Simulating datasets MCMC-D larger-smaller D.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['seaborn-dark', 'seaborn-darkgrid', 'seaborn-ticks', 'fivethirtyeight', 'seaborn-whitegrid', 'classic', '_classic_test', 'fast', 'seaborn-talk', 'seaborn-dark-palette', 'seaborn-bright', 'seaborn-pastel', 'grayscale', 'seaborn-notebook', 'ggplot', 'seaborn-colorblind', 'seaborn-muted', 'seaborn', 'Solarize_Light2', 'seaborn-paper', 'bmh', 'tableau-colorblind10', 'seaborn-white', 'dark_background', 'seaborn-poster', 'seaborn-deep']\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import pymc3 as pm\n",
    "import langevin\n",
    "import langevin_cached_model as lcm\n",
    "import lmfit as lm\n",
    "from lmfit.models import ExponentialModel\n",
    "from scipy.stats import pearsonr\n",
    "from scipy.optimize import minimize_scalar\n",
    "\n",
    "SMALL_SIZE = 16\n",
    "MEDIUM_SIZE = 18\n",
    "BIGGER_SIZE = 20\n",
    "\n",
    "plt.rc('font', size=SMALL_SIZE)          # controls default text sizes\n",
    "plt.rc('axes', titlesize=SMALL_SIZE)     # fontsize of the axes title\n",
    "plt.rc('axes', labelsize=MEDIUM_SIZE)    # fontsize of the x and y labels\n",
    "plt.rc('xtick', labelsize=SMALL_SIZE)    # fontsize of the tick labels\n",
    "plt.rc('ytick', labelsize=SMALL_SIZE)    # fontsize of the tick labels\n",
    "plt.rc('legend', fontsize=SMALL_SIZE)    # legend fontsize\n",
    "plt.rc('figure', titlesize=BIGGER_SIZE)  # fontsize of the figure title\n",
    "\n",
    "SEED = 35010732 # from random.org\n",
    "np.random.seed(SEED)\n",
    "\n",
    "print(plt.style.available)\n",
    "plt.style.use('seaborn-white')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# function to calculate A and B from the dataset\n",
    "def OUanalytic1(data):\n",
    "    N = data.size\n",
    "    data1sq = data[0]**2\n",
    "    dataNsq = data[-1]**2\n",
    "    datasq = np.sum(data[1:-1]**2)\n",
    "    datacorr = np.sum(data[0:-1]*data[1:])\n",
    "    coef = [(N-1)*datasq,\n",
    "       (2.0-N)*datacorr,\n",
    "       -data1sq-(N+1)*datasq-dataNsq,\n",
    "       N*datacorr]\n",
    "    B=np.roots(coef)[-1]\n",
    "    Q=(data1sq+dataNsq)/(1-B**2)\n",
    "    Q=Q+datasq*(1+B**2)/(1-B**2)\n",
    "    Q=Q-datacorr*2*B/(1-B**2)\n",
    "    A = Q/N\n",
    "    P2A = -N/2/A**2\n",
    "    Btmp = (N-1)*(1+B**2)/(1-B**2)**2\n",
    "    tmp = (2+6*B**2)*(data1sq+dataNsq) + (4+12*B**2)*datasq - (12*B+4*B**3)*datacorr\n",
    "    P2B = Btmp - tmp/A/2/(1-B**2)**3\n",
    "    PAB = (N-1)*B/A/(1-B**2)\n",
    "    dA = np.sqrt(-P2B/(P2A*P2B-PAB**2))\n",
    "    dB = np.sqrt(-P2A/(P2A*P2B-PAB**2))\n",
    "    return A,dA,B,dB\n",
    "\n",
    "def OUresult1(data,deltat):\n",
    "    A, dA, B ,dB = OUanalytic1(data)\n",
    "    tau = -deltat/np.log(B)\n",
    "    dtau = deltat*dB/B/np.log(B)**2\n",
    "    return A,dA,tau,dtau"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# function to calculate A and B from the dataset\n",
    "def OUanalytic2(data):\n",
    "    N = data.size\n",
    "    data1sq = data[0]**2\n",
    "    dataNsq = data[-1]**2\n",
    "    datasq = np.sum(data[1:-1]**2)\n",
    "    datacorr = np.sum(data[0:-1]*data[1:])\n",
    "    coef = [(N-1)*datasq,\n",
    "       (2.0-N)*datacorr,\n",
    "       -data1sq-(N+1)*datasq-dataNsq,\n",
    "       N*datacorr]\n",
    "    B=np.roots(coef)[-1]\n",
    "    Q=(data1sq+dataNsq)/(1-B**2)\n",
    "    Q=Q+datasq*(1+B**2)/(1-B**2)\n",
    "    Q=Q-datacorr*2*B/(1-B**2)\n",
    "    A = Q/N\n",
    "    P2A = -N/A**2/2\n",
    "    Btmp = B**2*(1+2*N)\n",
    "    tmp = (1+Btmp)*(data1sq+dataNsq) + (2*Btmp + N + 1 -B**4*(N-1))*datasq - 2*B*(1+B**2+2*N)*datacorr\n",
    "    P2B = -tmp/((1-B**2)**2*(data1sq+dataNsq + (1+B**2)*datasq - 2*B*datacorr))\n",
    "    PAB = (N-1)*B/A/(1-B**2)\n",
    "    dA = np.sqrt(-P2B/(P2A*P2B-PAB**2))\n",
    "    dB = np.sqrt(-P2A/(P2A*P2B-PAB**2))\n",
    "    return A,dA,B,dB\n",
    "\n",
    "def OUresult2(data,deltat):\n",
    "    A, dA, B ,dB = OUanalytic2(data)\n",
    "    tau = -deltat/np.log(B)\n",
    "    dtau = deltat*dB/B/np.log(B)**2\n",
    "    return A,dA,tau,dtau"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "A,D = 1.0,0.5 # tau = 2\n",
    "delta_t_list=np.linspace(0.01,4,50)\n",
    "#M=1000 # number of data sets\n",
    "N=50000 # length of data set\n",
    "#print(np.exp(-delta_t*D/A))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# let us first calculate the standard deviation for each point of the acf\n",
    "# all acfs are stored in acf_all for later analysis\n",
    "\n",
    "result_Bayes_array = None\n",
    "for delta_t in delta_t_list:\n",
    "    data = langevin.time_series(A=A, D=D, delta_t=delta_t, N=N)\n",
    "    \n",
    "    results = OUresult1(data,delta_t)\n",
    "    if result_Bayes_array is None:\n",
    "        result_Bayes_array = results\n",
    "    else:\n",
    "        result_Bayes_array = np.vstack((result_Bayes_array, results))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c1d5f59e8>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.semilogy(delta_t_list,result_Bayes_array.T[3]/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10e4ff6a0>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.semilogy(delta_t_list,result_Bayes_array.T[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5800000000000001\n"
