{
 "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)"
   ]
  },
  {
   "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 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": [
    "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": "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": 26,
   "id": "1db86a4c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "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",
       "23\t 18.90(99)\n",
       "24\t 15.26(74)\n",
       "25\t 12.26(54)\n",
       "26\t 9.82(40)\n",
       "27\t 7.84(32)\n",
       "28\t 6.21(24)\n",
       "29\t 4.93(18)\n",
       "30\t 3.93(13)\n",
       "31\t 3.142(92)\n",
       "32\t 2.519(66)\n",
       "33\t 2.013(49)\n",
       "34\t 1.609(41)\n",
       "35\t 1.287(35)\n",
       "36\t 1.024(28)\n",
       "37\t 0.820(23)\n",
       "38\t 0.661(20)\n",
       "39\t 0.532(16)\n",
       "40\t 0.429(14)\n",
       "41\t 0.348(11)\n",
       "42\t 0.2858(85)\n",
       "43\t 0.2357(80)\n",
       "44\t 0.1985(87)\n",
       "45\t 0.1722(90)\n",
       "46\t 0.1558(90)\n",
       "47\t 0.1473(94)\n",
       "48\t 0.1453(98)\n",
       "49\t 0.150(10)\n",
       "50\t 0.161(10)\n",
       "51\t 0.179(11)\n",
       "52\t 0.205(13)\n",
       "53\t 0.240(17)\n",
       "54\t 0.288(21)\n",
       "55\t 0.349(27)\n",
       "56\t 0.427(35)\n",
       "57\t 0.524(42)\n",
       "58\t 0.648(50)\n",
       "59\t 0.804(63)\n",
       "60\t 0.997(77)\n",
       "61\t 1.239(91)\n",
       "62\t 1.55(11)\n",
       "63\t 1.96(14)\n",
       "64\t 2.46(16)\n",
       "65\t 3.08(19)\n",
       "66\t 3.83(22)\n",
       "67\t 4.76(26)\n",
       "68\t 5.96(31)\n",
       "69\t 7.47(37)\n",
       "70\t 9.36(49)\n",
       "71\t 11.75(62)\n",
       "72\t 14.75(75)\n",
       "73\t 18.53(87)\n",
       "74\t 23.2(1.0)\n",
       "75\t 29.1(1.2)\n",
       "76\t 36.4(1.5)\n",
       "77\t 45.5(1.9)\n",
       "78\t 57.0(2.5)\n",
       "79\t 70.9(3.3)\n",
       "80\t 88.4(4.4)\n",
       "81\t 110.7(5.9)\n",
       "82\t 138.2(7.3)\n",
       "83\t 171.4(8.4)\n",
       "84\t 213(10)\n",
       "85\t 266(13)\n",
       "86\t 336(15)\n",
       "87\t 425(17)\n",
       "88\t 540(19)\n",
       "89\t 688(20)\n",
       "90\t 892(22)\n",
       "91\t 1196(28)\n",
       "92\t 1716(33)\n",
       "93\t 2859(32)\n",
       "94\t 6411(36)\n",
       "95\t 23726(44)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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\n"
   ]
  },
  {
   "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",
    "Here is an example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "034d1fdf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Corr T=96 N=1\n",
       "x0/a\tCorr(x0/a)\n",
       "------------------\n",
       "0\t-0(115)\n",
       "1\t-1(58)\n",
       "2\t 1.0(2.7)\n",
       "3\t 1(33)\n",
       "4\t-0(57)\n",
       "5\t 0(56)\n",
       "6\n",
       "7\t-1(27)\n",
       "8\n",
       "9\n",
       "10\t-1(11)\n",
       "11\t 0(19)\n",
       "12\n",
       "13\t-0(13)\n",
       "14\n",
       "15\n",
       "16\t 0(12)\n",
       "17\t-0.9(3.7)\n",
       "18\t 0.1(7.8)\n",
       "19\t-0.8(4.1)\n",
       "20\n",
       "21\t-0.4(3.9)\n",
       "22\t 0.9(1.8)\n",
       "23\t 0.2(2.9)\n",
       "24\t 0.97(50)\n",
       "25\t-0.80(97)\n",
       "26\t-0.93(45)\n",
       "27\t-0.999(52)\n",
       "28\t-0.22(71)\n",
       "29\t 0.80(32)\n",
       "30\t-0.70(27)\n",
       "31\t-0.00(28)\n",
       "32\t 0.957(58)\n",
       "33\t-0.24(14)\n",
       "34\t-0.993(14)\n",
       "35\t-0.658(79)\n",
       "36\t 0.070(84)\n",
       "37\t 0.630(54)\n",
       "38\t 0.917(23)\n",
       "39\t 0.9997(12)\n",
       "40\t 0.960(11)\n",
       "41\t 0.865(17)\n",
       "42\t 0.756(17)\n",
       "43\t 0.650(18)\n",
       "44\t 0.561(22)\n",
       "45\t 0.494(23)\n",
       "46\t 0.451(24)\n",
       "47\t 0.428(25)\n",
