CODE_4_MP_FIT.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "11183bfd",
   "metadata": {},
   "source": [
    "Contact : dhilip@iitrpr.ac.in <br>\n",
    "\n",
    "    - Apoorv Kushwaha & Dr. T.J. Dhilip Kumar\n",
    "        Quantum Dynamics Lab (410), IIT Ropar."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fc97f14",
   "metadata": {},
   "source": [
    "### Fitting curve into a function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "46a1938f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import important libraries\n",
    "import math\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy.special import legendre\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f14eaf97",
   "metadata": {},
   "source": [
    "#### read input file (PES)  give separation (remove header such as r, theta, phi, etc)\n",
    "*The code assumes first column to be R (Radial Coordinate), 2nd to be theta (Angular coordinate) and 3rd column to be E(Potentials)*\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d78f36e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_Vnf = pd.read_csv('2D_Vlam.dat',sep=',')  # import Vlam file\n",
    "lm=4\n",
    "symmetric = True            # Verify if rigid rotor is symmetric (else put False)\n",
    "if symmetric:\n",
    "    sym = 2\n",
    "else:\n",
    "    sym = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "088c0953",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>2</th>\n",
       "      <th>4</th>\n",
       "      <th>6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1256.895511</td>\n",
       "      <td>1025.120059</td>\n",
       "      <td>109.648713</td>\n",
       "      <td>136.071870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>887.264354</td>\n",
       "      <td>793.555514</td>\n",
       "      <td>102.553127</td>\n",
       "      <td>58.351987</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>611.061814</td>\n",
       "      <td>581.225705</td>\n",
       "      <td>78.972119</td>\n",
       "      <td>25.401750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>411.099894</td>\n",
       "      <td>411.871091</td>\n",
       "      <td>57.091952</td>\n",
       "      <td>10.889040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>269.369246</td>\n",
       "      <td>284.128951</td>\n",
       "      <td>39.542237</td>\n",
       "      <td>4.470996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>-0.005858</td>\n",
       "      <td>-0.003273</td>\n",
       "      <td>0.000129</td>\n",
       "      <td>0.000010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>-0.005047</td>\n",
       "      <td>-0.001974</td>\n",
       "      <td>-0.000416</td>\n",
       "      <td>0.001024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>-0.003658</td>\n",
       "      <td>-0.003119</td>\n",
       "      <td>0.000211</td>\n",
       "      <td>-0.000308</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>-0.002881</td>\n",
       "      <td>-0.002007</td>\n",
       "      <td>-0.000323</td>\n",
       "      <td>0.001012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>-0.001723</td>\n",
       "      <td>-0.002852</td>\n",
       "      <td>0.000546</td>\n",
       "      <td>-0.000797</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              0            2           4           6\n",
       "0   1256.895511  1025.120059  109.648713  136.071870\n",
       "1    887.264354   793.555514  102.553127   58.351987\n",
       "2    611.061814   581.225705   78.972119   25.401750\n",
       "3    411.099894   411.871091   57.091952   10.889040\n",
       "4    269.369246   284.128951   39.542237    4.470996\n",
       "..          ...          ...         ...         ...\n",
       "95    -0.005858    -0.003273    0.000129    0.000010\n",
       "96    -0.005047    -0.001974   -0.000416    0.001024\n",
       "97    -0.003658    -0.003119    0.000211   -0.000308\n",
