Untitled1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import math\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "R=2000 #Helix Radius\n",
    "\n",
    "w=np.pi/3 #length of arc\n",
    "\n",
    "v=3000 # velocity in Z\n",
    "\n",
    "theta0=-0.3 # angle at the origin\n",
    "\n",
    "D=0 #D=500 - Use for helixes far from the origin\n",
    "\n",
    "z0=0 #z0=200 - Z shifting\n",
    "\n",
    "t=np.random.rand(50)\n",
    "\n",
    "X=-R*np.sin(w*t+theta0)+(R-D)*np.sin(theta0)\n",
    "\n",
    "Y=-R*np.cos(w*t+theta0)+(R-D)*np.cos(theta0)\n",
    "\n",
    "Z=z0+v*t\n",
    "\n",
    "hits1 = pd.DataFrame()\n",
    "hits1['x'] = X\n",
    "hits1['y'] = Y\n",
    "hits1['z'] = Z\n",
    "hits1['helix'] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "R=4000 #Helix Radius\n",
    "\n",
    "w=np.pi/2 #length of arc\n",
    "\n",
    "v=2000 # velocity in Z\n",
    "\n",
    "theta0=0.2 # angle at the origin\n",
    "\n",
    "D=0 #D=500 - Use for helixes far from the origin\n",
    "\n",
    "z0=0 #z0=200 - Z shifting\n",
    "\n",
    "t=np.random.rand(100)\n",
    "\n",
    "X=-R*np.sin(w*t+theta0)+(R-D)*np.sin(theta0)\n",
    "\n",
    "Y=-R*np.cos(w*t+theta0)+(R-D)*np.cos(theta0)\n",
    "\n",
    "Z=z0+v*t\n",
    "\n",
    "hits2 = pd.DataFrame()\n",
    "hits2['x'] = X\n",
    "hits2['y'] = Y\n",
    "hits2['z'] = Z\n",
    "hits2['helix'] = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "R=1500 #Helix Radius\n",
    "\n",
    "w=np.pi/5 #length of arc\n",
    "\n",
    "v=1000 # velocity in Z\n",
    "\n",
    "theta0=-0.6 # angle at the origin\n",
    "\n",
    "D=0 #D=500 - Use for helixes far from the origin\n",
    "\n",
    "z0=100 #z0=200 - Z shifting\n",
    "\n",
    "t=np.random.rand(25)\n",
    "\n",
    "X=-R*np.sin(w*t+theta0)+(R-D)*np.sin(theta0)\n",
    "\n",
    "Y=-R*np.cos(w*t+theta0)+(R-D)*np.cos(theta0)\n",
    "\n",
    "Z=z0+v*t\n",
    "\n",
    "hits3 = pd.DataFrame()\n",
    "hits3['x'] = X\n",
    "hits3['y'] = Y\n",
    "hits3['z'] = Z\n",
    "hits3['helix'] = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "hits = pd.concat([hits1, hits2, hits3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(hits['x'], hits['y'])\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-528.9655705172449"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R = 1000\n",
    "w = np.pi/4\n",
    "D = 0\n",
    "theta = -0.3\n",
    "\n",
    "R*np.sin(w*theta)+(R-D)*np.sin(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.23561944901923448"
      ]
     },
     "execution_count": 179,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w*theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "171.04036100644169"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R*np.sin(w+theta)+(R-D)*np.sin(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "171.04036100644166"
      ]
     },
     "execution_count": 181,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R*((np.sin(w)*np.cos(theta))+(np.cos(w)*np.sin(theta))+((1-D)*np.sin(theta)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "466.5605676677812"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = R*((np.sin(w)*np.cos(theta))+(np.sin(theta)*((np.cos(w)))))\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1839.8257410091537"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y = R*(np.cos(w)*np.cos(theta) - np.sin(w)*np.sin(theta)+np.cos(theta))\n",
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X/r: 0.2458089812165244\n",
      "Y/r: 0.9693182886716284\n"
     ]
    }
   ],
   "source": [
    "print(\"X/r:\", X/r)\n",
    "print(\"Y/r:\", Y/r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1898.0615165432241"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = np.sqrt(X**2 + Y**2)\n",
    "r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7335962508631505"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cos(w+theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.679585565414341"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sin(w)*np.cos(theta)+np.cos(w)*np.sin(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "384.0653587530015"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R*(np.sin(w*theta)+((1-D)*np.sin(theta)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5646424733950354"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sin(A + B) = sin A cos B + cos A sin B\n",
    "# cos(A + B) = cos A cos B - sin A sin B\n",
    "A = 0.5\n",
    "B = 0.1\n",
    "\n",
    "np.sin(A+B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6546913374900216"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sin(w)*np.cos(theta) + np.cos(theta)*np.sin(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "679.2900452076797"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R*(np.sin(w)*np.cos(theta)+np.sin(theta)*np.cos(w))+((1-D)*np.sin(theta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08521693479083237"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sin(0.6) - np.sin(0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.07957521384265565"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sin(0.7) - np.sin(0.6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.644217687237691"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sin(0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1499999999999997"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arcsin(0.912763940260521)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "dfh = hits\n",
    "dfh['stepped_z'] = dfh.z\n",
    "dfh['r'] = np.sqrt(dfh['x'].values**2+dfh['y'].values**2+dfh['stepped_z'].values**2)\n",
    "dfh['rt'] = np.sqrt(dfh['x'].values**2+dfh['y'].values**2)\n",
    "dfh['a0'] = np.arctan2(dfh['y'].values,dfh['x'].values)\n",
    "dfh['z1'] = dfh['stepped_z'].values/dfh['rt'].values\n",
    "\n",
    "dfh['z2'] = dfh['stepped_z']/dfh['r']\n",
    "dfh['x2'] = dfh['x'].values/dfh['r'].values\n",
    "dfh['y2'] = dfh['y'].values/dfh['r'].values\n",
    "\n",
    "dfh['t1'] = np.arcsin(dfh['rt']/(2*dfh['r']))\n",
    "dfh['t2'] = (2 * dfh['r']) - dfh['t1']\n",
    "dfh['t0'] = dfh['t1'] - dfh['a0']\n",
    "\n",
    "dfh['z3'] = np.arctan2(dfh['stepped_z'].values,dfh['rt'].values)\n",
    "\n",
    "# dfh['theta0'] = np.arcsin(np.sqrt(dfh['x']**2+dfh['y']**2)/(2*dfh['r']))- np.arctan2(dfh['y'],dfh['x'])\n",
    "\n",
    "dfh[\"w_div_v\"] = np.arcsin((dfh['y'] * np.sin(dfh['t0']) - dfh['x'] * np.cos(dfh['t0'])) / dfh['r']) / (dfh['z'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "dfh.drop([\"w_div_v\"], axis=1, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "cx = np.array([0.96, .96, .4, .25, 0.20, 0.0108, 0.0108])\n",
    "cx = np.array([1, 1, 1, 1, 1, 1, 1])\n",
    "dfh['a1'] = dfh['a0']+1*(dfh['rt']+(0)*dfh['rt']**2)/1000*(1/3)/180*math.pi\n",
    "dfh['sina1'] = np.sin(dfh['a1'].values)\n",
    "dfh['cosa1'] = np.cos(dfh['a1'].values)\n",
    "dfh['z4'] = dfh['sina1'] / dfh['z3']\n",
    "\n",
    "ss = StandardScaler()\n",
    "dfs = ss.fit_transform(dfh[['sina1','cosa1','z1','z2','z3','x2','y2']].values)\n",
    "# dfs[:,4] = dfh['z5'].values\n",
    "dfs = np.multiply(dfs, cx)\n",
    "\n",
    "features = pd.DataFrame(dfs, columns=['sina1','cosa1','z1','z2','z3','x2','y2'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>z</th>\n",
       "      <th>helix</th>\n",
       "      <th>stepped_z</th>\n",
       "      <th>r</th>\n",
       "      <th>rt</th>\n",
       "      <th>a0</th>\n",
       "      <th>z1</th>\n",
       "      <th>z2</th>\n",
       "      <th>...</th>\n",
       "      <th>y2</th>\n",
       "      <th>t1</th>\n",
       "      <th>t2</th>\n",
       "      <th>t0</th>\n",
       "      <th>z3</th>\n",
       "      <th>a1</th>\n",
       "      <th>sina1</th>\n",
       "      <th>cosa1</th>\n",
       "      <th>z4</th>\n",
       "      <th>w_div_v</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-36.084729</td>\n",
       "      <td>-10.791096</td>\n",
       "      <td>53.950095</td>\n",
       "      <td>1</td>\n",
       "      <td>53.950095</td>\n",
       "      <td>65.796414</td>\n",
       "      <td>37.663715</td>\n",
       "      <td>-2.851009</td>\n",
       "      <td>1.432416</td>\n",
       "      <td>0.819955</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.164007</td>\n",
       "      <td>0.290273</td>\n",
       "      <td>131.302555</td>\n",
       "      <td>3.141282</td>\n",
       "      <td>0.961332</td>\n",
       "      <td>-2.850790</td>\n",
       "      <td>-0.286722</td>\n",
       "      <td>-0.958014</td>\n",
       "      <td>-0.298254</td>\n",
       "      <td>-0.010761</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-1837.744276</td>\n",
       "      <td>346.790157</td>\n",
       "      <td>2787.502971</td>\n",
       "      <td>1</td>\n",
       "      <td>2787.502971</td>\n",
       "      <td>3356.745484</td>\n",
       "      <td>1870.178450</td>\n",
       "      <td>2.955082</td>\n",
       "      <td>1.490501</td>\n",
       "      <td>0.830418</td>\n",
       "      <td>...</td>\n",
       "      <td>0.103311</td>\n",
       "      <td>0.282305</td>\n",
       "      <td>6713.208664</td>\n",
       "      <td>-2.672777</td>\n",
       "      <td>0.979858</td>\n",
       "      <td>2.965962</td>\n",
       "      <td>0.174729</td>\n",
       "      <td>-0.984617</td>\n",
       "      <td>0.178321</td>\n",
       "      <td>-0.000203</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1898.959288</td>\n",
       "      <td>397.613753</td>\n",
       "      <td>2901.476492</td>\n",
       "      <td>1</td>\n",
       "      <td>2901.476492</td>\n",
       "      <td>3490.373749</td>\n",
       "      <td>1940.139962</td>\n",
       "      <td>2.935189</td>\n",
       "      <td>1.495499</td>\n",
       "      <td>0.831280</td>\n",
       "      <td>...</td>\n",
       "      <td>0.113917</td>\n",
       "      <td>0.281636</td>\n",
       "      <td>6980.465863</td>\n",
       "      <td>-2.653554</td>\n",
       "      <td>0.981406</td>\n",
       "      <td>2.946477</td>\n",
       "      <td>0.193880</td>\n",
       "      <td>-0.981025</td>\n",
       "      <td>0.197554</td>\n",
       "      <td>-0.000194</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1327.426893</td>\n",
       "      <td>51.174403</td>\n",
       "      <td>1939.648332</td>\n",
       "      <td>1</td>\n",
       "      <td>1939.648332</td>\n",
       "      <td>2350.939520</td>\n",
       "      <td>1328.412954</td>\n",
       "      <td>3.103060</td>\n",
       "      <td>1.460125</td>\n",
       "      <td>0.825052</td>\n",
       "      <td>...</td>\n",
       "      <td>0.021768</td>\n",
       "      <td>0.286429</td>\n",
       "      <td>4701.592612</td>\n",
       "      <td>-2.816632</td>\n",
       "      <td>0.970295</td>\n",
       "      <td>3.110789</td>\n",
       "      <td>0.030799</td>\n",
       "      <td>-0.999526</td>\n",
       "      <td>0.031742</td>\n",
       "      <td>-0.000295</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-1194.572704</td>\n",
       "      <td>3.909025</td>\n",
       "      <td>1737.622334</td>\n",
       "      <td>1</td>\n",
       "      <td>1737.622334</td>\n",
       "      <td>2108.637143</td>\n",
       "      <td>1194.579100</td>\n",
       "      <td>3.138320</td>\n",
       "      <td>1.454590</td>\n",
       "      <td>0.824050</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001854</td>\n",
