diff --git a/src/test_christoffel_stepbystep.ipynb b/src/test_christoffel_stepbystep.ipynb
index 074dfdb..f3b09b1 100644
--- a/src/test_christoffel_stepbystep.ipynb
+++ b/src/test_christoffel_stepbystep.ipynb
@@ -159,6 +159,16 @@
     "Cijkl.shape"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# normalize the stiffness tensor to density\n",
+    "Cijkl_norm = Cijkl /density"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -182,7 +192,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
@@ -191,63 +201,17 @@
        "(450, 3, 3)"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "Mil = ch._christoffel_matrix(wavevectors, Cijkl)\n",
+    "Mil = ch._christoffel_matrix(wavevectors, Cijkl_norm)\n",
     "\n",
     "Mil.shape"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Step 3: Normalize the Christoffel matrices\n",
-    "\n",
-    "$$\n",
-    "M_{il(norm)} = \\frac{M_{il}}{\\rho}\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "norm_Mil = Mil / density"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(array([[ 59.4,   0. ,   0. ],\n",
-       "        [  0. ,  59.4,   0. ],\n",
-       "        [  0. ,   0. , 118.8]]),\n",
-       " array([[11.19276427,  0.        ,  0.        ],\n",
-       "        [ 0.        , 11.19276427,  0.        ],\n",
-       "        [ 0.        ,  0.        , 22.38552855]]))"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# check\n",
-    "Mil[0], norm_Mil[0]"
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -259,7 +223,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
@@ -268,13 +232,13 @@
        "((450, 3), (450, 3, 3))"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "eigenvalues, eigenvectors = ch._calc_eigen(norm_Mil)\n",
+    "eigenvalues, eigenvectors = ch._calc_eigen(Mil)\n",
     "\n",
     "eigenvalues.shape, eigenvectors.shape"
    ]
@@ -293,7 +257,7 @@
     "V_p = \\sqrt{ \\frac{\\lambda_1}{\\rho} }, \\quad V_{s1} = \\sqrt{ \\frac{\\lambda_2}{\\rho} }, \\quad V_{s2} = \\sqrt{ \\frac{\\lambda_3}{\\rho} }\n",
     "$$\n",
     "\n",
-    "where $\\rho$ is the material density. If the Christoffel tensor has already been normalised with respect to the density, the general formulae are as follows:\n",
+    "where $\\rho$ is the material density. If the stiffness of the Christoffel tensor has already been normalised with respect to the density, the general formulae are as follows:\n",
     "\n",
     "$$\n",
     "v_p = \\sqrt{\\lambda_n}, \\quad \\lambda_n = v^2_p\n",
@@ -304,7 +268,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
@@ -313,7 +277,7 @@
        "(450, 3)"
       ]
      },
-     "execution_count": 11,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -326,7 +290,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
@@ -344,7 +308,7 @@
        "       [3.02647863, 3.31846894, 4.95976291]])"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -356,7 +320,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
@@ -410,7 +374,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [
     {
@@ -419,13 +383,13 @@
        "(450, 3, 3, 3)"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 13,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "dMilk = ch._christoffel_gradient_matrix(wavevectors, Cijkl)\n",
+    "dMilk = ch._christoffel_gradient_matrix(wavevectors, Cijkl_norm)\n",
     "\n",
     "dMilk.shape"
    ]
@@ -447,7 +411,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
@@ -456,7 +420,7 @@
        "(450, 3, 3)"
       ]
      },
-     "execution_count": 15,
+     "execution_count": 14,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -483,7 +447,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [
     {
@@ -492,7 +456,7 @@
        "(450, 3, 3)"
       ]
      },
-     "execution_count": 16,
+     "execution_count": 15,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -513,7 +477,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
@@ -522,7 +486,7 @@
        "(450, 3)"
       ]
      },
-     "execution_count": 17,
+     "execution_count": 16,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -535,25 +499,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 17,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([[17.75488102, 17.75488102, 25.10919354],\n",
-       "       [26.55988968, 17.75488102, 22.53753526],\n",
-       "       [17.55089769, 20.07852322, 25.52255753],\n",
-       "       [20.7581618 , 22.72141005, 23.46868979],\n",
-       "       [27.76084197, 21.48549935, 21.54844796],\n",