       "98    -0.002881    -0.002007   -0.000323    0.001012\n",
       "99    -0.001723    -0.002852    0.000546   -0.000797\n",
       "\n",
       "[100 rows x 4 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_Vnf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "578172b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_dummy = np.arange(2.5,12.5,0.1) # Radial coordinates for plotting Vlam data\n",
    "len(x_dummy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6c31e6c7",
   "metadata": {
    "scrolled": false
   },
   "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"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "# Plot raw data\n",
    "# change x and y limits (in plot) as needed for each plot!\n",
    "x_i, x_f = [-20,-7,-2,-1], [120,50,8,6]\n",
    "y_i, y_f = 2.5, 8\n",
    "\n",
    "for i in range(0,lm):\n",
    "    y_dummy = df_Vnf[str(i*2)] # reads column names (which were originally interegrs) as string\n",
    "    # Plot the noisy exponential data\n",
    "    plt.scatter(x_dummy, y_dummy,s=20, color='#00b3b3', label='Data')\n",
    "    plt.title(\"V_lambda = %d\" %(i*2))\n",
    "    plt.ylim(x_i[i], x_f[i])\n",
    "    plt.xlim(y_i, y_f)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f26dc49",
   "metadata": {},
   "source": [
    "#### In MOLSCAT arrays NPOWER, E and A control curve fitting parameters. (READ HERE):\n",
    "https://github.com/molscat/molscat\n",
    "\n",
    "##### The 3 common functions are included that can be edited. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "218a04d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Template functions to fit V_lambdas\n",
    "\n",
    "from scipy.optimize import curve_fit\n",
    "\n",
    "d,e,f,rmsx2 = np.zeros(lm),np.zeros(lm),np.zeros(lm),np.zeros(lm)\n",
    "g,h,l,rmsx3 = np.zeros(lm),np.zeros(lm),np.zeros(lm),np.zeros(lm)\n",
    "m,n,rmsx5 = np.zeros(lm),np.zeros(lm),np.zeros(lm)\n",
    "\n",
    "# A more generalized function will give less error but overfit\n",
    "\n",
    "def exp_fit_3(x, d,e,f):\n",
    "    return  d*np.exp(-1*x)+ e*np.exp(-2*x)+ f*np.exp(-3*x)\n",
    "\n",
    "def fit_12_exp(x, g,h,l):\n",
    "    return  g*np.exp(-l*x)+ h*np.power(x,-12)\n",
    "\n",
    "def fit_12_6(x, m,n):\n",
    "    return  m*np.power(x,-12) + n*np.power(x,-6)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b404f7d2",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "V_lam =  0 \t : \t\tError \t\t Covarance\n",
      "exp_fit_3 \t : \t  0.22829246611015414 138976827.39995882\n",
      "fit_12_exp \t : \t  0.15145159922069543 9.840184475256984e+18\n",
      "fit_12_6 \t : \t  0.3237985518231173 24168895.928409763\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "V_lam =  2 \t : \t\tError \t\t Covarance\n",
      "exp_fit_3 \t : \t  0.3149295831910745 93216798.58397247\n",
      "fit_12_exp \t : \t  0.22060647113997042 3.5836623679326477e+21\n",
      "fit_12_6 \t : \t  0.41958040423818643 16648986.218482744\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "V_lam =  4 \t : \t\tError \t\t Covarance\n",
      "exp_fit_3 \t : \t  0.14883109401479064 41955570.599254906\n",
      "fit_12_exp \t : \t  0.05275712569857684 1.7376686232141249e+19\n",
      "fit_12_6 \t : \t  0.11468817914104838 7618087.726315987\n"
     ]
    },
    {
     "data": {