     ]
    }
   ],
   "source": [
    "A,D = 1.0,0.5\n",
    "tau_real = A/D\n",
    "delta_t_list=np.linspace(0.01,4,50)\n",
    "#M=1000 # number of data sets\n",
    "N=50000 # length of data set\n",
    "#print(np.exp(-delta_t*D/A))\n",
    "pick_delta = 7\n",
    "print(delta_t_list[pick_delta])\n",
    "data = langevin.time_series(A=A, D=D, delta_t=delta_t_list[pick_delta], N=N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# compile model for reuse\n",
    "sm = lcm.OU_DA()\n",
    "sm.samples=20000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:25<00:00, 479.05draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8956776325136708, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    }
   ],
   "source": [
    "trace = sm.run(x=data,\n",
    "                d_bound=5,\n",
    "                a_bound=5,\n",
    "                delta_t=delta_t_list[pick_delta],\n",
    "                N=50000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x1c2169f898>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x1c2168a748>],\n",
       "       [<matplotlib.axes._subplots.AxesSubplot object at 0x1c20ef1ef0>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x1c20ee4518>],\n",
       "       [<matplotlib.axes._subplots.AxesSubplot object at 0x1c231caac8>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x1c23ef99b0>]],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.01\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:28<00:00, 461.55draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8904578362857501, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.8869578060228461, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.09142857142857143\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:26<00:00, 310.28draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8830644068323763, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.17285714285714288\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:21<00:00, 502.05draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8827142905221208, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2542857142857143\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:21<00:00, 500.10draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.33571428571428574\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:24<00:00, 485.14draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8869801753745356, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.41714285714285715\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:22<00:00, 499.63draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8842055292183355, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.8917563882102434, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.4985714285714286\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:18<00:00, 522.25draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5800000000000001\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:19<00:00, 513.67draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8804857820425098, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6614285714285715\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:21<00:00, 500.15draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8807267450473683, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.8842514441533041, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7428571428571429\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:21<00:00, 502.08draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8790447109989358, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.8791336075550115, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8242857142857143\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:21<00:00, 502.47draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8916745630026423, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.8843231356347905, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9057142857142858\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:21<00:00, 503.43draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9871428571428572\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:23<00:00, 493.40draws/s]\n",
      "The acceptance probability does not match the target. It is 0.888930499225652, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0685714285714287\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:20<00:00, 510.73draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8856303238161055, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.1500000000000001\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:18<00:00, 525.12draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8900478039915326, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.8821656473876152, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.2314285714285715\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:13<00:00, 558.29draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.312857142857143\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:17<00:00, 530.00draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3942857142857144\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:22<00:00, 498.85draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8918389527871756, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.8863517195771229, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4757142857142858\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:17<00:00, 526.14draws/s]\n",
