abr_2.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ABR test for orginial data with any sampling or add noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import integrate\n",
    "import itertools, operator, random, math\n",
    "from scipy.sparse.linalg import spsolve_triangular\n",
    "from sklearn import linear_model\n",
    "import utils as ut\n",
    "import pandas as pd\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def abr(t, pop, popt):\n",
    "    la, lb, lr, ra, rb, rr = pop\n",
    "    ka, da, dab = 400, 2, 400\n",
    "    kb, kbb, db, dba = 2, 30, 2.8, 30\n",
    "    kr, krb, dr = 0.1, 1.5, 0.2\n",
    "    at, bt, rt = popt\n",
    "\n",
    "    dladt = ka*(at-la-ra)*lr - da*la - dab*la*lb**2\n",
    "    dlbdt = (bt-lb-rb)*(kb + kbb*lb) - db*lb - dba*la*lb**2\n",
    "    dlrdt = (rt-lr-rr)*(kr+krb*lb) - dr*lr\n",
    "    dradt = ka*(at-la-ra)*rr - da*ra - dab*ra*rb**2\n",
    "    drbdt = (bt-lb-rb)*(kb + kbb*rb) - db*rb - dba*ra*rb**2\n",
    "    drrdt = (rt-lr-rr)*(kr+krb*rb) - dr*rr\n",
    "    dpop = np.array([dladt, dlbdt, dlrdt, dradt, drbdt, drrdt])\n",
    "    return dpop"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test 1 \n",
    "three different setting - varies both on initial and total molecule number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "dt, pts = 0.01, int(60/0.01)\n",
    "tspan = np.linspace(dt, 60, num=pts)\n",
    "pop00 = [0.2, 0, 0, 0, 0.8, 1]\n",
    "pop01 = [0, 0.5, 1, 0.2, 0, 0]\n",
    "popt1 = [1, 1, 1]\n",
    "\n",
    "##\n",
    "sol1 = integrate.solve_ivp(fun =lambda t,x :abr(t,x,popt1), t_span=[tspan[0], tspan[-1]], y0=pop00, method='RK45', rtol=1e-10,atol=1e-10,t_eval=tspan)\n",
    "dpop1 = abr(sol1.t, sol1.y, popt1)\n",
    "##\n",
    "sol2 = integrate.solve_ivp(fun =lambda t,x :abr(t,x,popt1), t_span=[tspan[0], tspan[-1]], y0=pop01, method='RK45', rtol=1e-10,atol=1e-10,t_eval=tspan)\n",
    "dpop2 = abr(sol2.t, sol2.y, popt1)\n",
    "\n",
    "\n",
    "# sol4 = integrate.solve_ivp(fun =lambda t,x :abr(t,x,popt1), t_span=[tspan[0], tspan[-1]], y0=pop01, method='RK45', rtol=1e-10,atol=1e-10,t_eval=tspan)\n",
    "# dpop4 = abr(sol4.t, sol4.y, popt1)\n",
    "\n",
    "\n",
    "# sol5 = integrate.solve_ivp(fun =lambda t,x :abr(t,x,popt1), t_span=[tspan[0], tspan[-1]], y0=pop02, method='RK45', rtol=1e-10,atol=1e-10,t_eval=tspan)\n",
    "# dpop5 = abr(sol5.t, sol5.y, popt1)\n",
    "\n",
    "# sol6 = integrate.solve_ivp(fun =lambda t,x :abr(t,x,popt1), t_span=[tspan[0], tspan[-1]], y0=pop03, method='RK45', rtol=1e-10,atol=1e-10,t_eval=tspan)\n",
    "# dpop6 = abr(sol6.t, sol6.y, popt1)\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "pop_data = np.hstack([sol1.y, sol2.y])\n",
    "dpop_data = np.hstack([dpop1, dpop2])\n",
    "dpop_diff = np.hstack([ut.time_different(dt, dpop1, sol1.y), ut.time_different(dt, dpop2, sol2.y)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    " label = ['la', 'lb', 'lr', 'ra', 'rb','rr']\n",
    " theta, descr = ut.lib_terms(pop_data,2,label)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "clf = linear_model.Lasso(alpha=1e-5, fit_intercept=False, max_iter=1e5)\n",
    "clf.fit(theta, dpop_diff.T)\n",
    "Xi_std = clf.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "sol_res = integrate.solve_ivp(ut.sparseGalerkin, [tspan[0], tspan[-1]], pop00, method='RK45', atol=1e-10, rtol=1e-10, t_eval=tspan,args=(Xi_std.T,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot(sol_res.y[0])\n",
    "plt.plot(sol1.y[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "dic = {}\n",
    "dic['la'], dic['ra'] = ['rb', 'rr'], ['lb','lr']\n",
    "dic['lb'], dic['rb'] = ['ra', 'rr'], ['la', 'lr']\n",
    "dic['lr'], dic['rr'] = ['ra', 'rb'], ['la', 'lb']\n",