      "image/png": 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U/WZpQhCRYBGZIyK7RGSniPS1Mp7qJr/s4uuDA1mXPJgffthjdThKKXUKq0sI/wIWGmM6ALHATovjqV4REUTgev5gzx7tYaSUql0sSwgiEghcCkwDMMYUGmMyrIqnRkREEInrkfT4+CKLg1GqYbN6PoTCwkImTJjAxRdfTIcOHfj888+r/qGqyMpG5TZACjBdRGKBjcADxpicsjuJyARgAkDLli1rPMgLKiKCSFYBcPjwhR+HRClVeVbPh/Diiy/SuHFjdu/ejdPpJD3d+vl1rawysgPdgP8zxnQFcoA/n76TMeYdY0wPY0yP8PDwmo7xwgoOppnHUQAyjnpaHIxStUcNT4dQK+ZDeP/99/nLX/4CgM1mIywsrPIfoJpYmRASgARjzIlOunNwJYj6S4TmwdkAFGT6WxyMUg2X1fMhZGRkAPDXv/61dIKco0ePnvf1LhTLEoIxJgk4JCInUu0goOLKu3qgRdNiAArzQ6lL40gpVZ2MObdl48YzH18bnJgP4e233y53n+LiYhISEujXrx8//fQTffv2veBzG5wPq3sZ/QH4WES2AHHA360Np/q1jHIAUGQiakWdoVLqwqnsfAihoaH4+vpy/fXXA3DTTTfx008/1VSY5bI0IRhjNrnbB2KMMdcZY45ZGU9NiGzrKkLmE8HhwzqVplK1SU3NhyAijBgxguXLlwOwZMmSChuya4rVJYQGJ7BNGAFkUYQfe/akWB2OUqqMmpoPAeAf//gHzz77LDExMXz44YdMmTKlWj7TudD5EGra7NlE39yZXUTzwgvzePLJkVZHpFSN0/kQqo/Oh1CXlHk4be9efVpZKVV76GinNS02luffXcdTIeuIHTTM6miUUuWoTfMh1BRNCDXNz48+9wy0Ogql1Fk0xPkQtMpIKaUUoAnBEusnvclg3wX0bDPX6lCUUqqUJgQrbP2FJXnD2BPfVp9WVkrVGpoQLBD95M08NeR9Xnw2UROCUnVQSkoKvXv3pmvXrqxcuZKhQ4eSkZFBRkYGU6dOtTq886aNyhbwH3opzw+91OowlKpTUgoKas2c5EuWLKFDhw7MmDEDgAEDBgAQHx/P1KlTue+++6wM77xpCUEpVevNSkyk1ZIlXLlmDa2WLGFWBfMMVEZ8fDzR0dH87ne/o1OnTgwZMoS8PNdzQZs2baJPnz7ExMRw/fXXc+zYqSPqbNq0iccee4xvvvmGuLg48vLyiIqKIjU1lT//+c/s27ePuLg4Hn300SrFaAVNCFY4coQ3B/0fN7T+nE8+2WJ1NErVaikFBYzfvJk8p5PM4mLynE7Gb95MSgVzDVTGnj17uP/++9m+fTvBwcGlM5bdcccd/OMf/2DLli106dKFv/3tb6ccFxcXx3PPPcctt9zCpk2b8PHxKd328ssv07ZtWzZt2sTkyZOrFJ8VNCFYIS2N1UuD+TL+RubPT7A6GqVqtfi8PDxtp96qHDYb8XlVe9K/devWxMXFAdC9e3fi4+PJzMwkIyODyy67DIBx48axYsWKKl2nLtGEYIUyw1ckJGijslIVifLxodDpPGVdkdNJVJlv5uej7OQ1Hh4eFBcXV+l89YEmBCsEB9PMIwmA1MP6K1CqIuFeXkyLjcXHZiPQbsfHZmNabGy1NCwHBQUREhLCypUrAdcQEydKC5VRleGzawPtZWQFEZoEHodjkJNetW85SjUEYyIiGBwWViO9jGbMmMGkSZPIzc2lTZs2TJ8+vdLHhoaG0q9fPzp37sw111xT59oRdPhriyyLvosrdk0n1LGZ1MJYq8NRqkbp8NfVpyrDX5+1hCAiNiAWaA7kAduNMdbPBl3HtWztCbsgt6ix1aEopRRQQUIQkbbA48BgYA+QAngDF4tILvA2MMMY4yzvHKp8LdoHYfu2hDyacOxYNiEh/laHpJRq4Cpq0XwB+Ahoa4y5yhhzmzFmlDEmBhgJBAG310SQ9ZFnq+Y04ShgY8sWnUpTNTx1qbq6rqjqz7TchGCMGWOMWWHOcAVjTLIx5nVjzIwqXb0hK9P1dPv2DGtjUaqGeXt7k5aWpknhAjLGkJaWhre393mfozJtCI2BfpxsQ9gGbNCqoipyJ4T19GL37lyro1GqRkVGRpKQkEBKipaOLyRvb28iIyPP+/iK2hAGAn8GGgE/A8m42hCuA9qKyBxgijEm67yv3pA1b04EGwGIjy+yOBilapbD4aB169ZWh6FOU1EJYSjwO2PMwdM3iIgdGA5cCXxeTbHVb82bl1YZHdbRK5RStUC5CcEYU+5QfcaYYuCr6giowfD05Ip/duO95M/pPrqn1dEopdT5PaksIncZYyr/+J46o56P3oKmAqVUbXG+A+n87ey7KKWUqksqalQub6B+AZpUTzgNS8FX8xg3IZvdHi3YkDgAm45zp5SyUEVVRk2Aq4Bjp60XYHW1RdSAeG7+mcUpvyedUA4dyqNVKx3oTillnYoSwteAvzFm0+kbRGR5dQXUkMjQodwz7xNKWoXj63ut1eEopRo4He1UKaXqucqOdnpOtdYiMuH8Q1JKKVWbnWsz5qRqiaKhKilhyYPv8EDsB7z22i6ro1FKNXDnmhCkWqJoqGw29r+5nje23MkH79XdafeUUvXDuSaEERc6ABHxEJGfReTrC33uWk+EsIBMAI4d1R5GSilrlZsQROQ292xppYwxCWW2txWR/hcghgeAnRfgPHVS28bpAKRlNrM4EqVUQ1dRt9NQ4GcR2Qhs5OSMaRcBlwGpuEZDPW8iEgkMA14EHq7KueqqVhd54b/nONnFoaSmQliY1REppRqqiibI+RfQDZgFhAOD3O8TgduNMTcaY/ZU8fqvA48B5c6tICITRGSDiGyoj2On+3doT0d2APDzzwUWR6OUasgqbEMwxpQYYxYbY541xkw0xjxojHn7TENinysRGQ4kG2M2niWGd4wxPYwxPcLDw6t62VrHo0ULOrEdgBUr0iyORinVkJ21UVlEIqrp2v2AkSISD3wKXCEiH1XTtWqviIjSEsLqddkWB6OUasgqTAgi0gWYUx0XNsb8xRgTaYyJAkYDS40xt1XHtWqz//n6lpYQlm0pZlZiosURKaUaqop6GQ3E9c399poLp2FJKSjg9vz80hKCSWvK+M2bSSnQtgSlVM2rqIQwD7jJGLO3uoMwxiw3xgyv7uvUNvF5eRT6+2OCsvDnOBQ1wuO4F/F5eVaHppRqgCpKCJ8AT5/+LIK6cKJ8fCh0OtnRqmVpKaHwgC9RPvqQmlKq5lXU7XQisA1oeA29NSTcy4tpsbHsbtu2NCGMOt6KcC8viyNTSjVEFc6pbIx5QUTuqKlgGqIxERGkP/EEM/2X8Eb7/3HbfZdbHZJSqoHS+RCUUqqeq+x8CBWWEMqcLAaIKru/MeaL845OKaVUrXPWhCAi7wMxwHZODjFhAE0IF1DKyy/zxKvBrPa/gu/XXaxjGimlalxlSgh9jDEdqz2SBs7z66/ZkjKFHSkXs307XHaZ1REppRqayiSEH0WkozFmR7VH04B5/v73XFWwkCHd0ujSZajV4SilGqDKJIQZuJJCElCAa9Y0Y4yJqdbIGhif0aN5brTVUSilGrLKJIT3cQ1fsZUKhqlWSilVt1UmIRw0xsyr9kgU+19+lTc+8Odgh2v44qsWVoejlGpgKpMQdonIJ8B8XFVGgHY7rQ6N/vki047Fk/1LACkpUA+nf1BK1WKVGafIB1ciGAKMcC8NbiC6mlBw0ckhLHZoE75SqoadtYRgjLmrJgJR4IiNpdP67ayjt3Y9VUrVuMrMmDZDRILLvA9xP6ymLrCgvn1LSwhbthRZHI1SqqGpTJVRjDEm48QbY8wxoGu1RdSAecTElM6etnGjTpKjlKpZlUkINhEJOfFGRBpRyTGQ1DmKji5NCLt3649YKVWzKnPXmQKsFpE5uMYwuhl4sVqjaqj8/PALyMT/+HGysrSnkVKqZp21hGCMmQncCBwFUoAbjDEfVndgDVVOVCvtaaSUskS5CUFE/E+8NsbsMMb82xjzZtkxjcruoy4M6dy5tNpo+3aLg1FKNSgVlRDmisgUEblURPxOrBSRNiIyXkT+B1xd/SE2LIF9+5ZJCHVn8iKlVN1XbhuCMWaQiAwFJgL93I3JRcAvwAJgnDEmqWbCbDgC+/alI98AsGlTEeBpbUBKqQbjbHMqfwPuu5OqEVKmp9GunRYHo5RqUCrT7VTVJD8/jr3yIB++/B27dhVaHY1SqgHRzu61UOyfHibW6iCUUg2OlhCUUkoBlRvL6BUR6VQTwSiXzNWreav1XXQLXMPTT1sdjVKqoajUfAjAOyJiB6YDs4wxmdUbVsPm6XQSFX+En+lDwPcG16ylSilVvSrzpPJ7xph+wB1AFLBFRD4RkYHVHVxD5dOtG7kjm/PXWz7nk0901FOlVM2oVKOyiHgAHdxLKrAZeFhEJhpjdGr4C83Xlxvmvs8NVsehlGpQzpoQRORVYCSwBPi7MWade9M/ROSX6gxOKaVUzalML6NtuOZEmFgmGZzQqxpiUsDhBQv4esCtDOu4lrFjrY5GKdUQVKbKaBPQQeSUhs1M4IA2LleflGXLuGTVQkbyEY59hnffFXx9rY5KKVWfVaaEMBVYA7wDvAv8CHwK7BaRIdUYW4O2IzaWRhyjIz9TWCi8MC/V6pCUUvVcZRJCPNDVGNPDGNMd1/SZ24DBwD+rMbYGK6WggAnBwWSIcA1LAZj8ZQYpBTqtplKq+lQmIXQwxpSOzO+eD6GrMWZ/VS4sIi1EZJmI7BSR7SLyQFXOV5/E5+Xh4XCwtFEjrnAnBLM5jPi8PIsjU0rVZ5VJCLtF5P9E5DL3MtW9zgvXcNjnqxj4kzEmGugD3C8iHatwvnojyseHQqeTRR070p9VeFBEyZ4gGhX6WB2aUqoeq0xCGAfsBR4EHgL2A3fiSgbn/XCaMeaIMeYn9+vjwE4g4nzPV5+Ee3kxLTaWFYMGEUA23VkHTmHnOi+rQ1NK1WMVJgT3A2nzjTFTjDHXG2OuM8a8YozJNcY4jTHZFyIIEYnC1Tax9gzbJojIBhHZkJKSciEuVyeMiYhg2WOP8asIQ9zVRkuXWhyUUqpeqzAhGGNKgFwRCaquANzzMn8OPGiMyTpDDO+4G7R7hIeHV1cYtVITHx92RUaWtiNoQlBKVafKPIeQD2wVkcVAzomVxpg/VvXiIuLAlQw+NsZ8UdXz1Uf5AwYw8JPP8SSfzZu9SU2FsDCro1JK1UeVaUNYAPwVWAFsLLNUibiedJsG7DTGvFrV89VXzcaOxZMC+vEDAMuXWxuPUqr+OmsJwRgzQ0R8gJbGmAs5dlE/4HZcpY9N7nVPuOdxVm5xV1zBBhEGmaUsYxBLl8KoUVZHpZSqjyozuN0I4BXAE2gtInHAc8aYkVW5sDFmFTrQ/1l5e3uzMzKSuENLaReeRKtWTa0OSSlVT1WmDeFZXIPYLQcwxmwSkdbVGJM6zWX/+x+NW7Rgt7+/1aEopeqxyiSEYmNM5mmD25lqikedQVR0tNUhKKUagEoNfy0itwIeItJORN4EVldzXOoMnOnp7FuVyIoVVkeilKqPKpMQ/gB0AgqAWUAWrqeWVQ2aOXQom0Mv56IBEYwbZ3U0Sqn6qDK9jHKBJ92Lskh8YCC3sI2Wngfp2rUlubno/AhKqQtKjKm4OUBELgYeAaIok0CMMVdUa2Rn0KNHD7Nhw4aavmyt8Ov+/dhyc2nRsRM2m3bOUkpVnohsNMb0ONt+lWlUng28BbwHlFQ1MHV+WrdpY3UISql6rrK9jP6v2iNRleN0kr9jH3O3t+P668HT0+qAlFL1RWUaleeLyH0i0kxEGp1Yqj0y9Rsfvf02aZ6eDIk5wujRMHeu1REppeqTys6H8CiurqYnxjFqmBX5Fss2hoMlJdxkZgPwzjsWB6SUqlfOmhCMMa3PsGiFtgX69+/PYuA2PsLbo5DvvoO9e62OSilVX5SbEETksTKvbzpt29+rMyh1Zh07dmSFnx8hZDDEy1Vf9PBrxy2OSilVX1RUQhhd5vVfTtt2dTXEos4iraiIpdHRpAN/znWNGD7/E08SjxdYG5hSql6oKCFIOa/P9F7VgPi8PEyXLrwF9GENLXz3QYYXMz8vtjo0pVQ9UFFCMOW8PtN7VQOifHxwduzIv4Ei4JG81wH4dqaPlWEppeqJihJCrIhkichxIMb9+sT7LjUUnyoj3MuL9268kSP+/nwC3GE+xNujgJXLbNq4rJSqsnITgjHGwxgTaIwJMMbY3a9PvHfUZJDqpNtbt2b87bfzKhBMJqPlMwDefdfauJRSdV9lnkNQtcz9v/sdW4FldjsTi/8DwPTpUFhobVxKqbpNE0Id1LVrV7p27crLxcX0Zi1d7DtISYGvvrI6MqVUXaYJoY66++67WQTE+/szMWQ2HdoUYK/MyFRKKVUOvYXUUWPHjmXdunUcGT6cideN4j6HDdHOwEqpKtCEUEeFhIQwc+bMU9alFBQQn5dHlI8P4V5eFkWmlKqrtMqonvhqwwYemvQyA36fSsu53zMrMdHqkJRSdYwmhDpu8eLFDL/qKi4fMICEDy6j4OOLyJ95MeM3byalQIe0UEpVniaEOu6HH35gwaJFfBQayohu0/DrEg/X7cdhsxGfl2d1eEqpOkTbEOq4u+++Gw8/Px6NiCA/MBDYBkCR00aUj2tIC21bUEpVhiaEOq5ly5b89dFHuSgxkfGbN+Ow2bDn5vLWRRdzeJcX34W51nvabBQ6nUyLjWVMRITVYSulaiFNCPXEmIgIBoaEkLx7N21uu4dhidNYm2fg33soaOokz+kEYPzmzQwOC9OSglLqN7QNoZ6YPHkyPS6+GFtyMv4ph4jK2ERBgVD8n86njE2rbQtKqfJoQqgnDhw4QGJiIu8uWACffsoUeZRQUinZFAbLTlYRFTmdpW0LSilVliaEemL8+PEAzJw5k5TOnQl78SGm8CcAPN6Nxj/HBx+bjWmxsaXVRSkFBazPyNDuqUopQBNCvdG1a1cGDRpERkYG999/Pzz+OHcMS2cgSynJ9uayLy7hwKBBpQ3KsxITabVkCVeuWUOrJUv0QTalFGJM3Zn8rEePHmbDhg1Wh1Fr/frrr3Tp0oWcnBw+++wzbho8mN0xo4hJWEAB3rzwvJMnn7KRUlBAqyVLShuaAXxsNg4MGqSNzVVUXFxMTk4O+fn55OfnU1BQUPpvQUEBxcXFpyxXXnklXu6f+apVqzhy5Aj9+/enWbNmAGzfvp2dO3dis9lOWTw8PLDb7b/51+Fw0LZtW4KCggDIysoiJyeHwMBA/Pz8LPu5KGuJyEZjTI+z7ae9jOqR1q1bM3nyZO677z7uu+8+Ltu+nYvnTubd3vcxrvg9nvqrDZOVxVVPOPG02U5JCCcamzUhQElJCSkpKSQlJZGUlERycjJOp5M777yzdJ8bb7yRw4cPs3DhwtKb79ChQ/n222/P6VpJSUk0adIEgL///e98++23LFiwoDQh/Pe//+X5558/p3POnz+f4cOHAzBlyhSee+45nn32WZ555pnS7TfccAOenp54enri5eVVupz+/sQyduxYbr75ZgC2bdvG9OnTiYmJYdy4cQDk5OTw4Ycf4u3tXXrMmV6XXefn54e/v/85fTZVvSxNCCJyNfAvwAN4zxjzspXx1AcTJ05kzpw5LF26lPvuu4/Zs2dz+9e3YEb9gTuz3+SvkwPJO7SDwtudpxzX0BqbN27cyP79+4mPj+fAgQMcOHCAhISEUxJAWY0bNz4lIaxfv55Dhw6RlZVVmhC8vLyw2Wz4+fnh7e1dupy4EXp6euJwOH7zjf6Efv364evrS9OmTUvXdezYkRtvvBGn01m6lJSU4HQ6S0sZJSUlp5Q6GjVqVHq8j48PTZo0KY0RoLCwsHTf3NzcSv28evXqVfqA47bt23n11Ve5/vrrGTduHCkFBfy4bx/33nvvOf0Orh4xgm/nzQMgISGBDh060LJ1a2asXFn6EOXAgQPJycnB5nDgdDgI9PYmwMenNHkZu518m41QX1+CfX0JCwvjkUceKY11zezZ+IgwduxYfHx8SCkoYMGqVfjk5dHYzw+Hw4GnpyfZQHJJCVEBATRxr3c4HGQ6nRwuLqZjeDiNvb1LYy/vYc/qXn++58Lb27cyvxPLqoxExAPYDVwJJADrgTHGmB3lHaNVRpUTHx9Ply5dyM7O5tNPP+WWW26BI0f4aMhMxm17BCceTBi4nA8fycVhs1FUjx9Yy8vLY8qUKSQlJfHvf/+7dH3btm3Zv39/uceFhYXRrFkzGjVujE+jRrSOiGDqa6+Vbp/33XckFxdzVd++tHDfbIuKijhWUsKB/Pxq/wOvynpjDB/FxzNh