180130_MSM_test.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TEST Build in FUNC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## BIT"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### BITXOR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-5^6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### BITAND"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-5&6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### BITGET\n",
    "- <font color=blue>From MATLAB -> 10111</font>\n",
    "\n",
    "> bitget(29,1:8)\n",
    "\n",
    "> ans = 1     0     1     1     1     0     0     0\n",
    "\n",
    "\n",
    "\n",
    "- but python is 11101\n",
    "</font> >>>so we need inverse order\n",
    "\n",
    "***\n",
    "\n",
    "- <font color=blue>MATLAB bitget(29,1) mean the first bit (right most)</font>\n",
    "> ans = 1\n",
    "\n",
    "-  python is a[-1] when a is represent number of bits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0b11101\n",
      "1\n",
      "11101\n"
     ]
    }
   ],
   "source": [
    "a=bin(29)\n",
    "print(a)\n",
    "a=a[2:]\n",
    "print(a[-1])\n",
    "print(a)\n",
    "\n",
    "def bitget(number,position):\n",
    "    bi_number = bin(number)\n",
    "    bi_number = bi_number[2:]\n",
    "    return bi_number[-position]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1'"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bitget(29,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OPTIMIZOR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### fminbnd \n",
    "\n",
    "* [scipy ref](https://docs.scipy.org/doc/scipy-0.16.0/reference/generated/scipy.optimize.fminbound.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "ename": "IndentationError",
     "evalue": "unindent does not match any outer indentation level (<ipython-input-4-325e50db084d>, line 14)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-4-325e50db084d>\"\u001b[1;36m, line \u001b[1;32m14\u001b[0m\n\u001b[1;33m    x0=np.zeros(4)\u001b[0m\n\u001b[1;37m                  ^\u001b[0m\n\u001b[1;31mIndentationError\u001b[0m\u001b[1;31m:\u001b[0m unindent does not match any outer indentation level\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.optimize import minimise\n",
    "\n",
    "\n",
    "a=np.array(range(4))\n",
    "b=np.array(range(4,8))\n",
    "\n",
    "def sm(x,a,b):\n",
    "      sm=np.zeros(1)\n",
    "      a=a*np.exp(x)\n",
    "      sm += sum(b-a)\n",
    "      return sm\n",
    "\n",
    " x0=np.zeros(4)\n",
    " print sm(x0,a,b) #checking my function\n",
    "\n",
    " opt = minimize(sm,x0,args=(a,b),method='nelder-mead', options={'xtol': 1e-8,     'disp': True})  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting lmfit\n",
      "Requirement already satisfied: numpy in c:\\programdata\\anaconda3\\lib\\site-packages (from lmfit)\n",
      "Requirement already satisfied: scipy in c:\\programdata\\anaconda3\\lib\\site-packages (from lmfit)\n",
      "Requirement already satisfied: six in c:\\programdata\\anaconda3\\lib\\site-packages (from lmfit)\n",
      "Installing collected packages: lmfit\n",
      "Successfully installed lmfit-0.9.7\n"
     ]
    }
   ],
   "source": [
    "!pip install lmfit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "__array__() takes 1 positional argument but 2 were given",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-12-ede382601f4f>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     29\u001b[0m \u001b[1;31m# do fit, here with leastsq model\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     30\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[0mb\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mgamma_k\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msigma\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[0mA_template\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 31\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[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\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;36mleastsq\u001b[1;34m(self, params, **kws)\u001b[0m\n\u001b[0;32m   1300\u001b[0m         \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mseterr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mall\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'ignore'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1301\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1302\u001b[1;33m         \u001b[0mlsout\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mscipy_leastsq\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[0mvars\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mlskws\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1303\u001b[0m         \u001b[0m_best\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0m_cov\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0minfodict\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0merrmsg\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mier\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlsout\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1304\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\\minpack.py\u001b[0m in \u001b[0;36mleastsq\u001b[1;34m(func, x0, args, Dfun, full_output, col_deriv, ftol, xtol, gtol, maxfev, epsfcn, factor, diag)\u001b[0m\n\u001b[0;32m    