{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# First order Nomoto model for ship maneuvering dynamics\n",
    "> Implementation of the so called first order Nomoto model for ship maneuvering dynamics\n",
    "\n",
    "- toc: true\n",
    "- branch: master\n",
    "- badges: true\n",
    "- comments: true\n",
    "- categories: [simulation, dynamics, manoeuvring, system identification, nomoto]\n",
    "- image: images/nomoto.png\n",
    "- hide: false\n",
    "- search_exclude: true\n",
    "- metadata_key1: metadata_value1\n",
    "- metadata_key2: metadata_value2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first order Nomoto model can be written as:\n",
    "$$ K \\cdot \\delta=r+T_{1} \\cdot \\dot{r}+T_{2} \\cdot \\ddot{r} $$\n",
    "where $r$ is yaw rate with its time derivatives and $\\delta$ is the rudder angle. $K$, $T_{1}$\n",
    " and $T_{1}$ are the coefficients describing the hydrodynamics of the ship.\n",
    " \n",
    " For slow manoeuvres this equation can be further simplified by removing the $\\ddot{r}$ term:\n",
    " $$ K \\cdot \\delta=r+T_{1} \\cdot \\dot{r}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#hide\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#collapse\n",
    "from scipy.integrate import solve_ivp\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display, Latex, Math\n",
    "from scipy.optimize import least_squares\n",
    "import altair as alt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The simulation model can be expressed in Python as a state space model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_r1d(K,T_1,delta,r):\n",
    "    return (K*delta - r)/T_1 \n",
    "    \n",
    "def nomoto(t,states):\n",
    "    \"\"\"\n",
    "    Simulation model for heading and yaw rate using Nomoto with only K and T_1\n",
    "    \"\"\"\n",
    "    # states:\n",
    "    psi = states[0]\n",
    "    r = states[1]\n",
    "    \n",
    "    r1d_ = calculate_r1d(K=K, T_1=T_1, delta=delta, r=r)\n",
    "    d_states_dt = np.array([r,r1d_])\n",
    "    return d_states_dt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate a pull out manoeuvre\n",
    "Simulating a simple pull out manoeuvre:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": [
    "#collapse\n",
    "K = 0.1\n",
    "delta = 0.15\n",
    "T_1 = 10\n",
    "\n",
    "states_0 = np.array([0,0])\n",
    "t = np.linspace(0,30,100)\n",
    "\n",
    "sol = solve_ivp(fun = nomoto,t_span=[t[0],t[-1]],t_eval=t, y0 = states_0)\n",
    "psi = sol.y[0,:]\n",
    "r = sol.y[1,:]\n",
    "\n",
    "fig,ax=plt.subplots()\n",
    "ax.plot(t,np.rad2deg(psi));\n",
    "ax.grid(True)\n",
    "ax.set_title('Simulation with Nomoto model $\\delta$=%0.1f degrees' %np.rad2deg(delta))\n",
    "ax.set_ylabel('$\\psi$ [deg]')\n",
    "ax.set_xlabel('time [s]');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate a ZigZag test\n",
    "A ZigZag test can be simulated by adding an auto pilot to the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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": [
    "#collapse\n",
    "def nomoto_zigzag(t, states, K, T_1, angle=np.deg2rad(10)):\n",
    "    \"\"\"\n",
    "    Simulation model for heading and yaw rate using Nomoto with only K and T_1\n",
    "    Also including an autopilot for ZigZag test:\n",
    "    \"\"\"\n",
    "    \n",
    "    \n",
    "    # states: \n",
    "    psi = states[0]\n",
    "    r = states[1]\n",
    "    \n",
    "    #ZigZag autopilot:\n",
    "    sign=-1\n",
    "    psi_pluss = ((psi>=0) and (psi<angle))\n",
    "    psi_minus = ((psi>=-angle) and (psi<=0))\n",
    "    \n",
    "    if (\n",
    "        (psi_pluss and (r>=0)) |\n",
    "        (psi<-angle) |\n",
    "        (psi_minus and (r>=0))\n",
    "        \n",
    "        \n",
    "    ):\n",
    "        sign=1   \n",
    "    delta_=sign*delta\n",
    "    \n",
    "    #Nomoto equation:\n",
    "    r1d_ = (K*delta_ - r)/T_1 \n",
    "    d_states_dt = np.array([r,r1d_])\n",
    "    \n",
    "    return d_states_dt\n",
    "\n",
    "## Simulation:\n",
    "K = 0.2\n",
    "delta = 0.15\n",
    "T_1 = 10\n",
    "angle=np.deg2rad(10)\n",
    "states_0 = np.array([0,0])\n",
    "t = np.linspace(0,100,100)\n",
    "\n",
    "sol = solve_ivp(fun = nomoto_zigzag,t_span=[t[0],t[-1]],t_eval=t, y0 = states_0, args=(K,T_1,angle))\n",
    "psi = sol.y[0,:]\n",
    "r = sol.y[1,:]\n",
    "\n",
    "fig,ax=plt.subplots()\n",
    "ax.plot(t,np.rad2deg(psi));\n",
    "ax.grid(True)\n",
    "ax.set_title('Simulation ZigZag%0.0f/%0.0f with Nomoto model' % (np.rad2deg(angle),np.rad2deg(angle)))\n",
    "ax.set_ylabel('$\\psi$ [deg]')\n",
    "ax.set_xlabel('time [s]');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Perform simple system identification\n",
    "Is this very simple model good to describe the dynamics for one \"real\" ZigZag model test? This will be investigated by first loading some model test data and then fitting the simple Nomoto model to this data. Model test data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>delta</th>\n",
       "      <th>x0</th>\n",
       "      <th>y0</th>\n",
       "      <th>psi</th>\n",
       "      <th>r</th>\n",
       "      <th>delta_deg</th>\n",
       "      <th>psi_deg</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>time</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0.00</td>\n",
       "      <td>0.008786</td>\n",
       "      <td>-25.137978</td>\n",
       "      <td>-0.063029</td>\n",
       "      <td>-0.001346</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.503417</td>\n",
       "      <td>-0.077114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0.02</td>\n",
       "      <td>0.008786</td>\n",
       "      <td>-25.103222</td>\n",
       "      <td>-0.063109</td>\n",
       "      <td>-0.001346</td>\n",
       "      <td>-0.002182</td>\n",
       "      <td>0.503417</td>\n",
       "      <td>-0.077114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0.04</td>\n",
       "      <td>0.008786</td>\n",
       "      <td>-25.068771</td>\n",
       "      <td>-0.063222</td>\n",
       "      <td>-0.001433</td>\n",
       "      <td>-0.002182</td>\n",
       "      <td>0.503417</td>\n",
       "      <td>-0.082114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0.06</td>\n",
       "      <td>0.008786</td>\n",
       "      <td>-25.034290</td>\n",
       "      <td>-0.063301</td>\n",
       "      <td>-0.001433</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.503417</td>\n",
       "      <td>-0.082114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0.08</td>\n",
       "      <td>0.008786</td>\n",
       "      <td>-24.999577</td>\n",
       "      <td>-0.063382</td>\n",
       "      <td>-0.001433</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.503417</td>\n",
       "      <td>-0.082114</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         delta         x0        y0       psi         r  delta_deg   psi_deg\n",
       "time                                                                        \n",
       "0.00  0.008786 -25.137978 -0.063029 -0.001346  0.000000   0.503417 -0.077114\n",
