Simulating datasets MCMC-D 10x smaller.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "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",
    "import theano.tensor as tt\n",
    "\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": 3,
   "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": 4,
   "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": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Ornstein_Uhlenbeck(pm.Continuous):\n",
    "    \"\"\"\n",
    "    Ornstein-Uhlenbeck Process\n",
    "    Parameters\n",
    "    ----------\n",
    "    B : tensor\n",
    "        B > 0, B = exp(-(D/A)*delta_t)\n",
    "    A : tensor\n",
    "        A > 0, amplitude of fluctuation <x**2>=A\n",
    "    delta_t: scalar\n",
    "        delta_t > 0, time step\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, A=None, B=None,\n",
    "                 *args, **kwargs):\n",
    "        super(Ornstein_Uhlenbeck, self).__init__(*args, **kwargs)\n",
    "        self.A = A\n",
    "        self.B = B\n",
    "        self.mean = 0.\n",
    "\n",
    "    def logp(self, x):\n",
    "        A = self.A\n",
    "        B = self.B\n",
    "\n",
    "        x_im1 = x[:-1]\n",
    "        x_i = x[1:]\n",
    "\n",
    "        ou_like = pm.Normal.dist(mu=x_im1*B, tau=1.0/A/(1-B**2)).logp(x_i)\n",
    "        return pm.Normal.dist(mu=0.0,tau=1.0/A).logp(x[0]) + tt.sum(ou_like)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "A,D = 1.0, 0.1\n",
    "tau_real = A/D\n",
    "delta_t_list=np.linspace(0.01,20,50)\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": 7,
   "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": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c1bf19438>]"
      ]
     },
     "execution_count": 8,
     "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/tau_real,result_Bayes_array.T[3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c1c3aed68>]"
      ]
     },
     "execution_count": 9,
     "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": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "18.776122448979592\n"
     ]
    }
   ],
   "source": [
    "AA,DD = 1.0,0.1\n",
    "tau_real = AA/DD\n",
    "delta_t_list=np.linspace(0.01,20,50)\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 = -4\n",
    "print(delta_t_list[pick_delta])\n",
    "data = langevin.time_series(A=AA, D=DD, delta_t=delta_t_list[pick_delta], N=N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:24<00:00, 1415.58draws/s]\n",
      "/Users/hstrey/anaconda3/lib/python3.6/site-packages/mkl_fft/_numpy_fft.py:1044: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  output = mkl_fft.rfftn_numpy(a, s, axes)\n"
     ]
    }
   ],
   "source": [
    "d_bound=0.3\n",
    "a_bound=3\n",
    "delta_t=delta_t_list[pick_delta]\n",
    "# compile model for reuse\n",
    "with pm.Model() as model:\n",
    "    D = pm.Uniform('D', lower=0, upper=d_bound)\n",
    "    A = pm.Uniform('A', lower=0, upper=a_bound)\n",
    "\n",
    "    B = pm.Deterministic('B', pm.math.exp(-delta_t * D / A))\n",
    "\n",
    "    path = Ornstein_Uhlenbeck('path',A=A, B=B, observed=data)\n",
    "    \n",
    "    trace = pm.sample(20000,tune=10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "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)\n",