375\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtuple\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    376\u001b[0m         \u001b[0margs\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[0m\n\u001b[1;32m--> 377\u001b[1;33m     \u001b[0mshape\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdtype\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_check_func\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'leastsq'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'func'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    378\u001b[0m     \u001b[0mm\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    379\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[1;33m>\u001b[0m \u001b[0mm\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\\minpack.py\u001b[0m in \u001b[0;36m_check_func\u001b[1;34m(checker, argname, thefunc, x0, args, numinputs, output_shape)\u001b[0m\n\u001b[0;32m     24\u001b[0m def _check_func(checker, argname, thefunc, x0, args, numinputs,\n\u001b[0;32m     25\u001b[0m                 output_shape=None):\n\u001b[1;32m---> 26\u001b[1;33m     \u001b[0mres\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0matleast_1d\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mthefunc\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[1;33m:\u001b[0m\u001b[0mnuminputs\u001b[0m\u001b[1;33m]\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[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     27\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0moutput_shape\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mand\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mres\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[0moutput_shape\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     28\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0moutput_shape\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[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(b, m0, gamma_k, sigma, kbar, data, A_template)\u001b[0m\n\u001b[0;32m    127\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    128\u001b[0m     \u001b[0minput_param\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m4\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 129\u001b[1;33m     \u001b[0minput_param\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    130\u001b[0m     \u001b[0minput_param\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mm0\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    131\u001b[0m     \u001b[0minput_param\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mgamma_k\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mTypeError\u001b[0m: __array__() takes 1 positional argument but 2 were given"
     ]
    }
   ],
   "source": [
    "from lmfit import model, minimize, Minimizer, Parameters, Parameter, report_fit\n",
    "from MSM_util import *\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "GLD = pd.read_excel('data_GVZ_GLD.xlsx')\n",
    "date_GLD = GLD.iloc[:,3]\n",
    "GLD = GLD.loc[:,'GLD']\n",
    "GLD_d = GLD - np.mean(GLD)\n",
    "kbar = 5\n",
    "data = GLD_d\n",
    "\n",
    "\n",
    "A_template = T_mat_temp(kbar)\n",
    "\n",
    "input_param = [1.5, 1.5, 0.1, 383.4037]\n",
    "m0 = input_param[1]\n",
    "b = input_param[0]\n",
    "gamma_k = input_param[2]\n",
    "sigma = input_param[3]\n",
    "\n",
    "# create a set of Parameters\n",
    "params = Parameters()\n",
    "params.add('m0', value= 1.5, min=1.2, max=1.8)\n",
    "\n",
    "\n",
    "# do fit, here with leastsq model\n",
    "minner = Minimizer(MSM_likelihood_new, params, fcn_args=(b, gamma_k, sigma, kbar, data, A_template))\n",
    "result = minner.minimize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      " Func-count     x          f(x)          Procedure\n",
      "    1        1.42918      10365.9        initial\n",
      "    2        1.57082      4663.28        golden\n",
      "    3        1.65836      4763.33        golden\n",
      "    4        1.61143      4697.98        parabolic\n",
      "    5        1.51672      4633.54        golden\n",
      "    6        1.45836      4626.74        parabolic\n",
      "    7        1.47243      4625.97        parabolic\n",
      "    8        1.47276      4625.97        parabolic\n",
      "    9         1.4731      4625.97        parabolic\n",
      "   10        1.48976      4627.03        golden\n",
      "   11        1.47343      4625.97        parabolic\n",
      "\n",
      "Optimization terminated successfully;\n",
      "The returned value satisfies the termination criteria\n",
      "(using xtol =  0.001 )\n"
     ]
    }
   ],
   "source": [
    "from scipy.optimize import fminbound\n",
    "from MSM_util import *\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "GLD = pd.read_excel('data_GVZ_GLD.xlsx')\n",
    "date_GLD = GLD.iloc[:,3]\n",
    "GLD = GLD.loc[:,'GLD']\n",
    "GLD_d = GLD - np.mean(GLD)\n",
    "kbar = 5\n",
    "data = GLD_d\n",
    "\n",
    "estim_flag = []\n",
    "A_template = T_mat_temp(kbar)\n",
    "\n",
    "input_param = [1.5, 1.5, 0.1, 383.4037]k\n",
    "m0 = input_param[1]\n",
    "b_i = input_param[0]\n",
    "g_j = input_param[2]\n",
    "sigma = input_param[3]\n",