       "      <td>0.287190</td>\n",
       "      <td>4216.987097</td>\n",
       "      <td>-2.851130</td>\n",
       "      <td>0.968523</td>\n",
       "      <td>3.145270</td>\n",
       "      <td>-0.003677</td>\n",
       "      <td>-0.999993</td>\n",
       "      <td>-0.003797</td>\n",
       "      <td>-0.000331</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-1529.988801</td>\n",
       "      <td>144.780590</td>\n",
       "      <td>2259.445229</td>\n",
       "      <td>1</td>\n",
       "      <td>2259.445229</td>\n",
       "      <td>2732.566540</td>\n",
       "      <td>1536.823721</td>\n",
       "      <td>3.047245</td>\n",
       "      <td>1.470205</td>\n",
       "      <td>0.826858</td>\n",
       "      <td>...</td>\n",
       "      <td>0.052983</td>\n",
       "      <td>0.285050</td>\n",
       "      <td>5464.848029</td>\n",
       "      <td>-2.762195</td>\n",
       "      <td>0.973498</td>\n",
       "      <td>3.056186</td>\n",
       "      <td>0.085303</td>\n",
       "      <td>-0.996355</td>\n",
       "      <td>0.087625</td>\n",
       "      <td>-0.000252</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-1101.546759</td>\n",
       "      <td>-23.075524</td>\n",
       "      <td>1598.866060</td>\n",
       "      <td>1</td>\n",
       "      <td>1598.866060</td>\n",
       "      <td>1941.728720</td>\n",
       "      <td>1101.788429</td>\n",
       "      <td>-3.120647</td>\n",
       "      <td>1.451155</td>\n",
       "      <td>0.823424</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.011884</td>\n",
       "      <td>0.287664</td>\n",
       "      <td>3883.169775</td>\n",
       "      <td>3.408312</td>\n",
       "      <td>0.967419</td>\n",
       "      <td>-3.114237</td>\n",
       "      <td>-0.027352</td>\n",
       "      <td>-0.999626</td>\n",
       "      <td>-0.028273</td>\n",
       "      <td>-0.000360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-1357.019428</td>\n",
       "      <td>63.167593</td>\n",
       "      <td>1985.385842</td>\n",
       "      <td>1</td>\n",
       "      <td>1985.385842</td>\n",
       "      <td>2405.670138</td>\n",
       "      <td>1358.488819</td>\n",
       "      <td>3.095077</td>\n",
       "      <td>1.461466</td>\n",
       "      <td>0.825294</td>\n",
       "      <td>...</td>\n",
       "      <td>0.026258</td>\n",
       "      <td>0.286244</td>\n",
       "      <td>4811.054033</td>\n",
       "      <td>-2.808833</td>\n",
       "      <td>0.970723</td>\n",
       "      <td>3.102981</td>\n",
       "      <td>0.038602</td>\n",
       "      <td>-0.999255</td>\n",
       "      <td>0.039766</td>\n",
       "      <td>-0.000288</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-636.024251</td>\n",
       "      <td>-88.821071</td>\n",
       "      <td>923.876729</td>\n",
       "      <td>1</td>\n",
       "      <td>923.876729</td>\n",
       "      <td>1125.150764</td>\n",
       "      <td>642.196256</td>\n",
       "      <td>-3.002840</td>\n",
       "      <td>1.438621</td>\n",
       "      <td>0.821114</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.078941</td>\n",
       "      <td>0.289405</td>\n",
       "      <td>2250.012122</td>\n",
       "      <td>3.292245</td>\n",
       "      <td>0.963360</td>\n",
       "      <td>-2.999103</td>\n",
       "      <td>-0.142008</td>\n",
       "      <td>-0.989866</td>\n",
       "      <td>-0.147409</td>\n",
       "      <td>-0.000627</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-559.357334</td>\n",
       "      <td>-89.076052</td>\n",
       "      <td>814.052126</td>\n",
       "      <td>1</td>\n",
       "      <td>814.052126</td>\n",
       "      <td>991.713685</td>\n",
       "      <td>566.405482</td>\n",
       "      <td>-2.983672</td>\n",
       "      <td>1.437225</td>\n",
       "      <td>0.820854</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.089820</td>\n",
       "      <td>0.289600</td>\n",
       "      <td>1983.137770</td>\n",
       "      <td>3.273272</td>\n",
       "      <td>0.962905</td>\n",
       "      <td>-2.980376</td>\n",
       "      <td>-0.160519</td>\n",
       "      <td>-0.987033</td>\n",
       "      <td>-0.166703</td>\n",
       "      <td>-0.000712</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>-176.829939</td>\n",
       "      <td>-45.964363</td>\n",
       "      <td>261.798420</td>\n",
       "      <td>1</td>\n",
       "      <td>261.798420</td>\n",
       "      <td>319.249061</td>\n",
       "      <td>182.706185</td>\n",
       "      <td>-2.887285</td>\n",
       "      <td>1.432893</td>\n",
       "      <td>0.820044</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.143977</td>\n",
       "      <td>0.290206</td>\n",
       "      <td>638.207916</td>\n",
       "      <td>3.177491</td>\n",
       "      <td>0.961489</td>\n",
       "      <td>-2.886222</td>\n",
       "      <td>-0.252604</td>\n",
       "      <td>-0.967570</td>\n",
       "      <td>-0.262722</td>\n",
       "      <td>-0.002217</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>-1536.959611</td>\n",
       "      <td>148.504748</td>\n",
       "      <td>2270.765825</td>\n",
       "      <td>1</td>\n",
       "      <td>2270.765825</td>\n",
       "      <td>2746.029122</td>\n",
       "      <td>1544.117388</td>\n",
       "      <td>3.045269</td>\n",
       "      <td>1.470591</td>\n",
       "      <td>0.826927</td>\n",
       "      <td>...</td>\n",
       "      <td>0.054080</td>\n",
       "      <td>0.284997</td>\n",
       "      <td>5491.773247</td>\n",
       "      <td>-2.760272</td>\n",
       "      <td>0.973621</td>\n",
       "      <td>3.054253</td>\n",
       "      <td>0.087229</td>\n",
       "      <td>-0.996188</td>\n",
       "      <td>0.089592</td>\n",
       "      <td>-0.000251</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>-534.903629</td>\n",
       "      <td>-88.539032</td>\n",
       "      <td>779.016110</td>\n",
       "      <td>1</td>\n",
       "      <td>779.016110</td>\n",
       "      <td>949.119146</td>\n",
       "      <td>542.181752</td>\n",
       "      <td>-2.977557</td>\n",
       "      <td>1.436817</td>\n",
       "      <td>0.820778</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.093285</td>\n",
       "      <td>0.289657</td>\n",
       "      <td>1897.948635</td>\n",
       "      <td>3.267214</td>\n",
       "      <td>0.962772</td>\n",
       "      <td>-2.974402</td>\n",
       "      <td>-0.166413</td>\n",
       "      <td>-0.986056</td>\n",
       "      <td>-0.172847</td>\n",
       "      <td>-0.000744</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>-354.256881</td>\n",
       "      <td>-75.260948</td>\n",
       "      <td>519.471898</td>\n",
       "      <td>1</td>\n",
       "      <td>519.471898</td>\n",
       "      <td>633.256031</td>\n",
       "      <td>362.163152</td>\n",
       "      <td>-2.932258</td>\n",
       "      <td>1.434359</td>\n",
       "      <td>0.820319</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.118848</td>\n",
       "      <td>0.290001</td>\n",
       "      <td>1266.222061</td>\n",
       "      <td>3.222259</td>\n",
       "      <td>0.961968</td>\n",
       "      <td>-2.930151</td>\n",
       "      <td>-0.209870</td>\n",
       "      <td>-0.977729</td>\n",
       "      <td>-0.218167</td>\n",
       "      <td>-0.001117</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>-1477.129876</td>\n",
       "      <td>117.673964</td>\n",
       "      <td>2174.352141</td>\n",
       "      <td>1</td>\n",
       "      <td>2174.352141</td>\n",
       "      <td>2631.267197</td>\n",
       "      <td>1481.809648</td>\n",
       "      <td>3.062097</td>\n",
       "      <td>1.467363</td>\n",
       "      <td>0.826352</td>\n",
       "      <td>...</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>0.285437</td>\n",
       "      <td>5262.248958</td>\n",
       "      <td>-2.776659</td>\n",
       "      <td>0.972598</td>\n",
       "      <td>3.070717</td>\n",
       "      <td>0.070816</td>\n",
       "      <td>-0.997489</td>\n",
       "      <td>0.072811</td>\n",
       "      <td>-0.000263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>-99.995978</td>\n",
       "      <td>-28.108949</td>\n",
       "      <td>148.801830</td>\n",
       "      <td>1</td>\n",
       "      <td>148.801830</td>\n",
       "      <td>181.469814</td>\n",
       "      <td>103.871597</td>\n",
       "      <td>-2.867563</td>\n",
       "      <td>1.432556</td>\n",
       "      <td>0.819981</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.154896</td>\n",
       "      <td>0.290254</td>\n",
       "      <td>362.649374</td>\n",
       "      <td>3.157817</td>\n",
       "      <td>0.961378</td>\n",
       "      <td>-2.866959</td>\n",
       "      <td>-0.271194</td>\n",
       "      <td>-0.962525</td>\n",
       "      <td>-0.282089</td>\n",
       "      <td>-0.003901</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>-1401.324362</td>\n",
       "      <td>82.165411</td>\n",
       "      <td>2054.437907</td>\n",
       "      <td>1</td>\n",
       "      <td>2054.437907</td>\n",
       "      <td>2488.207434</td>\n",
       "      <td>1403.731143</td>\n",
       "      <td>3.083026</td>\n",
       "      <td>1.463555</td>\n",
       "      <td>0.825670</td>\n",
       "      <td>...</td>\n",
       "      <td>0.033022</td>\n",
       "      <td>0.285958</td>\n",
       "      <td>4976.128910</td>\n",
       "      <td>-2.797067</td>\n",
       "      <td>0.971389</td>\n",
       "      <td>3.091192</td>\n",
       "      <td>0.050379</td>\n",
       "      <td>-0.998730</td>\n",
       "      <td>0.051863</td>\n",
       "      <td>-0.000278</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>-1078.568752</td>\n",
       "      <td>-28.996096</td>\n",
       "      <td>1564.877280</td>\n",
       "      <td>1</td>\n",
       "      <td>1564.877280</td>\n",
       "      <td>1900.787265</td>\n",
       "      <td>1078.958445</td>\n",
       "      <td>-3.114715</td>\n",
       "      <td>1.450359</td>\n",
       "      <td>0.823278</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.015255</td>\n",
       "      <td>0.287774</td>\n",
       "      <td>3801.286756</td>\n",
       "      <td>3.402490</td>\n",
       "      <td>0.967163</td>\n",
       "      <td>-3.108438</td>\n",
       "      <td>-0.033148</td>\n",
       "      <td>-0.999450</td>\n",
       "      <td>-0.034274</td>\n",
       "      <td>-0.000368</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>-1545.272616</td>\n",
       "      <td>152.992432</td>\n",
       "      <td>2284.297634</td>\n",
       "      <td>1</td>\n",
       "      <td>2284.297634</td>\n",
       "      <td>2762.116909</td>\n",
       "      <td>1552.827789</td>\n",
       "      <td>3.042908</td>\n",
       "      <td>1.471057</td>\n",
       "      <td>0.827010</td>\n",
       "      <td>...</td>\n",
       "      <td>0.055390</td>\n",
       "      <td>0.284934</td>\n",
       "      <td>5523.948885</td>\n",
       "      <td>-2.757974</td>\n",
       "      <td>0.973768</td>\n",
       "      <td>3.051941</td>\n",
       "      <td>0.089531</td>\n",
       "      <td>-0.995984</td>\n",
       "      <td>0.091943</td>\n",
       "      <td>-0.000249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>-398.714871</td>\n",