       "48\t 0.422(27)\n",
       "49\t 0.435(27)\n",
       "50\t 0.464(27)\n",
       "51\t 0.511(28)\n",
       "52\t 0.577(32)\n",
       "53\t 0.660(38)\n",
       "54\t 0.760(41)\n",
       "55\t 0.867(41)\n",
       "56\t 0.958(30)\n",
       "57\t 1.00000(28)\n",
       "58\t 0.931(55)\n",
       "59\t 0.67(14)\n",
       "60\t 0.15(23)\n",
       "61\t-0.54(23)\n",
       "62\t-0.999(17)\n",
       "63\t-0.40(37)\n",
       "64\t 0.88(23)\n",
       "65\t 0.19(57)\n",
       "66\t-0.89(31)\n",
       "67\t 0.99(10)\n",
       "68\t-0.83(52)\n",
       "69\t-0.4(1.0)\n",
       "70\t 0.2(1.4)\n",
       "71\t-0.6(1.4)\n",
       "72\t 0.3(2.2)\n",
       "73\t-0.8(1.5)\n",
       "74\t 0.4(2.8)\n",
       "75\t-0.7(2.6)\n",
       "76\t 0.7(3.1)\n",
       "77\t-1.00(55)\n",
       "78\t 0.99(84)\n",
       "79\t-0.7(6.9)\n",
       "80\t 1.0(4.0)\n",
       "81\t-0.8(9.3)\n",
       "82\t 0(22)\n",
       "83\t-1(13)\n",
       "84\t-0(31)\n",
       "85\t 1(24)\n",
       "86\t 1.0(5.0)\n",
       "87\t-1(43)\n",
       "88\t-1(14)\n",
       "89\t-1(22)\n",
       "90\t-1(35)\n",
       "91\t-1(43)\n",
       "92\t 1(43)\n",
       "93\t 1(18)\n",
       "94\t-0(105)\n",
       "95\t 1(17)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "some_new_corr=np.sin(my_correlator+2*correlator_incomplete)\n",
    "\n",
    "some_new_corr"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6479a999",
   "metadata": {},
   "source": [
    "Some functions might also return correlators with missing values. We already looked at the forward derivative. \n",
    "The forward derivative is not defined for the last value. \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. \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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[-1]==None\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fcf947ea",
   "metadata": {},
   "source": [
    "You can also take a plateau or perform a fit, even though some values might be missing. "
   ]
  },
  {
   "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."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2fbe1263",
   "metadata": {},
   "source": [
    "## Matrix Correlators\n",
    "\n",
    "A correlator can not only contain a list of Obs, but also a list of matrices of obs. \n",
    "This is useful, if there are multiple sources and sinks used. In our example, the sources have a different Gaussian smearing applied. \n",
    "\n",
    "We will load such a correlator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b529a36c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data has been written using pyerrors 2.0.0+dev.\n",
      "Format version 0.1\n",
      "Written by jan on 2022-01-27 10:49:51 +0100 on host endwings, Linux-5.13.0-27-generic-x86_64-with-glibc2.10\n",
      "[[Obs[0.95214(67)] Obs[0.01240(11)] Obs[0.005965(72)] Obs[0.002719(40)]]\n",
      " [Obs[0.01241(12)] Obs[0.004389(60)] Obs[0.002672(41)] Obs[0.001432(25)]]\n",
      " [Obs[0.005975(74)] Obs[0.002672(41)] Obs[0.001741(29)] Obs[0.000990(18)]]\n",
      " [Obs[0.002729(41)] Obs[0.001433(25)] Obs[0.000990(18)] Obs[0.000596(12)]]]\n"
     ]
    }
   ],
   "source": [
    "matrix_V1V1= pe.input.json.load_json(\"./data/matrix_correlator_V1V1\")\n",
    "\n",
    "print(matrix_V1V1.content[0]) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "617f478b",
   "metadata": {},
   "source": [
    "We printed out the content at timeslice 0. As we can see, it is a matrix of Obs. \n",
    "\n",
    "Let us try to get the effective mass. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "1e66c026",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Something is wrong\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    matrix_V1V1.m_eff() #This does not work! \n",
    "except:\n",
    "    print(\"Something is wrong\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11e4e0ee",
   "metadata": {},