    "a_mean = trace['A'].mean()\n",
    "d_mean = trace['D'].mean()\n",
    "a_std = trace['A'].std()\n",
    "d_std = trace['D'].std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "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 (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [02:02<00:00, 977.58draws/s] \n",
      "/Users/hstrey/anaconda3/lib/python3.6/site-packages/mkl_fft/_numpy_fft.py:1044: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  output = mkl_fft.rfftn_numpy(a, s, axes)\n",
      "The acceptance probability does not match the target. It is 0.9066098768495573, 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 0.8845501300619815, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "There were 75 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "The acceptance probability does not match the target. It is 0.6310094463324577, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "There were 5 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "The number of effective samples is smaller than 25% for some parameters.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.41795918367346935\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:24<00:00, 1424.72draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8259183673469387\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:25<00:00, 1407.67draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.233877551020408\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:18<00:00, 1524.67draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.6418367346938774\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:27<00:00, 1369.57draws/s]\n",
      "The acceptance probability does not match the target. It is 0.7188761867617955, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.0497959183673466\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:21<00:00, 1477.12draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.457755102040816\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:23<00:00, 1441.81draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.865714285714285\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:19<00:00, 1506.47draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.2736734693877545\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:24<00:00, 1412.81draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.681632653061224\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:20<00:00, 1483.56draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.0895918367346935\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:22<00:00, 1458.79draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.497551020408163\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:27<00:00, 1371.50draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.905510204081632\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:19<00:00, 1500.92draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.313469387755101\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:25<00:00, 1410.92draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.721428571428571\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:30<00:00, 1326.93draws/s]\n",
