{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7c1065dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import pyerrors as pe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "20f67709",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('./base_style.mplstyle')\n",
    "import shutil\n",
    "usetex = shutil.which('latex') not in ('', None)\n",
    "plt.rc('text', usetex=usetex)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5764fd0",
   "metadata": {},
   "source": [
    "We can load data from a preprocessed file which contains a list of `pyerror` `Obs`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fbfa65f5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data has been written using pyerrors 2.0.0.\n",
      "Format version 0.1\n",
      "Written by fjosw on 2022-01-06 11:11:19 +0100 on host XPS139305, Linux-5.11.0-44-generic-x86_64-with-glibc2.29\n",
      "\n",
      "Description:  Test data for the correlator example\n"
     ]
    }
   ],
   "source": [
    "correlator_data = pe.input.json.load_json(\"./data/correlator_test\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae93c7c2",
   "metadata": {},
   "source": [
    "With this list a `Corr` object can be initialised"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "33a8fdec",
   "metadata": {},
   "outputs": [],
   "source": [
    "my_correlator = pe.Corr(correlator_data)\n",
    "my_correlator.gamma_method()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5f954607",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Corr T=96 N=1\n",
      "x0/a\tCorr(x0/a)\n",
      "------------------\n",
      "8\t 548(13)\n",
      "9\t 433(11)\n",
      "10\t 343.1(8.6)\n",
      "11\t 273.2(6.6)\n",
      "12\t 217.5(5.6)\n",
      "13\t 172.9(4.9)\n",
      "14\t 137.6(4.6)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "my_correlator.print([8, 14])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b00d670b",
   "metadata": {},
   "source": [
    "The `show` method can display the correlator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b71529d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "my_correlator.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c659557e",
   "metadata": {},
   "source": [
    "## Manipulating correlators"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7f37e9f",
   "metadata": {},
   "source": [
    "Arithmetic operations are overloaded for `Corr` objects as is the case for `Obs` objects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "bcc9b40e",
   "metadata": {},
   "outputs": [],
   "source": [