    "a_m0 = fminbound(MSM_likelihood_new, 1.2, 1.8, args=( b_i, g_j, sigma, kbar, data, A_template), xtol=1e-03, maxfun=500, full_output=1, disp=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-10268.720277847146"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(a_m0[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### fmincon \n",
    "This has various issues due to the typr of problems as [This link](https://stackoverflow.com/questions/49926/open-source-alternative-to-matlabs-fmincon-function).\n",
    "\n",
    "- [stack overflow scipy minimize](https://stackoverflow.com/questions/27851087/matrix-constraints-with-scipy-optimize-minimize)\n",
    "- [scipy ref](https://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "scipy.optimize.minimize(fun, x0, args=(), method=None, \n",
    "                        jac=None, hess=None, hessp=None, bounds=None, \n",
    "                        constraints=(), tol=None, callback=None, options=None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# INPUT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pandas import DataFrame as df\n",
    "kbar = 8\n",
    "input_param = [1.5, 1.2, 0.8, 1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## input from xls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ydxC59/zApai7tksP+PijswcDAJZsLwMgdYH4+3bncMVGwP+fpmX/xfYyVDfa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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25ac9ed39b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "GLD = pd.read_excel('data_GVZ_GLD.xlsx')\n",
    "date_GLD = GLD.iloc[:,3]\n",
    "GLD = GLD.loc[:,'GLD']\n",
    "GLD_d = GLD - np.mean(GLD)\n",
    "kbar = 5\n",
    "plt.plot(date_GLD,GLD_d)\n",
    "data = GLD_d\n",
    "\n",
    "input_param = [50, 1.99,0.945585657754, 5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TEST My own function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## - T_mat_temp \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "A = np.fromfunction(lambda i, j: i ^ j, (2**kbar, 2**kbar), dtype=int)\n",
    "A_template = A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   0.,    1.,    2., ...,  253.,  254.,  255.],\n",
       "       [   1.,    0.,    3., ...,  252.,  255.,  254.],\n",
       "       [   2.,    3.,    0., ...,  255.,  252.,  253.],\n",
       "       ..., \n",
       "       [ 253.,  252.,  255., ...,    0.,    3.,    2.],\n",
       "       [ 254.,  255.,  252., ...,    3.,    0.,    1.],\n",
       "       [ 255.,  254.,  253., ...,    2.,    1.,    0.]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_A = df(A)\n",
    "A = A.astype(float)\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_A.to_excel('T_mat_temp.xlsx')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MSM_starting_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output_parameters=np.zeros((4*4,3))\n",
    "output_parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "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>LL</th>\n",
       "      <th>b</th>\n",
       "      <th>g</th>\n",
       "      <th>m</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Empty DataFrame\n",
       "Columns: [LL, b, g, m]\n",
       "Index: []"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pandas import DataFrame as df\n",
    "LL_storage = df(columns=['LL','b','g', 'm'])\n",
    "LL_storage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "LL_storage.loc[len(LL_storage),'LL'] = sum(a_m0[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "LL_storage.loc[len(LL_storage)-1,'LL'] = 9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "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>LL</th>\n",
       "      <th>b</th>\n",
       "      <th>g</th>\n",
       "      <th>m</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-10268.7</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        LL    b    g    m\n",
       "0        5  NaN  NaN  NaN\n",
       "1 -10268.7  NaN  NaN  NaN\n",
       "2        9  NaN  NaN  NaN"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LL_storage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "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>LL</th>\n",
       "      <th>b</th>\n",
       "      <th>g</th>\n",
       "      <th>m</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-10268.7</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        LL    b    g    m\n",
       "1 -10268.7  NaN  NaN  NaN\n",
       "0        5  NaN  NaN  NaN\n",
       "2        9  NaN  NaN  NaN"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LL_storage.sort_values(by = ['LL'], ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "startingvals = [0. ,0. , 0.]\n",
    "startingvals[0] = LL_storage.loc[0,'b']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [],
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def MSM_starting_values(data,startingvals,kbar,A_template):\n",
    "    # options=optimset('fminbnd');\n",
    "    xtol = 1e-3\n",
    "#     LLs = []\n",
    "#     output_parameters=[]\n",
    "    \n",
    "    # implicit  booleanness of the empty list is quite pythonic.\n",
    "    if not startingvals:\n",
    "        print('No starting values entered: Using grid-search')\n",
    "        # A grid search used to find the best set of starting values in the\n",
    "        # event none are supplied by the user\n",
    "        b = [1.5, 3, 6, 20]\n",
    "        lb = len(b)\n",
