Least Squares estimation of TS parameters_Trust_Region_Reflective.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import odeint\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import least_squares\n",
    "from scipy.integrate import odeint\n",
    "import scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def toggle_switch(yz, t, beta_y, beta_z, n_x, n_y, Km1, Km2, delta):\n",
    "    \"\"\"\n",
    "    Right hand side for cascade X -> Y -> Z.  Return dy/dt and dz/dt.\n",
    "    \"\"\"\n",
    "    # Unpack y and z\n",
    "    y, z = yz\n",
    "\n",
    "    # Compute dy/dt\n",
    "    dy_dt = beta_y/ (1 + (z/Km1)**n_x) - delta*y\n",
    "    \n",
    "    # Compute dz/dt\n",
    "    dz_dt = beta_z/ (1 + (y/Km2)**n_y) - delta*z\n",
    "    \n",
    "    \n",
    "    # Return the result as a NumPy array\n",
    "    return np.array([dy_dt, dz_dt])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def general_toggle_switch(yz, t, *args):\n",
    "    \"\"\"\n",
    "    Right hand side for cascade X -> Y -> Z.  Return dy/dt and dz/dt.\n",
    "    \"\"\"\n",
    "    #args = (np.array(args).reshape(2, 6))\n",
    "    args1 = np.array([args[0], args[1], args[2], args[3], args[4], args[5], args[6], args[7]])\n",
    "    args2 = np.array([args[8], args[9], args[10], args[11], args[4], args[5], args[12], args[13]])\n",
    "    \n",
    "    # Unpack y and z\n",
    "    y, z = yz\n",
    "    \n",
    "    # Compute dy/dt\n",
    "    dy_dt = generalized_hill_function(yz, args1) - args1[7]*y\n",
    "    \n",
    "    # Compute dz/dt\n",
    "    dz_dt = generalized_hill_function(yz, args2) - args2[7]*z\n",
    "    \n",
    "    # Return the result as a NumPy array\n",
    "    return np.array([dy_dt, dz_dt])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generalized_hill_function(y, args):\n",
    "    a1    = 0#args[0]\n",
    "    a2    = 0#args[1]\n",
    "    b1    = args[2]\n",
    "    b2    = args[3]\n",
    "    n1    = args[4]\n",
    "    n2    = args[5]\n",
    "    beta  =\n",
    "    args[6]\n",
    "    x1, x2= y\n",
    "    return beta*(1 + a1*x1**n1 + a2*x2**n2)/(1 + b1*x1**n1 + b2*x2**n2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "def residuals(p):\n",
    "    p = tuple(p)\n",
    "    sim_P = odeint(general_toggle_switch, iv, t, args = p).T\n",
    "    #print(sim_P)\n",
    "    res = (sim_P - exp_P)**2\n",
    "    #print(np.sum(res.flatten()**2))\n",
    "    return res.flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x106aede10>]"
      ]
     },
     "execution_count": 58,
     "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": [
    "# Number of time points we want for the solutions\n",
    "n = 800\n",
    "\n",
    "# Time points we want for the solution\n",
    "t = np.linspace(0, 50, n)\n",
    "\n",
    "# Initial condition\n",
    "iv = yz_0 = np.array([0.0, 0.0])\n",
    "\n",
    "# Parameters\n",
    "beta_y = 5.0\n",
    "beta_z = 5.0\n",
    "n_x = 2\n",
    "n_y = 2\n",
    "x_0 = 2.0\n",
    "Km1 = 5\n",
    "Km2 = 10\n",
    "delta = 0.18\n",
    "\n",
    "\n",
    "# Package parameters into a tuple\n",
    "args = (beta_y, beta_z, n_x, n_y, Km1, Km2, delta)\n",
    "\n",
    "# Integrate ODES\n",
    "yz_og = scipy.integrate.odeint(toggle_switch, yz_0, t, args=args).T\n",
    "\n",
    "y_og, z_og = yz_og[0], yz_og[1]\n",
    "\n",
    "plt.plot(t, y_og)\n",
    "plt.plot(t, z_og)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_og_scaled = []\n",
    "z_og_scaled = []\n",
    "\n",
    "for i in range(0, len(y_og)):\n",
    "    y_og_scaled.append((y_og[i] - np.mean(y_og))/np.std(y_og))\n",
    "    z_og_scaled.append((z_og[i] - np.mean(z_og))/np.std(z_og))\n",
    "    \n",
    "y_og_scaled = np.array(y_og_scaled) + np.abs(np.min((y_og_scaled)))\n",
    "z_og_scaled = np.array(z_og_scaled) + np.abs(np.min((z_og_scaled)))\n",
    "\n",
    "                                             \n",
    "#for ii in range()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "yz_scaled = np.array(list(zip(y_og_scaled, z_og_scaled))).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "exp_P = yz_scaled# + np.random.randn(len(yz_og))*0.5\n",
    "exp_P = exp_P#[::5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x106b9a290>]"
      ]
     },
     "execution_count": 63,
     "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.plot(t, y_og_scaled)\n",
    "plt.plot(t, z_og_scaled)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a1    = 0#args[0]\n",
    "a2    = 0#args[1]\n",
    "b1    = args[2]\n",
    "b2    = args[3]\n",
    "n1    = args[4]\n",
    "n2    = args[5]\n",
    "beta  = args[6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Iteration     Total nfev        Cost      Cost reduction    Step norm     Optimality   \n",
      "       0              1         9.2210e+05                                    6.97e+07    \n",
      "       1              2         1.7371e+05      7.48e+05       7.18e+00       1.07e+07    \n",
      "       2              4         1.7290e+04      1.56e+05       2.66e+00       3.62e+05    \n",
      "       3              6         5.9678e+03      1.13e+04       9.98e-01       7.28e+04    \n",
      "       4              7         2.5535e+03      3.41e+03       1.99e+00       1.36e+04    \n",
      "       5              8         1.3341e+03      1.22e+03       5.10e+00       2.90e+03    \n",
      "       6              9         1.0476e+03      2.86e+02       3.53e+00       6.76e+02    \n",
      "       7             11         9.5872e+02      8.89e+01       1.44e+00       3.03e+02    \n",
      "       8             13         9.1939e+02      3.93e+01       6.26e-01       2.81e+02    \n",
      "       9             14         8.8006e+02      3.93e+01       1.12e+00       6.55e+02    \n",
      "      10             15         6.8390e+02      1.96e+02       1.64e+00       8.67e+02    \n",
      "      11             17         2.6192e+02      4.22e+02       8.74e-01       2.26e+04    \n",
      "      12             18         3.4303e+01      2.28e+02       1.34e+00       9.27e+03    \n",
      "      13             19         1.8374e+01      1.59e+01       2.60e+00       6.26e+03    \n",
      "      14             20         3.4094e+00      1.50e+01       2.60e+00       1.41e+03    \n",
      "      15             21         1.5595e+00      1.85e+00       4.79e+00       6.77e+02    \n",