       "      <td>-80.058266</td>\n",
       "      <td>583.524287</td>\n",
       "      <td>1</td>\n",
       "      <td>583.524287</td>\n",
       "      <td>711.254854</td>\n",
       "      <td>406.672933</td>\n",
       "      <td>-2.943437</td>\n",
       "      <td>1.434874</td>\n",
       "      <td>0.820415</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.112559</td>\n",
       "      <td>0.289929</td>\n",
       "      <td>1422.219779</td>\n",
       "      <td>3.233366</td>\n",
       "      <td>0.962137</td>\n",
       "      <td>-2.941071</td>\n",
       "      <td>-0.199181</td>\n",
       "      <td>-0.979963</td>\n",
       "      <td>-0.207019</td>\n",
       "      <td>-0.000994</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>20 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              x           y            z  helix    stepped_z            r  \\\n",
       "0    -36.084729  -10.791096    53.950095      1    53.950095    65.796414   \n",
       "1  -1837.744276  346.790157  2787.502971      1  2787.502971  3356.745484   \n",
       "2  -1898.959288  397.613753  2901.476492      1  2901.476492  3490.373749   \n",
       "3  -1327.426893   51.174403  1939.648332      1  1939.648332  2350.939520   \n",
       "4  -1194.572704    3.909025  1737.622334      1  1737.622334  2108.637143   \n",
       "5  -1529.988801  144.780590  2259.445229      1  2259.445229  2732.566540   \n",
       "6  -1101.546759  -23.075524  1598.866060      1  1598.866060  1941.728720   \n",
       "7  -1357.019428   63.167593  1985.385842      1  1985.385842  2405.670138   \n",
       "8   -636.024251  -88.821071   923.876729      1   923.876729  1125.150764   \n",
       "9   -559.357334  -89.076052   814.052126      1   814.052126   991.713685   \n",
       "10  -176.829939  -45.964363   261.798420      1   261.798420   319.249061   \n",
       "11 -1536.959611  148.504748  2270.765825      1  2270.765825  2746.029122   \n",
       "12  -534.903629  -88.539032   779.016110      1   779.016110   949.119146   \n",
       "13  -354.256881  -75.260948   519.471898      1   519.471898   633.256031   \n",
       "14 -1477.129876  117.673964  2174.352141      1  2174.352141  2631.267197   \n",
       "15   -99.995978  -28.108949   148.801830      1   148.801830   181.469814   \n",
       "16 -1401.324362   82.165411  2054.437907      1  2054.437907  2488.207434   \n",
       "17 -1078.568752  -28.996096  1564.877280      1  1564.877280  1900.787265   \n",
       "18 -1545.272616  152.992432  2284.297634      1  2284.297634  2762.116909   \n",
       "19  -398.714871  -80.058266   583.524287      1   583.524287   711.254854   \n",
       "\n",
       "             rt        a0        z1        z2    ...           y2        t1  \\\n",
       "0     37.663715 -2.851009  1.432416  0.819955    ...    -0.164007  0.290273   \n",
       "1   1870.178450  2.955082  1.490501  0.830418    ...     0.103311  0.282305   \n",
       "2   1940.139962  2.935189  1.495499  0.831280    ...     0.113917  0.281636   \n",
       "3   1328.412954  3.103060  1.460125  0.825052    ...     0.021768  0.286429   \n",
       "4   1194.579100  3.138320  1.454590  0.824050    ...     0.001854  0.287190   \n",
       "5   1536.823721  3.047245  1.470205  0.826858    ...     0.052983  0.285050   \n",
       "6   1101.788429 -3.120647  1.451155  0.823424    ...    -0.011884  0.287664   \n",
       "7   1358.488819  3.095077  1.461466  0.825294    ...     0.026258  0.286244   \n",
       "8    642.196256 -3.002840  1.438621  0.821114    ...    -0.078941  0.289405   \n",
       "9    566.405482 -2.983672  1.437225  0.820854    ...    -0.089820  0.289600   \n",
       "10   182.706185 -2.887285  1.432893  0.820044    ...    -0.143977  0.290206   \n",
       "11  1544.117388  3.045269  1.470591  0.826927    ...     0.054080  0.284997   \n",
       "12   542.181752 -2.977557  1.436817  0.820778    ...    -0.093285  0.289657   \n",
       "13   362.163152 -2.932258  1.434359  0.820319    ...    -0.118848  0.290001   \n",
       "14  1481.809648  3.062097  1.467363  0.826352    ...     0.044721  0.285437   \n",
       "15   103.871597 -2.867563  1.432556  0.819981    ...    -0.154896  0.290254   \n",
       "16  1403.731143  3.083026  1.463555  0.825670    ...     0.033022  0.285958   \n",
       "17  1078.958445 -3.114715  1.450359  0.823278    ...    -0.015255  0.287774   \n",
       "18  1552.827789  3.042908  1.471057  0.827010    ...     0.055390  0.284934   \n",
       "19   406.672933 -2.943437  1.434874  0.820415    ...    -0.112559  0.289929   \n",
       "\n",
       "             t2        t0        z3        a1     sina1     cosa1        z4  \\\n",
       "0    131.302555  3.141282  0.961332 -2.850790 -0.286722 -0.958014 -0.298254   \n",
       "1   6713.208664 -2.672777  0.979858  2.965962  0.174729 -0.984617  0.178321   \n",
       "2   6980.465863 -2.653554  0.981406  2.946477  0.193880 -0.981025  0.197554   \n",
       "3   4701.592612 -2.816632  0.970295  3.110789  0.030799 -0.999526  0.031742   \n",
       "4   4216.987097 -2.851130  0.968523  3.145270 -0.003677 -0.999993 -0.003797   \n",
       "5   5464.848029 -2.762195  0.973498  3.056186  0.085303 -0.996355  0.087625   \n",
       "6   3883.169775  3.408312  0.967419 -3.114237 -0.027352 -0.999626 -0.028273   \n",
       "7   4811.054033 -2.808833  0.970723  3.102981  0.038602 -0.999255  0.039766   \n",
       "8   2250.012122  3.292245  0.963360 -2.999103 -0.142008 -0.989866 -0.147409   \n",
       "9   1983.137770  3.273272  0.962905 -2.980376 -0.160519 -0.987033 -0.166703   \n",
       "10   638.207916  3.177491  0.961489 -2.886222 -0.252604 -0.967570 -0.262722   \n",
       "11  5491.773247 -2.760272  0.973621  3.054253  0.087229 -0.996188  0.089592   \n",
       "12  1897.948635  3.267214  0.962772 -2.974402 -0.166413 -0.986056 -0.172847   \n",
       "13  1266.222061  3.222259  0.961968 -2.930151 -0.209870 -0.977729 -0.218167   \n",
       "14  5262.248958 -2.776659  0.972598  3.070717  0.070816 -0.997489  0.072811   \n",
       "15   362.649374  3.157817  0.961378 -2.866959 -0.271194 -0.962525 -0.282089   \n",
       "16  4976.128910 -2.797067  0.971389  3.091192  0.050379 -0.998730  0.051863   \n",
       "17  3801.286756  3.402490  0.967163 -3.108438 -0.033148 -0.999450 -0.034274   \n",
       "18  5523.948885 -2.757974  0.973768  3.051941  0.089531 -0.995984  0.091943   \n",
       "19  1422.219779  3.233366  0.962137 -2.941071 -0.199181 -0.979963 -0.207019   \n",
       "\n",
       "     w_div_v  \n",
       "0  -0.010761  \n",
       "1  -0.000203  \n",
       "2  -0.000194  \n",
       "3  -0.000295  \n",
       "4  -0.000331  \n",
       "5  -0.000252  \n",
       "6  -0.000360  \n",
       "7  -0.000288  \n",
       "8  -0.000627  \n",
       "9  -0.000712  \n",
       "10 -0.002217  \n",
       "11 -0.000251  \n",
       "12 -0.000744  \n",
       "13 -0.001117  \n",
       "14 -0.000263  \n",
       "15 -0.003901  \n",
       "16 -0.000278  \n",
       "17 -0.000368  \n",
       "18 -0.000249  \n",
       "19 -0.000994  \n",
       "\n",
       "[20 rows x 21 columns]"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfh.head(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>z</th>\n",
       "      <th>helix</th>\n",
       "      <th>stepped_z</th>\n",
       "      <th>r</th>\n",
       "      <th>rt</th>\n",
       "      <th>a0</th>\n",
       "      <th>z1</th>\n",
       "      <th>z2</th>\n",
       "      <th>x2</th>\n",
       "      <th>y2</th>\n",
       "      <th>t1</th>\n",
       "      <th>t2</th>\n",
       "      <th>t0</th>\n",
       "      <th>z3</th>\n",
       "      <th>a1</th>\n",
       "      <th>sina1</th>\n",
       "      <th>cosa1</th>\n",
       "      <th>z4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>175.000000</td>\n",
       "      <td>175.000000</td>\n",
       "      <td>175.000000</td>\n",
       "      <td>175.000000</td>\n",
       "      <td>175.000000</td>\n",
       "      <td>175.000000</td>\n",
       "      <td>175.000000</td>\n",
       "      <td>175.000000</td>\n",
       "      <td>175.000000</td>\n",
       "      <td>175.000000</td>\n",
       "      <td>175.000000</td>\n",
       "      <td>175.000000</td>\n",
       "      <td>175.000000</td>\n",
       "      <td>175.000000</td>\n",
       "      <td>175.000000</td>\n",
       "      <td>175.000000</td>\n",
       "      <td>175.000000</td>\n",
       "      <td>175.000000</td>\n",
       "      <td>175.000000</td>\n",
       "      <td>175.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-1643.963136</td>\n",
       "      <td>1169.140132</td>\n",
       "      <td>1087.939780</td>\n",
       "      <td>1.857143</td>\n",
       "      <td>1087.939780</td>\n",
       "      <td>2489.453131</td>\n",
       "      <td>2138.692661</td>\n",
       "      <td>0.894846</td>\n",
       "      <td>0.828147</td>\n",
       "      <td>0.530563</td>\n",
       "      <td>-0.665690</td>\n",
       "      <td>0.261633</td>\n",
       "      <td>0.406314</td>\n",
       "      <td>4978.499947</td>\n",
       "      <td>-0.488532</td>\n",
       "      <td>0.595686</td>\n",
       "      <td>0.907289</td>\n",
       "      <td>0.234682</td>\n",
       "      <td>-0.871791</td>\n",
       "      <td>0.892131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1101.363050</td>\n",
       "      <td>1530.577624</td>\n",
       "      <td>681.803275</td>\n",
       "      <td>0.640710</td>\n",
       "      <td>681.803275</td>\n",
       "      <td>1752.380344</td>\n",
       "      <td>1745.928444</td>\n",
       "      <td>2.558419</td>\n",
       "      <td>0.660826</td>\n",
       "      <td>0.251822</td>\n",
       "      <td>0.146996</td>\n",
       "      <td>0.350819</td>\n",
       "      <td>0.104421</td>\n",
       "      <td>3504.704488</td>\n",
       "      <td>2.485063</td>\n",
       "      <td>0.323407</td>\n",
       "      <td>2.564079</td>\n",
       "      <td>0.413586</td>\n",
       "      <td>0.122123</td>\n",
       "      <td>1.029310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-3205.321485</td>\n",
       "      <td>-261.881758</td>\n",
       "      <td>3.939638</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.939638</td>\n",
       "      <td>12.988621</td>\n",
       "      <td>12.376733</td>\n",
       "      <td>-3.138134</td>\n",
       "      <td>0.318310</td>\n",
       "      <td>0.303315</td>\n",
       "      <td>-0.933602</td>\n",
       "      <td>-0.278950</td>\n",
       "      <td>0.093211</td>\n",
       "      <td>25.480635</td>\n",
       "      <td>-2.851130</td>\n",
       "      <td>0.308169</td>\n",
       "      <td>-3.131334</td>\n",
       "      <td>-0.558215</td>\n",
       "      <td>-0.999993</td>\n",
       "      <td>-0.506651</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-2810.208121</td>\n",
       "      <td>-34.593772</td>\n",
       "      <td>519.358048</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>519.358048</td>\n",
       "      <td>950.565282</td>\n",
       "      <td>606.594448</td>\n",
       "      <td>-2.673560</td>\n",
       "      <td>0.325419</td>\n",
       "      <td>0.309446</td>\n",
       "      <td>-0.804031</td>\n",
       "      <td>-0.067974</td>\n",
       "      <td>0.290004</td>\n",
       "      <td>1900.810546</td>\n",
       "      <td>-2.232868</td>\n",