    "new_correlator = 1 + 1 / my_correlator ** 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "416cf39a",
   "metadata": {},
   "source": [
    "In addition to that various useful methods for the manipulation of `Corr` objects are implemented. A correlator can for example be periodically shifted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e8d65dd5",
   "metadata": {},
   "outputs": [],
   "source": [
    "shifted_correlator = my_correlator.roll(20)\n",
    "shifted_correlator.tag = r'Correlator shifted by $x_0/a=20$'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "634dd613",
   "metadata": {},
   "source": [
    "or symmetrised"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "127a661d",
   "metadata": {},
   "outputs": [],
   "source": [
    "symmetrised_correlator = my_correlator.symmetric()\n",
    "symmetrised_correlator.tag = 'Symmetrised correlator'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d733872",
   "metadata": {},
   "source": [
    "The full list of `Corr` methods can be found in the documentation.\n",
    "\n",
    "We can visually compare different `Corr` objects by passing `comp` to the `show` method. The argument <code>auto_gamma</code> tells `show` to calculate the y-errors using the gamma method with the default parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8e264aed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "shifted_correlator.show(comp=symmetrised_correlator, logscale=True, auto_gamma=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "232e88af",
   "metadata": {},
   "source": [
    "## Effective mass"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83dc751c",
   "metadata": {},
   "source": [
    "The effective mass of the correlator can be obtained by calling the `m_eff` method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c686f7e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "m_eff = symmetrised_correlator.m_eff()\n",
    "m_eff.tag = 'Effective mass'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a9d13b2",
   "metadata": {},
   "source": [
    "We can also use the periodicity of the lattice in order to obtain the cosh effective mass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5acde8cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "periodic_m_eff = symmetrised_correlator.m_eff('periodic')\n",
    "periodic_m_eff.tag = 'Cosh effective mass'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c658b000",
   "metadata": {},
   "source": [