      "      16             22         2.1011e-01      1.35e+00       4.94e+00       7.96e+01    \n",
      "      17             23         5.4445e-02      1.56e-01       5.19e+00       5.36e+00    \n",
      "      18             26         4.9842e-02      4.60e-03       4.31e-01       8.28e+00    \n",
      "      19             27         1.4867e-02      3.50e-02       1.10e-01       2.57e+00    \n",
      "      20             29         1.3061e-02      1.81e-03       6.91e-02       2.43e-01    \n",
      "      21             30         1.1336e-02      1.73e-03       1.47e-01       9.71e-01    \n",
      "      22             31         1.0696e-02      6.40e-04       2.92e-01       2.44e+00    \n",
      "      23             32         8.8568e-03      1.84e-03       8.71e-02       1.55e-01    \n",
      "      24             33         8.3070e-03      5.50e-04       6.93e-02       2.23e-01    \n",
      "      25             34         7.5460e-03      7.61e-04       1.34e-01       5.10e-02    \n",
      "      26             35         6.3643e-03      1.18e-03       2.58e-01       3.20e-01    \n",
      "      27             36         5.0446e-03      1.32e-03       4.78e-01       7.40e-01    \n",
      "      28             37         3.0296e-03      2.01e-03       4.41e-01       2.70e-01    \n",
      "      29             39         2.3440e-03      6.86e-04       2.91e-01       3.35e-02    \n",
      "      30             40         1.7346e-03      6.09e-04       4.24e-01       2.41e-01    \n",
      "      31             41         1.6835e-03      5.11e-05       8.55e-01       9.83e-01    \n",
      "      32             42         8.3648e-04      8.47e-04       2.22e-01       6.58e-02    \n",
      "      33             43         8.2361e-04      1.29e-05       6.36e-01       2.91e-01    \n",
      "      34             44         7.4849e-04      7.51e-05       1.09e-01       1.55e-01    \n",
      "      35             46         7.2659e-04      2.19e-05       5.58e-02       1.36e-01    \n",
      "      36             47         7.0554e-04      2.11e-05       5.27e-02       1.77e-01    \n",
      "      37             48         6.7440e-04      3.11e-05       5.29e-02       2.08e-01    \n",
      "      38             49         6.4273e-04      3.17e-05       5.25e-02       2.59e-01    \n",
      "      39             50         6.2473e-04      1.80e-05       5.19e-02       3.44e-01    \n",
      "      40             51         5.7339e-04      5.13e-05       1.30e-02       1.43e-02    \n",
      "      41             52         5.6814e-04      5.24e-06       2.58e-02       4.93e-02    \n",
      "      42             53         5.6385e-04      4.30e-06       1.36e-02       5.14e-03    \n",
      "      43             54         5.6132e-04      2.52e-06       5.67e-02       2.40e-02    \n",
      "      44             55         5.5911e-04      2.21e-06       5.76e-02       1.38e-03    \n",
      "      45             56         5.5139e-04      7.72e-06       2.28e-01       6.59e-03    \n",
      "      46             57         5.4309e-04      8.30e-06       2.23e-01       4.03e-03    \n",
      "      47             58         5.1277e-04      3.03e-05       8.41e-01       7.29e-02    \n",
      "      48             59         4.8073e-04      3.20e-05       8.33e-01       8.13e-02    \n",
      "      49             61         4.5686e-04      2.39e-05       4.22e-01       6.79e-03    \n",
      "      50             62         3.9273e-04      6.41e-05       1.46e+00       1.11e-01    \n",
      "      51             66         3.8269e-04      1.00e-05       2.63e-02       4.16e-02    \n",
      "      52             67         3.7999e-04      2.70e-06       2.54e-02       3.02e-02    \n",
      "      53             68         3.7819e-04      1.80e-06       2.58e-02       2.51e-03    \n",
      "      54             69         3.7255e-04      5.64e-06       1.03e-01       9.21e-03    \n",
      "      55             70         3.6766e-04      4.89e-06       1.06e-01       4.46e-02    \n",
      "      56             71         3.4450e-04      2.32e-05       4.13e-01       1.55e-03    \n",
      "      57             72         3.3659e-04      7.91e-06       4.06e-01       1.80e-01    \n",
      "      58             73         3.0897e-04      2.76e-05       4.00e-01       7.50e-03    \n",
      "      59             74         2.9545e-04      1.35e-05       8.12e-01       3.15e-02    \n",
      "      60             78         2.9359e-04      1.86e-06       3.34e-02       3.49e-02    \n",
      "      61             79         2.9259e-04      1.00e-06       2.45e-02       2.33e-03    \n",
      "      62             80         2.9146e-04      1.12e-06       4.69e-02       6.48e-03    \n",
      "      63             81         2.9041e-04      1.05e-06       5.01e-02       6.11e-04    \n",
      "      64             82         2.8750e-04      2.91e-06       1.82e-01       6.50e-03    \n",
      "      65             85         2.8742e-04      8.37e-08       1.40e-02       1.02e-02    \n",
      "      66             86         2.8728e-04      1.39e-07       4.95e-03       5.37e-04    \n",
      "      67             87         2.8723e-04      5.52e-08       3.79e-03       2.46e-03    \n",
      "      68             88         2.8708e-04      1.43e-07       1.15e-02       1.06e-04    \n",
      "      69             89         2.8693e-04      1.56e-07       1.55e-02       3.81e-04    \n",
      "      70             90         2.8646e-04      4.64e-07       4.58e-02       6.31e-04    \n",
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      "      73             95         2.8593e-04      4.49e-08       6.01e-03       9.32e-05    \n",
      "      74             96         2.8585e-04      8.03e-08       1.03e-02       3.57e-04    \n",
      "      75             97         2.8578e-04      7.25e-08       1.42e-02       1.27e-03    \n",
      "      76             99         2.8574e-04      3.91e-08       3.73e-03       2.02e-05    \n",
      "      77             100        2.8567e-04      7.33e-08       1.46e-02       3.23e-05    \n",
      "      78             101        2.8549e-04      1.78e-07       2.88e-02       2.27e-05    \n",
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      "      81             106        2.8479e-04      7.66e-08       7.70e-03       1.15e-03    \n",
      "      82             107        2.8472e-04      7.17e-08       1.44e-02       3.97e-04    \n",