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\"psi_deg\": -20.398519350518708, \"delta_deg\": 20.027682433018413, \"x0\": 26.397185714189984, \"psi\": -0.35602132519832674, \"delta\": 0.349549, \"y0\": -4.547735564075404}, {\"time\": 40.74, \"r\": 0.2107984244041974, \"psi_deg\": -20.15843357792767, \"delta_deg\": 20.027682433018413, \"x0\": 26.422375064615334, \"psi\": -0.3518310379794188, \"delta\": 0.349549, \"y0\": -4.561283564695536}, {\"time\": 40.76000000000001, \"r\": 0.2129800859691888, \"psi_deg\": -19.915404948663987, \"delta_deg\": 20.047220293832375, \"x0\": 26.45392974380627, \"psi\": -0.34758938822215885, \"delta\": 0.34989000000000003, \"y0\": -4.557922951594434}, {\"time\": 40.78, \"r\": 0.20996315999848994, \"psi_deg\": -19.670319176072955, \"delta_deg\": 20.047220293832375, \"x0\": 26.478800626984764, \"psi\": -0.34331183454065123, \"delta\": 0.34989000000000003, \"y0\": -4.5712427315986845}, {\"time\": 40.8, \"r\": 0.2147752821815715, \"psi_deg\": -19.434204831818246, \"delta_deg\": 20.047220293832375, \"x0\": 26.50182099332988, \"psi\": -0.33919086182221925, \"delta\": 0.34989000000000003, \"y0\": -4.590132441612021}, {\"time\": 40.82, \"r\": 0.2147752821815715, \"psi_deg\": -19.17809048756354, \"delta_deg\": 20.027682433018413, \"x0\": 26.52703708190636, \"psi\": -0.3347208232533884, \"delta\": 0.349549, \"y0\": -4.603179507175981}, {\"time\": 40.84, \"r\": 0.2086790965396892, \"psi_deg\": -18.941976143308832, \"delta_deg\": 20.047220293832375, \"x0\": 26.548172619557608, \"psi\": -0.3305998505349564, \"delta\": 0.34989000000000003, \"y0\": -4.627470178757911}, {\"time\": 40.86, \"r\": 0.21438881682896144, \"psi_deg\": -18.69983322739045, \"delta_deg\": 20.027682433018413, \"x0\": 26.57527602189795, \"psi\": -0.3263736593918008, \"delta\": 0.349549, \"y0\": -4.6346063042322765}, {\"time\": 40.88, \"r\": 0.22054733617132694, \"psi_deg\": -18.450633168144723, \"delta_deg\": 20.047220293832375, \"x0\": 26.59865066858693, \"psi\": -0.3220242978617979, \"delta\": 0.34989000000000003, \"y0\": -4.65315794777078}, {\"time\": 40.90000000000001, \"r\": 0.21573521398824674, \"psi_deg\": -18.19437596557165, \"delta_deg\": 20.066758154646337, \"x0\": 26.62220213851246, \"psi\": -0.3175517659449477, \"delta\": 0.350231, \"y0\": -4.671436406537583}, {\"time\": 40.92, \"r\": 0.2152864149351521, \"psi_deg\": -17.95620447798959, \"delta_deg\": 20.027682433018413, \"x0\": 26.64772050533326, \"psi\": -0.31339488930226805, \"delta\": 0.349549, \"y0\": -4.68409408972437}, {\"time\": 40.94000000000001, \"r\": 0.2179168755532409, \"psi_deg\": -17.70097584708019, \"delta_deg\": 20.027682433018413, \"x0\": 26.67109980643929, \"psi\": -0.30894030934754163, \"delta\": 0.349549, \"y0\": -4.702344806169805}, {\"time\": 40.96, \"r\": 0.21400235147634866, \"psi_deg\": -17.45677578783446, \"delta_deg\": 19.98866400717, \"x0\": 26.70235611009653, \"psi\": -0.3046782142801384, \"delta\": 0.34886799999999996, \"y0\": -4.697746980204181}, {\"time\": 40.98, \"r\": 0.21836567460633416, \"psi_deg\": -17.21051858526139, \"delta_deg\": 20.027682433018413, \"x0\": 26.727928208555717, \"psi\": -0.3003802152884877, \"delta\": 0.349549, \"y0\": -4.710146907273367}, {\"time\": 41.0, \"r\": 0.21355355242325536, \"psi_deg\": -16.95631852601566, \"delta_deg\": 20.008201867983963, \"x0\": 26.75559378164171, \"psi\": -0.29594358729588505, \"delta\": 0.349209, \"y0\": -4.716927492459644}, {\"time\": 41.02, \"r\": 0.21316708707064252, \"psi_deg\": -16.72108989510626, \"delta_deg\": 20.027682433018413, \"x0\": 26.78121945325694, \"psi\": -0.2918380731915575, \"delta\": 0.349549, \"y0\": -4.72932898320432}, {\"time\": 41.04, \"r\": 0.22105846892490616, \"psi_deg\": -16.467775549205836, \"delta_deg\": 20.047220293832375, \"x0\": 26.80853990602723, \"psi\": -0.2874169038130593, \"delta\": 0.34989000000000003, \"y0\": -4.73558576199558}, {\"time\": 41.06, \"r\": 0.21842800830681874, \"psi_deg\": -16.21446120330542, \"delta_deg\": 20.027682433018413, \"x0\": 26.83576879935843, \"psi\": -0.2829957344345612, \"delta\": 0.349549, \"y0\": -4.741689419584416}, {\"time\": 41.08000000000001, \"r\": 0.21887680735991616, \"psi_deg\": -15.96717542906867, \"delta_deg\": 20.027682433018413, \"x0\": 26.85791055934401, \"psi\": -0.2786797834807866, \"delta\": 0.349549, \"y0\": -4.765011746678134}, {\"time\": 41.1, \"r\": 0.22195606703110102, \"psi_deg\": -15.712832511504573, \"delta_deg\": 20.047220293832375, \"x0\": 26.885402692900552, \"psi\": -0.27424066214016457, \"delta\": 0.34989000000000003, \"y0\": -4.770897497396262}, {\"time\": 41.12000000000001, \"r\": 0.21977440546610544, \"psi_deg\": -15.458489593940472, \"delta_deg\": 20.008201867983963, \"x0\": 26.905932803019983, \"psi\": -0.2698015407995425, \"delta\": 0.349209, \"y0\": -4.799615901429644}, {\"time\": 41.14, \"r\": 0.21887680735991336, \"psi_deg\": -15.209146676376383, \"delta_deg\": 20.047220293832375, \"x0\": 26.928520065980877, \"psi\": -0.26544968592152035, \"delta\": 0.34989000000000003, \"y0\": 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-13.944346373564883, \"delta_deg\": 20.027682433018413, \"x0\": 27.06164741883428, \"psi\": -0.2433747562572384, \"delta\": 0.349549, \"y0\": -4.8679083886628085}, {\"time\": 41.26000000000001, \"r\": 0.22291599883777624, \"psi_deg\": -13.681917741009764, \"delta_deg\": 20.027682433018413, \"x0\": 27.09088882634291, \"psi\": -0.2387945125676452, \"delta\": 0.349549, \"y0\": -4.867367602435778}, {\"time\": 41.28, \"r\": 0.21983673916659072, \"psi_deg\": -13.433460536790971, \"delta_deg\": 20.066758154646337, \"x0\": 27.11851524049285, \"psi\": -0.2344581163037273, \"delta\": 0.350231, \"y0\": -4.872637022305006}, {\"time\": 41.3, \"r\": 0.22375126324347955, \"psi_deg\": -13.178089047563207, \"delta_deg\": 20.027682433018413, \"x0\": 27.14603366163471, \"psi\": -0.2300010430009816, \"delta\": 0.349549, \"y0\": -4.877534043753847}, {\"time\": 41.32, \"r\": 0.22028553821968536, \"psi_deg\": -12.920660415008092, \"delta_deg\": 20.027682433018413, \"x0\": 27.172120927701133, \"psi\": 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41.42, \"r\": 0.22471119505015688, \"psi_deg\": -11.643374393914142, \"delta_deg\": 20.047220293832375, \"x0\": 27.29620015080221, \"psi\": -0.203215219216201, \"delta\": 0.34989000000000003, \"y0\": -4.9686287466189}, {\"time\": 41.44000000000001, \"r\": 0.227341655668245, \"psi_deg\": -11.382860046368005, \"delta_deg\": 20.027682433018413, \"x0\": 27.321297621042838, \"psi\": -0.1986683861028361, \"delta\": 0.349549, \"y0\": -4.984526321616763}]}, \"$schema\": \"https://vega.github.io/schema/vega-lite/v4.0.2.json\"}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.LayerChart(...)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#collapse\n",
    "df = pd.read_csv('example_zigzag.csv', sep=';', index_col=0)\n",
    "df['delta']*=-1  # Nomoto has another sign convention\n",
    "df['delta_deg']=np.rad2deg(df['delta'])\n",
    "df['psi_deg']=np.rad2deg(df['psi'])\n",
    "\n",
    "display(df.head())\n",
    "\n",
    "source = df.reset_index()\n",
    "alt.layer( \n",
    "    alt.Chart(source).mark_line(color='blue').encode(x='time',y='psi_deg'),                                         \n",
    "    alt.Chart(source).mark_line(color='orange').encode(x='time',y='delta_deg')\n",
    "    \n",
    "         ,).interactive()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When examing this test a bit closer, it seems that:\n",
    "* The first rudder order is at time=1.15 s\n",
    "* There is a 0.5 degrees initial rudder angle (to get the model on a straight course).\n",
    "* There is also a very small yaw rate at the start. (But this can be handled by using this as the initial state in the simulations).\n",
    "\n",
    "To simplify further analysis the initial part is removed and the rudder angle is \"zeeroed\" around the initial value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#collapse\n",
    "df['delta']-=df.iloc[0]['delta']\n",
    "df['delta_deg']=np.rad2deg(df['delta'])\n",
    "df.index-=df.iloc[0].name\n",
    "mask=df.index>1.15\n",
    "df=df.loc[mask]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We attempt to estimate the coefficients using least square fit. We then need to first get the $\\dot{r}$ by performing numerical derivation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": [
    "#collapse\n",
    "df['r1d']=np.gradient(df['r'],df.index)\n",
    "fig,ax=plt.subplots()\n",
    "df.plot(y='r1d',ax=ax, label='$\\dot{r}$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data is now very noisy but we try to do the leas sqyare fit anyway:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "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": [
    "#collapse\n",
