5ZMT2FN5gUsdPcbCKXMgNN4wbV9jh3630MRb7LqF9p1s4nJnr/GqWOMYOXfAmd0226+OCvRnUWYcBUW1SIPuZsOFTxqC/nA5w7DR4rdUEtmEm9yn2AhleU4CvWZpP6nG5KdqvZdtVhv1msHT7xZyYALzbtF5ggNMLMpwfn8Pn2OyxT1UbOweOn+pk6PVdrLthwGfNAQFRSpcbvpYG+Fyvd1QskndlLRbaMjMSBlNbFjQx/syhky+TeVtVG53vWIjEQfdQmZLMbSbMuMICbTdulLjIPFZEJetJpA2WJqtsu3f9UD3kM8ZAtWS0k643Mkd0HVJu4WchMkkWDY5gR2OJNWkLVQuDYONN40NpFRutf76TQYcrblE3eUuXXLamWTfqhoAtVnPF4gaFci8CTEUHPc895DPGYJd5Y109PTZdwsFRcKExe5Sa8SzPCeBtu4+9lTaaWHpF6BKU5duUlVfNY5Te1T1zMi+1a7o5qJa/EyCJVkGNbY0gyNrtUouK33HpsiK3ERONjqQbe9mfM4QFBTVEhHszw0TbHQZ6+uF0o0qEUfXFnIa89NjCAvyZ3OxA8vi7Nug85LuXDZYTmwAYYJMY7cQqOvghgnRRI3S/+NOI2kaRI5TtclssNySbe9pyWVOMQRCiHwhRKkQokII8aSV8SAhxCuW8X1CiLQBY9+2HC8VQqxwhj626O0zs+1EHUuzE2yHy53drerjZ69xpSo+R5C/H4snqR4FffZ6FKTfDAGhOnposJRsVIl5oQZ9t4GK+lYqG9pYbpRMqRk8QqhVQeV70GV9xp8QEczMcVEUODIhciNDNgRCCD/gt8BKYDLwgBBi8lVinwUuSiknAk8DP7WcOxnV4zgHyAd+Z/k8l/DR6SYutvcYN98o2Qj+wcrPqnEqy3MSaWzt5tBZO0k1ASGQsUz9LXRje8doOgn1RepGZIf+5L7+WlAaJ5K9RuXCGFTSzc9N5HjNZaqa2t2omDHOWBHMASqklCellN3Ay8Daq2TWAs9bXr8GLBUqgH8t8LKUsktKeQqosHyeS9hcVEeQv4lFmTbC5aRU0UITbobAUFep4bPcPCmOAD/hePRQW73qFa2xT787wgFDUFBUy5TkSMZEhbhYKR8k5QYIiTZ0D/XvT3pScpkzDEEyUDXgfbXlmFUZS7P7S0CMg+cCIIR4QghRKIQobGiw3hHIHlJK8nMTGRVoo4Bc3XG4dNZu/XbN9REeHMD89FjHkmoylqswSO0ecoySjZAwRbVPNKDucieHq5p1S0pX4eevgh3KCmz24U6NCSUrMZzNRZ7Ty9gZhsBaDObVV7ktGUfOVQelfFZKmSelzIuLu74EmP9am8uv7p9hW6Bko1Ip07hio+b6WZ6TwJkL7ZTV2YmaCApX7rkTb6uVmsY2rQ1wdu+g3EK694ALyV6jws9P77IpsiInkf1nmmho6XKjYrZxhiGoBlIGvB8LnLMlI4TwByKBJgfPdR8lGyFlrt3+rprrZ9nkBITAfgtLUDOrS1VQV+R6xbyZ0k2AdCjAYXNxHWkxo2zX2NIMnQmLVbBDyQabIvm5iUgJW094xqrAGYZgP5AhhBgvhAhEbf5enQ20HnjU8vpu4D2pfAPrgfstUUXjgQzgIyfoNHiaz6o4bO0Wcinx4cHMSHEwaqI/DNIgLluDmsBEjYOEXEOxy5097KlsZIVuSelaAkJg4lK132i2XnY6KzGc1JhRHhNGOmRDYPH5fwkoAE4Ar0opi4QQPxRC3GYR+xMQI4SoAL4OPGk5twh4FSgG3gW+KKUcnjCR/ptNlg4bdTXLc1TURE2znXpC4QmQnGeZ8Wqs0tWiMuGz1qjwRQO2l9TT0yeNO/JpnEP2rdBaCzUHrA4LIViRk8juykYudw5/4qRT8giklJuklJlSynQp5VOWY/8ppVxved0ppbxHSjlRSjlHSnlywLlPWc6bJKUcvqlfyQbVaSgmfdhU8BX6oyYccw