      "      83             109        2.8470e-04      1.58e-08       4.51e-03       3.86e-04    \n",
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      "      90             118        2.8388e-04      2.23e-08       6.55e-03       3.82e-03    \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
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      "      91             119        2.8387e-04      1.04e-08       7.10e-03       1.95e-03    \n",
      "      92             120        2.8385e-04      2.02e-08       1.62e-03       1.16e-04    \n",
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      "      166            203        2.8097e-04      2.05e-08       4.97e-03       1.28e-04    \n",
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      "      182            221        2.8027e-04      2.52e-08       1.65e-03       1.22e-04    \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      183            222        2.8024e-04      3.05e-08       5.05e-03       6.48e-04    \n",
      "      184            223        2.8020e-04      3.71e-08       8.16e-03       6.58e-04    \n",
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      "      201            243        2.7943e-04      1.90e-08       2.93e-03       9.44e-04    \n",
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      "      274            326        2.7500e-04      4.97e-08       6.88e-03       5.54e-05    \n"
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      "      350            415        2.6813e-04      4.27e-08       7.88e-03       3.63e-03    \n",
      "      351            416        2.6809e-04      3.81e-08       1.65e-03       1.83e-04    \n",
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      "      365            432        2.6670e-04      5.08e-08       5.75e-03       1.39e-04    \n"
     ]
    },
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     "name": "stdout",
     "output_type": "stream",
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      "      366            433        2.6658e-04      1.20e-07       1.34e-02       5.09e-05    \n",
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      "      396            467        2.6409e-04      1.86e-07       1.93e-02       4.28e-04    \n",
      "      397            468        2.6381e-04      2.78e-07       3.05e-02       3.09e-03    \n",
      "      398            471        2.6377e-04      4.36e-08       3.31e-03       9.38e-05    \n",
      "      399            472        2.6370e-04      6.82e-08       6.45e-03       4.08e-05    \n",
      "      400            473        2.6357e-04      1.30e-07       1.31e-02       3.63e-05    \n",
      "      401            474        2.6331e-04      2.60e-07       2.61e-02       3.63e-05    \n",
      "      402            475        2.6279e-04      5.25e-07       5.14e-02       7.37e-04    \n",
      "      403            477        2.6267e-04      1.19e-07       1.48e-02       3.15e-03    \n",
      "      404            479        2.6262e-04      4.83e-08       3.47e-03       3.77e-04    \n",
      "      405            480        2.6255e-04      7.02e-08       6.43e-03       4.24e-05    \n",
      "      406            481        2.6242e-04      1.33e-07       1.30e-02       3.54e-05    \n",
      "      407            482        2.6215e-04      2.68e-07       2.57e-02       3.25e-05    \n",
      "      408            483        2.6161e-04      5.40e-07       5.10e-02       5.15e-04    \n",
      "      409            485        2.6151e-04      9.96e-08       1.46e-02       5.04e-03    \n",
      "      410            487        2.6144e-04      6.75e-08       3.44e-03       6.05e-05    \n",
      "      411            488        2.6138e-04      5.88e-08       5.55e-03       1.43e-04    \n",
      "      412            489        2.6125e-04      1.36e-07       1.28e-02       5.35e-05    \n",
      "      413            490        2.6106e-04      1.91e-07       1.81e-02       1.15e-03    \n",
      "      414            491        2.6091e-04      1.48e-07       3.08e-02       6.15e-03    \n",
      "      415            493        2.6074e-04      1.70e-07       6.35e-03       7.24e-03    \n",
      "      416            494        2.6064e-04      9.69e-08       7.79e-03       3.80e-04    \n",
      "      417            495        2.6043e-04      2.08e-07       1.88e-02       2.36e-03    \n",
      "      418            496        2.6010e-04      3.39e-07       3.06e-02       1.84e-04    \n",
      "      419            497        2.5929e-04      8.10e-07       7.19e-02       1.76e-03    \n",
      "      420            499        2.5902e-04      2.62e-07       3.03e-02       7.76e-03    \n",
      "      421            501        2.5893e-04      9.07e-08       6.57e-03       5.66e-03    \n",
      "      422            502        2.5890e-04      3.27e-08       6.34e-03       4.66e-03    \n",
      "      423            503        2.5885e-04      4.91e-08       1.87e-03       2.02e-04    \n",
      "      424            504        2.5882e-04      3.46e-08       2.62e-03       8.69e-04    \n",
      "      425            505        2.5878e-04      3.83e-08       3.99e-03       7.38e-04    \n",
      "      426            506        2.5870e-04      7.55e-08       6.02e-03       3.93e-05    \n",
      "      427            507        2.5856e-04      1.46e-07       1.26e-02       4.49e-05    \n",
      "      428            508        2.5826e-04      2.93e-07       2.50e-02       3.38e-05    \n",
      "      429            509        2.5767e-04      5.91e-07       4.95e-02       5.05e-04    \n",
      "      430            511        2.5757e-04      1.05e-07       1.45e-02       6.06e-03    \n",
      "      431            513        2.5749e-04      8.15e-08       3.44e-03       8.21e-05    \n",
      "      432            514        2.5742e-04      6.55e-08       5.41e-03       2.78e-04    \n",
      "      433            515        2.5727e-04      1.48e-07       1.24e-02       5.66e-05    \n",
      "      434            516        2.5706e-04      2.13e-07       1.79e-02       1.23e-03    \n",
      "      435            517        2.5682e-04      2.38e-07       3.06e-02       3.61e-03    \n",
      "      436            519        2.5671e-04      1.12e-07       6.33e-03       9.31e-03    \n",
      "      437            520        2.5662e-04      8.64e-08       7.65e-03       1.75e-04    \n",