    "\n",
    "def estimator(parameters, X):\n",
    "    delta=X['delta']\n",
    "    r=X['r']\n",
    "    \n",
    "    K=parameters[0]\n",
    "    T_1=parameters[1]\n",
    "    \n",
    "    return calculate_r1d(K=K, T_1=T_1, delta=delta, r=r)  \n",
    "    \n",
    "def error_function(x, X, ys):\n",
    "    return ys-estimator(x,X)\n",
    "\n",
    "data = df.copy()\n",
    "ys=data.pop('r1d')\n",
    "X=data.copy()\n",
    "\n",
    "kwargs={\n",
    "    'X':X,\n",
    "    'ys':ys,\n",
    "}\n",
    "\n",
    "initial_guess=[1,1]\n",
    "result = least_squares(fun=error_function, x0=initial_guess,\n",
    "                       kwargs=kwargs)\n",
    "\n",
    "result_soft_l1 = least_squares(fun=error_function, x0=initial_guess,\n",
    "                       kwargs=kwargs, loss='soft_l1')\n",
    "\n",
    "y_pred = estimator(parameters=result.x, X=X)\n",
    "y_pred_soft_l1 = estimator(parameters=result_soft_l1.x, X=X)\n",
    "\n",
    "fig,ax=plt.subplots()\n",
    "time=data.index\n",
    "ax.plot(time,ys, label='measurement')\n",
    "ax.plot(time,y_pred, label='curve fit');\n",
    "ax.plot(time,y_pred, ':', label='curve fit (soft_l1)');\n",
    "ax.legend()\n",
    "ax.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle K=0.74, T_1=1.57$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#hide_input\n",
    "K_=result.x[0]\n",
    "T_1_=result.x[1]\n",
    "display(Math('K=%0.2f, T_1=%0.2f' % (K_,T_1_)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We try to simulate with the estimated coefficients:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#collapse\n",
    "def nomoto_replay(t, states, K, T_1, deltas):\n",
    "    \n",
    "    # states:\n",
    "    psi = states[0]\n",
    "    r = states[1]\n",
    "    \n",
    "    i=np.argmin(np.abs(deltas.index-t))\n",
    "    delta=deltas.iloc[i]\n",
    "    \n",
    "    r1d_ = calculate_r1d(K=K, T_1=T_1, delta=delta, r=r)\n",
    "    \n",
    "    d_states_dt = np.array([r,r1d_])\n",
    "    \n",
    "    return d_states_dt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YtmxZ6zmzZ8/mlVdeaf3clY7AwMALWiQdnZ+Tk0NqaipLlixh3LhxHDt27KJze03W13B0Bcz4EyROvPi4EMqxmBHK50bbdlOq9A7VcajYj6LDsPoPcHBZ12UtSX8I6kpd4mExZMgQPvjgA0aMGEF5eTn3338/NTU1zJs3jxEjRjB9+nSbDBbHxMTw1FNPMWPGDEaOHMmYMWO45ppriImJ4fHHH2fSpEnMmjWLMWPGtJ7z0ksvsWfPHkaMGMHQoUN54403Oq3jiiuu4KuvvmodHO/o/BdffJHhw4czcuRIfH19ufLKKxkxYgRarZaRI0f2/vvqm+CHv0CfETDpwa7Lb3gS3r4M9M29q1fFdlizaIe7bepCTtZhd51f3i3lk7FS1pd3/9zl98kj29bImsoenGsjTp06JYcNG2ZV2erqajur6T321HjkyBHrC9eWSrn0NilPrmv38EX35fE1Uj4WJOWP/+q5QBtzqf6Poy7kpOJU6suV7ohRt4BvaPfPn/4IAF7NFTYWpuJ0/CPgpv9C/8usKz9wtjLW8eNzUFVgX20qVuFyjkMI4SGE2CeEWGn63FcIsVMIcVII8ZkQooOwHBWX4sCnYGiCsQsvPnSmkr+tyOLXn+7j2e+PcayonS6psL7g5Y/G2KxMFHQCycnJHD582Cl1X7IU7IGSY+0eOlfZQHZJDXpjO3/vK54Cox4yn7azQBVrcMWoqoeAo0CQ6fMzwAtSyqVCiDeA/wVed5Y4FStpqoG+0yH6fDSUwSj5+8ojvL8tDx9PDdFBPnx3qJDXN+Vw8/hEHps/FB9Pj/M2fENp8I0l0IXCc1V6yepHlHtj8a7WsOuduTqeWHmELNM8HX9PuLXxKA/M7E+Qj2mNj5BEGLdIeSGZ80/wCeqoBhUH4FKOQwgRD8wFngQeFkoc4kzgFlORD4DHUR2H65Px6AUtBSklf1p+iM/2nOHO9GR+N3sQAd5aKuubeXlDNu9uPUXWuSo+XDSBED9To1IIZTO0gNCAxqODylTcgoI9cHYvXPV8q9NY/lMBv1t2gPhQX/48dwhh/l4s/fEwb23O5YesIt66fRwDok1riExfAtP+oDoNF0BIJ3UDtIcQ4gvgKSAQ+D2wENghpexvOp4ArJZSDm/n3HuAewCio6PHLl261FGyL6K2tpaAgACn1W8t9tLp2VxJi1fIBfu+P9XC0uPNXN3Pk+sHXNzb+FOxntf2N5EcrGHJBB88NYLg4GD6JScQ2FBAk3f4RTZdCYPBgIeHazs2e2rMzs6mqqqq0zKDjr1MZOkWtk96D4PWj8Nlev61p4kh4RoeGu2Dt1ZxJrW1tZxr8eXV/U0YpeRPE3yJCbDoVZcSjbEFo4fzeq0v1f/xGTNm7JVSjuuyoDUj6I7YgHnAa6bfM4CVQCSQbVEmATjUlS01qso67KJT3yLlM32lXP3H1l3ZJTVywJ++k3d9sFsajcYOT1118JxMWrJSPrLsgJRSidSprq6WsuSYlEVZUnZyrrNRo6q6iKpqrpfyn/FSLr9PSimlrrZJjvvHWnn5/2XKuqaWC4qa78uckho59u8/yPSn18uKuibloEEv5duzpVz1e1t/hW5xqf6P44ZRVenA1UKIPGApShfVi0CIEMLcpRYPnHOOPBWrOLUJ6nWQNLl11z9XHcVLq+Gf16V2uujPVakx/CqjH5/tOcO6I8XnDwREKQPtLjCvozO6k1Z9z549/PrXv7ZJvdakWs/MzGTnzp2tnx2RAv4Cig4rg9sjbwLgyVVHqaxv5sWbRuPn1X6PeUpkAG/dPo7i6kZ+9/kB5eVR4wHh/WDfR0rknopTcBnHIaX8o5QyXkqZDNwMbJBS3gpsBBaYit0BdJ7bQcW5HP4SvIOg/ywAtpwsY/2xEh6c2Z/IQO8uTobfzBrI4D6B/PGrQxjN0TU+waDxhPoyeyrvNd1Jqz5u3DheeuklOys6T1vH4fAU8Anj4fcnIHkqhwqq+PKnAhZN6cvQ2M7HK0YnhvLolUNYf6yEbw+Y3hknLYaWetjzrgOEq7SHyziOTliCMlCeDYQD7zhZj0pH6Jvg6EoYMh88fQD49/oTxAb7sDA92SoTXloNz984koq6ZqoaTSsDCg34hUFTtUNXC7RVWvVly5a1zsSeNm0aoDzI582b13reHXfcwezZs0lOTmb58uU88sgjpKamcsUVV9DSonzn5ORkysoU57lnzx4yMjIuqmvFihWkpaUxevRoZs2aRXFxMXl5ebzxxhu8+uqrrbPGLbXu37+fiRMnMmLECK677joqKpS5MxkZGSxZsoQJEyYwcOBANm/uYcp78ziqdyBoPHh2zTHC/b14YEZ/q05fODmZkQkh/H3lESrrm5VIvX4zYffb5xcEU3EoLuk4pJSZUsp5pt9zpZQTpJT9pZQ3Sik7T0Oq4jxO/QhNVTD0WgB255WzO6+Ce6al4K21flB2eFwwt01Mor7JQLPB9NDxj4Tv/wQfXgvvzT2/7XpLOd5cf+F+87bvY+V4ne7iY1Zw/Phx7rnnHg4ePEhQUBCvvfYa5eXlfPXVV2RlZXHw4EH+/Oc/d2rjiSeeYM2aNRw4cIBvv/223TI5OTmsWrWKb775httuu40ZM2Zw6NAhfH19WbVqlVVaAaZMmcKOHTvYt28fN998M88++yzJycncd999LF68mP379zN16tQLzrn99tt55plnOHjwIKmpqfztb39rPabX69m1axcvvvjiBfu7xb7/whtToK6MQwVVbD5Zxt3TUgg0h9p2gYdG8M/rhlNR38LTq01zQMb9L9QUwonve6ZJpVe4pONQcVMSJsAN70Bf5a36P5tyCPP34qbxid029evLBiAEVDSaHIeHp9LycDBt06pv2bKFoKCg1rTqy5cvx8/Pr1Mb6enpLFy4kLfeeguDwdBumSuvvBJPT09SU1MxGAxcccUVAKSmppKXl2e13oKCAubMmUNqairPPfccWVlZnZavqqqisrKS6dOnA3DHHXe0pnMHuP766wEYO3Zst3RcwNEV0FgFfuG8vimbQB8tt6Z1754YFhvMwsnJfLbnDDmltTDwCrjuP9BvRs80qfQKl5rHoeLm+ARDqjIcdaa8nvXHSnhgRn98vbofAhrm70Wgj5Z6vaSuSY+/txZu/1pJw+0XcXEsv5efsqZDR/iHd368A2yRVv2NN95g586drFq1ilGjRrWbxdYy7bqnp2drvea06wBarRajUckY3NjY2G5dDz74IA8//DBXX301mZmZPP74493+zu3p8vDwaNXRLRqrITcTxt/N2apGVh8u4t5p/axubVhyf0Y/Ptpxmv9syuHZBSNh5M3d16NiE9QWh4ptKD0OW19qjXT5bPcZBHDzhO63Nsz4e2vRCCirNfVOajyguU6J2nIQtkirnpOTQ1paGk888QQRERGcOXOmR1qSk5PZu3cvAF9++WW7ZaqqqoiLU9Y1+eCDD1r3d5QWPTg4mNDQ0Nbxi//+97+trQ+bkL1WWYxpyDw+26187+62NsxEBHhz0/gEvtp3lsKqBmXnzv+c765UcRiq41CxDYeXw9q/gtGA3mDksz1nmDEoiriQni0yBKARgiAvQVVDC00tBqWryjdE6fYwOmZQ1BZp1f/whz+0riU+bdo0Ro4c2SMtjz32GA899BBTp07tcCLf448/zo033sjUqVOJiIho3T9//nxWrlzZOjhuyQcffMAf/vAHRowYwf79+/nrX2244t7RleAXgT52PJ/vPsO0AZEkhHXetdcZd09NwSjhnc2nlB05G5Tkh+oguWOxZrKHu23qBEDrsKnON6ZK+fblUkopM4+XyKQlK+XqQ4W9MnnkyBFZUVklDxZUyjPldcrOplopz/4kZV1ZbxV3iZpW3Xo6nAB4cJmUO9+Ua7OKZNKSlfL7w13fE13dl79Zuk8O+ctqWV7bJOWRFUrK9RM/9EB1z7lU/8dxwwmAKu5K1VkoPKAMWAJf7ztLkI+WGYMje23aQyMI8/Okor6FFoMRPP3Aw0ud/OUupC6ACXezfF8BEQFezBwc1WuT903vR32zgQ+3n4YBs5W0/Qecl2Lo54jqOFR6z8k1ys9BV1LfrGdNVhFzR8R0KwS3MyICvJFSoqttUpLjBUSBd4Dd062radV7ydmfoDKfmsYW1h8tYd6IWDw9ev/IGdQnkFlDonh/2ynqjRoYdj0cW+nymQUuJVTHodJ7qs5CWApEDmbtkWLqmw1cMyrOZua9PT0I9vVEV9eszCb3j4TAmNYMqyouyqqHYfk9/JBVTJPeyPyRsTYzfX9GPyrqW1i66wyM/IWybnldqc3sq3SO6jhUes9lf4HFu0EIvtl/jthgHyYkh9m0ivAAbwxGeX42uTQq6zqouCb15XBuP6Rk8O2Bc8SH+jIm0XbZjccmhTGhbxhvbc6lOWYs3P6NksNKxSGojkPFNnhoqW3Ss+VkGVemxqDR2LY14O/lgbdWQ3lds7KjTge6bGhpfz6DipPJ2wxIqmPS2ZJdxvyRsZ0muOwJ901PobCqkXVHTQkxa4rVsS8HoToOld6x9SV47yrQN7P5RCnNBiOXD422eTVCCEL9vahr0iuhub7ByoHGSpvXpWIDcjPBK5C11fEYjJKrhsfYvIrpA5Vw70935StO4/+GKOlNVOyO6jhUesfJH5RBSa0Xa48UE+LnybikULtUFernhUBQXt+sRFZ5+kOD6jhcktxMSJ7C2mPl9AnyYXic7Vft89AI/mdcAptPlpHfHAgxIyDra5vXo3IxquNQ6TnN9XBmJ/TLQG8wsuF4CTMHRaG1QeRMe3h6aAj00VJR14JRSmUyoL4B9I7rruooA257x99//33Onev98jF5eXkMH37RopeuzZ2raZr5OD+eLGXW0Cibd1OZ+Z/x8WgELN2dD8Oug3M/QUWeXepSOY/qOFR6Tv42JZ1ESgZ7T1dQWd/CLDt0U1kS5u+F3mikplEPPqbBVhcNw7SV43BLAvuwrSqM+mYDs4bY756ICfZl5uAolu0tQD/oamWn2uqwO2qSQ5Wek7NR6TJKnMzaH/Lw8tAwbWDvJ/21xzO7nuFYuZJSu77ZgEaAj6eHEl3Vw6y5g8MGs2TCki7LPfnkk3z44YckJCQQGRnJ2LFjycnJYfHixZSWluLn58eLL77I2LFjW8/54osv2LNnD7feeiu+vr5s376d5557jhUrVtDQ0MDkyZP5z3/+0+Gb+N69e1m0aBF+fn5MmTKldb/BYODRRx8lMzOTpqYmFi9ezL333ovRaOSBBx5g06ZN9O3bF6PRyKJFi1iwYEG79u3KtpfBL4J1p4bj7+XBpH7hdq1uwdgE1h0tYWt5ANNjx8CRr2HKb+xa588dtcWh0nP6jICJ9yM9fVl7tJhJ/cIJ8Lb/u4hWIzAYpTL/z86p1vfu3cvSpUvZt28fy5cvZ/fu3QDcc889vPzyy+zdu5fnn3+ehx9++ILzFixYwLhx4/j444/Zv38/vr6+PPDAA+zevZvDhw/T0NDAypUrO6z3zjvv5KWXXmpNsGjmnXfeITg4mN27d7N7927eeustTp06xfLly8nLy+PQoUO8/fbbF53nMIxG2PICMncj644WM3VApM0mgnbEjMGRBPlo+XrfWZj7L7jpI7vWp6K2OFR6g2n96JySGk7r6rlraordqrJsGTQ0GzhZUkNciC/h/l5QVQCevuAf0YmFnrF582auu+661jU3rr76ahobG9m2bRs33njjeU0NDV3a2rhxI88++yz19fWUl5czbNgw5s+ff1G5tmtk/PKXv2T16tUA/PDDDxw8eJAvvviitezJkyfZsmULN954IxqNhj59+jBjhpPWqSg+DPU6CkLTKK5usnvXJYC31oO5I2L5et9Z/nHtLCUFv4pdUa+wSs+oKlDyRvmFkXlcmbF7mQ3yEFmDj6cGH60HlfUthAd4Q0udsga1HRwHXLwmh9FoJCQk5IJ06u2lLLeksbGRX/3qV+zZs4eEhAQef/zxDtfUkFJ22IUlpeTll19mzpw5F+zvziqBdiU3E4DVdYPQiCpmDLJP12Vbrhsdx6e78ll7pJhrA45C9jq48mmH1P1zRO2qUukZmU/Dy2PAaOTHk2X0jwogthcp1LuDEIJgP0/qmvWl2uC5AAAgAElEQVQ0643KIHlLvTJQb2OmTZvGV199RUNDAzU1NaxYsQI/Pz/69u3LsmXLAOVhfujQoYvOtVwDw+wkIiIiqK2tbW0xtEdISAjBwcFs2bIFgI8//rj12Jw5c3j99ddb1yE/ceIEdXV1TJkyhS+//BKj0UhxcTGZmZk2+f7dJjcTIgfz7SnJmMRQxbE7gHFJocSF+PLVvrNQcgR2vg4Vpx1S988R1XGodB8pW+P0Gw2Snbk6pg6wz9t+R4T4KivIVTU0KysPgl2iq8aMGcNNN93EqFGjuOGGG1rX6/7444955513GDlyJMOGDWv3jX/hwoXcd999jBo1Cm9vb+6++25SU1O59tprGT9+fKf1vvfeeyxevJhJkybh63veId91110MHTqUMWPGMHz4cO699170ej033HAD8fHxrfvS0tIIDg627cXoCinB0ExjYgaHz1bbLVCiPTQawTWjYtmSXUZ5wuXKzuOrHVb/zw5rcq+726aux2EdPdZZlq2sgbDrLbn5RKlMWrJSbjhabFNtUiprPHS2hsTJ4mp5oqhaSqNRyqLDii4n4QrrcdTU1EgppSwrK5MpKSmysPDCtS8ctR7Hyv1nZdKSlXJPXnmPbPX0vjxRVC2TlqyU727JlfKVCVK+N7dHdqzhUv0fR12PQ8Vu5G5UfqbMYPPJUjw9BGkptk1qaA3Bvl40tBho0hvBLxy0jukWcVXmzZvHqFGjmDp1Kn/5y1/o06ePYwWY0txvzdUR4K1lZLxjWzwDogMZFhukRFcNngunt6m5q+yEOjiu0n1yMyE4EcJS2HxyC+OSwvDzcvytFOLnSWFVA5UNLUQHOfghaSMWL17M1q1bL9j30EMPceedd3bbltPGNcy8Pw9iRrI1+3ImpoTZLYNAZ1w7Ko4nvzvK2RmXERe1BqrPgp/jX2oudVTHodJ9Zv0NqgoorW3mSGE1j1wxyG5VyU4Wa/L00BDgraWyvoWoQG8EgKEFtF5202NrXn31VWdL6DVSSmUiZv42qqLTOK2r545JyU7RMndEDE9+d5SvS6JZfP/Wrk9Q6RFqV5VK9wnvBynT2ZpdBsDU/vYZBPXx8aGqqqpT5xHs50mT3kBji0EJES47bveVAVXOI6VEp9PhY6gBaWSPxwgA0vs7NljCTGyIL6MTQ1h9uFDZ0dKovEyo2BS1xaHSPY59B41VMPJmfjxZSqifJ8NibZ/5FCA+Pp4DBw5QW1vbYRmjUVJS1Uh9iZZgjxaoL4NSg8PHOxobG/Hx8XFond3FXhp9fHyIL/gWvAJYoYsjIqCKgdEBNq/HWq4arrQ6Co/tJubLa2DBuzDoCqfpuRRRHYdK99jxGjRWIkfezJaTZaT3j7D5ok1mPD09qa2tZdy4cZ2We/qdnZytrGbD4tHw7ByY9Cu4/Am7aOqIzMxMRo8e7dA6u4tdNa5cg0xKZ0tuJen9I+yWDdcarhjehye/O8qKwkDu0XjA8VWq47AxaleVivU01ylp1FNmkFNaS0lNE1Oc1CVhyeyh0eSW1pFd7QHJU9T4fUdjNMDImznX93rKapud1k1lJiHMj5HxwazKKoMBlyv3g9HgVE2XGqrjULGe09tb06hvz9EB2D3zqTWY8yH9cKQIBl0FZSegLNvJqn5GaDxg2h/43pgGOG98w5IrU2M4UFCFLn4W1JXC2b3OlnRJoToOFevJNadRn8T2XB2xwT4khvk5WxUxwb6MjA9mTVYxDL0Gbv4UgmKdLevnw7l90FjN1uwyksP9iHNQ6pnOMC9Vu7JuqJJB+cQaJyu6tFAdh4r1VORBQhpGrS87csuZ2C/cqX3Zlswe1ocDZyopMgbD4KvAy/kO7WeBlPDxjRhXPszOXJ1LtDYAEsP9GBoTxIoT9TDvBWV1QBWboToOFeu5+WO4dRknS2opr2tmUorzu6nMzBmmdFetPVoMlfmw6Tlo6jgaS8VGFGdBXSmngydQ12xwGccBcPnQaPbmV1A26BfQx82W3nVxVMeh0j08fdmeo8zfcIXxDTP9IgNIifDnh6wiKM+Fjf+AvM3OlnXpY0qjvqF5CELgUi8Tlw+NRkrYcKQITq6F/J3OlnTJoDoOFetY8//gmwcA2J6rIyHMl/hQ1+kOEkIwe1gftufoqIocB14BcPIHZ8u69MnNhPABrCnQMiw2iFB/15m1Pyw2iLgQX344UgIrHoJtLzlb0iWD6jhUukZKyPoaGqswGiU7T5Uzsa/rvFmamT0sGr1RkplTBX2nw8l16ixye6JvhtNbaUmexr78CtL7uU43FSgvE7OGRLElpwx9v8sVJ6dvcrasSwLVcah0jS4HqgsgJYOjRdVU1re4VDeVmVHxIUQGerMmq0iJ36/Kh9LjzpZ16eLhCXet56eYX9BikC41vmFm9rA+NLYYOeSXBs21SsZclV7jMo5DCJEghNgohDgqhMgSQjxk2h8mhFgrhDhp+hnqbK0/O8xp1PvNcKn5G23RaASXD40m83gpjX1ngtYHSo85W9alixAQPZR1xf54eWgYn+x6WWgn9A0jyEfLsvIU8PBWuy9thMs4DkAP/E5KOQSYCCwWQgwFHgXWSykHAOtNn1UcSW4mhCRCaF925OpIDvcjJtj5sfrtMWdYH+qbDWwr9YElp2HYtc6WdOny4/OQs5Gt2TrGJIXg6+XhbEUX4emhYcbgKNacqEEmT1UnAtoIl3EcUspCKeVPpt9rgKNAHHAN8IGp2AeA+iRwNDGjYMwdGCTsPFXukq0NM5NSwgn01rLmcDF4unbSQbemsQo2/pOG7B85UljtcuMbllw+NBpdXTP7xz8Dd37vbDmXBKKzlNXOQgiRDPwIDAfypZQhFscqpJQXdVcJIe4B7gGIjo4eu3TpUseIbYfa2loCAtrPDrq7djdba7fiLbzBPHdOmn9c+Lfo6PNF+9v5G1pzrsFgQNNmsZ22tizLNxok5+r0hPg081DsfUR7Rrf3FW1KZ9eyI17f38iRcgNvTKoj9ciznE66EV1Emp0UKnRXZ42hhg/LPsSIEa3QdngPtLfP8nN37gWDwYCHh8cF+7q65zqy6aGvwa/+HGXe8RQ0ehMf4MntUf9DvFf8RWW7S0/+5p3RoJc8sL6e2cme3DTINlFfttYIcK75HF+Uf4FWaBFCIOj95Fq9Xo9Wa30u289u+myvlLLzrKK4YHZcIUQA8CXwGylltbUzk6WUbwJvAowbN05mZGTYTWNXZGZm0lH9/1j2Dyr1lfQL6XfBjWH+3fx9W4+JNsc7Kme2I7q2af5ZUVlBaGho57b1jUrfsEZwprwBanTUcI4j/ke4afJNVl+TntLZteyImtBzPPjpPrwHTSdo38Okep0FO98P3dW59NhSjhUcIykoCU9PT+Di62+5r6P7wLJ8ew8ay2OVlZWEhp5/57rIVps62tPUeqz0OCAo1vZBI5spNBynMLSQ28bfZvU16Iie/M27YmLeDrKrm8jw2AO6XLi2dwto2UPjc7uf42ThSYaEDQHRvhPvLvU19QT6BdpA3YW4lOMQQniiOI2PpZTLTbuLhRAxUspCIUQMUOI8hb2jurma4vpifjv2tywavsjZcqy7+d+fp4Qw3rWWhe/torG+nvjk98irynOExB6RMSgSLw8N3x/RMa5fBmSbwnJdJD0KQJYuizCfMFZcu8JhaVts+rB7ZTyEDGfaubuZGB1AWfCTnK09axvbdmDm4Gj+vvIINboiAg8tg6uec7m0NDlVOQwOG8zn8z+3mc3u/s0/x7q6XWaMQyj/Pe8AR6WU/2dx6FvgDtPvdwDfOFqbrViZsxKAoeFDnazESsxp1BPTaDEY2W0a30gOTiavOs/Z6jok0MeTSf3CWXe0GPpfrqw7XXLE2bJaqW2uZX3+eoZHDHeZXF/doqkG9I1U9Eknv7ye9P4RxATEcK72nLOVdchlg6MA2KEZBYYmlwvLLWsoY2fhTgaGDnS2FKtwGccBpAO/BGYKIfabtquAp4HLhRAngctNn92SnYU7ifWPJa2PffvbbUZrGvUZHDpbRV2zgYkp4SQFJVHeWE51c7WzFXbIjEGR5OnqKYiYrOzI2eBcQRacrDxJTXMNV/e72tlSeoZ3IDx0kLWBSpxKev8I4gLiXLrFkRzhT0qEP5+VJChdrznrnS3pAnYV7kJv1HP9gOudLcUqXMZxSCm3SCmFlHKElHKUaftOSqmTUl4mpRxg+lnubK09pbi+mL4hfd3nLTN3o/JPljSZHbnK/I2JKeGkBKcAcKDkgDPVdUrGIOUNc/1ZTxh/F4T3d7Ki85jfzAeEDHCykl4gBJtzq4gM9GZAVAB9g/tS3VxNVlmWs5V1yMzBUfx4qg5DwiTIdi3HUVKv9MAPCh3kZCXW4TKO4+dASX0J0X72j0SyGbmZkDjRlNhQx8DoACICvJnQZwICQZbOdR8SyRH+JIf7selEKcz9Fwy60tmSWimsKwSgj38fJyvpAVLC61Mw7vgP27LLSDel1p+TPAeAfSX7nCywY2YOjqLZYORoxOWQMB4MLc6W1EpJQwm+Wl/8Pf2dLcUqVMfhIErqSyhrKCMhMMHZUqxn7r8g4480643syatozXzq5+lHjH+MS49zAEwfGMm2nDIaWwxQUwTVhc6WBEBuZS4h3iH4ebrW4KxVlByF4kMUNQh0dc1MNqUZCfcJx1fr69LdVeOSwwj01vJR0zS45lUlZYqLcLr6NJG+kW7TG6E6DgexPn89EslliZc5W4r1JE6EpEkcKKikocVwwcS/pKAkTleddqK4rskYFEVji5Hd2YXw4gjY0bsQTFugN+r54fQPjIgc4WwpPcOURn2TfhhwfplYIQRxAXEuPUDupdUwdWAEG46VII1GqHINJ1feWM7Ws1sZGz3W2VKsRnUcDuJ09WkCPJW+YLfg0BeQuwmAbdk6hFDGN8wkBSWRXZnd7uQwV2FiSjheWg0bs6shMQ1yMp0tidL6UpoMTcxImOFsKT0jNxPC+vFDgSd9I/wvWCY2NiCW/Jp852mzgoxBUZTUNFGx/Hfw+mQwGpwtidPVpzFIA7OTZztbitWojsNBlNSXEOkX6WwZ1iEl/PAX2PseANtyyhgWG0SI3/lZt4PCBtFoaORg2UFnqewSXy8PJqaEs+lECfSbCcWHoKbYqZrM4xsx/jFO1dEjDC2QtwVD3+nsOlVOev8LU8+MjhpNdmW2S8/xmTZA+R/caxwAjZVw9icnKzo/MB7p6ybPB1TH4TCK64uJ8o1ytgzrKDsBNecgJYOGZgP78iuZ3CYXkTmkOLcy1wkCrWf6wEhySusoipik7DB1tTgLt3YczXUw5nayw2cqy8S2uScmxSjXOKcqxxnqrKJPsA+D+wSyrLw/IFwiLLesQVlR021eLFEdh0OoaqriYOlB4gN7n8fHIZgfrikZ7D1dQbPBeFFiw9iAWLQarcsPkGcMUv4Z11ZEg1+40+dz7C7ajUC4Z0SVbwhc+TSr6wcpy8S2uSfiAuIAXHqcA5SXiY1n9BhiRrlEWO7e4r34an0J8Q7purCLoDoOB7D93HYAZibOdLISK8nZCKF9ITSZbTllaDWCCW3WWvDQeJAYmMjpatceIE+J8CchzJdNJ3Rw4/tw2V+cqmfbuW1MjZ/qnhFVxVlg0LMtW8fw2OALui4Bgr2D8dP6uYXjaDFITodMgrN7oKHCaVpajC1szN/InOQ5aIT7PI7dR6kbU1yv9KuPihrlZCVWICWUHoWUDAC25ugYlRCCv/fFac2SgpLYX7IfozQ6VmM3EEK0huU2JaRDsPNafXqjnpL6EgaHDXaahh7TWA1vTKV5w1P8lF/R7mp/QgjiAuM4onOd9C7tMTY5FF9PD1YwFW76CLTOW1tG16BDL/WkRqQ6TUNPUB2HAyiuL8ZX60ugp+2zVNocIeDBfXD5E1Q3tnCooJLJHay/MSZqDLpGnUvH7gNkDIyivtnAnlPlsOc9OPadU3SU1JdgkAb3HN/I2wLSQJbXSPRGyZQOlom9LPEyfir5iaqmKgcLtB5vrQeT+4WzPN8XBs916rot5vGNKD83Gf80oToOB3Cg9IBbTe5BowGfIHbllmOUMKmDRXqGRSix/K7uOCb3D8fLQ0PmiVLY+QbsetMpOs7UnAEg1j/WKfX3itxM8PTj+6pEvLQaxiW3v4KzOWWGq98T0wdFclpXT8HJg7D9NaWl7QTM94Q7RVSB6jjsjsFo4GDpQfcZ+PryLtj6bwC25ejw1moYndi+dvNbkjmc0FXx89IyoW+Ykn6k30wlM2pLg8N1rD61Gq1Gy8Aw98iAegG5GyFpMptyqxmXFIqPZ/vLxMYEKK2pwlrXmKXfEeaw3DP71sCaPyqRhE7g25xv0Wq07jO/y4TqOOzMuTploHBGohtM+GqshsPLlWVBUeZvjEvu+CFhdhyu/pAAZUD0RHEtuuh0Ja12/naHazhVdYqRkSOJ8HXdZVbbpeoslJ2gLm4Kx4pq2h3fMGNuTZnve1clOcKfpHA/vq4yJRV0Upj2iYoTzEiY4XbBEqrjsDP51cpM2lGRbjAwburHJiUDXW0Tx4pqLpq/YYmv1pfkoGTWnF7jOI09xByWu66+P3h4OSUst7Cu0D27qfwj4fZv2eo7HaBTxxHiHUK4TzjrTq9zlLoeM31gJN/meyFDkp3iOIzSSHlDOYmBiQ6vu7eojsPOmMNVk4KSnKzECnIzlQiThDS2m9KodzQwbmZ28mxyKnNocaFMo+3RPyqAuBBf1ufUQuIkqHbsG7E5osot529ovSBlOusLtAT6aEmNC+6wqDlT7tHyoy6djgaU7qqGFgPFERPh1GYw6B1af2VTJXqpd6uJf2ZUx2Fn1uStwVfr6x7dE6Z+bLTebMvREeDd+UMClElfRmmkpMG1xzmEEEwfFMm2HB3NN38OC951aP05lTkYpMH9HIeUkPk0sjiLLdllTEoJx0PTeZBHXEAcDfoGl17oC5QJjJ4egu2kKguW6U46tP6tZ7cC7pleX3UcdkRv1HOw9CCpEamuH1FlaIH48TDsOgC25+hI6xuG1qPzW6SPn3LTF9c5NweUNUwfGEltk569BXUOr3vZiWUATI2b6vC6e0VxFmQ+he7kTs5WNjBlQNcvQK0D5HWuPfbl761lfHIY75YOhkdPQ9QQh9b/Y8GPAIyLHufQem2B6jjsiHlyj3mRG5fGwxOufQ3G/JJzlQ2cKqu7KKVEe0T7KwtTnao6ZW+FvSa9fwSeHoLMEyVK9Nj3f3RY3QW1BQwLH9b6UHUbTH3/m/XDgc7HN8yY56lkV2bbTZatmD4wkkPFTRQ3OP7Frri+mAl9JhDs3Xmr3hVRHYcdMYepusXknpqi1lj27TnK+IY1D4mkoCTCfMJYdWqVXeXZggBvLeOSwth0vBSa6+GY4zTrGnSE+3btiF2O3I0QMZB1Z7X0CfIhJaLrFer6hfQj2DuY70997wCBvWPaQGV84diWr+GdOUoiRwdRWl/qHl3Y7dCl4xBChFmxuckkBcdibqq7/HKxUsIbU2HVw4AyfyPM34tB0V3PdNdqtEyLn+bSqbQtyRgUybGiGqpjJkPlaajIc0i9ugad+z0k9E1wehuy73S25ZSR3j/Cqi5XX60v46LHtU5uc2UG9wkkKtCbg2er4MwOOO2YMG0pJWUNZe53T5iwpsVxDtgD7O1kc91FGZzINznfIBCunxW35AjUlUDcOKSUbMtRBkE1XQyCmunj34eyhjJajK4dWQXKjGGArUZl1rt5sSp7crz8OKUNpe6XakSXAxot+SFpVNS3XLT+RmfE+MdQWFfo8pFVQgimDojkk3OxSA8vpYXlAH4q+YlGQ6PbTfwzY43jOCqlTJFS9u1oA3T2FuqO5FTmkB6XTqCXi+eoskijnqerp7Cq0arxDTPRftFIJLoG178NBkUrb5iri4IhoA+csr/jyDyTCcCCgQvsXpdNiR4Kj5zih2YlAZ81XZdmYgNiadA3uHTOKjNTB0RQ2KChLmqcQ+4HgE0Fm9AIDVckX+GQ+myNNY5jko3K/KyQUlJSX8KA0AHOltI1OUo/NsFxbMtRkq51NX/DEnOLamfhTrvIsyVCCCb3C2dbrg45/n8hdozd6yxtKCXEO8Q9uyU8tGw+Vc2AqACig6xPBpgQmADAziLXvyfMDjHLZzQUHYK6MrvXWVZfRrRfNAFeAXavyx506TiklI0AQoiH29n+VwgxylxG5TyVTZW0GFtcf3xD3wynt7amUd+Wo6NPkA99rRgENTM+ejyBXoFsPbfVPhptTHr/CMpqmzk+6D6Y/IDd63PLvuyGCnhtMi3HvmfXKV23WhsA6XHpBHgGsKtwl50E2o7IQG8G9wnk27ohMPCK1pQ79qS0odQtJ/6Z6U5U1TjgPiDOtN0DZABvCSEesb009+Z4xXHg/DwHl+b6t2D0LzEaJTtydEzuH96teSceGg+Ghg11+QV8zJgfgluzdUoUTaV9B3Hza/LdL6Lq1GYoyeJEhaSxxdhtx+Gp8SQhMMHl53KYmdI/gmXnImi88RMI72fXuqSUHC8/7vovlZ3QHccRDoyRUv5OSvk7FEcSCUwDFtpBm1uzu2g3gOtnQtV6wZB5EDOCEyU16OqaO81P1RFRflEunyXXTGyIL30j/NmWXQZvzYRVv7NbXcfLj3Oy4iTDw4fbrQ67kJsJXgH8UJWIRkBaSliXp7TFPEDuDqQPiKBZb2R3XjnUltq1rp1FO6loqmBY+DC71mNPuuM4EoFmi88tQJKUsgFosqmqS4AzNWeI8Y9p7et1Wfa+D6VK62hrtjK43Z2BcTNRflEU1xe7RWQVKGM4O3J1GBImKl11dsq1daJCSdd9df+r7WLfbuRmQlI6m3MrGZkQQpCPZ7dNxATEcK72nMtHVgGk9Q3D00NQsf0jeL4/lNtvQuvpKiV/3fx+8+1Wh73pjuP4BNghhHhMCPEYsBX4VAjhD7j2WpFOIL86n+SgZGfL6BTP5kpY8RAcXQHA9pwyksP9iAvp/lKawyKGYZRGt8iKCkrXRF2zgbzg8dBcC+f22aWe8sZywM0W6qnMh/IcGhOncaCgqsPV/rpiUOgg6vX1bD/n+BT23cXPS8uYxFBWlJm6lu2YLbe0oRSBIMyn+604V8FqxyGl/DtwN1AJVAH3SSmfkFLWSSlvtZdAd0RKyenq0y6fETes3PSw7H8ZeoORnbnlHa721xUzE2aiFVqO6o7aUKH9mNQvHCFgfcMgQNhtPkdZQxneHt4EeLpR9Iy+GYYvYK/nGAxG2aOuS4BZSbOA8+N9rs7UARGsLQnEEBhrV8dR1lBGmE8YWo3WbnXYG6sdh1BGS4cAwVLKF4ESIcQEuylzYwpbCqltqXUPx+EXAX1GcvhcNTVN+m5N8rLEQ+NBTEAMRXVFNlZpH0L8vBgWG8T603rok2q3+P0DpQeI8LVuxrXLENEfFrzD2pJgfDw1jEnqWWKIQK9AAr0C3SZoYsqASEBwNjRNuR+MRpvXYTAaWJO3hriAOJvbdiTd6ap6DWW+xi9Mn2uAV22u6BIgrykPgNTIVOcK6QyjkdCK/cpSqhpN6/yNiSk9j/6J9oumuN71s+SaSe8XwU/5FTTOfAJm/8Pm9gtrC9lXso9ZibNsbttuGI1QngvA1uwyJvQNx1vb/gqQ1hDrH+s2A+SpccEE+WiVrAINFVBk+4QYOVU51LbUkhaTZnPbjqQ7jiNNSrkYaASQUlYAXnZR5eaU6Evw0ni5diRNxSm0+jrofxkA27J1DO4TSESAd49NxvjHcLLyJM2G5q4LuwCT+0fQYpDsZDjE2n6FxqJ6pfU1KdaN5scWH4KXRlO153NOltSS3oNACUtiAmLI0mW5RdCEh0YwuV8EH5WkIOf9G4JtH9hijjycFj/N5rYdSXccR4sQwgOQAEKISMD2bblLgJKWEhKDEvHQ9PxNze6E92PLlE9g6DU06Q3szivvUTSVJdPip1HTXMOOwh02EmlfxieH4uWhUcJyj31n82y5ZQ1KK86tJv+Z+va3tigZD7o7f6MtGfEZlDWUcbDUPdLZpQ+IIKvah1NJC8Df9nNvSuuVUF93nvwH3XMcLwFfAVFCiCeBLcA/7aLKzSluKXb58Q0Ao4c3ePqyL7+SJr2xx4OgZibEKENe7pAVFZRImtGJIWzNKYNtL8GPz9nUvvkh4VaOI2cjRA5hQ4GGUD9PhsYE9crc6OjRAG4zzjHV5Cj3Zh2Dnz5UAgVsSE5lDuBm90Q7dCeq6mPgEeApoBC4Vkq5zF7C3JWjuqOU6F08R1VTDbwzh9Dy/YCSZkQjYELf3oUHhnqH4qnxdK9xjv4RZJ2rpiF+Cpzbr/Rt24j1+esJ9wkn1CfUZjbtSnO9kka93wy2ZpcxuV+E1RmSO8KcEdhdxjmSTOHoZUe3wLcPwtm9NrMtpeSLk1+QHJSMt0fPu4RdgW4t5CSlPCalfFVK+YqU0j3iLh3MYd1hAOb2netkJZ2QtwXO7EAK5c+/PaeM1PgQgn27P8nLEiEEUX5RFNW6R2QVQHr/cKSE/Z4jAalcGxvQYmhhV9Euru1/LRrhJuul5W8DQxOFkekUVjX2upsKlLU5wnzC3KbFYU6C+UlxAhIBeZttZru6uZq6ljouT7rcZjadhTULObWX3LB1c4RIk44rhBDHhRDZQohHHVVvdymsLUSDxrXX4MheD55+VAUPob5Zz778ym5lw+2M/iH9+fHsjzToG2xiz96MiA8hwFvL6vI48PSz2XwOXaMyCz8u0I3CLuPGwQ3vkNmg5GrqaWh2WwaFDmJD/gb0Rr1N7NmbSf3COdPoQ2P4MDj1o83smgfGXbo3wkqseRUKNG3jgPs5n+TwPmCo/aSdxzQo/ypwpanOXwghHFJ3dymqKyLYI9i1J/fkrIfkqUiNJztPlaM3Sib1IgzXkqv6XkVdS51brEEO4OmhIa1vGJtPVUPSZCixTUPaPDDuVuV2qRwAACAASURBVDPGfUMgdQGbTtURH+pLYpifTczOSppFRVNF65iPq2MOEsn2HwVndkGLbV6C3Gop6S6wJq3636SUfwMiuDDJ4VjAUa/VE4BsKWWulLIZWApc01HhQl02pR/cTvO3v4Wdb0LRYYeIlFJyqOwQoVoX7tMuP6XE6ZvCcLecLMNLq+n1+IaZxKBEALdJeAhKWO6psjrOXf46LFxpE5uHyg4BbuQ4aopg2yu0VBWxLVvH1AG2m7Ronux2rs49uqtign1JifBnfeNgMDRBoW0iwrad2wbg9pP/ALrzWtw2yWEzkGxTNR0TB1iG6hQAF8ygEULcg5LqHd9kH2pytuMp6vASyuLzZeFpHE79k11FFjYXkledx0zfmWRmZtq1rp7iX5tHSthYsnWB1BprWbO/nv7Bgh1bbdOXW6mvBGDL/i2Q03t7tbW1dr+WXjVKVPk7aw8wNb5n4zxtdX5S+AmhHqEUHSqiVLjGm3Zn17JP4VoGH3+Fr/P8qGmKJqy5xGbXvahFGfPasHsDNQE1vdLpKBJ9m3j3bDxjp76PIbfhohQkPdG49txaIrWRHN11lGPimO3EdoK9rmV3HMd/gV1CiK9Q5nJcB3xgc0Xt096rzwUpN6WUbwJvAvj29ZWHb/yGI2cE2/YdZFT9VgaFDOfmadPxEIDRAB6270raXLAZCmFk0EgyMjJsbt92LCQc+Pr7DRTUNvDo1EFkTLfNGgR6o57HPnqMxtBGMqZk9NpeZmam3a+llJJ/H1iHThtBRv2n4BMEM//cLRttdf79878zPXE6l6VfZmO1PafTa/n5exAYS374ZDw0udxzzfReB0uYadA38OTHT+LRx4OMcR3Ub61OB1Ebdo7MT/YRMHQyoxMv7kHoicY/ffon5vWbx4y0GTZS2TX2upbdCcd9ErgTqEBJdHinlPIpmytqnwLAchpnPNBpuzcxuplHrxrC548swGPivfy/rDge/PQnDJnPwBd3Ks7DxphnCrtsV5VBD7Xnu5CydMo16Gn20/bQarSkRqSy8cxGt0inDeZImgi25uiQlf+/vfOOj+sqE/ZzZjTqfdR7L+69x72kmCSkkIQsCS0QdmEpCyTswrewu5SFXSBLhxASICE9JLHjuMu9d8uyiq1i9d7blPP9cWdk2ZYsjTTljn0f/+YnzZ1bXh/due85b62A829P6nxWaaW1vxWjv5c0b7JalBl15mr2ljYzO3nyEXbDCfAJYH7cfLZVbnPaOV2NvfTO5ZM74W8fh4HuSZ2vz9xH12DXLeHfAMfDcU9KKZ+zvVxTh3pkjgHZQoh0IYQv8Cjw3s0OsMeN+xv0/PtHpvJvd+fzwbl6dpR1Q9F7sMX5TQvre+rRCR2h+sklTbmMK0fgf7Lh0i4AClusGIN8J53kdT0b0jbQOdhJx4DrW3A6i6VZRpq6BmiKWgitl6Bz4vb4zoFOzNLsPV3/ak5CfzvdScs5W9PB8hzn+2VmRc+ivqfeayKrooL9yI0NoaymEYo3w5XJVUOw+/y8xuc1BuMJxz3pjH0mg5TSDHwR2AoUAa9LKQtHlQfB7qrd12x7ankGn12WzucvLaYs61Nw7Hk4/5ZT5Txef5z4oHj0QqWlRi7tBKGHxLlIKSlssbAka/JJXtdjn1V5UyKgPWv+kMUWrFc+cZ/P5nKldInXOEGbikDvy17rNKTEJYojITgBi7R4VdDE4kwjf6tPQOoMkw7LtTvG08LSnCCZ5xnPiiNfCHH2Jq9zKBFXLkVK+YGUMkdKmWkzm41KiG/IUFTLcJ69K4/ZKeE8emk9poT58N6XoaPGaTJe6rjE3Ni5Tjuf0yndBskLwT+M4oYuOgbkUIkFZ2LvpexND4nkyEBSIgPZ1GAE/3ComPiD4nSjkpF/R9IdzhLPtcx5Ap6pYGeFmfBAA9MTw5x+iYSgBMB7So+AojjaTQa6omZNWnEcqDlAYnAi06NUXDHbAcajOPKAj9zktRFY4ioBJ4Kv3pf63nqs8toajD56HT9+cAat/ZJfR3wT9AandX5r72+nY6CDnAiV9hjvrIX6c5CzHlDCcAGWZTtfcdiTHwtbRl0UqpKlWVEcLm/DOuMRCJ14pHlzXzNzY+di0DnPT+BqpCGQvaVN3JEdjd7JK1CA1DCldtu+GudlYruaRelKs68LfrOg7gz0tU/4XI29jWSEZXhPFYExGE8eR+U4XtXuEHa8+Op8MVvNQ0lYw8mODeGR+Sn84pSZyieOQv5Gp1yzskvpI6zadrFltpau2Yri2FfaTHyQIGECbWLHIiogijkxc7ymjaydpVlGugbMnJ72LVj1rQmfp7mv2XuK2F38AF7cSGlZKU1dAyx3wUQCFLPdjOgZQ6sxbyAs0MDUhFA29+ZCwpxrAkscpaG3gdigWCdK51luDfV3HfaZXmVn5Yiff3VdNr4+On686wpIqZTgmGS3r+JWpT2maqviZq2D+34FMVMYMFs4Ut7CVKPrfDFTjFO8pkquHXv2/MGyZuV+6HfcuW+2mqnrqfOeiKrSrVB3hoJq5f53hX/DTkpIilf5vUDxfb1Wn0Tfk9sgemLWhLb+Nlr7W4cKPt4KONI69m9CiGeEEHfZenGoFn+DP/56f7aUbxnx85gQfz67LJ3N5+qoPf4+/PUBKJxcCOb7l94n0j9SvbWJQuNh9j+AEJyobKPfZGVqlOsUR3RgNL3mXnpMPS67hrMxBvuRHx/KgbIW+PVC2PKMw+f4sOJDBiwD6vZ12ZESynZB+nIKytrJiwshNtTfZZeLD4qnoacBiwtC4V3F4gwjgxYrJyrbJlxifX+NUjgzPSzdmaJ5FEdWHL8FeoEHge1CiHeEECGuEWty+AgfciNzqeqsGnWfJ5ek4eej45dVKRA7DXb/QMlzmCCVnZWsTlmtTrt2/Xk48RIMKg/x/aXN+OgEeZEuVBy2sMPqLlVZMcdkWZaRE5VtWKLylEq5DuailLWV4SN8WJvqBe1iW8qgo4qB1JUcq2hlhQtXGwBxQXGYpXko38kbmJ8eiV4n6DjyZ/hRMvS0OHwO+3fA27v+DccRxZEC7AGellLOAt4EvucSqZxAQlACNd2jR0wZg/14aG4Sb56qo2PRN5XY/QmG5/aZ+2gbaBuKHFEdZ1+Fzf8y9BDcX9bM7JRwAnyc7wS1MyN6BgCbLjun9pO7WJIVxaDFSnnIXOi4Am0VDh3f3NeMMcDoHU7Qsp0AHPeZjckiXWqmApgaNRWAzZed22nRlQT7+TAzKYx9LaFg7p9QmfXKrkrig+K9vgfHcBy5u3OA/wIuCiFOAeuBB4QQa9RoukoITqC+t/6my+LPLEvHZLHyx6ZciM5TusBNINu5vkeZQcUFxU1YXpdSuh3SloJfMG09g5yr6WBZlmv/ZKmhqeRH5lPU4l1tW+anKTPMvYM2e7aDD4rmvmbvSfIKTYAZj7Kt1p8Ag555aa6teDDVOJWUkJQhf6C3sDjTyDsNMUjfoAmF5VZ1Vg0V/7xVcKh1rJTyXillFrAa+CsQCDwOfOAK4SZDSmgKZquZs82jV7bMiA5mRU40rx2vxrLoi0r3t07H8zrskSKqdH61VULTxaFoqgOXmpHSNWG415MUkkRTnzoK/I2XYD8fZiSFsak2FIJiHEoE7DX1cqD2APHBKrwPRmLKvfDA79hb2sziTCN+Pq5PXE0LS6Ois8Ll13EmSzKjGLDqaTXOc3gi0TXYRWlbKakhKg2amSCOKI5tQogKIcQW4N+BfwH+JqX8tJRyvmvEmzjrU9ejE7ohx9RoPDo/hYbOAQr8VsGXz0CY4/H7e6v3YvQ3MjN65kTFdR1l25Wf2VfzN0L8leW3q4kOiPaqJEA7izOMnK3ppH/1fyjJcePkZKNSQGFxwmJXieY8upugr42qll7Km3tcFoZ7PWmhaVR1Vt2QY6Vm5qZG4KvXcUo/HZpLoHP8bXAP1Byg39LP6pTVLpTQ/ThS5HA2kAl8HdgL/BJFeaiSYN9gkoKTqOiouOl+a/JjiAr2428n6pWEQIvJ4USfup46ciNzMehV6BhvKoGIdDBmIaVkX2kzSzKN+Ohdb4NPDkmm29TtdWG5izKMmK2SIyFrIX382d92k+WyhGWuEs15HHwO/jeP/ReVv42r/Rt20sLS6Lf0j/m9VBP+Bj2zU8J5o3sarP4OONCkzX5P2H1+twqOFjm0SCkLpZRvSyk32WpIqZa0sLRRcznsGPQ6HpqbxO7iRhraOuH/5igRVg5Q31OvXv/G3T+Gp/eDEFS09FLT3seybPc8JOyRRVsrtrrles5iXloEBr3gUFkzVB4cd3UBu1nOK5L/SndA8kJ2X+oiKSKA9Kggt1x2dvRsAI7VH3PL9ZzF4kwj2xpCaZ/3zxA8/u9PQ28DgT6BBBuCXSid+/GC0I+JkxqaSmVn5ZjL4kfnJ2OxSt460wgpC+HMq0Ohq2MxaBmkpb9FvYoDwE+5afeXKg82V9SnGom4oDiiAqK8bsUR6OvDzKRwDl1ugTc/DQf+b1zHNfY2Eu4Xrs6V53Daq6CpCHPmOg6WNbMiJ9pp3f7GIiM8gwCfAK/0c0gJJ0oqFaU7Tup66ogLinPb+LqLW1pxZIRl0G/p53zzzVvHpkUFMSclnHdP1cK8T8NAx7h7MnxQrsQFJIckj7GnB9jxPeXBZ4sU21vaTFJEAKlG5/SSHg/RAdFe02t6OIszjZyv7cSUsnRc+RxmaWZ75XZyI3LdJOEkKFX8XueDFtIzaHGbmQpAJ3SkhqZ6neKYlRyOv0HH4PG/wssP4t83dgZ892A3R+qOkBWe5QYJnUDDhXHveksrjnmx8wC41D52D9P7ZydS3NBFkWEqROfD8RfGdY2ytjJ0QsddaXdNSlanIyUUvqM0oBECk8XK4UvO7SU9HmICY7zWQW6xSsoCZ0NPo+IUvQlNpiY6BjrYmOmc2mcupXQ7hKeyrT4EH51gSaZ7y6OkhaZ5lY8DwNdHx/y0SN5pVzplhrffWH37eso7yuk2dXN3+t2uFm/ydDXAb8Yf1HFLK47E4EQEgtqesUs53zM9Hr1O8PcztlVH7clxNamv66kjJSQFvU5lPThaLkFbOWSvA+BEZRtdA2ZW5Li3A1luZC7FbcVc7rjs1utOljm2SJrdA7YVxBjx+x0Wpa6VV/Tg2PB9uPcX7C1rZk5KBCH+7jWtZYZnUt1dPeQ49hYWZxrZ1hyJNSBqXIrDXpdLtWWIhlPmWEHSW1pxGPQGogOjx9UDwBjsx/LsKN4/XYt1+sPw5PtKKZIxqO+pV2f+RomtTpctDLeguAkfnWBplntnlx/J+AgAZxrPuPW6k8XfoGdWSjhbqv2VEutVh266f6elE/CSDm/GTJqiF3G+ppMVue6Xd1H8IgAutIzfNKIGlCKYgrrIeUS0nRvTfGlXjPb+NKqmdBsEj99Pe0srDlBKjxS3Fo+r//X9sxOp7ejnaL0V0peD7ubDY7KaqOisUGfCV/EWRfFFKIlHe0qamJvq/tllQrBShsXbqqKC8qAorOuk65G34P7f3nTfOpMS2x8dqHLFceY1KHyH/WWK32m5myLshpMRngHgdX6O6YlhBPv5cIxp+A22QOvNV9Fl7WUE+AQQ7hfuJgkniMUMl3YPWSfGwy2vONakrKG4rZiqrtELHtpZNyUWf4OOD87VKbkcH35LGdBROFR7iM7BziFfimqQEtJXwPzPANDQ2U9RXScrc91rpgKlqVaEX4R3+jkyjVglHO6IAB/fm+57tOcoc2LmEGRwT1jrhNn7Yzj1V/aWNGMM8mVqgnP7zY+HUN9QjP5GyjvK3X7tyeCj17EgPZI/tc/k6PxfQGTGTfc/0XCCaVHT1B9RVX1UCQjSFMdVZsXMAhiXMy7Q14cVOdFsK2zA6hMIZ1+DEy+Our89zHRJgqoaIIIQsPIZxVcD7ClWZpcrPWCWAIgPjh9XgILamJUcjp+PjqNlDbDt26NG2vWaeum0dKq+VWxAbx20lGHNWsfekiaWZTu/3/x4SQtL87qaVQBLMo2cadFTrU9SvmejYLKYuNJ1hdkxs90o3QRJmA2Pv0VzzNJxH3LLKw57R77xLos3TI2jvrOfM3U9MP1hxeTT1zbivnXddfjr/Yn0j3SStE6i9jSY+ofeFpQ0EhfqT16cZ6rgr0xayanGU14Xlutv0DMnJYID5R1w4b1RqyfbO02q3b8R2XoCgLLQxbT0DLq8jPrNmB0zm6LWIjoHOz0mw0RYbItA66ouVPq1jGICr+6uxiIt6u0IOhxDAGSv5avvjn9yd8srjnD/cML8wsbMILezJi8WH51ga2EDzHwULANQ+PcR963tqVVfco95AF68B7b+q/LWYmVfqXuTvK5nTuwcJNLrTBOgPCiK6jsZSLblc4zQKdKeMe4VisOYxfYGxZx2hwf8G3amRSmBJzfrmaNG8uNCCQ80YGq7Akd+C00jr5rsFg7VdgS101UPu75Pb1MlRy63jvuwW15xAKSHpnO47vC49g0LNLA408jWwnpk3EyIyhlxpjlgGeBkw0n1Jf5V7IPBbsjZAMDJqna6+s0eiZ6xExOo+FYa+7zTzyElXPSfBf3t0HBjGOb+mv0IBJnhmR6QcJxYrfgNtEH2evaUNDElPpToEM/1h7BXix3vhE4t6HSChemRvN+Tr2wYpVru8YbjgBcojtJtsPfHnCmtZNAy/sKTt4XimB83nytdV8bdxnTD1DjKm3sobeqB2Z9QIpOum2mWd5TT0t/CXekqS/wr3gKGQCUqDCgobkSvEyx1U5mRkRhSHF7oIJ+ZFE6AQc+OPns+x40Pin3V+8jxzyE2SMVhlzodx+f/nPal3+ZEZRur89wfKDGc5NBkBMLrVhygFME80x+NOSQRyveMuE9RaxH5kfmE+bm+CvWkKN0GoYm8Xx9OkO/4c9FuC8WRHZENKD6J8bB+SixCwIfn62HpP8N9v7ohNNd+LlX1EZZSURyZqxW7JUr+xtyUCMICPFc/KcgQRGJwIvuqHe+e5ml8fXTMS4tge7UOkuaD5ca+0019TUT5qLywoc0Wv+dSOxarZE2+ZxWHn96P+KB4Tjed9qgcE2GRLZ+jOnz+qObLio4KciJy3C+cI1hMcHkPMmstBcVNDvXouS0Uh70A4Xh7HceE+jMnJYKthbb9pbwhZtueja6q4ob155RGVLnKKqixs58LdZ5J8rqejRkbOd5wnD5zn6dFcZhFGUYu1nfR8uhmuONr13xmsppo7W8lVO/+sNZxIyX8bjnJVe+w62IjxiBfZiZ5Prdgftx8zjWdG1eOlZrIjQ0h2AAHLVPAPwy6r32u9Jh6aOprIi0szTMCjpfKgzDQSU30Mmo7+h1ahd4eiiNQebg7Uh9nw9RYCms7udLaC4d+Bb+YC91XTS1Xuq7gq/PF6O/eTOybEjsNntoFefcAStIfeC4MdzhJIUqDrObeZg9L4jjKDBOOlNuch8NmmNVd1QCE6VVskmi8APVnGdQHUlDcxKq8GI+F4Q4nOyKbLlOX10VW6XSC3Eg9v26ZqzR/C0245nN7EIjqI6raKyEggi29UwAcyvO6LRRHbFAsGWEZbCnfMu5jNkxVlM3WwnrF9COtUPQeAFJKtpRvId+Yr66IKp0OEudCgNI7uqCkiegQP6bEe342HBOg3JTe1koWYEZSGIG+eo6XVCsTiINXy6xvurwJgEx/FTvGi5X7/rjPHDr6TKzxsH/DzpAlwMtqVgHkReqp7hhQJpbX8f6l99EJHVOMUzwgmQPMeQK+Xsb2si6mxIcSG+o/7kNvC8WhEzrmx83ncsflcS+LU41B5MaGsOtiI8TkK9FVtrDczsFOWvtbWZc6/kxLl9NRDe9/BVqV2Y7ZYmVfSZNHw3CHYy/FUd1d7WFJHMegVyqj7q3sBaG7JpKmtK2UzLBM4gwqMlleT/EWSJzLwfYwDHrhln7z48GuOMZT1UFt5EcqjuSG3b9Rmr9ZLUOflbWXMT1q+lC5HVViWzV3DEpOVLaxKs8xq8RtoThAcWJ3m7pp6W8Z9zGr8mI4VtFK14AZptwPlQegu4m6HsUxrqob48J7cOJPysoIOH2lnc5+syrMVKD0RokJiPG6boB2FmUYKWvspi9xCVQeUhyLKMl/qo6m6mqAmuOQexdnGs0sTDe6vV7ZaGSHZ2PQGbzynkgIFkQG+VLUKqH1EtRdLeJZ11NHQpCKng0jcegX8JtlHCy6gsUqWeVgOaLbRnEMZZA74OdYlRuNySI5UNYM+RuVh3LJlqFqu6q6OYreU3wcRsVkUlDchE7AHVnqUBx6nZ6liUspbC70tCgTYlGGUh3ggt8sMPUMtZNt6mtSd6tYaYUlX6Imfh21PZ6PphpOoCGQpYlLKW0r9bQoDqMTgkUZkbzeZMvTsK1CrdKqVMxWY+HT4RRvAQE7yroICzAwK9mxYInbRnHYE3EKW8b/4JqTGkGIvw+7LzZB3Ax45GWY+tGhEELV3BxdDVB1GPLvHdq0u7iROSkRhAWqY3YJiq+ptb8Vk9XkaVEcZlpiGEG+erb12rq5VeyjrruOhp4GdSd5hcbD+v9ia4PivPd0/sb1ZIRlUNVVhWWYqcdbWJRh5FxnIKaIrKF+LRdbL2KymtTZasFObytcOYI1+04KihtZkRONj94xVXDbKI7E4EQSgxM52XBy3McY9DqWZ0ezu7gRCcqqwy+EvVf2MidmjnpqVF18H5AwRVEcNe19FNZ2snaKukwoMYExSCQtfeM3F6oFg17HvLRIdl+xwrKvQcJsdlbtRCLV2+FtsFd5oFlM7LrYSEKQINWoruq9aaFpmK3mcTVbUxv2aLvKkLlD5stdVbsAWJ2y2pOi3ZzS7SCtFIctoaVnkHUTeE7cNopDCEF2RLbDztmVudE0dg1woa4TBnuQe/+Xuu5qdUVMWMyQuhSi8wDYWaT0vpjIDeFKMsMUM9qx+mMelmRiLMyIpKShm+ZFz0Lmamp7agnwCVBv17/yPfDSR+gt3cOR8hZmxvh4WqIbsOc6nG0au9um2siOCcYY5Mt2FsDcJ2Gwh7qeOmIDY4eqJaiSki0QHMu7jXH46MSE8rxuG8UBSicuRxsK2WObC4qbQO9L56Hn6LUMqCvxb9HT8KkPhso8b7/QQEZUEJnRwR4W7Fpmx8wmLiiOgisFnhZlQthnmEcvt0BTCc2dV4gOUEfU2ogUfwB+oewdyMZkkcyKVll7Y2CacRp+ej+HLAFqQQjBogwjf25IR274AQSEq7cj6HDyNsLyb7C9qJFFGUZCJxAscVspjrigODoGOug13Rh7PRrRIX7MSApTwnL1BurSlZr1CYEqURx9bdeUdu7sN3H4covqzFSgfNHSQtPGncGvNqYnKvkcZ0sr4FcLqG0qVK9j3GqF4g8hay07StoJCzCQFa6+r7tBbyArPIua7hpPizIhFmVEUtfRT1VTBzRe5ErXFfUrjukPcTn9MS419bB2gsES6ruTXEhepGLKcTT8b2VuDKeq2mjrGWRbmOLXyOzrdrp8E+Ktp5Qy6jb2ljRhskjVmansxATGeGWxQ1D8HHNTI9hdZaYufgpnBprIjcz1tFgjU3sSehqx5tzF7ouNrMyNRq+CbPGRmIglQC3Y+3P0bfkODX9cRV1P3VCVBFVSdRg6qtlZpHwHJzrBVIXiEEL8RAhxUQhxVgjxjhAifNhn3xJClAkhioUQGyZznaUJS/HX+zsUWQVKWK5Vwt7SJoqFmZxBExlXVLC07u+AywVKBy8b2y80EBnky5yUCM/JdRNiAmNo7m3GbDV7WpQJsSjDSHFDFyejlOiqe1JUlAQ6nNLtIPScC1xAS8+g6qKphhMXFEd9T73X1awCyIwOJirYl/2DOZTplByqRfGLPCzVKEgJ73we3v8K24sayI8PJSkicEKnUoXiALYD06SUM4AS4FsAQogpwKPAVOBO4NdCiAkbaoUQpISm0NDj2OxmZlI4xiBfdl9spK6/iUS/SBhQQX2dok1gNSnJiYDJYmX3xUZW58WodnY5LWoaZmn2yqQvuOrnOC8UE1Vip0pXT8u/AZ/bzfbLA+h1wqPd/sYiMzyTblO3VwZNCCFYmGHktcYUKn0UX0FG+M17kXuMpovQVkFP2jqOV7SybhI5PapQHFLKbVJK+xT0MGBf690HvCqlHJBSlgNlwILJXCsuKM5hG7tOJ1ieE83e0mbqu+uJy9kI9/5iMmI4h/NvQngqJM0D4Fh5K539Ztbmq9NMBbAqeRWR/pEcrD3oaVEmxIykMAIMek4N+KKXkogalZYF1/tA/Ex2XmxkbmoE4YG+npZoVO7JUEyt4222pjYWZxgp7fKhPDSWQCnUVfh0OEXvA4I9ugVY5cTNVADqi8+DTwOv2X5PRFEkdqpt225ACPE54HMAsbGxFBQUjHhya7uVku4Svv3utzEIZYYglSyNkX/aVs/Ngxa6A3oxmbrobeiloKAAYTUhdTdGJHR3d496fWdhGGxnyaUCqlIepHyP0kzm5aIBfHRAfREFzRfHPIc75ByJGGLYUb4DQ6uBQTmInxi9E93AwAAF7xXc9Hz2v9dY2276+Q1vRz8+Ks5EYf9OIvRBHLJMx1xQ4LGxHIn42m0E9NVwLP4TFNUN8EiuLwUqk/F6knyTeLvobdpr2hkYGGDv+3s9LdJNGS5jx4DEEGHiQx9J8uAg+3Ztw6r3XHfF4Qz/m889/jesobm8cKSBcD9Bc+kpCsomZplwm+IQQuwARgpF+jcp5bu2ff4NMAMv2w8bYf8Rv9FSyt8DvweYN2+eXLly5YhyRDVHcWHnBd5tf9ch+QH8osEg/HlkySNMP/IC1J2Fp3besF9BQQGjXd9pmAch5WVSY6eQGpGGlJLvHN3N8pxI7lw7f1yncIucI9Be1s53DnyHt9pubMk7IuMPgnMPtijnxan3sWyFknTpqbEckd/9P9D7sissE7jA5zYuJjM6WF0yXkfdxTp+Wo+pqwAAH0lJREFUeOSHvNH6hrJhfM06PcswGf3joB34aObdLF+5RlnxqYChv3lXPRSUY17zXYq2w32zk1m9avqEz+u2/52Ucu3NPhdCPAlsBNbIq16yamB4U+8kYFIpptOiprHz4Z30mnsxW80I+z9bLP7Qz2HbhU1/PfK7Qxj0BqZHT4ewZDj+AnTUQJgHEsB8fCHvasZycUMXV1r7+MKKLPfL4iD3Z93PquRVmKwm/PX+DFoHh8bYjv39gQMHWLp06Zi5EiN9Pto5Rzvm+s9Hu8apqjY+/ocjrJ02Bfb/HDJW3vQ4t9JWoRTcW/efbC1sICsmWHX5PCPxWN5jbMzYiMlqGvqbq5nrZfzW2+c4WdnOV5+4dyifSlWExMG/XORweSc9g6Wsm6Q5WxVqUQhxJ/AMsEJKOXx++R7wihDip0ACkA0cnez1fHQ+hPo63qNiVU4Sv9xdRkevibC8jbDze0qS1YKnJiuSY7RXwam/wvzPQrDi4NpxQXH4TzQu292MtxdzkD6IcH/Pd6sbzrwUP/x9/DlW1cG6s/8BA12gv8PTYikUKf1BOtLu5OjmMr6wQsV9Qq4jxDdE+akPUU85n1G4XsblmWlsPXue2vP7SOwrdv8zYTyExPHh5SYCffVDYcQTRRXOceCXQAiwXQhxWgjxWwApZSHwOnAB+BD4Jymlx6qhrbCF5e4va4boHDBmw8XN7hfk3Buw579hWCLj9qJGZiaHE+NAMxaNieHro2NeaiR7K/uVUOgKFfVSL3oP4qazrS4Ai1UONSTTcC2LbdF27afehQ+fhQGV5HmB0rn0rw8ia06x40Ijy7Oj8TdMroqAKhSHlDJLSpkspZxlez097LPvSykzpZS5Usrxt/BzATOTwgn192FPiS0EM+8e5aHR1+5eQc69BUkLICINgIbOfs5caZ9UeJ2GYyzOVPqQ9yUugZoT6NXQS91qgYh0mPlxthbWkxgewLREz3d/vB1IjwoiJsSP3YN5YDUriXZq4eJmKNtBWcsA9Z39TqkqoQrF4S346HXckRPNnpImJVlpxiOw4QdKVzh3UXcWGgth+sNDm+xZoOumaLNLd2Ff6p81zACrmdDOIg9LBOj08MDv6JnzOfaWNrNuSqx662jdYtjrVr1an6BEWpbv8bRIVyl6HyLS2VQfgU4oCc2TRVMcDrIiJ5qGzgEu1ndB7BRY+Hnwd+Os7vTLoPeF6Q8Nbdp2oZ7kyAByYtXvBL1VmG7rz/FhZyoYggjoU0HJjPYrAOwpaWLQbOXOadpEwp0szjRS3Q39sXNUY770MXUrpfXzN7LDltNjDJ58qLCmOBzEnoG7p6RJ2dDXBqdfAVO/ewQwD8DUByBQccx19JrYX9rM3dPitdmlGzHodSxIj2RPRS88U0Ft4l2eFainGZ6bCQd/wdbCeiKDfJmfpm4H862GvapAaeAsJbrNXc+Em2BsOQ5WE01J65UePU5KDtYUh4PEhvqTFxfCnmKb4qg+AX//gvuWph/5OXz0t0NvtxbWY7ZK7pmh8oqctyCLM41cbuqhodfqaVGg8B2QFgZSV7KrqJG1+eotO3OrkmYMJDbUjxfFffCNS2DwfKCKRe8H2et5r0VJGVjvpGAJTXFMgBW50RyvbKV7wAzpd4BvCFzc5PoLd9pSWIatLDadqyM5MoDpieMLb9VwHksylXpVZ86dZfbJZ6Fsh+eEOfcmROeztyOGrgEzd0/XJhLuRgjB4gwjeyv6kO70e96E5ujF8PgbbD5Xz9SEUNKjnNMBUh3/Oy9jZU4MJovkYFkz+PhBznolcsHiwoqvHTXws6lw7I9Dm9p6BjlQ1sw90xM0M5UHyI8PVaLsagQhXaVKpWJP0H4FrhyG6Q/ywbk6wgIMLM1SaZ+QW5xFGUaauwdo3vULeO0TnhWmrQK9uY+a9j5OVrU7dTKhKY4JMDc1giBf/VU/x9QHoLcFygtcd9Ezr4C0QuaqoU1bC+uxWCUbNTOVR9DrlEiavRVddIbmKk5IT1D4NgADeR9l+4UGNkyNxaDXvtqewB5tV1PfoOTU9LZ6TphNX2X2qWfYcq4OgHs0xeFZfH10LMmKoqDYFpabvQ78wqDqiGsuaDHD8RchfQVEXi3ZvPlcHWnGQKYmaLH6nmJxppErrX3UBE1TQqX72twvxLxPw2Ovsbc5hG7NTOVRUiIDiQ/zZ0efrcGXp6Kreprh8h5ajPPZdLaOaYmhpDnJTAWa4pgwK3KiqWnv41JTj2Ku+ueTsPrfXHOxki3QWa2E/tpo6R7g4KUW7pmhRVN5EvsM87iYAkio9EC5eL8QyL2TTWdrNTOVh7Hnc7xRG400BEG5hxTHhXdBWigOXcrpK+3cMz3BqafXFMcEuSEsN8j2ZXVFF7MTLylFFXPuHNq0tbABi1U6/YbQcIycmBCMQb7s6M2G3LuVh7g7OfESHPoVvQMmtl9o4K5pcZqZysMszjTS0GulJ3ae51Yc59+GqBx2diqtjZxppgJNcUyY5MhAMqODrioOgA++obRmdDYPPg8fe0nJDLax6WwtGdFB5Me7+UGlcQ06nWBRppFzrQL56CuQvtx9F5cSDvwcSj5kx8Umegct3DfLA5WaNa5hmW3Fdyr4Doif6dqgmZHoaoDKAzD1AY42WJiRFEaKcWItYkdDUxyTYEVODIcvt9A3aK+7KKDw70q2pjMJCIfEuUNvGzv7OXy5hY3TNTOVGlieHUX7gKSkoRu6m9znEK06DK2XYeZjvHuqhrhQfxama0l/niYhPICM6CCe710BD/ze/b05gmPgCweoyXyE8g6r01cboCmOSbEiN5pBs5XD5S3KhtmPg2WA2IYC51yguxH+sAaqj1+z+d3TtVgl3Ddbm12qgeU2s+XR80XwP9lKWRh3cPqv4BtMW+pd7Clp4t5ZCei0pD9VcEdWFEfKWxgwmd0fWSUExE7l/XLFbO6KYAlNcUyChemR+PnormaRx8+EhDkk1G51jq/j0K+g9iQERFyz+e1TNcxKDveKBj23A/FhASQGC7ZWSIjJh9Jtrr/oQDecfwem3s/m4k7MVsl9szR/l1pYlh1Nv8lKx9+egudv2sPOudSfh7c/D+1X+OBcHRlhOpIjnWumAk1xTAp/g9IQZe9wP8fcTxLUWwVXJtlvqq9dSfabch8YrzbjuVDbSVFdJw/M0VYbamJ6lJ6j5a2YMtZA5SGluZMr6WmC5Pkw+xO8d7qWrJhgpsRrYdlqYVFGJHqd4JwlBVovKbWr3MHpV+D8W1R2wdnqDubHucZMpimOSbIiJ5rLzT1UtdiaKk17kMqUhyAsaXInPvI7GOyCZV+7ZvM7p6ox6AUbZ2izSzUxLcqHQYuVcwELwGqCyy6uXRaZDk+8y5XgGRytaOX+WVr1ADUR4m9gdnI4r3dOVTaUbHX9RS0mOPc65GzgraJedAIWxU+uYdNoaIpjklwNy7U1d/ILpjzjE5PrQ97TDAd/AXkbIX7G0GaTxco7p2pZmRtDZJDvZMTWcDI5ETr8DTo2tacqtctKXfig6GmGrnoA3jhRjRDwwJxJTlQ0nM6y7Ci21QdhicyCYjf0oCvbCT1NWGc+xlsna1iWHU2Ev2se8ZrimCTpUUEkRwZcG5YLcGk3nPzzxE4aEAF3/QjW/Ps1m3cWNdLcPcCj85MnKK2Gq/DVKwXudpe2wUN/hOXfdN3FDjwHP5+BpaeNN49fYVlWFAnhAa67nsaEuCM7CimhwrgcKva73nx55hUINHLMZy417X086EJztqY4JokQglW5Mewva6Z3cFi89qm/wIffmlgJCp0eZv+D0td8GK8eqyI21G9olaOhLpbnRFPe3EOV8Q4Id5FyN/Up91bunRysNVPb0c/H5mkTCTUyMymcsAADb1lXwoN/AJ3BtReMyoEFn+etM40E+epZ78KOoJricAJ3To2j32S9Gl0FsOyrMNitzA7Hi5Twt4/DqRvDOWva+9hT0sTH5iXjo2UGq5Ihs2Vpk1Lm/MSLzr/I+beUycj8p3j9eDVhAQbWOaGHtIbz8dHrWJkbzWsVgVjy73d9f47V36Zvydf54Fw9d02PJ8DXNf4N0BSHU1iQHklEoIEt5+uvboybrvQkP/RraKsc34lO/QWKNyvO1et45YhyDm12qV7sZsuCi41KY6XdPwSrE5s8SQlHfw/R+XTELGRrYT33z0rA3+C6B4TG5FidF0NLzyBFRefg4C/Bahn7IEexWuHSLrBa+eBcHd0DZh50sc9LUxxOwEevY8PUOHZdbGTAPOzGWPPvIHSw5Zmx8zoaL8KWZyHtDpj9xDUf9ZssvHKkirX5sS6JydZwDkII1uTFsq+smf7sjdBdD9XHnHeBlktQfw4WfJb3ztYyaLbysDaRUDUrcqLR6wQVpwtg279NPkx/JC7tgr98FIo388rRKjKigliU4doKApricBJ3Touje8DM3pLmqxvDEmH9f0LWmpsf3NsKr38CfAPhgT+A7to/y3una2nrNfGppWnOF1zDqWyYGseg2cpeMRf0vkO9MpxCVBZ8+SxyxqO8euwKU+JDmaZ1flQ14YG+zE2N4E9NueDj79z7wc7xP0JQNMWhSzhR2cZjC1JcHpqtKQ4nsTQrisggX/5+uubaDxY8pbyEULJ9R6J4i2LOevhFCL22PICUkhcOlJMXF8LiDKNrhNdwGvPTIogINLC5pAdy74Jzb4B5cPInthfKC0/mZP0ghbWdPLYwZfLn1XA5a/JiOFFvpi9tDRT+3bnmqrYKKPkQZn+CV47X4avX8eBc14dma4rDSRj0Ou6dmcD2Cw30mEYwS5XvhZ9OgX0/VcLyLGZouKB8Nvtx+NJxSFt2w2GHL7dysb6LTy5J0xK8vAAfvY61+bHsutiIacbHIThW6aUyWTZ/DV59HKTkxYOVhPj78IBWq8wrWJMfA8DR4FXQ06iE5jqLw78Boadv9qd5+1QNd02Pc0uOl6Y4nMgDcxIZNFs5Vj9CGeW46Ypi2Pk9+FEKfD8Ofr/iaimC8JFnj3/cX054oIH7tYeE17Bhahxd/WYOijnwhYPXdG2cEJ21SimJkDgaugbYcq6Oj81LJsjPzVVXNSZEZnQw6VFBvNSYo+RoNRY558RWi9LnfvrDbCqHrn4zH1/gnlWoduc5kemJYWTFBHOwtvfGDwMi4LFX4MoxKNsOlkGlVHro6AqhsLaDHUUNfHVtjhY540Usy44iyFfPB+fqWZEbA/2dSr/4gPCJnXDv/wASlnyJvxyqxCIlTyxOdarMGq5DCME90+P5dUEZLc+cwRjuJL+UTg9PH0AOdPKXFy6QGR3EAjeV1ddWHE5ECMEDcxIpabNS0dwz8k7J82HVv8La70L+R0A/elLQL3eVEeLnwyc1p7hX4W/Qs2FaHB+cr6O/qw1+Pl0pITMRWi7ByZdg7ifpCUziL4crWT8lllSj8/pHa7iee2bEY5XwYXG7ssE8MLkTmvqVZFC9D4frJGerO/jMsgy3mbM1xeFkHpqThF7AS4cqJnWe4voutpyv51NL0wgLcHHGqYbTeWB2El39ZnZV9CsmymPPw+Aok4mbsf+nSnTW8m/yt6NVdPSZeHpF5tjHaaiKvLgQMqKD2HSmDt55Gl5+aHInPPY8PDcLupv4w77LGIN83VoxW1McTiYm1J8F8XreOF5NV/+NiXzj5SdbLxLs58Onl6U7UToNd7E400hMiB/vnKqBJV+C/vYRKwKMyfrvw6OvMBgQzR/3l7MwPZLZKRFjH6ehKoQQbJwez5HyFrpD0pRgmeayiZ1soEuZUMROobTHn10XG3licZpbzdma4nAB61MNdA+YeeP4xKJp9pY0saOokS+uziI8UKuC643odYL7ZiVQUNxIW+RsSF6ofNkHR/B/jYR5UCmTHRAOmat4/fgV6jr6+cJKbbXhrdwzIwGrhM36taDzUVYNE+Hwb6G3BVZ9m+f3leNv0PEJN/u8NMXhAtLD9MxLjeCFA+WYLI6VnDBbrPznpgukGgO1hD8v56G5yZgsktdPVMPa70FXHZSMs7z23h/D75ZDfyd9gxb+b2cp89MitAKXXkxObDD58aG8dLYPOf1hxXfV0zz2gcPpqIH9P4O8jTSGTeWdUzU8PDfZ7W0WNMXhIv5pVRbVbX28ecKxVcdLhyopbezmX+/Ox89Hi6TyZnLjQliYHslfDldiSV4E/3gEpj049oGXdimRVAmzwT+UPx+qoLFrgG9syNNyebwYIQQfX5DMhbpOLmZ9RnFuH/2DYyc5+ypIC2z4Pr8puITZauUzHjBna4rDRazMjWZWcjjP7SilZ2CEvI4RuNzUzU+2XmRlbjTrtYqntwSfXJJGdVsfO4saICZP2Vh/bvRs8saL8OanIToX7v4Jnf0mfrPnEitzo90WaqnhOu6bnUiAQc+fin3hY3+Gxf/k2AmWfQ0+v48qawx/PVzJI/OTSYtyf4SdpjhchBCC72zMp76zn5/vKBlz/95BM//48kn8fPT894MztJnlLcK6KbEkhPnzpwMVyobmMvj9Snj7szeGZDZcgD/fB3o/eOxV8A3iuR2ldPSZ+Pr6XHeLruECQv0N3DszgffP1NGZcRf4h46vgnJPsxKaLQRE5/C/24vR6wRfWZsz9rEuQFMcLmRuaiSPLUjmhQMVHK9oHXU/s8XKN944S3FDF889OovYUBfX7ddwGz56HZ9els6hyy0cvtyiFCpc9x9w4V14fo3St6P2tLJzSJyy0njiXYhMp7C2gxcPVvDYghStmOEtxMcXptBnsvD2iWpoKoZfL1Tavo6GeRDe+CQ8vxYGujhf08G7p2v5zLJ0jz0rVKU4hBBfF0JIIUSU7b0QQvyfEKJMCHFWCDHH0zI6yrN35pMcEcDTfz1BdduNETWDZitffOUUm8/V8a935bMyN8YDUmq4kn9YlEpsqB8/2VqMlFIxTzz6CvS2wVufUSojAwRGwpPvQUweA2YL33zzLOEBBp7ZkOfZ/4CGU5mRFMaclHB+v/cyA8EJSoTV20+N3LfHYoK/Pw0V+2DDD5C+wfzggyIiAg183oP5PKpRHEKIZGAdUDVs811Atu31OeA3HhBtUoQFGnj+yXkMmKw8+JuD7C1pUh4ewJHLLTz8u0N8WFjP/9s4haeWT7KmkYYq8Tfo+ec12ZyobGNroa3ZV9498OUz8NldcP+Nt/WPPyymsLaTHz4wnbBALQH0VkIIxcRU29HPG2daFV+H1Qx/uhtqTl7dsa1C6bNx/i0lKm/WY7x1soaDl1r42rocQv09d1+oRnEAPwO+CQwvLXsf8GepcBgIF0LEj3i0ismKCeH1pxfj66PjiReOsuAHO5n//R088vvD1LT18evH52iJfrc4H5uXzJT4UL799/O09tgc43ofSJp7Q1Xk987U8sf95Ty5OJX1U13XN1rDc9yRHcWclHB+tbuM3tB0eHKTEi31h1VQtEnZ6dTLUHtKmVgs+wq17X3856YLzE2N4PGFnq1VJuRYnencIYQQ9wJrpJRfFkJUAPOklM1CiE3Aj6SU+2377QSekVIeH+Ecn0NZlRAbGzv31Vdfdd9/4Dq6u7sJDg6+YbvJKjlYa6ak1YpOQGa4jiUJPvjqPeMIH01ONeENMsL45LzSZeW7B/uYatTzz3P88NHd+Hc/Wmfmt2cHyA7X8S/z/J16b9xKY+lpnCFjcauFHx7t5840A4/m+eJj6iah9gNqE+7GbAjGMNiOzmpiwD8as1XywyP91HRb+e6SAOKCxjfnd1TOVatWnZBSzhtzRymlW17ADuD8CK/7gCNAmG2/CiDK9vtmYNmwc+wE5o51rblz50pPsnv3bo9ef7x4g5zeIKOU45fzr4crZOozm+Q/vnxCdvebhrYPmi3yuR0lMuNbm+VDvzlwzWfultHTeIOczpLx2bfOyPRnN8kzV9pG3cdqtcpvvnFGpj6zSb5/psah8zsqJ3BcjuN57ray6lLKtSNtF0JMB9KBM7YQ1CTgpBBiAVANDG+qnATUulhUDQ2X8fjCVLr6zfz3hxc5Vt7KmvxYpJTsKWmirqOfe2cm8IMHpmu9Nm4Tnr0rn4LiJj770nHe+sISkiMDr/ncZLHy3fcKee34Fb60OouNMxI8JOm1eNzHIaU8J6WMkVKmSSnTUJTFHCllPfAe8IQtumoR0CGlrPOkvBoak+XpFZm88fnFTEsM48PzdXxYWE9+fCh/+uR8/u+x2QRrSuO2ISzAwIufWsCA2crDvz1EQXHj0Kz+eEUrj/zuEC8fqeLpFZl8bZ1ncjZGQu136AfA3UAZ0At8yrPiaGg4h3lpkbzwSS0TXEMpTfPKUwv50iun+OSfjhERaEAnBC09gxiDfHnu0VncN0tdHUBVpzhsqw777xJwMCdfQ0NDw7uYmhDGB1++g01n6zhR2YrFKpmXGsndM+JVuQJVn0QaGhoatyH+Bj0PzU3ioblJnhZlTDzu49DQ0NDQ8C40xaGhoaGh4RCa4tDQ0NDQcAhNcWhoaGhoOISmODQ0NDQ0HEJTHBoaGhoaDqEpDg0NDQ0Nh9AUh4aGhoaGQ6iirLqzEUI0ASO003IbUUCzB68/XrxBTm+QEbxDTm+QEbxDTm+QERyXM1VKGT3WTrek4vA0Qojjcjw17T2MN8jpDTKCd8jpDTKCd8jpDTKC6+TUTFUaGhoaGg6hKQ4NDQ0NDYfQFIdr+L2nBRgn3iCnN8gI3iGnN8gI3iGnN8gILpJT83FoaGhoaDiEtuLQ0NDQ0HAITXFoaGhoaDiEpjicjBCiQghxTghxWghx3NPyAAghXhBCNAohzg/bFimE2C6EKLX9jPCkjDaZRpLzu0KIGtt4nhZC3O1hGZOFELuFEEVCiEIhxJdt21U1njeRUzXjKYTwF0IcFUKcscn4Pdv2dCHEEdtYviaE8PWUjGPI+aIQonzYWM7ypJw2mfRCiFNCiE229y4ZS01xuIZVUspZKorzfhG487ptzwI7pZTZwE7be0/zIjfKCfAz23jOklJ+4GaZrscM/IuUMh9YBPyTEGIK6hvP0eQE9YznALBaSjkTmAXcKYRYBPy3TcZsoA34jAdlhNHlBPjGsLE87TkRh/gyUDTsvUvGUlMctwFSyr1A63Wb7wNesv3+EnC/W4UagVHkVBVSyjop5Unb710oX9JEVDaeN5FTNUiFbttbg+0lgdXAm7btahjL0eRUFUKIJOAe4Hnbe4GLxlJTHM5HAtuEECeEEJ/ztDA3IVZKWQfKQwaI8bA8N+OLQoizNlOWx01qdoQQacBs4AgqHs/r5AQVjafNtHIaaAS2A5eAdiml2bZLNSpQeNfLKaW0j+X3bWP5MyGEnwdFBPg58E3AantvxEVjqSkO57NUSjkHuAvFPLDc0wJ5Ob8BMlFMBHXA/3pWHAUhRDDwFvAVKWWnp+UZjRHkVNV4SiktUspZQBKwAMgfaTf3SjWCANfJKYSYBnwLyAPmA5HAM56STwixEWiUUp4YvnmEXZ0ylpricDJSylrbz0bgHZQvgxppEELEA9h+NnpYnhGRUjbYvrRW4A+oYDyFEAaUh/HLUsq3bZtVN54jyanG8QSQUrYDBSj+mHAhhI/toySg1lNyXc8wOe+0mQOllHIA+BOeHculwL1CiArgVRQT1c9x0VhqisOJCCGChBAh9t+B9cD5mx/lMd4DnrT9/iTwrgdlGRX7w9jGR/HweNrsxn8EiqSUPx32karGczQ51TSeQohoIUS47fcAYC2KL2Y38JBtNzWM5UhyXhw2URAovgOPjaWU8ltSyiQpZRrwKLBLSvk4LhpLLXPciQghMlBWGQA+wCtSyu97UCQAhBB/A1ailFhuAP4d+DvwOpACVAEPSyk96pgeRc6VKGYVCVQAn7f7EjyBEGIZsA84x1Vb8r+i+A9UM543kfMxVDKeQogZKA5bPcok9nUp5X/Yvkevoph/TgH/YJvVe4SbyLkLiEYxCZ0Gnh7mRPcYQoiVwNellBtdNZaa4tDQ0NDQcAjNVKWhoaGh4RCa4tDQ0NDQcAhNcWhoaGhoOISmODQ0NDQ0HEJTHBoaGhoaDqEpDg0NDQ0Nh9AUh4bGGAghwoUQ/zjsfYIQ4s2bHTPB69hLnv/HTfbJtJXw9ni+gMbti5bHoaExBrYigZuklNNcfJ3vAt1Syv8Zx77dUspgV8qjoTEa2opDQ2NsfgTYZ/o/EUKkCVuzKSHEJ4UQfxdCvG9r6vNFIcTXbM10DgshIm37ZQohPrRVTd4nhMgb66JCiBXDmgSdspez0dDwND5j76KhcdvzLDDNVh3VvgIZzjSUsuX+QBnwjJRythDiZ8ATKMXmfo9SkqJUCLEQ+DVKIbqb8XXgn6SUB2xVbvud9P/R0JgUmuLQ0Jg8u23NkrqEEB3A+7bt54AZtof+EuANpR4eAOPp3XAA+KkQ4mXgbSlltZPl1tCYEJri0NCYPMOLxlmHvbeifMd0KA11HOpJLaX8kRBiM3A3cFgIsVZKedEZAmtoTAbNx6GhMTZdwIT9C7YGSuVCiIdBKcMthJg51nFCiEwp5Tkp5X8Dx1GaBmloeBxNcWhojIGUsgU4IIQ4L4T4yQRP8zjwGSHEGaAQpUf5WHzFds0zQB+wZYLX1tBwKlo4roaGStDCcTW8BW3FoaGhHrqBz40nARCl0ZWGhkfQVhwaGhoaGg6hrTg0NDQ0NBxCUxwaGhoaGg6hKQ4NDQ0NDYfQFIeGhoaGhkP8f6qLz6Ea8WiuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#collapse\n",