      "The acceptance probability does not match the target. It is 0.890490597994585, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.5571428571428572\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:29<00:00, 281.75draws/s]\n",
      "The acceptance probability does not match the target. It is 0.9037129279844466, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.6385714285714286\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:15<00:00, 545.53draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.7200000000000002\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:20<00:00, 512.11draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8946924085162586, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.8813385450767158, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.8014285714285716\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:15<00:00, 542.54draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.882857142857143\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:18<00:00, 523.99draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8847601478095011, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.9642857142857144\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:19<00:00, 518.96draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8873007913580885, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.8834357808309812, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.045714285714286\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:18<00:00, 522.65draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8831433426710051, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.8813475168076812, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.1271428571428572\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:23<00:00, 492.62draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8900397391957722, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.2085714285714286\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:20<00:00, 508.14draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8821837236330341, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.8895405674915002, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.29\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:22<00:00, 499.65draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8906687425623868, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.8798103437691969, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.3714285714285714\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:21<00:00, 500.61draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8837926265032933, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.452857142857143\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:28<00:00, 461.89draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8870837792698791, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.8905050129608727, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.5342857142857143\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:18<00:00, 519.45draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8827507365566772, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.6157142857142857\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:21<00:00, 501.20draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.697142857142857\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:45<00:00, 389.79draws/s]\n",
      "The acceptance probability does not match the target. It is 0.941447403904701, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.8831204794403901, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.7785714285714285\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:15<00:00, 539.99draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.86\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:21<00:00, 503.97draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8809780216942649, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.9414285714285713\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:46<00:00, 383.92draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8795381739496447, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.9248609612663448, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.0228571428571427\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:20<00:00, 507.61draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8896479500375769, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.104285714285714\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:24<00:00, 485.17draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8881703925567049, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.1857142857142855\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:30<00:00, 451.05draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8868581789969977, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.9000639215392091, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.267142857142857\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:18<00:00, 521.22draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.3485714285714288\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:20<00:00, 508.15draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.43\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:18<00:00, 525.19draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.5114285714285716\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:24<00:00, 485.02draws/s]\n",
