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 observables 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, ca=0, **kwargs):\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 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": [],
   "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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06ZrqwZ49e/bLy8vzO378uN+dd97Zp1+/fn379evX99///ncrACgoKDD/4Ac/iIyIiIi77777eqrWvUxTYGDgwKlTp3aPiIiIGzx4cNTx48f9ACAtLc1yyy23REVHR8fGxsb2TU9PtxQVFZkGDx4cFRsb2zcqKir2zTffbFt9nb///e8doqKiYqOjo2PvvvvuXrWf58knn+x6zz33hCckJER37dq1//Lly9tOnz69W1RUVOxtt90WWV5eLgDw9NNPd+nXr1/fyMjIuPvvv7+nzfE5/e53v+vUp0+fuKioqNjRo0f3BoCNGze2jomJiY2JiYnt27dv7Llz5254rsFkhq5mRBLiiXOCOI2wCr/0lmsjrDyRp04K6In4XrndhwcKgg+duND6UqXNBACXKm2mQycutK6uqTFCZmZmyyVLlnybk5OTtmbNmg7Z2dkBBw8ePDRp0qTTCxYs6FR9XF5enmX//v2H1q9fnzNjxoyepaWlAgDp6emBH3zwwddffvll1rPPPts1Pj6+NDs7O+PFF188Nnny5F5msxl33HHH+ZUrV7YFgK1bt7YKCwur6N69e9XDDz/c/cknnzyZlpZ26L333vt6+vTp4QAwa9asroMHDy7Jzc1NHzdu3PkTJ0741xV7WVmZKTEx8WJubm76D37wg+JZs2Z1BYCJEyf2mj59emFWVlZGampqZo8ePSoDAwNtGzduzM3IyDi0ffv27F/96lfdbDYbUlNTA15++eUu27dvz87KyspYuHDht3U91zfffGPZsWNH9tq1a3OnT5/ea9iwYReys7MzAgICbO+8804wADzzzDOFaWlph3JyctLLyspMq1evrk76QtPS0jKys7Mzli1b9g0ALFiwIPSVV175JjMzM2Pnzp2ZrVu3NiZDvQ4mMz7gz1uyET5ro/3n0ls123/e0ogZtI1KQjgnSP05z8kDuDYnjydOCuip+F651cFjRYHljkSmWnmlzZR2vCjwWuc0VP/+/S/27NmzsmXLltqjR4/y5OTkIgCIj48v+/bbb2uSiJSUlLNmsxn9+/cv7969e/m+ffsCAOC222670LlzZysA7N69O2jq1KlnAOCuu+4qPn/+vN/Zs2dNEydOPLtmzZr2ALBy5cr2KSkpZwHgv//9b5snnniiR0xMTOyYMWMiSkpKzEVFRaadO3cGTZky5QwATJgwoahNmzZ1/udqMpkwbdq0swAwZcqUM7t372597tw508mTJ/1/+tOfngeAwMBADQoKstlsNpkxY0a3qKio2KFDh0YVFhb65+fn+23evLnNmDFjzlX3x6l+LbWNGDGiyGKxaFJSUpnVapXx48dfAIC4uLiyI0eO+APARx99FDRgwICYqKio2B07dgSlpaW1BIDo6OiycePG9Xrttdfat2jRQgHg5ptvLnn66ae7/+53v+t0+vRpc1M00bHPjA9w7r/hcp8Zo0Z5sINl/XngyCjD+hcZOYTd6OHw5Fb9w4JLLS1MtktOCY2lhcnWr2tw6fXOawiLxVLThmMymRAQEKDV21arVaofE5ErzqveDwwM/M4aheHDh1+cOnWq5fjx436bNm1q+9JLLx0HAFXFV199dSgwMLDudqQGqh2js4ULF7Y/c+aM38GDBw9ZLBYNCwvrX1ZWVu/Kiur3yWw2w8/PT02OfksmkwlVVVVSWloqTz31VM9du3ZlREREVD755JNdL126ZAKAbdu25Xz00UdBH3zwQfDLL7/cJSsrK/33v/99wd133130wQcfBN92220xGzduzBk4cOAl196B62PNjK8wqn+KUROTeeIU/R7qipo1p59G1awZxLD+Rc6TJzr/NCb5MPJa5Hb/MyC0qG+XNiUBLUw2AAhoYbL17dKm5H8GhDb5CIZ33323ndVqRXp6uiUvL88SHx9/1Y130KBBxUuXLu0A2PvjtGvXrqp9+/Y2k8mE5OTk84888kj3iIiIstDQUCsA3HrrrRfmzp1b05S1Y8eOlgBw8803Fy9btqwDALzzzjttLly4UGeVoM1mw9KlS9sBwLJlyzokJSUVt2vXzhYaGlqxYsWKtgBQVlYmxcXFpqKiInPHjh0rLRaLrl+/Puj48eP+AHDnnXdeWL9+fbuCggIzAJw8ebJR1Y+lpaUmAAgNDa0qKioyrV+/vh0AWK1WfP311/5jxowpfvXVV485ap/M6enplqSkpLKXXnqpYMCAARfT0tICGvO8DcGaGV9g5ARgRo3yMHJOEA/9i9xqU3yaZV9Q95NDJzEkuhPMpmv/9XQtHjkyyqm2yGNiIp/iZzLhX9MH53x4oCD48dV7I/6QEn/YXaOZwsLCKuLj4/uWlJSY//KXv3xTV23K/Pnzjz/wwAPhUVFRsS1btrQtW7asZoXtBx544Oztt9/e95VXXjlaXbZo0aK8adOm9YiKioq1Wq0yaNCg4ltuueXbefPmHU9JSekdERERl5iYWNKlS5eKumJq2bKlbffu3a3++Mc/du3QoUPlu+++exgA3nzzzSM///nPe7744otdW7Roof/617++njZt2tnk5OSIqKio2AEDBpT26tXrEgAkJiZeeuqpp07cdtttMSaTSfv161e6du3ao3U93/V07NjR+sADD5zq27dvXEhISFV8fPxFAKiqqpKJEyf2Ki4uNquqTJs2rbBjx47Wp556quuOHTvaiIhGR0eXjR8//oYnqHKtntTeKDExUVNTU90dRtPL2mRPYK5IQFrZOzU2tEnHOTFyTkIakxjZrJfnBLn/7UbPCXIj5nRx9QZttSkmLd6FfXnnUVphRaC/GTd1b4sVUwc1KqExKq4aBg7R98lkxtfnZmogEdmjqomuXmf//v1H4+PjTzf0PCPnmWmolJSU8NGjRxc9+OCD59zx/NfibfPlNJX9+/d3jI+PD69dbkjNjIiMAvBXAGYAr6vqvFqPWwC8ASABwBkA96nqUcdjswFMBWAF8LiqbnaUHwVQ7CivMuIfms8ysn+KkROTGTQniJE1F0bVpnyaVViTyABAaYUV+/LO49OsQgzv27nR8bnEA2uwPHJyQcC4fkpMihqt9gzA4bM2JgCcAZgax+VkRkTMAF4FMBJAPoAvRWSdqmY4HTYVwDlVjRCRCQDmA7hPRGIBTAAQB6ArgI9FJEpVqzt8DFXVBmf5zU7oAGiLQEjl5ZoZbREIaWz/FKMmJvMwzrUpAPDYqr2Nrk1JP34BZRVX9ksqq7Ai4/gF9yUzHtiR2COb0IzUHCasvEGcZwB2p8Y0uzQF1so0jBGNk0kAclX1sKpWAFgNYGytY8YCWO7YXgNguNi7Zo8FsFpVy1X1CIBcx/WoAax9RiBdInFRLbCq4KJakC6RsPYZ0eBrGTrM28NcrzaloeK6tkFL/ytrq1r6mxHbtY0hsRIRUf0Z0cwUBiDPaT8fwKBrHaOqVSJSBKCDo3xnrXPDHNsK4N8iogAWquqiup5cRB4C8BAAdOkcgtT1/+faq/FCqWcteKXkSdyMA4iVb5ChPbGzcgAeX/kWEtuXN+hatwG47Qf27cQ9TyM14WX7zqXjSF2/vVHxJQIGfi5dG32tf+e1RllFEIDLtTBlFVXYsm0rgnNLGnSt1gr0adkBOVUtcMlmQoDJhj4ty9E6Zx1ScxsVnkPjX9+NY1RMrl3n7W+D8K+8oKvK7+1ejPt6FLsSmCGM/Z4TUUN48mimW1X1mIh0ArBFRDJV9bPaBzmSnEUAEBsZri3bd23qON0u/zRQZgO24nvYiu8BsN+uj9k64Lb2rl3bqPfTyM+lsdeKqQQsx4BLTq1DFrMgOrQNWrZveI3KS7cBewqB3+4Gnks0IaGTBWZpXGxWtV8LAA5WdkVCJ8Dc+H7EhvOE78HP2gM/u8m+/aP1wMYx1Y8EOX7qb2UW8FYdlY0To4AHohsdoqHfcyKqPyOSmWMAujvtd3OU1XVMvoj4AQiGvSPwNc9V1erfhSLyHuzNT1clMwT0CQYs5to3aaB3IyYFD/l6DTodfrdmP27LRABAYe97cKrP+Hpfp2DXGgy/cPV1PmlzD0IH1f86RkroBES3A7LO2d+rALN9P6HTd59bF7MASY7uMUkudJOxKvD8TntcADB/jz2uF29uWEJj9A3aOcHafRIel2C54oHoy+/JlYkRNZlNs7ti52tdriq/+ZETGDXX7X1pyLsYkcx8CSBSRHrBnohMADCx1jHrAEwG8AWA8QC2qqqKyDoAb4nIn2DvABwJYLeItAJgUtVix/YdAF4wIFaf5HyTLrfaYDGbGn2TPtVnfE3S4sp/8qGDxiMdV18ntHGXM+TGahZ7glBTm5LgGTfoPYWXEyzA/jvrnL28IUmSkTdooxKs6mv5alIEAFAbWp/eBwBofeorlHS8