-       "       [32.82474072, 17.90867688, 20.14843909],\n",
-       "       [27.53796823, 26.21150498, 19.78026365],\n",
-       "       [18.69947453, 28.05020057, 22.31781173],\n",
-       "       [17.93107493, 31.21136785, 21.28368726],\n",
-       "       [19.24616973, 17.33475982, 26.77048673]])"
+       "array([[3.34555889, 3.34555889, 4.73133475],\n",
+       "       [5.00468997, 3.34555889, 4.24675622],\n",
+       "       [3.30712223, 3.78340366, 4.80922509],\n",
+       "       [3.91146821, 4.28140382, 4.42221402],\n",
+       "       [5.23098586, 4.0485207 , 4.06038213],\n",
+       "       [6.1851782 , 3.3745387 , 3.79657793],\n",
+       "       [5.18898968, 4.93904371, 3.7272025 ],\n",
+       "       [3.523549  , 5.28550981, 4.20535363],\n",
+       "       [3.37875917, 5.88116975, 4.01049317],\n",
+       "       [3.62656298, 3.26639529, 5.04437285]])"
       ]
      },
-     "execution_count": 18,
+     "execution_count": 17,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -579,7 +543,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [
     {
@@ -588,7 +552,7 @@
        "(450, 3, 3)"
       ]
      },
-     "execution_count": 19,
+     "execution_count": 18,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -617,7 +581,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 19,
    "metadata": {},
    "outputs": [
     {
@@ -626,7 +590,7 @@
        "(450, 3)"
       ]
      },
-     "execution_count": 20,
+     "execution_count": 19,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -663,7 +627,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 20,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -679,7 +643,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 21,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -695,7 +659,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 22,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -711,7 +675,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 23,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -729,7 +693,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 24,
    "metadata": {},
    "outputs": [
     {
@@ -771,9 +735,9 @@
        "      <td>4.731335</td>\n",
        "      <td>3.345559</td>\n",
        "      <td>3.345559</td>\n",
-       "      <td>25.109194</td>\n",
-       "      <td>17.754881</td>\n",
-       "      <td>17.754881</td>\n",
+       "      <td>4.731335</td>\n",
+       "      <td>3.345559</td>\n",
+       "      <td>3.345559</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
@@ -782,9 +746,9 @@
        "      <td>4.812982</td>\n",
        "      <td>3.345559</td>\n",
        "      <td>3.226995</td>\n",
-       "      <td>22.537535</td>\n",
-       "      <td>17.754881</td>\n",
-       "      <td>26.559890</td>\n",
+       "      <td>4.246756</td>\n",
+       "      <td>3.345559</td>\n",
+       "      <td>5.004690</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
@@ -793,9 +757,9 @@
        "      <td>4.836447</td>\n",
        "      <td>3.317070</td>\n",
        "      <td>3.221318</td>\n",
-       "      <td>25.522558</td>\n",
-       "      <td>20.078523</td>\n",
-       "      <td>17.550898</td>\n",
+       "      <td>4.809225</td>\n",
+       "      <td>3.783404</td>\n",
+       "      <td>3.307122</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
@@ -804,9 +768,9 @@
        "      <td>4.854540</td>\n",
        "      <td>3.344671</td>\n",
        "      <td>3.165071</td>\n",
-       "      <td>23.468690</td>\n",
-       "      <td>22.721410</td>\n",
-       "      <td>20.758162</td>\n",
+       "      <td>4.422214</td>\n",
+       "      <td>4.281404</td>\n",
+       "      <td>3.911468</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
@@ -815,9 +779,9 @@
        "      <td>4.877352</td>\n",
        "      <td>3.307152</td>\n",
        "      <td>3.169422</td>\n",
-       "      <td>21.548448</td>\n",
-       "      <td>21.485499</td>\n",
-       "      <td>27.760842</td>\n",
+       "      <td>4.060382</td>\n",
+       "      <td>4.048521</td>\n",
+       "      <td>5.230986</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>...</th>\n",
@@ -837,9 +801,9 @@
        "      <td>4.876995</td>\n",
        "      <td>3.311479</td>\n",
        "      <td>3.165452</td>\n",
-       "      <td>26.085941</td>\n",
-       "      <td>17.028408</td>\n",
-       "      <td>20.282967</td>\n",
+       "      <td>4.915384</td>\n",
+       "      <td>3.208669</td>\n",
