[Showcase2]_MSM_fitparam_kbar5_m20_RV22_mean.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from pandas import DataFrame as df\n",
    "from MSM_util import *\n",
    "from lmfit import minimize, Minimizer, Parameters, Parameter, report_fit\n",
    "import sys, scipy, numpy\n",
    "\n",
    "# print(scipy.__version__, numpy.__version__, sys.version_info)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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OwLa9xUF1kUiGUC7zGQpGjPVvz1i1vdLHVJSahAp6JaUYE5iMvWhARzIzxD9B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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1eb7310bac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Hyper parameters\n",
    "\n",
    "# How much period taken into calculation and prediction\n",
    "m = 20\n",
    "# number of days prediction\n",
    "RV = 22\n",
    "# kbar\n",
    "kbar = 5\n",
    "\n",
    "xls_data = pd.read_excel('data_GVZ_GLD.xlsx')\n",
    "date_GLD = xls_data.iloc[:,3]\n",
    "GLD = xls_data.loc[:,'GLD']\n",
    "\n",
    "GLD2 = GLD.shift(1)\n",
    "GLD2[0] = GLD[0]\n",
    "GLD_r = GLD/GLD2\n",
    "\n",
    "GLD_d = GLD_r - np.mean(GLD_r)\n",
    "plt.plot(date_GLD,GLD)\n",
    "plt.title('de-mean data')\n",
    "plt.plot(date_GLD,200*GLD_r)\n",
    "\n",
    "data = GLD_d[::-1]\n",
    "\n",
    "\n",
    "startingvals = [1.2, 1.2, 0.5 , 1.2 ]\n",
    "LB = [1, 1, 0.001, 0.0001]\n",
    "UB = [1.99, 50, 0.99999, 5]\n",
    "op_methods = 'slsqp'\n",
    "\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fit data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==========init params=========\n",
      "m0 =   1.2000\n",
      "b =   1.2000\n",
      "gamma_k =   0.5000\n",
      "sigma =   1.2000\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-7-463aeb0e26ce>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0moutput\u001b[0m \u001b[1;33m=\u001b[0m\u001b[0mmsm_fitseries\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkbar\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mLB\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mUB\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mop_methods\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstartingvals\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mm\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mRV\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32mC:\\Users\\lawof\\Documents\\Fractals\\Thanasarn_MSM\\GIT_MSM\\MSM_util.py\u001b[0m in \u001b[0;36mmsm_fitseries\u001b[1;34m(data, kbar, LB, UB, op_methods, startingvals, m, RV)\u001b[0m\n\u001b[0;32m    252\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mm\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    253\u001b[0m         \u001b[0mdata2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdata\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m:\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mm\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 254\u001b[1;33m         \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mMSM_fitdata\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkbar\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mLB\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mUB\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mop_methods\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstartingvals\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    255\u001b[0m         \u001b[0mre2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mMSM_likelihood_new\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mparams\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkbar\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdata2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mRV\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    256\u001b[0m         \u001b[0moutput\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mloc\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"RV\"\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mre2\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m**\u001b[0m \u001b[1;36m2\u001b[0m \u001b[1;33m*\u001b[0m \u001b[1;36m100\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Users\\lawof\\Documents\\Fractals\\Thanasarn_MSM\\GIT_MSM\\MSM_util.py\u001b[0m in \u001b[0;36mMSM_fitdata\u001b[1;34m(data, kbar, LB, UB, op_methods, startingvals)\u001b[0m\n\u001b[0;32m    229\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    230\u001b[0m     \u001b[0mminner\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mMinimizer\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mMSM_likelihood_new\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfcn_args\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkbar\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 231\u001b[1;33m     \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mminner\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mminimize\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmethod\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mop_methods\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    232\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    233\u001b[0m     \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"\\n\\n ==========fitted results==========\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\lmfit\\minimizer.py\u001b[0m in \u001b[0;36mminimize\u001b[1;34m(self, method, params, **kws)\u001b[0m\n\u001b[0;32m   1647\u001b[0m                         val.lower().startswith(user_method)):\n\u001b[0;32m   1648\u001b[0m                     \u001b[0mkwargs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'method'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mval\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1649\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mfunction\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1650\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1651\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\lmfit\\minimizer.py\u001b[0m in \u001b[0;36mscalar_minimize\u001b[1;34m(self, method, params, **kws)\u001b[0m\n\u001b[0;32m    774\u001b[0m             \u001b[0mret\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdifferential_evolution\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpenalty\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0m_bounds\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    775\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 776\u001b[1;33m             \u001b[0mret\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mscipy_minimize\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpenalty\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvars\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mfmin_kws\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    777\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    778\u001b[0m         \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0maborted\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_abort\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\_minimize.py\u001b[0m in \u001b[0;36mminimize\u001b[1;34m(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)\u001b[0m\n\u001b[0;32m    456\u001b[0m     \u001b[1;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'slsqp'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    457\u001b[0m         return _minimize_slsqp(fun, x0, args, jac, bounds,\n\u001b[1;32m--> 458\u001b[1;33m                                constraints, callback=callback, **options)\n\u001b[0m\u001b[0;32m    459\u001b[0m     \u001b[1;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'dogleg'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    460\u001b[0m         return _minimize_dogleg(fun, x0, args, jac, hess,\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\slsqp.py\u001b[0m in \u001b[0;36m_minimize_slsqp\u001b[1;34m(func, x0, args, jac, bounds, constraints, maxiter, ftol, iprint, disp, eps, callback, **unknown_options)\u001b[0m\n\u001b[0;32m    388\u001b[0m             \u001b[1;31m# Compute the derivatives of the objective function\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    389\u001b[0m             \u001b[1;31m# For some reason SLSQP wants g dimensioned to n+1\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 390\u001b[1;33m             \u001b[0mg\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfprime\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0.0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    391\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    392\u001b[0m             \u001b[1;31m# Compute the normals of the constraints\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\optimize.py\u001b[0m in \u001b[0;36mfunction_wrapper\u001b[1;34m(*wrapper_args)\u001b[0m\n\u001b[0;32m    290\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mwrapper_args\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    291\u001b[0m         \u001b[0mncalls\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m+=\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 292\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mfunction\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mwrapper_args\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    293\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    294\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mncalls\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\slsqp.py\u001b[0m in \u001b[0;36mapprox_jacobian\u001b[1;34m(x, func, epsilon, *args)\u001b[0m\n\u001b[0;32m     61\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     62\u001b[0m         \u001b[0mdx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mepsilon\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 63\u001b[1;33m         \u001b[0mjac\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx0\u001b[0m\u001b[1;33m+\u001b[0m\u001b[0mdx\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m+\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mf0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mepsilon\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     64\u001b[0m         \u001b[0mdx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0.0\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     65\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\optimize.py\u001b[0m in \u001b[0;36mfunction_wrapper\u001b[1;34m(*wrapper_args)\u001b[0m\n\u001b[0;32m    290\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mwrapper_args\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    291\u001b[0m         \u001b[0mncalls\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m+=\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 292\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mfunction\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mwrapper_args\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    293\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    294\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mncalls\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\lmfit\\minimizer.py\u001b[0m in \u001b[0;36mpenalty\u001b[1;34m(self, fvars)\u001b[0m\n\u001b[0;32m    544\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    545\u001b[0m         \"\"\"\n\u001b[1;32m--> 546\u001b[1;33m         \u001b[0mr\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__residual\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfvars\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    547\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mr\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mndarray\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mand\u001b[0m \u001b[0mr\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msize\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    548\u001b[0m             \u001b[0mr\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mreduce_fcn\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mr\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\lmfit\\minimizer.py\u001b[0m in \u001b[0;36m__residual\u001b[1;34m(self, fvars, apply_bounds_transformation)\u001b[0m\n\u001b[0;32m    