    "        g = [.1, .5, .9]\n",
    "        lg = len(g)\n",
    "        sigma = np.std(data)*np.sqrt(252)\n",
    "        \n",
    "        LL_storage = df(columns=['LL','b','g', 'm'])\n",
    "        #output_parameters=np.zeros((lb*lg,3))\n",
    "        #LLs=zeros((lb*lg,1))\n",
    "        m0_lower = 1.2\n",
    "        m0_upper = 1.8\n",
    "        \n",
    "        index = 1\n",
    "        \n",
    "        # I know that adding one by one row on DF is quiet inefficient \n",
    "        # I will try to use lambda, map instead of double for loop if I have a time \n",
    "        \n",
    "        for i in range(0,lb):\n",
    "            for j in range(0,lg):\n",
    "                a_m0 = fminbound(MSM_util.MSM_likelihood_new, 1.2, 1.8, \n",
    "                                 args=( b[i], g[j], sigma, kbar, data, A_template), \n",
    "                                 xtol=1e-03, maxfun=500, full_output=1, disp=3)\n",
    "                LL_storage.loc[len(LL_storage),'LL'] = sum(a_m0[1])\n",
    "                LL_storage.loc[len(LL_storage)-1,'b'] = b[i]\n",
    "                LL_storage.loc[len(LL_storage)-1,'g'] = g[i]\n",
    "                LL_storage.loc[len(LL_storage)-1,'m'] = a_m0[0]\n",
    "        \n",
    "        LL_storage = LL_storage.sort_values(by = ['LL'], ascending=False)\n",
    "        startingvals = [0. ,0. , 0., sigma]\n",
    "        startingvals[0] = LL_storage.loc[0,'b']\n",
    "        startingvals[1] = LL_storage.loc[0,'m']\n",
    "        startingvals[2] = LL_storage.loc[0,'g']\n",
    "        \n",
    "    return startingvals, LLs\n",
    "    \n",
    "# ## ติดค้างก่อย\n",
    "# function [startingvals,LLs,output_parameters] =...\n",
    "    \n",
    "#                 temp_in = [b(i);1.5;g(j);sigma];\n",
    "#                 [m0,LL]=fminbnd('MSM_likelihood',m0_lower,m0_upper,options,kbar,data,A_template,[b(i);g(j);sigma]);\n",
    "#                 parameters=[b(i);g(j);m0];\n",
    "#                 output_parameters(index,:)=parameters';\n",
    "#                 LLs(index)=LL;\n",
    "#                 index=index+1;\n",
    "#             end\n",
    "#     end\n",
    "#     [LLs,index]=sort(LLs);\n",
    "#     startingvals=[output_parameters(index(1),:),sigma]';\n",
    "#     output_parameters=output_parameters(index,:);\n",
    "# end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MSM_likelihood \n",
    "\n",
    "output form matlab using demean GLD\n",
    "\n",
    "[parameters,LL,exitflag,output]=fmincon('MSM_likelihood',startingvals,...\n",
    "    [],[],[],[],LB,UB,[],options,kbar,data,A_template);\n",
    "   \n",
    "   param = [50,1.99,0.945585657754,5]\n",
    "   LL = 56886.6637963524\n",
    "   exitflag = 4\n",
    "   output = \n",
    "   \n",
    "  [LL,LLs] = MSM_likelihood(parameters,kbar,data,A_template);\n",
    "  LL = 56886.6637963524\n",
    "  LLs = \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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    },
    {
     "ename": "NameError",
     "evalue": "name 'data' 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-45-1772317325cc>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      7\u001b[0m \u001b[0mA\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtransition_mat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mA_template\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0minput_param\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mkbar\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      8\u001b[0m \u001b[0mg_m\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mgofm\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0minput_param\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mkbar\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 9\u001b[1;33m \u001b[0mT\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[0m\n\u001b[0m\u001b[0;32m     10\u001b[0m \u001b[0mpi_mat\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mk2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     11\u001b[0m \u001b[0mLLs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mzeros\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'data' is not defined"
     ]
    }
   ],
   "source": [
    "if len(input_param) == 1 :\n",
    "    input_param = [estim_flag[0], input_param, estim_flag[1], estim_flag[2]]\n",
    "\n",
    "sigma = input_param[3]/np.sqrt(252)\n",
    "k2 = 2**kbar\n",
    "\n",
    "A = transition_mat(A_template,input_param,kbar)\n",
    "g_m = gofm(input_param,kbar)\n",
    "T = len(data)\n",
    "pi_mat = np.zeros((T+1,k2))\n",
    "LLs = zeros(1,T)\n",
    "pi_mat[0,:] = (1/k2)*np.ones((1,k2))\n",
    "\n",
    "# Likelihood Algorithm\n",
    "\n",
    "pa = (2*np.pi)**(-0.5)\n",
    "s = np.matlib.repmat(sigma*g_m, T, 1)\n",
    "w_t = np.matlib.repmat(data, 1, k2)\n",
    "w_t = np.divide(pa*np.e**(-0.5*np.power(np.divide(w_t,s),2)),s)\n",
    "w_t = w_t + 10**-16\n",
    "\n",
    "for t in range(0,T) :\n",
    "    piA = np.matmul(pi_mat[t,:],A)\n",
    "    C = np.multiply(w_t[t,:],piA)\n",
    "    ft = sum(C) \n",
    "    \n",
    "    # stop div by zero if prob are too low\n",
    "    if ft==0:\n",
    "        pi_mat[t+1,0] = 1\n",
    "    else :\n",
    "        pi_mat[t+1,:] = np.divide(C, ft)\n",
    "        \n",
    "    LLs[t] = np.log(np.dot(w_t[t,:],piA))\n",