       "      <td>0.314611</td>\n",
       "      <td>-2.671263</td>\n",
       "      <td>-0.123325</td>\n",
       "      <td>-0.970513</td>\n",
       "      <td>-0.127949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>-1482.037376</td>\n",
       "      <td>358.949200</td>\n",
       "      <td>947.530532</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>947.530532</td>\n",
       "      <td>2221.223599</td>\n",
       "      <td>1536.823721</td>\n",
       "      <td>2.371916</td>\n",
       "      <td>0.346382</td>\n",
       "      <td>0.327303</td>\n",
       "      <td>-0.595531</td>\n",
       "      <td>0.301443</td>\n",
       "      <td>0.492079</td>\n",
       "      <td>4442.160351</td>\n",
       "      <td>-1.878165</td>\n",
       "      <td>0.333448</td>\n",
       "      <td>2.397019</td>\n",
       "      <td>0.311042</td>\n",
       "      <td>-0.907768</td>\n",
       "      <td>1.006979</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>-571.715113</td>\n",
       "      <td>2186.863697</td>\n",
       "      <td>1642.095350</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1642.095350</td>\n",
       "      <td>3749.603430</td>\n",
       "      <td>3560.851803</td>\n",
       "      <td>2.729097</td>\n",
       "      <td>1.434336</td>\n",
       "      <td>0.820315</td>\n",
       "      <td>-0.561365</td>\n",
       "      <td>0.583223</td>\n",
       "      <td>0.495485</td>\n",
       "      <td>7498.712089</td>\n",
       "      <td>2.980634</td>\n",
       "      <td>0.961961</td>\n",
       "      <td>2.738912</td>\n",
       "      <td>0.597658</td>\n",
       "      <td>-0.801750</td>\n",
       "      <td>1.875626</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>-12.126204</td>\n",
       "      <td>4685.088530</td>\n",
       "      <td>2907.409773</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>2907.409773</td>\n",
       "      <td>5976.439308</td>\n",
       "      <td>5635.289632</td>\n",
       "      <td>3.138320</td>\n",
       "      <td>5.278033</td>\n",
       "      <td>0.982521</td>\n",
       "      <td>-0.154465</td>\n",
       "      <td>0.783926</td>\n",
       "      <td>0.496607</td>\n",
       "      <td>11952.387672</td>\n",
       "      <td>3.425460</td>\n",
       "      <td>1.383551</td>\n",
       "      <td>3.145270</td>\n",
       "      <td>0.812722</td>\n",
       "      <td>-0.582652</td>\n",
       "      <td>2.393800</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 x            y            z       helix    stepped_z  \\\n",
       "count   175.000000   175.000000   175.000000  175.000000   175.000000   \n",
       "mean  -1643.963136  1169.140132  1087.939780    1.857143  1087.939780   \n",
       "std    1101.363050  1530.577624   681.803275    0.640710   681.803275   \n",
       "min   -3205.321485  -261.881758     3.939638    1.000000     3.939638   \n",
       "25%   -2810.208121   -34.593772   519.358048    1.000000   519.358048   \n",
       "50%   -1482.037376   358.949200   947.530532    2.000000   947.530532   \n",
       "75%    -571.715113  2186.863697  1642.095350    2.000000  1642.095350   \n",
       "max     -12.126204  4685.088530  2907.409773    3.000000  2907.409773   \n",
       "\n",
       "                 r           rt          a0          z1          z2  \\\n",
       "count   175.000000   175.000000  175.000000  175.000000  175.000000   \n",
       "mean   2489.453131  2138.692661    0.894846    0.828147    0.530563   \n",
       "std    1752.380344  1745.928444    2.558419    0.660826    0.251822   \n",
       "min      12.988621    12.376733   -3.138134    0.318310    0.303315   \n",
       "25%     950.565282   606.594448   -2.673560    0.325419    0.309446   \n",
       "50%    2221.223599  1536.823721    2.371916    0.346382    0.327303   \n",
       "75%    3749.603430  3560.851803    2.729097    1.434336    0.820315   \n",
       "max    5976.439308  5635.289632    3.138320    5.278033    0.982521   \n",
       "\n",
       "               x2          y2          t1            t2          t0  \\\n",
       "count  175.000000  175.000000  175.000000    175.000000  175.000000   \n",
       "mean    -0.665690    0.261633    0.406314   4978.499947   -0.488532   \n",
       "std      0.146996    0.350819    0.104421   3504.704488    2.485063   \n",
       "min     -0.933602   -0.278950    0.093211     25.480635   -2.851130   \n",
       "25%     -0.804031   -0.067974    0.290004   1900.810546   -2.232868   \n",
       "50%     -0.595531    0.301443    0.492079   4442.160351   -1.878165   \n",
       "75%     -0.561365    0.583223    0.495485   7498.712089    2.980634   \n",
       "max     -0.154465    0.783926    0.496607  11952.387672    3.425460   \n",
       "\n",
       "               z3          a1       sina1       cosa1          z4  \n",
       "count  175.000000  175.000000  175.000000  175.000000  175.000000  \n",
       "mean     0.595686    0.907289    0.234682   -0.871791    0.892131  \n",
       "std      0.323407    2.564079    0.413586    0.122123    1.029310  \n",
       "min      0.308169   -3.131334   -0.558215   -0.999993   -0.506651  \n",
       "25%      0.314611   -2.671263   -0.123325   -0.970513   -0.127949  \n",
       "50%      0.333448    2.397019    0.311042   -0.907768    1.006979  \n",
       "75%      0.961961    2.738912    0.597658   -0.801750    1.875626  \n",
       "max      1.383551    3.145270    0.812722   -0.582652    2.393800  "
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfh.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>z</th>\n",
       "      <th>helix</th>\n",
       "      <th>stepped_z</th>\n",
       "      <th>r</th>\n",
       "      <th>rt</th>\n",
       "      <th>a0</th>\n",
       "      <th>z1</th>\n",
       "      <th>z2</th>\n",
       "      <th>x2</th>\n",
       "      <th>y2</th>\n",
       "      <th>t1</th>\n",
       "      <th>t2</th>\n",
       "      <th>t0</th>\n",
       "      <th>z3</th>\n",
       "      <th>a1</th>\n",
       "      <th>sina1</th>\n",
       "      <th>cosa1</th>\n",
       "      <th>z4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.0</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-947.391542</td>\n",
       "      <td>27.610532</td>\n",
       "      <td>1395.425295</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1395.425295</td>\n",
       "      <td>1690.608497</td>\n",
       "      <td>954.385728</td>\n",
       "      <td>-0.571866</td>\n",
       "      <td>1.451944</td>\n",
       "      <td>0.823526</td>\n",
       "      <td>-0.560350</td>\n",
       "      <td>-0.032337</td>\n",
       "      <td>0.287572</td>\n",
       "      <td>3380.929421</td>\n",
       "      <td>0.859439</td>\n",
       "      <td>0.967624</td>\n",
       "      <td>-0.566314</td>\n",
       "      <td>-0.061349</td>\n",
       "      <td>-0.988021</td>\n",
       "      <td>-0.064242</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>562.579139</td>\n",
       "      <td>131.414272</td>\n",
       "      <td>841.781012</td>\n",
       "      <td>0.0</td>\n",
       "      <td>841.781012</td>\n",
       "      <td>1014.628113</td>\n",
       "      <td>566.542193</td>\n",
       "      <td>2.989749</td>\n",
       "      <td>0.018275</td>\n",
       "      <td>0.003301</td>\n",
       "      <td>0.006835</td>\n",
       "      <td>0.082748</td>\n",
       "      <td>0.002511</td>\n",
       "      <td>2029.258643</td>\n",
       "      <td>2.991814</td>\n",
       "      <td>0.005840</td>\n",
       "      <td>2.992398</td>\n",
       "      <td>0.142467</td>\n",
       "      <td>0.012762</td>\n",
       "      <td>0.147381</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-1902.090186</td>\n",
       "      <td>-89.076052</td>\n",
       "      <td>53.950095</td>\n",
       "      <td>1.0</td>\n",
       "      <td>53.950095</td>\n",
       "      <td>65.796414</td>\n",
       "      <td>37.663715</td>\n",
       "      <td>-3.138134</td>\n",
       "      <td>1.432416</td>\n",
       "      <td>0.819955</td>\n",
       "      <td>-0.567714</td>\n",
       "      <td>-0.164007</td>\n",
       "      <td>0.281600</td>\n",
       "      <td>131.302555</td>\n",
       "      <td>-2.851130</td>\n",
       "      <td>0.961332</td>\n",
       "      <td>-3.131334</td>\n",
       "      <td>-0.286722</td>\n",
       "      <td>-0.999993</td>\n",
       "      <td>-0.298254</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-1390.248128</td>\n",
       "      <td>-56.533128</td>\n",
       "      <td>610.007536</td>\n",
       "      <td>1.0</td>\n",
       "      <td>610.007536</td>\n",
       "      <td>743.488119</td>\n",
       "      <td>425.047502</td>\n",
       "      <td>-2.998048</td>\n",
       "      <td>1.435120</td>\n",
       "      <td>0.820461</td>\n",
       "      <td>-0.565778</td>\n",
       "      <td>-0.109952</td>\n",
       "      <td>0.286030</td>\n",
       "      <td>1486.686344</td>\n",
       "      <td>-2.761715</td>\n",
       "      <td>0.962217</td>\n",
       "      <td>-2.994422</td>\n",
       "      <td>-0.194748</td>\n",
       "      <td>-0.999163</td>\n",
       "      <td>-0.202396</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>-1072.034091</td>\n",
       "      <td>-28.514499</td>\n",
       "      <td>1555.234016</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1555.234016</td>\n",
       "      <td>1889.166616</td>\n",
       "      <td>1072.472676</td>\n",
       "      <td>-2.888689</td>\n",
       "      <td>1.450137</td>\n",
       "      <td>0.823238</td>\n",
       "      <td>-0.562016</td>\n",
       "      <td>-0.016212</td>\n",
       "      <td>0.287805</td>\n",
       "      <td>3778.045427</td>\n",
       "      <td>3.178891</td>\n",
       "      <td>0.967091</td>\n",
       "      <td>-2.887593</td>\n",
       "      <td>-0.034793</td>\n",
       "      <td>-0.993882</td>\n",
       "      <td>-0.035977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>-417.146657</td>\n",
       "      <td>77.415957</td>\n",
       "      <td>2037.174891</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2037.174891</td>\n",
       "      <td>2467.573110</td>\n",
       "      <td>1392.420562</td>\n",
       "      <td>3.046751</td>\n",
       "      <td>1.463033</td>\n",
       "      <td>0.825576</td>\n",
       "      <td>-0.555410</td>\n",
       "      <td>0.031331</td>\n",
       "      <td>0.289895</td>\n",
       "      <td>4934.860190</td>\n",
       "      <td>3.287502</td>\n",
       "      <td>0.971222</td>\n",
       "      <td>3.055703</td>\n",
       "      <td>0.047435</td>\n",
       "      <td>-0.980179</td>\n",
       "      <td>0.048839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>-36.084729</td>\n",
       "      <td>400.325835</td>\n",
       "      <td>2907.409773</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2907.409773</td>\n",
       "      <td>3497.318893</td>\n",
       "      <td>1943.761264</td>\n",
       "      <td>3.138320</td>\n",
       "      <td>1.495765</td>\n",
       "      <td>0.831325</td>\n",
       "      <td>-0.543871</td>\n",
       "      <td>0.114466</td>\n",
       "      <td>0.290273</td>\n",
       "      <td>6994.356186</td>\n",
       "      <td>3.425460</td>\n",
       "      <td>0.981488</td>\n",
       "      <td>3.145270</td>\n",
       "      <td>0.194875</td>\n",