      "      438            521        2.5650e-04      1.28e-07       8.52e-03       2.17e-03    \n",
      "      439            522        2.5635e-04      1.51e-07       1.52e-02       3.90e-03    \n",
      "      440            524        2.5628e-04      6.25e-08       3.37e-03       2.80e-04    \n",
      "      441            525        2.5620e-04      8.14e-08       6.12e-03       4.47e-05    \n",
      "      442            526        2.5605e-04      1.54e-07       1.23e-02       3.79e-05    \n",
      "      443            527        2.5574e-04      3.09e-07       2.46e-02       3.78e-05    \n",
      "      444            528        2.5511e-04      6.24e-07       4.86e-02       6.08e-04    \n",
      "      445            530        2.5500e-04      1.18e-07       1.45e-02       6.08e-03    \n",
      "      446            532        2.5491e-04      8.39e-08       3.44e-03       7.45e-05    \n",
      "      447            533        2.5484e-04      6.95e-08       5.32e-03       2.40e-04    \n",
      "      448            534        2.5469e-04      1.57e-07       1.22e-02       5.77e-05    \n",
      "      449            535        2.5446e-04      2.29e-07       1.78e-02       1.08e-03    \n",
      "      450            536        2.5413e-04      3.24e-07       3.05e-02       7.81e-04    \n",
      "      451            539        2.5402e-04      1.11e-07       4.16e-03       2.02e-03    \n",
      "      452            540        2.5397e-04      5.26e-08       3.75e-03       8.27e-05    \n",
      "      453            541        2.5385e-04      1.22e-07       9.32e-03       1.05e-04    \n",
      "      454            542        2.5364e-04      2.03e-07       1.54e-02       9.96e-05    \n",
      "      455            543        2.5316e-04      4.83e-07       3.59e-02       8.52e-04    \n",
      "      456            544        2.5235e-04      8.12e-07       5.97e-02       3.54e-04    \n",
      "      457            545        2.5038e-04      1.97e-06       1.39e-01       8.05e-03    \n"
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     "output_type": "stream",
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      "      459            550        2.5005e-04      1.01e-07       7.74e-03       5.48e-03    \n",
      "      460            551        2.4999e-04      5.75e-08       6.77e-03       4.92e-03    \n",
      "      461            552        2.4994e-04      5.04e-08       7.04e-03       6.77e-03    \n",
      "      462            553        2.4988e-04      6.07e-08       1.57e-03       3.74e-04    \n",
      "      463            554        2.4984e-04      4.18e-08       2.43e-03       1.44e-03    \n",
      "      464            555        2.4978e-04      5.55e-08       3.69e-03       9.18e-05    \n",
      "      465            556        2.4961e-04      1.75e-07       1.17e-02       4.56e-05    \n",
      "      466            557        2.4926e-04      3.54e-07       2.34e-02       7.51e-05    \n",
      "      467            558        2.4875e-04      5.03e-07       4.59e-02       1.69e-02    \n",
      "      468            560        2.4854e-04      2.18e-07       6.90e-03       3.90e-03    \n",
      "      469            561        2.4850e-04      3.92e-08       6.40e-03       6.51e-03    \n",
      "      470            562        2.4843e-04      6.48e-08       1.86e-03       2.76e-04    \n",
      "      471            563        2.4839e-04      4.19e-08       2.32e-03       1.27e-03    \n",
      "      472            564        2.4834e-04      5.17e-08       3.85e-03       6.06e-04    \n",
      "      473            565        2.4824e-04      9.34e-08       5.63e-03       7.62e-05    \n",
      "      474            566        2.4806e-04      1.82e-07       1.17e-02       5.39e-05    \n",
      "      475            567        2.4770e-04      3.64e-07       2.32e-02       3.67e-05    \n",
      "      476            568        2.4696e-04      7.35e-07       4.60e-02       6.41e-04    \n",
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      "      479            573        2.4663e-04      8.37e-08       5.06e-03       4.53e-04    \n",
      "      480            574        2.4645e-04      1.85e-07       1.15e-02       6.32e-05    \n",
      "      481            575        2.4617e-04      2.81e-07       1.74e-02       1.08e-03    \n",
      "      482            576        2.4569e-04      4.73e-07       3.02e-02       1.94e-04    \n",
      "      483            577        2.4477e-04      9.24e-07       6.74e-02       2.16e-02    \n",
      "      484            580        2.4450e-04      2.69e-07       7.58e-03       1.88e-04    \n",
      "      485            581        2.4443e-04      7.41e-08       8.06e-03       1.06e-02    \n",
      "      486            582        2.4432e-04      1.08e-07       7.61e-03       4.40e-03    \n",
      "      487            583        2.4428e-04      4.26e-08       6.31e-03       9.72e-03    \n",
      "      488            584        2.4419e-04      8.35e-08       1.90e-03       4.39e-04    \n",
      "      489            585        2.4414e-04      4.76e-08       2.28e-03       2.06e-03    \n",
      "      490            586        2.4408e-04      5.96e-08       3.87e-03       8.05e-05    \n",
      "      491            587        2.4400e-04      8.24e-08       4.68e-03       1.05e-04    \n",
      "      492            588        2.4380e-04      1.99e-07       1.13e-02       2.63e-04    \n",
      "      493            589        2.4341e-04      3.96e-07       2.27e-02       5.23e-05    \n",
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      "      495            591        2.4101e-04      1.60e-06       8.83e-02       7.27e-03    \n",
      "      496            592        2.3884e-04      2.17e-06       1.16e-01       9.49e-04    \n",
      "      497            593        2.3434e-04      4.50e-06       2.66e-01       3.89e-03    \n",
      "      498            594        2.2858e-04      5.76e-06       4.41e-01       4.01e-03    \n",
      "      499            595        2.2284e-04      5.73e-06       8.14e-01       9.63e-03    \n",
      "      500            599        2.2187e-04      9.79e-07       4.33e-03       5.00e-03    \n",
      "      501            600        2.2136e-04      5.11e-07       8.90e-03       3.50e-02    \n",
      "      502            601        2.2064e-04      7.20e-07       9.22e-03       5.37e-03    \n",