      "The acceptance probability does not match the target. It is 0.7008566027952062, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.12938775510204\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:15<00:00, 1593.67draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.537346938775509\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:28<00:00, 1361.12draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.9453061224489785\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:18<00:00, 1538.35draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.353265306122448\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [01:16<00:00, 1574.90draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.761224489795917\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:50<00:00, 2368.26draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.169183673469387\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:50<00:00, 2396.77draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.577142857142857\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:49<00:00, 2433.47draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.985102040816326\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:49<00:00, 2411.09draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.393061224489795\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:50<00:00, 2381.28draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.801020408163264\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:50<00:00, 2368.97draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.208979591836734\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:51<00:00, 2326.01draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.616938775510203\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:54<00:00, 2217.79draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11.024897959183672\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:50<00:00, 2371.52draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11.432857142857141\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:50<00:00, 2380.47draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11.84081632653061\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:52<00:00, 2287.43draws/s]\n",
      "The acceptance probability does not match the target. It is 0.708540437369903, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.24877551020408\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:50<00:00, 2360.32draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.65673469387755\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:50<00:00, 2395.19draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.064693877551019\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:49<00:00, 2410.06draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.472653061224488\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:50<00:00, 2382.09draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.880612244897957\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:49<00:00, 2403.07draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "14.288571428571426\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:53<00:00, 2246.20draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8840265543573051, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "14.696530612244896\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:51<00:00, 2351.44draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15.104489795918365\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:54<00:00, 2216.02draws/s]\n",
