pyerrors/examples/02_pcac_example.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append('..')\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pyerrors as pe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Primary observables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can load data from preprocessed pickle files which contain a list of `pyerror` `Obs`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_obs_names = ['f_A', 'f_P']\n",
    "\n",
    "p_obs = {}\n",
    "for i, item in enumerate(p_obs_names):\n",
    "    p_obs[item] = pe.load_object('./data/B1k2_' + item + '.p')    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now use the `pyerrors` function `plot_corrs` to have a quick look at the data we just read in "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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": [
    "pe.plot_corrs([p_obs['f_A'], p_obs['f_P']], label=p_obs_names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Secondary observables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One way of generating secondary observables is to write the desired math operations as for standard floats. `pyerrors` currently supports the basic arithmetic operations as well as numpy's basic trigonometric functions.\n",
    "\n",
    "We start by looking at the unimproved pcac mass $am=\\tilde{\\partial}_0 f_\\mathrm{A}/2 f_\\mathrm{P}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "uimpr_mass = []\n",
    "for i in range(1, len(p_obs['f_A']) - 1):\n",
    "    uimpr_mass.append((p_obs['f_A'][i + 1] - p_obs['f_A'][i - 1]) / 2 / (2 * p_obs['f_P'][i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For more complicated secondary obsevables or secondary obsevables we use over and over again it is often useful to define a dedicated function for it. Here is an example for the improved pcac mass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pcac_mass(data, **kwargs):\n",
    "    if 'ca' in kwargs:\n",
    "        ca = kwargs.get('ca')\n",
    "    else:\n",
    "        ca = 0\n",
    "    return ((data[1] - data[0]) / 2. + ca * (data[2] - 2 * data[3] + data[4])) / 2. / data[3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can construct the derived observable `pcac_mass` from the primary ones. Note the additional key word argument `ca` with which we can provide a value for the $\\mathrm{O}(a)$ improvement coefficient of the axial vector current."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "impr_mass = []\n",
    "for i in range(1, len(p_obs['f_A']) - 1):\n",
    "    impr_mass.append(pcac_mass([p_obs['f_A'][i - 1], p_obs['f_A'][i + 1], p_obs['f_P'][i - 1],\n",
    "                             p_obs['f_P'][i], p_obs['f_P'][i + 1]], ca=-0.03888694628624465))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To calculate the error of an observable we use the `gamma_method`. Let us have a look at the docstring"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mSignature:\u001b[0m \u001b[0mpe\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mObs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgamma_method\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mDocstring:\u001b[0m\n",
       "Calculate the error and related properties of the Obs.\n",
       "\n",
       "Keyword arguments\n",
       "-----------------\n",
       "S -- specifies a custom value for the parameter S (default 2.0), can be\n",
       "     a float or an array of floats for different ensembles\n",
       "tau_exp -- positive value triggers the critical slowing down analysis\n",
       "           (default 0.0), can be a float or an array of floats for\n",
       "           different ensembles\n",
       "N_sigma -- number of standard deviations from zero until the tail is\n",
       "           attached to the autocorrelation function (default 1)\n",
       "e_tag -- number of characters which label the ensemble. The remaining\n",
       "         ones label replica (default 0)\n",
       "fft -- boolean, which determines whether the fft algorithm is used for\n",
       "       the computation of the autocorrelation function (default True)\n",
       "\u001b[0;31mFile:\u001b[0m      ~/.local/lib/python3.6/site-packages/pyerrors/pyerrors.py\n",
       "\u001b[0;31mType:\u001b[0m      function\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "?pe.Obs.gamma_method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can apply the `gamma_method` to the pcac mass on every time slice for both the unimproved and the improved mass."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "masses = [uimpr_mass, impr_mass]\n",
    "for i, item in enumerate(masses):\n",
    "    [o.gamma_method() for o in item]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now have a look at the result by plotting the two lists of `Obs`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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": [
    "pe.plot_corrs([impr_mass, uimpr_mass], xrange=[0.5, 18.5], label=['Improved pcac mass', 'Unimproved pcac mass'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tertiary observables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now construct a plateau as (tertiary) derived observable from the masses. At this point the distinction between primary and secondary observables becomes blurred. We can again and again resample objects into new observables which allows us to modulize the analysis. Note that `np.mean` and similar functions can be applied to the `Obs` as if they were real numbers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result\t 4.79208242e-03 +/- 2.09091228e-04 +/- 1.90500140e-05 (4.363%)\n",