40YcxlBUUMA/LrqIq0JC+OrQIZ7Zvh17cTFFhYU8GBlJ34AA9oaE8HRODp42G/mHDnHjwYOM6taN/F69GL95M/asLHJnzKBfQADNbDb2ZWTwU2oqUlyMKSykpd2On9NJak4OyTk5UFiIrWdPPvzgA8ZERLB3717atWuHNG1K4PTppQ9R3tupE5mZmZX+fbdu3ZoXV64sfRgzc9QoyMkhPT2dhbm5jN+8maKnnqL4558rfU4A708/5f3+/RkTEUHcFVew+ccf8XvmGZwxMUyLjeXgRx8xZepUUktKEA8PjIcHUQEBNPbx4ZjTyd78fNd6m43YkBBa+PnR9/e/57miIjxtNnK//55Lfv2Vx8eNIyMmhvGbN+Px66/kL1nC1U2a0CUkBA8PD3bm5jI3JQUPDw9KRLglMpIejRqx6fhxPjlyBK+OHSlp04ZpsbH0LSrin3PnMq2wkMK33iox+/adtQBgZULoCzxrjLnK/f4vAMaYl8o7pnXr1ubLL78kLi6OkpISPvzwQ7p160ZMTAxFRUV8/PHH9OjRg86dO5Ofn8+nn35K7969iY6OJjc3l88++4y+ffvSvn17srOzmTNnDv379+eiiy4iMzOTL7/8kksvvZQ2bdpw7Ngx5s6dy+WXX05UVBSpqal8/fXXDBo0iBYtWpCcnMw333zDlVdeSUREBElJSSxcuJCrr76apk2bkpiYyOLFixk6dCiNGzfm0KFDLFmyhOHDhxMWFkZ8fDzLly/n2muvJSQkhP3797NixQquv/56goKC2Lt3L6tWrWLUqFH4+/vzyy+/8OOPP3LzzTfj6+vLzp07Wbt2LaNHj8bb25tt27axYcMGxo4di8Ph4PXXX2fz5s0sWLCArVu3cuTIETZt2oRjcTh3fHI1vfv8zNhx2+g1+jqifHyI37KF3bt3M3bsWFIKCli2ejV5hw8zbuxYAFavXk1CQkJptcGqVatISkpi1KhRAHz//fekpaVxww03ALBs2TKysrK49tprAfjuu+/Iy8tjxIgRACxatIiioiKGDRsGwMKFCwG4+uqrAViwYAEOh4MhQ4YArmoOHx8fBg8eDMDcuXMJDAxk4MCBpKen8+mnn5KZmcnOnTvx8PBg8DXX4BESwuX9+tEqJITrrruOSZMm0fmSS4jPy2P2yy9zLC0NPz8/0kNCwOlkv58fG5s25Z1LL8WsWEFORAR/KijA02bjxh076Nm1K5MGDuSTQ4dYMns22xs3ZkujRrzbqRNFy5ZR2KYND2ZnE1RUxPA9e+jZpw8T+vfno337WDVnDgf8/Tlit/O3li05tm8f/du0YX9xMa/v2EHHwkISRZjYujWxvr7M3L2bd1q0IDE0FP+cHB7Zv58bg4LY2K0bf4yPZ8jBgySVlPBMUREtfH2ZnZlJ4tGj2IuKMHY7zRo35mYvL45kZfFVWhoSGoocPUrc+PG0aNKEN+fPJ/n4cfpu386GLl0I8fPjvtGjmfTVV4xas4aixo3x+fVXvEpK6BsVxf/sdvz27cOjqIjC4GAKmjThrqws5h8+zPc9e+IICODjdu3ofuAAr+7axYLgYF7q0wenCJckJDBy924mpqQwPymJjCZNyA0Lo8nWrdhFaNO+PXv9/PBYuxan00lmq1YkRUby6qWX8klICG8tXszghAS8tmzhj1ddxWVOJ1cGBhL+4YcE5OeT1qkThYGBRKxYQXRQECvj4ijy8qLZjh2wfz8pPXrQtGVL0vfvZ+K99zJk4ULsx49zw/z5tBDhP4MHUwgs/PFH/pKRQdPLL8dRXEzY4sVgDEeGDsUjOJjm+/czKCyM6Q4HjrQ0GicnQ1AQX950E+FHjvCvf/6TJ4DwUaP4MSmJz1atAmw8dPMttEk4TMjqjTixkTTmWrz3JxB4rJCSgCCSe7fHe2c8vsvW0+qi9my+ugs/tmjGV6mpMPn/ePjO22m5aSerNi3nC5uNO+4Yx9GfUhi0JQGnw0H+2N54rD+Ix/YknC0iKRrRHo+9ubT+9Tj7Eg/gHBPHs9/PxezZc9YZU6ysMooADpV5nwD0Pn0nEZkATACIqIffYKvLwIEDOXjwIGlpadx333089dRTAIz9eBi2wfmIj1BYaKOntzfceivxgwdDQACz3ENg9E5OJiIzE8/ExFpVcigsLOTnn39mx44dJCYmMu7OOzl08CA33HADqamprFixAh9/f3K7diU9O5u7ly9n1J/+RJy/P7sSErjns89ICw9neLNm9O/Xj1szM7l3+3akcWMKg4LIb9SIQ088QZNWrShZvJhpBw/iU1DA/p49CV62jNzHHyc6PZ2MwYMZ8+WXdNi5k6TQUNY99hjvHThAXkgIe8aPZ/GIEUwLDGRAbCwPbNvGkwkJPLRoEe137ybb3585o0bBv/7FkL176R0YyJc33MB9K1bQZv9+joWEEHTttThCQ8kMCsJuDObgQZg7lxnjx1PQsSMlxtB72zZ6zpxJUtOmBFx9NQ8uXEjTpCQSmzdn8ZAh8M03xCYn06hFC5YMGsTw+fO5p3Vrxo4ciQC99uzhidmzeTooiMPR0WzKzKT9kSPc+OOPrOrfn1GLFuGfnc0vF19M80su4eZFi/DNzWVndDRre/cmeNYsfldQwKEWLTgUEABAm+RkfFatIuTyy0t/Z45MIehYHskfraUrnuzp5k9i5xDaLi2kCAd7srJJv9iTVitCKcKBd5E3oYFZOGw2MiMjIa0d+ZmFXLs3AZ7qiT05mawj3hzdfReOAif2ZsXYbE52x/dlMXb8G2XjEehk7arLKcZOeE4Kuw44+f2a+XAv0LkzbAvi3ayJvFHyID79+lHocEDQX/nkQ2/6l6yhuMTOhuI3cGKjD2vJO+zN2h96U4IHl1+7nOME8MP2fnzBDdhvdBLRvTuOYZt4eUFnnuVv+Pdqid9NN3F1Yh8S4+NZSySruQSAMcxiP61Zu7sPAGM7fMzu7DGspyfshb9lPU1gbi60bg0DXyYdPzLpxm0DSljQogU0akYiD/IIMTgoYiwfs56JbKczXsn5jMn9lLWHerNzTzS+vrncXPIZMLdSf19WlhBuAq4yxtzjfn870MsY84fyjtEqo3Nz4MABunTpwvHjx1m7di29evX67U6zZ/PGzSsZEJ1G5M/vn+x9ZAyI1HjvozNVeyxevJiv583j1++/Z9+uXewoKgIgEHgACPLwIMTfn4uCgmjp40NKbi5BJSUE5uYSkJeHX5nnLOb27s117uR4UXo6e8aN40ijRjSfMaN0nyN33EHTY8cqHXNSSAj/27yZB7ZvJ7O4mAN33UV4Vhax06fz5IABPLB9O69OmcJl27ZR5OGB024nKiAAY7ezPT+fQhGKPTwo9vBAPDxoHxzM1pwcbn3wQTLcja5PffUVd6anc+egQaxq1QqAEWvXMvLnn+kfFsb3x46RB5TYbBjAw8OTvsHNWZiay/FCBwVOb7y9s1k6vAcvX3stI7/ZStSCbLof286BwTZ+6tKFJZ0GMPLevbQ8kEKx00FxiSfGaSfKO5hdWYUUFTsodtopKXHgLHEQ6OGDf+OteN6zkY3t2sFRH5gwkMjgbOIeeoOv4+JcP6AxV0J25f//+AWk0+Mvb7MuNpaNAwbQKcITc9yLax58kW8HxeJjs9H91SGsWnJu32dHPPwy8wd2dr15phf81JiZDy/mjwNyyLDbYWZ7mN3unM7Z7+bpbB8TwupBg4i55yjFn11Ex0v/R9o9yWSFhvKPzIE8cIcDG04Qg9gMIgY/u428kmIQ41ovTkQMjTwdNOm+lMTbMjgaEgI/heH1nw7c0TWFl/+RS2RiInkpDux/7Y5fYT4CtPD1IiE/DwOl5xGBNn4+xOfm4sSQ5jWk1pcQEoAWZd5HAoctiqVeatWqFW+//TYhISFnTgbAT6FX8pDciH2PYe6BbDxtNqLi41ny1FNsiYpiX8uW5OzaRXi3btChAzRpwnnN1el0QlYWZGZCVhbHUlJITUqiSU4OgcePQ3o6ew4dYtOePYQePcoh4OAdd9D9mWd49KWXiFi2jAXAt8Dv2rXj0r59We7pyXPvvQclJa7zuuuao06/tAjFfn6kenlxrEzXy1x/f5JGjmReSckp+784dixPtmzJ3xISyHQ4yPf0JM/TE+PlxVs9e3Lrjh1k2O0UOBwUOBzYvLz4X3Awhe6G6FbTpwOurry93OvHP/BA6flPJFmAy5csIa/ECfkekGvHK9+TGRf34M7kH8j3K3QdsDOEl4sf4eIJLdnoXO76We4KZv7C37Mg30704WB2pORh8j1c5ynwgCKP3/4ObtuFT/P9dA0M5L7iWF6bHcq+Pr1xdNnItNhYWpgAUr/tSupph+0s51eaBnSN68mO9tkE2mwUOiDfacPpHcitd93FEvdgi8fDCwgN9iDEx06uFHG4OBexG7A76RDkR4S/Fw4HJJfk8XNOBoXBhayLjWVabCzRAQGMvPM4Xx86zKoBvfCxFTEtNha5x05kz0zmJB/Gww5Om5PbWzWnb1gI67OOMT3xIHYHlEgJ97VpxcAmoWR0vp3vdrliKrj7Fx57Qhg28Ersea5Sscd1CRRdlsTz0RczonkTvklJ4ondu3DYhSJKeLVzNDdENGNu8hEe3LENh13Y6NmU97vHEB0QwAeTs7jntm84ZLdRbELd7XI+hF16cuDJsu11sxJTy1nfjfGbNxNos1HUI51pP+UwJsKVqKaFhbmOeWddmcEqQ0tL9qeeq3Hpev7gLCnn13gKK0sIdlyNyoOARFyNyrcaY7aXd4yWEKpuw4YNdOvWDZvN9UxiVhY88ww4HPDo867nEx76ZBYvfPwRZ7zt+/lBQAD4+ICvr2vx8YFHHwV3V0c+/hj+/ne49VZSHnmE+Lw82q1dS7C7faCypo4YwcCPPyb2+eeJ+flnPvnpJ1bGxPCHRx/lqx49GLN+PQ/NnEmGnx+Zfn4UBQTwh7g4Hk5I4KiPD1m+vmT5+mJ8fNhw2WV0X7nyjM9efJda3h9meX/I5a+/a+FuPNJ8cUYe5/3LohkTEcETn6byz0+yseU4KMm2c7EE45nnRWYmpGQ4yc0SMKf+tP/0fhpTm6zFYbOR+3Ebij+6mKeego6T3H/gGxuT93T53cpFDL6+godPCcc9ChCvEjyGHWTGk8GMiYhg0yZ4/qUSWsQU8uQjNsK9vMjJgddfhxJHMTm2QpoHOAgPcODlBd7ekG8rJJ0CWgV60TTAEy8vCAoCjxBXqa6Vtw8hHl7Y7a7vDDXVg6YhrT/fczUODt5p8vI6chaWPpgmIkOB13F1O33fGPNiRftrQqia9evX079/f6644grmzZt3SpdHdw0RsxITuXPqYRz/bUl0px94rd02+qfHw86dOHfuxFZOj4/9U6cScPfdrv+IU6fC/fez5/bbiR09Gk+bjeg9e1jxxBPYgoLY5XSSWVJCekEB6cePkzFoEEO7deOt48c5vH49aUePkj5sGBn9+/OUu8ols7i49FqBdjuzu3fnuvXrL8gNHk7+MbXy9sGvxIuUFEhJgb2Hi/jlSCEex73Iz7CTlgapqZCU4uRoqiEn08aa1ULLlq4YRtxQwtdfevDuR0XcM9b18/3nP+Hxxyv+3fj4GQIDIShACAx05dO4S10xHVrjy9plnlxxBVx1lSvWnw7mk7rNl+bBDvz9XXk6315Amj2f9o28aRHkVVqQ0/kwVJ14MM0Y8w3wjZUxNCTZ2dkEBARw0UUXnZIM4GQt0OjmEbyyuBk/7bOxYd8NDPa6gWHDoMWdabwdvo5wk4s9L49/tW7NiKAg/hcfz6vbthEfFMShJUtcN9mbbya9d2+G7NxJntNJXnIya/btw6dHDwK3b+dYSsop1/bp1o0Of/oTU9evJ++aa06uL1PlUlaR00nXwECmxcb+5gYf7uXFmIgIBoeFld4EA/Hi0CGITovgwKCT699/3Ys7d8KLL0JEhBfhXl6MGwczZ5a9msO9nO7kqC9paZQmhO4xHhxLhsjQk8cMGgSvvQYhIRAc7PpWHRR08nVgINjtZyqPuWLqeTXcUKZwFe7lxVXtvOA31d1e7uVU4V5emghUpejQFQ1MQkICjRs3xtPTE3A1PAcEBJzyMFNmJnz6KcyaBStWuEoPAPgUQ8+j0C4DzzbZLB3TiSt3rjjlW7q3CCvbtmXB8uX8fd48CrduhYSEU4MIDYXYWIiLg9hYfMLCzuub/b59sG1/ITsPF0GGJ3npDpKTKV2OHnX9e6JQIwKFhWB3fw3q0wfWroUffoBLXB1AeOABePttCA8/uYSFuZbQ0FNfn1iaNnVVuSlVW1W2hKAJoQE7duwY3bt35+DBg/Tv35+RI0cyYsQI2rU7+dUzMRFemZHHmzMKKNkd/JtzSFAeJjoBnvwFAO8NP5P/t624mhyXunby8YGLB2LvFMOnt91GYqNGPLZjF/YiO8V5wmOR7enrG05ODhzJKOJAWhFh3g7+/MDJu+xlg5wcOGT4fm0xrUJc33YvvRRWrjz757TbXTf2Jk1g6VLXN3WAOXNcbShDh7pu6gDFxeDhcX7t5krVVpoQ1FmtWbOGJ598khUrVlBcpo6+Q4cOXH755fj5+WG32ykE3jx0iOKcpmC7BvIvwhYfiONXfwryPSFkNcxMB8DrSCEFE27A4TjOqMf+wefBwXh16MDxOwdBWuWHxmjaFI4cOfk+IgIOH4YDB05WzzzwAGzc6LrRN2585qVJE1fVjE3H9VUNmCYEVWkZGRksXLiQ+fPn880335CRkVHuvp7XXovHhAlMi42lbeJhBl55D/kdu+P/zM0UOZ28FtmVxc81xctL+Pjjkw2aE68MJPXoqXflE52U/PxOLr6+rht4kybgflwAgA0b3AWNi7V6RqlzpQlBnZeioiJWrVrF5s2bfzNUc1Z+PiFt2jBp3LjSMXFERHuxKFXLaUJQSikFVD4haM2qUkopQBOCUkopN00ISimlAE0ISiml3DQhKKWUAjQhKKWUctOEoJRSCtCEoJRSyk0TglJKKUATglJKKTdNCEoppQBNCEoppdw0ISillAI0ISillHLThKCUUgrQhKCUUspNE4JSSilAE4JSSik3TQhKKaUATQhKKaXcNCEopZQCNCEopZRy04SglFIK0ISglFLKTROCUkopQBOCUkopN00ISimlAE0ISiml3DQhKKWUAixKCCIyWUR2icgWEflSRIKtiEMppdRJVpUQFgOdjTExwG7gLxbFoZRSys2ShGCMWWSMKXa/XQNEWhGHUkqpk+xWBwDcDfy3vI0iMgGY4H6bLSK/1EhUpwoDUi24rpX0MzcM+pkbhvaV2UmMMdVydRH5Dmh6hk1PGmPmuvd5EugB3GCqK5ALQEQ2GGN6WB1HTdLP3DDoZ24YKvuZq62EYIwZXNF2ERkHDAcG1eZkoJRSDYUlVUYicjXwOHCZMSbXihiUUkqdyqpeRv8GAoDFIrJJRN6yKI7KesfqACygn7lh0M/cMFTqM1dbG4JSSqm6RZ9UVkopBWhCUEop5aYJoQIi4i0i60Rks4hsF5G/WR1TTRERDxH5WUS+tjqWmiAi8SKy1d2mtcHqeGqCiASLyBz3MDI7RaSv1TFVJxFp7/79nliyRORBq+OqTiLykPvetU1EZomId4X7axtC+UREAD9jTLaIOIBVwAPGmDUWh1btRORhXM+IBBpjhlsdT3UTkXighzGmwTywJCIzgJXGmPdExBPwNcZkWBxWjRARDyAR6G2MOWB1PNVBRCJw3bM6GmPyROQz4BtjzAflHaMlhAoYl2z3W4d7qfcZVEQigWHAe1bHoqqHiAQClwLTAIwxhQ0lGbgNAvbV12RQhh3wERE74AscrmhnTQhn4a462QQkA4uNMWstDqkmvA48BjgtjqMmGWCRiGx