      "The acceptance probability does not match the target. It is 0.6529499634633417, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15.512448979591834\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:50<00:00, 2382.37draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15.920408163265304\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:51<00:00, 2328.21draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16.328367346938776\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:50<00:00, 2380.55draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16.736326530612246\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:51<00:00, 2320.08draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "17.144285714285715\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:51<00:00, 2319.04draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "17.552244897959184\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:50<00:00, 2389.67draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "17.960204081632654\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:49<00:00, 2405.59draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "18.368163265306123\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:50<00:00, 2360.79draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "18.776122448979592\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:51<00:00, 2337.24draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19.18408163265306\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:50<00:00, 2366.93draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19.59204081632653\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:50<00:00, 2364.74draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [A, D]\n",
      "Sampling 4 chains: 100%|██████████| 120000/120000 [00:49<00:00, 2408.34draws/s]\n"
     ]
    }
   ],
   "source": [
    "result_array = None\n",
    "for delta_t in delta_t_list:\n",
    "    print(delta_t)\n",
    "    data = langevin.time_series(A=AA, D=DD, delta_t=delta_t, N=N)\n",
    "    with pm.Model() as model:\n",
    "        D = pm.Uniform('D', lower=0, upper=d_bound)\n",
    "        A = pm.Uniform('A', lower=0, upper=a_bound)\n",
    "\n",
    "        B = pm.Deterministic('B', pm.math.exp(-delta_t * D / A))\n",
    "\n",
    "        path = Ornstein_Uhlenbeck('path',A=A, B=B, observed=data)\n",
    "    \n",
    "        trace = pm.sample(20000,tune=10000)\n",
    "        \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": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c247e1cf8>]"
      ]
     },
     "execution_count": 14,
     "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": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c273d55c0>]"
      ]
     },
     "execution_count": 15,
     "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": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c1c6c4518>]"
      ]
     },
     "execution_count": 16,
     "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/DD**2+AA**2/DD**4*result_array.T[3]**2)\n",