      "The acceptance probability does not match the target. It is 0.893529308302085, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.592857142857143\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:22<00:00, 494.75draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8902296617644494, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.8849149237705672, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.6742857142857144\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:18<00:00, 524.50draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.755714285714286\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:24<00:00, 487.07draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8874019038867046, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.8864547423093703, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.837142857142857\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:22<00:00, 494.47draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.9185714285714286\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:22<00:00, 263.13draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 2 chains: 100%|██████████| 41000/41000 [01:22<00:00, 498.78draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8821927094222122, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    }
   ],
   "source": [
    "result_array = None\n",
    "for delta_t in delta_t_list:\n",
    "    print(delta_t)\n",
    "    data = langevin.time_series(A=A, D=D, delta_t=delta_t, N=N)\n",
    "    trace = sm.run(x=data,\n",
    "                d_bound=5,\n",
    "                a_bound=5,\n",
    "                delta_t=delta_t,\n",
    "                N=50000)\n",
    "    a_mean = trace['A'].mean()\n",
    "    d_mean = trace['D'].mean()\n",
    "    a_std = trace['A'].std()\n",
    "    d_std = trace['D'].std()\n",
    "    results = [a_mean,a_std,d_mean,d_std]\n",
    "    if result_array is None:\n",
    "        result_array = results\n",
    "    else:\n",
    "        result_array = np.vstack((result_array, results))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1082369b0>]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.semilogy(delta_t_list,result_array.T[3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c20507f28>]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.semilogy(delta_t_list,result_array.T[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c1ecfc8d0>]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "dtau = np.sqrt(result_array.T[1]**2/D**2+A**2/D**4*result_array.T[3]**2)\n",
    "plt.semilogy(delta_t_list,dtau/tau_real,\"o\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1c20728588>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.semilogy(delta_t_list,result_array.T[3]/D,\"o\",label=r\"$dD$\")\n",
    "plt.semilogy(delta_t_list,result_array.T[1]/A,\"o\",label=r'$dA$')\n",
    "plt.semilogy(delta_t_list,dtau/tau_real,\"o\",label=r'$d\\tau$')\n",
    "plt.xlabel(r'$\\Delta t/\\tau$')\n",
    "plt.ylabel(\"relative error\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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69QOQGktri0iu6wZzcbyN5OTkcPz4cWbOnNnkscLCQvr37+8c1fP555+zZcsWZs2ahUajoaysDIDU1FQ+/fRTqqqqMBqNgP1DiclkavBp35vz25ONGze2+PnR0dFend/4+S1trXTk+9r4uVqtFpvNBkBZWRl6vZ7Q0NAGz4mJiWnVPaQksfjA8OHDAWT4Z2sbP9deU6nfHaY32o+3kZMnTwLntktwKCoqYvPmzdx6662A/ZPqSy+9BMDChQtZuHBhk2sdOHCAwYMHA/ZRQ8OGDSM8PLxF54sL01nva2RkJGazmbKyMmcMACUlJej1ep+8hiuSWHwgKioKQIaAtjZHHWXd0/bur4hke1Jpw/pKt27dADh48CAjR450Hl+8eDEmk8k5cmjZsmXk5OTw+OOPN/kUfejQIebPn4+qqgwePBibzcb69eu59957nc/x5nxx4TrrfXV86F2zZo2zdlVaWsr27dsZNmyYT17DFUksPhAQYP81fvHFFzz77LN+jqaTG3xTmyaSxtLS0ujVqxcvv/wyISEhxMfHk5WVRVZWFmAv8BYXF/Pqq68yZswY7rjjjibX6Nevn/MNBGD79u0UFRU5C6reni8uXGe9rxkZGVx77bU8++yzmEwmEhMTee211xoMR24NUrz3Aa1Wi06nk9n3XYBOp2PRokX06tWL+fPnM2fOHLRaLbfccgvBwcGkpaWxZMkSTCaTc6ROY+Hh4cTHxzvfQNauXcvAgQOJj48H8Pp8ceE683195pln+PWvf83ixYt56KGHGDJkCJdffrlPX6MxjaPI01UpipIGHFm3bh3JyS0vAgcHBxMaGirL5wuvTZo0ialTpzboMhEdX2e/rydOnHC0xtJVVT1a/zHpCvOR4OBg5xA/IbyxevVqf4cgWkFXvq/SFeYjYWFhmEwmf4chhBB+J4nFRyIjI7FYLHT1rkUhhJDE4iPdu3cH7OPDhRCiK2t2YlEUZaKiKBGtGUxH5hj5cfDgQT9HIoQQ/uVNi+Vd4NHWCqSjS0hIAODw4cN+jkQIIfzLm8SiAfJaK5CO7uKLLwagurraz5EIIYR/eTPc+HFgrqIoJcAaoFBVValU1xkxYgQAtbW1fo5ECCH8y5vEMhMIB153HHCxkqhNVdUuOTfGUbzPyXGx+q4QQnQh3iSBH+q+hAs6nQ6wr2b61FNP+TkaIYTwn2YnFlVVf9uagXR0wcHBREZGEhkZ6e9QhBDCr7zutlIUpR9wLZAK1ADHgSxVVsQjPT0dq9Xq7zCEEMKvvJogqSjK88Au4DngD9jrLi8CexRF+bvvw+tYQkJCOHbsmL/DEH6UnZ2Noihe19oKCwvp27cvW7ZsaaXIhGg73kyQ/D0wB/gMGAlEAlHAKOATYLaiKHe2RpAdxaFDh9i/f7+/wxB+tHv3biIiIkhJSfHqvLVr1xIVFUVmZmYrRSZE2/GmK+x+YIOqqtc2Ov4DcL2iKOvqnvOGr4LraCIiIigoKPB3GMKPdu/e7dxt0Bvr1q1j3LhxaLWyypLo+Lz5V6wAqzw8vgrod2HhdGzdu3fHZrPJKsetKOtwFhNXTmTwG4OZuHIiWYez/BKHxWJhyZIljBs3jsGDBzNjxgzy8/PZs2ePM7G8+uqrKIri9mv+/PkAlJeXs2nTJiZMmOC8fnPPFaI98qbFchaI9/B4AlB1YeF0bDExMYB9LkuvXr38HE3nk