486\u001b[0m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mnfev\u001b[0m \u001b[1;33m+=\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    487\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 488\u001b[1;33m         \u001b[0mout\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0muserfcn\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mparams\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0muserargs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0muserkws\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    489\u001b[0m         \u001b[0mout\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_nan_policy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mout\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnan_policy\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mnan_policy\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    490\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Users\\lawof\\Documents\\Fractals\\Thanasarn_MSM\\GIT_MSM\\MSM_util.py\u001b[0m in \u001b[0;36mMSM_likelihood_new\u001b[1;34m(*args)\u001b[0m\n\u001b[0;32m    174\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    175\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mt\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mT\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 176\u001b[1;33m         \u001b[0mpiA\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmatmul\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpi_mat\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mA\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    177\u001b[0m         \u001b[0mC\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmultiply\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mw_t\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpiA\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    178\u001b[0m         \u001b[0mft\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mC\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "output =msm_fitseries(data, kbar, LB, UB, op_methods, startingvals, m, RV)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>RV</th>\n",
       "      <th>m0</th>\n",
       "      <th>b</th>\n",
       "      <th>gamma_k</th>\n",
       "      <th>sigma</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4.428739</td>\n",
       "      <td>1.523221</td>\n",
       "      <td>49.999556</td>\n",
       "      <td>0.952785</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>9.347267</td>\n",
       "      <td>1.470767</td>\n",
       "      <td>27.063332</td>\n",
       "      <td>0.920657</td>\n",
       "      <td>0.220607</td>\n",
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       "      <th>2</th>\n",
       "      <td>14.104999</td>\n",
       "      <td>1.523887</td>\n",
       "      <td>49.989319</td>\n",
       "      <td>0.952167</td>\n",
       "      <td>0.270997</td>\n",
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       "      <th>3</th>\n",
       "      <td>4.404874</td>\n",
       "      <td>1.524391</td>\n",
       "      <td>49.991477</td>\n",
       "      <td>0.952635</td>\n",
       "      <td>0.151441</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9.351746</td>\n",
       "      <td>1.472488</td>\n",
       "      <td>26.716742</td>\n",
       "      <td>0.920885</td>\n",
       "      <td>0.220660</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>9.357927</td>\n",
       "      <td>1.471576</td>\n",
       "      <td>26.899620</td>\n",
       "      <td>0.920564</td>\n",
       "      <td>0.220733</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>14.100547</td>\n",
       "      <td>1.523654</td>\n",
       "      <td>49.645422</td>\n",
       "      <td>0.951422</td>\n",
       "      <td>0.270954</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>9.374800</td>\n",
       "      <td>1.471573</td>\n",
       "      <td>26.862351</td>\n",
       "      <td>0.919786</td>\n",
       "      <td>0.220932</td>\n",
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       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>2.174743</td>\n",
       "      <td>1.608107</td>\n",
       "      <td>49.999999</td>\n",
       "      <td>0.713122</td>\n",
       "      <td>0.106410</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9.393597</td>\n",
       "      <td>1.471854</td>\n",
       "      <td>26.955190</td>\n",
       "      <td>0.920383</td>\n",
       "      <td>0.221153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>9.398814</td>\n",
       "      <td>1.472136</td>\n",
       "      <td>27.048684</td>\n",
       "      <td>0.920273</td>\n",
       "      <td>0.221215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>14.091664</td>\n",
       "      <td>1.525268</td>\n",
       "      <td>49.997647</td>\n",
       "      <td>0.952297</td>\n",
       "      <td>0.270869</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>45.125678</td>\n",
       "      <td>1.524946</td>\n",
       "      <td>49.981832</td>\n",
       "      <td>0.952608</td>\n",
       "      <td>0.484718</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>12.006221</td>\n",
       "      <td>1.414688</td>\n",
       "      <td>15.983614</td>\n",
       "      <td>0.999990</td>\n",
       "      <td>0.250023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>14.073218</td>\n",
       "      <td>1.525089</td>\n",
       "      <td>49.948731</td>\n",
       "      <td>0.953026</td>\n",
       "      <td>0.270691</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>4.382920</td>\n",
       "      <td>1.525805</td>\n",
       "      <td>49.964871</td>\n",
       "      <td>0.952490</td>\n",
       "      <td>0.151063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>9.435207</td>\n",
       "      <td>1.473071</td>\n",
       "      <td>27.464808</td>\n",
       "      <td>0.920190</td>\n",
       "      <td>0.221643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>4.371516</td>\n",
       "      <td>1.526241</td>\n",