       "      <td>-0.958014</td>\n",
       "      <td>0.198551</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 x           y            z  helix    stepped_z            r  \\\n",
       "count    50.000000   50.000000    50.000000   50.0    50.000000    50.000000   \n",
       "mean   -947.391542   27.610532  1395.425295    1.0  1395.425295  1690.608497   \n",
       "std     562.579139  131.414272   841.781012    0.0   841.781012  1014.628113   \n",
       "min   -1902.090186  -89.076052    53.950095    1.0    53.950095    65.796414   \n",
       "25%   -1390.248128  -56.533128   610.007536    1.0   610.007536   743.488119   \n",
       "50%   -1072.034091  -28.514499  1555.234016    1.0  1555.234016  1889.166616   \n",
       "75%    -417.146657   77.415957  2037.174891    1.0  2037.174891  2467.573110   \n",
       "max     -36.084729  400.325835  2907.409773    1.0  2907.409773  3497.318893   \n",
       "\n",
       "                rt         a0         z1         z2         x2         y2  \\\n",
       "count    50.000000  50.000000  50.000000  50.000000  50.000000  50.000000   \n",
       "mean    954.385728  -0.571866   1.451944   0.823526  -0.560350  -0.032337   \n",
       "std     566.542193   2.989749   0.018275   0.003301   0.006835   0.082748   \n",
       "min      37.663715  -3.138134   1.432416   0.819955  -0.567714  -0.164007   \n",
       "25%     425.047502  -2.998048   1.435120   0.820461  -0.565778  -0.109952   \n",
       "50%    1072.472676  -2.888689   1.450137   0.823238  -0.562016  -0.016212   \n",
       "75%    1392.420562   3.046751   1.463033   0.825576  -0.555410   0.031331   \n",
       "max    1943.761264   3.138320   1.495765   0.831325  -0.543871   0.114466   \n",
       "\n",
       "              t1           t2         t0         z3         a1      sina1  \\\n",
       "count  50.000000    50.000000  50.000000  50.000000  50.000000  50.000000   \n",
       "mean    0.287572  3380.929421   0.859439   0.967624  -0.566314  -0.061349   \n",
       "std     0.002511  2029.258643   2.991814   0.005840   2.992398   0.142467   \n",
       "min     0.281600   131.302555  -2.851130   0.961332  -3.131334  -0.286722   \n",
       "25%     0.286030  1486.686344  -2.761715   0.962217  -2.994422  -0.194748   \n",
       "50%     0.287805  3778.045427   3.178891   0.967091  -2.887593  -0.034793   \n",
       "75%     0.289895  4934.860190   3.287502   0.971222   3.055703   0.047435   \n",
       "max     0.290273  6994.356186   3.425460   0.981488   3.145270   0.194875   \n",
       "\n",
       "           cosa1         z4  \n",
       "count  50.000000  50.000000  \n",
       "mean   -0.988021  -0.064242  \n",
       "std     0.012762   0.147381  \n",
       "min    -0.999993  -0.298254  \n",
       "25%    -0.999163  -0.202396  \n",
       "50%    -0.993882  -0.035977  \n",
       "75%    -0.980179   0.048839  \n",
       "max    -0.958014   0.198551  "
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfh[dfh.helix == 1].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>x</th>\n",
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       "      <th>count</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.0</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
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       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-2298.620541</td>\n",
       "      <td>2076.638803</td>\n",
       "      <td>1059.348756</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1059.348756</td>\n",
       "      <td>3324.967090</td>\n",
       "      <td>3151.547660</td>\n",
       "      <td>2.525587</td>\n",
       "      <td>0.330779</td>\n",
       "      <td>0.314000</td>\n",
       "      <td>-0.755417</td>\n",
       "      <td>0.534125</td>\n",
       "      <td>0.494609</td>\n",
       "      <td>6649.439571</td>\n",
       "      <td>-2.030978</td>\n",
       "      <td>0.319419</td>\n",
       "      <td>2.543922</td>\n",
       "      <td>0.549646</td>\n",
       "      <td>-0.807221</td>\n",
       "      <td>1.706351</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>950.683548</td>\n",
       "      <td>1469.482392</td>\n",
       "      <td>580.190147</td>\n",
       "      <td>0.0</td>\n",
       "      <td>580.190147</td>\n",
       "      <td>1749.083189</td>\n",
       "      <td>1650.337704</td>\n",
       "      <td>0.227840</td>\n",
       "      <td>0.010794</td>\n",
       "      <td>0.009214</td>\n",
       "      <td>0.125063</td>\n",
       "      <td>0.173762</td>\n",
       "      <td>0.001745</td>\n",
       "      <td>3498.168047</td>\n",
       "      <td>0.226154</td>\n",
       "      <td>0.009713</td>\n",
       "      <td>0.218248</td>\n",
       "      <td>0.179272</td>\n",
       "      <td>0.120884</td>\n",
       "      <td>0.512715</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-3205.321485</td>\n",
       "      <td>2.477641</td>\n",
       "      <td>3.939638</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.939638</td>\n",
       "      <td>12.988621</td>\n",
       "      <td>12.376733</td>\n",
       "      <td>2.159999</td>\n",
       "      <td>0.318310</td>\n",
       "      <td>0.303315</td>\n",
       "      <td>-0.933602</td>\n",
       "      <td>0.190755</td>\n",
       "      <td>0.490944</td>\n",
       "      <td>25.480635</td>\n",
       "      <td>-2.443438</td>\n",
       "      <td>0.308169</td>\n",
       "      <td>2.192784</td>\n",
       "      <td>0.200115</td>\n",
       "      <td>-0.979772</td>\n",
       "      <td>0.649367</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-3157.153861</td>\n",
       "      <td>770.689170</td>\n",
       "      <td>590.711987</td>\n",
       "      <td>2.0</td>\n",
       "      <td>590.711987</td>\n",
       "      <td>1931.618746</td>\n",
       "      <td>1839.078612</td>\n",
       "      <td>2.329759</td>\n",
       "      <td>0.321189</td>\n",
       "      <td>0.305802</td>\n",
       "      <td>-0.864590</td>\n",
       "      <td>0.398584</td>\n",
       "      <td>0.493283</td>\n",
       "      <td>3862.741337</td>\n",
       "      <td>-2.213466</td>\n",
       "      <td>0.310781</td>\n",
       "      <td>2.356491</td>\n",
       "      <td>0.408902</td>\n",
       "      <td>-0.912524</td>\n",
       "      <td>1.315704</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>-2672.050618</td>\n",
       "      <td>1926.246287</td>\n",
       "      <td>1080.752252</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1080.752252</td>\n",
       "      <td>3466.881824</td>\n",
       "      <td>3294.122377</td>\n",
       "      <td>2.517182</td>\n",
       "      <td>0.328076</td>\n",
       "      <td>0.311728</td>\n",
       "      <td>-0.770848</td>\n",
       "      <td>0.555463</td>\n",
       "      <td>0.495061</td>\n",
       "      <td>6933.268587</td>\n",
       "      <td>-2.022121</td>\n",
       "      <td>0.317011</td>\n",
       "      <td>2.536347</td>\n",
       "      <td>0.568941</td>\n",
       "      <td>-0.822329</td>\n",
       "      <td>1.794677</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>-1669.699852</td>\n",
       "      <td>3333.898395</td>\n",
       "      <td>1558.021575</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1558.021575</td>\n",
       "      <td>4851.859862</td>\n",
       "      <td>4594.900497</td>\n",
       "      <td>2.709621</td>\n",
       "      <td>0.339074</td>\n",
       "      <td>0.321116</td>\n",
       "      <td>-0.651716</td>\n",
       "      <td>0.687116</td>\n",
       "      <td>0.496155</td>\n",
       "      <td>9703.226442</td>\n",
       "      <td>-1.836476</td>\n",
       "      <td>0.326908</td>\n",
       "      <td>2.720320</td>\n",
       "      <td>0.706889</td>\n",
       "      <td>-0.707309</td>\n",
       "      <td>2.162341</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>-12.126204</td>\n",
       "      <td>4685.088530</td>\n",
       "      <td>1990.310921</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1990.310921</td>\n",
       "      <td>5976.439308</td>\n",
       "      <td>5635.289632</td>\n",
       "      <td>2.940046</td>\n",
       "      <td>0.353187</td>\n",
       "      <td>0.333026</td>\n",
       "      <td>-0.523978</td>\n",
       "      <td>0.783926</td>\n",
       "      <td>0.496607</td>\n",
       "      <td>11952.387672</td>\n",
       "      <td>-1.669055</td>\n",
       "      <td>0.339511</td>\n",
       "      <td>2.940118</td>\n",
       "      <td>0.812722</td>\n",
       "      <td>-0.582652</td>\n",
       "      <td>2.393800</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 x            y            z  helix    stepped_z            r  \\\n",
       "count   100.000000   100.000000   100.000000  100.0   100.000000   100.000000   \n",
       "mean  -2298.620541  2076.638803  1059.348756    2.0  1059.348756  3324.967090   \n",
       "std     950.683548  1469.482392   580.190147    0.0   580.190147  1749.083189   \n",
       "min   -3205.321485     2.477641     3.939638    2.0     3.939638    12.988621   \n",
       "25%   -3157.153861   770.689170   590.711987    2.0   590.711987  1931.618746   \n",
       "50%   -2672.050618  1926.246287  1080.752252    2.0  1080.752252  3466.881824   \n",
       "75%   -1669.699852  3333.898395  1558.021575    2.0  1558.021575  4851.859862   \n",
       "max     -12.126204  4685.088530  1990.310921    2.0  1990.310921  5976.439308   \n",
       "\n",
       "                rt          a0          z1          z2          x2  \\\n",
       "count   100.000000  100.000000  100.000000  100.000000  100.000000   \n",
       "mean   3151.547660    2.525587    0.330779    0.314000   -0.755417   \n",
       "std    1650.337704    0.227840    0.010794    0.009214    0.125063   \n",
       "min      12.376733    2.159999    0.318310    0.303315   -0.933602   \n",
       "25%    1839.078612    2.329759    0.321189    0.305802   -0.864590   \n",
       "50%    3294.122377    2.517182    0.328076    0.311728   -0.770848   \n",
       "75%    4594.900497    2.709621    0.339074    0.321116   -0.651716   \n",
       "max    5635.289632    2.940046    0.353187    0.333026   -0.523978   \n",
       "\n",
       "               y2          t1            t2          t0          z3  \\\n",
       "count  100.000000  100.000000    100.000000  100.000000  100.000000   \n",
       "mean     0.534125    0.494609   6649.439571   -2.030978    0.319419   \n",
       "std      0.173762    0.001745   3498.168047    0.226154    0.009713   \n",
       "min      0.190755    0.490944     25.480635   -2.443438    0.308169   \n",
       "25%      0.398584    0.493283   3862.741337   -2.213466    0.310781   \n",
       "50%      0.555463    0.495061   6933.268587   -2.022121    0.317011   \n",
       "75%      0.687116    0.496155   9703.226442   -1.836476    0.326908   \n",
       "max      0.783926    0.496607  11952.387672   -1.669055    0.339511   \n",
       "\n",
       "               a1       sina1       cosa1          z4  \n",
       "count  100.000000  100.000000  100.000000  100.000000  \n",
       "mean     2.543922    0.549646   -0.807221    1.706351  \n",
       "std      0.218248    0.179272    0.120884    0.512715  \n",
       "min      2.192784    0.200115   -0.979772    0.649367  \n",
       "25%      2.356491    0.408902   -0.912524    1.315704  \n",