    "plt.semilogy(delta_t_list,dtau/tau_real,\"o\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1c262a00f0>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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s3LkTgGHDhnUp3717N2vXru3Ir3S2fft29u/f79rqqK2t5cwzz2TQoEFxx450bbr46Qr7DbAImGutbQd2paZKcd4B6oCLcVZVxhhTAJSTZE5HRHqHaB6l6vUqGvY3UFJUQsUZFWnNrwwZMgSAzZs3M3ny4XndCxYsoLm52XWo8a5dzsdrbMI9HA6zatUqbrjhBs/n87o2nfwElozsx2KtDUdm/C80xuzB2VflJmAY8FC66yMiuaV8THlaA0ms0tJSxo4dy8MPP0xRURElJSVUV1dTXe18L44m7jsbMGAA4MzKb2tr68jNbNiwgd27dzN9+nTP5/O6Np38zGP5AfB9Y8zVxph/ikxcTAtr7c9w5rhcDSzD6Yo7P4XdbyIigcjPz2f+/PmMHTuWefPmcfvtt5OXl8eVV17JgAEDKC0tjbvGGMMVV1zB0qVLmTNnTkf5ypUrmTBhAiUl3jkir2vTKRQOdy9FYYx5CzgJ6J/gtKzcjyURY0wp8G5tbS0jRozIdHVERDzNnDmTWbNmJewKS5dt27ZFW06jrbXvdT7WY/ZjERHp6Z555plMV6Fb/Cbv11hrG494poiI9Fp+ciy/Ab6XqoqIiEjP4CewZGRUmIiI5Ba/S7rcZYzZizOfZJcmJ4qISCw/geVmnAUhH40WuMzszLlRYSIiEiyNChMRkUB1O7BYa69PZUVERKRn8N1tZYwZBnwOZ7Lkb3FWFx5mrX0r4LqJiEgO8rVZsjHmVmAr8DjwI5wVhqcAG40xD6dzmRcREclOfpbN/wrwAM7e9l/i8EZbr+Psx/ItnF0kRUSkF/PTYrkNeM5a+1XghWihtbbOWvtF4H+ArwdbPRERyTV+AsspwJMJjv+B+M24RESkl/ETWD7EWa7eyyjgo6OrjoiI5Do/geUZ4EZjzPGxB4wxZcC3geeCqpiIiOQmP4FlLk7C/k2cLYrDwDeNMcuBtUALcFfgNRQRkZzS7cBird0OfBJnn/lpOEHmS8AMnNzLWdrRUUREfE2QtNbWA9dF5qsMA/KB3dbatlRUTkREck9SC0ZGVjXeHXBdRESkB/A1815ERORIFFhERCRQCiwiIhIoBRYREQmUls0XEZFAadl8EREJlJbNFxGRQGnZfBERCZSWzRcRkUBp2XwREQmUls0XEZFAadl8EREJlJbNFxGRQGnZfBERCVS3A4sx5h2ciZGPW2vfQcvmi4iICz85lu3AHcDbxpi1xpgKY0xJiuolIiI5yk+O5VxgBHALcAj4d6DOGPOcMeZaY8wxqamiiIjkEl9rhVlrG6y18621ZwOjcUaKDQL+A9hpjFmagjqKiEgOSXrZfGvtVmAB8EOc5Vz6A5cFVC8REclRySyb3w/4PM5Q4y8ARcBmYB5Ocl9ERHoxP6PCLgYuxwkmA4GdOF1gj1tr16ameiIikmv8tFiW46wXthynZVJrrW1PSa1ERCRn+QksVwBPWWsPpqoyPUH1lmqqXq+iYX8DJUUlVJxRQfmY8kxXS0QkbbodWKy1GvF1BNVbqqn8050cDLcAUL+/nso/3Qmg4CIivYZnYDHGtAFXW2t/Hfm5HWfhyUTC1lrfAwJ6iqrV93UElaiD4RaqVt+nwCIivUaiILAY+FvMz0cKLL1aw6G9EAq5l4uI9BKegcVae33Mz9elvDY5rqS1jfqC+Je0pFVrdIpI79HtCZLGmFXGmOkJjl9ojHkzmGrlpormfPq3dx0o17+9nYrm/AzVSEQk/RLlWAbgLI0fdS6wIrLKcaw84AKcZV56rfKpd8HKOVQNGkBDn3xKWtuo2HeA8vMeyHTVRETSJlGOpQjYABRHfg4DP438cROit29NXHY55UB57T3QuA2KR8B5D0DZ5ZmumYhI2iTKsew2xlwFfAonaNwFrADecDm9DWd/liWpqGROKbtcgUREerWEQ4OttU8DTwMYY0YBj1hr16SjYiIikpv8TJC8/kjnGGOOs9ZqZ0kRkV7M12RGY8zVOEvjD6TriLI+wDHAqUDfwGonIiI5x8/qxrcD9+HsHrkPZ8TYNuBYYADQBMxPQR1FRCSH+Nno63rgz8DxwGSchP5ncUaNfRtno6/VQVdQRERyi5/AUgosttZ+aK3dAuwBplpr26y1Pwd+C/xzCuooIiI5xE9gacHZjyXqHaCs08/PAycHUSkREcldfgLLW8CUTj9b4JOdfh4M9AuiUiIikrv8jAr7T+BnkT3vvwk8BfzOGHM3TtC5BScHIyIivZifeSyPGGNGADfhdIstx5lpf3fklH3AdwOvoYiI5BQ/XWFYa+8AhllrD1lrw9bar+AsTnkpcLK19tUU1FFERHKI790erbWtMT//MbjqiIhIrku0bP6qJO4XttZ67tkiIiI9X6IWyxi0FXGgqrdUU/V6FQ37GygpKqHijArKx5RnuloiIoFKtGx+aRrr0eNVb6mm8pVKDrYdBKB+fz2Vr1QCKLiISI/iO8cCYIw5ERgJvI2zRlirtbY98VW9W9XrVR1BJepg20GqXq9SYBGRHsXXqDBjzNnGmHVAHfAK8AmcUWFbjTHa3SqBhv31vspFRHJVtwOLMeZMYCXO8vidtyf+AGdey6+NMRcEW72eo6TNPV3lVS4ikqv8tFh+CLwLnI6zfH4IwFr7WqTsLeD7QVewp6j4xwf0b+/aW9i/vZ2Kf3xA9ZZqZiybQdljZcxYNoPqLdUZqqWIyNHzE1gmA/9prW0iZrSYtXYfsAiYEGDdepTyPkOpfP8DTmhpJRQOc0JLK5XvfwADhlL5SiX1++sJE+5I6iu4iEiu8pVjAZoTHOufxP16j+l3UX4ozLPbdvDGe3U8u20H5YfCVA0Z7JnUFxHJRX4CwRrgK24HjDFFwNeAtUFUqkcquxwunA/FI4GQ83jhfBpa9rme3rC/Ib31ExEJiJ/hxncBLxhjXgSexOkOO8sYMwG4GRgFfCv4KvYgZZc7fzop2Tif+pbGuFNLCgalq1Yi0kMlmpSdygnbflY3ftUY8wXgEeDBSPG/Rh7rgS9ba58PpFa9SMWevVQOCHMw73DjsX97OxV79mawViKS6xJNygZSOmG724HFGHOstfY5Y8xYYBLwMSAfeA94LXZxSume8t3boKiQqiGDaeiTT0lrGxV79lK+v0lLwIhIt7h9ViSalB39u9uxtAYWYL0x5hfW2nuB1yN/5GgVj6C8sY7y/Qe6FFcfN1JLwIjIEXm1TGIDR1Si/G1QuV0/yfvjAGWUgzb9Ligo7FpWUKjRYiLSLV4tk5DHx/ugguMoKSpxPeZV7pefwPI48A1jTGkgzywOjRYTkRh+Jk17fSaEw+2E2wu6lrUX0LzrfM4eerXrsbOHXn30lcdfV1g7MA54xxizGdgFtMWco/1YkuE2WmzTL6l3WUcsqG8UIpIefnOlR0q6x96rpKjE9bOivWUwzbvPp99xNYQK9hKO/Lx/36k8e7CQg+2Xxh17dudw7p529L+zn8DyOeD9yN/7Aycd/dOLl4phZ1H54QoO5oU6yvq3h6kYdlYGayUiXtwCCHiPvoL4IFE+ptyza+u+NffR3NYcd6+y4vPY8WENobyWjvPD7QXkN36e1n1ltO6b1OVewwcXsmNvE2EmxR3bQVMgr4Wf4cajA3lG6Zby9Sug9R/xo8X2rqD6pE9rtJhIivlpaXi1Mvr36e8rSIB311bjofj5bgfbDrJ218sc3Bnf+hjY8gkKC9ppajncsVRYkM+c8w0P1Fi2740PIicOLowrS0ZS+7FIGjRuo5xw/GixopBGi4mkmN/uKK9WhtfILK8gUfV6lWfXlpf2/D207otvfTTSwkNfnsgDNZYde5s4cXAhc843XDxpOABzl//FNegEQYElWxWPgMa6uOKqY4dqwzARn7xaH17lfrujvAKIXw37G7hs5Bx+9+FDcV1bRQWFHGiLH9ST1zbE9V4nDi7k4knDOwJJZ9Eyr6BztBRYstX0u+APN0NLp+ZqQSEN+SHX0xv2N2hCpfR6fvIc63et58nNTwbSHZUXyqM9HL+JbnHfYg60HKQlfHj93oJQP4r6FrK3OX51jZKiEp793+GuifW8vvmEj/1dXMA545gr+d+CfN+tD6+gE4RQONy7N5qKDJ9+t7a2lhEjRmS6Ol29sRRq74HGbU4LZvpdzPAYLVbct7jLNymA/vn9qZxSqeAiWS2o9axiu6/A+T/Qv09/1w9xr2BwQtEJAL66o8AJGLEBZNaICn67to7Q0Kc7gkT4gwv48pkjeXJbVdz5935mHjctitmXpJM+g9bHBZx/ypvSkTdJRevDy7Zt25g+fTrAaGvte13qmdJnlqPjMgy5YmCR63+eUCiUsItMrRnJRkGuZ+U3z+EWVCC57qjiguP5oG56lwBy8IMLeOK9f+LAgaGw5/Qu5694qYBD/S+NO7+lcSInDnZPrAOuuZQdNKW09ZEMBZYcUz6mHLaupmrLChryoKQdKkbNZO7fn3Q9P9pFpoS/ZFqQ61lBfALd7+RhrxZLou6owgF96T/sd3Ff7Jp3nc+BPafGBZADtMTeHoC9TS3QdHrc+Q/UWOacb1wT6/0L8thzIP5+QY3kCpK6wrK5K8zNG0tdcy8zRo91XX4/UbP+hKITOv5zqyUjXvwmvruT5wDnA9mrNRFydj4n7NEpFHttoi4vr27iWWNnsXzTE766o0LAdTM+4Pfv/oL2/D3ktQ3hstFf59Fnh3p2X/kRAt69v5wn1m+P69oC95Fc9116WkZaK4m6whRYci2wPDTBdbRY9XEjqSwudM2xzH1prq//oJVTKgH3yVuSG4Lq+vTKW8waO6tL4vtI5UHmORIlyr3yjK+9Fx8MTh8yje8/+1hc/uNHM671nOcxuLCA5tb4uSFerQm/5w8fXMjL3/Oe+u4WcDLVBabAkkDOBZbKwXh9l6o+9ztdu8jGXEL5ufcyY9mMwP6DKrhkP69gkOgLg1cg8vve8SpPJNGXG7+tnMtGznENIH66loZHPrD9XOMVQO679DQgflgvZFfrIxlK3vckHvNbKBxC+cu/oLxzF1n9L2DoaVScUeHrP2iiyVuglky6+W19+J2DkcywW6/g4TeoHKk7Nral8YWRX+flD37lGuwGFRzHkuePo6nlux1lS97L54mCN7t8gAM0tbTFlUXt2NvkOc/jlt9ucL2msSnxZESvYJEtrY+gqcWSay0WjxwLfQqh6YP484tHwi0bPROnfodUen279Nvn3puDURC5iUSveaKuTzdBdkcl0wpuaXT/QH5i/XbXb/VXfHY3/71jfty9eP9L7G44tdu/t5dE3VFn37/KtYvsSF1YPZG6whLIucACrvNbWP4NPNONle7bHAc57t+rVeTV555Mt0yQgnyOIAKF39xEotfc6xq/QoS4b+p9geRYvP69WxonenYJeeU5hg8u5PuXN8XdK9H8DzeJuq+8Wg5ewS6XurCCosCSQE4GFjceSf1oi8VLUCN4vNY38vsNNplA5PV7JNMK8HqORPcPIlD4zU0kes29XttkvjA8+8VnAxkVVj7GfaRTouDhrMDr9rvj2u3kN+Hulf84UoDIpgR6JimwJNBjAotXF9mF851Jlm6tnJjJl5356To7oegEGvY3+Op+8ZJMVwoE0wpIJth5vSbJJLH9SPSaR1saR9taSnawhp+hsl55jhDO/Aw/geKyTwzn9+u2BxZAJLFeG1iMMf8CzMZpIb8GfNNa2xxzTik9IbCAd/A4UtDppkSjjTL5AQv+8gB+JfpGn8mAmijQP/vFZ12fJ5k8mNc3dD8BxGs0VX4oRJvLZ1AyI7OGd2q5KICkXq8cFWaMOQu4HvgUcABYDNwMPJDJeqWUyxIwgBNsWmK++bU0OeXR491oyUQ/aLw+gDLRJZRotnVQAS3R0h+p7gKce9ZcwN9rHm2duCkfU+7aCvEqj80pbN/bxNzlf+G1v3/QpXUQLe9fkOdrBFZbOBzXcokuoOh3ZFZ0NJcCSeb12MAC7AFustbuBzDGvEFv3fWycZtHeV3Xlkz0Z0gYXLw+mMD9A3DS8ZNSlsSObtUcxIe732AX/V38/B6JAoXb6xR9Xf2+5kHlAR6osa6B4jdr6uJaGokCiJcjtTLcAkWqN6mSo9djA4u1dhOwCcAYcwJQAVwZlCZaAAAQNUlEQVSXyTpljNfcl1B+IC2ZKL/fhuHoA1EyQcrrw93vfTp/8AcVKPzmNNyu8WplgPd8Cq9AtMNjMUS37qtEvPIi0efxE/S8usiC2qRKjl7O51iMMVcAC2OKd1prT40cHwU8DTxurf1Xl+tL6Sk5Fi9eOZbYoNJZ7PEkcjJBS2Z5db/DinvCXJxEcy3cWgfgPQvcq3XglRsJegSWF43MyrzenLyfCPwB+LG1doHHOaX09MAC7on92nu8WzJhly6NIwxdltRI9CHqduyW327wHE7gls9IZmkTjcCS3pq8Pw54BifPsizT9ck4r8S+n5ZM4