notebook_pert.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Processing perturbation coefficients using `sandy`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture --no-stdout\n",
    "import sandy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define a multigroup perturbation as a series of tabulated pairs `(energy value, perturbation coefficient)`, \n",
    "where the energy values are the right bounds of the energy bins that define the perturbation coefficient as a \n",
    "step function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ENERGY\n",
       "(0.0, 1e-05]               1.00000e+00\n",
       "(1e-05, 0.0001]            1.40000e+00\n",
       "(0.0001, 0.001]            1.30000e+00\n",
       "(0.001, 0.01]              1.20000e+00\n",
       "(0.01, 0.1]                1.10000e+00\n",
       "(0.1, 1.0]                 6.00000e-01\n",
       "(1.0, 100000.0]            1.80000e+00\n",
       "(100000.0, 1000000.0]      1.90000e+00\n",
       "(1000000.0, 10000000.0]    1.90000e+00\n",
       "(10000000.0, 20000000.0]   1.60000e+00\n",
       "dtype: float64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid   = [1e-5, 1e-4, 1e-3, 1e-2, 1e-1, 1e0, 1e5, 1e6, 1e7, 2e7] # right bounds of each energy interval\n",
    "values = [   1,  1.4,  1.3,  1.2,  1.1, 0.6, 1.8, 1.9, 1.9, 1.6]\n",
    "series = pd.Series(values, index=grid)\n",
    "pert = sandy.Pert(series)\n",
    "pert"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `pert` variable is a `sandy.Pert` instance and it contains perturbation coefficients \n",
    "into a `pandas.Series` with a `pandas.IntervalIndex` that defines the energy bins."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Perturbation values are given in fractions!\n",
    "> As such, a perturbation value is obtained multiplying the reference value by the perturbation coefficient.\n",
    "> Then, a perturbation coefficient equal to one does not apply any perturbation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For plotting and analysis purposes we are often interested in tabulated values that are not indexed by energy bins, \n",
    "but by scalar energy values.\n",
    "By calling attribute `.right` the instance returns a `pandas.Series` with perturbation coefficients as `.values` and the \n",
    "right bounds of the energy bins as `.index`.\n",
    "\n",
    "Try also `pert.left` and `pert.mid`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.00000e-05   1.00000e+00\n",
       "1.00000e-04   1.40000e+00\n",
       "1.00000e-03   1.30000e+00\n",
       "1.00000e-02   1.20000e+00\n",
       "1.00000e-01   1.10000e+00\n",
       "1.00000e+00   6.00000e-01\n",
       "1.00000e+05   1.80000e+00\n",
       "1.00000e+06   1.90000e+00\n",
       "1.00000e+07   1.90000e+00\n",
       "2.00000e+07   1.60000e+00\n",
       "dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pert.right"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can resort to the outputs produced by attributes `.right` and `.left` to plot the perturbation coefficients.\n",
    "*Notice that for a correct rendering of the output of `.left` 'steps-post' should be assigned to \n",
    "the drawstyle argument*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 5))\n",