CRDOR/qdRs09XpO0zAlOwJwil4dmZ2Vl+Y8ePToyJycnvbrsySef7Nq6dWvrCy+8cPJa53322WeBS5Ys6bBs2bK8ax3jSep6nc2dy8mMow/MLwFshn1o9hJVTReRFwCkquo6AIsBrBCRXABnYU944DjuHQAZAKoAPKqqVhHpDOA9x/TNfgDeUtVNrsbqq5xv0iVfrUHr7/3YpRuGp918jLyxGlWbYqSvi4DyWhM2l1uBw0Xui9GoBMvIz84jqQ0998xFywv2jlLdDv4NZW0i8E3CbCY09WGrAtLft9chH1wTjLi7i2Bq+t4PP/zhD0t/+MMfGraMQrXKyko0xbpEZFCfGVX9EMCHtcp+7bR9CcC91zj3JQAv1So7DCC+oXFYS8/jzOevN/Q0n9EHgEWOoTz7dZxv5OAjmwr+UDIKX1s7AfDDvN1V6GMuxLOtN8EkjZtg8fd+wJnPGxcPAOyt7I7Mi8NQDvt/CpesQObpSmzbthUDWzTuDylXYzLyWiGV3eGPy68PAPxRiY75W3HmpHte38FLN6HcmgDnztLlVkXagT3oE7Cv3tcx+rOzqWB/VTeMMHXAx1vPIN4vv9Hfy2quvFftracRUJkJM+xZn9lajoBzmdDtf8BZc0eX4vJ5tipgyahIFKS1BgB88Mve2PXPEkzZlHOjEpqkpKTohISEkv/85z9tiouLzf/85z+Pjho1qmTDhg1BCxYs6Lxt27bcJ598suvRo0f9v/nmG8uJEyf8586dm/fFF1+03rp1a5vOnTtXfvzxx7nV6x+NGTPm3NatW9tYLBZdtWrV4X79+pWnpKSEWywWW1paWmBSUlLJlClTzvziF7/oWVZWZurZs2f5W2+9dTQ/P7/FT3/6014HDx48BNhrWsaMGRORnZ2d8fnnnwc++eST3UtLS03t2rWrWrly5dGePXtWfv7554HTpk0LB4AhQ4ZcqOv1bdiwIWjOnDldW7dubT169GjALbfccmHFihXfms1mrFmzps2vf/3rMKvVKu3bt6/64osvsrdt2xY4c+bMHuXl5aaAgADbsmXLjsTHx5dXVVXhkUce6bZt27ZgEdHJkyef/t///d8rhn0mJSVF9+/fv3TXrl2tS0tLTUuXLj3y0ksvdcnKymo5duzYs6+88spxABgxYkSfEydO+JeXl5umT59+8umnnz5dVVWF++67L/zAgQOtREQfeOCB07/5zW8Kf/e733VaunRpiNls1qioqEsbNmw4XN/Pln86+AC/yguwXDwGy0V7V6Xqbb/KOr/v17W/qhu+tnZy3HwE5WiBr62dsL+qm8FR19831g6oqJV3V8AP31o7uCkiY8X75aOPuRAWVAJQWFCJPuZCxPvluy2mnuYz8EfVFWX+qEIP85kGXcfIz6460X7t4jB8bEvAaxeH4Q8lo2BT91XxtNbimkSmmhlWtFb3j67yeOnvB6MgrTWqHAsiVpWZUJDWuqam5gapqqqSgwcPHpo/f37eCy+8UGeP7W+++cayY8eO7LVr1+ZOnz6917Bhwy5kZ2dnBAQE2N55552a+IKDg6uys7MzHn744cLHHnuspv/niRMn/L/66qvM119/Pf9nP/tZr9///vf52dnZGXFxcWXPPfdc14EDB16qrKyUzMxMfwB444032t99993nysvL5fHHH+/xwQcffJ2enn5o8uTJp59++ukwAJg6dWr4X/7yl2+zsrIyro74soMHD7Z67bXXvs3NzU07evSo5Y033mh3/Phxv1/+8pfh77777tdZWVkZ77///tcAEB8ff+nLL7/MPHToUMZvfvObY88++2w3AFiwYEHIt99+65+RkZGenZ2dMW3atDr/4fv7+9vS0tIOPfjgg6fuvffeiP/7v//7NjMzM/3tt9/uWL0e1MqVK4+mp6cf2rdvX8bChQs7FxQUmL/44ovAEydOtMjJyUnPzs7OePTRR88AwCuvvBKalpaWkZ2dnbFs2bJvGvK5evJopgYzB7ZFh9umuTsMt3K1r8SpbKAi68qyCrTA6W53okMjJ2z96Xpg422Nj6n/SeDDPVePQuo3IBEdOjduYmhXYzL6WvP0cl+eWUktkNApDGaZ6raYhiqwdWftztItMPTmOxvUPGTkZ7f7JHB4D1A92UA5WuAwwnAkeqpLzXGuvFdy6ivYDv4NZuvlKRBsZgukXwo6hHyv8UE1ufeb/ilP7AtE1aUr/6CuumTCif2B6N+4tXyutbK0c/m99957DgBuueWWi88884x/XcePGDGiyGKxaFJSUpnVapXx48dfAIC4uLiyI0eO1JwzefLkswDw85///Oz/+3//ryaZueeee875+fnhzJkz5uLiYvOPfvSjEsdxZ+69997eAHD