+       "      <td>3.821927</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>446</th>\n",
@@ -848,9 +812,9 @@
        "      <td>4.854745</td>\n",
        "      <td>3.342711</td>\n",
        "      <td>3.166828</td>\n",
-       "      <td>26.198323</td>\n",
-       "      <td>17.960696</td>\n",
-       "      <td>18.433161</td>\n",
+       "      <td>4.936560</td>\n",
+       "      <td>3.384341</td>\n",
+       "      <td>3.473367</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>447</th>\n",
@@ -859,9 +823,9 @@
        "      <td>4.836353</td>\n",
        "      <td>3.318637</td>\n",
        "      <td>3.219843</td>\n",
-       "      <td>25.428975</td>\n",
-       "      <td>20.628592</td>\n",
-       "      <td>17.562545</td>\n",
+       "      <td>4.791591</td>\n",
+       "      <td>3.887053</td>\n",
+       "      <td>3.309317</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>448</th>\n",
@@ -870,9 +834,9 @@
        "      <td>4.813008</td>\n",
        "      <td>3.345199</td>\n",
        "      <td>3.227329</td>\n",
-       "      <td>24.088264</td>\n",
-       "      <td>21.434537</td>\n",
-       "      <td>19.575681</td>\n",
+       "      <td>4.538961</td>\n",
+       "      <td>4.038918</td>\n",
+       "      <td>3.688653</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>449</th>\n",
@@ -881,9 +845,9 @@
        "      <td>4.731335</td>\n",
        "      <td>3.345559</td>\n",
        "      <td>3.345559</td>\n",
-       "      <td>25.109194</td>\n",
-       "      <td>17.754881</td>\n",
-       "      <td>17.754881</td>\n",
+       "      <td>4.731335</td>\n",
+       "      <td>3.345559</td>\n",
+       "      <td>3.345559</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
@@ -891,36 +855,36 @@
        "</div>"
       ],
       "text/plain": [
-       "     polar_ang  azimuthal_ang  phase_Vp  phase_Vs1  phase_Vs2   group_Vp  \\\n",
-       "0          0.0            0.0  4.731335   3.345559   3.345559  25.109194   \n",
-       "1          9.8            0.0  4.812982   3.345559   3.226995  22.537535   \n",
-       "2         11.2          222.5  4.836447   3.317070   3.221318  25.522558   \n",
-       "3         12.4           85.0  4.854540   3.344671   3.165071  23.468690   \n",
-       "4         13.6          307.5  4.877352   3.307152   3.169422  21.548448   \n",
-       "..         ...            ...       ...        ...        ...        ...   \n",
-       "445      166.4          146.6  4.876995   3.311479   3.165452  26.085941   \n",
-       "446      167.6            9.0  4.854745   3.342711   3.166828  26.198323   \n",
-       "447      168.8          231.5  4.836353   3.318637   3.219843  25.428975   \n",
-       "448      170.2           94.0  4.813008   3.345199   3.227329  24.088264   \n",
-       "449      180.0            0.0  4.731335   3.345559   3.345559  25.109194   \n",
+       "     polar_ang  azimuthal_ang  phase_Vp  phase_Vs1  phase_Vs2  group_Vp  \\\n",
+       "0          0.0            0.0  4.731335   3.345559   3.345559  4.731335   \n",
+       "1          9.8            0.0  4.812982   3.345559   3.226995  4.246756   \n",
+       "2         11.2          222.5  4.836447   3.317070   3.221318  4.809225   \n",
+       "3         12.4           85.0  4.854540   3.344671   3.165071  4.422214   \n",
+       "4         13.6          307.5  4.877352   3.307152   3.169422  4.060382   \n",
+       "..         ...            ...       ...        ...        ...       ...   \n",
+       "445      166.4          146.6  4.876995   3.311479   3.165452  4.915384   \n",
+       "446      167.6            9.0  4.854745   3.342711   3.166828  4.936560   \n",
+       "447      168.8          231.5  4.836353   3.318637   3.219843  4.791591   \n",
+       "448      170.2           94.0  4.813008   3.345199   3.227329  4.538961   \n",
+       "449      180.0            0.0  4.731335   3.345559   3.345559  4.731335   \n",
        "\n",
        "     group_Vs1  group_Vs2  \n",
-       "0    17.754881  17.754881  \n",
-       "1    17.754881  26.559890  \n",
-       "2    20.078523  17.550898  \n",
-       "3    22.721410  20.758162  \n",
-       "4    21.485499  27.760842  \n",
+       "0     3.345559   3.345559  \n",
+       "1     3.345559   5.004690  \n",
+       "2     3.783404   3.307122  \n",
+       "3     4.281404   3.911468  \n",
+       "4     4.048521   5.230986  \n",
        "..         ...        ...  \n",
-       "445  17.028408  20.282967  \n",