      "  t_int\t 1.09826949e+00 +/- 1.84087104e-01 S = 2.00\n"
     ]
    }
   ],
   "source": [
    "pcac_plateau = np.mean(impr_mass[6:15])\n",
    "pcac_plateau.gamma_method()\n",
    "pcac_plateau.print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also use a weighted average with given `plateau_range` (passed to the function as kwarg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def weighted_plateau(data, **kwargs):\n",
    "    if 'plateau_range' in kwargs:\n",
    "        plateau_range = kwargs.get('plateau_range')\n",
    "    else:\n",
    "        raise Exception('No range given.')\n",
    "    \n",
    "    num = 0\n",
    "    den = 0\n",
    "    for i in range(plateau_range[0], plateau_range[1]):\n",
    "        if data[i].dvalue == 0.0:\n",
    "            raise Exception('Run gamma_method for input first')\n",
    "        num += 1 / data[i].dvalue * data[i]\n",
    "        den += 1 / data[i].dvalue\n",
    "    return num / den"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result\t 4.78698515e-03 +/- 2.04149923e-04 +/- 1.85998184e-05 (4.265%)\n",
      "  t_int\t 1.06605715e+00 +/- 1.79069383e-01 S = 2.00\n"
     ]
    }
   ],
   "source": [
    "w_pcac_plateau = weighted_plateau(impr_mass, plateau_range=[6, 15])\n",
    "w_pcac_plateau.gamma_method()\n",
    "w_pcac_plateau.print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case the two variants of the plateau are almost identical\n",
    "\n",
    "We can now plot the data with the two plateaus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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": [
    "pe.plot_corrs([impr_mass, uimpr_mass], plateau=[pcac_plateau, w_pcac_plateau], xrange=[0.5, 18.5],\n",
    "              label=['Improved pcac mass', 'Unimproved pcac mass'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Refined error analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are two way of adjusting the value of S. One can either change the class variable `Obs.S_global`. The set value is then used for all following applications of the `gamma_method`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result\t 4.79208242e-03 +/- 2.02509166e-04 +/- 2.05063968e-05 (4.226%)\n",
      "  t_int\t 1.03021214e+00 +/- 1.94552148e-01 S = 3.00\n"
     ]
    }
   ],
   "source": [
    "pe.Obs.S_global = 3.0\n",
    "pcac_plateau.gamma_method()\n",
    "pcac_plateau.print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively one can call the gamma_method with the keyword argument S. This value overwrites the global value only for the current application of the `gamma_method`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result\t 4.79208242e-03 +/- 2.04669865e-04 +/- 1.97135904e-05 (4.271%)\n",
      "  t_int\t 1.05231340e+00 +/- 1.88061498e-01 S = 2.50\n"
     ]
    }
   ],
   "source": [
    "pcac_plateau.gamma_method(S=2.5)\n",
    "pcac_plateau.print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can have a look at the respective normalized autocorrelation function (rho) and the integrated autocorrelation time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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"
    },
    {
     "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": [
    "pcac_plateau.plot_rho()\n",
    "pcac_plateau.plot_tauint()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Critical slowing down"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`pyerrors` also supports the critical slowing down analysis of arXiv:1009.5228"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result\t 4.79208242e-03 +/- 2.28649024e-04 +/- 1.67571716e-05 (4.771%)\n",
      "  t_int\t 1.31333644e+00 +/- 5.19554793e-01 tau_exp = 10.00,  N_sigma = 1\n"
     ]
    }
   ],
   "source": [
    "pcac_plateau.gamma_method(tau_exp=10, N_sigma=1)\n",
    "pcac_plateau.print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The attached tail, which takes into account long range autocorrelations, is shown in the plots for rho and tauint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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"
    },
    {
     "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": [
    "pcac_plateau.plot_rho()\n",
    "pcac_plateau.plot_tauint()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Additional information on the ensembles and replicas can be printed with print level 2 (In this case there is only one ensemble with one replicum.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result\t 4.79208242e-03 +/- 2.28649024e-04 +/- 1.67571716e-05 (4.771%)\n",
      "  t_int\t 1.31333644e+00 +/- 5.19554793e-01 tau_exp = 10.00,  N_sigma = 1\n",
      "1024 samples in 1 ensembles:\n",
      " : ['B1k2r2']\n"
     ]
    }
   ],
   "source": [
    "pcac_plateau.print(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Monte Carlo history of the observable can be accessed with `plot_history` to identify possible outliers or have a look at the shape of the distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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": [
    "pcac_plateau.plot_history()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If everything is satisfactory, dump the `Obs` in a pickle file for future use. The `Obs` `pcac_plateau` conatains all relevant information for any follow up analyses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "pcac_plateau.dump('B1k2_pcac_plateau')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": "3.6.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}