0D5dS37UBUoDp7qrB90TEz+qgatBoYJbVQVQnY0wi8ApwEDgCZBpjFlV0jCaEszDGlBhj4nANwNdLRDpbHFK1EpHhQLIxZqPVsdSwfsaYbsA1wP0icqnVAVUzO9AN+D9jTFcgB/iztSHVDHf12EhgttWxVCcRCQGuBVoDzQE/EbmtomM0IVSSuzi9HLja2kiqXT9gpLtO/VPgChH5yNqQqp8x5rD732TgS6CXtRFVuwQgoUyJdw6uBNEQXAP8ZIw5anUg1Www8KsxJsUYUwR8AVxS0QGaECogIuEnJu8RER9cP+BdlgZVzYwxfzHGRBpjonAVq5caYyr8VlHXiYifiASceA0MAbZZG1X1MsYkAYdE5MQomIOAHRaGVJPGUM+ri9wOAn1ExNfdQWYQsLOiA2rD8Ne1WTNghrtHgg34zBjTILphNjBNgC9dfzPYgU+MMQutDalG/AH42F2Fsh+4y+J4qp2I+AJXAhOtjqW6GWPWisgc4CegGPiZswxhod1OlVJKAVplpJRSyk0TglJKKUATglJKKTdNCEoppQBNCEoppdw0IagGT0RK3KNfbhOR+SeePTnDfj4i8r27G/KJdQ+JSL6IBFUxht+LSL3v9qlqN00ISkGeMSbOGNMZSAfuL2e/u4EvjDElZdaNAdYD11cxhveBP1bxHEpViSYEpU71IxBRzraxwNwTb0SkLeAPPIUrMZxYf6eIfCEiC0Vkj4j8s8y28SKyW0SWi8i7IvJvAGNMLhAvIvV9yAxVi2lCUMrNXRU0CJh3hm2eQBtjTHyZ1SeGQFgJtBeRxmW2xQG3AF2AW0SkhYg0B/4K9MH1tGyH0y6zARhwQT6MUudBE4JSrvHiNwFpQCNg8Rn2CQMyTls3GvjUGOPENXDYTWW2LTHGZBpj8nGNEdQK14B53xtj0t2DjZ0+2mYyrlEplbKEJgSl3G0IuG7anpy5DSEPKJ1+UERigHbAYvfIsKMpU20EFJR5XYJrjCQ5Sxze7usoZQlNCEq5GWMycTXsPuKeMrXstmOAR5k5accAzxpjotxLcyBCRFpVcIl1wGUiEuKewerG07ZfTD0fZVXVbpoQlCrDGPMzsBnXN/7TLQL6u1+PxjVvQllflnPciXMnAn8H1gLf4apKyiyzSz/3eqUsoaOdKlVJItIVeNgYc3sVzuFvjMl2lxC+BN43xnx5Ic6tVFVpCUGpSnKXHpaVfTDtPDzrbsDeBvwKfOVeH4arB5JSltESglJKKUBLCEoppdw0ISillAI0ISillHLThKCUUgrQhKCUUsrt/wHfRU6+MZ95aQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "V_lam =  6 \t : \t\tError \t\t Covarance\n",
      "exp_fit_3 \t : \t  0.12900166205340446 28155458.452740107\n",
      "fit_12_exp \t : \t  0.09243002146046839 2.3794638286931063e+19\n",
      "fit_12_6 \t : \t  0.12547630352370695 5052023.254694882\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# select inital range for analytical fit (leave high energy points for beter fit)!\n",
    "\n",
    "# starting point for fitting into function\n",
    "ini_val = [8,7,5,4] \n",
    "\n",
    "# cov and error variables\n",
    "covx1,covx2,covx3 = np.zeros(lm),np.zeros(lm),np.zeros(lm)\n",
    "er1,er2,er3 = np.zeros(lm),np.zeros(lm),np.zeros(lm)\n",
    "\n",
    "# Fitting data into analytic function and plotting for visualization\n",
    "for ii in range(0,lm):\n",
    "    y_dummy = df_Vnf[str(ii*sym)]\n",
    "    \n",
    "    # fitting with various functions\n",
    "    \n",
    "    parsx1, covx1 = curve_fit(f=exp_fit_3, xdata=x_dummy[ini_val[ii]:], ydata=y_dummy[ini_val[ii]:], \n",
    "                                  p0=[0,0,1000])\n",
    "    d[ii],e[ii],f[ii] = parsx1\n",
    "    \n",
    "    parsx2, covx2 = curve_fit(f=fit_12_exp, xdata=x_dummy[ini_val[ii]:], ydata=y_dummy[ini_val[ii]:], \n",
    "                            p0=[0,1000,2],bounds=((-np.inf, -np.inf, 0.5), (np.inf, np.inf, 5)))\n",
    "    g[ii],h[ii],l[ii] = parsx2\n",
    "    \n",
    "    parsx3, covx3 = curve_fit(f=fit_12_6, xdata=x_dummy[ini_val[ii]:], ydata=y_dummy[ini_val[ii]:], \n",
    "                                  p0=[0,1000])\n",
    "    m[ii],n[ii] = parsx3\n",
    "    \n",
    "    # calculate error for each fir\n",
    "    er1[ii] = np.sqrt(np.average(np.power((exp_fit_3 (x_dummy[ini_val[ii]:], *parsx1) - y_dummy[ini_val[ii]:]),2)))\n",
    "    er2[ii] = np.sqrt(np.average(np.power((fit_12_exp (x_dummy[ini_val[ii]:], *parsx2) - y_dummy[ini_val[ii]:]),2)))\n",
    "    er3[ii] = np.sqrt(np.average(np.power((fit_12_6(x_dummy[ini_val[ii]:], *parsx3) - y_dummy[ini_val[ii]:]),2)))\n",
    "    \n",
    "    # print error and covariance\n",
    "    print('V_lam = ', ii*sym, '\\t : \\t\\tError \\t\\t Covarance')\n",
    "    print('exp_fit_3 \\t : \\t ', er1[ii], np.linalg.cond(covx1))\n",
    "    print('fit_12_exp \\t : \\t ', er2[ii], np.linalg.cond(covx2))\n",
    "    print('fit_12_6 \\t : \\t ', er3[ii], np.linalg.cond(covx3))\n",
    "    \n",
    "    # plot original curve\n",
    "    plt.scatter(x_dummy, y_dummy,s=20, color='#00b3b3',label = 'no fit')\n",
    "    \n",
    "    # plot fitted curves\n",