    "We can compare the two and see how the standard effective mass deviates from the plateau at the center of the lattice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "1d6ea22a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LOLfqaxIRUWdoV1JDyK9QVTMAsgD6az23tFxE+kVkSkSmTp06NY8qEhFRK7UiIOVRHCzCcJIXfJmgNGy64MqdG3hNVU2pakxVY6tXr55v3YmIqEVa0WW3H8CIZztUmhEnIv0ANqrqkCmarXSuiOSCrlmriUd2Ycvxh+eWr70VW265r55LExFRFURVm/9LLqRoAyi0giAi0wC2meKY+R41x4wGnOtb7icWi+nU1FS53XPtWQ7s+WP1xxMRUdVEZFpVY6XlLXkOSVXTZcp7PJuZku9B5/qWExFRZ+JMDUREZAUGJI/JAym8vvdavItFeH3vtZg8kGp3lYiIukbNXXYicqmq/nszKtNOkwdS2PTr+7H05oeAdVuw5tgElqd3YhLA5u2VstCJiKgR5tNC6gcAEbnWWygiVzagPm2z9tCDWJp4CNiwFbhoCbBhK5YmHsLaQw+2u2pERF1hPkkN/0lEdgHYLCKTpkwAxAHc0LCatdhlbx0F1m0pLly3xSknIqKmm09AmoYz15wAeLax1Wmfk5esx5pjE04LyXVswilvX7WIiLrGfLrsZlT1JQDTqvqS+wVgrMF1a6njm27D2fRO4MhB4Pw54MhBnE3vxPFNt7W7akREXWE+LaQeEfkSgA1mxgTAaS1dB+CDDatZi23e3o9JAGsfvR2XvXUUJy9Zj+Ob7mBCAxFRi8x7pgYRuc60jNztbapqZRceZ2ogIrJHM2ZqiInIDgD7APwRQPPnICIiogWrngdj/6CqwwCgqkcaVJ+2mXhkl2kZLXcKzM8Tj+xqb8WIiLpEPS2kjeZZpIiIhOFMivpcQ2rVBs6M3nNn9d4y91AiImqCegJSCsAwgAiAF1WVazQQEdG8zTsgqeofRWTc1kQGIiLqLDWNIYnIBhHZJSKfMEWTIvLZJtSLiIi6TK1JDQk4GXU7RORVOKu2bm54rYiIqOvU2mWXNV10DwPOs0jwrNpKREQ0X7UGpFnv8hPeB2OJiIjqUWuXXRhAVkT2esaRiIiI6lZrQIoA6IUz2/cOEfm/IrKv8dUiIqJuU2uX3ZSZleEIgMcAQESWN7xWRETUdWptIWnpyrCqGjgLqYgkRCRuvkcrHNMvIkkRiZuykIiMlDk+KSJR8zVY4+sgIiLL1NpCuhlAv1kpdhxARlVfrnSCiIQA9KrqgNkeh9Pt5z0mCiCnqmmzfQbACjhdhP0ikjCHhgHsVdVRs2/M1GGgxtdBRESWqTUgzahqWEQ2wFmy/L+JyHJVrbR0+Q4AM57tvIhEVTXrKQsD6APgBpZZtyWlqivcg0Qk4QYtOM9ATZlziYiow9XaZbdfRD6rqkdU9WFV3REQjAAghOJnlWZREkRUtbSVE1bVrDdomVZSxnNMxFynbLceERF1jpoCkqr+UVUfd7dF5HOlY0pVCpXbYYJLX0lZCEBEVfOeuqRUNWeCVlxEIiXn9IvIlIhMnTp1ah5VJCKiVqp1Lrufi8ik+xySqj4GZ9mJSvIoDkBhADm/A00raJ+qZkp2DcPTOjIJEN5EhtnSa5mAFVPV2OrVqwOqSERE7VZrl10SzpiQ+xzSH+B0nVWyH8BGz3aoZPwIQCGxIauqWRGJlLR44iju9suhuPsurKq+QY6IiDpDrUkNWvIc0pdEZFvACXkRGXdTueEkIwBw1lUHsA1OUHsWTjID4ASYFSXXyXl+zppWUsScW9TFR0REnafWgLTRJDU87inToJM8mXGl5T3mxyycNO9y5/f4lPlek4iIOlOtSQ33AvjPIvKqiDwkIntR8kwRERHRfNS8Yqyq7haRJEwyg0lsICIiqsu8ljD3jCMRERE1RK1ZdkRERE3BgERERFZgQCIiIiswIBERkRUYkIiIyArzyrLrVhOP7MKW4w/PLV97K7bccl8bakREtHCIauBECx0vFovp1NRUYy+6ZzmwJ3CxXCIiKiEi06oaKy1nlx0REVmBAalGkwdSeH3vtXgXi/D63msxeSDV7ioRES0IHEOqweSBFDb9+n4svfkhYN0WrDk2geXpnZgEsHl7f7urR0TU0dhCqsHaQw9iaeIhYMNW4KIlwIatWJp4CGsPPdjuqhERdTwGpBpc9tZRYN2W4sJ1W5xyIiKqCwNSDU5esh44NlFceGzCKSciorowINXg+KbbcDa9EzhyEDh/DjhyEGfTO3F8023trhoRUcdjUkMNNm/vxySAtY/ejsveOoqTl6zH8U13MKGBiKgB+GDsfPHBWCKieeGDsUREZDV22dVgzlx2e5Y75ZzLjoiobuyyIyKilirXZdeSFpKIJADkAYQA5FQ1W+aYMIAeAGOqmjHlSQBJc1hcVUervSYREXWOpgckEQkB6FXVAbM9DqC35JgonKCSNttnAKwwuyMAxgBkPNcIvCYREXWWViQ17AAw49nOmwDkFQYw4Nme9RwzAqfVNFLjNYmIqIO0IiCF4HStuWbhBKACVS20foywpwsuYo4PiYgblAKvKSL9IjIlIlOnTp2q8yUQEVGztSvLLlRuhwk6fe62qqY8+x4WkUg11zTnpQAnqaGOulaNK8oSEc1fKwJSHsXBIgwg53egSVTY57aOzHbETWSA0xKq6Zqt5AQdE3g8D85uKX8KEREZreiy2w9go2c7VCbLLgogq6pZEYmYllAOQMZzWFhVc9Vek4iIOkfTW0iqmheRcRGJm6JCcoKITAPYBmec6Fk4yQyAE3hWmGMSJjhFYLryKl2TiIg6Ex+MbbDJAymsPfSgZ/LV2zj5KhGRR1sfjO0WXOKciGj+OLlqA3GJcyKi+WMLqYGCljhnWjgRUXkMSA108pL1WHNswmkhucwS52vAtHAiokrYZddAXOKciGj+2EJqIC5xTkQ0f0z7bpYyS5wzLZyIuh3Tvi0QlBbOpAci6mZsITVQUEB5fe+1WHPz94uTHo4cxOuP3o41wy8Xn1SmhUVE1OnYQmqBoiw6b7n5HpQWTkTUzZhl10InL1kPHJsoLjRp4a7JAym8vvdavItFeH3vtZg8kAIRUTdgC6mFjm+6DcvTO53ZHNZtAY5NmLTwO7AGHGMiou7GMaQWq5RlxzEmIuoGHEOyxObt/cD2fmDPcqwZfhlrPPs4xkRE3YxjSBapZoyJiGihYgupheaMAe1Z7pSbMaCgMSbA0+WHRTi591o+WEtzcKyROhXHkCxTaYypkPRQErAOfYjTE1ExzghCNis3hsSAZCufpIWgpAd+MiYg+IPLxCO7sPjoC1h7yVlcdu4ETi65AsffWop31n/cir+T747/Bvc/++qc8ju2fRB39l7VhhpRozGpYQEISnpo9/IWDIh2WHvoQefRAfeDi7tQ5KO3A9v7sfiyq7Bp9meFgOU+XnDosta82Qf9ndy5+DH81cWPzwmYmxd/FsBwS+pI7cGA1EGC1lsC2jvG1O6A2C2C3tCDPrgEBaxmC/o7mfyPldj0/jfnBMzJ/1iJzWALaiFjlp1FJh7ZZf6DOskO7s8Tj+wCELzekttVs+bm72PR109izc3fx6Zf38/ZHhaYLbfch8mee/H6JRucGT0u2YDJnnsLrdCgbE0bHi+oNCPJ2kMPOsFow1bgoiUXAuahBwEAdy5+DN9b/ACuwCkI3sUVOIXvLX4Ady5+rGX1p+ZoSQtJRBIA8gBCAHKqmi1zTBhAD4AxVc0ElCcBJM3pcVUdbfLLaLqgufCC1ltq9idfdsm1RlBCQtCMHkHZmtW0tJv9+irVPyhgPhH6PH6x6E3se/93cfm5Y3htyTp8761PAaHP40awBdXJmh6QRCQEoFdVB8z2OIDekmOicAJV2myfAbCiXLk5LQJgDEDGvXY3aOeDtdV0yQV1GTYiqC3kDLIDI19AfNHUnDfrA//7l9g+9C8Agj94/OI9f43/mT+KwR99tfCGPfrmjdjwnr/GZgBPLf87/F16J5Z5Atab6Z14avkX8MUWvMag+gcFzJef/iG++f7HC/X/wLEJfDO9E6NPL8aN192NDavei6VLLsLZc+cLpy9dchE2rHpvYZtBy06taCHtADDj2c6LSLSklRQG0AfADSyzJhj5lptzRwBMmWMIwZ98g4JBNcGiUsAJ+uQL1D/OVM0bdj2anYEWdP3N7/4vLN0x981686O3F64R9MHjzsWPAUseAM45uz5w7rf4/pIHgMXvAzCML/75eUw+vwxrf3Sbpw7L8MXYeTRC0GsMqn9QC++LMMHIc4+WJR7CF3/0VQB3494nX0Tvu1MYfP9TnoD8X3Hvk2dx43Wfce5R71WFwHPl7p/it/d8siGvvVUWakBtRUAKwemuc82iJIiYbriMpyjsCVjlyiMAcgBCIjKiqkPea4pIP4B+AFi3bl2dL6EzBP1H3nLLfZg8cNWc1sWWKoNFUMBpxWB50Bt2vQGl2RloQdevppUb2OV2/bDzVc71w9js2b/GfLnq/eAS9BqD6h/Uwrv83DHfe3T5uWMAgNi5KewNPVHUgronvRPDeQD4TPn74mH7G/6dvVdhw6r34t5nDuNE/iyuCC3FXTdcjRuvu6LdVSuodA/LUtWmfgEYBNDv2U4CSFQ4fgTOmFBV5WbfNIBIuWv29PTognP3pb7FL/4kqb//9kf0/N0h/f23P6Iv/iRZtO/N0b9Qzb2g+s7bqrkX9M3Rv5hzTLnzf//tjzjneuVecMpV9fzdIee6Xu+87ZTX8BoqCfodQa/xVz/8R33x6zH9/bf+0nmN3/pLffHrMf3VD/+xqtdYr6DrV/P7q/l3rFelv4MiPv+GQa8hsP7Pfdu5bunXc99WVdU3vtPje/03vtNT1e+v5nd4rR96ak7Zd35+WNcPPTXn6zs/P+x/n2oUdP0fZ3+nH/raz4r2fehrP9MfZ3/XkN/faKX3EMCU+rxXt6KFlIfTSnKF4bRs5jAJDPu0JOmhtNxsR/RCIsNsg+tspaCph4DKY0xBLZh6B5urHSyvJzU96HfU+wxOI8bhKo1x1dtdBQQnt9Srmq7XSv+GQa8xsP4BLbxl8d1458dfxuLP/KBwj9758ZexrPduAMCfve3/+//sbc+/4fXDeCL0edz7zGG8ln8Dl4feO6eF8cRLJ3DvM4cBAB+757mi/UEtlHpbWEFdivc+c7hojAwAzp47j3ufOWxVK6lWrQhI++G0blyh0oADFBIbsqqaE5EIAJif55TDCWjeoBZWVd8gt5AEZeEFBax6n08JCgbVzsVXz5pPk4s+grjP75hcFMN2BL8Z1vsagwSNcQVd/52Tv8GhP80d33nn5G+Kfk+lDx71qveDSzX3sJ76f/f1D+PIHz6FwR99FR84dxS/W7Ieo29+Chte/zDuvAb40/siuNTn9//pfRFcajafeOkEhh9/xbypL8KJ/FkMP/4KAODG664o2Y+a9zciYFUKiK/lz/rem3LlnaLpAUlV8yIyLiJxU1QITiIyDWAbnPGgZ+EkLQBOgHGz7OaUm3MTJkBF4CQ+dL2ggBX0RlHvp/dqPrkHvdkFjXNtH/oX59N5ye/YbvbX+xqDAl5QwAwa46pmnM+rdHwHfnXwaSnXo96gHvQa661/UNLGpX8zDDz5FeDTDxR+P578Ci79m28UrhHUwqh3f1DACsoEDDr/8tBSnPAJPpeHlgKwfwysnJY8h6QmbdunvMf8mMWFdG7vft/yStek8up9PqWagBP0yTcwIFTRXVT4HZj7hl3vawwKeEEBs+7uqioEffCoV71BPSgpoe76ByVtnH4VyB8F/vVm4O03gYuXAW+/4ZQbr+XP4lMX/QqDy4oz8Q7k/4vZ/yYAmXNppzy4hdLsgHfXDVcXBSzACWh33XA1AAQGPFsDFqcO6iJBb4bVjl/U01VU7xhQkKAur6AWUNFrxNyAV293VWnrYM1bR7Bm+i5MnPyNNQ8X1xvUg1owTRcUsAB84f1TGLx4biZe+O2LAXwSl4eWlWmBLDPfK7dQggJWvfvdrrtyXYJBAc3WLD0GpC4S9GYYFLAa0VUU9GZXb1JBUJdXUAsoSOD4SkDAa3brphGCgnrgB5cqAkK7DS47gGU3zn2WafCJfwBwN+664Wr84sf/A39/yU+KZoP4qxu+BACBLZSggFXvfsAJSjdedwWu3P1T/HL3J4qOCwpoQV2C7cLlJ8ifz/IXQaqdhaFSFlrQEhvt9u6eFVj09ZPOHGuu8+fw7j9fhkV7zgBY2DNJuDr+Nf7TCuBrc/8d8a3LgLvPAK+k8c74P83J5FvcezdwTQLAhaQDvxZG6Rs+4ASsvZ+9xneMqdb9QV1uH7vnOd+AdkVoKX65+xOB+xvdpVeaKcjlJyhQvS2gaj/9V+r2q6bbsJ1qyiCDf1JCp+uEbsdAq652kh1K/h2xymnh4OB9TjDytKAWf+YHwNODwDUJTDyyCzcefxg3AsB7APw/AE8CE1nn/8qR02/4dpkdOf0GAATuD+qS86aF+wlqwQW1oNo1kwUDEhXY0J3U7Gds6mV7wGwFG/5O6rZ1l28mHrY5mXh6+jDEp+tYTx+GwNyDVz4KHLwPOPVrYPWHgK27sMW0noICRtB+oHKXXJCggFdNl2CQZiRGMCCRVWz/9F3tc0Jkt+++/mEcObW95Fmm7YVnmaRMC0rcFtQraeDZb84NaEChS6+u+pW82V+5+6cA5vdgrZ+gFhRQ+Tmo0t/RqFYUx5CofeYxTkXUcH5/h+UCzrZvOAHnBx8F/nZ0zlgnnh4Evvxvra3/PNUzBlaqXEAq9zs4hkRWaPZDnUQN4bZynh680CXnBiMAOH3YNxsUpw+3tp7zVNoCO5E/i7/f9zKOnH4Dd/Ze1ZCpiSpl8pXDgEQttSDGH6g7XJNwvvYsn9vqCUqKeH4v8MI9c6/58d1WpMQHdek1YmqiSkGtHC5hTkTd5/m9pqvOaaEXfn5+b3Xnu0kRRw466eJHDjrbW3c5+68fBj73CLD6zwGI8/1zj1gRjKpRLrmhlqSH+QQ1tpCIqPsEPbxb2sJxA5fbwgnq0mty0kOzVZP0EKRSJt9vy5zDpAYioloFdckt8KSHao6plBjxmegHfJMaGJCIiBotaCaIDlIpgy4oE6/WLDuOIRERNZqb9ODlTXpYAKpJWrjxuisKD/X+cvcnAjP0GJCIiBotKOlhAWjGIoFMaiAiarSgpAfLVTNTRCOmHyrFgERE1GilSQ+n/g/w2C3OIoHXD1/Yf/F7ixcR7JDnlIDGZOKVYkAiImq0oLTyVR8EQuvnpoWv+mDr6linoBnJ54NjSERErXbwPicYbdjqZOJt2OpsH+ys6bNqTVoIwoBERNRqHT4XXrMwIBERtVoXpIXPR0vGkEQkASAPIAQgp6rZMseEAfQAGFPVTKVzq7kmEZGVAhYI7FZND0giEgLQq6oDZnscQG/JMVE4QSVtts8AWFHu3GquSURkrdOvAvmjwL/eXJxld3ruCqzdpBUtpB0AZjzbeRGJlrRowgD6AAyY7VkTpGJ+55YrZyuJiDpCrZO7uixJCwfqX9XWTysCUghO15prFk4AKjDdcxlPUVhVsyISL3Nu4DVFpB9APwCsW7du/rUnImo1b8CydGXloGeVKgWsctr1HFKo3A4RGYHTWqr13KJyVU0BSAHO5Ko11Y6IiOpSKWD9Q5lzWpFll0dxsAgDyPkdaBIV9rkJDRXOrfqaREQd6ZW0s4wFxPn+SrrdNWq6VrSQ9gMY8WyHymTZRQFkVTUnIpFK54pIrpprEhF1pA5f4G++WrIekidFG0BhzAgiMg1gG4AIgGfhjAUBzhjSioBzfcv9cD0kIuooC2CBv0rKrYfUkjEkN53bp7zH/JgFsKLGcxd++5WIulOXzuTAmRqIiGzTpTM5MCAREdmmCxb488PlJ4iIbNPhC/zNFwMSEZGNrkk4X3uWL4hEhmqwy46IiKzAFhIRkW1K57Lbs9z57s5l1wFz3c1HS55Dajc