      "      503            603        2.2050e-04      1.36e-07       2.57e-03       1.32e-04    \n",
      "      504            604        2.2029e-04      2.10e-07       6.70e-03       4.77e-04    \n",
      "      505            605        2.1990e-04      3.94e-07       1.35e-02       5.34e-05    \n",
      "      506            606        2.1909e-04      8.05e-07       2.69e-02       8.32e-04    \n",
      "      507            608        2.1884e-04      2.49e-07       9.75e-03       4.69e-03    \n",
      "      508            610        2.1871e-04      1.36e-07       4.86e-03       1.72e-03    \n",
      "      509            611        2.1857e-04      1.33e-07       4.57e-03       1.87e-03    \n",
      "      510            612        2.1820e-04      3.74e-07       1.33e-02       1.32e-03    \n",
      "      511            614        2.1807e-04      1.25e-07       4.56e-03       4.05e-03    \n",
      "      512            615        2.1793e-04      1.42e-07       5.03e-03       8.15e-05    \n",
      "      513            616        2.1758e-04      3.49e-07       1.14e-02       8.21e-04    \n",
      "      514            617        2.1704e-04      5.45e-07       2.00e-02       7.08e-03    \n",
      "      515            619        2.1698e-04      5.50e-08       9.42e-03       1.50e-02    \n",
      "      516            620        2.1676e-04      2.17e-07       2.15e-03       6.05e-04    \n",
      "      517            621        2.1666e-04      1.03e-07       2.76e-03       2.78e-03    \n",
      "      518            622        2.1652e-04      1.42e-07       4.71e-03       2.36e-03    \n",
      "      519            623        2.1637e-04      1.46e-07       5.11e-03       6.78e-05    \n",
      "      520            624        2.1595e-04      4.21e-07       1.32e-02       3.07e-04    \n",
      "      521            625        2.1525e-04      7.08e-07       2.63e-02       1.23e-02    \n",
      "      522            627        2.1520e-04      4.33e-08       9.57e-03       1.76e-02    \n",
      "      523            628        2.1494e-04      2.61e-07       2.15e-03       6.95e-04    \n",
      "      524            629        2.1483e-04      1.10e-07       2.70e-03       3.38e-03    \n",
      "      525            630        2.1469e-04      1.45e-07       4.64e-03       2.89e-03    \n",
      "      526            631        2.1453e-04      1.52e-07       5.09e-03       7.74e-05    \n",
      "      527            632        2.1417e-04      3.64e-07       1.13e-02       6.55e-04    \n",
      "      528            633        2.1358e-04      5.92e-07       1.99e-02       6.13e-03    \n",
      "      529            635        2.1347e-04      1.11e-07       9.47e-03       1.26e-02    \n",
      "      530            636        2.1328e-04      1.91e-07       2.15e-03       4.82e-04    \n",
      "      531            637        2.1318e-04      1.02e-07       2.73e-03       2.15e-03    \n",
      "      532            638        2.1302e-04      1.51e-07       4.75e-03       2.12e-03    \n",
      "      533            639        2.1261e-04      4.18e-07       1.30e-02       6.13e-05    \n",
      "      534            640        2.1173e-04      8.72e-07       2.58e-02       1.44e-03    \n",
      "      535            642        2.1145e-04      2.86e-07       9.71e-03       4.48e-03    \n",
      "      536            644        2.1129e-04      1.54e-07       4.87e-03       1.55e-03    \n",
      "      537            645        2.1107e-04      2.21e-07       6.22e-03       1.13e-03    \n",
      "      538            646        2.1064e-04      4.33e-07       1.31e-02       7.18e-05    \n",
      "      539            647        2.0975e-04      8.90e-07       2.57e-02       9.76e-04    \n",
      "      540            649        2.0946e-04      2.89e-07       9.68e-03       5.16e-03    \n",
      "      541            651        2.0930e-04      1.62e-07       4.86e-03       1.41e-03    \n",
      "      542            652        2.0907e-04      2.26e-07       6.17e-03       1.18e-03    \n",
      "      543            653        2.0863e-04      4.44e-07       1.29e-02       7.40e-05    \n",
      "      544            654        2.0772e-04      9.11e-07       2.55e-02       9.03e-04    \n",
      "      545            656        2.0742e-04      2.98e-07       9.65e-03       5.35e-03    \n",
      "      546            658        2.0725e-04      1.69e-07       4.86e-03       1.30e-03    \n",
      "      547            659        2.0702e-04      2.31e-07       6.12e-03       1.20e-03    \n",
      "      548            660        2.0656e-04      4.55e-07       1.28e-02       7.61e-05    \n"
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    },
    {
     "name": "stdout",
     "output_type": "stream",
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      "      549            661        2.0563e-04      9.33e-07       2.53e-02       8.25e-04    \n",
      "      550            663        2.0532e-04      3.07e-07       9.63e-03       5.52e-03    \n",
      "      551            665        2.0515e-04      1.76e-07       4.86e-03       1.18e-03    \n",
      "      552            666        2.0491e-04      2.36e-07       6.08e-03       1.22e-03    \n",
      "      553            667        2.0445e-04      4.67e-07       1.27e-02       7.83e-05    \n",
      "      554            668        2.0349e-04      9.55e-07       2.51e-02       7.53e-04    \n",
      "      555            670        2.0304e-04      4.52e-07       1.23e-02       4.41e-03    \n",
      "      556            671        2.0287e-04      1.64e-07       1.95e-02       2.19e-02    \n",
      "      557            672        2.0229e-04      5.80e-07       4.31e-03       2.34e-04    \n",
      "      558            673        2.0205e-04      2.41e-07       5.82e-03       3.17e-03    \n",
      "      559            674        2.0167e-04      3.79e-07       9.98e-03       1.67e-04    \n",
      "      560            675        2.0083e-04      8.38e-07       2.11e-02       2.07e-03    \n",
      "      561            676        1.9954e-04      1.30e-06       3.90e-02       1.88e-02    \n",
      "      562            679        1.9916e-04      3.74e-07       4.63e-03       1.98e-04    \n",
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      "      564            681        1.9853e-04      3.98e-07       9.78e-03       1.06e-04    \n",