       "50%      2.536347    0.568941   -0.822329    1.794677  \n",
       "75%      2.720320    0.706889   -0.707309    2.162341  \n",
       "max      2.940118    0.812722   -0.582652    2.393800  "
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfh[dfh.helix == 2].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>z</th>\n",
       "      <th>helix</th>\n",
       "      <th>stepped_z</th>\n",
       "      <th>r</th>\n",
       "      <th>rt</th>\n",
       "      <th>a0</th>\n",
       "      <th>z1</th>\n",
       "      <th>z2</th>\n",
       "      <th>x2</th>\n",
       "      <th>y2</th>\n",
       "      <th>t1</th>\n",
       "      <th>t2</th>\n",
       "      <th>t0</th>\n",
       "      <th>z3</th>\n",
       "      <th>a1</th>\n",
       "      <th>sina1</th>\n",
       "      <th>cosa1</th>\n",
       "      <th>z4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.0</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>25.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-418.476703</td>\n",
       "      <td>-177.795351</td>\n",
       "      <td>587.332846</td>\n",
       "      <td>3.0</td>\n",
       "      <td>587.332846</td>\n",
       "      <td>745.086561</td>\n",
       "      <td>455.886532</td>\n",
       "      <td>-2.694693</td>\n",
       "      <td>1.570029</td>\n",
       "      <td>0.810890</td>\n",
       "      <td>-0.517467</td>\n",
       "      <td>-0.240398</td>\n",
       "      <td>0.290618</td>\n",
       "      <td>1489.882505</td>\n",
       "      <td>2.985311</td>\n",
       "      <td>0.956879</td>\n",
       "      <td>-2.692041</td>\n",
       "      <td>-0.433111</td>\n",
       "      <td>-0.897612</td>\n",
       "      <td>-0.451998</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>242.732025</td>\n",
       "      <td>74.656395</td>\n",
       "      <td>271.108069</td>\n",
       "      <td>0.0</td>\n",
       "      <td>271.108069</td>\n",
       "      <td>366.589213</td>\n",
       "      <td>251.690378</td>\n",
       "      <td>0.085171</td>\n",
       "      <td>0.866100</td>\n",
       "      <td>0.057448</td>\n",
       "      <td>0.111776</td>\n",
       "      <td>0.042465</td>\n",
       "      <td>0.056798</td>\n",
       "      <td>733.135208</td>\n",
       "      <td>0.133690</td>\n",
       "      <td>0.125368</td>\n",
       "      <td>0.083707</td>\n",
       "      <td>0.075376</td>\n",
       "      <td>0.036120</td>\n",
       "      <td>0.052131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-884.295048</td>\n",
       "      <td>-261.881758</td>\n",
       "      <td>125.161173</td>\n",
       "      <td>3.0</td>\n",
       "      <td>125.161173</td>\n",
       "      <td>127.387810</td>\n",
       "      <td>23.713600</td>\n",
       "      <td>-2.854038</td>\n",
       "      <td>1.186936</td>\n",
       "      <td>0.764760</td>\n",
       "      <td>-0.617859</td>\n",
       "      <td>-0.278950</td>\n",
       "      <td>0.093211</td>\n",
       "      <td>254.682408</td>\n",
       "      <td>2.642709</td>\n",
       "      <td>0.870669</td>\n",
       "      <td>-2.848673</td>\n",
       "      <td>-0.558215</td>\n",
       "      <td>-0.957405</td>\n",
       "      <td>-0.506651</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-563.157013</td>\n",
       "      <td>-234.903146</td>\n",
       "      <td>459.806515</td>\n",
       "      <td>3.0</td>\n",
       "      <td>459.806515</td>\n",
       "      <td>570.901433</td>\n",
       "      <td>338.387964</td>\n",
       "      <td>-2.746417</td>\n",
       "      <td>1.232373</td>\n",
       "      <td>0.776516</td>\n",
       "      <td>-0.581536</td>\n",
       "      <td>-0.271563</td>\n",
       "      <td>0.300882</td>\n",
       "      <td>1141.501983</td>\n",
       "      <td>2.955511</td>\n",
       "      <td>0.889117</td>\n",
       "      <td>-2.742867</td>\n",
       "      <td>-0.469683</td>\n",
       "      <td>-0.921556</td>\n",
       "      <td>-0.494021</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>-388.282854</td>\n",
       "      <td>-190.146385</td>\n",
       "      <td>560.331540</td>\n",
       "      <td>3.0</td>\n",
       "      <td>560.331540</td>\n",
       "      <td>707.736291</td>\n",
       "      <td>432.341558</td>\n",
       "      <td>-2.686210</td>\n",
       "      <td>1.296039</td>\n",
       "      <td>0.791724</td>\n",
       "      <td>-0.548626</td>\n",
       "      <td>-0.250511</td>\n",
       "      <td>0.310400</td>\n",
       "      <td>1415.162182</td>\n",
       "      <td>2.996610</td>\n",
       "      <td>0.913625</td>\n",
       "      <td>-2.683695</td>\n",
       "      <td>-0.442063</td>\n",
       "      <td>-0.896984</td>\n",
       "      <td>-0.472659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>-299.053026</td>\n",
       "      <td>-158.346778</td>\n",
       "      <td>751.975177</td>\n",
       "      <td>3.0</td>\n",
       "      <td>751.975177</td>\n",
       "      <td>968.396600</td>\n",
       "      <td>610.184651</td>\n",
       "      <td>-2.654629</td>\n",
       "      <td>1.358815</td>\n",
       "      <td>0.805404</td>\n",
       "      <td>-0.523826</td>\n",
       "      <td>-0.227744</td>\n",
       "      <td>0.320508</td>\n",
       "      <td>1936.472692</td>\n",
       "      <td>3.066925</td>\n",
       "      <td>0.936357</td>\n",
       "      <td>-2.652661</td>\n",
       "      <td>-0.388244</td>\n",
       "      <td>-0.882835</td>\n",
       "      <td>-0.420913</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>-19.676906</td>\n",
       "      <td>-13.234582</td>\n",
       "      <td>1094.543528</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1094.543528</td>\n",
       "      <td>1431.224033</td>\n",
       "      <td>922.158717</td>\n",
       "      <td>-2.549497</td>\n",
       "      <td>5.278033</td>\n",
       "      <td>0.982521</td>\n",
       "      <td>-0.154465</td>\n",
       "      <td>-0.103892</td>\n",
       "      <td>0.328007</td>\n",
       "      <td>2862.120059</td>\n",
       "      <td>3.182045</td>\n",
       "      <td>1.383551</td>\n",
       "      <td>-2.549359</td>\n",
       "      <td>-0.288749</td>\n",
       "      <td>-0.829696</td>\n",
       "      <td>-0.331640</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                x           y            z  helix    stepped_z            r  \\\n",
       "count   25.000000   25.000000    25.000000   25.0    25.000000    25.000000   \n",
       "mean  -418.476703 -177.795351   587.332846    3.0   587.332846   745.086561   \n",
       "std    242.732025   74.656395   271.108069    0.0   271.108069   366.589213   \n",
       "min   -884.295048 -261.881758   125.161173    3.0   125.161173   127.387810   \n",
       "25%   -563.157013 -234.903146   459.806515    3.0   459.806515   570.901433   \n",
       "50%   -388.282854 -190.146385   560.331540    3.0   560.331540   707.736291   \n",
       "75%   -299.053026 -158.346778   751.975177    3.0   751.975177   968.396600   \n",
       "max    -19.676906  -13.234582  1094.543528    3.0  1094.543528  1431.224033   \n",
       "\n",
       "               rt         a0         z1         z2         x2         y2  \\\n",
       "count   25.000000  25.000000  25.000000  25.000000  25.000000  25.000000   \n",
       "mean   455.886532  -2.694693   1.570029   0.810890  -0.517467  -0.240398   \n",
       "std    251.690378   0.085171   0.866100   0.057448   0.111776   0.042465   \n",
       "min     23.713600  -2.854038   1.186936   0.764760  -0.617859  -0.278950   \n",
       "25%    338.387964  -2.746417   1.232373   0.776516  -0.581536  -0.271563   \n",
       "50%    432.341558  -2.686210   1.296039   0.791724  -0.548626  -0.250511   \n",
       "75%    610.184651  -2.654629   1.358815   0.805404  -0.523826  -0.227744   \n",
       "max    922.158717  -2.549497   5.278033   0.982521  -0.154465  -0.103892   \n",
       "\n",
       "              t1           t2         t0         z3         a1      sina1  \\\n",
       "count  25.000000    25.000000  25.000000  25.000000  25.000000  25.000000   \n",
       "mean    0.290618  1489.882505   2.985311   0.956879  -2.692041  -0.433111   \n",
       "std     0.056798   733.135208   0.133690   0.125368   0.083707   0.075376   \n",
       "min     0.093211   254.682408   2.642709   0.870669  -2.848673  -0.558215   \n",
       "25%     0.300882  1141.501983   2.955511   0.889117  -2.742867  -0.469683   \n",
       "50%     0.310400  1415.162182   2.996610   0.913625  -2.683695  -0.442063   \n",
       "75%     0.320508  1936.472692   3.066925   0.936357  -2.652661  -0.388244   \n",
       "max     0.328007  2862.120059   3.182045   1.383551  -2.549359  -0.288749   \n",
       "\n",
       "           cosa1         z4  \n",
       "count  25.000000  25.000000  \n",
       "mean   -0.897612  -0.451998  \n",
       "std     0.036120   0.052131  \n",
       "min    -0.957405  -0.506651  \n",
       "25%    -0.921556  -0.494021  \n",
       "50%    -0.896984  -0.472659  \n",
       "75%    -0.882835  -0.420913  \n",
       "max    -0.829696  -0.331640  "
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfh[dfh.helix == 3].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f7ae71a6240>"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(dfh['a0'], dfh['helix'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>z1</th>\n",
       "      <td>50.0</td>\n",
       "      <td>-1.050094</td>\n",
       "      <td>0.012326</td>\n",
       "      <td>-1.064612</td>\n",
       "      <td>-1.060673</td>\n",
       "      <td>-1.053153</td>\n",
       "      <td>-1.041715</td>\n",
       "      <td>-1.024094</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>z3</th>\n",
       "      <td>50.0</td>\n",
       "      <td>-1.381776</td>\n",
       "      <td>0.026495</td>\n",
       "      <td>-1.413066</td>\n",
       "      <td>-1.404538</td>\n",
       "      <td>-1.388297</td>\n",
       "      <td>-1.363695</td>\n",
       "      <td>-1.326039</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>z2</th>\n",
       "      <td>50.0</td>\n",
       "      <td>-1.402573</td>\n",
       "      <td>0.032487</td>\n",
       "      <td>-1.440991</td>\n",
       "      <td>-1.430497</td>\n",
       "      <td>-1.410536</td>\n",
       "      <td>-1.380361</td>\n",
       "      <td>-1.334324</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sina1</th>\n",
       "      <td>50.0</td>\n",
       "      <td>1.226561</td>\n",
       "      <td>0.399899</td>\n",
       "      <td>0.469533</td>\n",
       "      <td>0.930139</td>\n",
       "      <td>1.260835</td>\n",
       "      <td>1.551107</td>\n",
       "      <td>1.826905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y2</th>\n",
       "      <td>50.0</td>\n",
       "      <td>1.285271</td>\n",
       "      <td>0.480887</td>\n",
       "      <td>0.364927</td>\n",
       "      <td>0.931220</td>\n",
       "      <td>1.332503</td>\n",
       "      <td>1.677410</td>\n",
       "      <td>1.994136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x2</th>\n",
       "      <td>50.0</td>\n",
       "      <td>-1.103818</td>\n",
       "      <td>0.787796</td>\n",
       "      <td>-2.238487</td>\n",
       "      <td>-1.764109</td>\n",
       "      <td>-1.204541</td>\n",
       "      <td>-0.512719</td>\n",
       "      <td>0.385945</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cosa1</th>\n",