   "source": [
    "Many methods we could use for regular correlators do not work with matrix-correlators. \n",
    "In order to get the effective mass, we need to convert to a regular correlator first. \n",
    "\n",
    "One way to do it, is to pick a smearing out of the matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "e50b3569",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Corr T=64 N=1\n",
       "x0/a\tCorr(x0/a)\n",
       "------------------\n",
       "0\t 0.95214(67)\n",
       "1\t 0.05672(10)\n",
       "2\t 0.008450(29)\n",
       "3\t 0.0016713(95)\n",
       "4\t 0.0004133(34)\n",
       "5\t 0.0001174(12)\n",
       "6\t 0.00003618(40)\n",
       "7\t 0.00001171(15)\n",
       "8\t 0.000003917(58)\n",
       "9\t 0.000001333(22)\n",
       "10\t 0.0000004611(96)\n",
       "11\t 0.0000001613(34)\n",
       "12\t 0.0000000571(13)\n",
       "13\t 0.00000002021(49)\n",
       "14\t 0.00000000719(18)\n",
       "15\t 0.000000002575(69)\n",
       "16\t 0.000000000927(27)\n",
       "17\t 0.000000000334(11)\n",
       "18\t 0.0000000001197(44)\n",
       "19\t 0.0000000000430(17)\n",
       "20\t 0.00000000001544(66)\n",
       "21\t 0.00000000000553(25)\n",
       "22\t 0.000000000001987(93)\n",
       "23\t 0.000000000000715(34)\n",
       "24\t 0.000000000000258(12)\n",
       "25\t 0.0000000000000933(47)\n",
       "26\t 0.0000000000000338(18)\n",
       "27\t 0.00000000000001230(71)\n",
       "28\t 0.00000000000000445(27)\n",
       "29\t 0.00000000000000163(10)\n",
       "30\t 0.000000000000000606(38)\n",
       "31\t 0.000000000000000244(15)\n",
       "32\t 0.0000000000000001549(82)\n",
       "33\t 0.000000000000000236(17)\n",
       "34\t 0.000000000000000575(46)\n",
       "35\t 0.00000000000000155(12)\n",
       "36\t 0.00000000000000424(32)\n",
       "37\t 0.0000000000000117(11)\n",
       "38\t 0.0000000000000324(30)\n",
       "39\t 0.0000000000000903(96)\n",
       "40\t 0.000000000000252(26)\n",
       "41\t 0.000000000000701(71)\n",
       "42\t 0.00000000000195(18)\n",
       "43\t 0.00000000000545(44)\n",
       "44\t 0.00000000001520(62)\n",
       "45\t 0.0000000000424(16)\n",
       "46\t 0.0000000001186(42)\n",
       "47\t 0.000000000330(11)\n",
       "48\t 0.000000000920(52)\n",
       "49\t 0.00000000257(13)\n",
       "50\t 0.00000000721(34)\n",
       "51\t 0.00000002017(87)\n",
       "52\t 0.0000000567(22)\n",
       "53\t 0.0000001603(58)\n",
       "54\t 0.000000460(16)\n",
       "55\t 0.000001336(41)\n",
       "56\t 0.00000393(11)\n",
       "57\t 0.00001174(27)\n",
       "58\t 0.00003632(71)\n",
       "59\t 0.0001175(19)\n",
       "60\t 0.0004128(47)\n",
       "61\t 0.0016748(97)\n",
       "62\t 0.008456(38)\n",
       "63\t 0.05671(13)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "single_smearing=matrix_V1V1.smearing(0,0)\n",
    "single_smearing"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48b62bb4",
   "metadata": {},
   "source": [
    "**.smearing(i,j)** picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice. \n",
    "But there is a more usefull way to retrieve a single value per timeslice. \n",
    "We might want a linear combination of different sources and sinks. \n",
    "We can formalize this as\n",
    "\n",
    "$$C_{\\textrm{projected}}(t)=v_1^T \\underline{C}(t) v_2$$\n",
    "\n",
    "If we choose the vectors to be $v_1=v_2=(0,1,0,0)$, we should get the same correlator as in the cell above. \n",
    "\n",
    "Thinking about it this way is usefull in the Context of the generalized eigenvalue problem (GEVP), used to find the source-sink combination, which best describes a certain energy eigenstate.\n",
    "A good introduction is found in https://arxiv.org/abs/0902.1265."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "bd96f8bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  -0.71920537,  162.3903938 , -492.21321233,  714.06804297])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vec=matrix_V1V1.GEVP(t0=3,ts=6,state=0)\n",