       "      <td>49.999999</td>\n",
       "      <td>0.952540</td>\n",
       "      <td>0.150867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>14.015508</td>\n",
       "      <td>1.525206</td>\n",
       "      <td>49.999977</td>\n",
       "      <td>0.952427</td>\n",
       "      <td>0.270136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>26.546455</td>\n",
       "      <td>1.473875</td>\n",
       "      <td>27.814125</td>\n",
       "      <td>0.923222</td>\n",
       "      <td>0.371776</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           RV        m0          b   gamma_k     sigma\n",
       "0    4.428739  1.523221  49.999556  0.952785  0.151851\n",
       "1    9.347267  1.470767  27.063332  0.920657  0.220607\n",
       "2   14.104999  1.523887  49.989319  0.952167  0.270997\n",
       "3    4.404874  1.524391  49.991477  0.952635  0.151441\n",
       "4    9.351746  1.472488  26.716742  0.920885  0.220660\n",
       "5    9.357927  1.471576  26.899620  0.920564  0.220733\n",
       "6   14.100547  1.523654  49.645422  0.951422  0.270954\n",
       "7    9.374800  1.471573  26.862351  0.919786  0.220932\n",
       "8    2.174743  1.608107  49.999999  0.713122  0.106410\n",
       "9    9.393597  1.471854  26.955190  0.920383  0.221153\n",
       "10   9.398814  1.472136  27.048684  0.920273  0.221215\n",
       "11  14.091664  1.525268  49.997647  0.952297  0.270869\n",
       "12  45.125678  1.524946  49.981832  0.952608  0.484718\n",
       "13  12.006221  1.414688  15.983614  0.999990  0.250023\n",
       "14  14.073218  1.525089  49.948731  0.953026  0.270691\n",
       "15   4.382920  1.525805  49.964871  0.952490  0.151063\n",
       "16   9.435207  1.473071  27.464808  0.920190  0.221643\n",
       "17   4.371516  1.526241  49.999999  0.952540  0.150867\n",
       "18  14.015508  1.525206  49.999977  0.952427  0.270136\n",
       "19  26.546455  1.473875  27.814125  0.923222  0.371776"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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txEQESwndwxw7WcqhXM9mJ3KGCLogeJj0/DLi3OA/txEbKc3/PY03shM5QwRd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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d16431c588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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S1kNZYWDBN7TmpjrePD/KG+HFz4O44/vp2o7QXZyWqRXtLnf8+p2baygIpOdP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\nGGOMcVhAMMYYA1hAMMYY4xBVzXYbkiY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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d1643d8e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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v4vg3On3Umz3Pgmgt2f0/foftHo7a/UDmz1o+hVqzq6yw276s4xKIhZ7FXqOL\nVnex2jTXjjroDYI1yABzYtEjIeiAXfXPhQ91FLIX4ISIxQgbASXHqDgh5PjdWMiqGhOoKuO7KEGV\nbQUs4RUCqCtyu8iY9jUfs0QlJ+0kF/sO5euDPH+B4DfmJdER9ELGk4UepA8dCC65aHRCBCSoqlZI\nViy/9zK+ixJklnFpyRJeVbHo0n1TzPsbrQO4r2m05TGHQhVyD4gtdEVIQVz0hK7WWyjmksil3IXM\nqSKo5CJVSRluk4tU1dFRVcZ3UeSqMBBBz6nNFpUbrEFY6OWiN0EP2uWSTsRxbiUdeLZopAS90x/i\n+oKTO8iym+OUCxlPyVFuUWUhlwtZXDvqLNz9fLveQiJGOLvsLSkkqCVvtdZCKh7DmSX/RVB1PRcZ\n0x6EhX52OWPvIy32/VXrLZTyqcANMsCMuujREXR7U2JRKzeoOuiTBFWxrVproZBLIp/2dkKUi1kI\nYdWFWfTzz69mPNcO8RoL75YtO+Ry0TryKpAlblVli+41ulhOJwJJ0InLfZgFBTGoHIBpVIpZbAWc\nXBQdQXdxQgshQ56CjWEFgotFV3VBcxt66bYO+iRBCXqQK7yi7XJR1Vs0iKSicazknMUE0W0dfx2U\nC1ns1INtJxk9QV9AUOrNHprdQWA1IMYJKttRlYUz8oG6WCGp2NAq5JLIpeK+u1y26y1suiyZ4JVU\nIobldEKZhb4fQB2XcRYNDBBC+N4p6jQqxRz6Q4GrAcaiR0bQZW/CRSaEfG3QIU9AMNmOKk8IWXFu\nkfH37cYEKix0mT7u5wqn0x9YdeQDnD+lJXXJRUHUcRmnXLT2YZz2Sd1vdNHuDY04fwE1zV68EhlB\nd9ObcLRDboDLJZOMYy2f8jU5Rq5QVFjoqUQMZ5fTCx3/q0cdDBRm6fod+rljf1dBLvlV1nMJ2kKv\nFHPWPozDc2ArwJDRaZhQFz0ygg4s3uggyNZz0/DbwlS9Qlk0fVt12dmgjl+Q82ctr6aErhDCEnQf\ne4lOsug+iAnHfxw5j9lCV8TmgnXFt+stZJNxFHP+h2lNw28LU/UKpVzMLebyUmxhuU0fd4sJZSOK\nuZSSTdHjTh/dwXAU2x4EixZ5O8nyDn6FDVir7PVldyVIVDFX0IkoQ0SPENFniegJIvoZ+/F3ElGV\niB6zf16nf7inUy7kcNDq4dhhXe5qzQo5c1u2VTXSwvQr21GHhb5z0MLQ4S7/SZaumk1pvyNdvNaR\nV4H0oXuLaT6yAAAe3UlEQVSdM7WGlZAVpMvl/GoGMXLustiqNbFs9+Q1haBDF51Y6B0ArxRCvATA\nXQDuJaKX2c+9Wwhxl/3zUW2jdMiiySVeqwyqZrOQQbM7wEHLn2zHaq2FXCqOgqIVSrmYRW8gcO2o\n4+zzFSeF+B366bWOvArW8il0B0PHRsws9uzCXGsBulyScbvzzwIuF1PcLZKgk4vmzkRhcWzfTdo/\nwQVankJ5wRPalKQiid+75NV601NjiUlGsegOLRSvddAnGV3QfbTQg54/JTtN3+vGqHx/KYC0/3HK\nCzSK2KoFU4f+NCpFa5UdVCy6I9OCiOJE9BiAawAeEkJ82n7qrUT0OBG9l4iKM957PxFdIqJLu7u7\nioY9nVGBHwcndLPbx36ja9SECMLCVGnhLFqPQ7UgnltOIx5zV8bXDdsHwdRBH6dkp+l7FXS5sRpk\n2CJgWbiL+NCDvqBOUhmtUoOJRXck6EKIgRDiLgAVAHcT0YsBvAfA7bDcMDsA3jXjvQ8IIS4KIS6u\nr68rGvZ0FqnLvW2HRpmQVCTxXdAVnxCL+LBllq5KQUzYS3Y/jt9wKLBTbwe+5FdloddGlRaDFfRy\nIYsrh/M7/xy0ejjq9AM//pME3T1rIeefEKIO4OMA7hVCXLWFfgjg1wDcrWOAi7BIXe6TCAVzfOhr\n+RTSCffNcheh2e2j1uwpPSHy6QQKuaSjyXzQ6qGhKAZ+nHIh67pz0iLsHnfQHQwDL9sqLWqvoYv7\njS5SiRjyqeAaLQPOO/+YFuEiCbrRhZMol3UiKti3swBeA+ApItoYe9l3A/i8niEuRtlhLHKQjQlm\nIZOjtn1ILtJVx9tp6KWukL/Ngj8WuillW1VVXNyzs0SDjvhyGthgQsjoNIJOLnJioW8A+DgRPQ7g\nL2D50D8C4BeJ6HP2498O4J9rHKdjNh0mt1TrTcRjhHPLwW4CTeKl+/kibCkOWZQ4TS7SdUEtF7O4\ncqC/QJLqpCi35FJxpBIxz7HoQWeJSpy67aRgBn1BnUS2wwzKQp8bLyaEeBzAS6c8/mYtI/JIuZjF\n1aM2uv3hqeFk2/U2zq9kkIiblVu1WcjgE1/Uu3kMjFvoapes5WIWn3zmOoQQp1p7ujpFlQsnBZJ0\niq0pFiIRKckW3TNE0J1mW1ZrLWSSscA3cadRWSBSRzVmqZkCKgWrLve8uuIm7pADliAtUqDILdV6\nC8k44aziFUq5kEWzO0B9Tueg7XoL6YT6E1Jucut2u1RrLaxkEljOBJ/UoqKeS80QQXeabSlDjoN2\nEU3DbfcuFURO0J3GIpuYlACcCJLuRhfVWgsbq1nljRkqixx/DSek08/3iklJaSUFFropLhfA2T7M\nVs2c4z9Jxa4p5TRjWiWRE/RNBz44WbbVTAvdR0HS8P9LF87cJbOmkD+/CiRZjVHMCHkt5b3Vc+n0\nBzju9I1xXzhpdGFaUuA4lWIO3cEQu8fOMqZVEjlB31i1TrLTlmxXDttKy7aqxK/emLo67TheIdX0\nNIbIpRIo5pK+uFxMERSvLhdTskQl5aIV6TXLwjUxKXCcICNdIifoIx/cKennJ0lF5k2I86vSB6zP\n5dLtD3H1SM8KpZhLIps8vXNQuzfA9WN9jSF0+zBNS2pZy6dw3Om73nc5EfTg9wMAax+sOxji+gwL\n9yQG3YzjP8ktATa6iJygA5gbyy3F3hQLa5x0wrog6bQwdw5aEEJPyBcR2YI6+4K6c6D3grq5qrcu\nuq4IIbd4zRY1zUKXyTnPzhDELUMijGYRZF30aAr6HAtNV1KNKnTXRR9ZOJr+/3nj39Z8QspGJ7rK\nEJ/EoJviQ/dWz+VE0M3woc9z25maJSrJpRJYy6dY0FUhBWWWD65ab2Etn0I24DTnWTjNdnXLyMLR\n6fI4ZTLrvqCWC1k0NJYhNq1TjlcLfe/YjMJcklGRvRk+6K2anpBblTjZ2NVBZAW92x/iemOGD86A\nokqnITsv6bIwdTdmKBeyqDV7aHan1+iu1q3Pl/sFOj5ffo4OqvUWUokYzhjiovCa/r/f6CJGMKZR\nRD5tbWzPMgqqdT0htypZpGqkSiIr6MDsSJFqraklwkIV5UIWnf5QSa/IaehuzCA3q2atMnR/vu5I\nIRnhYoqgjAp0HbsU9GYXxVzKmP8HON1tWq01jd0QlVidi/yPRY+moI8E5eaNUSGEsUlFEt1ldHWH\n3JXnbApta44h9sNCN8V/DliWdYyAWtOloB+bk1QkqRRmd/7ZMihkdBbl4uleAl1EUtBPkotu9mHt\nN7po94ZGTwjtgq45y3HuppbiOuiTlPIpZJIxvcfPoPkTixGKOffZoiZliUpmbWx3+gNcO9IX8qoK\nv7uPSSIp6KvZJJbTialLbtM2tKahczIMhwI7B3oF6exyBokZnYP8aAxBRNqqVrZ7A+wedYwJWZSU\n8insu3S57DU6gfYSnUa5kEWrN0BtoibQjr3qNjXCRRJUXfRICjow2wenO2ROBavZJHKpuJbkomtH\nHfQGerNk4zHChr2xO8l1uzGE7uNvRTqpP34yht40g8BLtmit2UMxZ5agz8q23DI85FgyL1JHF9EV\n9BkndBgmhLQwdbgMpBtKd6edWXXR/So767Qu+6KYFoMuKeVT2HfhQx8MBWrNrjEhi5JZG9uj+WvY\nBXWSfDqBUgCx6JEVdKvRxc1Xx2q9hVwqjkLOjBCtWehKLvKr0065kJs6fl110G/+/CyuH3fQ7qkt\nQ3ySlGXWkt+thV5vdiGEOUlFEnl8J+dQtdZCTGPIq0qCqIseWUEvF7M4bPdx1L7RBycjPEysozyO\nPgvdJwu5mMXVwzZ6E81+t33aw5AXjB3FZYi3NMfQu2Utn0Kt2V24U9MoS3TJjJh6yUo2geV04iZB\n3Kq1cH4lg6RhjWmmUZ5hVOrE/KPiklmha9sHZocsSsqFDPYaXS0WZiGXRD49t1mVJyqFLIZTGo1U\nay0spxNY0dwYQlcserXWwrnljLYYereU8ikIYVnciyAjY0qG+dBlTaCbBN3wkONxpIWuK0FwGmbN\nSoWUZyS3VGt6Q+ZU4bQM7aL4FXJXnhGp41eW7skFXa2FtG1YDLqk6DJbtGZYHZdxpqXPm1S2eB6V\nYg6d/hDXXUYfuSG6gj4lW7TZ7aPW7IViQshMVtVuF79OiFkrJN0x6JLzqxnECMojXUzqVDTOmst6\nLtJCNy1sEbh5H0k2pjE9ZFESRF30uYJORBkieoSIPktETxDRz9iPl4joISJ62v5d1D9c56wvpZGK\nx0aFqADz6yiPoyO5yM8s2fMzGo3ozhKVJOMxnFvJKHW5+BHD7xa39Vzk600LWwSsVd5Ruz8qsmZy\nY5ppBBGL7sRC7wB4pRDiJQDuAnAvEb0MwDsAPCyEuAPAw/Z9Y4jJWOixg2l6HeVxRhamwslQb/bQ\n7A58+f+nNRo57lgnp18uL9Uby7vH+mP43SIt7EWzRfcbXSxnEsbtCQAngijPAdPLXk+iy216GnO/\nRWFxbN9N2j8CwBsAPGg//iCA79IyQg9MLtm2fQqZU8HIwlToMpDHwq8Vyqzj75cgqg79PMlhMM+H\nLsNw3VjoJvrPgZvddn7PX68spRMo5JJmuVwAgIjiRPQYgGsAHhJCfBrAOSHEjv2SKwDOzXjv/UR0\niYgu7e7uKhm0UyYttGqthUSMcG7FvBNyGqotzBNB8scHOVkXveqzIJaLWewcqKt4dxLyaZ4PN52I\nYzmdiJagjyKVLEGU8zcMBpnE71h0R4IuhBgIIe4CUAFwNxG9eOJ5Actqn/beB4QQF4UQF9fX1z0P\neBHKhSyuHXXQ7Vux0NV6C+dXM4gbVCb0NFRbmH7XsakUbmz267cgbhay6A2Esu7rowuSoRZiaWnx\n5KK9hnlZopI1u8ja1pjL5cxSGpmkmY1ppnFa1UgdLOQ4E0LUAXwcwL0ArhLRBgDYv6+pH543ysUs\nhLB6aALhCnkCLEFSamHWWsgm4yj6lCVbLt7Y7Ldat1ZI6z51mpHlDVSdUNv1FlazSSxpjuF3i5ts\n0f1Gx1gLnYhuMGqq9VZo3C0SGXrpVyy6kyiXdSIq2LezAF4D4CkAHwZwn/2y+wB8SNcg3VKZCF3c\nDlFSAmC5JnoDMbP7+aJU602Ui/5lyY4KFNVPjv9Gwb8V0uaM0Em3+BVy6ZbSgiV0hRDYb3RHMewm\nUi6elJDYqjVDdf4CllHT7g1dF05bFCcW+gaAjxPR4wD+ApYP/SMAfh7Aa4joaQCvtu8bxfgJ3bNj\nWMNmoQO4IfTSC37X8Z7M1qzWWr52ipqVXOYW01d4pXxqlCjkhONOH72BMNblApz4oIdDge16W3tR\nOdX4Hbo4d+0ohHgcwEunPL4H4FU6BqWKDXvzrVpv4cpBG0MRnpAn4EZB+oZbvYf5V2stfH2l4Pnv\nOGUySmG73sLLnr/m2+cvpRNYzc7uTbkIMob/b/k4/kWRPnQhhKNV2KiOiyG9UadRLmSx3+jiq/tN\ndAfDULpcAEvQX3KL/nPPvOBThaQTcZxdTqNaa4WiscUkKpOLgsiSXc4ksZKxGo0EtUJSFSl02O7j\nuNM32iBYy6fQHQxx3JnenHuSUZao4RY6ADzy1/sAwnX+AuMlMPwJXYy0oAMnjS7ClpQAACuZ2Z2X\nFiWoLFnpA716GMwKSVWkUDUEIXMy29Opv1Z2ODJ1UxQ4ma+floJuYMjoaaxkkljNJn1zuURf0G0L\nLUxJReNYFyTvyUVBZcnKRhNBCWKlqKbRRRhWeDJb1LGgN80XdCngn/7rPeu+wcd/Frp6G0zjOSLo\nbWzVWjizlApVDCugzmUQVAx1Ra6QAhLEzUIGR50+Difq4i+KTG4xeYVXWrBA177BlRYlZ5fTSMYJ\nW3bZZ1NDRk9jWtVIXURf0O1Y6M9u1Y0+GWexWchg+0CNhZmME84u+5slWy5kcdzp46krRwDga5SL\n9fk31gNxy/ZBG6lEDGcMrEookb5wp6GL+40u0okYcilzjZxYjEarujCev4AV6eJXXfToC7o9CZ66\nchTS5VoO9WYPDYcbXbOo1lrYWM36niVbHvOBruVTyPosHrJ2uVdBD0Onq0Vrou8dW1miJv9PwMk5\nHLYIF0mlmEWzO0Ct6W2V6IToC/rYJPDbOlSBFCSvbhe/Y9Al8jOfqB4Esn8xCv30uMrZCuj4LUI+\nFUcqEXMci15rmp1UJJFCHrYNUYmfddEjL+jjIhJOC11NtmO1FkyWrPzM/lAEIohn8mmkEjFlFrrJ\nEBHW8s6zRfcMLsw1jhTyMJ6/gDXuQi45quuuk/DtMCzISiaJ5UwCR22zY4hnoaKmcrc/xNWjYLJk\nZYGldm8YiIUeixE2VzOejl+7N8D1404oBGWRei77jQ5uWzPf6i0Xw+1Df+HGCh77qe/w5bMib6ED\nJxMhDCfkJGeXrdonXlwuVw7aECKY/59obFMroOMvcxHcsmM3ug5DyGtpAQt9/7hrdJao5BsvFHHH\n2SXc5UOmpQ783KN4Tgi69GFVQuiDi8cI51cy2PYQi75ldw0Kqg7G6IIaUGMIGQu/CMOhsLJrG108\nsX0w+jum47SeS7s3QKM7MLKX6CTPW8vjoX/xbaO2hsxsIu9yAYDnn13CY88eYCUbzn93slGEE7r9\nIQ5aPRy0eoGnTQe9qbVp18X/Fx94DO3+AO3eEB37d7s3QKdv/W73hujY97uD4U1/59YQuCeculxq\nTXN7iTLuCafCLcg/e+UdePPLnmd8eNYsyoUs/u8z1/FnT121RLrZw0GrPxLsg1YPh2O3D1o9tHqD\nG/5GJhkLzMK5tZQHENwF5W/dvobfX30Wj1zeRyYZRzoRQyYZRyYZw2o2iUwyhkwijnQyhnQiftNr\n0ok4NguZUFjoa/kUjjt9dPoDpBOzQ0T3QpD2zyzOc0LQ8+kE8iHMMJPcdiaPP/zLKr7/Ny/d8Hg+\nFcdqNomVrFUv4nlrOazat1ezSazmkqPnbz+TP/UE18k/+KZb8XUby4GJxzfdvob/9xNGFwZVxni2\n6MYpYbrSig+Dy4VxTnhV7jnEP/mW2/A3n1dE3i4Hu5JJYCWbRDIeji2Q1WwS3/6Cs0EP4zlBKX/S\nLNqJoLOFHi1Y0ENALpXAPV9zJuhhMCHAaT2XkaCzDz1ShMPEYxjGESWH6f/7jS7iMcJq1p/+sow/\nsKAzTIQYFeg6Pl3Q9xpdFHNJxHyu7cPohQWdYSLEajaJGDmx0DvsP48gLOgMEyFiMUIxlxo1r5jF\nfkjquDCLMVfQiegWIvo4EX2BiJ4gorfZj7+TiKpE9Jj98zr9w2UYZh6lfGrUXm4WLOjRxEmUSx/A\njwkhHiWiZQCfIaKH7OfeLYT4D/qGxzDMojjJFmVBjyZzLXQhxI4Q4lH79hGAJwGUdQ+MYRh3WAW6\nOjOfHwwF6q1eKApzMYuxkA+diC4AeCmAT9sPvZWIHiei9xJRUfHYGIZxQSmfOrU7Tq3ZhRAnETFM\ndHAs6ES0BOCDAH5UCHEI4D0AbgdwF4AdAO+a8b77iegSEV3a3d1VMGSGYU5jLZ9CrdnFYDi9h6Ws\nxhiGbkXMYjgSdCJKwhLz9wkh/gAAhBBXhRADIcQQwK8BuHvae4UQDwghLgohLq6vr6saN8MwMyjl\nUxACqM+IdJH10tlCjx5OolwIwG8AeFII8Utjj2+Mvey7AXxe/fAYhlmUec2iuY5LdHES5XIPgDcD\n+BwRPWY/9q8AfB8R3QVAALgM4Ae1jJBhmIVYm1PPhS306DJX0IUQnwQwLT/4o+qHwzCMV+bVc5Ex\n6uxDjx6cKcowEUPWOJ/VW7TW7GI5kwhN+WXGOfyNMkzEKOROaqJPY6/RZXdLRGFBZ5iIkU7EsZxO\nnLIpyoW5ogoLOsNEkNLS7PT/veMuZ4lGFBZ0hokgp9VzqTW7o1Z1TLRgQWeYCFLKpaZuigoh7MJc\nbKFHERZ0hokgpXxqlOI/zlGnj95A8KZoRGFBZ5gIIn3oQtxYz0XGoPOmaDRhQWeYCLKWT6E7GOK4\n07/hcdnJqLTEgh5FWNAZJoIUc9OzRUcWeo4FPYqwoDNMBJHZojcJOhfmijQs6AwTQUozCnSNCnOx\nyyWSsKAzTASRUSyToYv7jQ4yyRhyKSeFVpmwwYLOMBFkVk30/UaP/ecRhgWdYSJIPhVHKhGbIugd\njnCJMCzoDBNBiAhrU9L/OUs02rCgM0xEmVbPhUvnRhsWdIaJKKX8zfVcao0uhyxGGBZ0hokoloXe\nGd1v9wZodAcs6BGGBZ1hIopVoKs3us9JRdFnrqAT0S1E9HEi+gIRPUFEb7MfLxHRQ0T0tP27qH+4\nDMM4ZS2fwnGnj05/AIAF/bmAEwu9D+DHhBAvBPAyAD9CRC8E8A4ADwsh7gDwsH2fYRhDmIxFH2WJ\nsqBHlrmCLoTYEUI8at8+AvAkgDKANwB40H7ZgwC+S9cgGYZZnFG2qF2Qq8YWeuRZyIdORBcAvBTA\npwGcE0Ls2E9dAXBO6cgYhvGEjDevNW+00FnQo4tjQSeiJQAfBPCjQojD8eeEVUVfzHjf/UR0iYgu\n7e7uehoswzDOKU24XPYbHcRjhJUM9xONKo4EnYiSsMT8fUKIP7AfvkpEG/bzGwCuTXuvEOIBIcRF\nIcTF9fV1FWNmGMYBpQmXy36ji2IuhViMghwWoxEnUS4E4DcAPCmE+KWxpz4M4D779n0APqR+eAzD\nuKWQTSJG4xY6Z4lGHSc1NO8B8GYAnyOix+zH/hWAnwfw+0T0AwC+AuB79AyRYRg3xGKEYi41aju3\n3+iimGd3S5SZK+hCiE8CmLVGe5Xa4TAMo5JSPjVqO7fX6OLO8ysBj4jRCWeKMkyEKY4V6NrnOi6R\nhwWdYSLMWj6FvUYH/cEQ9WaPBT3isKAzTIQp5VOoNXuot6yaLtxLNNqwoDNMhFnLp1BrdnH92Kq6\nWOT2c5GGBZ1hIkwxn4IQwJd3GwC4jkvUCbz1d6/Xw9bWFtrtdtBDmUkmk0GlUkEyySFfTLiQPvOn\nrx5b99nlEmkCF/StrS0sLy/jwoULsHKYzEIIgb29PWxtbeG2224LejgMsxBrdj2XZ3ZtQWcLPdIE\n7nJpt9tYW1szUswBu9nu2prRKwiGmYUU8GeuWYLOPvRoE7igAzBWzCWmj49hZiEF/Uu7x1jJJJCM\nG3HKM5rgb5dhIoxM9e/2h1hbSgc8GkY3LOgALl++jBe/+MVBD4NhlJNOxLGctrbK2H8efVjQGSbi\nyMgWFvToE3iUyzg/8z+fwBe2D+e/cAFeuLmCn/67L5r7un6/jze+8Y149NFH8aIXvQi/9Vu/hVwu\np3QsDBMExVwKX9lrosQbopGHLXSbL37xi3jLW96CJ598EisrK/jVX/3VoIfEMEqQyUQcgx59jLLQ\nnVjSurjllltwzz33AADe9KY34Zd/+Zfx9re/PbDxMIwqpKuFs0SjD1voNpOhiRyqyEQF9qE/d2BB\nt/nqV7+KT33qUwCA97///Xj5y18e8IgYRg3Sd15kQY88LOg2L3jBC/Arv/IruPPOO1Gr1fDDP/zD\nQQ+JYZTALpfnDkb50IPiwoULeOqpp4IeBsNo4VV3nsMPftvtuHOD289FHRZ0hok4pXwKP/HaO4Me\nBuMDc10uRPReIrpGRJ8fe+ydRFQlosfsn9fpHSbDMAwzDyc+9N8EcO+Ux98thLjL/vmol0EIIby8\nXTumj49hGAZwIOhCiP8NYF/XADKZDPb29owVTVkPPZPJBD0UhmGYU/HiQ38rEf1DAJcA/JgQoubm\nj1QqFWxtbWF3d9fDUPQiOxYxDMOYjFtBfw+AnwUg7N/vAvD9015IRPcDuB8Abr311pueTyaT3AmI\nYRhGAa7i0IUQV4UQAyHEEMCvAbj7lNc+IIS4KIS4uL6+7nacDMMwzBxcCToRbYzd/W4An5/1WoZh\nGMYf5rpciOh3AbwCwBki2gLw0wBeQUR3wXK5XAbwgxrHyDAMwziA/IwuIaJdAF9x+fYzAK4rHI5q\neHze4PF5g8fnHZPH+DwhxFyfta+C7gUiuiSEuBj0OGbB4/MGj88bPD7vhGGM8+DiXAzDMBGBBZ1h\nGCYihEnQHwh6AHPg8XmDx+cNHp93wjDGUwmND51hGIY5nTBZ6AzDMMwpsKAzDMNEBOMEnYjuJaIv\nEtEzRPSOKc8TEf2y/fzjRPQNPo7tFiL6OBF9gYieIKK3TXnNK4joYKxW/E/5NT778y8T0efsz740\n5fkgj98Lxo7LY0R0SEQ/OvEaX4/fjHr/JSJ6iIietn8XZ7z31LmqcXz/noiesr+/PySiwoz3njoX\nNI7PUb+EAI/fB8bGdpmIHpvxXu3HTzlCCGN+AMQBfAnA7QBSAD4L4IUTr3kdgD8GQABeBuDTPo5v\nA8A32LeXAfzVlPG9AsBHAjyGlwGcOeX5wI7flO/6CqyEicCOH4BvBfANAD4/9tgvAniHffsdAH5h\nxvhPnasax/cdABL27V+YNj4nc0Hj+N4J4O0Ovv9Ajt/E8+8C8FNBHT/VP6ZZ6HcDeEYI8WUhRBfA\n7wF4w8Rr3gDgt4TFnwMoTNSW0YYQYkcI8ah9+wjAkwDKfny2QgI7fhO8CsCXhBBuM4eVIKbX+38D\ngAft2w8C+K4pb3UyV7WMTwjxp0KIvn33zwEEVtt5xvFzQmDHT0JEBOB7APyu6s8NCtMEvQzg2bH7\nW7hZMJ28RjtEdAHASwF8esrT32wvh/+YiF7k68Cs+jofI6LP2KWLJzHi+AH4Xsw+kYI8fgBwTgix\nY9++AuDclNeYchy/H9aKaxrz5oJO3mp/h++d4bIy4fh9C4CrQoinZzwf5PFzhWmCHgqIaAnABwH8\nqBDicOLpRwHcKoT4egD/CcD/8Hl4LxdC3AXgtQB+hIi+1efPnwsRpQC8HsB/n/J00MfvBoS19jYy\ntpeIfhJAH8D7ZrwkqLnwHliulLsA7MBya5jI9+F069z4c2kS0wS9CuCWsfsV+7FFX6MNIkrCEvP3\nCSH+YPJ5IcShEOLYvv1RAEkiOuPX+IQQVfv3NQB/iJtr1Qd6/GxeC+BRIcTVySeCPn42V6Ubyv59\nbcprgp6H/wjAdwJ4o33RuQkHc0ELwlm/hKCPXwLA3wPwgVmvCer4ecE0Qf8LAHcQ0W22Ffe9AD48\n8ZoPA/iHdrTGywAcjC2PtWL73H4DwJNCiF+a8Zrz9utARHfDOsZ7Po0vT0TL8jaszbPJWvWBHb8x\nZlpGQR6/MT4M4D779n0APjTlNU7mqhaI6F4APw7g9UKI5ozXOJkLusbnpF9CYMfP5tUAnhJCbE17\nMsjj54mgd2Unf2BFYfwVrB3wn7Qf+yEAP2TfJgC/Yj//OQAXfRzby2Etvx8H8Jj987qJ8f1TAE/A\n2rX/cwDf7OP4brc/97P2GIw6fvbn52EJ9OrYY4EdP1gXlh0APVh+3B8AsAbgYQBPA/gYgJL92k0A\nHz1trvo0vmdg+Z/lHPwvk+ObNRd8Gt9v23PrcVgivWHS8bMf/00558Ze6/vxU/3Dqf8MwzARwTSX\nC8MwDOMSFnSGYZiIwILOMAwTEVjQGYZhIgILOsMwTERgQWcYhokILOgMwzAR4f8DZXilZ8CEdCkA\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d1656d5630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kp6eQJEKSq9mP+D5TacmCy+X7LLnE95jk8m0758RccrPSIh6/yyX8+fvj+fzLvb6KToNS\nV99IXYPvx1/B8b1WahsaA/b7Xu89WMuj72+kX/cMrh7fN6LxL9m8l7v/sYKhvbLpneNGFRpVUUAV\n51Gd53p4v0KjU6imroH/98FGMtKSufncwRGN/3gFU+M/FdigqpsARGQeMAkITPwjgPsBVHWtiPQX\nkTxV3RHqgI/lnstHsPirvdz+fDGvz5gQsa+7W/dWc9dLyynsm8ML07523Mva+R08VM9lj/yL254r\nimj8HaWq3D1/JctLK1leWsm4fl35/tf6RzusuFFZU8etc4spyHGz6NavkxXGLpjh1LdbF/p269Lu\n4xsble898Rn3LljF+H5dGZibGcLoWlflrWPGvGJ6d03n+R+d3u7rr6rc9lwxv39rHSMKsjl3aM8Q\nRxo6wWSo3kDgkjulzrZAJcCVACJyKtAP8K/4oMA7IrJURKa2dhIRmSoiS0RkSXsXZO6SmszMyWPZ\nd7COO18siUi7Ym19I9PnFoHAI1PGtjvpA2SkJfPItb74f/JCZOIPhReWlPJy0TZuPW8w5w7N5dev\nrmFVWWW0w4oLqsrPXl7BjiovMyePjdukHwoul/DHqwtJS3Zx67yiiEwAp6r8fP5Ktld5ebiD119E\nuP/K0Qzrlc2MuUVs3n0whJGGVqhu7t4P5IhIMXALUISvTR/gLFUtBCYCN4vIhJbeQFVnq+p4VR2f\nm5vb7kBO6u3hvyYO4501O3n606/a/T7B+v1b6yjZWsFvvz26Q7Udv5EFHn526TDeXbuTv360ueMB\nhtna7VX89ysrOWNQd2ZccCK//84YumakcMvcIg4eqo92eDHv+SVbeW1FOT++aChjT+ga7XCirpfH\nzW+/PZqV26r4w1vrwn6+l5dtY2FJGbdfMIRxIbj+6alJzL7uZFwu4UdPL43Zv4FgEv82ILDBrY+z\nrYmqVqnqDU6C/z6QC2xy9m1zHncC8/E1HYXVv53Zn3OG5vLr19awdntV2M7z/rqdzP5wE9897QQu\nHZUfsve9/oz+XDA8j/tfX8vKbbFbcz5wqJ6bnllGljuFhyYXkuQSumem8dA1Y/ly90HuWbAq2iHG\ntA07D3DvgtWcNbgHP5oQ+Ruyseqikb343ukn8KcPN/Gv9eG7Nbh590F+8cpKTh3QjRvPCV2bfN9u\nXXhkyljW79zPnS8tj8lv7sEk/sXAEBEZICKpwGRgQWABEclx9gH8O/ChqlaJSIaIZDllMoCLgNZv\n+4eIiPD774wh253CrXOL8NaFfqWg7ZVefvx8CcN6ZfHf3xwR0vcWER64ajTdMlK5ZW4RB2Kw1uD7\niryCzbsPMnNKIT2z3E37vjaoO7ecN4QXl5Yyv8im7W2Jt66BW+YWkZ6axB+vHhPzvUAi7eeXjmBI\nz0xuf76YPQcOhfz96xoamTGviCSX8NA1vkpLKH19SC53XjKM15aXM/vDTSF971BoM/Graj0wHXgT\nWAM8r6qrRGSaiExzig0HVorIOnxNOjOc7XnAv0SkBPgceE1V3wj1L9GSHplp/PHqMXyx4wC/fm11\n2wcch4ZG5bbniqipbWDWteNCsrJRc10zUnl4ciFf7fHVSmLN3M+38kpxGbddcCJnDDq6B9Wt5w3m\n1P7duHv+Sr6M4bbOaPntG2tZU17F778zmp7Z7rYPSDDpqUnMnDKWypo67nwx9LXmB9/+gpLSSu7/\n9mgKctJD+t5+P5owkG+Myue3b6zl/9a3775luATVxq+qi1T1RFUdpKr/42x7XFUfd55/4uwfqqpX\nquo+Z/smVR3j/Iz0HxspE07MZeqEgfz90y28sXJ7yN73kffW8+mmvfxq0kgG9wxfz4PTBnbn1vOH\n8PKybTG14MXqsiruXbiKrw/p0Wq3teQkFw9NLiQl2cUtc5fZ+qwB3l2zg79+tJkbzuzPecPyoh1O\nzBqen83PJvrud4Xyft3HG3fz2D83MvmUviFtom1ORPjdVaMZ0jOLW+YWsXVvddjOdbw61cjdltxx\n0VBG9fZw18vLKa+s6fD7fbppDzPfXc8VY3tz1cl92j6gg245bwinDujG3f9YyaZdB8J+vrbs99Zx\n87PL6NolhQfb+IpckJPOA1eNYeW2Ku5/fW0Eo4xdO6q8/OTF5YzIz+auidEZaBhPrj+jv6+n2Gtr\nWLd9f4ffb9/BWv7zuRIGdM/gF5eFtom2JRlpyfzpupNpbFR+9PRSampjowLU6RN/arKLmVPGUlvf\nyG3zijs0l8jeg7XMmFdEv+4Z3PetkyIySCnJJTw8uZDUZBe3zC2Kas1ZVfnpyyv4as9BZk4eS4/M\ntgcKXTgijx+c0Z+/frSZt1dHdFhHzGloVG5/rpia2gZmThlLWnLomwg7GxHhAed+3S1zl3Xofp2q\nctfLy9lz8BAzp4wN6XKUx9K/RwYPTxnLmu1V/PTl2LjZ2+kTP8CAHhn88vKRfPblXh77YEO73kNV\nueOFEvYdrGPWtWPDsqpRa/I9vprzqrIqfvt6+Lu4tebvn23h1eW+roenDQx+ZPFPLx3GyIJsfvJi\nSUi+dcWrP324kY837uGXl4e3ibCzCbxf95tFa9r9PnM/38qbq3Zw58XDOKm3J4QRtu3coT358YUn\n8o/iMubEQDfthEj8AFed3IfLxxTw4DvrWfrVvuM+/ol/fcl7a3fy828MZ2RBZD80cLjmPOejL3l3\nTeRrziu3VXLfwtWcfWIuN5496LiOTUtO4hHnW9eMucUJOW970ZZ9/OGtL/jm6Hy+Mz78TYSdzYQT\nc/mPrw/gqU++4p12fHPcsHM/v3rVd1/qh2dFZy6sm84ZzMUj8/jNojV8vDGsM9i0KWESv4jw6ytO\nIt/jZsa8Iqq8dUEfW7K1gt++sZaLRuTx/TAsXB2suyYOY0R+Nne8UML2Sm/EzlvlreOmZ5bRLSOV\nB68pbFfXw4G5mfz6Wyfx+ea9PPJe+751xasqbx23zisi3+Pmf64YZfMYtdMdFw9t+ua4oyr4z/+h\n+gZumVtMl9Rk/vCd6HWddbmEP1xdyIAeGUx/tohtFdH79pswiR8g253CzCljKa/08vP5K4Nqa6vy\n1jF97jJ6Zrn53VWjo/pH605J4pFrx3KovpHbniuKyNznqspdLy1nW0UNs64d26H5g64c14crx/Xm\nkffW88nGPSGMMnb55zEqq/BNCeBJT9wpGToqLdnXxdNb18h/Pl9MY5Cf/9+9sY415VU8cFX0u85m\nOjd76+obmfb00rCMMQpGQiV+gHEndOX2C4awsKSMF5ceu4uk/2ZmWYWXmVMKI7KiUVsG5Wbyq0kn\n8emmvTz6fvhrzk998hWLVmznJxcPZXz/bh1+v/smnUT/7hnc9lwRew/WhiDC2PbSsm0scKYEOLmf\nTcnQUYNyM7nnshF8tGEPf/6/tgdGfbBuJ0/860uu/1o/zh8eG11nB+Vm8uA1hazYVhl0BTTUEi7x\nA9x4zmBOH9iNexasOmYXybmfb/VNt3zhiZzcr+NJL1S+Pa433yos4KF3vuDzL/eG7TzLSyv49Wur\nOW9YT6aGaI73wIno7oijiejaY9OuA/zilZWcPjC0UwIkumtO6culo3rxwJvrWF5a0Wq5XfsPcccL\nJQzNy+Knlw6PYIRtu2BEHrddMISXlpVGZE6x5hIy8fuGaY8l1ZkFsKUukmu3V/FLZ5DS8d7MDDff\n/YpRnNCtC7fNK6KiOvQ158oaX3/93My0kLeLjizw8PNvDOe9tTtjoodDOPjalYtITXbx0DVjQz4l\nQCITEf73itH0zEpjxrziFidCU1V+8mIJVd56Zk4ZG5bR9R1163lDuGB4T361cHVYK3AtScjED75Z\nAH/nzAL4+zeP7CJZXVvP9GeLyHKn8Mer23czM9wy05J5ZMo4dh04FPIh7arKnS+WUF7hZdZ3x9E1\nDOsCfP9r/bhwRB73v77mmLW2ePXAG+tYVVbFA1eNoZfHpmQINY8zgHDznoPc28JkgE9+vJkP1u3i\n7m8MZ2ivrChE2DaXS/jjNYWc0K0LNz2zNKJdnRM28cPhWQD//H9f8s8vDs+l8csFq9m46wAPXVMY\nldWMgjWqj4f/umQYb63eEdKvi3M+2sybq3Zw18RhIZmqtiX+iehyM9O4ZW4R+4+jl1Ws+2DdTv7i\ntCtfOCI22pU7o9MGdmf6uYN5YWkpC0vKmravKa/ifxet5fxhPbnu9Oj1wgtGtjuFP113MjW1Ddz4\n98hNbZLQiR/g7m+M4MS8TH78fAm79h/ileJtPLdkKzedM4izhkR2+cb2+OFZA5qGtK8u6/gU1MVb\nK7j/9TVcOCIv7P2dc7qk8vCUsWzdWx21m1yhtnO/lzte8M3aGmvtyp3RjPOHMO6EHH42fwWl+6qp\nqW3g1rlFeLqkRL0XXrCG5GXxh6vHULy1osVvL+GQ8InfnZLEI1PGsd9bx03PLOXn81cyvl9Xbr/g\nxGiHFhT/FNQ56SlMn7uM6tr2T+FcUV3Lzc/4uq7+/qoxEfmjOaV/N26/4EQWlJTxQhu9rGJdY6Py\n4+dLOHConkditF25s0lOcvHw5LGowm3zivnVq6tZv/MAf7x6DN2DmFIkVlxyUj7Tzx3Mym1VEVm8\nRWKxljV+/HhdsmRJRM/59Ceb+e9XVuFJT2HRjK/TO0xTtYbLxxt2890nPgM4YhFu/6LcgQt2JzkL\nwbsE36NTZl91LTuqvLww7QwK++ZELPaGRuV7f/mM4q0VLLzlTAb3jE6b7D+KtvHu2p0IIAICuJwn\nghyxTcRXBgSX83xn1SHeWr2D/71yFFNOPSEqv0OieqV4GzPmFQMwdcJAfhaH37YaGpW6hsZ2VxhE\nZKmqjg+mbOQmnIl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cLCITWjpQRKaKyBIRWbJr164Qh2U6K/+0DaratK2iug5vXaPN02NM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\nfCqr5QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d165506978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kp6eQJEKSq9mP+D5TacmCy+X7LLnE95jk8m0758RccrPSIh6/yyX8+fvj+fzLvb6KToNS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\nZKmqjg+mbOQmnIl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cLCITWjpQRKaKyBIRWbJr164Qh2U6K/+0DaratK2iug5vXaPN02NM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\nfCqr5QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d16575bc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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0BfnMyYncvmImfzhSQ3Pn2Nd7OH2pjabOvqgZ5gE/X9wVketwBv4H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\nTTAa+JVSaoLRwK+UUhOMBn6llJpg/h/OIplPi9BVvQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d1657d52e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    " msm_plot(xls_data[\"GVZ\"], output, m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope :  -0.000660505652855\n",
      "Intercept :  11.3649091073\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-0.00066050565285520808, 11.364909107349215)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "datainreg = xls_data[\"GVZ\"][::-1]\n",
    "data_lastm = datainreg\n",
    "data_lastm = data_lastm.iloc[-m:]\n",
    "\n",
    "linreg(df(output['RV']), df(data_lastm))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## XLSX"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "180210RV22m10.xlsx\n"
     ]
    },
    {
     "ename": "NameError",
     "evalue": "name 'output' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-3-592f284a47a2>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[0mwriter\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpd\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mExcelWriter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"\"\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mjoin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdate\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtoday\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstrftime\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'%y%m%d'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mnamew\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mwriter\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpath\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 5\u001b[1;33m \u001b[0moutput\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mto_excel\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mwriter\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'Sheet2'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      6\u001b[0m \u001b[0mwriter\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msave\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'output' is not defined"
     ]
    }
   ],
   "source": [
    "from datetime import date\n",
    "namew=\"RV22m10.xlsx\"\n",
    "writer = pd.ExcelWriter(\"\".join((date.today().strftime('%y%m%d'),namew)))\n",
    "print(writer.path)\n",
    "output.to_excel(writer, 'Sheet2')\n",
    "writer.save()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### load"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xls_file = pd.ExcelFile('180209RV22m10.xlsx')\n",
    "output = xls_file.parse('Sheet2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Average params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "output2 = msm_averageparams(output, kbar, m, data, RV, LB , UB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>RV</th>\n",
       "      <th>m0</th>\n",
       "      <th>b</th>\n",
       "      <th>gamma_k</th>\n",
       "      <th>sigma</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>10.691455</td>\n",
       "      <td>1.502392</td>\n",
       "      <td>39.116365</td>\n",
       "      <td>0.930174</td>\n",
       "      <td>0.235937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10.691455</td>\n",
       "      <td>1.502392</td>\n",
       "      <td>39.116365</td>\n",
       "      <td>0.930174</td>\n",
       "      <td>0.235937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>10.691455</td>\n",
       "      <td>1.502392</td>\n",
       "      <td>39.116365</td>\n",
       "      <td>0.930174</td>\n",