+h0REC5alc91VUu45JHbZERGRFRiQiIg60QKc645jSEREnWaBznXHFhIRUac5eJ8TjDZsBS5a4nz/9ANOeQdjQCIi6jQLdK47BiQiok6zQOe6Y0AiIuo0C3Suu654DklETgE4WsMpqwCcblJ1GsX2OtpeP8D+OtpeP8D+OtpeP2CedVy1TMKXX3rRFUtELz6n8vZr/37+xOk3dTb4zNbUL8B6VV1dWtgVAalWIjLl99CWTWyvo+31A+yvo+31A+yvo+31A+yvYyvrxy47IiKyAgMSERFZgQHJX6rdFaiC7XW0vX6A/XW0vX6A/XW0vX6A/XVsWf04hkRERFZgC4mIiKzAgERERFbg5KoeIpIEkDSbcVUdbWd9AEBEQgD6AeRVNeUpTwDIAwgByKlqth31M3UJwb+O1txPc7/CAHoAjKlqxlOehx33sVwdrbiPpn45ADEAcP+tLbyHfnW04h663Htm49+hy6eOzb+Hqsov8wVgHMAMgGS76+KpUxzAIIB+T1nIW0cA47bV0ab7CSAKIOrZPmPbfSxXR1vuo7lX05bfQ9862nIPS+o5DudN3ap7WK6OrbqHbCEVGwEwBedTqhVUNSMikZLiHXD+MFx5EYlqmz5VlakjYM/9DAPoAzBgtmdFJArnU7Qt99G3jqYubb+PqpqH03KD+bd2l2C25m+xQh0BC+6hRwzOm7vLmnvoUVpHoAX3kGNIxSJwbnZIREbaXZkKQnCa965Z2PEfrZQV91NVM6o64CkKm//sIVhyHyvUEbDkPgKAiMQBJOAET8Cie+jyqSNgyT00H4SmSopDsOgelqkj0IJ7yIDkoaopVXX7b+NlPvXbKtTuCpSy8X6a/0h9FQ4JtagqZZXW0ab7qM54QhbOmGE5odbUxp9fHS27h/kqDgs1uRoV+dWxFfeQXXaGGcCL6IWBumZMUtgoeRT/wYbhDORaw8b7aeq0z9PyyMOy+1haRxvvo+miHRORDCy8h8CcOkZgwT0UkX44XbERAJsBrBSRHCy6hxXqGEUL7iED0gU5FP8RhFW17f+xytgPpz/XFWpzf7Mfq+6n6YbIqmrO88nOqvtYpo5W3EfzRrVRVYdMkfuGZM09rFBHK+6hFmegboaTvJATEWvuYYU6htCCe8iZGjzMp1HA+USVtiEgmf7wATifoEZ0bpoogEI3RVsE1BFo8/00b/TP4sIbVFhVV5h9VtzHKuoItPE+mjckd8bnKAC4n5YtuochVK4jYMH/bfNvPQLnDX7EvOFbcQ9dFeoINPEeMiAREZEVmNRARERWYEAiIiIrMCAREZEVGJCIiMgKDEhEHcxklhEtCAxIRJ1tuN0VIGoUBiSiDmVaR39odz2IGoUBiahz7QCQbncliBqFAYmoc220YTYRokbhXHZEbWLmq4vCmcQyibkTWAadO+NTPogLc44NqGpv42pM1FxsIRG1T1xV0wAm4azCmcaFBfogIv0iEjeThpZKwJnYFJ7jR+Asf52Gs/yCjWtkEZXFgETUPm5A2QxgDABUdSNQmAx01jNRbbzk3JXeNWtMiylhghHgtLbaOkEnUa0YkIjaxBNQEu60/55lJzbjwuzPOQCFrjczE3Pp8tKlAajX5xgiqzEgEbWBiAyaLrkoTOAxwcgNSCEUL4IW8vx8U5nlCfKen3eYReoSPscRWYlJDUTtkcWFIJN0A4enyy2P4jGgfKWLqWpaRDZ7uvb2mmvatnAjUVlcD4nIQt4AZZIacp4WT87CFYKJ6sYuOyILmZZS2G3xeLroNjMY0ULFLjsiS7mJDi5OFUQLHbvsiIjICuyyIyIiKzAgERGRFRiQiIjICgxIRERkBQYkIiKyAgMSERFZgQGJiIis8P8BukQRx+TlS3cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "periodic_m_eff.show([4,47], comp=m_eff, ylabel=r'$am_\\mathrm{eff}$', auto_gamma=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "472ab97b",
   "metadata": {},
   "source": [
    "## Derivatives"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d99414fe",
   "metadata": {},
   "source": [
    "We can obtain derivatives of correlators in the following way"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "03007f8a",
   "metadata": {},
   "outputs": [],
   "source": [
    "first_derivative = symmetrised_correlator.deriv()\n",
    "first_derivative.tag = 'First derivative'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c0311739",
   "metadata": {},
   "outputs": [],
   "source": [