3U4i3nfzaO61r66QX5FPvO+mwfA5IzJbRaHzWZj9uzZ/PDDD/zxj3+kT58+fPnll0yfPp3S0lIGDhxoj2nyZC655BIAPv/8c15//XWWLVtGYGAgAElJSQBs3LgRvV7PqFGjnK/R3HOFaI+8SSzZwJ8URVmpquqO+g8oijIU+BPgn4+P7YRjvbCDBw9KYmkFC7cudCYVh+raahZuXdimiWXlypVkZ2ezfPlyhg4dCsDIkSPZtm0bYN8fHSAlJcVZa1m1ahVJSUnOFRrqW7t2LWPGjMFgMDiPNfdcIdojb5d0uRL4SVGUbMAxvLgvMBEoAZ7wbXgdi2NrY1mIsnUUVLiuX7k73lqWLl3K+PHjnUnFISMjg4MHD9KjR48m5+zfv9/VShXU1NTw9ddfe5xU6+5cIdqrZtdYVFU9DgwHPgAuBR6o+7oU+BAYoapql35HTU1NBWRZl9YSH+K6J9bd8daQk5PD8ePHmTRpUpPHCgsL6d+/PxqNpsFxm83G/v376du3b5Nzvv/+e0wmE2PHjnX5ep7OFaK98mo/FuCMqqo3Yx9qHI+9rhKhqupNXT2pAM7ur9zcXD9H0jnNumgWQbqgBseCdEHMumhWm8Vw8uRJAKKjoxscLyoqYvPmzc76Sn25ublUVFS4bHWsW7eOYcOGER4e7vL1PJ0rRHvlTVfYu8BS4DFVVa1AYeuE1HFlZGQA5958hG856igLty6koKKA+JB4Zl00q03rK926dQPsdbSRI0c6jy9evBiTyeRyqHFhof2/SuOCu81mY/369dx7771uX8/duUK0Z94kFtmP5Ty6d+9OaGio881H+N7kjMltmkgaS0tLo1evXrz88suEhIQQHx9PVlYWWVn2cSuOwn19wcHBgH1Wfm1trbM2s337doqKihg/frzb13N3rhDtmTfzWB4H/qwoyu2KosQpiqI57xldjFarJSUlBYvF4u9QRCvR6XQsWrSIXr16MX/+fObMmYNWq+WWW24hODiYtLS0JucoisLNN9/MihUrePjhh53H165dy8CBA53bWrvi7lwh2jONzda8vboURfkZ6AEEeXhah9uPRVGUNODIunXrnKO6LsQvfvELAFnzSZzXpEmTmDp1qseuMCHaqxMnTjha2+mqqh6t/5jsx+Jjx48fp7Ky0t9hiA5g9erV/g5BiFbhbfF+k6qqpa0VTGdw6aWXsmHDBn+HIYQQfuNNjeVd4NHWCqSz6NevH6WlpbIvixCiy/ImsciosGawWq1YrVZOnTrl71CEEMIvvF3SZa6iKCXAGqBQVdXmVf67kBMnTgD2vVliY2P9HI0QQrQ9bxLLTCAceN1xwMVs4A43KszXEhMTAft6YfUn0AkhRFcho8J8zLFe2NGjR/0biBBC+EmzE4uqqr9tzUA6i/T0dEDWCxNCdF1ed1spihINXIF9suR7QAUQrarqzz6OrUNyLESZlyfjHIQQXZNXG2wrijIbOA68DTwLZACjgN2Korwsy7yc25OlqKjIz5EIIYR/eLNs/jTgBex72/8a+/BjgK3Y92P5A/ZdJLu0oKAgNBoNxcXF/g5FCCH8wpsWy0PAF6qq3gZsdBxUVTVHVdUbgc+Au3wbXsdkMBgoLZUFCoQQXZM3iaUf8F8Pj3+CvWusywsKCqKiosLfYQghhF94k1jOYt850p1UoPzCwukcLr30UkJCQvwdhhBC+IU3iWU18EdFUZpMJ1cUZTBwH/CFrwLryPr06UNJSYm/wxBCCL/wJrE8hr1gvwf7FsU24B5FUVYBmwEzMNfnEXZAZrOZqqoqWT5fCNElNTuxqKqaC1wMZAHjsCeZXwMTsddeRqiqerg1guxIsg5nsfzH5QCM++c4sg5n+TkiIYRoW15NkFRVNR+YXjdfJRrQAUWqqta2RnAdTdbhLOZ9N4+QiSHwAxzbfox5cfMA/LpPuxBCtKUWLRhZt6qxzABsZOHWhVTXVhOcHowhzkD59nKqJ1SzcOtCSSxCiC6jS69E7GsFFfkAaDQaDNEGyveUU1tZSwH5fo5MCCHajldLugjP4mvPbU+j0WvABme3n21wXAghOjtJLD4063QxQXVbEkeOsU/5Kf2qmFmnZXkXIUTXIV1hPjQ5IApOnWZht0is/UNAA9UHKpmoSfN3aEII0WZk2XxfGj+XyZ/MZPIJ+5L5Q2O17Dhp5cvw65ng59CEEKKtyLL5vjT4JpiyCCJSAA23XBwNwJvf5vg3LiGEaEOybL6vDb4JHtgN80q47qWvAPjkk0+w2aSAL4ToGmTZ/FbUp08foqOjOXPmDNu2bfN3OEII0SZk2fxWpNFouPbaawH44IMP/ByNEEK0DVk2v5VNmzaN6OhoPvroI3+HIoQQbUKWzW9l48eP55FHHmHv3r0cPXrU3+EIIUSrk2Xz28DUqVMB+Pjjj/0ciRBCtD5ZNr8NfPfddwC8++67fo5ECCFanyyb3wbGjRvHhAkTWL9+PcXFxURFRfk7JCGEaDXNTiyKohzAPjHybVVVDyDL5jdbSkoKf/3rX7nkkkv47LPPuO222/wdkhBCtBpvaiy5wBPAPkVRNiuKMktRlPhWiqvT6dWrFxERETLsWAjR6XlTYxkLJAMPADXA/wA5iqJ8oSjKnYqihLVOiJ3Dtm3bKC0tZfXq1ZhMJn+HI4QQrcartcJUVS1QVXWRqqqjgXTsI8XCgf8AJxVFWdEKMXYKY8aMISgoiOrqatauXevvcIQQotW0eD8WVVWPA4uBv2JfziUI+JWP4up0AgMDGTxqMGhg2l+mMXHlRLIOZ/k7LCGE8LmWLJsfCFyNfajxNUAIcBCYj724L1zIOpzFydSTYIOyLWWcKDrBvO/mATA5Y7J/gxNCCB/yZlTYdcBN2JNJKHASexfY26qqbm6d8DqPhVsXEjQoyP6DBUo3l6K7TMfCrQslsQghOhVvWiyrsK8Xtgp7y2SdqqrWVomqEyqoKEAfpcfY00j1sWpKvi0h6rIoCioK/B2aEEL4lDeJ5WbgY1VVq1srmM4sXh9OvrmUiGERVB2qonJ/JTWFNaQmxfg7NCGE8ClvhhuvkKTScrPOlBBktRJ+cbjzWPm3Z5h1psSPUQkhhO+5bbEoilIL3K6q6jt1P1uxLzzpiU1VVa8HBHQFk4tOQIiRhd0iOdHTSO1pM9avi7l6iMxpEUJ0Lp6SwDLgUKOfZX/dlopIZnJpDpMrKjHfEsC7u23c+VE13xRHMcbfsQkhhA+5TSyqqv620c/TWz2azmz8XPhkJpir0Os03NBPz71Z1SzLy5DEIoToVJpdY1EUZb2iKOM9PD5FUZQ9vgmrExp8E0xZBBEpgIbHv9ETEhrGirU/UVVV5e/ohBDCZzzVWIKxL43vMBb4sG6V48a0wFXYl3kR7gy+yf4FZKa9zqkvvuCdd97ho48+4pZbbvFzcEII4RueWiwhwHbgSN2XDfhHvZ/rfx0C/gB83ZrBdibTp0/nzTffJCUlhWXLlvk7HCFEF5N1OIuJKycy+I3BPl9iylONpUhRlFuB4dh3i5wLfAjsdPH0Wuz7syz3WWRdgMViYezYsbz99ttcuvRSSgJLiA+JZ9ZFs2Q2vhCi1WQdzmLed/OorrXPIMmvyPfpElMehwarqvo58DmAoiipwKuqqm664FcVACxatIg333wTgAPrDxB9VbTPb7AQQjS2cOtCZ1JxqK6t9tkSU95MkPzt+ZKKoigyjdwL119/PQAB3QM48+0ZbDb7aG7HDRZCiNbgbikpXy0x5dVkRkVRbse+NH4oDZNSABAGDAAMPomsC+jZsydBqUHUVtRiOmGi+lg1xjQj4LsbLIQQjcWHxJNfke/yuC94M9x4DvA6cCUwCLgM6Im9BvNLoA+wyCdRdSHJo5MxnzKDDgo/KsRmtbdafHWDhRBdl7sC/ayLZqHXBDZ4rl4TyKyLZvnkdb3Z6Ou3wA4gFhiJvaB/ORAB3Id9o68ffBJVFzJnxhwAwoaEcXb7WU6uPEmQRu+zGyyE6JocBfr8inxs2Jz126zDWZhLh1KdfwPWmkhsNrDWRFKdfwPm0qE+eW1vusLSgMdUVT0LnFUU5QwwRlXVw8A/FUUZA/w/YKVPIusi7oqO4PlEPadLzERd3o1Tn51iWqiVyUMryDqcxcKtCymoKJDRYkIIt1y9V3gq0FccfJTKkiFwZkiDx1/IVrkuM+mC4/EmsZix78ficAAYXO/nDcAzFxxRV7PuaWb01fL4+moOTdbxh2M6XllZTHz8I6waFt1qwwGFEJ2Du6HDjZOKQ0FFAWdLXK/2kefmuLe86Qr7GRhV72cVuLjez5FAw047cX6lJ7ixvz2/v7/XwopfB9M7Ssvcfx2nNLe0wVNltJgQXZurmom7lolW4/rtPT4knsRIo8vH3B33ljeJ5f+A3yqK8paiKCHAx8AYRVFffi9RAAAgAElEQVSeUhTlJuAB7DUY4Y2IZPp01zGxp45vcmqJCIRPpwVj02o4tuAYlnJLg6fLaDEhuiZ3NRNXo7sArDYrNqu+wTGbVc/oqNt5+EoFo17X4DGjXsfDVyo+idWbeSyvAs9i3/PejH2L4uXAU3Xfg4FHfBJVVzJ+LuiNrLgxmI9+Y0Sj0ZARG8JFD/bHfNrM8cXHsVrO7QAto8WE6FhasnSKL1omGks3lwX6NT8mcV1mEs/dMIikSCMaICnSyHM3DPJJfQW8nMeiquoTiqLMU1XV8TF6mqIorwJRwHeqqhb6JKqupG5Ryoh1T0PpCQo0cbxe+AvmzpzGzMKZHHn1CLn/yiXp90kEBwbLaDEhOhBPS6cALgfneFszsdqsBOmCGjwepAuiJHcilrJMLGWZDZ6fRxWnTp1Cc/wnbjIe5a6ZdxEcHOzTv7fGMdu7q1IUJQ04sm7dOpKTk/0dDgsWLODxxx9n27ZtHMx/i/+3ZCkHPyikW98Q/vn3P/CbKS/6O0QhRDNNXDnRZVdVhCECU62pSTKYN2oeC7cudHmOVqPFarM2OZ4QksDoqNv54Mj/YtWdQVvbjV+l38WaH5PILanCZrNhKcnHdGIvphN7qc3fR1XRcQDCwsLYuXMnaWlpXv/dTpw4wfjx4wHSVVU9Wv8xt4lFUZT1Xr+SfWtit3u2tEftLbFYrVaOHDlCz4otzo3B3tpZw4yPq0nvpiPr9f+h5+SZ/g5TCNGIqyG/j339GDYvNt5NCEmgoKLA7TmuWibXJM5k+YYYqsy1AFjNJjSnDtOLXH78YROVJ/ZirbQPBNIGhZJ58QhunDyBX/7yl1x88cUEBQW16O/rKbF46grLQLYibnNarZaePXvCgqm8s7WMq3sHcNtgA6kRWq5/r4oRv3mQ/2b/gtGjR/s7VCG6JFcJBHDZfRURGEGJqaTZ13Zc01WLxVXL5JqUu/h0nZHTe7+m+sQeTLn7qDl5CKwWjgMJKWkYleHUxvSmR/9f8ORtV3DDL1J88nvwRLrC2lmLxeHgzDD6vVzONX0CWHWTvah/sNjK1W9XcqRcS997+6LJ1MjESSEugLeTkBvXP8DeaggKCHKZQNx1ebl7fkJIArMumuXyNa5JnMm766I4ezKH6tyfMZ3YS03uXsxn8gDQBBgwxPcmMKkfgUn9CErqy/FF01r0e2mOlrZY3FIUJRFIAfYBVYBFVdWmnX+ixXqlp/LCFQd5INvEgh9qeHBkIL2itDz9SG/u+r9cdi/cTez1sVinWM9bDBSiq/OmlQHuJyG7G5nlrrBeVlPGr1IebtLKuDgtymXycPyf/eloMSsPL6X61ElMh7WEnUnmf7a8yNncA9hq7JMYtcZwApP7EzZ0Eoak/hjie6LRnRtenOSjOSkt4e3qxqOxLzTpWFDmirpr/EdRlAdVVV3h4/i6rvFzmVXxJ74+XszDX5gYFKvjir5h/Cc5mh4P6cj7vzwKPyyk6nAVyXcn89ym5xp8MpKZ+qIr8iaBBAUEedyTxNW1vJ1HFq6Pqat/nJuJsfyojiE3DOKaxJkNEs7k5N+TVpXGXY/8heX//ZzKY7uwVpcDcCLgCPrYdEIHjre3ShL7EBCVjEajAexzUBw1FsfPvpqT0hLN7gpTFGUY8BWQA3yCfV2wK4Ay4H3sLZgpdZuDdRjttSsMgJ0rKP/sKUYt2E/OWdi0/CVuPPMfbNiw2WwUryum4N0CAroF0OO+HhjTm35CSQhJYM2Na/wQvBBty9tuKnc0aHhuzHM+6fLi1K8pKhjQ5PmRRj1V1dWU5R+hJn8/1cd3YcrZRW2F/doBEXEE9hhs79ZK6IW+ew8CAvTUuni/Too08vCVCi9kq+SVVJFY97Ov5qS406JRYY0pipKNPXn8AggBCoEJqqquVxQlHPgWKFFVdYwPY2917Tqx1Dly5AjDhw+ne/fuJDyWwClOOR+rPFRJzss5WMosJNyaQLex3ZyfYsD+n2Tnna52kxai43K36KK7WejeSAhJAPB6mPBPR4ubDPl9fU0UNsBaU0VNwQFqTh6hpvAQNScPYz6dA1Z7K0MXGkVQ6hDi+15MdUxfAiLiXMbmqmXiy4mN3vBVjWUk8BdVVasURWkwm0ZV1TJFUZYCT19osKKp9PR0Vq5cyYQJEwj9TyiBMwIx2UwABPcMZsBfB3DstWPkvZFHxf4KkqYnoQ20z8Z1zNSXlZKFv7Xk36A3XVvu6hzuuEsSjmHCrpTVlPHcmOeaxGQuHcryDbucXV61FWdY+vk+zLl7KT262z5Sq24Oii6kG/q4DIy9hmOIzcAQ15OAyHg0Gg21QGqkkVwXi0H6q2XSEt4W700eHgvCu7XHhBcuu+wyXn75Ze655x5+PeDXlIwrOfcPe8wsrFdY+cOjfyBvVR7VR6uJHB1J1KAo7r/lfo+zfyW5iLbgyxno7moj7iYQuksgj414zO1ru2v9xIfEYy4dSsXBRykrLkevKWfL6QqWZf8PRfnHsZScpObkISz1RmoZk/pivOTXBCb1xRDXi9Bu0QTptZypNDe5viNZPLZql8uayXWZSe0ykTTmTWLZBEzDxS6RdYtS/h7Y7KO4hAt33303p0+f5rrrrqNfv35NHtf+Xcvc/nPZ+/peTq48ycmVJ7lzwZ0Y+hjQ9dER2j8UQ4IBjUbTYKVkacmI1uZuNJWnQSfejsByt7SJpwQCrj9cuRryG6gJJCVvBDMWPMjZAz9iPp3DMWstWx1P0AYQEBGLProHoUMmEZTcn8D4nvxj2rAmrQzAY/IAOkTLxB1vaiwjgY3Yd4n8L/AC8ARQAcwEUoGJqqpuaJVIW0lHqLE0sXMFtrXzyc/NITG5h30hy7o1xxxOnjzJ+vXrWbduHcv+u8y+/TEQ3CeYmCkxhA4MRaPRuPyPOG/UPEkuosXaYga6u3MctZbmflD6aFuu2zfwrMNZvPj1ixz68RCW3RYqdlVQdqYMtDqCUgZgSFAIiExAHxmPoVsCmtAoNNqGKwYnRRr59tFxXr92R+CT4j2AoihXAK8C6Y0eygf+pKrqqgsLte11uMSycwV8MpMns8/w2hYzO/4QQkJUCExZ1CS5OExcOZFjR45Rtq2M09mnMRebMWYYibs2jpAhIQ2K/dCy/6Ci8/KmNuLLkVnuZqB7KqC7i8vVmzicazXYbDZqzxbB6WNcFl1JTeERduzYwcGDB7HZbHTv3p2rr76a1aWJBGVchDYwpMlrtKfCelvwSfFeUZTuqqp+oShKLyAT6AnogKPAT/VWPBatad3TYK7i9iF6DDoN8aEaMFfZjzseLz0BEcnOlsysi2Yxr3oehlgDUeOjKPmmhFNZpzj6j6ME9QgiZkoM4b8IR6O1J5jGxVCpyXQe7pKEp+Pe1EbcdV8F6gJdto7dJRzH9VwlKU9dW+dLIAA5J08xa+E2rKePUZJ7GPOpY5iLjjrnjLwD9OzZk5jUPlSnjsIcN4D0/kO54ar+HMpWO3xhvS140xV2HPhfVVX/0rohta0O12KZF0njJdz2FtVyutLGmF5h9iTjoDc6WzKN3zjuG3Qfjy9+nAMfHKCmoIbAxEBiro0hYngEOp3O7SqqMiemffFFa2Jqr6n89+B/vVpp112rwV39wzE35HwjvOq/tqeE58qHW0/w8BsbOJt3CEtZEdaqs2hqysFUTvXZEqzV5VjKTtlbJo64DMEYYlLRx6RiiM1AH5NOYEwqC+8Y5bIG8qtfJPHBltwu1TJxx1fzWKqAmaqq/q/PI/SjDpdYFgyE0pwGh8Yvq+D7nFo+ujmYiT0bNUIjUuCB3S4vlXU4i6e+eYqT35+k6OMiTHkmghKCiJ4STcSICDS6hl1k7t4cpBXjH+4ShbsuIXdLuHtajt3bOoena7n7UNKSYci1tbXs2rWLrVu3smPHDnbu3Mk3m7ZgqTrb4HkafRBaYxjaoDB0xjD7UN+YVPQxaRhiUtGFxTTpCnYshSItE898NY/lbeBuRVG+aHwR0YbGz3Uup+/w7m+imPh/p5nybiUrbjQytW+97UhLT7i9lOM/78LghUQOj0S7W0tZVhlHlx6l8L+FxFwTQ+TISDQB9v944YZwj11k3naziIa8/f2563ZyN9rP3XIkrhIBeF5p1x13I7M8bVA3OWNysxLJzp072bhxIxs3bmTdhi+pOFu3FLwhiF5Kf4L6jMYQm4Y+Np2AiHh0xnA0AXq314w06jFZrC5HZj3w3naX5+SVVHWYIb/+5E2LZSlwC/b5Kgexz7yvbfQ02Y+lLexc0aSWcuaTp7jqnwf4Ka+WN683csuguv9QHlosrlitVp587UkW/G0BVceq0AZpMcQZMMYbCU0KxRZtwxBnIDAxEJ3RPgLG04qsnrpZJLmc05JuKk8jrbypZ3hqZbi7r+dbnbe59Y/rMpOwWCzs27ePffv2cebMGUpLS51fu47ks33/ccqO7cFqqrC/Ro90KrsrBCQNIDBRISAynmCD3u3cEHcJ5LkbBgGuh/WOfn692xaLu1FeXY2vusKONOd5qqo2HjHWrnXIxOLKzhWcXXk/1ywr5qtjtYxK0XHb0GBuemgB3S+d4TIZuRtFBvDpoU958l9PkvNTDpwCfbGegpyCc+UdHYQNDiNyVCThQ8NJjEz0upvF3RuQP1s4vmx1eXOtluwaCK6XHfF2ouD5kn9zZr83Pqexj7bl8ugHO6ksL8N8Jo+ak4ewFh0hpiaPnIP7qK5u2PLSaDQYQ8Ko0QahCQwmMKEPgT0GEZkxhLDucT5LIO58tC3XZY2lK9ZS3PHZcOPOqNMkFoCdK6j8fB5L1h5h2W4bewpM6PV6Fs25kz8YP3Fb2G+uCe9O4PjR45hOmqhUKyn5oQRLiYWAkADCh4UTOToSYy9jkz5rd1x9qvb0JgfuJ7m1ZLRTc98sffnG6+5a3i5H4mmhRG8L6BeSOP+x+R/kFuXSzdqN6xOvp5+xH8XFxRQXF1NQUEBubi4nTpzg+10HMJUWYTOfW7xDGxhCaFJvxo4azs813akISSAhNoYHJw/l5tF9GPP3jS5bDe5/J7DgN0N9Vv/o6PNMWpskFg86VWKpx2azsXPnTt58801+U/shwyJOsTm3lp/yavnDxXr7m7+X3WSNu2tsVhs1+2pI3p/Ml59/idVkxRBnoNul3eg2phsB4QFuPz17e9zT3AXw7k3c3fG26Cry1e/DUQz3pvXji1F9NpuNAwcOsHr1alavXs3GjRupqnL95h8QEEBiYiLJyclsP61FF9adgLDuBETEo4/LICAizt4ycTP/44H3tnu1ha10U7UtSSwedNbE0kDdEOW/fWPi+W9NqPeHEhuiBTQwr/mT1sB9y+D9ne8z5+U5FH5ZSKVaiUanodvwblx/+/VsD92OyXruk2pLPqG705IuIXfHveVpEl9LeNuC83ZYsbtzqqurycvLIzc3l9OnT9v/bhoNWq3W+b2iooINGzawevVqjhyx94r36dOHK6+8kj59+hAVFeX86tatm/O7VmtfPtBdzUKn0bhdCh5cj8zy1OUlLYq2I4nFgy6RWOqGKFttNg4WW+nTXYfNZiPHFk+PG//qVe3FE0fSOXrgKNVfV1P8TTEVZytI6ZVC8JhgNEM1pCSmtKim4I4Ge7ebN0NivdVWw3F9WXNydc6EpAl89913rFmzhh07dpCbm9sgmZxPSEgI48ePZ9KkSVx55ZVkZGS4fF5zJilC05nq9Tm6tdzVOaBjr6XVGUhi8aBLJJa6ZWDq11gWbrbxxIZq/n1tMDf1rfdvoAW1F3cqKytZvnw5r776Kps3b0aj0TB8+HCuueYaIjIjeKP4jQYtGUOtgYvMF7F642rKDpYB0O2ybkQPjsZoMLodhQS+abG0pLjt7QRCX42Sq66uZvfu3Wzbto3du3cTEhJCYmIiSUlJzu9xcXEcPHiQNWvWsGbNGjZu3EhlZSUBAQEMGjSI5ORkkpKSGnzFxNjndVitVmw2m/O7Tqdj0KBBGAwGj3F5KnpD02TwgoeZ7N8+Ok7qHO2YJBYPukRigSajwk4MvI/f3D2b745WMXO4gRcmBmJwTIj0svbSHDt27ODjjz/m008/5ccffwQgJiGGwEGBVFmrMB8xU3GsglqL/Q3JGGfEXGXGUmYhKT2JybdNZnPKZsyGc6OBgnRBzBk0h50/7OS191+j/Eg5IUoIkb+MJLJHpNc1Fk8DBJq75Imra+UV5xFZE8m1sdeSrkln7a61rNm1hrKSMgwWA6lBqYRYQygvL6e8vByLxeLsVurevbvzKzAwkD179rBt2zb27t2LxWJfRSk4OJiamhrnz6706dOHiRMnMnHiRMaOHUtYWFiDxz29gbt7zNXx8yWKxmT0VcfVZROLoigPAjOwD5L9CbhHVVVTo+ek0RUSiwvmJyN4ZG01C36oYUSSjvduNJIaWVd7uWGpz7rIGisoKOCzzz7j008/Zc0aezF5+PDhXHLJJc6v2NhYampqeP/991myZAk//PADxhAj0b+MRjdQhzZHS9ChINTtKrW1tQQFBxGYFEjp4VKohV4DezHz7pl0H9md14++7kwIM3rNIL40nnfWvcOn33xKlaWKmIwY7hh/B7+f+Hvi4lzv3OeJq6STWpnKW2+9xbvvvsvx48ebnBMQEEBUVBRhYWGEhoY2+NLpdM6RVadPn+b06dOUl9vXsYqLiyMzM5PMzEwuuugiMjMzSU+3j/AvKioiLy+vwVdCQgITJ04kLS0N8K6bytHK8GZpE09dW0eeb/4CkZJU2r8umVgURRkB/Au4BKgElgE7VVV9odHz0uiiicVRe/lgr5nffVyFTgNvXGdkytA4sFRd8PDk5jCbzWi1WnQ6ncfn/fTTTyxevJjly5dTU1ODRqPh4osv5oorrmDixImMHDkSg8FAYWEh7777Lm+88Qbbtm0jICCAq666Cp1Ox/bt2zl69Kjzmo5un8LCwgbHBg0aRI8ePTCbzdTU1GAymZzfNRoNvXv3ZsCAAQwYMICBAwcSGxsLQH5+Pu+88w5vvfUW27dvR6fTMWnSJEaPHk1CQgLx8fEkJCSQkJBAdHS0s7DdHCaTiaqqKiIjI737BdfjrnXgbmKhpwK6u6K7p2K8jNjqXLpqYukDJKiq+mXdzw8DPVRV/VOj56XRVRNLvdrLoWIrN62sZGu+ldljwnnuMhv6RmuFtUYXmbcKCwvZsmULw4cPp3v37h6fu2vXLpYtW8aKFSsIDg5myJAhDB06lKFDhzJkyBDi4+OdiWX37t3s2rXL+ZWXl0dgYCAGg6HBd7PZzL59+ygpOVfviY6OJiUlhR07dmC1Whk+fDi33XYbN998MzExMa36+/Dm0767kVnuOO6+t+8QXW35+K6qSyaW+hRFScC+u+V0VVXXNnosja6aWKBB7cUUksjsLT14+b1s7r1YzyuTjY2e7P3w5M7IZrORn5/Pnj17nF+HDx9m1KhR3HbbbSiK0iZxeFufSH80y+t5IeBdi0UWaew6fLUIZbukKMrNwJJGh0+qqjqg7vFU4HPgn42TisDetVXXvRWI/Rc5NiiFYZH2BHL4jJXIIA1RRo291iLQaDQkJiaSmJjIFVdc4bc4XshWm9Q0qsy1vJCtunwjT4w0ejUvxFP9xV2NpSPtyy5aT4dPLKqqLgeWu3pMUZShwCfA31VVXdymgXVgNz74krOL7KE11WwvqOXwQ7Ewfi6HDx8mNTX1vDUR4T1vRl9dl5lEnpturbySKpfnPHyl4jJJzLt2AOB5Xoirxy5OjZKWiXCp03aFKYoSA+wC7ldVdaWH56XRlbvC3KnrItu89yj51iiunfUi1oE3khgbRU1lOZN7a3ni6lSUW57xeUG/K3LXreVpYyl3Q3t9uRijEO50iBqLoijXAm+rqhrW6PhdwBwgGdgOPKiq6vfNuN6zwP8D9tc7nKWq6uONnpeGJJZmsWx9l1V/v5fVaiXv7zVTZYa7hxl56vl/EHf53f4Or0NryZIn7lognkZ5ycgs4SvtvsaiKMoo4C3ODURxHL8DeBV4Gnvx/U9AtqIoQ1RV9biMv6qqfwb+3DoRd00BXz7DTX1t3NTXyPMTApm/0cRrm6t486p7mfP4SR68IpWQ7//eKnNfOjt33Vqukorj+Y6WRuMWiKdNqoRoC35NLIqiBAKzgL8AFYCh3mMa7Allqaqq8+uOfQGowAPAzDYPuKurtxtlbIiWlycbmTnCwJ/Xm5g7dy7/fEHL/MsMzLhIj7Y0x16nAUkujbiqf7grrLtrsSTWjdhyVSh310XmOEeI1tb8GVqt4yrgMeBhoHFxvReQCnzsOKCqqhnIAia1VYCiHhejwpRoHR/cpfDtn9JJi9Dw+g4zVsf7oLnKPpR55wr7ZMx5kfbvO1e0bdztiKOWkltShQ37UN7HVu3i8r4xGPUNB0QY9TpuGZHi8rhjxJYrD1+peH2OEL7k766wzdj750oURZnX6LE+dd8PNjp+GOipKIpOVVXX60eI1jF+bpPFLNEbYfxcRq26m29/F8zZGgjQaiiqsPJdTi1T++Y0PKeDtmR8uZaWqyHCG/YVOQvyFzr6yl0XmRTpRVvxa2JRVTXXw8Phdd/PNjp+FntLKwQoa424hBuOROBqDbF1T6MpzSE80P6UF76rYdGmGg7ONJAc3qhbxtGScXetdqbxiC1HK8PB1WM/HStuMJrLcdzdWlqOmomrN/+WzAuRuSTCn/zdYvHE3YoSjuMXvlOT8F69CZUNNGrN/HVcIFMHhJAcbn8jPVpiJS2yXs9rqX9bMr5oZbyQrTr/3PixdzflNKmNVJlrz1szEaIz8HeNxZPSuu9hjY6HYk8qFW0bjvBo8E32RSojUgANhqgejL7/VYhI4cOfzfReXM7tH1bx6X4zNbU20OgadqlBw5ZMK3JX53jio10uj7tbXyuvpMrr0Vy1NpvUP0Sn155bLAfqvmfQsM6SAaiqqraPCTjiHDetmbGn7+euiyws323mrZ1mIoM0XN83gJsG6Bmfrmu42GW9kWe+4E0LpKWtDFlLS4iG2ntiyQGuA9YAKIqiByZjHxkmOoLBN9ENeKX70/yjOIe1BZG8dzKND774hv/bbibKqGFInJaEMA1v3xAMEcm8OPt2yndnM29kTbNrL83ZZ+R8dY7ztTJkLS0hmqfdJhZVVW2KojwPLFEU5QzwLXA/EA0s8Gtwwjt1LRkDcHXdl+mnt8n+x328v6uSYyVWKmqwjzDrPZE9b/6TkioLjAyG0hyOLbuP1DvqruWi2O+uuB6k17psmbRkL5HztTJkLS0hzmlPS7rMAx5SVTW00fHZ2CdRRmNf0mV2c5Z08eJ105AlXfyj0XbJjJ9b93OO8ymfqGZuWFHFE+Mi+fMYA3rruS2AHZuPjf4s2qt9RsD1niGe1uWShCBEQx1irTB/kcTSzsyLpP5AwOIqG7NWV/PWTjND47W8cZ2RwXH1it8RKaSf/JvX+4y4a4HINrlCNE+7XytMCIdKYzzBVfnOn6OMGt683sgN/QL4w6fVXLy0glkjDCSFa7DaoNZ2iNCMg1weVcCcgBWYSwvRR8Tyd8tNfBV4udt9Rnw5Z0QI0ZAkFtGu/N38G+bYXiFYU+M8VmkzcJkSyp4eZdz/WTUvfl/T4Jzf3bSGv8X9yLHTVfR7uYJl11n42+B/sTszDYCUrS8QayuiUBNDzkUPMyxTVgQSojVJYhE+4+1GVa6Ov1E+nGJtDXMCVpCoOU2erTt/t9hHhD1v/BfLb9Ty2jU2bEA1euZbprMw7nMMFTXEhmh5fnwgE3sGYNTUkLdyLt8cKefuoRpCw7ScPVtA9SePsULdR0FgOgUFBaSnpzN9+nT0er39L+Gq7tMOVwMQoj2TGovUWHzC242q3B13t5eITqNhsubrJglnS/gVfFt9A00XaICnvzTxl69MWNys0aDTQu8oLXse7Yv2iqcwmy3oVz/YdC20KYskuQjRiNRYhM+4a314O+nQ3fHAAK2HEVuX8XHNLxscf+5KBTYmNxhJ5jD3skDuukjP8t1mzFZICNUQH2qfMxMfGUyUvprTlTa0Z09QvvJ++i4sZv5lemZcZDh3kQ62rpkQ7YEkFuGSNxMOwfuNqtwdL60ys+A3Q72bF6Jzs+pygJEEinlgZGDDF9HowGYCNMSE2Gf9V1ZVcWWGlgGx9lWONufWsu6IhRFJOi5OPE6Yp3XNpPtMiAakK0y6wppw163lactb8G5pE0+TEVu0fa6rN3dwnXAar1HmwkvfmXjoCxMAWg0MiNEyIknHyBQdl6cFkN5Na18Xzd1WAlMW2f/sKuFIIhKdgHSFCbe8WUvL05LvC34z1Cc1lhYvxuhu1WU47yTMcwFEgaUKzFXMHhXI9KF6fjwZwKZjlWzKreWDn838a5s9sWZ00zA+fT+LLfMIdLWY5uePOK8FnGvlHP8BdrzT4fenEcITSSxdmLulUNwlEHcSI40eN5dy14XVJkueuEs4rloZV/3N/ue6RNQ9IZWrbpvLVXWJyGaz8fMpK+uP1LL2sIUthToCK/IAeHRtNeZaeOnKIACu/c8Jcs9asdogMkhDjwgtKeHV9PjhNVLCbfSI0JIYpqWbUSN1HNHpSGLpgLwd1uvuHHctE3fdVJFGvdsJh+B+cmG7m4zoacOy+o/X98lMNOYq+sfo6B+j4/7REdiuWQjr/wKlOeSX24gNPrdKc3SwBhtaNMDpKhsbjljIPWvDajs3B+daJYD/3hwMQNr8vVy/8rcsuCIAm83Gnz84wLDNd3PpPWVEdwv3PuFId5vwI6mxdLAai7fDep+7YRDgegVeTy0TVyOzHNfqkkueuHuj3rnC7cABqoobXMJitZFfriWn1MzxUhvdgjRc2cv+2e6pjTUMidNwQz89uWVW+iwpx1HOGhCrY2yqltEpAcSHaogMDSJy8nziL5+B0ehigzB3McmwaeFDslaYBx0tsYx+fr3X+3+A7Jsp2qIAAA76SURBVBnSqrwZODBkWsMai+N4ozpNTa2NLXm1bDxay5fHLHxzvJaKRuMmli5dyl0jIlDffZxb3zjCoht7MOr3z1Py6VOUFZ0gJVyDRnOuFWUNS6b63s1UVVVhNBoJDg729W9CdCFSvO+gXHVfeTus193zHee422dE1szygjcDBwbfBD0uOe+AAoNOw8iUAEamBPDYmEDMtfb6TnGVjZJqGyXVMCquAj55kuoz5UQZIdxSCJ/M5MMfS/ndx9WEGSAsUEOV2UaVBaote+GhEMC+v/cPs9IZ/rvn2aMbwL7s/zDZ8jlBlXlNu848tdZk1JtwQVos7aDF0pw5I3D+menetlikZdKOeNGlBtRtAY3L0W2HzsDaQzXsLqylygLGADDqNRiNRozaWoxaMyXV8P8uMRARFszcXWk8s2IT5Y+FYdRr+N8tNahntAyfejfDB/Ykdctf0FgabVfgruXl7rinbriWJCJJXn4nXWEe+DuxeDtnxF0BvSU1FtlnpJ3xpkttyiJYdTeulrJxPqeZSarKouXgaTOD6rYjuP+zKv611Yyp7p9LTLCGofFarDY4W2PjrAkSw7SsvcPelXbXx1UEBcDiq42g0XHgVA3J4VqM+obdcObL/ox57V+hLA9j92R0Vzzl+e/nrvVzvnOa+7uVRHRBpCusHfN2zkiLZqbXey1pmbRj3napuZuP45i42ficVXe7vLQxwOpMKgBLrjbyP1cGseukjR9zLfyYV8uuk7UYdBoigzSkhGtIi9Q6nx8WqCGw7nSb1cLIf1dyptpGiB5qasFsBattL3Cb85wb++/n/eqZEGBk0KIibh6g5/FLA7HZbCzbXEpmyZ/pf0stAZ8/0HTOT4CLSa6ehmxDw0RUf+6Qu98ttH4y6sTJTlosbdhicdXl9cB7273epKpFM9NF5+Pt6K8FA10nIo0ObC4+yHjobnN3jtWmZdXPJnYX1lJmAr0W9DrQ67TotTb0Wnsbq093Ldf1ta8offcnVYxNC2DaID2Hz1jpuagcgGCDhsw4LUPjtdTUwqlKm/Nr7mWB3DxQz86TtYx7o5K3bjAyqVcAmwoCmLeulCijhsRQLQmRBhIjg0gwVJIYpiEpXEuwoyVVb0Jsk98f+K5V1JJWl6/qWq2YvKQrzANfJxZPc0x80eUl3VeiAW/eONwlIk91EfDunGaOenPHarNx4LSVzWci2XywiJ/y7a2lEIOG7kYN0cH2r7t/YWBizwCOllh54VsT9w4zMDDOwJdHTDz8RTWnKm3kl9uotjR9jfhQDStuNDImNYADp2v5/kQtUxU9EUF1CcdDQrWGJVOYOYv4HYug9AT7TTFETHyYuO6R3v2ePNXO6pYJqqmupNZqX4VbZzCiHToNzc53L/xenC95NZMkFg9amli8Kbg/d8MgXshWXRbQPSUQkO4r4WMt+WTri0/JzVhGx8nx5uftOY2Sl81mHz2XX24l76yN/LNWcspsHD5j5c9jAsnopuWfm2v442fVnHgglKRwLW9sryH7UC0XJei4KEFL/xgt6ikr3+bU8l1OLd/lWIgJ1aHeZx9dN/x/y4k0BrDmrkSoKuaPWVXU1Nq7AE21NkwWDaZaKyaLvaUWZtAwNk3Hg3ULoy743sSIZB2jUgI4U2Xj1+9Xkl8ZQH6piTPVNKHVwKOjDTwzPoiy/9/e3QdZVddxHH/f3WUB5Wl5EibQEZm+WQZEmoMl1gSaWgam1YSaRDZZpj2o5ShNPuQY9oSJOTpjhZqNWj4HTKIzTooNFZlZfkeTUUIsXR5EFhC4tz9+58r1cs69ew/n7t7d+3nN7Jzd3/mdu7/748d+7+/h/M7OAkfdvI2FMwdxxpQ21m3J8+2HdzBqcI5RB+QYdUArowbDqME5DhqSY/LIFoa056rvcdfN4KI5lowlbYUyaEBL7HxJMTjEqTRnAiiQSLaS5nEqze/Ues1+bKOzT1Cr5ZqyQJTL5egYDB0jx/DuuEDUNpgF0zuZNamV8UNDb2Xj9gKPr4c7/rHvX/V3jW7h1MPb+dDBLRQKBXK5HNfMGkRLDti+kUKhwBPr9vBqV4GBrTCwLUd7K299nwPWvZ5n/et756cue3Qn86cN4JiJbQxph235dqxjFx+eOIBxQ1oY0Ap78rCnAHvyBfYUYOYh4c92vgDTx7cwOrodaeubBVa/nKezKx8blAAmDsvxo+PXcjpXsHlrFy9uzjN1XDRBVpynymCoTD2WFD2WpJsUk+QI+2klLfnVnIk0hXovK6405wQ1zXO8tul11vzyIp7ZsJ3DOlo4ZmIro4Yf2O0hvbckzV9Fva43d3SxO0+Y96nWU0t6rZj03fkCm3a00Nm1m85oWNBfy/NsZ54vHzeBD47cyPLnd/HI2t0smj2o9MXge5u79dbUY8lYpZsO4xR7IXHDZKl38xXpayr1irK4Js0ecAn5RwOzO4Yxe3+H9JLmOaJeV/vKK2jvbk+thrmUtoEHMOYDn2NM7BzLNbDyCmZMeImpB+3tPQGhHBlQYEkhqfdRaZPGSrv/ikhGag1eaYYAax3Si9tpoVKwqxQgk16r1nRg+APnM7z8fRR7cvtJQ2EphsKSVnhpwl2kCfSX+0/quCpMPZYUqvU+FEhE+rE0Q3qNqI7vQ4ElJW3SKCISr6V6FhERke5TYBERkUwpsIiISKYUWEREJFOavIdWgFdeeaW3yyEi0meU/M1sLT+nwALjAebNm9fb5RAR6YvGA/8uTVBggdXAscAGIP7pWiIiUq6VEFRWl59o+jvvRUQkW5q8FxGRTGkorAIzOwe4GJgA/A34pruvqpD/CGAxcDSwEVgCLHL3pugWpqivB4GTY04Ndfc36lPKxmRmpwC3u/vQKvmauo0V1VBfTdvGzKwVuAA4BzgYeBG4AViS1F6yal/qsSQws7OAG4HbgE8Bm4EVZnZoQv6xwMOEB8V9GrgJ+D7wrR4pcC+rtb4iUwiNeEbZV1d9S9tYzOwYQr3lquRr6jZW1N36ijRzG1sIXE2oq1OAO4GfAhfFZc6yfWmOJYaZ5YC1wDJ3PzdKGwA48KC7nx9zzeXAV4GD3b0rSrsS+Aowzt33fbB9P5GyvkYAm4AT3X15T5a3UZjZQMInyiuBbUC7uw+pkL9p2xikqq+mbWNm1kL4cLfY3ReWpC8BTnf3sTHXZNa+1GOJNxk4BLi/mBBV6kPAxxKumQWsLP6DRO4FRgJH1amcjSJNfU2Jjn+vb9Ea2onAJYRPkD/rRv5mbmNQe301cxsbDiwFfleW7sAYMzsw5prM2pcCS7x3Rsfny9JfAA6Lxi7jronLX/p6/VWa+poC7ASuMrNOM+sys7vMbFw9C9pgVhOeZXEdYfihmmZuY1B7fTVtG3P3Te5+nruvKTv1CeA/7r4t5rLM2pcCS7xh0XFrWfpWQp3FRfthCflLX6+/SlNfU4CBUZ65hO72DOCRaMij33P39e7evQeMB83cxtLUV9O3sVJm9kVCr2RRQpbM2pdWhcUrTgqWfyoqpucTrkn6FBWXvz9JU18/Bu5w90ejnx8zs38BTxImDm/NvJR9XzO3sTTUxiJmNo+wuOZu4PqEbJm1L/VY4m2JjuVLGYcQKjiuG7klJv/QknP9Wc315e7PlvyHL6b9iTDhOLUehewHmrmN1UxtLDCzbxCC6IPAvApLhzNrXwos8Z6LjpPK0icBnvAP81xCfggTZv1ZzfVlZp81s5llaTnC0MVrdSll39fMbaxmamNgZlcTem63Aqe5+5sVsmfWvhRY4j0HrAPmFBOi5bMnAysTrlkJzCpbbTEH6CTcLNifpamvc4HF0bLIopOAwcBjdSpnX9fMbSyNpm5jZnYBYRXdYuBsd99d5ZLM2pfmWGK4e8HMrgGuN7NNwOPAecBo4CcAZnYYMMbdn4wuuwH4GvB7M7uW0NW+BPhOlU8JfV7K+roaWAbcZma/IKw6uRL4rbs/0dPvoRGpjdVGbWwvMxsP/AB4GvgNcLSZlWb5M+EWgbq0L/VYErj7DYT18mcSJrxGACe4e3H53UJgVUn+DYQVF21R/i8Bl7r7D3uy3L0lRX2tINwNPJmwVv5S4JboegnUxmqjNrbXCYQhv/cS6qT8awR1bF+6815ERDKlHouIiGRKgUVERDKlwCIiIplSYBERkUwpsIiISKYUWEREJFMKLCIikikFFhERyZS2dBHpAWbWAWwg3A19prvfViHvfGBo9ECruPNLCHs4TaiwU61Ir1GPRaRnzCMElZ3Agip5FwGz405Eu/N+ErhPQUUalQKLSM9YQHjM68+B46INE/dhZpMJm3c+GXee8OzxdxD2vhJpSBoKE6kzM5sOTAMuB+4Dvg7MBy4ry3cvoTcC4TntVxW/d/eF0fdzCQ9dejS65gRgeZUi/MXdj9zf9yHSXQosIvVXHPpa6u4vmNnTwOfN7LvuXvrI15uAVuDjhGeJvBGlryrJMxd4yN13RT+/yNt3610E7CLs5Fv0AiI9SLsbi9SRmQ0CXgaecfdjo7QLgWuBk9x9WVn++4AZ7j425rUOB/4JnO7ud8ecbyM8Bvped/9M5m9GpJs0xyJSX6cCHcDSkrTbgT3AF2LyTwfWJLzWHMLkf9LQ1+FAO/BUqpKKZESBRaS+FgA7gDuLCdEDlR4GTjGz0cX06PsJwF8TXmsu8Ad3fyPh/LToqMcUS69SYBGpEzM7FPgIcL+7byk7vZTQuzijJO390XGfwGJmE4AjqbwabGp0VI9FepUCi0j9zAdyvH0YrOgeYCtvv6flfdExrscyBygA91f4fe8BNrv7+tqLKpIdBRaROjCzFuBs4L/AivLz7r6d8FzxI8zsqCh5UnR8KeYl5wJ/dPdXK/za8cD/0pZZJCtabixSH8cDEwnzHReaWVyegdFxAbCavcuCrzOzVYQJ/l8DI4CZwMVVfucG4KNmdhnwlLs/sF/vQCQlLTcWqQMzuws4rZvZtxB6GzngRuBEwt33L7n7IWZ2FvArYJK7r63wO6cDtwBHACvc/eT9eAsiqSmwiDQ4M7sHONTdp1XNLNIANBQm0vhWATf3diFEuks9FhERyZRWhYmISKYUWEREJFMKLCIikikFFhERyZQCi4iIZEqBRUREMqXAIiIimfo/LkWxwZ1uKiMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(delta_t_list/tau_real,result_array.T[3]/D,\"o\",label=r\"$dD/D$\")\n",
    "plt.semilogy(delta_t_list/tau_real,result_array.T[1]/A,\"o\",label=r'$dA/A$')\n",
    "plt.semilogy(delta_t_list/tau_real,dtau/tau_real,\"o\",label=r'$d\\tau/\\tau$')\n",
    "plt.semilogy(delta_t_list/tau_real,result_Bayes_array.T[3]/tau_real,color=\"k\",label=r\"$d\\tau/\\tau$ ind\")\n",
    "plt.semilogy(delta_t_list/tau_real,result_Bayes_array.T[1]/A,\"-.\",color=\"k\",label=r\"$dA/A$ ind\")\n",
    "plt.xlabel(r'$\\Delta t/\\tau$')\n",
    "plt.ylabel(\"relative error\")\n",
    "plt.legend(ncol=2)\n",
    "plt.savefig(\"optimaldt_1_05.png\",format='png',dpi=300,bbox_inches='tight',facecolor=\"white\",backgroundcolor=\"white\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}