zbfw5bl6CTq1gJcjw0eUOA5AiuopU0unjScT44a6nsJE+kdsiawGGMuwumuOiam/OvA7cAIYAPwL9baV7txy1uAQcAdxpg7ImXV1tofBFjt3BYNCN1tyRQO8Z3sl3h+hu96Jc8fqLEdf4891q9PnmvLxG9iPZoMT7RvugKIuMmKrjBjzBSc1kWetXZgp/JrgP8E7gHWAt8BzgZOt9a+G9Bzl9IbusL8SHI9MrVmjsxrSRCvrqVEEwjBe8+QoGamK3CIl6ztCjPG9MMZrXUvsB/o2+lYCCegLLLWzouUPQdYnNbIzWmvcG/h1ZJZ/g3386NdZF6tGbd79aCAE0QLxGv4rleSPNqa8Bp269WacAtqlRc5CzcqLyJByXRX2AXAXGAOcCxwa6djY4FRwFPRAmttizGmGpiZzkr2Sm45Ga8usuIR3pMwn/4utDb12O4zvxMIE00U9Cr3mkAI7oHCa9htonxJ5+MiRyvTgWUtTjNqrzGmMubYyZHHzTHlW4CPGWPyrbX+Oo3l6Ey/y72LLFFrxq3r7CjmymSKV6skqBbIkZY2SdSa8NPSUF5E0iGjgcVauz3B4UGRxw9jyj8E8oAiYF8q6iUevLrIyi73bs14STTr3+s50qA76191HpnldwKhVwvEK8dypAmEChSSjTLdYknEKz8ZLU/dyobizWvYsldrxivh7zXrP+Cus6NZQPFI6189UGM9V+BNpgWSaPiuSC7J5sAS3R/3GGBnp/KBOEFlf9prJN68WjPgb65Moq6zBIHFT6AIagHFHXubeOjL7htVJdMCUetDeopsDizvRB7H0DXPMgaw1trMj5OWrrxaM9D9uTJeEkzO9EqgewWKoBZQjI6+Av8TCEV6smwPLHXAxcCzAMaYAqAcqM5gvcQvP7P+vbrOCofQ+uR36BNdCLKxzvkZeKBmGJ9re5Hb+y7lxND77AgP48etl/NUy2e4KO9P3N4nprz9M76qn2gBRdAEQpFYWRtYrLVhY8z9wEJjzB7gZeAmYBjwUEYrJ0ev7HLWvreHka8/wPHh99kVGkbdaXMAmLDuDgpDhzpObQr3pf1QG0UxWyP3aTvIgafv4pP7LuG+gl8yIHLNiND73F/wSz7Rtokv5f8xrjyvNUR7OBwXcP7Y77OuAUTzPET8ydrAAmCt/ZkxphBnEuUtOEu6nG+t3ZLZmsnRemL9duauHUVTS1VHWeFaZ0HEqS1fi3zo/4Md4WP5cevl/JSfHR620Un/pgbm9v0dAzjUpXxA6BBX9VlFn5gxHgNCh/hhv1+R33awI3iNCL3PvxX8ko2TStk+8gua5yFylLJiSZdM0pIuqec1A91tNJWXP/W9mRF578eVb2sfxvC8fxByWdwkjGss8lY8slP+x2V75xyZcyOSDlm7pIvkHr9LuIP7yCy/ifIH277Mj0K/6OjWAjgQ7ssv+36VyqLfuw4ECHkt/+/Fa27N1tXw5197D4FW0BHpQoGllwtinkeUn5FZfjeKGviJK7nr9RD/HF7S0UX2U67gM+XfgPxT3QcCnP6VrgEhWu53bs26R+MDVOfVA7JwoqdIJqkrrJd0hXUnUEDiORiJNoQC9wURE3GbgZ5oo6iEuwZ6tRrcysH/jpquQt7bPhcO7TrRM/ocF853/q7uNslxvXYHye7oDYHFa6l2r0Dh1ZrwkmgJdy/dWQMrpYLaUbNxG75+c6+A49W6ShSIRDJIOZYexk/3VaKFEv2utOsl0RLuieaAZHSeh5+5NV4f+slM9PRaWcCru+1IS9z4aampVSRposCSY/wu0w7eCyV68Zv/SNStllNzQBItsnnSp70/kP1M9PTiNcjgSKtD+xlskGgQgtfvnQwFr15PXWFZ0BXmd6Mov4segr/WhFeOJVH+I9Hv0eP5yeMkGjjgZwRbovyO1728yhPlg/y2frx+76BzSwpeGaccSwLpDCxBJND9DtONblPr9hxJJ8qle/x88PodwZZMfsev6LyeIOqbTG4pHcFLQS1pCiwJBB1YErU+gkigJ7NR1Mvfm6ZAkU2CagH4HWyQjlaRX4kGRvjdisFv8MrmoBZU7iyFQVCBJYFkA4uf1sd9l57me6Z5In42irrv0tMUQHJdog8NP62JbGwVeUoQ1HzfymegzXRQg2D+XZMJnD6CjgJLAskEFr+tj+GDC9mxt8nXf89kNopSq6QXCuIbLATXKvL6gPWbW+rNQQ2CaYkmEzijQacbFFgSSCawnH3/Kl+tjxB47jSYTAJdwUICF1SryKtLCPzfxyuoBRW8sjWoQYqfO0HgLB4Jt2zs1l00jyVgfofvRlsPfofjaqMoSRuveT3JDsHu7oZvyQzlvuDf3O/ldb7frqJE85NSHtQiX25T2mIZEQmcLrzKfVJgSYLf1kfngOBnSXZtFCVZIVHQ8ZMI9nufREGt8/FYfoJXNga1oO6VTOAs7n6eOREFliQk0/oABQoR39IRvLIxqAV1L7+BMxrYjpJyLAGOClPQEJGckcJRYWqxJEmtDxHJaX5bgz7kpeSuIiLSaymwiIhIoBRYREQkUAosIiISKCXvIR+goaEh0/UQEckZnT4z82OPKbDACQBXXXVVpushIpKLTgD+1rlAgQXWAlOBeiCAdcBFRHqFfJygsjb2QK+fICkiIsFS8l5ERAKlrrAkGWO+DtwOjAA2AP9irX01s7XKTsaYY4H3XQ793lr7xXTXJ5sZYy4CHrfWHtOpLAR8H/gmMAx4GfiOtfbtzNQye3i8Xp/EpXsG+Im19ra0VS5LGGPygQrg68BJwN+BnwEPW2vDqXh/qcWSBGPMNcAjwH8BlwF7gRpjzOiMVix7nR55PB+Y3OnP3IzVKAsZY6bgvKdCMYfuAu4AHgSuAIqBWmNMcXprmF0SvF5lwH66vtcmA/PTWsHscSfwI5zX6iJgKfBTYE7keODvL7VYfIpE93uARdbaeZGy5wAL3ALcnMHqZasyYKe19tlMVyQbGWP64XyjvBfnA7Fvp2PHALcBldba+ZGyl3C+dc4G/j3tFc6wRK9XRBmw0Vq7Ot11yzbGmDzgX4AHrLX/GimuNcYcB9xmjPk5KXh/qcXi31hgFPBUtMBa2wJUAzMzVaksVwa8kelKZLELcFpvc4AFMcc+DQyk6/ttD/Aivff9luj1Ar3fOisGFgPLY8otcBwwjRS8v9Ri8e/kyOPmmPItwMeMMfnWWg1b7qoMOGiMeQU4AyffMh/nW5SGJTr5gNHW2r3GmMqYY9H3299iyrcAs1JdsSyV6PUCOA1oNsZsAMYDW4F7rbWPpbGOWSESJG5yOXQhsA0nRwwBv78