    "pert.right.plot(logx=True, drawstyle=\"steps\", ax=ax)\n",
    "plt.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Perturbation objects can also be printed to a `.csv` or text file with columns divided by a specific separator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1e-05,1.0\n",
      "0.0001,1.4\n",
      "0.001,1.3\n",
      "0.01,1.2\n",
      "0.1,1.1\n",
      "1.0,0.6\n",
      "100000.0,1.8\n",
      "1000000.0,1.9\n",
      "10000000.0,1.9\n",
      "20000000.0,1.6\n",
      "\n"
     ]
    }
   ],
   "source": [
    "pert.right.to_csv(\"pert.csv\", sep=\",\", header=False)\n",
    "with open(\"pert.csv\") as f:\n",
    "    text = f.read()\n",
    "print(text)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Perturbations could even be imported into `sandy` directly from a text file.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ENERGY\n",
       "(0.0, 1e-05]               1.00000e+00\n",
       "(1e-05, 0.0001]            1.40000e+00\n",
       "(0.0001, 0.001]            1.30000e+00\n",
       "(0.001, 0.01]              1.20000e+00\n",
       "(0.01, 0.1]                1.10000e+00\n",
       "(0.1, 1.0]                 6.00000e-01\n",
       "(1.0, 100000.0]            1.80000e+00\n",
       "(100000.0, 1000000.0]      1.90000e+00\n",
       "(1000000.0, 10000000.0]    1.90000e+00\n",
       "(10000000.0, 20000000.0]   1.60000e+00\n",
       "dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sandy.Pert.from_file(\"pert.csv\", sep=\",\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Eventually, a common request is to reshape the perturbation coefficients according the energy structure \n",
    "of, say, a cross section to directly implement a vector-vector multiplication.\n",
    "This can be done using method `.reshape` to which the new energy grid is provided."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ENERGY\n",
       "(0.0, 1e-05]               1.00000e+00\n",
       "(1e-05, 0.0001]            1.40000e+00\n",
       "(0.0001, 0.001]            1.30000e+00\n",
       "(0.001, 0.01]              1.20000e+00\n",
       "(0.01, 0.1]                1.10000e+00\n",
       "(0.1, 1.0]                 6.00000e-01\n",
       "(1.0, 100000.0]            1.80000e+00\n",
       "(100000.0, 1000000.0]      1.90000e+00\n",
       "(1000000.0, 2000000.0]     1.90000e+00\n",
       "(2000000.0, 5000000.0]     1.90000e+00\n",
       "(5000000.0, 10000000.0]    1.90000e+00\n",
       "(10000000.0, 20000000.0]   1.60000e+00\n",
       "dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_grid = [1e6, 2e6, 5e6, 1e7, 2e7]\n",
    "pert2 = pert.reshape(new_grid)\n",
    "pert2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The reshaped `pert2` objects contains the perturbation coefficients defined over a union between \n",