    "\n",
    "## Simulate:\n",
    "r0 = df.iloc[0]['r']\n",
    "states_0 = np.array([0,r0])\n",
    "K_=result.x[0]\n",
    "T_1_=result.x[1]\n",
    "deltas=data['delta']\n",
    "\n",
    "sol = solve_ivp(fun = nomoto_replay,t_span=[time[0],time[-1]],t_eval=time, y0 = states_0, \n",
    "                args=(K_,T_1_,deltas))\n",
    "\n",
    "\n",
    "df_simulation_replay=pd.DataFrame(index=df.index)\n",
    "df_simulation_replay['psi'] = sol.y[0,:]\n",
    "df_simulation_replay['r'] = r = sol.y[1,:]\n",
    "df_simulation_replay['psi_deg']=np.rad2deg(df_simulation_replay['psi'])\n",
    "\n",
    "## Plotting:\n",
    "fig,ax=plt.subplots()\n",
    "df.plot(y='psi_deg', label='psi model test', ax=ax)\n",
    "df_simulation_replay.plot(y='psi_deg', label='psi simulation', style='--', ax=ax)\n",
    "df.plot(y='delta_deg', ax=ax)\n",
    "\n",
    "ax.set_ylabel('$\\psi$ [deg]')\n",
    "ax.set_xlabel('time [s]');\n",
    "ax.grid(True)\n",
    "ax.set_title('ZigZag20/20 model test data')\n",
    "\n",
    "fig,ax=plt.subplots()\n",
    "df.plot(y='r', label='r model test', ax=ax)\n",
    "df_simulation_replay.plot(y='r', label='r simulation', style='--', ax=ax)\n",
    "\n",
    "ax.set_ylabel('$r$ [rad/s]')\n",
    "ax.set_xlabel('time [s]');\n",
    "ax.grid(True)\n",
    "ax.set_title('ZigZag20/20 model test data');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So this simple Nomoto model seem to capture the dynamics pretty well. It can be noted that the initial part of the test, with the first overshoot is not captured so well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Also using $T_2$\n",
    "Can also including the $T_2$ coefficient in the Nomoto's equation (above) make this even better? The first challange is then to determine the $\\ddot{r}$ using numerical derivation which is not so easy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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": [
    "#collapse\n",
    "df['r2d'] = np.gradient(df['r1d'], df.index)\n",
    "\n",
    "df_=df.copy()\n",
    "df_.index = pd.TimedeltaIndex(df_.index,unit='s')\n",
    "df_=df_.resample('0.25S').mean()\n",
    "df_.index=df_.index.total_seconds()\n",
    "\n",
    "fig,ax=plt.subplots()\n",
    "df.plot(y='r2d', ax=ax, label='numerical $\\ddot{r}$')\n",
    "df_.plot(y='r2d', ax=ax, label='resample numerical $\\ddot{r}$')\n",
    "ax.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It seems that the estimated $\\ddot{r}$ signal is not carying much usefull information. But we try to use it anyway:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#collapse\n",
    "def calculate_r2d(K,T_1,T_2,delta,r,r1d):\n",
    "    # K*delta = r + T_1*r1d + T_2*r2d\n",
    "    #--> r2d = (K*delta - r - T_1*r1d)/T_2\n",
    "    return (K*delta - r - T_1*r1d)/T_2\n",
    "\n",
    "def estimator_T2(parameters, X):\n",
    "    delta=X['delta']\n",
    "    r=X['r']\n",
    "    r1d=X['r1d']\n",
    "    \n",
    "    K=parameters[0]\n",
    "    T_1=parameters[1]\n",
    "    T_2=parameters[2]\n",
    "        \n",
    "    return calculate_r2d(K=K, T_1=T_1, T_2=T_2, delta=delta, r=r, r1d=r1d)  \n",
    "    \n",
    "def error_function_T2(x, X, ys):\n",
    "    return ys-estimator_T2(x,X)\n",
    "\n",
    "df['r2d'] = np.gradient(df['r1d'], df.index)\n",
    "data2 = df.copy()\n",
    "ys2=data2.pop('r2d')\n",
    "X2=data2.copy()\n",
    "\n",
    "\n",
    "kwargs={\n",
    "    'X':X2,\n",
    "    'ys':ys2,\n",
    "}\n",
    "\n",
    "initial_guess_T2=[1,1,1]\n",
    "result_T2 = least_squares(fun=error_function_T2, x0=initial_guess_T2,\n",
    "                       kwargs=kwargs)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle K=0.49, T_1=0.42, T_2=0.77$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#hide_input\n",
    "K_=result_T2.x[0]\n",
    "T_1_=result_T2.x[1]\n",
    "T_2_=result_T2.x[2]\n",
    "\n",
    "display(Math('K=%0.2f, T_1=%0.2f, T_2=%0.2f' % (K_,T_1_,T_2_)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "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": [
    "#collapse\n",
    "y_pred = estimator_T2(parameters=result_T2.x, X=X2)\n",
    "\n",
    "fig,ax=plt.subplots()\n",
    "time=data.index\n",
    "ax.plot(time,ys2, label='measurement')\n",
    "ax.plot(time,y_pred,label='curve fit', alpha=0.5);\n",
    "ax.legend()\n",
    "ax.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we look at the predicted $\\ddot{r}$ and compare to rudder actions it seems that there is some information after all:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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": [
    "#collapse\n",
    "fig,ax=plt.subplots()\n",
    "time=data.index\n",
    "\n",
    "ax.plot(time,y_pred,label='$\\ddot{r}_{pred}$');\n",
    "ax.plot(time,df['delta'])\n",
    "ax.legend()\n",
    "ax.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "#collapse\n",
    "def nomoto_replay_T2(t, states, K, T_1, T_2, deltas):\n",
    "    \n",
    "    # states:\n",
    "    # [psi, r, r1d]\n",
    "    \n",
    "    psi = states[0]\n",
    "    r = states[1]\n",
    "    r1d = states[2]\n",
    "    \n",
    "    \n",
    "    i=np.argmin(np.abs(deltas.index-t))\n",
    "    delta=deltas.iloc[i]\n",
    "    \n",
    "    r2d_ = calculate_r2d(K=K, T_1=T_1, T_2=T_2, delta=delta, r=r, r1d=r1d)\n",
    "    \n",
    "    d_states_dt = np.array([r,r1d,r2d_])\n",
    "    \n",
    "    return d_states_dt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "#collapse\n",
    "\n",
    "states_0 = np.array([0,r0,0])\n",
    "K_=result_T2.x[0]\n",
    "T_1_=result_T2.x[1]\n",
    "T_2_=result_T2.x[2]\n",
    "\n",
    "deltas=data2['delta']\n",
    "\n",
    "sol = solve_ivp(fun = nomoto_replay_T2,t_span=[time[0],time[-1]],t_eval=time, y0 = states_0, \n",
    "                args=(K_,T_1_,T_2_,deltas))\n",
    "\n",
    "\n",
    "df_simulation_replay_T2=pd.DataFrame(index=df.index)\n",
    "df_simulation_replay_T2['psi'] = sol.y[0,:]\n",
    "df_simulation_replay_T2['r'] = r = sol.y[1,:]\n",
    "df_simulation_replay_T2['psi_deg']=np.rad2deg(df_simulation_replay_T2['psi'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "#collapse\n",
    "fig,ax=plt.subplots()\n",
    "df.plot(y='psi_deg', label='psi model test', ax=ax)\n",
    "df_simulation_replay_T2.plot(y='psi_deg', label='psi simulation', style='--', ax=ax)\n",
    "df.plot(y='delta_deg', ax=ax)\n",
    "\n",
    "ax.set_ylabel('$\\psi$ [deg]')\n",
    "ax.set_xlabel('time [s]');\n",
    "ax.grid(True)\n",
    "ax.set_title('ZigZag20/20 model test data')\n",
    "\n",
    "fig,ax=plt.subplots()\n",
    "df.plot(y='r', label='r model test', ax=ax)\n",
    "df_simulation_replay_T2.plot(y='r', label='r simulation', style='--', ax=ax)\n",
    "\n",
    "ax.set_ylabel('$r$ [rad/s]')\n",
    "ax.set_xlabel('time [s]');\n",
    "ax.grid(True)\n",
    "ax.set_title('ZigZag20/20 model test data');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "...so this was not an improvement, but perhaps I've made something wrong here?"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}