    "\n",
    "LL = sum[LLs]\n",
    "\n",
    "if np.isinf(LL):\n",
    "    print('Log-likelihood is inf. Probably due to all zeros in pi_mat.')\n",
    "\n",
    "#     return LL, LLs\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### - transition_mat\n",
    "\n",
    "\n",
    "Calculate transition matric using template\n",
    "\n",
    "\n",
    "$$ \\gamma_{k}=1-(1-\\gamma_{1})^{(b^{k-1})} $$\n",
    "\n",
    "<font color = red>equation (3.2) [Page 21 in MSM book]</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'A' 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-39-253e503c2372>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     35\u001b[0m         \u001b[0mprob\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mprob\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mgamma\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mkbar1\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mm\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mbitget\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mi\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[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     36\u001b[0m \u001b[1;31m# print(prob) # PROB OK\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 37\u001b[1;33m \u001b[0mprint\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     38\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[1;36m2\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkbar\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\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     39\u001b[0m         \u001b[1;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkbar\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\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[1;31mNameError\u001b[0m: name 'A' is not defined"
     ]
    }
   ],
   "source": [
    "b = input_param[0]\n",
    "gamma_kbar = input_param[2]\n",
    "\n",
    "gamma = np.zeros((kbar,1))\n",
    "gamma[0]=1-(1-gamma_kbar)**(1/(b**(kbar-1))) #TOWARN : Equation does not conform bbut math is ok \n",
    "\n",
    "def bitget(number,position):\n",
    "    \n",
    "    bi_number = bin(number)\n",
    "    bi_number = bi_number[2:]\n",
    "    if len(bi_number) >= position :\n",
    "        \n",
    "        fn_output = bi_number[-position]\n",
    "    else :\n",
    "        fn_output = 0\n",
    "        \n",
    "    return fn_output\n",
    "\n",
    "for i in range(1,kbar):\n",
    "    gamma[i,0]= 1-(1-gamma[0])**(b**i)\n",
    "\n",
    "gamma = gamma/2\n",
    "gamma = np.append(gamma,gamma,axis=1)\n",
    "# print(gamma)\n",
    "gamma[:,0]=1-gamma[:,0]\n",
    "# print(gamma)\n",
    "kbar1 = kbar+1\n",
    "kbar2 = 2**kbar\n",
    "\n",
    "prob = np.ones((kbar2,1))\n",
    "\n",
    "for i in range(0,kbar2):\n",
    "    for m in range(1,kbar+1):\n",
    "\n",
    "        prob[i,0]=prob[i,0]*gamma[kbar1-m-1, int(bitget(i,m))]\n",
    "# print(prob) # PROB OK\n",
    "print(A)\n",
    "for i in range(0,2**(kbar-1)):\n",
    "        for j in range(i,2**(kbar-1)):\n",
    "            print(i,j)\n",
    "            print(int(A[i,j]))\n",
    "            print(kbar2-int(A[i,j])-1)\n",
    "            A[kbar2-i-1,j] = prob[kbar2-int(A[i,j])-1,0]\n",
    "            A[kbar2-j-1,i] = A[kbar2-i-1,j]\n",
    "            A[j,kbar2-i-1] = A[kbar2-i-1,j]\n",
    "            A[i,kbar2-j-1] = A[kbar2-i-1,j]\n",
    "            \n",
    "            A[i,j] = prob[int(A[i,j]),0]\n",
    "            A[j,i] = A[i,j]\n",
    "            A[kbar2-i-1,kbar2-j-1] = A[i,j]\n",
    "            A[kbar2-j-1,kbar2-i-1] = A[i,j]\n",
    "\n",
    "A    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def transition_mat(A_template,input_param,kbar):\n",
    "    b = input_param[0]\n",
    "    gamma_kbar = input_param[2]\n",
    "\n",
    "    gamma = np.zeros((kbar,1))\n",
    "    gamma[0]=1-(1-gamma_kbar)**(1/(b**(kbar-1))) #TOWARN : Equation does not conform bbut math is ok \n",
    "\n",
    "    def bitget(number,position):\n",
    "    \n",
    "        bi_number = bin(number)\n",
    "        bi_number = bi_number[2:]\n",
    "        if len(bi_number) >= position :\n",
    "        \n",
    "            fn_output = bi_number[-position]\n",
    "        else :\n",
    "            fn_output = 0\n",
    "        \n",
    "        return fn_output\n",
    "\n",
    "    for i in range(1,kbar):\n",
    "        gamma[i,0]= 1-(1-gamma[0])**(b**i)\n",
    "\n",
    "    gamma = gamma/2\n",
    "    gamma = np.append(gamma,gamma,axis=1)\n",
    "    gamma[:,0]=1-gamma[:,0]\n",
    "    \n",
    "    kbar1 = kbar+1\n",
    "    kbar2 = 2**kbar\n",
    "\n",
    "    prob = np.ones((kbar2,1))\n",
    "\n",
    "    for i in range(0,kbar2):\n",
    "        for m in range(1,kbar+1):\n",
    "            prob[i,0]=prob[i,0]*gamma[kbar1-m-1, int(bitget(i,m))]\n",
    "    \n",
    "    for i in range(0,2**(kbar-1)):\n",
    "        for j in range(i,2**(kbar-1)):\n",
    "            \n",
    "            A[kbar2-i-1,j] = prob[kbar2-int(A[i,j])-1,0]\n",
    "            A[kbar2-j-1,i] = A[kbar2-i-1,j]\n",
    "            A[j,kbar2-i-1] = A[kbar2-i-1,j]\n",
    "            A[i,kbar2-j-1] = A[kbar2-i-1,j]\n",
    "            \n",
    "            A[i,j] = prob[int(A[i,j]),0]\n",
    "            A[j,i] = A[i,j]\n",
