{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from resonance.linear_systems import SimplePendulumSystem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "sys = SimplePendulumSystem()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'pendulum_mass': 0.0, 'pendulum_length': 0.0, 'acc_due_to_gravity': 0.0}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys.constants"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "_SingleDoFCoordinatesDict([('angle', 0.0)])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys.coordinates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "_SingleDoFCoordinatesDict([('angle_vel', 0.0)])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys.speeds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys.coordinates['angle']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "sys.constants['pendulum_mass'] = 1.0  # kg\n",
    "sys.constants['pendulum_length'] = 1.0  # m\n",
    "sys.constants['acc_due_to_gravity'] = 9.81  # m/s**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "sys.coordinates['angle'] = np.deg2rad(10.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'pendulum_mass': 1.0, 'pendulum_length': 1.0, 'acc_due_to_gravity': 9.81}"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys.constants"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "_SingleDoFCoordinatesDict([('angle', 0.17453292519943295)])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys.coordinates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_x(pendulum_length, angle):\n",
    "    return pendulum_length * np.sin(angle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_y(pendulum_length, angle):\n",
    "    return pendulum_length * np.cos(angle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{}"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys.measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "sys.add_measurement('x', calc_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'x': 0.17364817766693033}"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys.measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "sys.add_measurement('y', calc_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'x': 0.17364817766693033, 'y': 0.984807753012208}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys.measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.17364817766693033"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys.measurements['x']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "sys.coordinates['angle'] = np.deg2rad(20.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'x': 0.3420201433256687, 'y': 0.9396926207859084}"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys.measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "traj = sys.free_response(2.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>angle</th>\n",
       "      <th>angle_acc</th>\n",
       "      <th>angle_vel</th>\n",
       "      <th>x</th>\n",
       "      <th>y</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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.00</th>\n",
       "      <td>0.349066</td>\n",
       "      <td>-3.424336</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.342020</td>\n",
       "      <td>0.939693</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.01</th>\n",
       "      <td>0.348895</td>\n",
       "      <td>-3.422656</td>\n",
       "      <td>-0.034238</td>\n",
       "      <td>0.341859</td>\n",
       "      <td>0.939751</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.02</th>\n",
       "      <td>0.348381</td>\n",
       "      <td>-3.417620</td>\n",
       "      <td>-0.068442</td>\n",
       "      <td>0.341377</td>\n",
       "      <td>0.939927</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.03</th>\n",
       "      <td>0.347526</td>\n",
       "      <td>-3.409230</td>\n",
       "      <td>-0.102579</td>\n",
       "      <td>0.340573</td>\n",
       "      <td>0.940218</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.04</th>\n",
       "      <td>0.346330</td>\n",
       "      <td>-3.397497</td>\n",
       "      <td>-0.136615</td>\n",
       "      <td>0.339448</td>\n",
       "      <td>0.940625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.96</th>\n",
       "      <td>0.345439</td>\n",
       "      <td>-3.388754</td>\n",
       "      <td>0.157201</td>\n",
       "      <td>0.338609</td>\n",
       "      <td>0.940927</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.97</th>\n",
       "      <td>0.346841</td>\n",
       "      <td>-3.402510</td>\n",
       "      <td>0.123242</td>\n",
       "      <td>0.339929</td>\n",
       "      <td>0.940451</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.98</th>\n",
       "      <td>0.347903</td>\n",
       "      <td>-3.412930</td>\n",
       "      <td>0.089162</td>\n",
       "      <td>0.340927</td>\n",
       "      <td>0.940090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.99</th>\n",
       "      <td>0.348624</td>\n",
       "      <td>-3.420001</td>\n",
       "      <td>0.054994</td>\n",
       "      <td>0.341605</td>\n",
       "      <td>0.939844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.00</th>\n",
       "      <td>0.349003</td>\n",
       "      <td>-3.423718</td>\n",
       "      <td>0.020773</td>\n",
       "      <td>0.341961</td>\n",
       "      <td>0.939714</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>201 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         angle  angle_acc  angle_vel         x         y\n",
       "time                                                    \n",
       "0.00  0.349066  -3.424336   0.000000  0.342020  0.939693\n",
       "0.01  0.348895  -3.422656  -0.034238  0.341859  0.939751\n",
       "0.02  0.348381  -3.417620  -0.068442  0.341377  0.939927\n",
       "0.03  0.347526  -3.409230  -0.102579  0.340573  0.940218\n",
       "0.04  0.346330  -3.397497  -0.136615  0.339448  0.940625\n",
       "...        ...        ...        ...       ...       ...\n",
       "1.96  0.345439  -3.388754   0.157201  0.338609  0.940927\n",
       "1.97  0.346841  -3.402510   0.123242  0.339929  0.940451\n",
       "1.98  0.347903  -3.412930   0.089162  0.340927  0.940090\n",
       "1.99  0.348624  -3.420001   0.054994  0.341605  0.939844\n",
       "2.00  0.349003  -3.423718   0.020773  0.341961  0.939714\n",
       "\n",
       "[201 rows x 5 columns]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "traj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f51c7acaf572468aa2e2e9a6266bb3a1",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([<matplotlib.axes._subplots.AxesSubplot object at 0x7f29060c0b70>,\n",
       "       <matplotlib.axes._subplots.AxesSubplot object at 0x7f2906034048>,\n",
       "       <matplotlib.axes._subplots.AxesSubplot object at 0x7f2905fe4400>,\n",
       "       <matplotlib.axes._subplots.AxesSubplot object at 0x7f2905f97860>,\n",
       "       <matplotlib.axes._subplots.AxesSubplot object at 0x7f2905fcacc0>],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib widget\n",
    "traj.plot(subplots=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mSignature:\u001b[0m \u001b[0msys\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfree_response\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfinal_time\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minitial_time\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msample_rate\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mDocstring:\u001b[0m\n",
       "Returns a data frame with monotonic time values as the index and\n",
       "columns for each coordinate and measurement at the time value for that\n",
       "row. Note that this data frame is stored on the system as the variable\n",
       "``result`` until this method is called again, which will overwrite it.\n",
       "\n",
       "Parameters\n",
       "==========\n",
       "final_time : float\n",
       "    A value of time in seconds corresponding to the end of the\n",
       "    simulation.\n",
       "initial_time : float, optional\n",
       "    A value of time in seconds corresponding to the start of the\n",
       "    simulation.\n",
       "sample_rate : integer, optional\n",
       "    The sample rate of the simulation in Hertz (samples per second).\n",
       "    The time values will be reported at the initial time and final\n",
       "    time, i.e. inclusive, along with times space equally based on the\n",
       "    sample rate.\n",
       "\n",
       "Returns\n",
       "=======\n",
       "df : pandas.DataFrame\n",
       "    A data frame indexed by time with all of the coordinates and\n",
       "    measurements as columns.\n",
       "\u001b[0;31mFile:\u001b[0m      /opt/conda/lib/python3.6/site-packages/resonance/system.py\n",
       "\u001b[0;31mType:\u001b[0m      method\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sys.free_response?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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