pyerrors/examples/02_correlators.ipynb

{
 "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') != ''\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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
      "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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
      "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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
      "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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
      "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"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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