    "the original and the new energy grids."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course the two plots overlap as the information does not change."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjgAAAFgCAYAAAC2QAPxAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAZ2ElEQVR4nO3df3DV5Z3o8fenJEgFVzuieytQYLgo+IsagiBFBV0Qf1QKc50Wt11wanEvdWdnrtZf9ypt7bW9s+p0q1KHOpC7tbWu/LB2pdvWP1yq22qDdauICFg0KfdeAk7ZjT8GkOf+EbQxJjknyQnfk4f3a8YZc86T7/nwTIxvnnNOEiklJEmScvKRogeQJEmqNANHkiRlx8CRJEnZMXAkSVJ2DBxJkpSdmqIeePjw4WnMmDFFPbwkScrAxo0bd6eUTuh4e2GBM2bMGBobG4t6eEmSlIGIeK2z232KSpIkZcfAkSRJ2TFwJElSdgp7DU5n9u/fT3NzM++8807RowxoQ4YMYeTIkdTW1hY9iiRJhaiqwGlubuaYY45hzJgxRETR4wxIKSX27NlDc3MzY8eOLXocSZIKUVVPUb3zzjscf/zxxk0fRATHH3+8p2CSpCNaVQUOYNxUgHsoSTrSVV3gSJIk9ZWB00uXXHIJf/zjH7tdc9ttt/HEE0/06vpPPvkkl112Wa8+V5KkI11Vvch4IEgpkVJi/fr1Jdd+/etfPwwTSZKkjjzB6cTdd9/N6aefzumnn863v/1tduzYwcSJE1m6dCl1dXU0NTUxZswYdu/eDcDtt9/OhAkTmD17NgsXLuTOO+8EYPHixaxevRpo+9UUy5Yto66ujjPOOIOXX34ZgGeffZbp06dz1llnMX36dLZs2VLMH1qSpIxU7QnO136yiZd2/ntFr3nqSX/Gsk+f1u2ajRs3smrVKp555hlSSkydOpXzzz+fLVu2sGrVKpYvX/6B9Y2NjaxZs4bf/va3HDhwgLq6OiZPntzptYcPH85zzz3H8uXLufPOO3nggQeYMGECGzZsoKamhieeeIJbbrmFNWvWVOzPLEnSkahqA6coTz31FPPnz2fo0KEALFiwgF/+8peMHj2aadOmdbp+3rx5fPSjHwXg05/+dJfXXrBgAQCTJ09m7dq1AOzdu5dFixaxdetWIoL9+/dX+o8kSWrnmUfuYtjWdUWPMWC1jp/P1CuuK3qMkqo2cEqdtPSXlFKnt78XPOWu78xRRx0FwKBBgzhw4AAAt956K7NmzWLdunXs2LGDmTNn9mxgSVKPDNu6jlH7ttM0eFzRoww4o/Ztp2nrOsDAGXDOO+88Fi9ezE033URKiXXr1vH973+fFStWdLp+xowZXHPNNdx8880cOHCAxx9/nC996UtlP97evXsZMWIEAA0NDZX4I0iSSmgaPI7Tbnmq6DEGnE13zCh6hLIZOB3U1dWxePFizj77bACuvvpqPvaxj3W5fsqUKVx++eVMmjSJ0aNHU19fz7HHHlv2491www0sWrSIu+++mwsuuKDP80uSJIiePMVSSfX19amxsfEDt23evJmJEycWMk9ftLa2MmzYMN566y3OO+88VqxYQV1dXaEzDdS9lKT+9t4phCc4PVeNexcRG1NK9R1v9wSnApYsWcJLL73EO++8w6JFiwqPG0mSjnQGTgX88Ic/LHoESZLUjj/oT5IkZcfAkSRJ2TFwJElSdgwcSZKUHQOngtr/As7DoaGhgWuvvfawPZ4kSQOFgdONlBIHDx4segxJktRDBk4HO3bsYOLEiSxdupS6ujpuv/12pkyZwplnnsmyZcsAePPNN7n00kuZNGkSp59+Og8//PD7n3/PPfdQV1fHGWecwcsvvwzAs88+y/Tp0znrrLOYPn06W7ZsAdpOYObNm8fcuXM55ZRT+NrXvvb+dR588EHOPvtsPvnJT3LNNdfw7rvvArBq1SpOPvlkzj//fJ5++unDtS2SJA0o1ftzcH56E/zfFyp7zf90Blz8rZLLtmzZwqpVq/jMZz7D6tWrefbZZ0kpcfnll7NhwwZaWlo46aSTePzxx4G23yf1nuHDh/Pcc8+xfPly7rzzTh544AEmTJjAhg0bqKmp4YknnuCWW25hzZo1QFv8vPjiixx99NFMmTKFSy+9lKFDh/Lwww/z9NNPU1tby9KlS/nBD37A7NmzWbZsGRs3buTYY49l1qxZnHXWWZXdI0mSMlC9gVOg0aNHM23aNK6//np+/vOfvx8Rra2tbN26lXPPPZfrr7+eG2+8kcsuu4xzzz33/c9dsGABAJMnT2bt2rVAWwAtWrSIrVu3EhHs37///fWzZ8/m+OOPf/9zn3rqKWpqati4cSNTpkwB4O233+bEE0/kmWeeYebMmZxwwgkAfPazn+WVV17p/w2RJGmAqd7AKeOkpb8MHToUaHsNzs0338w111zzoTUbN25k/fr13HzzzcyZM4fbbrsNgKOOOgqAQYMGceDAAQBuvfVWZs2axbp169ixYwczZ858/zoR8YHrRgQpJRYtWsQ3v/nND9z36KOPfmi9JEn6MF+D042LLrqIlStX0traCsAf/vAHdu3axc6dOzn66KP5/Oc/z/XXX89zzz3X7XX27t3LiBEjgLbX3bT3i1/8gjfeeIO3336bRx99lE996lNceOGFrF69ml27dgHwxhtv8NprrzF16lSefPJJ9uzZw/79+3nkkUcq/4eWJCkD1XuCUwXmzJnD5s2bOeeccwAYNmwYDz74INu2beMrX/kKH/nIR6itreW73/1ut9e54YYbWLRoEXfffTcXXHDBB+6bMWMGX/jCF9i2bRtXXnkl9fVtvxD1G9/4BnPmzOHgwYPU1tZy3333MW3aNL761a9yzjnn8PGPf5y6urr3X3wsSZL+JFJKhTxwfX19amxs/MBtmzdvZuLEiYXMU4SGhgYaGxu59957K37tI20vJalcm+6YAcBptzxV8CQDTzXuXURsTCnVd7y95FNUEbEyInZFxItd3H9sRPwkIv4tIjZFxFWVGFiSJKm3ynkNTgMwt5v7vwy8lFKaBMwE7oqIwX0fLX+LFy/ul9MbSZKOdCVfg5NS2hARY7pbAhwTbW/vGQa8ARzo7UApJd8p1EdFPe2o6vXMI3cxbOu6oseQqsKofdtpGjyu6DHUzyrxLqp7gYnATuAF4G9TSp3+foOIWBIRjRHR2NLS8qH7hwwZwp49e/wfdB+klNizZw9DhgwpehRVkWFb1zFq3/aix5CqQtPgcbSOn1/0GOpnlXgX1UXA88AFwDjgFxHxy5TSv3dcmFJaAayAthcZd7x/5MiRNDc301n8qHxDhgxh5MiRRY+hKtM0eFxVvTBQkvpTJQLnKuBbqe3YZVtE/B6YADzb0wvV1tYyduzYCowkSZKOZJV4iup14EKAiPhz4BTg1QpcV5IkqVdKnuBExEO0vTtqeEQ0A8uAWoCU0v3A7UBDRLwABHBjSml3v00sSZJUQjnvolpY4v6dwJyKTSRJktRH/i4qSZKUHQNHkiRlx8CRJEnZMXAkSVJ2DBxJkpQdA0eSJGXHwJEkSdkxcCRJUnYMHEmSlB0DR5IkZcfAkSRJ2TFwJElSdgwcSZKUHQNHkiRlx8CRJEnZMXAkSVJ2DBxJkpQdA0eSJGXHwJEkSdkxcCRJUnYMHEmSlB0DR5IkZcfAkSRJ2TFwJElSdgwcSZKUHQNHkiRlx8CRJEnZMXAkSVJ2DBxJkpQdA0eSJGXHwJEkSdkxcCRJUnYMHEmSlB0DR5IkZcfAkSRJ2SkZOBGxMiJ2RcSL3ayZGRHPR8SmiPiXyo4oSZLUM+Wc4DQAc7u6MyKOA5YDl6eUTgOuqMhkkiRJvVRTakFKaUNEjOlmyZXA2pTS64fW76rQbJIkqcqM2redTXfMKGvtfxw3kWlLv9fPE3WuEq/BORn4WEQ8GREbI+KvuloYEUsiojEiGltaWirw0JIk6XBpHT+fpsHjih6jLCVPcMq8xmTgQuCjwK8i4tcppVc6LkwprQBWANTX16cKPLYkSTpMpl5xHXBd0WOUpRKB0wzsTim9CbwZERuAScCHAkeSJOlwqMRTVD8Gzo2Imog4GpgKbK7AdSVJknql5AlORDwEzASGR0QzsAyoBUgp3Z9S2hwR/wz8DjgIPJBS6vIt5ZIkSf2tnHdRLSxjzd8Bf1eRiSRJkvrIn2QsSZKyY+BIkqTsGDiSJCk7Bo4kScqOgSNJkrJj4EiSpOwYOJIkKTsGjiRJyo6BI0mSsmPgSJKk7Bg4kiQpOwaOJEnKjoEjSZKyY+BIkqTsGDiSJCk7Bo4kScqOgSNJkrJj4EiSpOwYOJIkKTsGjiRJyo6BI0mSsmPgSJKk7Bg4kiQpOwaOJEnKjoEjSZKyY+BIkqTsGDiSJCk7Bo4kScqOgSNJkrJj4EiSpOwYOJIkKTsGjiRJyo6BI0mSsmPgSJKk7Bg4kiQpOwaOJEnKTsnAiYiVEbErIl4ssW5KRLwbEf+lcuNJkiT1XDknOA3A3O4WRMQg4H8BP6vATJIkSX1SU2pBSmlDRIwpsexvgDXAlEoM1VfPPHIXw7auK3qMbrWOn8/UK64regxJkrLU59fgRMQIYD5wfxlrl0REY0Q0trS09PWhuzRs6zpG7dveb9fvq1H7tld9gEmSNJCVPMEpw7eBG1NK70ZEtwtTSiuAFQD19fWpAo/dpabB4zjtlqf68yF6bdMdM4oeQZKkrFUicOqBHx2Km+HAJRFxIKX0aAWuLUmS1GN9DpyU0tj3/j0iGoB/Mm4kSVKRSgZORDwEzASGR0QzsAyoBUgplXzdjSRJ0uFWzruoFpZ7sZTS4j5NI0mSVAH+JGNJkpQdA0eSJGXHwJEkSdkxcCRJUnYMHEmSlB0DR5IkZcfAkSRJ2TFwJElSdgwcSZKUHQNHkiRlx8CRJEnZMXAkSVJ2DBxJkpQdA0eSJGXHwJEkSdmpKXqAI9WofdvZdMeMosfoVOv4+Uy94rqix5Akqdc8wSlA6/j5NA0eV/QYnRq1bzvDtq4regxJkvrEE5wCtJ2OVOcJSbWeKkmS1BOe4EiSpOwYOJIkKTsGjiRJyo6BI0mSsmPgSJKk7Bg4kiQpOwaOJEnKjoEjSZKyY+BIkqTsGDiSJCk7Bo4kScqOgSNJkrJj4EiSpOwYOJIkKTsGjiRJyo6BI0mSsmPgSJKk7JQMnIhYGRG7IuLFLu7/y4j43aF//jUiJlV+TEmSpPKVc4LTAMzt5v7fA+enlM4EbgdWVGAuSZKkXqsptSCltCEixnRz/7+2+/DXwMgKzKUCjdq3nU13zCh6jE61jp/P1CuuK3oMSVKVq/RrcL4I/LSrOyNiSUQ0RkRjS0tLhR9aldA6fj5Ng8cVPUanRu3bzrCt64oeQ5I0AJQ8wSlXRMyiLXC6/Kt/SmkFh57Cqq+vT5V6bFVO2+lIdZ6QVOupkiSp+lQkcCLiTOAB4OKU0p5KXFOSJKm3+vwUVUR8AlgLfCGl9ErfR5IkSeqbkic4EfEQMBMYHhHNwDKgFiCldD9wG3A8sDwiAA6klOr7a2BJkqRSynkX1cIS918NXF2xiSRJkvrIn2QsSZKyY+BIkqTsGDiSJCk7Bo4kScqOgSNJkrJj4EiSpOwYOJIkKTsGjiRJyo6BI0mSsmPgSJKk7Bg4kiQpOwaOJEnKjoEjSZKyY+BIkqTsGDiSJCk7Bo4kScpOTdEDSD0xat92Nt0xo+gxOtU6fj5Tr7iu6DEkSXiCowGkdfx8mgaPK3qMTo3at51hW9cVPYYk6RBPcDRgtJ2OVOcJSbWeKknSkcoTHEmSlB0DR5IkZcfAkSRJ2TFwJElSdgwcSZKUHQNHkiRlx8CRJEnZMXAkSVJ2DBxJkpQdA0eSJGXHwJEkSdkxcCRJUnYMHEmSlB0DR5IkZcfAkSRJ2TFwJElSdgwcSZKUnZKBExErI2JXRLzYxf0REd+JiG0R8buIqKv8mJIkSeUr5wSnAZjbzf0XA+MP/bME+G7fx5IkSeq9koGTUtoAvNHNknnAP6Q2vwaOi4iPV2pASZKknqqpwDVGAE3tPm4+dNv/6bgwIpbQdsrDJz7xiQo8dOf+47iJ/XZtSZJU/SoRONHJbamzhSmlFcAKgPr6+k7XVMK0pd/rr0tLkqQBoBLvomoGRrX7eCSwswLXlSRJ6pVKBM5jwF8dejfVNGBvSulDT09JkiQdLiWfooqIh4CZwPCIaAaWAbUAKaX7gfXAJcA24C3gqv4aVpIkqRwlAyeltLDE/Qn4csUmkiRJ6iN/krEkScqOgSNJkrJj4EiSpOwYOJIkKTsGjiRJyo6BI0mSsmPgSJKk7Bg4kiQpOwaOJEnKjoEjSZKyY+BIkqTsGDiSJCk7Bo4kScqOgSNJkrJj4EiSpOwYOJIkKTsGjiRJyo6BI0mSsmPgSJKk7Bg4kiQpOwaOJEnKjoEjSZKyY+BIkqTsGDiSJCk7Bo4kScqOgSNJkrJj4EiSpOwYOJIkKTsGjiRJyo6BI0mSsmPgSJKk7Bg4kiQpOwaOJEnKjoEjSZKyY+BIkqTslBU4ETE3IrZExLaIuKmT+4+NiJ9ExL9FxKaIuKryo0qSJJWnZOBExCDgPuBi4FRgYUSc2mHZl4GXUkqTgJnAXRExuMKzSpIklaWcE5yzgW0ppVdTSvuAHwHzOqxJwDEREcAw4A3gQEUnlSRJKlM5gTMCaGr3cfOh29q7F5gI7AReAP42pXSw44UiYklENEZEY0tLSy9HliRJ6l45gROd3JY6fHwR8DxwEvBJ4N6I+LMPfVJKK1JK9Sml+hNOOKGHo0qSJJWnnMBpBka1+3gkbSc17V0FrE1ttgG/ByZUZkRJkqSeKSdwfgOMj4ixh144/DngsQ5rXgcuBIiIPwdOAV6t5KCSJEnlqim1IKV0ICKuBX4GDAJWppQ2RcRfH7r/fuB2oCEiXqDtKa0bU0q7+3FuSZKkLpUMHICU0npgfYfb7m/37zuBOZUdTZIkqXf8ScaSJCk7Bo4kScqOgSNJkrJj4EiSpOwYOJIkKTsGjiRJyo6BI0mSsmPgSJKk7Bg4kiQpOwaOJEnKjoEjSZKyY+BIkqTsGDiSJCk7Bo4kScqOgSNJkrJj4EiSpOwYOJIkKTsGjiRJyo6BI0mSsmPgSJKk7Bg4kiQpOwaOJEnKjoEjSZKyY+BIkqTsGDiSJCk7Bo4kScqOgSNJkrJj4EiSpOwYOJIkKTsGjiRJyo6BI0mSsmPgSJKk7Bg4kiQpOwaOJEnKjoEjSZKyU1bgRMTciNgSEdsi4qYu1syMiOcjYlNE/Etlx5QkSSpfTakFETEIuA+YDTQDv4mIx1JKL7VbcxywHJibUno9Ik7sp3klSZJKKucE52xgW0rp1ZTSPuBHwLwOa64E1qaUXgdIKe2q7JiSJEnlK3mCA4wAmtp93AxM7bDmZKA2Ip4EjgH+PqX0DxWZUBogRu3bzqY7ZhQ9RqdG7dtO0+BxRY8hSYdNOSc40cltqcPHNcBk4FLgIuDWiDj5QxeKWBIRjRHR2NLS0uNhpWrVOn5+VQdE0+BxtI6fX/QYknTYlHOC0wyMavfxSGBnJ2t2p5TeBN6MiA3AJOCV9otSSiuAFQD19fUdI0kasKZecR1wXdFjSJIOKecE5zfA+IgYGxGDgc8Bj3VY82Pg3IioiYijaXsKa3NlR5UkSSpPyROclNKBiLgW+BkwCFiZUtoUEX996P77U0qbI+Kfgd8BB4EHUkov9ufgkiRJXYmUinmmqL6+PjU2Nhby2JIkKQ8RsTGlVN/xdn+SsSRJyo6BI0mSsmPgSJKk7Bg4kiQpOwaOJEnKjoEjSZKyY+BIkqTsGDiSJCk7Bo4kScpOYT/JOCJagNcKefDqMBzYXfQQA5D71nvuXe+4b73n3vWO+9Yzo1NKJ3S8sbDAOdJFRGNnP1pa3XPfes+96x33rffcu95x3yrDp6gkSVJ2DBxJkpQdA6c4K4oeYIBy33rPvesd96333Lvecd8qwNfgSJKk7HiCI0mSsmPgSJKk7Bg4kiQpOwaOJEnKjoFThSJiaERsjIjLip5lIImIz0TE9yLixxExp+h5qtmhr7H/fWi//rLoeQYSv856z+9tvRMRH4mI/xkR90TEoqLnGSgMnAqKiJURsSsiXuxw+9yI2BIR2yLipjIudSPwj/0zZXWqxN6llB5NKX0JWAx8th/HrUo93MMFwOpD+3X5YR+2yvRk7470r7P2evHf7RH3va0rPdy7ecAIYD/QfLhnHagMnMpqAOa2vyEiBgH3ARcDpwILI+LUiDgjIv6pwz8nRsRfAC8B/+9wD1+wBvq4d+0+9X8c+rwjTQNl7iEwEmg6tOzdwzhjtWqg/L17z5H6ddZeA+X/d3ukfm/rSgPlf82dAvwqpfTfgP96mOccsGqKHiAnKaUNETGmw81nA9tSSq8CRMSPgHkppW8CHzqmjYhZwFDavrjfjoj1KaWD/Tt58Sq0dwF8C/hpSum5fh656vRkD2n7W+BI4Hn8i06P9i4iNnMEf52118OvuWEcgd/butLDvWsC9h1a419IymTg9L8R/OlvytD2P5apXS1OKf13gIhYDOw+kr8B0MO9A/4G+Avg2Ij4zyml+/tzuAGiqz38DnBvRFwK/KSIwQaArvbOr7PudbpvKaVrwe9tJXT1Nff3wD0RcS6woYjBBiIDp/9FJ7eV/PHRKaWGyo8y4PRo71JK36Htf9z6k073MKX0JnDV4R5mgOlq7/w66163/936va1bXX3NvQV88XAPM9Ad8UfTh0EzMKrdxyOBnQXNMtC4d33nHvaee9c77lvvuXcVZOD0v98A4yNibEQMBj4HPFbwTAOFe9d37mHvuXe94771nntXQQZOBUXEQ8CvgFMiojkivphSOgBcC/wM2Az8Y0ppU5FzViP3ru/cw95z73rHfes9967/+dvEJUlSdjzBkSRJ2TFwJElSdgwcSZKUHQNHkiRlx8CRJEnZMXAkSVJ2DBxJkpQdA0eSJGXn/wNkcqHcq7tEegAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 5))\n",
    "pert.right.plot(logx=True, drawstyle=\"steps\", label=\"original\", ax=ax)\n",
    "pert2.right.plot(logx=True, drawstyle=\"steps\", label=\"reshaped\", ax=ax)\n",
    "ax.legend(loc=2)\n",
    "plt.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Truncate perturbations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since perturbation coefficients are essentially fraction, if they are lower than 0 or higher than 2 they will introduce perturbations larger than 100%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we construct a `Pert` object with normally distributed perturbation coefficients.\n",
    "Since the distribution is centered in 1 and the standard deviation is 0.5, we end up having perturbation values that exceed the limits defined above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "grid = sandy.uniform_loggrid(1e-5, 2e7, 1000)\n",
    "np.random.seed(1)\n",
    "values = np.random.normal(1, 0.5, grid.size)\n",
    "pp = sandy.Pert(values, index=grid, name=\"original\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 5))\n",
    "bins = 50\n",
    "pp.right.plot(kind=\"hist\", ax=ax, bins=bins, alpha=0.5)\n",