    "second_derivative = symmetrised_correlator.second_deriv()\n",
    "second_derivative.tag = 'Second derivative'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "165550d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "symmetrised_correlator.show([5, 20], comp=[first_derivative, second_derivative], y_range=[-500, 1300], auto_gamma=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18c75d20",
   "metadata": {},
   "source": [
    "## Missing Values \n",
    "\n",
    "Apart from the build-in functions, another benefit of using ``Corr`` objects is that they can handle missing values. \n",
    "We will create a second correlator with missing values. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1db86a4c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Corr T=96 N=1\n",
      "x0/a\tCorr(x0/a)\n",
      "------------------\n",
      "0\t 62865(41)\n",
      "1\t 23756(32)\n",
      "2\t 6434(25)\n",
      "3\t 2886(20)\n",
      "4\t 1735(21)\n",
      "5\t 1213(21)\n",
      "6\n",
      "7\t 699(17)\n",
      "8\n",
      "9\n",
      "10\t 343.1(8.6)\n",
      "11\t 273.2(6.6)\n",
      "12\n",
      "13\t 172.9(4.9)\n",
      "14\n",
      "15\n",
      "16\t 88.0(3.9)\n",
      "17\t 70.6(3.2)\n",
      "18\t 56.6(2.6)\n",
      "19\t 45.3(2.1)\n",
      "20\n",
      "21\t 29.2(1.4)\n",
      "22\t 23.4(1.2)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "new_content=[(my_correlator.content[i] if i not in [6,8,9,12,14,15,20] else None ) for i in range(my_correlator.T) ] # We reuse the old example and replace a few values with None\n",
    "correlator_incomplete=pe.Corr(new_content)\n",
    "\n",
    "correlator_incomplete.print([0, 22]) # Print the correlator in the range 0 - 22"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "602d81fa",
   "metadata": {},
   "source": [
    "We see that this is still a valid correlator. It is just missing some values. \n",
    "When we perform operations, which generate new correlators, the missing values are handled automatically.\n",
    "\n",
    "Some functions might also return correlators with missing values. We already looked at the derivative. \n",
    "The symmertic derivative is not defined for the first and last timeslice. Whatever operation is performed on a `Corr` object, the correlators keeps its length **T**. So there will never be confusion about how to count timeslices. One can also take a plateau or perform a fit, even though some values might be missing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e2a52d30",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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