       "      <td>50.0</td>\n",
       "      <td>0.868276</td>\n",
       "      <td>1.130630</td>\n",
       "      <td>-0.762867</td>\n",
       "      <td>-0.077023</td>\n",
       "      <td>0.723045</td>\n",
       "      <td>1.713813</td>\n",
       "      <td>3.011605</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       count      mean       std       min       25%       50%       75%  \\\n",
       "z1      50.0 -1.050094  0.012326 -1.064612 -1.060673 -1.053153 -1.041715   \n",
       "z3      50.0 -1.381776  0.026495 -1.413066 -1.404538 -1.388297 -1.363695   \n",
       "z2      50.0 -1.402573  0.032487 -1.440991 -1.430497 -1.410536 -1.380361   \n",
       "sina1   50.0  1.226561  0.399899  0.469533  0.930139  1.260835  1.551107   \n",
       "y2      50.0  1.285271  0.480887  0.364927  0.931220  1.332503  1.677410   \n",
       "x2      50.0 -1.103818  0.787796 -2.238487 -1.764109 -1.204541 -0.512719   \n",
       "cosa1   50.0  0.868276  1.130630 -0.762867 -0.077023  0.723045  1.713813   \n",
       "\n",
       "            max  \n",
       "z1    -1.024094  \n",
       "z3    -1.326039  \n",
       "z2    -1.334324  \n",
       "sina1  1.826905  \n",
       "y2     1.994136  \n",
       "x2     0.385945  \n",
       "cosa1  3.011605  "
      ]
     },
     "execution_count": 287,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "idx = (dfh.helix == 2).values\n",
    "features.loc[idx].describe().T.sort_values(\"std\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 288,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>0.421337</td>\n",
       "      <td>0.458648</td>\n",
       "      <td>0.548449</td>\n",
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       "      <th>cosa1</th>\n",
       "      <td>50.0</td>\n",
       "      <td>-0.915049</td>\n",
       "      <td>0.121060</td>\n",
       "      <td>-1.021662</td>\n",
       "      <td>-1.004373</td>\n",
       "      <td>-0.980740</td>\n",
       "      <td>-0.850468</td>\n",
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       "      <td>-0.766230</td>\n",
       "      <td>-0.416326</td>\n",
       "      <td>-0.094593</td>\n",
       "      <td>0.108965</td>\n",
       "      <td>0.403893</td>\n",
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      "text/plain": [
       "       count      mean       std       min       25%       50%       75%  \\\n",
       "z2      50.0  0.740356  0.013923  0.723045  0.727484  0.738855  0.749543   \n",
       "z3      50.0  0.728164  0.019068  0.704555  0.710564  0.726035  0.740673   \n",
       "z1      50.0  0.479643  0.025018  0.448923  0.456629  0.476655  0.495861   \n",
       "x2      50.0  0.432222  0.048725  0.381253  0.395531  0.421337  0.458648   \n",
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       "y2      50.0 -0.307389  0.237017 -0.759189 -0.505055 -0.272618 -0.127683   \n",
       "sina1   50.0 -0.140236  0.330650 -0.766230 -0.416326 -0.094593  0.108965   \n",
       "\n",
       "            max  \n",
       "z2     0.769923  \n",
       "z3     0.768858  \n",
       "z1     0.533567  \n",
       "x2     0.548449  \n",
       "cosa1 -0.546017  \n",
       "y2     0.077384  \n",
       "sina1  0.403893  "
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     "execution_count": 288,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "idx = (dfh.helix == 1).values\n",
    "features.loc[idx].describe().T.sort_values(\"std\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {},
   "outputs": [
    {
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       "      <td>-0.211791</td>\n",
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       "      <td>0.116228</td>\n",
       "      <td>0.169512</td>\n",
       "      <td>0.242973</td>\n",
       "      <td>0.403079</td>\n",
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       "       count      mean       std       min       25%       50%       75%  \\\n",
       "y2      50.0 -0.977882  0.126394 -1.090157 -1.077756 -1.012304 -0.924570   \n",
       "sina1   50.0 -1.086325  0.180460 -1.405915 -1.218148 -1.100293 -0.975178   \n",
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       "\n",
       "            max  \n",
       "y2    -0.526057  \n",
       "sina1 -0.758984  \n",
       "z2     1.422444  \n",
       "z3     2.155580  \n",
       "cosa1  0.817259  \n",
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       "z1     6.819191  "
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     "metadata": {},
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    "idx = (dfh.helix == 3).values\n",
    "features.loc[idx].describe().T.sort_values(\"std\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {},
   "outputs": [
    {
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       "       count          mean      std       min       25%       50%       75%  \\\n",
       "z2     150.0 -3.848773e-16  1.00335 -1.440991 -1.379827  0.590091  0.736091   \n",
       "cosa2  150.0  4.736952e-17  1.00335 -1.405180 -0.969572 -0.094924  0.882632   \n",
       "sina1  150.0 -2.368476e-17  1.00335 -1.405915 -0.972732 -0.094593  0.889917   \n",
       "cosa1  150.0 -5.210647e-16  1.00335 -1.021662 -0.845395 -0.201502  0.444997   \n",
       "z1     150.0 -3.034610e-17  1.00335 -1.064612 -1.041512  0.242973  0.471749   \n",
       "z3     150.0  1.361874e-16  1.00335 -1.413066 -1.363259  0.531327  0.722265   \n",
       "x2     150.0  5.856426e-16  1.00335 -2.238487 -0.501353  0.382543  0.464967   \n",
       "y2     150.0  1.184238e-17  1.00335 -1.090157 -0.916366 -0.272618  0.882100   \n",
       "sina2  150.0  4.736952e-17  1.00335 -0.994417 -0.830876 -0.233513  0.385548   \n",
       "\n",
       "            max  \n",
       "z2     1.422444  \n",
       "cosa2  1.831282  \n",
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       "cosa1  3.011605  \n",
       "z1     6.819191  \n",
       "z3     2.155580  \n",
       "x2     3.522174  \n",
       "y2     1.994136  \n",
       "sina2  3.045981  "
      ]
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     "execution_count": 279,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features.describe().T.sort_values(\"std\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.326386</td>\n",
       "      <td>-0.984409</td>\n",
       "      <td>0.073588</td>\n",
       "      <td>0.087126</td>\n",
       "      <td>0.082608</td>\n",
       "      <td>-0.826828</td>\n",
       "      <td>0.335633</td>\n",
       "      <td>-0.999282</td>\n",
       "      <td>0.327229</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1.546144</td>\n",
       "      <td>2.221287</td>\n",
       "      <td>-1.093012</td>\n",
       "      <td>-1.106620</td>\n",
       "      <td>-1.102081</td>\n",
       "      <td>1.154444</td>\n",
       "      <td>-1.557059</td>\n",
       "      <td>2.182355</td>\n",
       "      <td>-1.547147</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.729392</td>\n",
       "      <td>0.059310</td>\n",
       "      <td>-0.797734</td>\n",
       "      <td>-0.801069</td>\n",
       "      <td>-0.799975</td>\n",
       "      <td>-0.581488</td>\n",
       "      <td>-0.728512</td>\n",
       "      <td>-0.004975</td>\n",
       "      <td>-0.729311</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.518544</td>\n",
       "      <td>0.147840</td>\n",
       "      <td>1.755039</td>\n",
       "      <td>1.745986</td>\n",
       "      <td>1.749036</td>\n",
       "      <td>1.512869</td>\n",
       "      <td>1.508700</td>\n",
       "      <td>0.292853</td>\n",
       "      <td>1.517651</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      sina1     cosa1        z1        z2        z3        x2        y2  \\\n",
       "0  0.586604 -0.946639  0.374771  0.389541  0.384629 -0.551361  0.595020   \n",
       "1  0.326386 -0.984409  0.073588  0.087126  0.082608 -0.826828  0.335633   \n",
       "2 -1.546144  2.221287 -1.093012 -1.106620 -1.102081  1.154444 -1.557059   \n",
       "3 -0.729392  0.059310 -0.797734 -0.801069 -0.799975 -0.581488 -0.728512   \n",
       "4  1.518544  0.147840  1.755039  1.745986  1.749036  1.512869  1.508700   \n",
       "\n",
       "      sina2     cosa2  \n",
       "0 -0.935743  0.587369  \n",
       "1 -0.999282  0.327229  \n",
       "2  2.182355 -1.547147  \n",
       "3 -0.004975 -0.729311  \n",
       "4  0.292853  1.517651  "
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5.63140061e-01, -9.08773772e-01,  1.49908313e-01,\n",
       "         1.94770262e-02,  7.69258980e-02, -5.95470087e-03,\n",
       "         6.42621272e-03, -9.35743394e-01,  5.87369019e-01,\n",
       "         8.24985991e-01,  9.70177412e-01],\n",
       "       [ 3.13330448e-01, -9.45033087e-01,  2.94351653e-02,\n",
       "         4.35628457e-03,  1.65215868e-02, -8.92974339e-03,\n",
       "         3.62484026e-03, -9.99282186e-01,  3.27228850e-01,\n",
       "         8.23984580e-01,  9.68407767e-01],\n",
       "       [-1.48429801e+00,  2.13243550e+00, -4.37204899e-01,\n",
       "        -5.53310140e-02, -2.20416214e-01,  1.24679942e-02,\n",
       "        -1.68162321e-02,  2.18235533e+00, -1.54714681e+00,\n",
       "         8.20031627e-01,  9.61466279e-01],\n",
       "       [-7.00216392e-01,  5.69373829e-02, -3.19093471e-01,\n",
       "        -4.00534578e-02, -1.59995058e-01, -6.28007557e-03,\n",
       "        -7.86793177e-03, -4.97482342e-03, -7.29311116e-01,\n",
       "         8.21043425e-01,  9.63236417e-01],\n",
       "       [ 1.45780205e+00,  1.41926236e-01,  7.02015663e-01,\n",
       "         8.72993138e-02,  3.49807222e-01,  1.63389802e-02,\n",
       "         1.62939589e-02,  2.92853455e-01,  1.51765065e+00,\n",
       "         8.29477705e-01,  9.78171926e-01],\n",
       "       [-1.76420990e-01, -6.92265105e-01, -1.66653655e-01,\n",
       "        -2.05068149e-02, -8.24650370e-02, -1.06210414e-02,\n",
       "        -1.90847391e-03, -7.71094661e-01, -1.83125424e-01,\n",
       "         8.22337954e-01,  9.65507789e-01],\n",
       "       [-1.23326503e+00,  1.34012570e+00, -4.13921582e-01,\n",
       "        -5.23101232e-02, -2.08481070e-01,  4.82896831e-03,\n",
       "        -1.39519109e-02,  1.34267152e+00, -1.28531191e+00,\n",
       "         8.20231694e-01,  9.61815939e-01],\n",
       "       [ 1.31101587e+00, -1.30256316e-01,  5.97843074e-01,\n",
       "         7.46850049e-02,  2.98809672e-01,  1.14320911e-02,\n",
       "         1.46959532e-02, -1.70428661e-02,  1.36519379e+00,\n",
       "         8.28642288e-01,  9.76677868e-01],\n",
       "       [ 4.63593342e-02, -8.60514955e-01, -8.39503155e-02,\n",
       "        -9.98218426e-03, -4.06144548e-02, -1.05345218e-02,\n",
       "         6.14445341e-04, -9.32943682e-01,  4.90770929e-02,\n",
       "         8.23034976e-01,  9.66733871e-01],\n",
       "       [ 1.09601970e+00, -4.57658415e-01,  4.55176413e-01,\n",
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       "         1.23392253e-02, -3.93664626e-01,  1.14175918e+00,\n",
       "         8.27489114e-01,  9.74620944e-01],\n",
       "       [ 1.59543270e+00,  4.33351508e-01,  8.04840770e-01,\n",
       "         9.96685633e-02,  3.99924154e-01,  2.13876151e-02,\n",
       "         1.77835381e-02,  6.22662379e-01,  1.66052683e+00,\n",
       "         8.30296892e-01,  9.79640185e-01],\n",