    "plt.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Pert` method `.truncate` replaces any perturbation coefficient below a given lower value with the boundary value itself. The same happens for the upper value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjgAAAFgCAYAAAC2QAPxAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAYZElEQVR4nO3df7Cld10f8PcnP5glQAbibsJKiCEliVLGSFjoItSKkA6mNcHWCJ2RZiiaWsRK2hkNlBH7RwfqtETUWg2gE5DahJ/ZMmBdUtARTXATkgKG/BAhrEnZNWmygJQY8u0f92xy9+69e5+99z7n3P2e12vmzj3Pc55zzuc++9zd935/PN9qrQUAoCfHzboAAICNJuAAAN0RcACA7gg4AEB3BBwAoDsnzLqAIbZu3drOPPPMWZcBAGwyN91001+31rYt3X9MBJwzzzwze/bsmXUZAMAmU1VfXm6/LioAoDsCDgDQHQEHAOiOgAMAdEfAAQC6I+AAAN0RcACA7gg4AEB3BBwAoDsCDgDQHQEHAOiOgAMAdEfAAQC6I+AAAN05YdYFALCy/b/264dsb/vZ182oEji2aMEBALoj4AAA3RFwAIDuCDgAQHcEHACgOwIOANAdAQcA6I6AAwB0R8ABALoj4AAA3RFwAIDuCDgAQHcEHACgO1YT55hmpWUAlqMFBwDojoADAHRHwAEAujNqwKmqy6vq81X1uar6varaUlWnVNXuqrpz8v0pY9YAAMyf0QJOVT0tyb9OsqO19uwkxyd5ZZIrklzfWjs7yfWTbQCADTN2F9UJSR5fVSckOSnJPUkuTnL15Pmrk7x85BoAgDkzWsBprf1Vkv+U5O4k9yZ5sLX2B0lOa63dOznm3iSnLvf6qrqsqvZU1Z79+/ePVSYA0KExu6iekoXWmmck+c4kT6iqnxj6+tbaVa21Ha21Hdu2bRurTACgQ2N2Ub00yV+21va31v42yQeTfH+Sr1bV9iSZfN83Yg0AwBwaM+DcnWRnVZ1UVZXkJUluS7IryaWTYy5Nct2INQAAc2i0pRpaazdW1fuT3Jzk4SSfSXJVkicmubaqXpOFEHTJWDUAAPNp1LWoWmtvTvLmJbu/lYXWHACAUbiTMQDQHQEHAOiOgAMAdEfAAQC6I+AAAN0RcACA7gg4AEB3BBwAoDsCDgDQHQEHAOiOgAMAdEfAAQC6I+AAAN0RcACA7gg4AEB3BBwAoDsCDgDQHQEHAOiOgAMAdEfAAQC6I+AAAN0RcACA7gg4AEB3BBwAoDsCDgDQHQEHAOiOgAMAdEfAAQC6I+AAAN0RcACA7gg4AEB3BBwAoDsCDgDQnRNmXQAwfVfuvmPVYy6/4JwpVAIwDi04AEB3BBwAoDsCDgDQHQEHAOiOgAMAdEfAAQC6I+AAAN0RcACA7gg4AEB3BBwAoDsCDgDQHQEHAOiOgAMAdEfAAQC6I+AAAN0RcACA7gg4AEB3BBwAoDsCDgDQHQEHAOiOgAMAdEfAAQC6I+AAAN0RcACA7pww6wIADrpy9x2rHnP5BedMoRLgWKcFBwDojoADAHRHwAEAujNqwKmqJ1fV+6vqC1V1W1W9oKpOqardVXXn5PtTxqwBAJg/Y7fgvD3J77fWvjvJeUluS3JFkutba2cnuX6yDQCwYUYLOFV1cpIfSPKuJGmtPdRaeyDJxUmunhx2dZKXj1UDADCfxmzBOSvJ/iS/U1Wfqap3VtUTkpzWWrs3SSbfT13uxVV1WVXtqao9+/fvH7FMAKA3YwacE5Kcn+S/ttaek+QbOYruqNbaVa21Ha21Hdu2bRurRgCgQ2MGnL1J9rbWbpxsvz8LgeerVbU9SSbf941YAwAwh0YLOK21/5PkK1V17mTXS5L8eZJdSS6d7Ls0yXVj1QAAzKexl2r42STvrarHJflikldnIVRdW1WvSXJ3kktGrgEYkeUVgM1o1IDTWrslyY5lnnrJmJ8LAMw3dzIGALoj4AAA3RFwAIDuCDgAQHcEHACgOwIOANAdAQcA6I6AAwB0R8ABALoj4AAA3RFwAIDuCDgAQHcEHACgOwIOANAdAQcA6I6AAwB054RZFwBsTlfuvmPWJQCsmRYcAKA7Ag4A0B0BBwDojoADAHRHwAEAuiPgAADdMU0cOmJqN8CCQS04VfXssQsBANgoQ7uofrOqPl1Vr62qJ49ZEADAeg3qomqtvaiqzk7yL5LsqapPJ/md1truUasDHqX76egMOV+XX3DOFCoBZmHwIOPW2p1J3pTkF5L8gyS/WlVfqKp/MlZxAABrMXQMzvdW1ZVJbkvyQ0l+pLX2PZPHV45YHwDAURs6i+rXk7wjyRtba988uLO1dk9VvWmUygAA1mhowLkwyTdba99Okqo6LsmW1trftNbeM1p1AEsYiwQMMXQMzseTPH7R9kmTfQAAm87QgLOltfb1gxuTxyeNUxIAwPoM7aL6RlWd31q7OUmq6rlJvrnKa+Awv3HLbxy277Xf99oZVALzaenvoN8/ejU04Lw+yfuq6p7J9vYkrxilIgCAdRp6o78/q6rvTnJukkryhdba345aGQDAGh3NYpvPS3Lm5DXPqaq01t49SlUAAOswKOBU1XuS/J0ktyT59mR3SyLgAACbztAWnB1JntVaa2MWAwCwEYZOE/9ckqeOWQgAwEYZ2oKzNcmfT1YR/9bBna21i0apCgBgHYYGnF8aswiAWRi67MPlF5wzciXARhs6TfwPq+q7kpzdWvt4VZ2U5PhxSwMAWJtBY3Cq6qeSvD/Jb012PS3Jh0eqCQBgXYZ2Uf1MkucnuTFJWmt3VtWpo1UFjG7n3Vcdtu+GMy6bQSUAG2/oLKpvtdYeOrhRVSdk4T44AACbztCA84dV9cYkj6+qC5K8L8n/GK8sAIC1GxpwrkiyP8lnk/zLJB9N8qaxigIAWI+hs6geSfKOyRcAwKY2dC2qv8wyY25aa2dteEUAAOt0NGtRHbQlySVJTtn4cgAA1m/QGJzW2n2Lvv6qtfYrSX5o3NIAANZmaBfV+Ys2j8tCi86TRqkIAGCdhnZR/edFjx9O8qUkP77h1QAAbIChs6hePHYhAAAbZWgX1b850vOttbdtTDnQF6tVA8zG0cyiel6SXZPtH0nyR0m+MkZRAADrMTTgbE1yfmvta0lSVb+U5H2ttZ8cqzAAgLUaGnDOSPLQou2Hkpy54dXAnBralXWs6v3nAzafoQHnPUk+XVUfysIdjX80ybtHqwoAYB2GzqL6D1X1sSR/f7Lr1a21z4xXFgDA2g1dTTxJTkpyoLX29iR7q+oZI9UEALAugwJOVb05yS8kecNk14lJfnfga4+vqs9U1Ucm26dU1e6qunPy/SlrKRwAYCVDW3B+NMlFSb6RJK21ezJ8qYafS3Lbou0rklzfWjs7yfWTbQCADTM04DzUWmtZGGCcqnrCkBdV1elJ/lGSdy7afXGSqyePr07y8oE1AAAMMjTgXFtVv5XkyVX1U0k+nuQdA173K0l+Pskji/ad1lq7N0km309d7oVVdVlV7amqPfv37x9YJgDAgIBTVZXkmiTvT/KBJOcm+cXW2q+t8rp/nGRfa+2mtRTWWruqtbajtbZj27Zta3kLAGBOrTpNvLXWqurDrbXnJtl9FO/9wiQXVdWFSbYkObmqfjfJV6tqe2vt3qranmTfmioHAFjB0C6qG6rqeUfzxq21N7TWTm+tnZnklUn+V2vtJ7KwntWlk8MuTXLd0bwvAMBqht7J+MVJfrqqvpSFmVSVhcad713DZ741C2N6XpPk7iSXrOE9ADYVK8fD5nLEgFNVZ7TW7k7yw+v5kNbaJ5N8cvL4viQvWc/7AQAcyWotOB/OwiriX66qD7TW/ukUagIAWJfVxuDUosdnjVkIAMBGWa0Fp63wGOjEruPuevTx3gPXJEnOP/kVsyoHYEOsFnDOq6oDWWjJefzkcfLYIOOTR60OAGANjhhwWmvHT6sQAICNMnSaOLCJ7Lz7qmX333DGZVOuZD4MnQIObB5Db/QHAHDMEHAAgO4IOABAdwQcAKA7Ag4A0B0BBwDojmnisEamDgNsXlpwAIDuCDgAQHcEHACgO8bgwBzb8qk7cl7dnyS59UVblz3maJaFsIQEsFlowQEAuiPgAADd0UUFdGW5bjJdZDB/tOAAAN0RcACA7gg4AEB3jMEBHnX6gZuSJDsfeHDGlQCsjxYcAKA7Ag4A0B1dVBzZJ95y+L4Xv2H6dWyQISuAX37BOVOopD83H7gm+46765B9Fz3yzKN6j424azJAogUHAOiQgAMAdEfAAQC6YwwOsCZLx8AsHX8DMEtacACA7gg4AEB3BBwAoDvG4MAmsty9XZa7B8x633M1u9Z5P5sh1nsfm7FqHOPPAJg+LTgAQHcEHACgO7qo4Bg1jW6klT7raD/PsgrAtGnBAQC6I+AAAN0RcACA7hiDAx1ZbazL0rE059X9Y5YzaOzOcscc9pplfq5d6/zv2azGBV25+45Vj7n8gnOmUAn0TQsOANAdAQcA6I4uKlhiSBcCx4aD3V97D1zz6L7zT37FrMoBpkgLDgDQHQEHAOiOgAMAdMcYHOjYkCnYm/G9j2TLpxbGSB2c4n7ri7bOtB5gc9KCAwB0R8ABALqjiwo6MXYXzXl//NeHbB/sGtro917ufRf/bGu5+/LpB2569PHOBx486tezgk+8Zfn9L37DdOuAZWjBAQC6I+AAAN0RcACA7hiDAyNbbtXqG864bEPee7VxMdMaN7PURn7O0VptPM8QS8cznbquioBZ0IIDAHRHwAEAuqOLCiaW60pKhncnrfT6oz12affI4pWwD9q3xinhR+pWOtJz0zR2t9qXc2gX1kWPPHPV16312rh5mT87q5nDdGjBAQC6I+AAAN0RcACA7ow2Bqeqnp7k3UmemuSRJFe11t5eVackuSbJmUm+lOTHW2v/d6w6OPZdufuOFZ975hfvS5LsPOs7plXOipZbKmHp+I4hxywdg7L3wg0obsrGHEez0dazxMVq464OjpXae/Jz1/wZwNqM2YLzcJJ/21r7niQ7k/xMVT0ryRVJrm+tnZ3k+sk2AMCGGS3gtNbuba3dPHn8tSS3JXlakouTXD057OokLx+rBgBgPk1lDE5VnZnkOUluTHJaa+3eZCEExU1CAYANNvp9cKrqiUk+kOT1rbUDVTX0dZcluSxJzjjjjPEKhDVYbuzFLkP2V7R4TM6W9kj+3wvPWdNrx7bSMg9Dxk4Bm8uofyVX1YlZCDfvba19cLL7q1W1ffL89iT7lntta+2q1tqO1tqObdu2jVkmANCZ0QJOLTTVvCvJba21ty16aleSSyePL01y3Vg1AADzacwuqhcmeVWSz1bVLZN9b0zy1iTXVtVrktyd5JIRa4BVHbyd/sEpvdPuelja/XHekudPP3DToc8fA8stTNM8/szA6kYLOK21P06y0oCbl4z1uQAAhkUCAN0RcACA7ow+TRzm2UrLAKw0HZmNtZ7xOUe73MSWTx26pMjiqfCLx1HtfODBRx/fcMZla64vOfIyJgddfsHwKfnQEy04AEB3BBwAoDu6qGDiYJfElvZIkhzV3Xa3fOqOnFf3P7qt26k/S7usdr1oyfN1f85tp0yxIuBItOAAAN0RcACA7gg4AEB3jMGBKdjI6crHutvr/ty6wvT5Y93ti8dhDfgZl1uVfr1Tx5daOpX85gP3HbL9rf13mEpOl7TgAADdEXAAgO7oooI1OGwF8EVdE8nRdSv11gV1LBnz3K/03lvaI6vegmBxt9Izv3hol9JdA+5eDGjBAQA6JOAAAN0RcACA7hiDQxdumIxTGDo+YfH03H0DpvPefOCaQ7ZPP4raYLMbsip5YmVyji1acACA7gg4AEB3BBwAoDvG4MAqdt591aBxOgw3z/f+ub3uT/7khke3z22nrHpfnJVMY6kHOFZpwQEAuiPgAADd0UXF5vaJt2Tn3fcdtnsWzfCLu1VufdHWqX8+AMNpwQEAuiPgAADdEXAAgO4Yg8PM/OlfLIyt+db+lW8Tv9z4m7HdXvcnSW49wtTweZ7mzIKNugZur/sPudb2Hrgm55/8ilVfd/OBaw67fcFFjzxzQ2qCHmjBAQC6I+AAAN3RRcUxYdeSpvhTlznmGwd2Z9/ezxx63Om/fMj2wVXB9x1316NdDOdtXJnQBXdIpgdacACA7gg4AEB3BBwAoDvG4PCoK3cfPl176TTtF5z1HWt+ryS5+cDGTPvet/fnkyTbD4w3XdtUcGbh9AM3ZecDDz66veXBhd+lg7cvODjO7PSjfN+D42oWTy3fe/Jz11EpbG5acACA7gg4AEB3dFHRtaXTXbf/yQ0zqgSGW3xbhPMmXVNrcfC2CEkOu+txcnh32GqWdj0vd6fxod3YMDYtOABAdwQcAKA7Ag4A0B1jcDgqf/rF+3LDwyuv/r0ey90e/mgdNrX7+62uzLFnrbco2HXcXdm7aNwNzDMtOABAdwQcAKA7uqiOcSvdMXhMK3UlbdRqw0tXDt/I97JyOJvRRt41+/QDN23Ye63F0G7syy84ZwrVMM+04AAA3RFwAIDuCDgAQHeMwWFUS8frLHe7+H2TMQO7xG3YtDbiNg4wTf5JAQC6I+AAAN0RcACA7hiDw4bZjH30G3l/EWDjDLmH19B75Wzke9EPLTgAQHcEHACgO7qoBhq6JIJmUACYPS04AEB3BBwAoDsCDgDQHWNwNtjQsToAHJm/T1kPLTgAQHcEHACgO7qoohkUgI3X+92aN/vtU2bSglNVL6uq26vqrqq6YhY1AAD9mnrAqarjk/yXJD+c5FlJ/llVPWvadQAA/ZpFC87zk9zVWvtia+2hJP89ycUzqAMA6FS11qb7gVU/luRlrbWfnGy/Ksnfa629bslxlyW5bLJ5bpLbp1Ti1iSWoH6M8/EY5+JQzsdjnItDOR+PcS4ONcb5+K7W2ralO2cxyLiW2XdYymqtXZXkqvHLOVRV7Wmt7Zj2525WzsdjnItDOR+PcS4O5Xw8xrk41DTPxyy6qPYmefqi7dOT3DODOgCATs0i4PxZkrOr6hlV9bgkr0yyawZ1AACdmnoXVWvt4ap6XZL/meT4JL/dWvv8tOs4gql3i21yzsdjnItDOR+PcS4O5Xw8xrk41NTOx9QHGQMAjM1SDQBAdwQcAKA7cx9wquqUqtpdVXdOvj9lheO+VFWfrapbqmrPtOsc02pLZ9SCX508/7+r6vxZ1DktA87HD1bVg5Nr4Zaq+sVZ1DkNVfXbVbWvqj63wvNzc20MOBfzdF08vao+UVW3VdXnq+rnljlmnq6NIedjLq6PqtpSVZ+uqlsn5+LfL3PMdK6N1tpcfyX55SRXTB5fkeQ/rnDcl5JsnXW9I/z8xyf5iyRnJXlckluTPGvJMRcm+VgW7mG0M8mNs657xufjB5N8ZNa1Tul8/ECS85N8boXn5+naWO1czNN1sT3J+ZPHT0pyx5z/vTHkfMzF9TH5837i5PGJSW5MsnMW18bct+BkYZmIqyePr07y8tmVMhNDls64OMm724Ibkjy5qrZPu9ApsZTIIq21P0py/xEOmZtrY8C5mButtXtbazdPHn8tyW1JnrbksHm6Noacj7kw+fP++mTzxMnX0tlMU7k2BJzktNbavcnCRZrk1BWOa0n+oKpumiwj0YunJfnKou29OfwXc8gxvRj6s75g0gT7sar6u9MpbVOap2tjiLm7LqrqzCTPycL/1Beby2vjCOcjmZPro6qOr6pbkuxLsru1NpNrYxZLNUxdVX08yVOXeerfHcXbvLC1dk9VnZpkd1V9YfI/umPdkKUzBi2v0YkhP+vNWVj75OtVdWGSDyc5e+zCNql5ujZWM3fXRVU9MckHkry+tXZg6dPLvKTra2OV8zE310dr7dtJvq+qnpzkQ1X17Nba4rFrU7k25qIFp7X20tbas5f5ui7JVw82jU2+71vhPe6ZfN+X5ENZ6MrowZClM+ZpeY1Vf9bW2oGDTbCttY8mObGqtk6vxE1lnq6NI5q366KqTszCP+bvba19cJlD5uraWO18zNv1kSSttQeSfDLJy5Y8NZVrYy4Czip2Jbl08vjSJNctPaCqnlBVTzr4OMk/TLLsTIpj0JClM3Yl+eeTke87kzx4sFuvQ6uej6p6alXV5PHzs/B7dN/UK90c5unaOKJ5ui4mP+e7ktzWWnvbCofNzbUx5HzMy/VRVdsmLTepqscneWmSLyw5bCrXxlx0Ua3irUmurarXJLk7ySVJUlXfmeSdrbULk5yWhWa2ZOGc/bfW2u/PqN4N1VZYOqOqfnry/G8m+WgWRr3fleRvkrx6VvWObeD5+LEk/6qqHk7yzSSvbJOpAb2pqt/LwuyPrVW1N8mbszBocO6ujQHnYm6uiyQvTPKqJJ+djLVIkjcmOSOZv2sjw87HvFwf25NcXVXHZyHEXdta+8gs/k2xVAMA0B1dVABAdwQcAKA7Ag4A0B0BBwDojoADAHRHwAEAuiPgAADd+f8IOcXUD84lGQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 5))\n",
    "bins = 50\n",
    "pp.right.plot(kind=\"hist\", ax=ax, bins=bins, alpha=0.5)\n",
    "pp.truncate().right.plot(kind=\"hist\", ax=ax, bins=bins, alpha=0.5)\n",
    "pp.truncate(low=0.15, high=1.85).right.plot(kind=\"hist\", ax=ax, bins=bins, alpha=0.5)\n",
    "pp.truncate(low=0.3, high=1.7).right.plot(kind=\"hist\", ax=ax, bins=bins, alpha=0.5)\n",
    "plt.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, method recenter replaces the outliers with the central value `1.0` or with another value of choice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 5))\n",
    "bins = 50\n",
    "pp.right.plot(kind=\"hist\", ax=ax, bins=bins, alpha=0.5)\n",
    "pp.recenter().right.plot(kind=\"hist\", ax=ax, bins=bins, alpha=0.5)\n",
    "pp.recenter(low=0.3, high=1.7).right.plot(kind=\"hist\", ax=ax, bins=bins, alpha=0.5)\n",
    "pp.recenter(low=0.5, high=10, value=2.5).right.plot(kind=\"hist\", ax=ax, bins=bins, alpha=0.5)\n",
    "plt.tight_layout();"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python3 (sandy-devel)",
   "language": "python",
   "name": "sandy-devel"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}