    "df_prior, remain_index = ut.bulid_prior(label, theta, descr, dic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# important, keep\n",
    "theta_dic = {}\n",
    "for i, term in enumerate(label):\n",
    "    theta_dic[term] = theta[:, remain_index[i]]\n",
    "    # clf = linear_model.Lasso(alpha=1e-5, fit_intercept=False, max_iter=1e5)\n",
    "    # clf.fit(theta_dic[term],dpop_diff[i].T)\n",
    "    # Xi_curr = clf.coef_\n",
    "    Xi_curr = ut.sparsifyDynamics(theta_dic[term], np.expand_dims(dpop_diff[i].T,1), 0.001)\n",
    "    df_prior[term].iloc[remain_index[i]] = Xi_curr.T[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "sol_res2 = integrate.solve_ivp(ut.sparseGalerkin, [tspan[0], tspan[-1]], pop00, method='RK45', atol=1e-10, rtol=1e-10, t_eval=tspan,args=(df_prior,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "              la         lb        lr          ra        rb        rr\n1      46.279969   5.649980  0.000000   15.666974  0.497452  0.000110\nrr    -31.589536   5.245584  0.000000   23.255069  0.000000  0.000000\nrb      9.261093  -4.198866  0.000000   -6.652560 -2.322399  0.009635\nra    -65.106239  -3.578080  0.011949  -12.214414  0.000000  0.000000\nlr     88.159863  -0.575612  0.000000  -25.973087  0.867282  0.000000\nlb    -35.208652  -2.009830  0.054939   15.564522  0.000000  0.000000\nla    -21.122345   0.908493  0.000000  -30.846350 -0.166418  0.030718\nrrrr   55.436022  -2.222112  0.000000   14.782594  0.722018 -0.158621\nrbrr  -51.870100  -6.316762  0.000000   74.741780  0.000000 -0.020101\nrbrb  -43.337163   0.019681 -0.011475    9.162493 -7.056445  0.000000\nrarr   10.505630   0.000000 -0.024002 -106.450739  1.795894  0.000000\nrarb   20.987976   0.000000  0.000000  -41.550567 -1.270109  0.000000\nrara    3.882134   3.131985  0.000000   19.354224 -0.082668 -0.017520\nlrrr  106.020250   0.000000  0.000000   28.178651  0.000000  0.000000\nlrrb  -28.937450  -5.345562  0.000000  -10.893243  3.007044  0.104333\nlrra  -89.851158   1.935757  0.000000   34.151420  0.000000  0.026705\nlrlr   46.557478   2.095878 -0.165266    9.654691 -0.898726  0.000000\nlbrr  -52.424472   0.028804  0.083899   79.544838 -2.525997  0.000000\nlbrb   40.873231  -1.983714  0.050204    9.038409  0.000000  0.049811\nlbra   37.761109   1.258187  0.022749  -38.520526 -3.840420  0.000000\nlblr  -69.531443   0.000000  0.000000  -15.579070  0.000000  0.000000\nlblb   35.799010  -9.414158  0.000000   -6.188190  3.933976 -0.048443\nlarr    3.907971   0.000000  0.004583 -101.733005  1.365356  0.020591\nlarb  -33.705150  -0.004997  0.000000   13.725041  3.649608  0.040261\nlara   44.675110   1.731753  0.000000    0.000000  0.000000  0.000158\nlalr -125.451171   1.233955 -0.019236   33.151528 -0.882361 -0.035935\nlalb -120.517716 -12.563046  0.000000    6.452238  0.000000  0.000000\nlala   56.167170  -0.029068 -0.027189   -4.498549  1.996083  0.000000",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>la</th>\n      <th>lb</th>\n      <th>lr</th>\n      <th>ra</th>\n      <th>rb</th>\n      <th>rr</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>1</th>\n      <td>46.279969</td>\n      <td>5.649980</td>\n      <td>0.000000</td>\n      <td>15.666974</td>\n      <td>0.497452</td>\n      <td>0.000110</td>\n    </tr>\n    <tr>\n      <th>rr</th>\n      <td>-31.589536</td>\n      <td>5.245584</td>\n      <td>0.000000</td>\n      <td>23.255069</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>rb</th>\n      <td>9.261093</td>\n      <td>-4.198866</td>\n      <td>0.000000</td>\n      <td>-6.652560</td>\n      <td>-2.322399</td>\n      <td>0.009635</td>\n    </tr>\n    <tr>\n      <th>ra</th>\n      <td>-65.106239</td>\n      <td>-3.578080</td>\n      <td>0.011949</td>\n      <td>-12.214414</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lr</th>\n      <td>88.159863</td>\n      <td>-0.575612</td>\n      <td>0.000000</td>\n      <td>-25.973087</td>\n      <td>0.867282</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lb</th>\n      <td>-35.208652</td>\n      <td>-2.009830</td>\n      <td>0.054939</td>\n      <td>15.564522</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>la</th>\n      <td>-21.122345</td>\n      <td>0.908493</td>\n      <td>0.000000</td>\n      <td>-30.846350</td>\n      <td>-0.166418</td>\n      <td>0.030718</td>\n    </tr>\n    <tr>\n      <th>rrrr</th>\n      <td>55.436022</td>\n      <td>-2.222112</td>\n      <td>0.000000</td>\n      <td>14.782594</td>\n      <td>0.722018</td>\n      <td>-0.158621</td>\n    </tr>\n    <tr>\n      <th>rbrr</th>\n      <td>-51.870100</td>\n      <td>-6.316762</td>\n      <td>0.000000</td>\n      <td>74.741780</td>\n      <td>0.000000</td>\n      <td>-0.020101</td>\n    </tr>\n    <tr>\n      <th>rbrb</th>\n      <td>-43.337163</td>\n      <td>0.019681</td>\n      <td>-0.011475</td>\n      <td>9.162493</td>\n      <td>-7.056445</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>rarr</th>\n      <td>10.505630</td>\n      <td>0.000000</td>\n      <td>-0.024002</td>\n      <td>-106.450739</td>\n      <td>1.795894</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>rarb</th>\n      <td>20.987976</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>-41.550567</td>\n      <td>-1.270109</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>rara</th>\n      <td>3.882134</td>\n      <td>3.131985</td>\n      <td>0.000000</td>\n      <td>19.354224</td>\n      <td>-0.082668</td>\n      <td>-0.017520</td>\n    </tr>\n    <tr>\n      <th>lrrr</th>\n      <td>106.020250</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>28.178651</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lrrb</th>\n      <td>-28.937450</td>\n      <td>-5.345562</td>\n      <td>0.000000</td>\n      <td>-10.893243</td>\n      <td>3.007044</td>\n      <td>0.104333</td>\n    </tr>\n    <tr>\n      <th>lrra</th>\n      <td>-89.851158</td>\n      <td>1.935757</td>\n      <td>0.000000</td>\n      <td>34.151420</td>\n      <td>0.000000</td>\n      <td>0.026705</td>\n    </tr>\n    <tr>\n      <th>lrlr</th>\n      <td>46.557478</td>\n      <td>2.095878</td>\n      <td>-0.165266</td>\n      <td>9.654691</td>\n      <td>-0.898726</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lbrr</th>\n      <td>-52.424472</td>\n      <td>0.028804</td>\n      <td>0.083899</td>\n      <td>79.544838</td>\n      <td>-2.525997</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lbrb</th>\n      <td>40.873231</td>\n      <td>-1.983714</td>\n      <td>0.050204</td>\n      <td>9.038409</td>\n      <td>0.000000</td>\n      <td>0.049811</td>\n    </tr>\n    <tr>\n      <th>lbra</th>\n      <td>37.761109</td>\n      <td>1.258187</td>\n      <td>0.022749</td>\n      <td>-38.520526</td>\n      <td>-3.840420</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lblr</th>\n      <td>-69.531443</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>-15.579070</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lblb</th>\n      <td>35.799010</td>\n      <td>-9.414158</td>\n      <td>0.000000</td>\n      <td>-6.188190</td>\n      <td>3.933976</td>\n      <td>-0.048443</td>\n    </tr>\n    <tr>\n      <th>larr</th>\n      <td>3.907971</td>\n      <td>0.000000</td>\n      <td>0.004583</td>\n      <td>-101.733005</td>\n      <td>1.365356</td>\n      <td>0.020591</td>\n    </tr>\n    <tr>\n      <th>larb</th>\n      <td>-33.705150</td>\n      <td>-0.004997</td>\n      <td>0.000000</td>\n      <td>13.725041</td>\n      <td>3.649608</td>\n      <td>0.040261</td>\n    </tr>\n    <tr>\n      <th>lara</th>\n      <td>44.675110</td>\n      <td>1.731753</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000158</td>\n    </tr>\n    <tr>\n      <th>lalr</th>\n      <td>-125.451171</td>\n      <td>1.233955</td>\n      <td>-0.019236</td>\n      <td>33.151528</td>\n      <td>-0.882361</td>\n      <td>-0.035935</td>\n    </tr>\n    <tr>\n      <th>lalb</th>\n      <td>-120.517716</td>\n      <td>-12.563046</td>\n      <td>0.000000</td>\n      <td>6.452238</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lala</th>\n      <td>56.167170</td>\n      <td>-0.029068</td>\n      <td>-0.027189</td>\n      <td>-4.498549</td>\n      <td>1.996083</td>\n      <td>0.000000</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 42
    }
   ],
   "source": [
    "ut.visual_param(Xi_std, descr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "              la         lb        lr          ra         rb        rr\n1      50.313690  15.169055  0.099967   31.833351   7.665716  0.099955\nrr      0.000000   0.000000 -0.099961   77.885773   1.011972 -0.299949\nrb      0.000000 -35.761182  0.000000   77.714370 -25.205560  1.500162\nra   -344.913797   0.000000  0.000000 -147.882205   5.865806  0.000000\nlr    105.193643  -1.594903 -0.299964    0.000000   0.000000 -0.099947\nlb     94.859797 -25.370724  1.500122    0.000000 -29.125918  0.000000\nla   -187.206197   8.322450  0.000000 -269.944715   0.000000  0.000000\nrrrr    0.000000   0.000000  0.000000    6.904794   0.308419  0.000000\nrbrr    0.000000   0.000000  0.000000  -69.945140  -1.349986 -1.500182\nrbrb    0.000000  20.350323  0.000000   57.791424  17.323041  0.000000\nrarr    0.000000   0.000000  0.000000  -80.646253  -3.698553  0.000000\nrarb    0.000000   0.000000  0.000000  -53.839722 -11.154068  0.000000\nrara  399.488759   0.000000  0.000000  116.536764   6.135741  0.000000\nlrrr    0.000000   0.000000  0.000000    0.000000   0.000000  0.000000\nlrrb    0.000000   0.000000  0.000000    0.000000   0.000000 -1.500186\nlrra    0.000000   0.000000  0.000000    0.000000   0.000000  0.000000\nlrlr   12.134096   0.034718  0.000000    0.000000   0.000000  0.000000\nlbrr    0.000000   0.000000 -1.500141    0.000000   2.875602  0.000000\nlbrb    0.000000  40.622984  0.000000    0.000000  51.183125  0.000000\nlbra -324.758059   0.000000  0.000000    0.000000 -25.159462  0.000000\nlblr -131.848902   2.117537 -1.500136    0.000000   0.000000  0.000000\nlblb  129.402757   8.603249  0.000000    0.000000  35.986092  0.000000\nlarr    0.000000   0.000000  0.000000  -21.076816   0.000000  0.000000\nlarb    0.000000  -7.176060  0.000000 -203.523991   0.000000  0.000000\nlara  449.811501   0.000000  0.000000  384.470950   0.000000  0.000000\nlalr -108.200610   1.380695  0.000000    0.000000   0.000000  0.000000\nlalb  -59.991064 -24.645159  0.000000    0.000000   0.000000  0.000000\nlala  136.968368  -0.618072  0.000000  305.130054   0.000000  0.000000",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>la</th>\n      <th>lb</th>\n      <th>lr</th>\n      <th>ra</th>\n      <th>rb</th>\n      <th>rr</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>1</th>\n      <td>50.313690</td>\n      <td>15.169055</td>\n      <td>0.099967</td>\n      <td>31.833351</td>\n      <td>7.665716</td>\n      <td>0.099955</td>\n    </tr>\n    <tr>\n      <th>rr</th>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>-0.099961</td>\n      <td>77.885773</td>\n      <td>1.011972</td>\n      <td>-0.299949</td>\n    </tr>\n    <tr>\n      <th>rb</th>\n      <td>0.000000</td>\n      <td>-35.761182</td>\n      <td>0.000000</td>\n      <td>77.714370</td>\n      <td>-25.205560</td>\n      <td>1.500162</td>\n    </tr>\n    <tr>\n      <th>ra</th>\n      <td>-344.913797</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>-147.882205</td>\n      <td>5.865806</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lr</th>\n      <td>105.193643</td>\n      <td>-1.594903</td>\n      <td>-0.299964</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>-0.099947</td>\n    </tr>\n    <tr>\n      <th>lb</th>\n      <td>94.859797</td>\n      <td>-25.370724</td>\n      <td>1.500122</td>\n      <td>0.000000</td>\n      <td>-29.125918</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>la</th>\n      <td>-187.206197</td>\n      <td>8.322450</td>\n      <td>0.000000</td>\n      <td>-269.944715</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>rrrr</th>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>6.904794</td>\n      <td>0.308419</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>rbrr</th>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>-69.945140</td>\n      <td>-1.349986</td>\n      <td>-1.500182</td>\n    </tr>\n    <tr>\n      <th>rbrb</th>\n      <td>0.000000</td>\n      <td>20.350323</td>\n      <td>0.000000</td>\n      <td>57.791424</td>\n      <td>17.323041</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>rarr</th>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>-80.646253</td>\n      <td>-3.698553</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>rarb</th>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>-53.839722</td>\n      <td>-11.154068</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>rara</th>\n      <td>399.488759</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>116.536764</td>\n      <td>6.135741</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lrrr</th>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lrrb</th>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>-1.500186</td>\n    </tr>\n    <tr>\n      <th>lrra</th>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lrlr</th>\n      <td>12.134096</td>\n      <td>0.034718</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lbrr</th>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>-1.500141</td>\n      <td>0.000000</td>\n      <td>2.875602</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lbrb</th>\n      <td>0.000000</td>\n      <td>40.622984</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>51.183125</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lbra</th>\n      <td>-324.758059</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>-25.159462</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lblr</th>\n      <td>-131.848902</td>\n      <td>2.117537</td>\n      <td>-1.500136</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lblb</th>\n      <td>129.402757</td>\n      <td>8.603249</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>35.986092</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>larr</th>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>-21.076816</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>larb</th>\n      <td>0.000000</td>\n      <td>-7.176060</td>\n      <td>0.000000</td>\n      <td>-203.523991</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lara</th>\n      <td>449.811501</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>384.470950</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lalr</th>\n      <td>-108.200610</td>\n      <td>1.380695</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lalb</th>\n      <td>-59.991064</td>\n      <td>-24.645159</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>lala</th>\n      <td>136.968368</td>\n      <td>-0.618072</td>\n      <td>0.000000</td>\n      <td>305.130054</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 43
    }
   ],
   "source": [
    "df_prior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}