    "            A[kbar2-i-1,kbar2-j-1] = A[i,j]\n",
    "            A[kbar2-j-1,kbar2-i-1] = A[i,j]\n",
    "    return A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_A = df(A)\n",
    "df_A.to_excel('transition_mat2.xlsx')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### - Test gamma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "gamma_kbar = input_param[2]\n",
    "\n",
    "gamma = np.zeros((kbar,1))\n",
    "gamma[0]=1-(1-gamma_kbar)**(1/(b**(kbar-1))) #TOWARN : Equation does not conform bbut math is ok \n",
    "\n",
    "for i in range(1,kbar):\n",
    "    gamma[i,0]= 1-(1-gamma[0])**(b**i)\n",
    "\n",
    "gamma = gamma/2\n",
    "gamma = np.append(gamma,gamma,axis=1)\n",
    "gamma[:,0]=1-gamma[:,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "      <td>0.934117</td>\n",
       "      <td>0.065883</td>\n",
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       "      <th>2</th>\n",
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       "      <td>0.095494</td>\n",
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       "      <th>3</th>\n",
       "      <td>0.863833</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
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       "      <td>0.329002</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
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       "</div>"
      ],
      "text/plain": [
       "          0         1\n",
       "0  0.955052  0.044948\n",
       "1  0.934117  0.065883\n",
       "2  0.904506  0.095494\n",
       "3  0.863833  0.136167\n",
       "4  0.810361  0.189639\n",
       "5  0.744521  0.255479\n",
       "6  0.670998  0.329002\n",
       "7  0.600000  0.400000"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df(gamma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### - Test prob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      " [  9.06423824e-03]\n",
      " [  6.66654294e-03]\n",
      " [  4.44436196e-03]\n",
      " [  2.66894686e-02]\n",
      " [  1.77929790e-02]\n",
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      " [  8.72422338e-03]\n",
      " [  9.15835621e-03]\n",
      " [  6.10557081e-03]\n",
      " [  4.49050972e-03]\n",
      " [  2.99367315e-03]\n",
      " [  6.24579552e-03]\n",
      " [  4.16386368e-03]\n",
      " [  3.06242789e-03]\n",
      " [  2.04161859e-03]\n",
      " [  2.14321316e-03]\n",
      " [  1.42880877e-03]\n",
      " [  1.05085665e-03]\n",
      " [  7.00571100e-04]\n",
      " [  1.78757231e-02]\n",
      " [  1.19171487e-02]\n",
      " [  8.76479430e-03]\n",
      " [  5.84319620e-03]\n",
      " [  6.13396401e-03]\n",
      " [  4.08930934e-03]\n",
      " [  3.00759486e-03]\n",
      " [  2.00506324e-03]\n",
      " [  4.18322721e-03]\n",
      " [  2.78881814e-03]\n",
      " [  2.05111289e-03]\n",
      " [  1.36740859e-03]\n",
      " [  1.43545327e-03]\n",
      " [  9.56968847e-04]\n",
      " [  7.03829019e-04]\n",
      " [  4.69219346e-04]\n",
      " [  2.81777567e-03]\n",
      " [  1.87851711e-03]\n",
      " [  1.38160700e-03]\n",
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      " [  3.16060971e-04]\n",
      " [  6.59408059e-04]\n",
      " [  4.39605372e-04]\n",
      " [  3.23319844e-04]\n",
      " [  2.15546562e-04]\n",
      " [  2.26272542e-04]\n",
      " [  1.50848361e-04]\n",
      " [  1.10945570e-04]\n",
      " [  7.39637133e-05]\n",
      " [  1.19418639e-02]\n",
      " [  7.96124259e-03]\n",
      " [  5.85531449e-03]\n",
      " [  3.90354300e-03]\n",
      " [  4.09779022e-03]\n",
      " [  2.73186015e-03]\n",
      " [  2.00922157e-03]\n",
      " [  1.33948105e-03]\n",
      " [  2.79460192e-03]\n",
      " [  1.86306794e-03]\n",
      " [  1.37024448e-03]\n",
      " [  9.13496322e-04]\n",
      " [  9.58953520e-04]\n",
      " [  6.39302347e-04]\n",
      " [  4.70192467e-04]\n",
      " [  3.13461645e-04]\n",
      " [  1.88241300e-03]\n",
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      " [  6.15321038e-04]\n",
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      " [  2.12126204e-04]\n",
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      " [  2.95043765e-04]\n",
      " [  1.96695843e-04]\n",
      " [  1.44665360e-04]\n",
      " [  9.64435730e-05]\n",
      " [  1.01242776e-04]\n",
      " [  6.74951842e-05]\n",
      " [  4.96411868e-05]\n",
      " [  3.30941245e-05]\n",
      " [  1.98738223e-04]\n",
      " [  1.32492148e-04]\n",
      " [  9.74449891e-05]\n",
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      " [  6.81960164e-05]\n",
      " [  4.54640110e-05]\n",
      " [  3.34377554e-05]\n",
      " [  2.22918369e-05]\n",
      " [  4.65081685e-05]\n",
      " [  3.10054457e-05]\n",
      " [  2.28038065e-05]\n",
      " [  1.52025377e-05]\n",
      " [  1.59590429e-05]\n",
      " [  1.06393619e-05]\n",
      " [  7.82501092e-06]\n",
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      " [  2.73438205e-03]\n",
      " [  1.82292137e-03]\n",
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      " [  2.93949159e-04]\n",
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      " [  4.94570191e-05]\n",
      " [  3.29713461e-05]\n",
      " [  8.41294555e-04]\n",
      " [  5.60863037e-04]\n",
      " [  4.12502123e-04]\n",
      " [  2.75001415e-04]\n",