    "    plt.plot(x_dummy,  exp_fit_3(x_dummy, *parsx1), linestyle='-.', linewidth=2, color='black', label = 'exp_fit_3')\n",
    "    plt.plot(x_dummy,  fit_12_exp(x_dummy, *parsx2), linestyle='-.', linewidth=2, color='red', label = 'fit_12_exp')\n",
    "    plt.plot(x_dummy, fit_12_6(x_dummy, *parsx3), linestyle='-.', linewidth=2, color='blue', label = 'fit_12_6')\n",
    "    \n",
    "    plt.legend(loc=\"upper right\")\n",
    "    plt.ylabel(\"Energy (cm^(-1))\")\n",
    "    plt.xlabel(\"R (Ang)\")\n",
    "    plt.axhline(y=0, color='grey', linestyle=':')\n",
    "    plt.title(\"V_lambda = %d\" %(ii*sym))\n",
    "    plt.ylim(x_i[ii], x_f[ii])\n",
    "    plt.xlim(y_i, y_f)\n",
    "    plt.show()\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ea52a1e",
   "metadata": {},
   "source": [
    "#### Template for saving each V lambdas as required by molscat!\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ef687640",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LAMBDA = 0, 2, 4, 6\n",
      "NTERM  =  3,3,3,3,\n",
      "NPOWER =  0,0,0,0,0,0,0,0,0,0,0,0,\n",
      "A      = \n",
      "-348.8743722006384 , -83949.20142334526 , 3068319.9675202463 ,\n",
      "189.01892882343208 , -75704.25692432174 , 2905221.5754147274 ,\n",
      "95.30131350741651 , -15284.365300642776 , 482111.164869272 ,\n",
      "36.59411392517567 , -3820.5464694103075 , 80866.25299646235 ,\n",
      "E      = -1,-2,-3,-1,-2,-3,-1,-2,-3,-1,-2,-3,-1,-2,-3,-1,-2,-3,-1,-2,-3,-1,-2,-3,-1,-2,-3,-1,-2,-3,\n"
     ]
    }
   ],
   "source": [
    "# Template for EXP-3 function\n",
    "\n",
    "print('LAMBDA = ', end=\"\")\n",
    "print(*range(0,lm*sym,sym), sep=\", \" )\n",
    "print('NTERM  = ', '3,'*lm)\n",
    "print('NPOWER = ', '0,0,0,'*lm)\n",
    "print('A      = ')\n",
    "for j in range (lm):\n",
    "    print(d[j],',',e[j],',',f[j],',')\n",
    "print('E      =', '-1,-2,-3,'*10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "82ac4c35",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LAMBDA = 0, 2, 4, 6\n",
      "NTERM  =  2,2,2,2,\n",
      "NPOWER =  0,12,0,12,0,12,0,12,\n",
      "A      = \n",
      "-6469.235133255057 , 154537014.19235426 ,\n",
      "95720712.86374603 , -339592255.7504787 ,\n",
      "17061269.267522562 , -17185512.192476466 ,\n",
      "19779368.030451823 , -2043182.4435008338 ,\n",
      "E      = \n",
      "1.394525631058717 ,\n",
      "3.8915070829651364 ,\n",
      "4.190473502064657 ,\n",
      "4.999999999999753 ,\n"
     ]
    }
   ],
   "source": [
    "# Template for EXP and R**-12 Function \n",
    "\n",
    "print('LAMBDA = ', end=\"\")\n",
    "print(*range(0,lm*sym,sym), sep=\", \" )\n",
    "print('NTERM  = ', '2,'*lm)\n",
    "print('NPOWER = ', '0,12,'*lm)\n",
    "print('A      = ')\n",
    "for j in range (lm):\n",
    "    print(g[j],',',h[j],',')\n",
    "print('E      = ')\n",
    "for j in range (lm):\n",
    "    print(l[j],',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "69806fca",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LAMBDA = 0, 2, 4, 6\n",
      "NTERM  =  2,2,2,2,\n",
      "NPOWER =  12,6,12,6,12,6,12,6,\n",
      "A      = \n",
      "181298782.33150506 , -104836.53263073681 ,\n",
      "142320687.2579218 , -47249.78626230899 ,\n",
      "18132606.257034905 , -5359.4855660850035 ,\n",
      "2149832.4721329277 , -1275.2826258973382 ,\n"
     ]
    }
   ],
   "source": [
    "# Template for LJ (12-6)\n",
    "\n",
    "print('LAMBDA = ', end=\"\")\n",
    "print(*range(0,lm*sym,sym), sep=\", \" )\n",
    "print('NTERM  = ', '2,'*lm)\n",
    "print('NPOWER = ', '12,6,'*lm)\n",
    "print('A      = ')\n",
    "for j in range (lm):\n",
    "    print(m[j],',',n[j],',')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3a22ee3a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7d27ce0f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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