UWPwbFHn8MKb8Q5wWYBGwL601ymKRpvh4nC6L23D+k38euA/oj9Ot2KtZa7cnODwIaLbWHoop/5DD78VeJdHrZYw5EScB/XGcVs0e4ErgUWNM2Fq7OD21zF7GmK8B5+F026fk/aXA4l80URj7TTta3p7GuuSCEPAFYKu1NtrKe94YMxD4rjHmx9bag5mrXtYLEf9ei5brvRZvL04XzhvW2vpI2cpIwLkbp1uo1zLGXIUz8GgZsBAn+Ab+/lKOxb/GyOMxMeUDcf4h9qe3OtnNWttmrV3VKahEPQMMwMlZibdGoJ8xpiCmfCCH34sSYa09YK2t6RRUop4BxkS+0PRKxphbgF8B/w1cFemGTsn7S4HFv3cij2NiyscAVjmDrowxJxpjvhEZhdJZYeTRbX6LHPYOzrfH2KHsY3ASsNKJMeZkY8y3IiPHOisEmuilX/yMMT/CGeH1K+CLnbq+UvL+UmDx7x2gDrg4WhCJ9uVAbaYqlcX6Af8P+GpM+WXAJmutlpVO7BXgIF3fb0OAc9D7zc1w4Oc4eTygY4rApcBLvfGLnzGmAqfLqwq4zlrb2ulwSt5fyrH4FJmpej+w0BizB2eW6k04CcOHMlq5LGStfdcY8xvgXmNMO/AW8CWcwHJxwosFa+1HxpgFwA8jr98m4Ac4A0R+mdHKZac/An8CHol8QNbjzCgvAz6TyYplgjHmBODfgL8AS4CzjDGdT3kNZ8h2oO8vBZYkWGt/ZowpxJmkdQvOki7nW2u3ZLZmWWs2zuzff8ZZDfUt4DJr7VMJr5Ko7+Pk727D6ft+BbjWWqscSwxrbZsxZhbOTPN7gGOB14HPWWtfy2jlMuN8nF6D0wC3JaeOIwXvL61uLCIigVKORUREAqXAIiIigVJgERGRQCmwiIhIoBRYREQkUAosIiISKAUWEREJlAKLiIgESjPvRdKg0/Ii/YCrrbX/leDc64FjolvFuhx/GGc5nBG9ce0ryX5qsYikx1U4QaUZZ4mbRH4MfM7tQGRBxVnAkwoqkq0UWETSYzbOdq8/B84xxnzM7SRjzFicBU1Xe9znTJwVfJ9IRSVFgqCuMJEUM8acAUwE5gFP4izGeT1wR8x5T3B4n/EfGmN+GP27tfbOyN8vwdmA6fnINefjbGKVyDpr7SeP9vcQ6S4FFpHUi3Z9LbbWbjHG/AW41hhzl7W28/avi4B8nK2cbwA+ipR3XpX2EqDaWtsS+fnvwNWdjv8YaMFZ+jxKq25LWml1Y5EUMsb0B3YAb1prp0bKbgMeAD5vrX065vwngcnW2uNd7nUK8FfgS9baZS7H++DskPiEtfbLgf8yIt2kHItIal0KDAEWdyp7HGgD/q/L+WcA6z3udTFO8t+r6+sUoC/w56RqKhIQBRaR1JqNs/Xr0miBtbYeWAlcZIwZFi2P/H0EzsZUbi4BnrPWfuRxfGLkccPRVlrkaCiwiKSIMWY08FngKZfd+BbjtC6+2qnsE5HHuMBijBkBfJLEo8FOjzyqxSIZpcAikjrXAyG6doNFrQA+pOuclkmRR7cWy8VAGEi0nfOpwF5r7Xb/VRUJjgKLSAoYY/KA64CdQE3scWttE7AMmGCMOTNSPCbyuNXllpcAf7LW7k7wtCcAu5Kts0hQNNxYJDVmACNx8h23GWPczukXeZwNrOXwsOD5xphXcRL8vwYGA/8HuP0Iz1kPTDfG3AH82Vr7h6P6DUSSpOHGIilgjPkd8MVunt6I09oIAY8AF+DMvt9qrR1ljLkGeAwYY619N8FzngH8BzABqLHWlh/FryCSNAUWkSxnjFkBjLbWTjziySJZQF1hItnvVeAXma6ESHepxSIiIoHSqDAREQmUAouIiARKgUVERAKlwCIiIoFSYBERkUApsIiISKAUWEREJFD/H9rnhkMw/DdQAAAAAElFTkSuQmCC\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]/DD,\"o\",label=r\"$dD/D$\")\n",
    "plt.semilogy(delta_t_list,result_array.T[1]/AA,\"o\",label=r'$dA/A$')\n",
    "plt.semilogy(delta_t_list,dtau/tau_real,\"o\",label=r'$d\\tau/\\tau$')\n",
    "plt.xlabel(r'$\\Delta t/\\tau$')\n",
    "plt.ylabel(\"relative error\")\n",
    "plt.legend()"
   ]
  },
  {
   "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"
    }
   ],
   "source": [
    "plt.semilogy(delta_t_list/tau_real,result_array.T[3]/DD,\"o\",label=r\"$dD/D$\")\n",
    "plt.semilogy(delta_t_list/tau_real,result_array.T[1]/AA,\"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]/AA,\"-.\",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_01.png\",format='png',dpi=300,bbox_inches='tight',facecolor=\"white\",backgroundcolor=\"white\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_label = \"1_01\"\n",
    "np.save(\"dtnorm_\"+data_label,delta_t_list/tau_real)\n",
    "np.save(\"dD_D_\"+data_label,result_array.T[3]/DD)\n",
    "np.save(\"dA_A_\"+data_label,result_array.T[1]/AA)\n",
    "np.save(\"dtau_tau_\"+data_label,dtau/tau_real)\n",
    "np.save(\"dtau_tau_ind_\"+data_label,result_Bayes_array.T[3]/tau_real)\n",
    "np.save(\"dA_A_ind_\"+data_label,result_Bayes_array.T[1]/AA)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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