      " [  2.88685974e-04]\n",
      " [  1.92457316e-04]\n",
      " [  1.41548018e-04]\n",
      " [  9.43653454e-05]\n",
      " [  1.96877422e-04]\n",
      " [  1.31251615e-04]\n",
      " [  9.65326044e-05]\n",
      " [  6.43550696e-05]\n",
      " [  6.75574921e-05]\n",
      " [  4.50383281e-05]\n",
      " [  3.31246752e-05]\n",
      " [  2.20831168e-05]\n",
      " [  1.32614458e-04]\n",
      " [  8.84096386e-05]\n",
      " [  6.50232966e-05]\n",
      " [  4.33488644e-05]\n",
      " [  4.55059808e-05]\n",
      " [  3.03373206e-05]\n",
      " [  2.23124155e-05]\n",
      " [  1.48749437e-05]\n",
      " [  3.10340682e-05]\n",
      " [  2.06893788e-05]\n",
      " [  1.52165718e-05]\n",
      " [  1.01443812e-05]\n",
      " [  1.06491836e-05]\n",
      " [  7.09945574e-06]\n",
      " [  5.22148969e-06]\n",
      " [  3.48099313e-06]\n",
      " [  5.62026219e-04]\n",
      " [  3.74684146e-04]\n",
      " [  2.75571745e-04]\n",
      " [  1.83714497e-04]\n",
      " [  1.92856456e-04]\n",
      " [  1.28570971e-04]\n",
      " [  9.45610512e-05]\n",
      " [  6.30407008e-05]\n",
      " [  1.31523819e-04]\n",
      " [  8.76825463e-05]\n",
      " [  6.44885366e-05]\n",
      " [  4.29923577e-05]\n",
      " [  4.51317337e-05]\n",
      " [  3.00878225e-05]\n",
      " [  2.21289153e-05]\n",
      " [  1.47526102e-05]\n",
      " [  8.85929927e-05]\n",
      " [  5.90619952e-05]\n",
      " [  4.34387663e-05]\n",
      " [  2.89591775e-05]\n",
      " [  3.04002376e-05]\n",
      " [  2.02668251e-05]\n",
      " [  1.49057931e-05]\n",
      " [  9.93719538e-06]\n",
      " [  2.07322868e-05]\n",
      " [  1.38215245e-05]\n",
      " [  1.01654198e-05]\n",
      " [  6.77694653e-06]\n",
      " [  7.11417942e-06]\n",
      " [  4.74278628e-06]\n",
      " [  3.48821242e-06]\n",
      " [  2.32547494e-06]\n",
      " [  5.93366557e-05]\n",
      " [  3.95577704e-05]\n",
      " [  2.90938486e-05]\n",
      " [  1.93958991e-05]\n",
      " [  2.03610734e-05]\n",
      " [  1.35740490e-05]\n",
      " [  9.98340707e-06]\n",
      " [  6.65560472e-06]\n",
      " [  1.38857998e-05]\n",
      " [  9.25719989e-06]\n",
      " [  6.80846188e-06]\n",
      " [  4.53897459e-06]\n",
      " [  4.76484202e-06]\n",
      " [  3.17656135e-06]\n",
      " [  2.33628928e-06]\n",
      " [  1.55752618e-06]\n",
      " [  9.35332147e-06]\n",
      " [  6.23554765e-06]\n",
      " [  4.58610476e-06]\n",
      " [  3.05740317e-06]\n",
      " [  3.20954498e-06]\n",
      " [  2.13969665e-06]\n",
      " [  1.57369866e-06]\n",
      " [  1.04913244e-06]\n",
      " [  2.18883839e-06]\n",
      " [  1.45922559e-06]\n",
      " [  1.07322754e-06]\n",
      " [  7.15485024e-07]\n",
      " [  7.51088828e-07]\n",
      " [  5.00725885e-07]\n",
      " [  3.68272603e-07]\n",
      " [  2.45515069e-07]]\n"
     ]
    }
   ],
   "source": [
    "prob = np.ones((kbar2,1))\n",
    "\n",
    "for i in range(0,kbar2):\n",
    "    for m in range(1,kbar+1):\n",
    "        prob[i,0]=prob[i,0]*gamma[kbar1-m-1, int(bitget(i,m))]\n",
    "print(prob)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "!python -v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: numpy in c:\\programdata\\anaconda3\\lib\\site-packages\n"
     ]
    }
   ],
   "source": [
    "!pip install numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_prob = df(prob)\n",
    "df_prob.to_excel('prob.xlsx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.00030974,  0.00838513,  0.00838513, ...,  0.00030974,\n",
       "         0.00030974,  0.00030974],\n",
       "       [ 0.00838513,  0.00030974,  0.00838513, ...,  0.00030974,\n",
       "         0.00030974,  0.00030974],\n",
       "       [ 0.00838513,  0.00838513,  0.00030974, ...,  0.00030974,\n",
       "         0.00030974,  0.00030974],\n",
       "       ..., \n",
       "       [ 0.00030974,  0.00030974,  0.00030974, ...,  0.00030974,\n",
       "         0.00838513,  0.00838513],\n",
       "       [ 0.00030974,  0.00030974,  0.00030974, ...,  0.00838513,\n",
       "         0.00030974,  0.00838513],\n",
       "       [ 0.00030974,  0.00030974,  0.00030974, ...,  0.00838513,\n",
       "         0.00838513,  0.00030974]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "       [ 0.00030993],\n",
       "       [ 0.00030993],\n",
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       "       [ 0.00030993],\n",
       "       [ 0.00030992],\n",
       "       [ 0.00030992],\n",
       "       [ 0.00030992],\n",
       "       [ 0.00030992],\n",
       "       [ 0.00030975],\n",
       "       [ 0.00030975],\n",
       "       [ 0.00030975],\n",
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       "       [ 0.00030974],\n",
       "       [ 0.00030974],\n",
       "       [ 0.00030974],\n",
       "       [ 0.00030974]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### - gofm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "code_folding": [
     9
    ],
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m0 = input_param[1]\n",
    "m1 = 2-m0\n",
    "kbar2 = 2**kbar\n",
    "g_m1 = list(range(0,kbar2))\n",
    "for i in range(0,kbar2): \n",
    "    g = 1\n",
    "    for j in range(0,kbar): #not req -1\n",
    "        if g_m1[i]&2**j != 0:\n",
    "            g = g*m1\n",
    "        else :\n",