-       "446  17.960696  18.433161  \n",
-       "447  20.628592  17.562545  \n",
-       "448  21.434537  19.575681  \n",
-       "449  17.754881  17.754881  \n",
+       "445   3.208669   3.821927  \n",
+       "446   3.384341   3.473367  \n",
+       "447   3.887053   3.309317  \n",
+       "448   4.038918   3.688653  \n",
+       "449   3.345559   3.345559  \n",
        "\n",
        "[450 rows x 8 columns]"
       ]
      },
-     "execution_count": 25,
+     "execution_count": 24,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -929,87 +893,102 @@
     "data"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "**I think I need to normalize the ``eigenvalue_gradients`` or ``group_velocities``  before calculating the group velocity magnitudes**"
-   ]
-  },
   {
    "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "0      1.000000\n",
-       "1      0.882355\n",
-       "2      0.994372\n",
-       "3      0.910944\n",
-       "4      0.832497\n",
-       "         ...   \n",
-       "445    1.007871\n",
-       "446    1.016853\n",
-       "447    0.990745\n",
-       "448    0.943061\n",
-       "449    1.000000\n",
-       "Length: 450, dtype: float64"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(data['group_Vp'] / density) / data['phase_Vp']"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 44,
    "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>polar_ang</th>\n",
+       "      <th>azimuthal_ang</th>\n",
+       "      <th>phase_Vp</th>\n",
+       "      <th>phase_Vs1</th>\n",
+       "      <th>phase_Vs2</th>\n",
+       "      <th>group_Vp</th>\n",
+       "      <th>group_Vs1</th>\n",
+       "      <th>group_Vs2</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>5</th>\n",
+       "      <td>14.6</td>\n",
+       "      <td>170.0</td>\n",
+       "      <td>4.892164</td>\n",
+       "      <td>3.340785</td>\n",
+       "      <td>3.110778</td>\n",
+       "      <td>3.796578</td>\n",
+       "      <td>3.374539</td>\n",
+       "      <td>6.185178</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>6</th>\n",
+       "      <td>15.6</td>\n",
+       "      <td>32.5</td>\n",
+       "      <td>4.914049</td>\n",
+       "      <td>3.302492</td>\n",
+       "      <td>3.117166</td>\n",
+       "      <td>3.727202</td>\n",
+       "      <td>4.939044</td>\n",
+       "      <td>5.188990</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
       "text/plain": [
-       "0      4.731335\n",
-       "1      4.246756\n",
-       "2      4.809225\n",
-       "3      4.422214\n",
-       "4      4.060382\n",
-       "         ...   \n",
-       "445    4.915384\n",
-       "446    4.936560\n",
-       "447    4.791591\n",
-       "448    4.538961\n",
-       "449    4.731335\n",
-       "Name: group_Vp, Length: 450, dtype: float64"
+       "   polar_ang  azimuthal_ang  phase_Vp  phase_Vs1  phase_Vs2  group_Vp  \\\n",
+       "5       14.6          170.0  4.892164   3.340785   3.110778  3.796578   \n",
+       "6       15.6           32.5  4.914049   3.302492   3.117166  3.727202   \n",
+       "\n",
+       "   group_Vs1  group_Vs2  \n",
+       "5   3.374539   6.185178  \n",
+       "6   4.939044   5.188990  "
       ]
      },
-     "execution_count": 27,
+     "execution_count": 44,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "data['group_Vp'] / density"
+    "data.iloc[5:7, :]"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "Something is wrong here Vs2 > Vp. I think I skipped the step where the volocitoies are ordered. TO FOLLOW UP!\n",
     "\n",
     "---\n",
+    "\n",
     "# TEST"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 27,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1062,7 +1041,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 28,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1078,18 +1057,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 29,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([[-133.42561669,   21.32574585,  153.13073556],\n",
-       "       [ -30.35018512,  -10.78150255,  115.24183953],\n",
-       "       [  45.78019137,   10.32751876,  191.4713609 ]])"
+       "array([[-25.14143899,   4.01841829,  28.85448192],\n",
+       "       [ -5.71889676,  -2.03156257,  21.71506303],\n",
+       "       [  8.62637863,   1.94601823,  36.07902033]])"
       ]
      },
-     "execution_count": 30,