      "      565            682        1.9766e-04      8.70e-07       2.11e-02       1.52e-04    \n",
      "      566            683        1.9604e-04      1.62e-06       3.88e-02       9.51e-05    \n",
      "      567            684        1.9258e-04      3.46e-06       8.24e-02       1.75e-02    \n",
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      "      569            687        1.8131e-04      4.35e-06       7.64e-02       4.02e-03    \n",
      "      570            688        1.7403e-04      7.29e-06       1.86e-01       4.52e-03    \n",
      "      571            690        1.6856e-04      5.46e-06       7.74e-02       3.28e-02    \n",
      "      572            693        1.6749e-04      1.08e-06       8.64e-03       4.20e-02    \n",
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      "      578            699        1.6443e-04      3.10e-07       4.80e-03       1.58e-04    \n",
      "      579            700        1.6381e-04      6.19e-07       9.70e-03       8.98e-04    \n",
      "      580            701        1.6263e-04      1.19e-06       1.90e-02       5.29e-03    \n",
      "      581            702        1.6085e-04      1.78e-06       3.76e-02       1.94e-02    \n",
      "      582            705        1.6036e-04      4.88e-07       2.15e-03       8.14e-04    \n",
      "      583            706        1.6000e-04      3.65e-07       4.47e-03       3.74e-03    \n",
      "      584            708        1.5978e-04      2.14e-07       2.21e-03       4.89e-04    \n",
      "      585            709        1.5942e-04      3.67e-07       5.23e-03       3.05e-03    \n",
      "      586            710        1.5877e-04      6.47e-07       9.62e-03       1.36e-04    \n",
      "      587            711        1.5748e-04      1.29e-06       1.94e-02       5.84e-04    \n",
      "      588            712        1.5546e-04      2.03e-06       3.77e-02       2.88e-02    \n",
      "      589            715        1.5469e-04      7.70e-07       4.65e-03       1.01e-03    \n",
      "      590            716        1.5432e-04      3.63e-07       4.76e-03       3.70e-03    \n",
      "      591            717        1.5365e-04      6.69e-07       9.38e-03       2.17e-04    \n",
      "      592            718        1.5231e-04      1.34e-06       1.93e-02       1.06e-03    \n",
      "      593            719        1.5005e-04      2.26e-06       3.76e-02       2.57e-02    \n",
      "      594            721        1.5002e-04      3.35e-08       1.83e-02       4.48e-02    \n",
      "      595            722        1.4838e-04      1.64e-06       4.29e-03       8.61e-04    \n",
      "      596            723        1.4801e-04      3.72e-07       4.44e-03       4.00e-03    \n",
      "      597            724        1.4753e-04      4.79e-07       9.15e-03       1.58e-02    \n",
      "      598            725        1.4676e-04      7.65e-07       9.47e-03       3.03e-03    \n",
      "      599            726        1.4635e-04      4.12e-07       9.09e-03       1.88e-02    \n",
      "      600            727        1.4553e-04      8.20e-07       9.38e-03       3.74e-03    \n",
      "      601            728        1.4511e-04      4.23e-07       9.04e-03       1.87e-02    \n",
      "      602            729        1.4428e-04      8.27e-07       9.37e-03       3.85e-03    \n",
      "      603            730        1.4379e-04      4.89e-07       9.43e-03       1.69e-02    \n",
      "      604            731        1.4299e-04      8.01e-07       9.41e-03       4.19e-03    \n",
      "      605            732        1.4253e-04      4.65e-07       9.07e-03       1.77e-02    \n",
      "      606            733        1.4169e-04      8.37e-07       9.37e-03       2.79e-03    \n",
      "      607            734        1.4109e-04      5.99e-07       9.91e-03       1.51e-02    \n",
      "      608            735        1.4028e-04      8.07e-07       9.43e-03       2.23e-03    \n",
      "      609            737        1.3988e-04      4.08e-07       4.91e-03       3.32e-03    \n",
      "      610            738        1.3912e-04      7.53e-07       9.40e-03       1.96e-04    \n",
      "      611            739        1.3762e-04      1.50e-06       1.93e-02       1.04e-03    \n",
      "      612            740        1.3550e-04      2.12e-06       3.73e-02       3.66e-02    \n",
      "      613            742        1.3401e-04      1.48e-06       9.16e-03       2.69e-03    \n",
      "      614            743        1.3333e-04      6.80e-07       9.75e-03       1.32e-02    \n",
      "      615            744        1.3249e-04      8.40e-07       9.36e-03       7.12e-04    \n",
      "      616            745        1.3178e-04      7.17e-07       1.99e-02       3.50e-02    \n",
      "      617            747        1.3061e-04      1.16e-06       4.66e-03       1.15e-03    \n",
      "      618            748        1.3019e-04      4.27e-07       4.70e-03       4.43e-03    \n",
      "      619            749        1.2938e-04      8.10e-07       9.25e-03       2.34e-04    \n",
      "      620            750        1.2781e-04      1.57e-06       1.90e-02       1.40e-03    \n",
      "      621            751        1.2512e-04      2.69e-06       3.70e-02       2.85e-02    \n",
      "      622            753        1.2343e-04      1.69e-06       1.82e-02       1.64e-02    \n",
      "      623            755        1.2275e-04      6.72e-07       4.32e-03       1.94e-03    \n",
      "      624            756        1.2192e-04      8.31e-07       9.26e-03       3.77e-03    \n",
      "      625            757        1.2021e-04      1.71e-06       1.90e-02       2.55e-04    \n",
      "      626            758        1.1705e-04      3.16e-06       3.40e-02       4.16e-03    \n",
      "      627            760        1.1597e-04      1.08e-06       1.83e-02       2.77e-02    \n",
      "      628            761        1.1420e-04      1.76e-06       1.82e-02       1.91e-02    \n",
      "      629            763        1.1345e-04      7.58e-07       4.32e-03       1.71e-04    \n",
      "      630            764        1.1258e-04      8.65e-07       9.33e-03       4.27e-03    \n",
      "      631            765        1.1080e-04      1.78e-06       1.83e-02       2.40e-04    \n",
      "      632            766        1.0750e-04      3.30e-06       3.42e-02       2.38e-03    \n",