/lw7mDNqs6+jwVW1W4ogMTmM3FdcSGBTEjZbQbFPNxMpaDyR9KbAc7rMhJpKdPsr3ETjFGN+BzmcVW6bgIpz/UbiE3MT42lMyEMMfC5yZZ/ia6haV1Sjaqntopcw3FOnv62FFSz7LJuiWlWwiJgrQbodT2/+2MlCjiw4M8wj2kDQGorliyT7uF3MiKnEQ+OtXEhVY7URPxk5X/W+8TXEtfr2rik7HCbk/tPZUXaOvu024hd5KZD42lKtnPCiaTYHlOAjtKG+wXY3Qx2hCAcguFJcKYmcOtic+wIicRs4RtJ+wsi4VQq4KTO6DbczIxPYLq/aomU+Zyu6Kbi2sJDfRjfrqNGlsa55NpqZhTVmBTJD8niY6ePnaWXV9ulLPQhqC3SzWpn5QPJv3rcBc5YyJIjgpxzD2UmQ+9ncoYaD6hvED5oe2UQ+mz9B5YnBVPkL/uPeA2oieofUcDt+bcCdFEhgQMe48Cfec7vQu6Wz/xRWvcQn/UxK7yRlq7eo2FUxdAUISOHrqa8i2qyJyd3gOHzl6ksbVb9x4YDiblq/3HzstWhwP8TCzNjmfbiXp6+qyHmroDbQjKNqsic2kLh1sTn2NFTgLdfWb7LSz9A1UP3rICm3HZPselalUSJWOZXdHNxXUE+AkWT9KJkm4nMx/MPaoiqQ3ycxK51NHDvpNNblTsSnzbEEipltfjF0HgqOHWxufIS4smJjSQAkdqrkxapYrQnTvoesW8gfIt6jnDuHK7lJKColrmpccSEazbrrqdsXMgZLShe2hRZhwhAX68W3TejYpdiW8bgsZyuHj6k00djVvxs7Sw3F5ST1evnaiJjFtA+Gn3UD/lm1UTlLhJhmJlda2cudCui8wNF37+MHGZ+nvZKKkeHKB6dWwuqsNsr1eHi/BtQ1Bu2c23M6vSuI4VOYm0dvWyu8JOC8uQ0ZA6X4eRAvRYNs4zl9vNJu5P2luWrQ3BsDEpH9ovQHWhTZH83ETqW7o4VNXsRsU+wbcNQVmBJU49xb6sxiXMn6haWDqWXLYS6ovVKs6XOfMh9LSr7FU7bC6uY8a4KOIjgt2gmMYq6UvVatbAPXRzVjwBfmLYehT4riHovARn9zh0MWlcR5C/HzdnxTvWwrJ/5dbvH/dVyh0LcDjX3MGxmks6Wmi4CYlSq1kDQxAxmF4dLsB3DUHldjD36v0BD2BFTgIX2ropPG0naiImHUaP14agfLNDAQ79bqHluiXl8JOZb1nNnrEpkp+byJkL7ZTUtrhRMYXvGoLyzRAcpXb1NcPK4knxBPqb7EcPCaEM96md0GOnculIpbFClSxw0C00MT6MCXG698Cw019S3SDLuL9Xx3DUHvJNQ2A2K0MwcandGi0a1xMW5M/CiY62sFwGvR1w+gP3KOdplG9Wz3byBy62dbPvVJNeDXgKsRMhZiKU2Q52iA0LYnZq9LDsE/imITh/CNoadLSQB7EiJ5Ga5g6KzlnPwPyY1BvBP+STG6KvUV6gyhbY6U3cv+eyakqSe/TS2CczX01guttsiqzITaSktoUzF2zLuALfNARlBSBMKltV4xHcMjkBk8D+bCggGCbcpAyBr/Uy7mpV5QocKDL3zvHzjB0dQs6YCDcopnGIjGXQ161cmzboX8G5e1UwJEMghIgWQmwRQpRbnq/peCGEmC6E2COEKBJCHBVC3Ddg7K9CiFNCiMOWx/Sh6OMwZQUwdjaE6kqMnkJ0aCBzxju4LM5YrkJIL1S4XC+P4uQOVa7Azv7A5c4ePqhoZGWubknpUYybp3oZG6xmU6JHkZsc4fZ9gqGuCJ4EtkkpM4BtlvdX0w58SkqZA+QDvxRCRA0Y/w8p5XTL4/AQ9bFPSy2cP6zDRj2QFTmJlNW1crKh1Viw3z/ua+6h8s2q+N64eYZi207U0dMnyc/VbiGPwj9INbYv32q4ms3PSeTg2WbqLne6TbWhGoK1wPOW188Dt18tIKUsk1KWW16fA+qB4at+1R96qMNGPY7+eHe70UNR4yAu2zACY8QhpfrfTb8Z/IxrBr1zrJaEiCBmpEQZymmGgYxlcOksNJTaFPm4lWuxAzW4nMRQDUGClPI8gOU53khYCDEHCAQqBxx+yuIyeloIEWRw7hNCiEIhRGFDwxCaOJQXQEQyJORe/2doXMKYqBCmjo100D20DM7sVs3bfYHaY9Byzu5Ktq2rl/fLGsjPSdQtKT2R/tVshe1cGBXyG0qBG91Ddg2BEGKrEOK4lcfawXyRECIJeAH4tJSyv5bwt4EsYDYQDXzL1vlSymellHlSyry4uOtcUPR2Q+UO9cfQvlOPZEVOIoermqm9ZGdZnLlC+ctPvu8exYabfjfYROOw0R2lDXT1mrVbyFOJHKvK2hi4NYUQ5OcksufkBZrbu92ill1DIKW8RUqZa+XxFlBnucH33+itFpYXQkQAG4HvSSn3Dvjs81LRBfwFcG1219nd0N2iw0Y9mE+WxXZmQylzlb/cV/YJyjdD0nQIN84LeOf4eWIsG+8aDyVjGZzZY7iaXZGTSJ9Z2m/l6iSG6hpaDzxqef0o8NbVAkKIQOAN4G9SynVXjfUbEYHaXzg+RH2MKdsMfkEq/FDjkUyMDyM9LpR3jtkxBH4Byl9evmXkh5G2N6n+xHb2tTp7+theUs/ynAT8tFvIc5m4zO5qdurYSJIig93WwnKohuAnwDIhRDmwzPIeIUSeEOI5i8y9wCLgMSthov8QQhwDjgGxwI+GqI8xHU3q5hEY6tKv0QyN1VOS2HfqAo2tXcaCGcuV37zOtfOHYadiG0iz3f2BXeWNtHX3abeQpzPuBggMt+seWpGTyM6yBtq77bRydQJDMgRSygtSyqVSygzLc5PleKGU8nHL679LKQMGhIh+HCYqpVwipZxicTU9LKW0Ezc4RO54Bu5/0aVfoRk6q6YmYZYO1FyZ6CNhpOWbYVQsjJlpKPbO8fNEBPszb4LOj/FoHFzNrshJpKvXzPulQwiOcRDfyyw2+Q23Bho7TEoIJz0ulI1H7bTuC09QfvORXI3U3AcVW1UWvMn25drda2ZLcR23TE4g0N/3LmuvI2OZWs3WF9sUmZ02mujQQLe4h/R/jMbjEEKweuoY9p26QEOLA+6hqn3QcdE9yrmbmgPKpWmnrMTuykZaOntZqd1C3oEDq1l/PxPLshN470Q93b1mm3LOQBsCjUeyeorFPWRvNpSxXPnPK99zj2LupqxAdbdKX2Io9u7xWkID/ViYEesmxTRDIiIJEqeoLGMDVuQm0NLVy+7KRpeqow2BxiPJTAhjYnwYG4+eMxZMngmjYlRE2EikfLMKlQ25pozXx/T0mSkoqmVJdgLBAdr16TVMXKa6JHZesikyPz3W8VauQ0AbAo1HIoRg1ZQk9p1qor7FILnM5Kf85xVbVJ+JkcTl81B71K5b6MOKRi6293DrVO0W8ioyloPsU90SbRAcMIhWrkNAGwKNx7JmahJSYj/VPmM5tF+Acwfdo5i7+LgJjbEh2HD0POFB/tw0afhKeGmug7GzITjSsNwEqFauja3dHDjjun0wbQg0HktmQjgZ8WFssBc9lL5E9ZcYaWGk5ZshwlKSwAZdvX0UFNWyLCeBIH/tFvIq/PzV/66dMNL+Vq6uLE2tDYHGo1k1JYmPTjdRb1SSd1S06j09kqqR9nap/gN26mLtLFPRQrdOG+M+3TTOI2M5tNYpF6ANwoL8WZThYCvX60QbAo1Hs9riHrIfPbRM9ZlocV/pXpdydg90t9otK7Hh6DmiRgVw40QdLeSV9HdJtJMLs9zSyvVYje2N5aGgDYHGo8lMCCczwQH3UP8Ns8I4HM9r6K+LNX6RTZGO7j62FteRn5NIgJ++lL2SsHiHkiKXT04gwE/YT7K8TvR/j8bjWTUlif2nm4w7NiXkQvgY1W9iJFC+GdJuNKyLtb20nrbuPu0W8nYylkP1R4ZJkVGjAlmUEceGo+cxuyB6SBsCjcezZuoYpMR4VSCEcg9Vboe+Hvcp5wqaTsKFcofcQrFhgczVJae9GweTIm+dNsZl7iFtCDQez8T4MHKTI3jrcI2xYMZy6LoMZ/cay3k6/W6CDNtNaFq7enmvpJ6VuUn4a7eQd5M8E0Ki7bqHlk1OoOBri5jmghak+j9I4xXcPj2Zo9WXjBvbT7gJTAHeH0ZaVgAxGRA9wabIthN1dPaYtVtoJGDyg4lL1f6WQVJkaJA/kxLDXaOCSz5Vo3Eyt04bgxDw5mGDkhNB4ZC2wLurkXa3wekP7CaRrT98jsSIYPJSbZee0HgRGcuhrQHOHxqWrx+SIRBCRAshtgghyi3PVv8rhRB9A5rSrB9wfLwQYp/l/Fcs3cw0mmtIiAhmfnoMbx2uMY6lzlgODSeg+az7lHMmJ9+Hvi7DshIXWrt4v6yBtdPH6Ab1I4X0pSopcphqZg11RfAksE1KmQFss7y3RseApjS3DTj+U+Bpy/kXgc8OUR/NCGbt9GTOXGjnUFWzbaH+ftTe6h4qL1Ddq8bNtymy4eh5es2S22cku1ExjUsJjVElJ4Yp6m2ohmAt8Lzl9fOovsMOYelTvAR47XrO1/ge+bmJBPqbeOuQwaZxTDqMHu+d1UilVHqn3wz+thfHrx+qISsxnOykCDcqp3E5mSvg3CFocU+f4oEM1RAkSCnPA1ie423IBQshCoUQe4UQ/Tf7GKBZStnfkLMasDnFEUI8YfmMwoYG17du03geEcEBLMtOYMPR8/T02dhUE0K5h07thJ4O9yo4VGqPqa5VBmGjlQ2tHKlq5s6ZejUw4hjG1axdQyCE2CqEOG7lsXYQ3zNOSpkHPAj8UgiRDlhzbtp0/kopn5VS5kkp8+LidJVFX2Xt9DFcaOvmgwqDRh2Zy6G3A05/6D7FnEG/W2Ci7bDRNw/VYBLKTaYZYSTkqCKDw1Azy64hkFLeYmkuf/XjLaBOCJEEYHmut/EZ5yzPJ4EdwAygEYgSQvhbxMYCdrqQaHydxZPiiQwJMHYPpd4IAaO8L8u4bDOMmaF6MVvBbJa8caiGBRNjSYgIdrNyGpcjhFoNVm5XRQfdyFBdQ+uBRy2vHwXeulpACDFaCBFkeR0LLACKpQr92A7cbXS+RjOQQH8Tq6YkUVBUR1tXr3WhgGAYf5NaYruoWqPTaWuE6v2QmW9T5MDZi1Rf7OAOvUk8cslcAT2WEGI3MlRD8BNgmRCiHFhmeY8QIk8I8ZxFJhsoFEIcQd34fyKlLLaMfQv4uhCiArVn8Kch6qPxAe6elUxHTx8bjxmUnMhYBhdPQ2O52/QaEhVbAWmYP/D6wRpCAvxYkZPoPr007mX8IvAPcfs+gb99EdtIKS8AS60cLwQet7zeDUyxcf5JYM5QdND4HjPHjWZCXCjrNZS2AwAAF19JREFUCqu4Ny/FulD/DbV8M8Rluk+566WsAEItlSit0NnTx8aj51iRk0Bo0JAuW40nExCiMuRL34H8nxj2onAmOrNY43UIIbg3L4X9py/aLjkRlaI6e3nDPkFfD1RuU8bLZP2SLCiq5XJnL3fPsmH4NCOHjOXQfAYay9z2ldoQaLySO2ck42cSrDtQbVsoYxmc2QOdl92n2PVQtQ86LxlmE7+yv4qxo0OYnx7jRsU0w0J/+LAbo4e0IdB4JfERwdw8KY5/Hqim11ZOQcYKMPfAqffdq9xgKStQxfIm3Gx1+OyFdnZXXuDevBRdUsIXiByr+mtoQ6DR2OeevBTqW7rYWW4jwTBlDgRFen4v4/LNkDofgq1nCq87UIVJwN2zxrpZMc2wkblCtSs1aFbjTLQh0HgtS7LiiQ0L5NX9NtxDfgEwcYkyBAblfYeVppPQUGIzbLTPLFlXWM2izDjGRIW4WTnNsJGZD7LPbrMaZ6ENgcZrCfAzcceMZLaeqONCq40EnKw10FYPNYXuVc5RSjap56xVVod3ljVQe7mT+2frTWKfInkWjIpx22pWGwKNV3NvXgq9ZslrtjaNM5Yp/3vJBvcq5iglGyFhCoxOszr88v6zxIQGsiTLeraxZoRi8lOlRso3Q5+NxElnfp3Lv0GjcSEZCeHMSYvmH/vOWm/qHRypknRObPC8LOPWBqjaC1mrrQ7Xt3Sy7UQ9d80aS6C/vlR9jqzVao/gjOtrZun/Lo3X88i8VM42tdveNM5aDU2V0FDqXsXsUfaualpuwxC8/FEVvWap3UK+ysSlKsvYDatZbQg0Xs+KnERiw4L4+94z1gUmWfzvnuYeKtkIkeMg8drE+54+My/uO8vCjFgmxIUNg3KaYScwVBmDExtcHuygDYHG6wn0N/HAnBS2ldRT1dR+rUBEEiTnqRuvp9DVqiJCslZbLSOwpbiO2sudPDovzf26aTyH7FtVj4pzB136NdoQaEYED8wZhwBe/MhGr+LsNepiumRQvtqdVL6nehPbcAs9v/s0yVEh3Jxlq9eTxifIXAEmfzjxtku/RhsCzYhgTFQIt2Qn8Mr+Krp6+64VyFqjnks3uVcxW5RshJDRMG7eNUOltS3sO9XEI/NS8dOZxL5NyGhIWwgn1rs02EEbAs2I4ZF5qTS1dbPhiJXy1LEZEJvpGfsEfT1qozhzJfhdW0n0b3tOE+hvsl1ZVeNbZN+qEg/rT7jsK7Qh0IwYbpwYS0Z8GH/cdRJpbfaUtQZO7YK2C+5XbiAnd0BnM0y+7Zqh5vZu3jhUw61TxxAdaruBvcaHyFoNCJdOYrQh0IwYhBD8y6IJlNS2WO9pnHOHSts/sd79yg3k+OuqBlL6kmuG/r73DO3dfTy+cPwwKKbxSMITVd2sYtf93w6pw4UQIhp4BUgDTgP3SikvXiVzM/D0gENZwP1SyjeFEH8FbgIuWcYek1Ievh5denp6qK6uprOz83pO11ghODiYsWPHEhAQMNyqOMza6WP4WUEpz+48ycKMuCsHE6dATAYUvQ55nx4eBXu71P5A1mrwD7piqLOnj7/uPs1NmXFkJ1kvQKfxUbJvg83fhQuVEJPu9I8faqujJ4FtUsqfCCGetLz/1kABKeV2YDp8bDgqgIF92P5DSvnaEPWgurqa8PBw0tLSEG7q6jOSkVJy4cIFqqurGT/ee2anQf5+PDY/jZ8VlHLi/OUrb6hCQO5d8P5PoaVWzbTcTcU26LoEuXdeM/T6wRoaW7v53KIJ7tdL49nk3K4MQdHrsOg/nP7xQ3UNrQWet7x+HrjdjvzdwDtSSivB3kOjs7OTmJgYbQSchBCCmJgYr1xhPTR3HKMC/fjjrpPXDubeCUgofsvtegHqQg4ZDRMWX3HYbJY8t+skU5Ijmaebz2iuJnIspMyF42+45OOHaggSpJTnASzP9oKe7wdeuurYU0KIo0KIp4UQQdZOAhBCPCGEKBRCFDY0WC8loI2Ac/HW32fUqEDuzUth/eFz1DR3XDkYN0k1/Tj+T/cr1tOhetFm36pKZA9gy4k6Tja28cSiCV77e9e4mNy7oL4I6kuc/tF2DYEQYqsQ4riVx9rBfJEQIgnVxH5gXdVvo/YMZgPRXOVWGoiU8lkpZZ6UMi8uLs6WmEYDYLmhwu+2V1w7mHunag/ZbCP5zFWUb4buVsi50i0kpeR/36tgXPQoVuYOg7tK4x3k3AG3PwORyU7/aLuGQEp5i5Qy18rjLaDOcoPvv9HXG3zUvcAbUsqeAZ99Xiq6gL8Ac4b24wwfzc3N/O53vxv0eX/96185d+7cx+/T0tJobLQS8aIZFGOiQrhvdgqvFlZduyrovxEff929Sh15BcISVILQALaeqOdYzSW+tGQi/n46kE9jg7B4mP4ABIU7/aOH+l+3HnjU8vpRwMjx+gBXuYUGGBGB2l84PkR9hg1bhqCvz0qW6wCuNgQa5/GFxRMBK6uC6PEwdjYcecl9palbG6C8AKbed0USmZSSp7eUkRozijtnOH+mp9E4wlCjhn4CvCqE+CxwFrgHQAiRB3xeSvm45X0akAJc3UX8H0KIOEAAh4HPD1EfAP7r7SKKz112xkd9zOQxEXz/1hyb408++SSVlZVMnz6dgIAAwsLCSEpK4vDhw2zatIk1a9Zw/Liycz//+c9pbW0lNzeXwsJCHnroIUJCQtizZw8Av/nNb3j77bfp6elh3bp1ZGVlOfVn8RX6VwWv7K/iCzdPJHlgq8cZD8PbX4WagzB2luuVObYOzL0w/cErDhcU1VF8/jI/v2eaXg1oho0h/edJKS9IKZdKKTMsz03/v727D6uqyhc4/v0JKL5GSqmoCJUm+IYmYGGOWlPgY3o1vDGlaUYkatp0r9e6M9exuY+Oc/Naat1xdKyxwl4t9foypoWTL1cUBEkkfEk0MtNw1BRB0XX/2AcEOsBRjpxzOL/P8/A85+y99t6/ddZhr732Xmct2/L0skrA9j7fGNPBGHO1yvZDjDE9bbeaxhhjztclHleaO3cud955J1lZWbzyyivs2rWL2bNns3///mq3iY+Pp1+/fqSkpJCVlUXTptaJKjAwkD179pCcnMy8efPqKwsNUlmrYNHnByuv6D7KGus98536CSRrBQT1gdvDyhddvWp4bfMBQgOb808RQfUTh1J21LVF4JZqunKvL1FRUTfc/37UKOse9j333MMnn9TzfewGJiigKWP7h/DXHUd4KiaUu9vZ7q/6t7L6Zu9bCQ/PgcbNbl4Q32fDD1/B0MqV+ieZ3/H1iZ9YkBChrQHlUvrtu0maN29e/trX15erFSaWqK1vfpMmVi9aHx8fSktv/nylDd1zQ+6iRRNf5qyvMmhXnzFQcu6mD/FLVgr4NLa6/9lcvHSFeRvz6N3xFh7ppa0B5VpaEThJy5Yt+emnn+yua9u2LSdPnqSwsJCSkhLWrl3r0HbKOW5t3pjnhnTh7wdO8eWBCr9B6RwDre+APW/fvIOXnLduC4WPgGatyxcv3foNJ84V89th4TTSoaaVi2lF4CRt2rQhJiaGHj16MH165Z+A+/n5MXPmTKKjoxk2bFilh7/jx49n4sSJREREcPHixaq7VU7y5H2d6dS6KbPX5XL5iq11JgJ9x8HRbXDiJnVYy/7AanVEJZUv+uFcMYv/fpjY7u2IDGldw8ZK1Q+xO1yvm+vXr59JT0+vtCw3N5ewsLBqtlA3qiF9rn/bd4KJ72bwUlw3nv2FbeCuotMwPxx6xsOI1517QGPgT/dZM0w9+2X5lJSTUjLYnHuSTb8eSOc2zWvZiVLOIyIZxph+VZdri0B5jYe7t+XBsLa8uvnAtbmNm7W2fqST/SFccPIP+Y5uh5P7rdaArRL4PPcH1n91gqlD7tJKQLkNrQiU1xARXh7RnUYizFy979rkNdETrfmDM95y7gG3L4BmbcofEhddKmXm6hy63N6CpIHOH0pYqRulFYHyKh0CmvLCL7uSmneKjzMKrIW33Q13PQhpf4ZLF5xzoO+zrbGF+k8q75o6e10ux89eZM6onjT21X895T7026i8zlMxoUSHtmbWmhzyf7Sd+Af+G1w4BbuXOecg2+ZDk1YQaf2uctP+H0hJO8Yz99+hD4iV29GKQHkdn0bCq49F4NNImPZBltWLKDjamjpy+4K6twpO7IOcVRD5NDQN4OS5YmaszCa8fSv+5aGuzsmEUk6kFYHySkEBTZn7aC/2fnuGWWtyrIWDXoKiH2Hnn+q2800zrV8u3zeV4stXePbdDIovX2FBQgRNfH3qHrxSTqYVgRtr0aIFAMePHyc+Pr7GtK+99hpFRdcmfhs6dChnzpy5qfF5uqE92zPxF3eSknaMd3YetSYI7zYMts6Hs9/d2E4PfwGHP4eB0zFNb+U/Vu0j89gZ/nt0b7q0df7wwUo5g1YE9ay2YantCQoK4uOPa57WuWpFsH79egICAq77WN5m+sN3M6Tb7cxak8PGnBPw8GwwV+Cz317/zi5fhPXTIaAzRCUxf9MBPsooYOqQu4jr2d75wSvlJA1y0Dk2vAgnvnLuPtv1hLi5NSbJz88nNjaW6OhoMjMz6dq1K2+//Tbh4eFMmDCBzz77jClTphAZGcnkyZM5deoUzZo1Y+nSpXTr1o0jR47w+OOPU1paSmxsbKX9lg1jfeXKFWbMmMHGjRsREZ555hmMMRw/fpzBgwcTGBhIamoqISEhpKenExgYyPz583nzzTcBSExM5Pnnnyc/P5+4uDgGDBjAjh076NChA6tXry4fAdVb+DQSFv6qD2P+ksaUFXtYMrYfgwe8AFvmWDNChQ93fGdb/gCFh2DsKv5n27cs+uIQCZGd+PUv9bmAcm/aInCyvLw8kpKSyM7OplWrVuWT1fj7+7Nt2zYSEhJISkpi0aJFZGRkMG/ePCZNmgTAtGnTSE5OZvfu3bRrZ3/KwiVLlnDkyBEyMzPJzs7miSeeYOrUqQQFBZGamkpqamql9BkZGbz11lukpaWxc+dOli5dSmZmJgAHDx5k8uTJ5OTkEBAQwMqVLpjH1w20aOLL8glR3N2uJUnvpPNJ89HWkNFrnoOzBY7t5NDnsH0hps9Y5uS147/+lscjvYOYPbKnzkGs3F7DbBHUcuV+M3Xq1ImYmBgAxowZw8KFCwF47LHHADh//jw7duxg9OjR5duUlJQAsH379vKT8dixY5kx4+dTOG/evJmJEyfi62sVXevWNXdF3LZtGyNHjiwfDXXUqFFs3bqV4cOHExoaSkREBGANeZ2fn3+j2fZ4tzT1I+Xp/iSnZPDCylxORr3Esz9OQFYkwFPrwP+W6jc+dQBWPk1pYBjPFf4zGw58w5P3duZ3j3THRweUUx6gTi0CERktIjkictU2K1l16WJFJE9EDonIixWWh4pImogcFJEPRKRxXeJxB1Wv/srel52Ir169SkBAAFlZWeV/ubm51W5flTHmuq4waxpLqmy4a9AhrwFuaebHX5+K4onoYObuKuU3ftO5euprePdRa6pJe07swywfRvHVRsSfmcznhy8w65FwXh6ulYDyHHW9NbQPGAV8WV0CEfEB3gDigHDgVyISblv9R+BVY0wX4B/A03WMx+WOHTtWPuXke++9x4ABAyqtb9WqFaGhoXz00UeAdaLeu3cvADExMbz//vsApKSk2N3/Qw89xOLFi8tP2qdPnwaqH8564MCBrFq1iqKiIi5cuMCnn37K/fff/7N0ytLYtxGzR/Zk2bh+fHG5J8nFUygpyKbo9Rj+kbYCU2q13kzxWX7c+EdKlzxA4YVLDDs3AxMQwqrJMYyPCdXbQcqj1HWqylxjTF4tyaKAQ8aYb4wxl4D3gRG2CeuHAGXdYZZjTWDv0cLCwli+fDm9evXi9OnTJCcn/yxNSkoKy5Yto3fv3nTv3p3Vq1cDsGDBAt544w0iIyM5e/as3f0nJiYSHBxMr1696N27NytWrAAgKSmJuLg4Bg8eXCl93759GT9+PFFRUURHR5OYmEifPn2cnOuG54GwtmyZPojIuCeZ4j+b/CJ/bt2QzMX/7MR3s7pw+Q+hBP7fHLZcDmN660VMTXiETyfFEB7UytWhK3XdnDIMtYhsAf7VGJNuZ108EFthIvuxQDQwC9hpjLnLtrwTsMEY06OaYyQBSQDBwcH3HD16tNJ6dxguuWLvnobCHT5XVzPG8NW3hZzcs46Wx7fSuOQMF5sHcT7kYbr2HURIoI4iqjxDdcNQ1/qwWEQ2A/a6sPzGGLPakWPbWWZqWG6XMWYJsASs+QgcOK5STiEi9AoOhOBxwDhXh6OU09VaERhjHqzjMQqAThXedwSOAz8CASLia4wprbDcY4WEhDSo1oBSyjvUx+8IdgNdbD2EGgMJwBpj3ZNKBcrGThgHONLCqJYnzrbmzvTzVMo71LX76EgRKQDuBdaJyEbb8iARWQ9gu9qfAmwEcoEPjTG2Ub6YAbwgIoeANsANjwHs7+9PYWGhnrycxBhDYWEh/v7+rg5FKXWTNZg5iy9fvkxBQQHFxcUuiqrh8ff3p2PHjvj5+bk6FKWUE9zww2JP4efnR2hoqKvDUEopj6NjDSmllJfTikAppbycVgRKKeXlPPJhsYicAo7WmtC+QKzfMHgqT48fPD8Pnh4/eH4ePD1+cE0eOhtjbqu60CMrgroQkXR7T809hafHD56fB0+PHzw/D54eP7hXHvTWkFJKeTmtCJRSyst5Y0WwxNUB1JGnxw+enwdPjx88Pw+eHj+4UR687hmBUkqpyryxRaCUUqoCrQiUUsrLNdiKQERiRSRPRA6JyIt21jcRkQ9s69NEJKT+o6yeA/GPF5FTIpJl+0t0RZzVEZE3ReSkiNidoEEsC235yxaRvvUdY20cyMMgETlboQxm1neMNRGRTiKSKiK5IpIjItPspHHbcnAwfncvA38R2SUie215eNlOGtefi4wxDe4P8AEOA3cAjYG9QHiVNJOAxbbXCcAHro77OuMfD7zu6lhryMNAoC+wr5r1Q4ENWDPV9QfSXB3zDeRhELDW1XHWEH97oK/tdUvggJ3vkduWg4Pxu3sZCNDC9toPSAP6V0nj8nNRQ20RRAGHjDHfGGMuAe8DI6qkGQEst73+GHhAROxNn+kKjsTv1owxXwKna0gyAnjbWHZizVbXvn6ic4wDeXBrxpjvjTF7bK9/wpoPpEOVZG5bDg7G79Zsn+t521s/21/VHjouPxc11IqgA/BthfcF/PwLVJ7GWJPnnMWaHMcdOBI/wKO25vzHItLJznp35mge3d29tmb/BhHp7upgqmO73dAH64q0Io8ohxriBzcvAxHxEZEs4CSwyRhTbRm46lzUUCsCe7Vp1VrYkTSu4khs/wuEGGN6AZu5dkXhKdz583fUHqyxW3oDi4BVLo7HLhFpAawEnjfGnKu62s4mblUOtcTv9mVgjLlijInAmpc9SkR6VEni8jJoqBVBAVDxCrkjcLy6NCLiC9yC+9wGqDV+Y0yhMabE9nYpcE89xeYsjpSRWzPGnCtr9htj1gN+IhLo4rAqERE/rJNoijHmEztJ3LocaovfE8qgjDHmDLAFiK2yyuXnooZaEewGuohIqIg0xnoAs6ZKmjXAONvreOALY3ta4wZqjb/KfdzhWPdPPcka4Elbr5X+wFljzPeuDup6iEi7snu5IhKF9f9U6NqorrHFtgzINcbMryaZ25aDI/F7QBncJiIBttdNgQeBr6skc/m5qMFMVVmRMaZURKYAG7F64LxpjMkRkd8D6caYNVhfsHdE5BBW7ZvguogrczD+qSIyHCjFin+8ywK2Q0Tew+rRESgiBcDvsB6UYYxZDKzH6rFyCCgCnnJNpNVzIA/xQLKIlAIXgQQ3upgAiAHGAl/Z7lED/DsQDB5RDo7E7+5l0B5YLiI+WJXUh8aYte52LtIhJpRSyss11FtDSimlHKQVgVJKeTmtCJRSystpRaCUUl5OKwKllPJyWhEopZSX04pAKaW83P8DBK2GYOvY5GMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, label='truth')\n",
    "plt.plot(x, p, label='prediction');\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-18.69384133615815,\n",
       " array([-0.00000000e+00, -0.00000000e+00, -1.00005819e+02, -1.12474543e+00,\n",
       "        -6.97435712e+06, -1.25043196e-07]))"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "func_wrapper(params, x[::n], y[::n])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}