    "assert len(vec)==matrix_V1V1.N\n",
    "vec"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c80b1f41",
   "metadata": {},
   "source": [
    "As we see, the eigenvector is of length **matrix_V1V1.N** and contains regular floats. \n",
    "We can use it to project the correlator. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "a8d1a547",
   "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": [
    "matrix_V1V1.projected(vec).m_eff().show(comp=single_smearing.m_eff())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a88dd33",
   "metadata": {},
   "source": [
    "There is a lot going on in this line of code. \n",
    "We start with our matrix correlator and we project it, using the vector we got from the GEVP routine. \n",
    "\n",
    "This gives us a new correlator with one Obs per timeslice. We then calculate its effective mass and plot it. \n",
    "We tell the **.plot()** function to show another correlator as a comparison. \n",
    "\n",
    "We can see, that the projected correlator (*blue*) converges to a mass plateau much quicker than the single smearing."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79826bbd",
   "metadata": {},
   "source": [
    "## Example Analysis\n",
    "\n",
    "We can use what we learned so far to perform an actually usefull analysis. \n",
    "The correlator **matrix_V1V1** we looked at corresponds to vector-charmonium. \n",
    "\n",
    "We might be interested in the mass of the $J/\\Psi$ state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "b68f757f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data has been written using pyerrors 2.0.0+dev.\n",
      "Format version 0.1\n",
      "Written by jan on 2022-01-27 10:49:51 +0100 on host endwings, Linux-5.13.0-27-generic-x86_64-with-glibc2.10\n",
      "Data has been written using pyerrors 2.0.0+dev.\n",
      "Format version 0.1\n",
      "Written by jan on 2022-01-27 10:49:51 +0100 on host endwings, Linux-5.13.0-27-generic-x86_64-with-glibc2.10\n",
      "Fit with 1 parameter\n",
      "Method: Levenberg-Marquardt\n",
      "`ftol` termination condition is satisfied.\n",
      "chisquare/d.o.f.: 0.37168849195965686\n",
      "--- The mass was calculated to be 3069.4(9.4) MeV ---\n"
     ]
    },
    {
     "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": [
    "# We do not just have V1V1, but also the two other spacial directions. We can average over them for better statistics. \n",
    "matrix_V2V2= pe.input.json.load_json(\"./data/matrix_correlator_V2V2\")\n",
    "matrix_V3V3= pe.input.json.load_json(\"./data/matrix_correlator_V3V3\")\n",
    "matrix_VnVn=(matrix_V1V1+matrix_V2V2+matrix_V3V3)/3. \n",
    "\n",
    "#We then solve the GEVP to get eigenvectors corresponding to the ground state. \n",
    "\n",
    "vec_ground=matrix_VnVn.GEVP(t0=3,ts=6,state=0)\n",
    "\n",
    "#Now we project the matrix-correlators to get new correlators belonging to the ground state.\n",
    "\n",
    "corr_ground=matrix_VnVn.projected(vec_ground)\n",
    "\n",
    "# We get the effective mass using the periodic cosh method. \n",
    "\n",
    "m_eff_Jpsi=corr_ground.m_eff(variant=\"cosh\")\n",
    "\n",
    "m_eff_Jpsi.show([5,25])\n",
    "\n",
    "#From the plot we can pick a plateau range and get a single value for the mass. \n",
    "\n",
    "m_Jpsi=m_eff_Jpsi.plateau([8,18])\n",
    "\n",
    "\n",
    "# Since the lattice spacing is known, we can multiply with hbar*c/a to see it in physical units \n",
    "\n",
    "m_Jpsi=m_Jpsi*197/0.0653\n",
    "\n",
    "#As a last step we call the gamma method to get the error \n",
    "\n",
    "m_Jpsi.gamma_method()\n",
    "\n",
    "print(\"--- The mass was calculated to be\" , m_Jpsi, \"MeV ---\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fca69475",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}