+     "execution_count": 29,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1101,18 +1080,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 30,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([[-133.42561669,   21.32574585,  153.13073556],\n",
-       "       [ -30.35018512,  -10.78150255,  115.24183953],\n",
-       "       [  45.78019137,   10.32751876,  191.4713609 ]])"
+       "array([[-25.14143899,   4.01841829,  28.85448192],\n",
+       "       [ -5.71889676,  -2.03156257,  21.71506303],\n",
+       "       [  8.62637863,   1.94601823,  36.07902033]])"
       ]
      },
-     "execution_count": 31,
+     "execution_count": 30,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1132,18 +1111,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 31,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([[-21.44569807,   3.42771889,  24.61293117],\n",
-       "       [ -4.54237322,  -1.61361812,  17.24771839],\n",
-       "       [  4.67893025,   1.05551634,  19.56918738]])"
+       "array([[-4.04102093,  0.64588636,  4.63782385],\n",
+       "       [-0.85592109, -0.30405467,  3.24999404],\n",
+       "       [ 0.88165258,  0.19889134,  3.68742932]])"
       ]
      },
-     "execution_count": 32,
+     "execution_count": 31,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1155,18 +1134,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 32,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([[-21.44569807,   3.42771889,  24.61293117],\n",
-       "       [ -4.54237322,  -1.61361812,  17.24771839],\n",
-       "       [  4.67893025,   1.05551634,  19.56918738]])"
+       "array([[-4.04102093,  0.64588636,  4.63782385],\n",
+       "       [-0.85592109, -0.30405467,  3.24999404],\n",
+       "       [ 0.88165258,  0.19889134,  3.68742932]])"
       ]
      },
-     "execution_count": 33,
+     "execution_count": 32,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1186,16 +1165,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 33,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([32.82474072, 17.90867688, 20.14843909])"
+       "array([6.1851782 , 3.3745387 , 3.79657793])"
       ]
      },
-     "execution_count": 34,
+     "execution_count": 33,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1207,16 +1186,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 34,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([32.82474072, 17.90867688, 20.14843909])"
+       "array([6.1851782 , 3.3745387 , 3.79657793])"
       ]
      },
-     "execution_count": 35,
+     "execution_count": 34,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1236,7 +1215,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 35,
    "metadata": {},
    "outputs": [
     {
@@ -1247,7 +1226,7 @@
        "       [ 0.23222296,  0.052387  ,  0.97125079]])"
       ]
      },
-     "execution_count": 36,
+     "execution_count": 35,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1259,7 +1238,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 36,
    "metadata": {},
    "outputs": [
     {
@@ -1270,7 +1249,7 @@
        "       [ 0.23222296,  0.052387  ,  0.97125079]])"
       ]
      },
-     "execution_count": 37,
+     "execution_count": 36,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1290,7 +1269,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 37,
    "metadata": {},
    "outputs": [
     {
@@ -1299,7 +1278,7 @@
        "array([0.46813036, 0.13431025, 0.48536834])"
       ]
      },
-     "execution_count": 38,
+     "execution_count": 37,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1311,7 +1290,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
+   "execution_count": 38,
    "metadata": {},
    "outputs": [
     {
@@ -1320,7 +1299,7 @@
        "array([2.41859939, 2.86906211, 2.90122615])"
       ]
      },
-     "execution_count": 39,
+     "execution_count": 38,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1339,7 +1318,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 39,
    "metadata": {},
    "outputs": [
     {
@@ -1348,7 +1327,7 @@
        "array([0.72299326, 0.27253055, 0.24036651])"
       ]
      },
-     "execution_count": 40,
+     "execution_count": 39,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1359,7 +1338,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 41,
+   "execution_count": 40,
    "metadata": {},
    "outputs": [
     {
@@ -1368,7 +1347,7 @@
        "array([2.98310074, 3.48292513, 0.22187522])"
       ]
      },
-     "execution_count": 41,
+     "execution_count": 40,
      "metadata": {},
      "output_type": "execute_result"
     }