      "      633            768        1.0626e-04      1.24e-06       1.81e-02       2.55e-02    \n",
      "      634            769        1.0414e-04      2.11e-06       1.81e-02       6.95e-03    \n",
      "      635            771        1.0352e-04      6.24e-07       8.80e-03       1.96e-02    \n",
      "      636            772        1.0235e-04      1.17e-06       9.20e-03       8.04e-04    \n",
      "      637            773        1.0054e-04      1.81e-06       2.04e-02       4.03e-03    \n",
      "      638            774        9.8129e-05      2.41e-06       3.64e-02       4.02e-02    \n",
      "      639            775        9.3758e-05      4.37e-06       3.54e-02       1.49e-02    \n",
      "      640            778        9.3005e-05      7.53e-07       4.33e-03       2.07e-03    \n",
      "      641            779        9.2092e-05      9.14e-07       9.06e-03       6.24e-03    \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      642            780        9.0151e-05      1.94e-06       1.82e-02       7.62e-04    \n",
      "      643            781        8.6333e-05      3.82e-06       3.72e-02       9.92e-03    \n",
      "      644            782        8.0847e-05      5.49e-06       7.12e-02       4.37e-02    \n",
      "      645            783        7.1199e-05      9.65e-06       1.37e-01       1.31e-02    \n",
      "      646            786        6.7859e-05      3.34e-06       1.83e-02       1.12e-02    \n",
      "      647            787        6.5498e-05      2.36e-06       2.20e-02       7.17e-04    \n",
      "      648            788        6.1687e-05      3.81e-06       3.49e-02       5.20e-03    \n",
      "      649            790        6.0873e-05      8.14e-07       1.75e-02       3.13e-02    \n",
      "      650            791        5.8017e-05      2.86e-06       1.76e-02       1.24e-03    \n",
      "      651            792        5.4281e-05      3.74e-06       4.51e-02       6.58e-03    \n",
      "      652            794        5.2388e-05      1.89e-06       1.76e-02       6.40e-03    \n",
      "      653            795        4.8860e-05      3.53e-06       3.52e-02       1.16e-02    \n",
      "      654            797        4.6789e-05      2.07e-06       1.75e-02       4.30e-04    \n",
      "      655            798        4.3915e-05      2.87e-06       3.02e-02       6.96e-03    \n",
      "      656            800        4.2085e-05      1.83e-06       1.73e-02       5.54e-03    \n",
      "      657            801        3.8941e-05      3.14e-06       3.48e-02       1.23e-02    \n",
      "      658            803        3.6923e-05      2.02e-06       1.73e-02       5.09e-04    \n",
      "      659            804        3.3807e-05      3.12e-06       4.36e-02       1.02e-03    \n",
      "      660            806        3.2245e-05      1.56e-06       1.74e-02       7.34e-03    \n",
      "      661            807        2.9645e-05      2.60e-06       3.47e-02       1.64e-02    \n",
      "      662            809        2.7527e-05      2.12e-06       1.73e-02       5.72e-04    \n",
      "      663            810        2.4868e-05      2.66e-06       4.33e-02       1.91e-03    \n",
      "      664            812        2.3553e-05      1.31e-06       1.73e-02       8.50e-03    \n",
      "      665            813        2.1400e-05      2.15e-06       3.46e-02       1.56e-02    \n",
      "      666            815        1.9409e-05      1.99e-06       1.73e-02       4.50e-04    \n",
      "      667            816        1.7272e-05      2.14e-06       4.15e-02       1.74e-03    \n",
      "      668            818        1.6261e-05      1.01e-06       1.73e-02       9.21e-03    \n",
      "      669            819        1.4573e-05      1.69e-06       3.45e-02       1.39e-02    \n",
      "      670            820        1.2416e-05      2.16e-06       3.45e-02       1.22e-02    \n",
      "      671            822        1.0922e-05      1.49e-06       1.72e-02       8.45e-05    \n",
      "      672            823        9.7258e-06      1.20e-06       2.71e-02       3.20e-03    \n",
      "      673            825        9.2489e-06      4.77e-07       1.71e-02       1.26e-02    \n",
      "      674            826        8.0532e-06      1.20e-06       1.71e-02       1.12e-04    \n",
      "      675            827        7.0771e-06      9.76e-07       3.30e-02       5.43e-03    \n",
      "      676            829        6.4907e-06      5.86e-07       1.71e-02       1.11e-02    \n",
      "      677            830        5.5800e-06      9.11e-07       1.70e-02       1.07e-04    \n",
      "      678            831        4.8645e-06      7.16e-07       3.26e-02       4.50e-03    \n",
      "      679            833        4.3435e-06      5.21e-07       1.70e-02       7.92e-03    \n",
      "      680            834        3.7450e-06      5.98e-07       1.69e-02       1.40e-04    \n",
      "      681            835        3.2536e-06      4.91e-07       3.22e-02       4.23e-03    \n",
      "      682            837        2.8903e-06      3.63e-07       8.39e-03       4.73e-04    \n",
      "      683            838        2.5335e-06      3.57e-07       2.29e-02       1.73e-04    \n",
      "      684            840        2.3822e-06      1.51e-07       8.62e-03       1.25e-03    \n",
      "      685            841        2.1268e-06      2.55e-07       1.69e-02       1.37e-03    \n",
      "      686            842        2.0012e-06      1.26e-07       3.39e-02       6.80e-03    \n",
      "      687            843        1.4919e-06      5.09e-07       3.43e-02       5.06e-03    \n",
      "      688            844        1.1569e-06      3.35e-07       3.41e-02       3.76e-03    \n",
      "      689            845        9.0951e-07      2.47e-07       3.41e-02       3.45e-03    \n",
      "      690            846        7.0728e-07      2.02e-07       3.41e-02       2.99e-03    \n",
      "      691            847        5.3649e-07      1.71e-07       3.41e-02       2.34e-03    \n",
      "      692            848        4.1141e-07      1.25e-07       3.40e-02       1.97e-03    \n",
      "      693            849        3.1269e-07      9.87e-08       3.41e-02       1.63e-03    \n",
      "      694            850        2.3640e-07      7.63e-08       3.41e-02       1.34e-03    \n",
      "      695            851        1.7786e-07      5.85e-08       3.41e-02       1.09e-03    \n",
      "      696            852        1.3356e-07      4.43e-08       3.41e-02       8.98e-04    \n",