33XeffeONN9r//ve/L3jvvffavf3224cPHDhgycnJaTls2LAowL7YZEhISOXp06fNxcXF5uTk5BIAmDJlypmtW7fWmfT179//YmxsbAUA/PjHPz77+eeft7ZYLLakpKTimJiYCgDo3LmzFQDOnj1rvu+++3odPXo0QES0srJSAGDr1q1tpk+ffqq6iaz6+NrGjRt3HgDi4+PLIiIiynr27FkJAN27dy8/fPiwf2hoaNn8+fM7b9y4sS0AFBQUtEhPTw8YMGDApby8PMvkyZO7jxkzpmjcuHEXACA6Orps3Lhxve66667zDzzwwPk6P8xrYM2Mm6zMsicetX9WZn33uTdS9cgoZ40dGWVV+w0IsP+2NrI1oLqDc4AjLldHIRnB+fMDXP/8avflcXd/kup+WM8l2PefS2hcPxcjP7vr9S1qDCO+nyUdb0JZmwhYzRb7Nc0WlLWJsHcCpuvrclMp/AJsV5T5BdjQJb7RfVc6d+5cVVRUdMX/YGfPnjV37NixppoxICBAAcDPzw9Wq7XOb7TFYlEAMJvN8PPzU5Nj8UuTyYSqqqqac0xOi2I65kQDALRu3frK11WHSZMmnXv//ffbHThwwCIi6N+/f7mqSkRERFlmZmZGZmZmRnZ2dsZ///vfq9cDuY7aCd21EjwAeO6558Juv/324pycnPT169fnVlRUNCgnqH4vTSZTzXtWvV9VVSUbNmwI2r59e1BqampmVlZWRt++fcvKyspMISEh1rS0tIyhQ4cW//Of/wyZMGFCOABs27Yt59FHHz311VdfBQ4cOLBvZWVlvWNhMuMmD0Tba1Cqa1Gqt12Z48IIRt18qjt+zneMT5i/x77fmBuGUTdWIzl/fs4/7v78jEogAWMSLCM/O6MTbUO+n2LCNwmzkd//MQBAfv/H2Pm3vuLuLkJovxL4tbTf+P1a2hDarwRxdzd6TYjg4GBbp06dKtetWxcEACdPnjR/+umnwcOGDWvYrJj19MYbb7QHgMWLF7cbOHDgxdqPd+jQwdqmTRvrpk2bWjuO6zB48OASAIiLiys3mUz49a9/3XXcuHFnAWDAgAGXzp496/fxxx+3AoDy8nJJTU0N6NixozUoKMi6efPm1gCwbNmya84gdvDgwVaZmZn+VqsVa9asaX/bbbcVDxky5OLu3buDqpu1Tp48aQaACxcumLt161YBAAsXLqzp5DV8+PALCxcu7FidTFQf31Dnz583BwcHW4OCgmx79+4N2L9/fysAOHHihJ/VasXPfvaz83Pnzj128ODBQKvViq+//tp/zJgxxa+++uqxkpISc+3E9Hp8qpmJXGfU8GWjRsM4x+Vpo5A8jaeOHDLqszNyniBDv59iQomjSanEq5qW3MzkB0zZlIP094OxdmoExv79sBGjmZYvX37kkUce6fHss892B4DnnnvueFxcXMOmQq+nc+fOmaOiomL9/f119erVdXZWXbp06ZFf/OIXPR9//HFTjx49yletWnW0+rF77rnn7Isvvtht/vz5xwB7Tcfq1au/fvzxx3sUFxebrVar/OIXvziZmJh4afHixUenTZsWLiLX7AAMAP369bs4ffr0HtUdgCdNmnTebDbjlVdeOTpu3LgIm82GDh06VO7YsSPnueeeK5g2bVqv+fPndx05cuT56mvMnDnzVHZ2tiUmJibOz89PJ0+efOpXv/rVqYa+PykpKUWLFi0K6d27d1zv3r0vxcfHXwSAo0ePtpg6dWq4zWYTAHjhhRfyq6qqZOLEib2Ki4vNqirTpk0r7NixY53NW3URVddGAniSuJgIXf7H59wdRoON/29XrPlB4+eIulHTvLsS17/yWuOdb4OgTqNhBIr7ehRjfPfG/5HkSkyePh0+4NrrSz1rwV+y2uGS7XKtQIDJhhnR5xq8rIVRMRl9HasCe89ZMO9QB8zqewYD25U3KlG7Ed/PK5b/8DLfv+uhParauA5oTvbv3380Pj6+4YsDGzTPTFMKCwvrn5qaeqhLly5V331003AeleXuWG6U/fv3d4yPjw+vXe5TNTMtW7dF4pifuzuM+tk2F9g+DwBwNABA9T/j22c1eOXjRAB/NDQ4h/9ubPT7WXToJNav2luzqCMAtPT3w8ihw5DoyqrSLsR0w94nI7nw+nZ8koPyQ1eOyS+3mVDZbTASh0e6JaYbcZ1BAObN2ojpk3/a6GvckO/nnqe95/+fqzzU9E9ZewbgOcH2xkjOAEyN4FPJjFcZOvty0jInGJjT6GZijzQkuhNu6t62ZpXqQH8zbureFkOi3dhr18dVr+R95Q2aK3nXhd9PD+A8A7AXOnbs2EF3x1Db6NGji0ePHu0Z1cxNjMkM3RBmk2DF1EH4NKsQU5en