{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7c1065dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\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",
    "plt.rc('text', usetex=True)"
   ]
  },
  {
   "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. 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": 6,
   "id": "b71529d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x395.55 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "my_correlator.show(auto_gamma=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c659557e",
   "metadata": {},
   "source": [
    "## Manipulating correlators"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "416cf39a",
   "metadata": {},
   "source": [
    "`Corr` objects can be shifted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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": 8,
   "id": "127a661d",
   "metadata": {},
   "outputs": [],
   "source": [
    "symmetrised_correlator = my_correlator.symmetric()\n",
    "symmetrised_correlator.tag = 'Symmetrised correlator'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d733872",
   "metadata": {},
   "source": [
    "We can compare different `Corr` objects by passing `comp` to the `show` method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8e264aed",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x395.55 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": 10,
   "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 priodicity of the lattice in order to obtain the cosh effective mass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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 form the plateau at the center of the lattice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1d6ea22a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x395.55 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "periodic_m_eff.show([4,47], comp=m_eff, ylabel=r'$am_\\mathrm{eff}$')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3762e68",
   "metadata": {},
   "source": [
    "Arithmetic operations and mathematical functions are also overloaded for the `Corr` class. We can compute the difference between the two variants of the effective mass as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e56d164c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x395.55 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "difference_m_eff = np.abs(periodic_m_eff - m_eff)\n",
    "difference_m_eff.show([0, 47], logscale=True, 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": 19,
   "id": "165550d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x395.55 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, there is another reason, why one should use a **Corr** instead of a list of **Obs**. \n",
    "Missing values are handled for you. \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."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6479a999",
   "metadata": {},
   "source": [
    "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. \n",
    "\n",
    "The important thing is that, whatever you do, correlators keep their length **T**. So there will never be confusion about how you count timeslices. You can also take a plateau or perform a fit, even though some values might be missing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "f3c4609c",
   "metadata": {},
   "outputs": [],
   "source": [
    "assert first_derivative.T == my_correlator.T == len(first_derivative.content) == len(my_correlator.content)\n",
    "assert first_derivative.content[0] is None\n",
    "assert first_derivative.content[-1] is None"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fcbcac4",
   "metadata": {},
   "source": [
    "There is a range of addtional methods of the `Corr` class which can be found in the documentation."
   ]
  }
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