       "      <td>0.235937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>10.691455</td>\n",
       "      <td>1.502392</td>\n",
       "      <td>39.116365</td>\n",
       "      <td>0.930174</td>\n",
       "      <td>0.235937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10.691455</td>\n",
       "      <td>1.502392</td>\n",
       "      <td>39.116365</td>\n",
       "      <td>0.930174</td>\n",
       "      <td>0.235937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>10.691455</td>\n",
       "      <td>1.502392</td>\n",
       "      <td>39.116365</td>\n",
       "      <td>0.930174</td>\n",
       "      <td>0.235937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>10.691455</td>\n",
       "      <td>1.502392</td>\n",
       "      <td>39.116365</td>\n",
       "      <td>0.930174</td>\n",
       "      <td>0.235937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>10.691455</td>\n",
       "      <td>1.502392</td>\n",
       "      <td>39.116365</td>\n",
       "      <td>0.930174</td>\n",
       "      <td>0.235937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>10.691455</td>\n",
       "      <td>1.502392</td>\n",
       "      <td>39.116365</td>\n",
       "      <td>0.930174</td>\n",
       "      <td>0.235937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10.691455</td>\n",
       "      <td>1.502392</td>\n",
       "      <td>39.116365</td>\n",
       "      <td>0.930174</td>\n",
       "      <td>0.235937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>10.691455</td>\n",
       "      <td>1.502392</td>\n",
       "      <td>39.116365</td>\n",
       "      <td>0.930174</td>\n",
       "      <td>0.235937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>10.691455</td>\n",
       "      <td>1.502392</td>\n",
       "      <td>39.116365</td>\n",
       "      <td>0.930174</td>\n",
       "      <td>0.235937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>10.691455</td>\n",
       "      <td>1.502392</td>\n",
       "      <td>39.116365</td>\n",
       "      <td>0.930174</td>\n",
       "      <td>0.235937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>10.691455</td>\n",
       "      <td>1.502392</td>\n",
       "      <td>39.116365</td>\n",
       "      <td>0.930174</td>\n",
       "      <td>0.235937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>10.691455</td>\n",
       "      <td>1.502392</td>\n",
       "      <td>39.116365</td>\n",
       "      <td>0.930174</td>\n",
       "      <td>0.235937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>10.691455</td>\n",
       "      <td>1.502392</td>\n",
       "      <td>39.116365</td>\n",
       "      <td>0.930174</td>\n",
       "      <td>0.235937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>10.691455</td>\n",
       "      <td>1.502392</td>\n",
       "      <td>39.116365</td>\n",
       "      <td>0.930174</td>\n",
       "      <td>0.235937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>10.691455</td>\n",
       "      <td>1.502392</td>\n",
       "      <td>39.116365</td>\n",
       "      <td>0.930174</td>\n",
       "      <td>0.235937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>10.691455</td>\n",
       "      <td>1.502392</td>\n",
       "      <td>39.116365</td>\n",
       "      <td>0.930174</td>\n",
       "      <td>0.235937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>10.691455</td>\n",
       "      <td>1.502392</td>\n",
       "      <td>39.116365</td>\n",
       "      <td>0.930174</td>\n",
       "      <td>0.235937</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           RV        m0          b   gamma_k     sigma\n",
       "0   10.691455  1.502392  39.116365  0.930174  0.235937\n",
       "1   10.691455  1.502392  39.116365  0.930174  0.235937\n",
       "2   10.691455  1.502392  39.116365  0.930174  0.235937\n",
       "3   10.691455  1.502392  39.116365  0.930174  0.235937\n",
       "4   10.691455  1.502392  39.116365  0.930174  0.235937\n",
       "5   10.691455  1.502392  39.116365  0.930174  0.235937\n",
       "6   10.691455  1.502392  39.116365  0.930174  0.235937\n",
       "7   10.691455  1.502392  39.116365  0.930174  0.235937\n",
       "8   10.691455  1.502392  39.116365  0.930174  0.235937\n",
       "9   10.691455  1.502392  39.116365  0.930174  0.235937\n",
       "10  10.691455  1.502392  39.116365  0.930174  0.235937\n",
       "11  10.691455  1.502392  39.116365  0.930174  0.235937\n",
       "12  10.691455  1.502392  39.116365  0.930174  0.235937\n",
       "13  10.691455  1.502392  39.116365  0.930174  0.235937\n",
       "14  10.691455  1.502392  39.116365  0.930174  0.235937\n",
       "15  10.691455  1.502392  39.116365  0.930174  0.235937\n",
       "16  10.691455  1.502392  39.116365  0.930174  0.235937\n",
       "17  10.691455  1.502392  39.116365  0.930174  0.235937\n",
       "18  10.691455  1.502392  39.116365  0.930174  0.235937\n",
       "19  10.691455  1.502392  39.116365  0.930174  0.235937"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1eb7189bbe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1eb72977ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1eb72a579e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1eb717e09b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1eb72c96208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1eb72f3c2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    " msm_plot(xls_data[\"GVZ\"], output2, m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope :  -4.71686314987e+13\n",
      "Intercept :  5.04301310203e+14\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-47168631498709.805, 504301310203267.0)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "datainreg = xls_data[\"GVZ\"][::-1]\n",
    "data_lastm = datainreg\n",
    "data_lastm = data_lastm.iloc[-m:]\n",
    "\n",
    "linreg(df(output2['RV']), df(data_lastm))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.6.1"
  },
  "toc": {
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": "block",
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}