4m/3D8SQ6E4wm3xh2ldj/XlLNv76yeUBC+GzNgIAnhgeiZkj6z8enjfo+uP3k8i3MJlxI6tN8WlWIdKrxiHu0Emf+8/UbBIMd1TZD3elacnHzRwZ1aCk5Vp8/QZtVNJXzZDvp1NzMQB7LSvQqOZiH2Gz2WxiMpl8pzMmeQxHh+E6h70zmXETq00xafEu7Ms7j7KqFLRctRc3dW+LFVMHufXmY/QNw1dj8lSelkAa+dkZlfQZyrm5mAAg7dSpU7EhISFFTGjISDabTU6dOhUMIK2ux5nMuMmnWYU1zQGACaUVVuzLO49PswrdehPyxBuGJ8bk64xKQvjZNS9VVVXTCgoKXi8oKOgHzmNGxrIBSKuqqqpzmn8mM26SfvwCyisqMcy0D3FyFOkaju0VNyHj+AWP+IuamjcmIfVTO+mr1lxrDRMSEgoB3OXuOKj5YTLjJnGhrfCmZR4GIAcBqMAl+OMAIlEa+i93h0ZE9eSc9IXP2oij837k5oiImicmM24yxLwfFaZctFT7ZGatUI6BkosW5v0A6lzI1auwnwt5Mn4/iXwLkxk3MZ88iAC9clZWi5ZDTqYBMcluiso4bKYgT8bvJ5FvYTLjLqEDIP6BQMXltcnEPxAI7e/GoMibsbaBiJorQ5IZERkF4K8AzABeV9V5tR63AHgDQAKAMwDuU9WjjsdmA5gKwArgcVXd7HSeGUAqgGOqOtqIWD1G5EggLBE4lmpPaPxb2fcjR7o7MvJSrG0goubK5aFzjoTjVQDJAGIB3C8isbUOmwrgnKpGAPgzgPmOc2MBTAAQB2AUgNcc16v2BIBDrsbokUxmYNJ7QMoS+37KEvu+qVErrRORm1htik8OnQQAfHLoJKw2Tq9C1NSMmAcgCUCuqh5W1QoAqwGMrXXMWADLHdtrAAwXEXGUr1bVclU9AiDXcT2ISDcAPwLwugExeiaTGYgeZd+OHsVEhsjLVE9++diqvQCAx1btxaTFu5jQEDUxI5KZMAB5Tvv5jrI6j1HVKgBFADp8x7l/AfAsrjF1cTUReUhEUkUk9dSpU418CUREDXfl5Je4YvJLImo6HtkBWERGAyhU1T0iMuR6x6rqIgCLACAxMdFr/hy6srPmWwA7axJ5nfTjF1DmtEo5AJRVWDn5JVETMyKZOQagu9N+N0dZXcfki4gfgGDYOwJf69y7ANwlIv8DIABAGxF5U1V/YkC8HuGKzppzgoE5Re4NiIgaLK5rG7T0N9fUzABAS38zYru2cWNURM2PEcnMlwAiRaQX7InIBAATax2zDsBkAF8AGA9gq6qqiKwD8JaI/An2meIiAexW1S8AzAYAR83M076UyBCRbxgS3Qk3dW9b09QU6G/GTd3bYkh0p4ZfrPYK3NWa7wrcRPXmcjKjqlUi8ksAm2Efmr1EVdNF5AUAqaq6DsBiACtEJBfAWdgTHjiOewdABoAqAI+qqrXOJ/I1tf/jmhNs/83/uIi8htkkWDF1ED7NKsTU5an42/0DMSS6E8wmafjFnFfgZm0tUYOIqtd0M/lOiYmJmpqa6u4wiKgZMnRtpiZOZkRkj6omNtkTEhmMS7QTERGRV2MyQ0RERF6NyQwRkaewWYGsTfbtrE32fSL6Th45zwwRUbNjswIrxtnXawOAtVPs67VxmROi78SaGSIiT5Cz5fLCs4D997FUezkRXRdrZoiIGunKmbztI5qARs7kXXAAqCi9sqyiFCg4eHkNNyKqE5MZIqJGumImb1eFDgD8Ay/XzAD2/dD+xlyfyIcxmWmg2n+JVeOaSkTkksiR9j4y1U1N/q3s+5Ej3R0ZkcfjpHkuMHSSLCIim9XeR2bVfcD9b9sTmSbo/MtJ88jbsWaGiMhTmMyX+8ewnwxRvXE0ExEREXk1JjNERETk1ZjMNILVpvjk0EkAwCeHTsJq851+R0RERN6GfWYayGpTTFq8C/vyzgMAHlu1Fzd1b4sVUwfBbBL3BkdERNQMsWamgT7NKsS+vPMorbCvmVJaYcW+vPP4NKvQzZERkVfbNheYE2z/AS5vb5vr3riIvABrZhoo/fgFlFVcufhbWYUVGccvYHjfzm6Kioi83tDZ9h8iajDWzDRQXNc2aOl/5bwPLf3NiO3axk0RERERNW+G1MyIyCgAfwVgBvC6qs6r9bgFwBsAEgCcAXCfqh51PDYbwFQAVgCPq+pmEQkA8BkAiyPGNar6GyNiddWQ6E64qXvbmqamQH8zbureFkOiO7k7NCLyYpxdnKjxXJ4BWETMALIBjASQD+BLAPeraobTMY8AGKCq00VkAoBxqnqfiMQCWAUgCUBXAB8DiAJgA9BKVUtEpAWA/wB4QlV3Xi+WppoB2GpTfJpViKnLU7