pyerrors/examples/02_correlators.ipynb

{
 "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 preprocessed pickle files which contain a list of `pyerror` `Obs`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c49ff771",
   "metadata": {},
   "outputs": [],
   "source": [
    "correlator_data = pe.load_object('./data/correlator_test.p')  "
   ]
  },
  {
   "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.correlators.Corr(correlator_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5f954607",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x0/a\tCorr(x0/a)\n",
      "------------------\n",
      "8\t548(13)\n",
      "9\t433(11)\n",
      "10\t343.1(8.6)\n",
      "11\t273.2(6.6)\n",
      "12\t217.5(5.6)\n",
      "13\t172.9(4.9)\n",
      "14\t137.6(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 640x395.55 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": "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": [
    "And we can compare different `Corr` objects by passing `comp` to the `show` method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8e264aed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "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)"
   ]
  },
  {
   "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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
      "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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
      "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)"
   ]
  },
  {
   "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 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])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ff177781",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}