      "      697            853        9.9848e-08      3.37e-08       3.41e-02       7.34e-04    \n",
      "      698            854        7.4502e-08      2.53e-08       3.41e-02       6.00e-04    \n",
      "      699            855        5.5493e-08      1.90e-08       3.42e-02       4.92e-04    \n",
      "      700            856        4.1334e-08      1.42e-08       3.42e-02       4.03e-04    \n",
      "      701            857        3.0815e-08      1.05e-08       3.42e-02       3.30e-04    \n",
      "      702            858        2.3054e-08      7.76e-09       3.43e-02       2.75e-04    \n",
      "      703            859        1.7374e-08      5.68e-09       3.43e-02       2.45e-04    \n",
      "      704            860        1.3297e-08      4.08e-09       3.43e-02       2.21e-04    \n",
      "      705            861        1.0270e-08      3.03e-09       3.44e-02       2.00e-04    \n",
      "      706            862        8.0250e-09      2.24e-09       3.44e-02       1.81e-04    \n",
      "      707            863        6.3633e-09      1.66e-09       3.44e-02       1.65e-04    \n",
      "      708            864        5.1149e-09      1.25e-09       3.44e-02       1.51e-04    \n",
      "      709            865        4.1486e-09      9.66e-10       3.45e-02       1.38e-04    \n",
      "      710            866        1.4869e-09      2.66e-09       8.44e-03       4.60e-06    \n",
      "      711            867        6.0569e-10      8.81e-10       1.83e-02       3.10e-06    \n",
      "      712            868        1.2864e-10      4.77e-10       3.52e-02       4.15e-06    \n",
      "      713            869        2.1319e-11      1.07e-10       6.91e-02       1.14e-06    \n",
      "      714            870        4.1162e-12      1.72e-11       1.38e-01       2.71e-07    \n",
      "      715            871        1.8281e-12      2.29e-12       2.76e-01       4.62e-08    \n",
      "      716            872        1.6208e-12      2.07e-13       6.93e-02       8.41e-09    \n",
      "`gtol` termination condition is satisfied.\n",
      "Function evaluations 872, initial cost 9.2210e+05, final cost 1.6208e-12, first-order optimality 8.41e-09.\n"
     ]
    }
   ],
   "source": [
    "initial_guess = [0, 0, 5, 3, 1, 2, 5, 0, 0, 1, 4, 1, 1, 1]\n",
    "fitted_params = least_squares(residuals, initial_guess, bounds=(0, np.inf), method = 'trf', max_nfev=10000, verbose=2, ftol=1e-012, xtol=1e-012).x\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "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.plot(t, exp_P[0], 'ro')\n",
    "plt.plot(t, odeint(general_toggle_switch, iv, t, args = tuple(initial_guess)).T[0], 'g-')\n",
    "plt.plot(t, odeint(general_toggle_switch, iv, t, args = tuple(fitted_params)).T[0], 'b-')\n",
    "plt.legend(['Experimental Data', 'Initial Guess', 'Fitted Parameters'], loc = 'best')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Product Concentration')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "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.plot(t, exp_P[1], 'ro')\n",
    "plt.plot(t, odeint(general_toggle_switch, iv, t, args = tuple(initial_guess)).T[1], 'g-')\n",
    "plt.plot(t, odeint(general_toggle_switch, iv, t, args = tuple(fitted_params)).T[1], 'b-')\n",
    "plt.legend(['Experimental Data', 'Initial Guess', 'Fitted Parameters'], loc = 'best')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Product Concentration')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "a1_node1 = fitted_params[0]\n",
    "b1_node1 = fitted_params[1]\n",
    "a2_node1 = fitted_params[2]\n",
    "b2_node1 = fitted_params[3]\n",
    "n1 = fitted_params[4]\n",
    "n2 = fitted_params[5]\n",
    "beta_node1 = fitted_params[6]\n",
    "delta_node1 = fitted_params[7]\n",
    "\n",
    "a1_node2 = fitted_params[8]\n",
    "b1_node2 = fitted_params[9]\n",
    "a2_node2 = fitted_params[10]\n",
    "b2_node2 = fitted_params[11]\n",
    "beta_node2 = fitted_params[12]\n",
    "delta_node2 = fitted_params[13]\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\frac{1+6x_1^{1}+0x_2^{1}}{1+1x_1^{1}+0x_2^{1}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Latex\n",
    "\n",
    "Latex('$\\\\frac{1+'+str(int(a1_node2))+'x_1^{'+str(int(n1))+'}+'+str(int(a2_node2))+'x_2^{'+str(int(n2))+'}}{1+'+str(int(b1_node2))+'x_1^{'+str(int(n1))+'}+'+str(int(b2_node2))+'x_2^{'+str(int(n2))+'}}$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\frac{1+0x_1^{1}+0x_2^{1}}{1+0x_1^{1}+1x_2^{1}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Latex('$\\\\frac{1+'+str(int(a1_node1))+'x_1^{'+str(int(n1))+'}+'+str(int(a2_node1))+'x_2^{'+str(int(n2))+'}}{1+'+str(int(b1_node1))+'x_1^{'+str(int(n1))+'}+'+str(int(b2_node1))+'x_2^{'+str(int(n2))+'}}$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Node 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\dot{x}_1 = \\frac{1+1e-10x_1^{1.947357600867335}+3.7371448717438415e-06x_2^{1.9997276981757783}}{1+1e-10x_1^{1.947357600867335}+1.5544637159667523x_2^{1.9997276981757783}} - 0.17997784805211872x_1 $"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Latex\n",
    "\n",
    "Latex('$\\dot{x}_1 = \\\\frac{1+'+str((a1_node1))+'x_1^{'+str((n1))+'}+'+str((a2_node1))+'x_2^{'+str((n2))+'}}{1+'+str((b1_node1))+'x_1^{'+str((n1))+'}+'+str((b2_node1))+'x_2^{'+str((n2))+'}} - ' + str(delta_node1)+'x_1 $')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\dot{x}_2 = \\frac{1+6.232998499542231x_1^{1.947357600867335}+0.02088512134645593x_2^{1.9997276981757783}}{1+1.398999913917224x_1^{1.947357600867335}+0.0006073708848403598x_2^{1.9997276981757783}} - 0.17827555689818342x_2 $"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Latex('$\\dot{x}_2 = \\\\frac{1+'+str((a1_node2))+'x_1^{'+str((n1))+'}+'+str((a2_node2))+'x_2^{'+str((n2))+'}}{1+'+str((b1_node2))+'x_1^{'+str((n1))+'}+'+str((b2_node2))+'x_2^{'+str((n2))+'}} - ' + str(delta_node2)+'x_2 $')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.27400995e-01, -3.11232534e-01,  2.53493571e-02,  6.17897403e-02,\n",
       "        1.08354256e+00,  3.24787384e-01,  7.51857915e+00,  3.24020050e+00,\n",
       "       -3.10881339e-01,  2.26759710e+00,  5.93163876e-03,  3.47355876e-01,\n",
       "        2.36944163e+00,  3.13245405e-01])"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fitted_params"
   ]
  }
 ],
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