F4ciKGRHdi518iMkxTzy7OGYDJ2xnRzJQEIFdVD6tqBYDVAMbWOmYsgOWO7TUAhouIOMpXq2q5qh4BkAsgSe1KHMe3cPx4zPhns0lq+scM79uZiQwREZEbGZHMhAHIc9rPd5TVeYyqVgEoAtDheueKiFlE9gEoBLBFVXcZECsRERH5GI/tAKyqVlW9CUA3AEki0q+u40TkIRFJFZHUU6dONWmMRERE5H5GJDPHAHR32u/mKKvzGBHxAxAMe0fg7zxXVc8D2AagzlXXVHWRqiaqamJISEjjX0U9fbH46Zr5H44GTKzZ/mLx0zf8uYnIt3F2caLGMaIDsB/sHYCHw56IfAlgoqqmOx3zKID+Th2A71HVH4tIHIC3cLkD8CcAIgG0B1CpqudFpCWAfwOYr6obrhdLU3UArjEnGJhT1HTPR0Q+y3l2ceeRkk0xuzg7AJO3c3lotqpWicgvAWyGfWj2ElVNF5EXAKSq6joAiwGsEJFcAGcBTHCcmy4i7wDIAFAF4FFVtYpIFwDLHSOlTADe+a5EhojIm11vdnFOyEl0fYbMM6OqHwL4sFbZr522LwG49xrnvgTgpVplBwAMNCI2IiJvwNnFiRrPYzsAezSbFcjaZN/O2mTfJyJyAWcXJ2o8JjMNZbMCK8YBa6fY99dOse8zoSEiF1TPLh7oSGg4uzhR/TGZaaicLcCxVKDion2/4qJ9P2eLe+MiIq9mNglWTB2Ev91vb2H/2/0Dm6TzL5EvYDLTUAUHgIrSK8sqSoGCg+6Jh4h8BmcXJ2ocJjMNFToA8A+8ssw/EAjt7554iIiImjkmMw0VORIISwT8W9n3/VvZ9yNHujcuIiKiZorJTEOZzMCk94CUJfb9lCX2fZP5+ucRERHRDWHIPDPNjskMRDtWV4iuc5UFIiIiaiJMZoiIPMCft2Tjr5/k1OyHz9oIAHhieCRmjoxyV1hEXoHJDBGRB5g5MopJC1EjMZlpqG1zge3zLu/PCbb/vn0WMHS2e2IiIiJqxpjMNNTQ2UxaiIiIPAhHMxEREZFXYzJDREREXo3JDBEREXk1JjNERETk1ZjMEBERkVczJJkRkVEikiUiuSIyq47HLSLytuPxXSIS7vTYbEd5lojc6SjrLiLbRCRDRNJF5Akj4iQiIiLf43IyIyJmAK8CSAYQC+B+EYmtddhUAOdUNQLAnwHMd5wbC2ACgDgAowC85rheFYCnVDUWwM0AHq3jmkRERESG1MwkAchV1cOqWgFgNYCxtY4ZC2C5Y3sNgOEiIo7y1aparqpHAOQCSFLVE6r6FQCoajGAQwDCDIiViIiIfIwRyUwYgDyn/XxcnXjUHKOqVQCKAHSoz7mOJqmBAHYZECsRERH5GI/uACwirQGsBTBDVS9c45iHRCRVRFJPnTrVtAESERGR2xmRzBwD0N1pv5ujrM5jRMQPQDCAM9c7V0RawJ7IrFTVd6/15Kq6SFUTVTUxJCTExZdCRERE3saIZOZLAJEi0ktE/GHv0Luu1jHrAEx2bI8HsFVV1VE+wTHaqReASAC7Hf1pFgM4pKp/MiBGIiIi8lEuLzSpqlUi8ksAmwGYASxR1XQReQFAqqqugz0xWSEiuQDOwp7wwHHcOwAyYB/B9KiqWkXkVgCTABwUkX2Op/qVqn7oarxERETkW8ReQeIbEhMTNTU11d1hEBF5FRHZo6qJ7o6DqLE8ugMwERER0XdhMkNERERejckMEREReTUmM0REROTVmMwQERGRV2MyQ0RERF6NyQwRERF5NSYzRERE5NWYzBAREZFXYzJDREREXo3JDBEREXk1JjNERETk1ZjMEBERkVdjMkNERERejckMEREReTUmM0REROTVmMwQERGRV2MyQ0RERF7NkGRGREaJSJaI5IrIrDoet4jI247Hd4lIuNNjsx3lWSJyp1P5EhEpFJE0I2IkIiIi3+RyMiMiZgCvAkgGEAvgfhGJrXXYVADnVDUCwJ8BzHecGwtgAoA4AKMAvOa4HgAsc5QRERERXZOfAddIApCrqocBQERWAxgLIMPpmLEA5ji21wD4u4iIo3y1qpYDOCIiuY7rfaGqnznX4BARUT1smwtsn3d1+e2zgKGzmz4eoiZgRDITBiDPaT8fwKBrHaOqVSJSBKCDo3xnrXPDGvLkIvIQgIcAoEePHg0KnIjI5wydfTlpmRMMzClybzxETcDrOwCr6iJVTVTVxJCQEHeHQ0RERE3MiGTmGIDuTvvdHGV1HiMifgCCAZyp57lERERE12REMvMlgEgR6SUi/rB36F1X65h1ACY7tscD2Kqq6iif4Bjt1AtAJIDdBsRERNR82axA1ib7dtYm+z6RD3M5mVHVKgC/BLAZwCEA76