    "            g=g*m0\n",
    "    g_m1[i]=g\n",
    "    \n",
    "g_m = np.sqrt(g_m1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def gofm(input_param, kbar):\n",
    "    m0 = input_param[1]\n",
    "    m1 = 2-m0\n",
    "    kbar2 = 2**kbar\n",
    "    g_m1 = list(range(0,kbar2))\n",
    "    for i in range(0,kbar2): \n",
    "        g = 1\n",
    "        for j in range(0,kbar): #not req -1\n",
    "            if g_m1[i]&2**j != 0:\n",
    "                g = g*m1\n",
    "            else :\n",
    "                g=g*m0\n",
    "        g_m1[i]=g\n",
    "    \n",
    "    g_m = np.sqrt(g_m1)\n",
    "    return g_m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.0736    ,  1.69308731,  1.69308731,  1.3824    ,  1.69308731,\n",
       "        1.3824    ,  1.3824    ,  1.12872487,  1.69308731,  1.3824    ,\n",
       "        1.3824    ,  1.12872487,  1.3824    ,  1.12872487,  1.12872487,\n",
       "        0.9216    ,  1.69308731,  1.3824    ,  1.3824    ,  1.12872487,\n",
       "        1.3824    ,  1.12872487,  1.12872487,  0.9216    ,  1.3824    ,\n",
       "        1.12872487,  1.12872487,  0.9216    ,  1.12872487,  0.9216    ,\n",
       "        0.9216    ,  0.75248325,  1.69308731,  1.3824    ,  1.3824    ,\n",
       "        1.12872487,  1.3824    ,  1.12872487,  1.12872487,  0.9216    ,\n",
       "        1.3824    ,  1.12872487,  1.12872487,  0.9216    ,  1.12872487,\n",
       "        0.9216    ,  0.9216    ,  0.75248325,  1.3824    ,  1.12872487,\n",
       "        1.12872487,  0.9216    ,  1.12872487,  0.9216    ,  0.9216    ,\n",
       "        0.75248325,  1.12872487,  0.9216    ,  0.9216    ,  0.75248325,\n",
       "        0.9216    ,  0.75248325,  0.75248325,  0.6144    ,  1.69308731,\n",
       "        1.3824    ,  1.3824    ,  1.12872487,  1.3824    ,  1.12872487,\n",
       "        1.12872487,  0.9216    ,  1.3824    ,  1.12872487,  1.12872487,\n",
       "        0.9216    ,  1.12872487,  0.9216    ,  0.9216    ,  0.75248325,\n",
       "        1.3824    ,  1.12872487,  1.12872487,  0.9216    ,  1.12872487,\n",
       "        0.9216    ,  0.9216    ,  0.75248325,  1.12872487,  0.9216    ,\n",
       "        0.9216    ,  0.75248325,  0.9216    ,  0.75248325,  0.75248325,\n",
       "        0.6144    ,  1.3824    ,  1.12872487,  1.12872487,  0.9216    ,\n",
       "        1.12872487,  0.9216    ,  0.9216    ,  0.75248325,  1.12872487,\n",
       "        0.9216    ,  0.9216    ,  0.75248325,  0.9216    ,  0.75248325,\n",
       "        0.75248325,  0.6144    ,  1.12872487,  0.9216    ,  0.9216    ,\n",
       "        0.75248325,  0.9216    ,  0.75248325,  0.75248325,  0.6144    ,\n",
       "        0.9216    ,  0.75248325,  0.75248325,  0.6144    ,  0.75248325,\n",
       "        0.6144    ,  0.6144    ,  0.5016555 ,  1.69308731,  1.3824    ,\n",
       "        1.3824    ,  1.12872487,  1.3824    ,  1.12872487,  1.12872487,\n",
       "        0.9216    ,  1.3824    ,  1.12872487,  1.12872487,  0.9216    ,\n",
       "        1.12872487,  0.9216    ,  0.9216    ,  0.75248325,  1.3824    ,\n",
       "        1.12872487,  1.12872487,  0.9216    ,  1.12872487,  0.9216    ,\n",
       "        0.9216    ,  0.75248325,  1.12872487,  0.9216    ,  0.9216    ,\n",
       "        0.75248325,  0.9216    ,  0.75248325,  0.75248325,  0.6144    ,\n",
       "        1.3824    ,  1.12872487,  1.12872487,  0.9216    ,  1.12872487,\n",
       "        0.9216    ,  0.9216    ,  0.75248325,  1.12872487,  0.9216    ,\n",
       "        0.9216    ,  0.75248325,  0.9216    ,  0.75248325,  0.75248325,\n",
       "        0.6144    ,  1.12872487,  0.9216    ,  0.9216    ,  0.75248325,\n",
       "        0.9216    ,  0.75248325,  0.75248325,  0.6144    ,  0.9216    ,\n",
       "        0.75248325,  0.75248325,  0.6144    ,  0.75248325,  0.6144    ,\n",
       "        0.6144    ,  0.5016555 ,  1.3824    ,  1.12872487,  1.12872487,\n",
       "        0.9216    ,  1.12872487,  0.9216    ,  0.9216    ,  0.75248325,\n",
       "        1.12872487,  0.9216    ,  0.9216    ,  0.75248325,  0.9216    ,\n",
       "        0.75248325,  0.75248325,  0.6144    ,  1.12872487,  0.9216    ,\n",
       "        0.9216    ,  0.75248325,  0.9216    ,  0.75248325,  0.75248325,\n",
       "        0.6144    ,  0.9216    ,  0.75248325,  0.75248325,  0.6144    ,\n",
       "        0.75248325,  0.6144    ,  0.6144    ,  0.5016555 ,  1.12872487,\n",
       "        0.9216    ,  0.9216    ,  0.75248325,  0.9216    ,  0.75248325,\n",
       "        0.75248325,  0.6144    ,  0.9216    ,  0.75248325,  0.75248325,\n",
       "        0.6144    ,  0.75248325,  0.6144    ,  0.6144    ,  0.5016555 ,\n",
       "        0.9216    ,  0.75248325,  0.75248325,  0.6144    ,  0.75248325,\n",
       "        0.6144    ,  0.6144    ,  0.5016555 ,  0.75248325,  0.6144    ,\n",
       "        0.6144    ,  0.5016555 ,  0.6144    ,  0.5016555 ,  0.5016555 ,\n",
       "        0.4096    ])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g_m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       " 508]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f=lambda x: x*2\n",
    "L=list(map(f,g_m1))\n",
    "\n",
    "# TODO: use Lambda function Reduce"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
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