       "       [ 1.22238671e+00, -2.75440803e-01,  5.37623597e-01,\n",
       "         6.73546544e-02,  2.69226042e-01,  8.70736394e-03,\n",
       "         1.37266666e-02, -1.83385304e-01,  1.27310447e+00,\n",
       "         8.28156816e-01,  9.75811166e-01],\n",
       "       [-6.74519804e-01,  8.48857737e-03, -3.12982418e-01,\n",
       "        -3.92661648e-02, -1.56877228e-01, -6.64341115e-03,\n",
       "        -7.57492656e-03, -5.53140357e-02, -7.02510548e-01,\n",
       "         8.21095565e-01,  9.63327759e-01],\n",
       "       [ 9.53567551e-01, -6.28326620e-01,  3.66949166e-01,\n",
       "         4.64249941e-02,  1.84966359e-01,  1.53645563e-03,\n",
       "         1.07679376e-02, -5.92992295e-01,  9.93635156e-01,\n",
       "         8.26770693e-01,  9.73342638e-01],\n",
       "       [ 1.12804746e+00, -4.14223590e-01,  4.75697087e-01,\n",
       "         5.97870457e-02,  2.38724583e-01,  6.00364769e-03,\n",
       "         1.26914602e-02, -3.43351939e-01,  1.17505354e+00,\n",
       "         8.27655631e-01,  9.74917575e-01],\n",
       "       [-1.26452105e+00,  1.43209973e+00, -4.17575447e-01,\n",
       "        -5.27838930e-02, -2.10353268e-01,  5.69483054e-03,\n",
       "        -1.43086942e-02,  1.43994138e+00, -1.31791414e+00,\n",
       "         8.20200317e-01,  9.61761089e-01],\n",
       "       [ 6.96250595e-01, -8.43884853e-01,  2.19903540e-01,\n",
       "         2.82086763e-02,  1.11878242e-01, -3.78968982e-03,\n",
       "         7.91184867e-03, -8.52297001e-01,  7.25924616e-01,\n",
       "         8.25564268e-01,  9.71201399e-01],\n",
       "       [-9.70915055e-01,  6.41761863e-01, -3.74890089e-01,\n",
       "        -4.72561636e-02, -1.88500146e-01, -1.49591857e-03,\n",
       "        -1.09567775e-02,  6.06522637e-01, -1.01165869e+00,\n",
       "         8.20566406e-01,  9.62401313e-01],\n",
       "       [ 1.77593564e+00,  8.69270043e-01,  9.47497233e-01,\n",
       "         1.16695729e-01,  4.69093620e-01,  2.86686195e-02,\n",
       "         1.97233978e-02,  1.11334817e+00,  1.84779796e+00,\n",
       "         8.31424562e-01,  9.81666620e-01],\n",
       "       [ 1.03221143e+00, -5.38646226e-01,  4.15045582e-01,\n",
       "         5.23461519e-02,  2.08772992e-01,  3.46432151e-03,\n",
       "         1.16363215e-02, -4.87880078e-01,  1.07541795e+00,\n",
       "         8.27162838e-01,  9.74040093e-01],\n",
       "       [-4.40347317e-01, -3.77180209e-01, -2.50797250e-01,\n",
       "        -3.12724046e-02, -1.25197194e-01, -9.23637330e-03,\n",
       "        -4.90737891e-03, -4.53141933e-01, -4.58300002e-01,\n",
       "         8.21624974e-01,  9.64255879e-01],\n",
       "       [-9.97394000e-01,  7.06324803e-01, -3.79504158e-01,\n",
       "        -4.78529490e-02, -1.90860422e-01, -9.33474047e-04,\n",
       "        -1.12590615e-02,  6.74362388e-01, -1.03927834e+00,\n",
       "         8.20526882e-01,  9.62332165e-01],\n",
       "       [-4.55372160e-01, -3.55443342e-01, -2.55138671e-01,\n",
       "        -3.18294444e-02, -1.27406169e-01, -9.10869201e-03,\n",
       "        -5.07836876e-03, -4.30897782e-01, -4.73967488e-01,\n",
       "         8.21588082e-01,  9.64191163e-01],\n",
       "       [-1.71337243e+00,  2.96410172e+00, -4.46196906e-01,\n",
       "        -5.64988973e-02, -2.25028765e-01,  2.08227761e-02,\n",
       "        -1.94260728e-02,  3.06702653e+00, -1.78604442e+00,\n",
       "         8.19954281e-01,  9.61331146e-01],\n",
       "       [ 6.67518535e-01, -8.60576062e-01,  2.04448971e-01,\n",
       "         2.62841453e-02,  1.04169948e-01, -4.29108206e-03,\n",
       "         7.59161911e-03, -8.73229549e-01,  6.96020983e-01,\n",
       "         8.25436811e-01,  9.70975572e-01],\n",
       "       [ 8.56957207e-01, -7.23218612e-01,  3.09902446e-01,\n",
       "         3.93782905e-02,  1.56666113e-01, -6.39546624e-04,\n",
       "         9.69818828e-03, -7.05522294e-01,  8.93144022e-01,\n",
       "         8.26304006e-01,  9.72513535e-01],\n",
       "       [-1.18262336e+00,  1.19509755e+00, -4.07549271e-01,\n",
       "        -5.14841399e-02, -2.05216676e-01,  3.47712534e-03,\n",
       "        -1.33737925e-02,  1.18942384e+00, -1.23248865e+00,\n",
       "         8.20286397e-01,  9.61911574e-01],\n",
       "       [-7.51196666e-01,  1.56665630e-01, -3.30799954e-01,\n",
       "        -4.15624825e-02, -1.65969936e-01, -5.51284582e-03,\n",
       "        -8.44936640e-03,  9.88315411e-02, -7.82482755e-01,\n",
       "         8.20943486e-01,  9.63061373e-01],\n",
       "       [-3.22051077e-01, -5.33996111e-01, -2.14929216e-01,\n",
       "        -2.66762012e-02, -1.06962799e-01, -1.00574216e-02,\n",
       "        -3.56205388e-03, -6.12653843e-01, -3.34952098e-01,\n",
       "         8.21929370e-01,  9.64790086e-01],\n",
       "       [-1.60648673e+00,  2.56295753e+00, -4.43475177e-01,\n",
       "        -5.61453271e-02, -2.23632435e-01,  1.67581491e-02,\n",
       "        -1.82089496e-02,  2.63997660e+00, -1.67458062e+00,\n",
       "         8.19977697e-01,  9.61372054e-01],\n",
       "       [-7.34174480e-01,  1.22832248e-01, -3.26952931e-01,\n",
       "        -4.10664561e-02, -1.64006120e-01, -5.77589087e-03,\n",
       "        -8.25520826e-03,  6.35879685e-02, -7.64728717e-01,\n",
       "         8.20976336e-01,  9.63118907e-01],\n",
       "       [ 5.02493744e-03, -8.36027826e-01, -1.00108400e-01,\n",
       "        -1.20340232e-02, -4.87793038e-02, -1.06369372e-02,\n",
       "         1.47024861e-04, -9.10249803e-01,  6.00031370e-03,\n",
       "         8.22899087e-01,  9.66494668e-01],\n",
       "       [-6.09067767e-01, -1.09423685e-01, -2.96780094e-01,\n",
       "        -3.71803049e-02, -1.48614848e-01, -7.49825049e-03,\n",
       "        -6.82883647e-03, -1.77542785e-01, -6.34248512e-01,\n",
       "         8.21233707e-01,  9.63569820e-01],\n",
       "       [ 1.19412281e+00, -3.18721235e-01,  5.18837047e-01,\n",
       "         6.50620439e-02,  2.59981362e-01,  7.87608039e-03,\n",
       "         1.34168891e-02, -2.33157168e-01,  1.24373159e+00,\n",
       "         8.28004982e-01,  9.75540328e-01],\n",
       "       [ 3.64864390e-01, -9.46680518e-01,  5.31388087e-02,\n",
       "         7.34061054e-03,  2.84310419e-02, -8.43240095e-03,\n",
       "         4.20406338e-03, -9.96111419e-01,  3.80905066e-01,\n",
       "         8.24182225e-01,  9.68756674e-01],\n",
       "       [-4.98233550e-01, -2.91174646e-01, -2.67258433e-01,\n",
       "        -3.33853339e-02, -1.33575053e-01, -8.71539147e-03,\n",
       "        -5.56628766e-03, -3.64977071e-01, -5.18663319e-01,\n",
       "         8.21485039e-01,  9.64010435e-01],\n",
       "       [-5.54036548e-01, -2.02476244e-01, -2.82449804e-01,\n",
       "        -3.53372626e-02, -1.41311905e-01, -8.13871978e-03,\n",
       "        -6.20181302e-03, -2.73672162e-01, -5.76857097e-01,\n",
       "         8.21355768e-01,  9.63783771e-01],\n",
       "       [ 3.22139065e-01, -9.45650814e-01,  3.34448053e-02,\n",
       "         4.86142395e-03,  1.85370056e-02, -8.84902585e-03,\n",
       "         3.72389200e-03, -9.99106247e-01,  3.36404032e-01,\n",
       "         8.24018034e-01,  9.68466812e-01],\n",
       "       [ 1.69539807e+00,  6.67193853e-01,  8.82733689e-01,\n",
       "         1.08984845e-01,  4.37743761e-01,  2.53272291e-02,\n",
       "         1.88598523e-02,  8.86215357e-01,  1.76425661e+00,\n",
       "         8.30913888e-01,  9.80748174e-01],\n",
       "       [-3.16724710e-01, -5.40459906e-01, -2.13243754e-01,\n",
       "        -2.64604839e-02, -1.06106644e-01, -1.00867142e-02,\n",
       "        -3.50152164e-03, -6.19184976e-01, -3.29398637e-01,\n",
       "         8.21943656e-01,  9.64815168e-01],\n",
       "       [-7.66859131e-02, -7.78606540e-01, -1.30957643e-01,\n",
       "        -1.59573524e-02, -6.43834743e-02, -1.07237465e-02,\n",
       "        -7.77921801e-04, -8.55562847e-01, -7.91629320e-02,\n",
       "         8.22639254e-01,  9.66037518e-01],\n",
       "       [-7.47420091e-01,  1.49113000e-01, -3.29951791e-01,\n",
       "        -4.14531116e-02, -1.65536940e-01, -5.57180049e-03,\n",
       "        -8.40628857e-03,  9.09618409e-02, -7.78543797e-01,\n",
       "         8.20950729e-01,  9.63074059e-01],\n",
       "       [ 1.32190618e+00, -1.11424168e-01,  6.05380555e-01,\n",
       "         7.56005387e-02,  3.02507225e-01,  1.17792461e-02,\n",
       "         1.48148296e-02,  4.47293520e-03,  1.37650742e+00,\n",
       "         8.28702922e-01,  9.76786194e-01],\n",
       "       [-3.99920957e-01, -4.33627482e-01, -2.38876499e-01,\n",
       "        -2.97436764e-02, -1.19133870e-01, -9.55369889e-03,\n",
       "        -4.44743672e-03, -5.10769352e-01, -4.16145634e-01,\n",
       "         8.21726218e-01,  9.64433514e-01],\n",
       "       [ 8.73256830e-01, -7.08387885e-01,  3.19370813e-01,\n",
       "         4.05496540e-02,  1.61368036e-01, -2.87286023e-04,\n",
       "         9.87889529e-03, -6.87817901e-01,  9.10100260e-01,\n",
       "         8.26381583e-01,  9.72651286e-01],\n",
       "       [-4.86678985e-01, -3.08829924e-01, -2.64029821e-01,\n",
       "        -3.29707381e-02, -1.31931395e-01, -8.82565803e-03,\n",
       "        -5.43473524e-03, -3.83107598e-01, -5.06614059e-01,\n",
       "         8.21512497e-01,  9.64058589e-01],\n",
       "       [-4.79034325e-01, -3.20377060e-01, -2.61878055e-01,\n",
       "        -3.26944711e-02, -1.30836077e-01, -8.89689061e-03,\n",
       "        -5.34770610e-03, -3.94957028e-01, -4.98642169e-01,\n",
       "         8.21530794e-01,  9.64090678e-01],\n",
       "       [-4.46311094e-02, -8.02560727e-01, -1.19028261e-01,\n",
       "        -1.44392799e-02, -5.83469028e-02, -1.07080179e-02,\n",
       "        -4.14924848e-04, -8.78572883e-01, -4.57525348e-02,\n",
       "         8.22739793e-01,  9.66214370e-01],\n",
       "       [-1.57638276e+00,  2.45412560e+00, -4.42241586e-01,\n",
       "        -5.59850962e-02, -2.22999619e-01,  1.56660339e-02,\n",
       "        -1.78659420e-02,  2.52422008e+00, -1.64318543e+00,\n",
       "         8.19988309e-01,  9.61390593e-01],\n",
       "       [ 3.30370414e-03, -8.34941733e-01, -1.00773184e-01,\n",
       "        -1.21184867e-02, -4.91153473e-02, -1.06403502e-02,\n",
       "         1.27553609e-04, -9.09232416e-01,  4.20646426e-03,\n",
       "         8.22893493e-01,  9.66484824e-01]])"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.c_[dfs, dfh['z2'].values, dfh['z3'].values]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.82498599, 0.82398458, 0.82003163, 0.82104342, 0.82947771,\n",
       "       0.82233795, 0.82023169, 0.82864229, 0.82303498, 0.82748911,\n",
       "       0.83029689, 0.82815682, 0.82109557, 0.82677069, 0.82765563,\n",
       "       0.82020032, 0.82556427, 0.82056641, 0.83142456, 0.82716284,\n",
       "       0.82162497, 0.82052688, 0.82158808, 0.81995428, 0.82543681,\n",
       "       0.82630401, 0.8202864 , 0.82094349, 0.82192937, 0.8199777 ,\n",
       "       0.82097634, 0.82289909, 0.82123371, 0.82800498, 0.82418222,\n",
       "       0.82148504, 0.82135577, 0.82401803, 0.83091389, 0.82194366,\n",
       "       0.82263925, 0.82095073, 0.82870292, 0.82172622, 0.82638158,\n",
       "       0.8215125 , 0.82153079, 0.82273979, 0.81998831, 0.82289349])"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfh['z2'].values"
   ]
  }
 ],
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