hquoi8ICJ3OQ5bDKCDo4PvkwBmOc5NB/AO7J2FNwF4VFWtACAiqwB8ASBaRPJFZKqrsRIR+TybFVgxDlg7xb6/dop9nwkN+TCxV5D4hsTERE1NTXV3GERE7pO1yZ7AVFy8XObfCkhZAkTXPduFiOxR1cQmipDIcEaMZvJ4f96Sjb9+knNV+RPDIzFzZJQbIiIiukEKDgAVpVeWVZQCBQevmcwQebtmkczMHBlVk7SEz9qIo/N+5OaIiIhukNABgH9grZqZQCC0v/tiIrrBvH5oNhEROYkcCYQl2puWAPvvsER7OZGPYjJDRORLTGZg0nv2PjKA/fek9+zlRD6qWTQzERE1Kybz5f4x7CdDzUCzqZmx2hSfHDoJAPjk0ElYbb4ziouIiKg5axY1M1abYtLiXdiXdx4A8Niqvbipe1usmDoIZpO4NzgiIiJySbOomfk0qxD78s6jtMI+aVRphRX78s7j06xCN0dGRERErmoWyUz68Qsoq7hy9suyCisyjl9wU0RERDfItrmO1bKD7fvV29vmujcuohuoWTQzxXVtg5b+5pqaGQBo6W9GbNc2boyKiOgGGDrb/kPUjDSLmpkh0Z1wU/e2CPS3D00M9Dfjpu5tMSS6k5sjIyIiIlc1i2TGbBKsmDoIf7t/IADgb/cPZOdfIiIiH9EsmpkAe0IzvG9nAKj5TURERN6v2SQzRETNARfWpeaIyQwRkQ/hwrrUHDWLZKb2XyrhszYC4F8qREREvqBZJDPOf6kQERGRbzFkNJOIjBKRLBHJFZFZdTxuEZG3HY/vEpFwp8dmO8qzROTO+l6TiIjqxrXoqLlxOZkRETOAVwEkA4gFcL+IxNY6bCqAc6oaAeDPAOY7zo0FMAFAHIBRAF4TEXM9r0lERLVUr0X32Kq9AOxr0U1avIsJDfk0I2pmkgDkquphVa0AsBrA2FrHjAWw3LG9BsBwERFH+WpVLVfVIwByHderzzWJiKgWrkVHzZERyUwYgDyn/XxHWZ3HqGoVgCIAHa5zbn2uCQAQkYdEJFVEUk+dOuXCyyAi8n5ci46aI6+fAVhVF6lqoqomhoSEuDscIiK3ql6LzhnXoiNfZ0QycwxAd6f9bo6yOo8RET8AwQDOXOfc+lyTiIhq4Vp01BwZMTT7SwCRItIL9oRjAoCJtY5ZB2AygC8AjAewVVVVRNYBeEtE/gSgK4BIALsBSD2uWX/b5gLb511dfvssri5LRD6lei26T7MKMXV5Kv52/0AMie7EtejIp7mczKhqlYj8EsBmAGYAS1Q1XUReAJCqqusALAawQkRyAZyFPTmB47h3AGQAqALwqKpaAaCuazY6yKGzLyctc4KBOUWNvhQRkafjWnTU3BgyaZ6qfgjgw1plv3bavgTg3muc+xKAl+pzTSIiIqLavL4DMBERETVvzSeZsVmBrE327axN9n0iIiLyes1ibSbYrMCKccCxVPv+2ilAWCIw6T3AZL7+uUREXoQL61Jz1DySmZwt9kSm4qJ9v+KifT9nCxA9yr2xEREZiAvrUnPUPJqZCg4AFaVXllWUAgUH3RMPERERGaZ5JDOhAwD/wCvL/AOB0P7uiYeIiIgM0zySmciR9j4y/q3s+/6t7PuRI90bFxEREbmseSQzJrO9s2/KEvt+yhJ2/iUiIvIRzaMDMGBPXKo7+7LTLxERkc9oHjUzRERE5LOYzBAREZFXax7NTLVXzZ4TbP/NVbOJiIi8XvNIZpxXzSYiIiKfwmYmIiIi8mpMZoiIiMirMZkhIiIir8ZkhoiIiLyaS8mMiLQXkS0ikuP43e4ax012HJMjIpOdyhNE5KCI5IrIKyIijvJ7RSRdRGwikuhKjEREROTbXK2ZmQXgE1WNBPCJY/8KItIewG8ADAKQBOA3TknPPwD8HECk46d6at40APcA+MzF+IiIiMjHuZrMjAWw3LG9HMDddRxzJ4AtqnpWVc8B2AJglIh0AdBGVXeqqgJ4o/p8VT2kqlkuxkZERETNgKvJTGdVPeHYLgDQuY5jwgDkOe3nO8rCHNu1yxtERB4SkVQRST116lRDTyciIiIv952T5onIxwBC63jof513VFVFRI0KrL5UdRGARQCQmJjY5M9PRERE7vWdyYyqjrjWYyJyUkS6qOoJR7NRYR2HHQMwxGm/G4BPHeXdapUfq0fMRERERDVcbWZaB6B6dNJkAB/UccxmAHeISDtHx987AGx2NE9dEJGbHaOYfnqN84mIiIiuydVkZh6AkSKSA2CEYx8ikigirwOAqp4F8CKALx0/LzjKAOARAK8DyAXwNYCPHOePE5F8AIMBbBSRzS7GSURERD5K7AOJfENiYqKmpqa6OwwiIq8iIntUlXN6kdfiDMBERETk1ZjMEBERkVdjMkNERERezaf6zIjIKQDfNOFTdgRwugmfrz4YU/14YkyAZ8bFmOrHm2PqqaohNzoYohvFp5KZpiYiqZ7WaY4x1Y8nxgR4ZlyMqX4YE5H7sJmJiIiIvBqTGSIiIvJqTGZcs8jdAdSBMdWPJ8YEeGZcjKl+GBORm7DPDBEREXk11swQERGRV2MyQ0RERF6NyUwDiUh3EdkmIhkiki4iT7g7pmoiYhaRvSKywd2xVBORtiKyRkQyReSQiAz2gJhmOj67NBFZJSIBbohhiYgUikiaU1l7EdkiIjmO3+08JK4/Oj6/AyLynoi0dXdMTo89JSIqIh09ISYReczxXqWLyB/cHZOI3CQiO0Vkn4ikikhSU8ZE1FSYzDRcFYCnVDUWwM0AHhWRWDfHVO0JAIfcHUQtfwWwSVVjAMTDzfGJSBiAxwEkqmo/AGYAE9wQyjIAo2qVzQLwiapGAvjEsd/UluHquLYA6KeqAwBkA5jtATFBRLoDuAPAt00cD1BHTCIyFMBYAPGqGgfgZXfHBOAPAH6rqjcB+LVjn8jnMJlpIFU9oapfObaLYb85h7k3KkBEugH4EYDX3R1LNREJBvBDAIsBQFUrVPW8W4Oy8wPQUkT8AAQCON7UAajqZwDO1ioeC2C5Y3s5gLubMiag7rhU9d+qWuXY3Qmgm7tjcvgzgGcBNPkohmvE9AsA81S13HFMoQfEpADaOLaD4YbvOlFTYDLjAhEJBzAQwC43hwIAf4H9P3abm+Nw1gvAKQBLHc1fr4tIK3cGpKrHYP+L+VsAJwAUqeq/3RmTk86qesKxXQCgszuDuYYpAD5ydxAiMhbAMVXd7+5YnEQBuE1EdonIdhH5vrsDAjADwB9FJA/2731T16oRNQkmM40kIq0BrAUwQ1UvuDmW0QAKVXWPO+Oogx+A7wH4h6oOBHAR7mk6qeHohzIW9kSrK4BWIvITd8ZUF7XPmeBR8yaIyP/C3sy60s1xBAL4FezNJp7ED0B72JufnwHwjoiIe0PCLwDMVNXuAGbCUUtK5GuYzDSCiLSAPZFZqarvujseAD8AcJeIHAWwGsAwEXnTvSEBAPIB5Ktqdc3VGtiTG3caAeCIqp5S1UoA7wK4xc0xVTspIl0AwPG7SZsprkdEfgZgNIAH1P2TU/WBPRnd7/jOdwPwlYiEujUq+/f9XbXbDXstaZN2TK7DZNi/4wDwLwDsAEw+iclMAzn+0loM4JCq/snd8QCAqs5W1W6qGg57Z9atqur22gZVLQCQJyLRjqLhADLcGBJgb166WUQCHZ/lcHhOp+l1sN984Pj9gRtjqSEio2BvwrxLVUvdHY+qHlTVTqoa7vjO5wP4nuP75k7vAxgKACISBcAf7l9F+ziA2x3bwwDkuDEWohvGz90BeKEfAJgE4KCI7HOU/UpVP3RfSB7tMQArRcQfwGEAD7ozGFXdJSJrAHwFe5PJXrhhyncRWQVgCICOIpIP4DcA5sHeNDEVwDcAfuwhcc0GYAGwxdFqslNVp7szJlV1a3PJNd6nJQCWOIZGVwCY3JS1WNeI6ecA/uro7H4JwENNFQ9RU+JyBkREROTV2MxEREREXo3JDBEREXk1JjNERETk1ZjMEBERkVdjMkNERERejckMEREReTUmM0RNSET+KSI/cHccRES+hPPMEDUhx0SLCapqdXcsRES+gjUzRC4SkW0iMtKx/TsR+ds1jusLILs6kRGR8SKyU0T2i8h/RCSkCcMmIvIZTGaIXPcbAP8rIg8AGAhgxjWOSwawyWl/m6rerKrxALbADcsXEBH5AiYzRC5S1c8ACIAnAUxQVauItBKR5SLyf44kBwDuxJXJzM9EZLeI7AfwCOxr5xARUQMxmSFykYj0B9AFQIWqFjuK7wGwRlV/DuAuEQkE0FZVjzvO+SmAJADDHDUzWQDSmz56IiLvx2SGyAUi0gXASgBjAZSIyCjHQ90A5Dm2rQCGAtjmdGp/ADtUtUREUgDcAuBg00RNRORbmMwQNZKjtuVdAE+p6iEAL8LefwYA8mFPaAD7v7Pa/WWWAXhERHbD3s/msKpebIq4iYh8DYdmE90AItIKwN9h7wfzHwBPARikqpVuDYyIyAcxmSEiIiKvxmYmIiIi8mpMZoiIiMirMZkhIiIir8ZkhoiIiLwakxkiIiLyakxmiIiIyKsxmSEiIiKvxmSGiIiIvBqTGSIiIvJq/x9FtKTl8Nnr+wAAAABJRU5ErkJggg==\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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}